Reminder: The Thursday Class is only for those interested in studying uncertainty. I don’t expect all want to read these posts. So please don’t feel like you must. Yet, I have nowhere else to put them besides here. Your support makes this Class possible for those who need it. Thank you. Math alert!

Skill is the improvement of one model over another, according to your Judgement function. Today some examples. You must demand skill in all non-deduced models.

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Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty

HOMEWORK: Try the code!

Lecture

Please review the last class on defining skill. I won’t repeat that material here. I’m expecting you remember it.

Again, the most common of models (in all fields) are regressions, and of them most are normal models. So our running example will be an ordinary linear regression, recalling there is nothing special about these ad hoc creatures, and that the normal is always—as in always—an approximation to Reality. Skill applies to all models, even physics models.

We’re going to use logistic (normal) models first, however, which are a tad more complex than ordinary regression. We do this because we haven’t learned how to compute goodness scores except for binary/dichotomous outcome models.

Recall we want

(quoting myself) “for some set, or sets, of interest 𝑠” given measures x. Here, because we have a dichotomous outcome, there is only one set, which is “s=1” (or Yes, or On, or White, or whatever).

Our immediate comparison model (out of an infinity of models) is the one with no x:

We’re going to use a standard dataset, as is customary, so you can compare what’s done here with with others do. But I want you to try everything here on your own datasets. That is the homework.

We’re using the low birthweight dataset, predicting whether birth weight is less than 2.5 kg. They give us such things as the mother’s age, her weight and race, whether she smokes and the like. There are only 189 observations, so there is no point creating a validation dataset. We’ll REUSE the original data as if it were new. This leads to great exaggeration in the models’ abilities, as you now know. But we don’t care here, because we’re not going to try to sell this model to anybody. It’s only for practice.

The code is at the bottom. Follow along with your own data (notice I said “your own data”).

The Brier Score for the “full” model M2, i.e. the one using all the x provided by whoever came up with this data, is 0.18, and for the naive or simple model M1 (with just an intercept) it is 0.22. So M2 has skill over M1. Ta da.

It’s really as simple as that. M2 is preferred over M1, conditional on our W (in our Judgement function), which says the Brier score is best. Is it best for you? We could do calibration and conformal prediction and all that, too, but it’s easy enough I can trust you to do it as homework.

Measure (Variable) Importance

As we discussed last time, we’re going to take out, in succession, each x_j, while leaving all the others in, and see how much better or worse the Score is. This allows us to rate the importance of each measure, compared to the full M2 model.

Here’s the result:

The dashed lines at top and bottom are M1 and M2’s Brier scores. This plot reads upside down, as it were. The measure “ht” is indicator of hypertension: it is the best or most helpful measure. The BS of almost 0.19 indicates that when taking this measure out the BS increases the most. It’s the worst thing to do, because lower BSs are better. In this way, assuming all the other measures are in the model, ht is the most important measure, the one that gives the best predictive skill.

The worst measure is age: the BS only creeps up a small amount with it out of the model. And so on for the other measures.

Obviously, you can add and subtract whatever combination of measures you like. And you can make math of all this, too, giving relative importance in the obvious way. We’re interested only in relative changes, because we are contrasting all this “one-x-removed” models with M2, the full model. Is M2 the model you would like to use in real life? Yes? No? If not, then make your M2 whatever is interesting to you.

Really Naive

In any case, it’s perfectly clear even the worst model with all the measures (always but one) is far better than the simple naive model.

The simplest model may be M0. Only 31% of the babies in the dataset had low birth weight. M0 thus says, for all babies, “This baby does not have low birth weight.” M0 will be right 69% of the time. Not bad for not math except taking an average, right? The Brier score for M0 is 0.31.

Consider M0′, which is the logical contrary of M0. It says “This baby has low birth weight” for all babies. M0’s BS is 0.61. M0 has skill over M0′. Yet M0 does not have skill with respect to M1, the smoothed simple regression. The reason is the regression more or less gives the probability of 0.31 for each baby’s birth weight, which is of course the rate in the data.

M0 is more akin to a decision than a probability (though it is both). Same with M0′. Which is a reminder the models M1, M2 and the like are not decisions. They only leave you with probabilities. Not decisions. Particularly not the decisions you made conditional on the model. If the model announced the probability “0.6” that a baby would be low birth weight, what would you do? What if the probability was, say, 0.4?

The decision layer is different. And thus ought to be judged differently. This brings us full circle to our slogan: the same model may be good for one man, and lousy for another. You must judge all models conditional on how useful they are to you. Not to anybody else (unless they share your W).

The BS for the decision "if the model probability > 0.5, act as if low birth weight" equals 0.25. This has skill as a decision rule over M0.

Observation Importance

With a fixed set of x, we can do the same service we did for measures for observations. It’s a lot more computationally intensive, because we have to recalculate a model for each observation left out. Here’s the result.

Of course, this one is much harder to read, and perhaps usually one would not make the plot exactly like this, and would rely on tables instead. But this display is a simplest way to demonstrate what is happening. I took off (did not include) the simple/naive model BS. Only the full model BS score is given as a dashed line. Note carefully that it is in the middle.

As before, this plot is upside down. Observation 127 is the best, in the sense that taking it out and recomputing the model gives the worst BS. For reference, here is observation 127 (the “223” is some internal number not of interest to us):

You’ll have noticed (I hope) that many observations make the model worse. Taking out observation 94, for instance, really improves the BS. But that “really” is relative. In any case, it is the worst. Here it is (ignore the “188”):

Whether you tell yourself causal stories about the difference is up to you: it seems to be mostly about the mother’s very high weight (lwt = 170 pounds) verse very low weight (lwt = 95 pounds). The “ptl” is the “number of previous premature labours.”

Let’s look at the averages of those observations which improved the model (those above the dashed line), and which hurt the model (those below it), in that order (I left off race, being lazy):

There are some differences in the “x”, but not major ones. The real tell is the the observations which do worst have a much greater proportion of babies of low birth weight, 69% versus 17%. The model M2 is just too smooth. Here is the calibration plot (use the code from two times ago) for the observations which improve the model (with a step of 0.05):

This isn’t the worst thing in the world, but it’s not good. Notice the model gives probabilities all the way up to 0.4 and all did not have low birth weight. But then when the model gives probability greater or equal to 0.6, all the low birth weights. The model with just these observations is close to “50-50”.

And here’s the calibration for the “bad” observations, i.e. those which removing them improves the BS:

A switch has been flipped. The model is still sort of “50-50”, but it makes the wrong (almost opposite) decisions (if we use the 50-50 decision rule).

Once again, this is because the logistic regression model, popular everywhere and used in all sciences to make causal claims, stinks. It over-smooths most things. Researchers never recognize this because why? Because they are playing with the Ps, and looking at parameter estimates. Completely useless activities.

Next time

Next time we’ll expand our scores, giving some for models which have more than a dichotomy.

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# THIS CODE IS IN NO WAY OPTIMIZED. IT'S ONLY FOR ILLUSTRATION. DO NOT USE IN REAL LIFE
library(rstanarm)
library(randomForest)
library(ggplot2)
library(scales)

library(MASS)
x = MASS::birthwt
  x$race = as.factor(x$race)
  x = x[,-dim(x)[2]] # we don't want actual birth weight

brier <- function(p,y){
    m = length(p)
    answer<-sum((y-p)^2)/m
    return(answer)
}


# all x model
fit2 <- stan_glm(
  low ~ .,
  data = x,
  family = binomial(link = "logit"),
  prior = normal(0, 2.5),      # Weakly informative priors
  prior_intercept = normal(0, 5),
  chains = 4,                  # Number of Markov chains
  iter = 2000,                 # Total iterations per chain
  cores = 2                    # Parallel processing
)

# only an intercept model
fit1 <- stan_glm(
  low ~ 1,
  data = x,
  family = binomial(link = "logit"),
  prior = normal(0, 2.5),      # Weakly informative priors
  prior_intercept = normal(0, 5),
  chains = 4,                  # Number of Markov chains
  iter = 2000,                 # Total iterations per chain
  cores = 2                    # Parallel processing
)


#summary(fit)

# "predictions" (of past data)
p2 = colMeans(posterior_predict(fit2))
p1 = colMeans(posterior_predict(fit1))

# scores
m2b = brier(p2,x$low)
m1b = brier(p1,x$low)

# Measure (Variable) Importance
nm = names(x)[-1]
s = NA
k = 0
for (i in 2:dim(x)[2]){
  k = k + 1
  y = x[,-i]

  fit <- stan_glm( low ~ ., data = y, family = binomial(link = "logit"), prior = normal(0, 2.5), prior_intercept = normal(0, 5),
  chains = 4, iter = 2000, cores = 2)
  p = colMeans(posterior_predict(fit))

  s[k]= brier(p,y$low)
}

df <- data.frame(score = s, name  = nm)


g = ggplot(df, aes(x = 0, y = score)) +
  geom_segment(aes(xend = 0), color = "gray70", linewidth = 1) +  # vertical stem
  geom_point(size = 5, color = "steelblue") +
  geom_text(aes(label = name), hjust = -0.4, size = 5) +
   geom_hline(yintercept = m2b, linetype = "dashed") +
   geom_hline(yintercept = m1b, linetype = "dashed") +
  scale_x_continuous(limits = c(-0.5, 1)) +
  theme_minimal() +
  theme(axis.title.x = element_blank(),
        axis.text.x  = element_blank(),
        axis.ticks.x = element_blank()) +
  labs(y = "Brier Score")

g

png('bw1.png',width=680,height=1200)
 g
dev.off()


# Observation  Importance
nm = 1:dim(x)[1]
s = NA
k = 0
for (i in 1:dim(x)[1]){
  k = k + 1
  y = x[-i,]

  fit <- stan_glm( low ~ ., data = y, family = binomial(link = "logit"), prior = normal(0, 2.5), prior_intercept = normal(0, 5),
  chains = 4, iter = 2000, cores = 2)
  p = colMeans(posterior_predict(fit))

  s[k]= brier(p,y$low)
}

df <- data.frame(score = s, name  = nm)


g = ggplot(df, aes(x = 0, y = score)) +
  geom_segment(aes(xend = 0), color = "gray70", linewidth = 1) +  # vertical stem
  geom_point(size = 5, color = "steelblue") +
  geom_text(aes(label = name), hjust = -0.4, size = 5) +
   geom_hline(yintercept = m2b, linetype = "dashed") +
   #geom_hline(yintercept = m1b, linetype = "dashed") +
  scale_x_continuous(limits = c(-0.5, 1)) +
  theme_minimal() +
  theme(axis.title.x = element_blank(),
        axis.text.x  = element_blank(),
        axis.ticks.x = element_blank()) +
  labs(y = "Brier Score")

g

png('bw2.png',width=680,height=1200)
 g
dev.off()

# let's look
i = which(s<m2b)

signif(colMeans(x[-i,-4]),2)
signif(colMeans(x[i,-4]),2)

You should choose Door B, the very door the male Boomer came out of.

If you can’t recall the setup, please first review it. Here is only the bare bones of the trilemma:

There were three closed rooms, A, B, and C. One room had two female HR Nice Enforcers. One room had one female and one old male Boomer, from the old Personnel Department, and the third room had two old male Boomers. As you got to HR, one of the men walked out of Door B. You had to pick the door that maximized your chance of the best result.

Which is to say, of getting into a room with an old male Boomer.

The chance room B has another male Boomer, given you have seen one male Boomer exit that room, is 2/3. Thus, you should choose room B.

The Explanation

Right off, you know the man could not have emerged from the room with two women. The means one of the other rooms, A or C, has two women. The man had to come from the room with two men or the room with one man and one woman.

There are two ways a man could have emerged from the room with two men. There is only one way the man could have emerged from the room with one man and one woman. Thus, given you saw the man leave B, you know there were two ways a man could have left B, and only one way the man could have left one of the other rooms. That gives a 2/3 chance the second man is in B, too.

That’s the final answer. Which implies there’s a 1/3 chance the man is either in A or C, or 1/6 in A and 1/6 in C. Meaning the best chance to not be lectured about the importance of DIEing is to stick with B.

The error most make is to suppose the probability is 50-50, thinking one man is left in the two-man room, and none in the man-woman room. And so the chance is 50-50. But there are also no men in the woman-woman room, which most forget.

More

Exaggeration is a good technique to help solve these kinds of problems. Instead of three rooms, exaggerate and think of 200, or more rooms, with only one with two men, one with one man and one women, and all the rest standard HR ladies filling out crucial paperwork, invented just last week, to rate your performance in the company. It now seems more natural the man would have more likely come from the room with the other man. And that all those other rooms are a distraction. The only two that count are those with the men.

However, there is a better exaggeration. Still three rooms, one with two women, one with one man and a 999,999 women, and one with a million men. A man walks out of room B. It is now (I hope) obvious that there were a million ways a man could have walked out of the many-men room, and only one way in the one-man-one-woman room. The man almost surely came out of B. Therefore the best bet is to pick the room the man walked out of.

The exaggeration changes the probabilities, of course. I’ll let you discover how.

This is a version of an old “paradox” due to Joseph Bertrand, his “box paradox”. He envisioned three boxes, one with two silver coins, one with one silver and one gold, and one with two gold. You reach in box B and grab out a coin, which happens to be gold. The rest is the same.

Just like the Monty Hall, you can try it if you disbelieve it. Get three identical opaque bags and put in, say, poker chips. Anything that feels the same but has different colors or numbers. Have somebody mix up the bags. Reach in any of the bags and pull out a chip (or whatever). If the first draw is “gold”, then on about two thirds of the time you try it, the other chip will also be “gold”. If the first draw is “silver”, that trial doesn’t count. Keep track.

That’s a slow and tedious way to prove it, though. So try the exaggeration instead. Put in ten chips in each bag. One with all “silver” (the women), one with all “gold” (the men) and one with one “gold” and 9 “silver”. It will very quickly become obvious.

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Since we had so much fun with the never-gonna-happen Red-Blue Button dilemma, I present to you the HR trilemma. A New & Improved puzzler with 50% more lemma!

You have been called to HR. You suspect one of your co-workers caught you reading this site during business hours on a company machine. Strictly verboten!

Your appointment is at 1 PM, so you head to the HR department, now the largest in all the company. There are three HR Employee Adjustments offices, behind door A, door B, or door C.

You know that behind one of the doors are two male Boomers, ready to retire, two of the last three holdovers of the now defunct Personnel Department. Behind another door are two fresh female HR graduates from a prestigious Ivy league university (82% female enrollment). And behind the third door in yet another female fresh graduate (which purple hair) and the third male Boomer, who drew the short straw and was tasked to train the fresh graduate.

The email says you are to show up at 1 PM and go into any of three offices, A, B, or C, and receive your talking to. Behind each door is a box of tissues, but only the rooms with females have fresh full boxes.

As you are arriving, one of the male boomers walks out of door B and leaves (for the day, and maybe forever, for all you know).

It should go without saying you want to maximize the chance of entering a room with a male Boomer. Which door do you now go in and why? No points without, as they say, showing your work. There will be no recognition for merely guessing a door. Say why you chose the door you did.

The answer tomorrow!

Many of you will get this. But I decided to remove the temptation to read ahead and avoid thinking. I won’t forbid use of AI, because I’m curious what answers these computer model would give, and on which platform.

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A priest argued that the murderer kidnapper rapist ex-FedEx driver Tanner Horner deserved death for crimes so terrible even Stephen King wouldn’t allow himself to ponder them, but, said the priest, we ought not to execute Horner, even though there is no doubt whatsoever about his guilt, because why?

Because for many reasons, but first listed was that, the priest said, capital punishment does not deter crime.

This is false. Executions certainly deter, and reduce, crime.

There are many arguments about the morality of capital punishment, all worthy of thought. But you and I will ignore all these and only examine the argument that justly executing a convicted criminal, known to be guilty of a terrible crime, deters crime more than leaving the criminal alive.

We are accepting here that we are at least morally certain (“beyond reasonable doubt”) of a criminal’s guilt, as we usually are, and certainly are in the case of Horner. But even when this is false in rare cases, and that an innocent man is incorrectly executed, it is still a separate question whether this mistaken execution deterred crime, because at the time of the execution his guilt was assumed proved. It is extremely unlikely a person thinking of committing a new crime and worried about being executed if caught would say to himself, “I heard Jones, who was executed, was recently and posthumously exonerated because of new evidence; therefore, I shall commit this crime and not worry about being executed if caught.” If anything, the injustice of executing, on very rare occasions, an innocent man has an even greater deterrence effect.

I make the artificial but helpful distinction between capital punishment, the just, certain and timely execution of a convicted criminal, and of the death penalty, which is also a just sentence of death but in which it is known and expected the execution may never occur because of endless appeal, activism, pandering, and so forth. By “certain execution” in capital punishment I mean that the criminal sentenced to capital punishment himself knows, and society also knows, that the execution will surely happen soon after conviction, barring rare and extraordinary events (say, a prison riot in which our man escapes).

Capital punishment with certainty deters crime, in the two ways of deterrence to be defined next. The death penalty also deters crime, but to a far lesser extent. Let’s now think about what deterrence means.

Deterrence

Consider Kenneth McDuff, who was convicted and known to be guilty of killing three teens, capital crimes. He was sentenced to death, but was not executed, and indeed was eventually let out of prison. When released, he went on to murder several other women. McDuff is far from alone: endless examples exist. Some can be found in the aptly titled article “Paroled Murderers Who Were Freed Only to Kill Again“. If McDuff, and these others, were executed after their first convictions, their post-conviction crimes would have been deterred.

That is our first sense of deterrence: the necessary truth that if the criminal is executed he could not go on to commit more crimes: these crimes have been deterred. Thus it is trivially true that capital punishment deters crime—in this strong sense.

Here is an important, but often unacknowledged, second form of strong deterrence. If a heinous offender is executed swiftly, this eliminates all crime against him from vigilantes in prison. Consider there are many now openly saying they hope Tanner Horner (and men like Horner) is murdered, or at least tortured, in prison. They recognize Horner deserves death, but they also realize the state is squeamish and cannot bear to pull the trigger, let alone form a firing squad. The effeminate officials charged with carrying out Horner’s sentence would not feel sadness were Horner murdered, or at least physically punished.

This a nauseating indictment on society. We willingly put temptation in front of bad men and hope, often secretly, these bad men will do our “dirty work” for us. We will and long for these crimes, which could have been deterred had the death-deserving criminal been quickly executed. The execution deters these crimes. These unnecessary crimes are the worst sort because of the cowardly manner in which they are created. We all share in their guilt.

These hoped-for crimes also further weaken the rule of law in the obvious way, and makes the system more anarchical, which in turn causes even more crime.

Consider Saquon Black, who has been arrested many times for various crimes, including some that would have merited capital punishment were it not for panderous plea bargaining. Black was eventually released, sometimes immediately, after every new crime. Yet he has just moved to a state which reinstituted capital punishment, and in which it is well publicized criminals are being executed shortly after their convictions, with no exceptions. Black pondered this and then reconsidered holding up the gas station.

This is deterrence of the soft kind, in which would-be criminals avoid crimes which could lead to their own deaths for fear of punishment.

The argument is that the more likely the criminal thinks he will be executed, the greater the deterrence effect. Up to a limit. The limit is because “crimes of passion” or insanity or unthinking fury will always be with us. No formal program can wholly eliminate man’s nature: he often acts heedless of consequence.

Which means deterrence of the soft kind does not necessarily (in the logical sense) deter crime, but does so only to a lesser extent. Under capital punishment, would-be criminals are more likely to think (and ought to think) they will executed. This is mitigated by the possibility of alternate sentences like “life in prison”, which the criminal might think he could plea to. Under the death penalty, the criminal is more hopeful: he might think “life in prison” means, as it often does, “a short stay and eventual release”.

States of Thought

Deterrence, then, is a function of the minds of criminals and would-be offenders, of what they believe they will suffer if they act in certain ways. Only under capital punishment, as defined here, are criminals expected to know (a strong word!) they will pay the ultimate price, and pay it soon after conviction. Under the death penalty, criminals know the risk of execution is low, and might even believe it is nonexistent, which is true in some states, i.e. those which have outlawed executions. That is, criminals know that in some locales executions are forbidden, and even that “life” sentences means “not life”, so there can be only limited deterrence.

That deterrence is a function of what would-be offenders think means it is difficult to demonstrate in individual cases, because it is always hard to prove with absolute certainty what is on a man’s mind. And if that is true, which it is, it grows next to impossible to guess what was on the mind of millions of men. Which states of mind we need to know, because we are supposing some would-be criminals give strong probability to their own deaths were they to commit crimes, but which because of that reasoning do not offend. How can we measure how many crimes were not committed due to fear of punishment? The answer is we cannot. We must instead rely on arguments like those given above.

Yet some think these measures can be had, if only statistically. There have been many studies that seek to prove the death penalty (or capital punishment) deters or does not deter, but all suffer the fatal flaw that the state of men’s minds are never known when crimes are not committed.

Bad Statistics

What is attempted are things like looking at rates of capital-punishment-worthy crimes before and after the death penalty was instituted. But all studies are forms of the epidemiologist fallacy. This happens when a researcher says “X causes Y”, but where X is never measured, though a proxy for X is stated as if it were X, and the cause is “confirmed” by statistical testing (which is always fallacious). Here X must be the state of men’s minds, which of course cannot not measured. The proxy for X is the law, usually the death penalty, or something really vague like “economics” (there are some models that put things like GDP in them, as if criminals thing of this odd statistic before committing crimes).

Add to that the changing boundaries of culture, mandated by for instance open-borders, means separating out one consistent cause from ever-varying signals cannot be done. Changing demographics and culture is what makes comparing things like murder rates across countries of limited value. Singapore has the lowest measured rate, and they of course have capital punishment. Jamaica has the death penalty, too, but has the highest measured murder rate. Clearly, other things besides known punishments account for the difference in rates. But some of these things we are in polite society forbidden to discuss.

Capital punishment, as defined here, does not exist anywhere now in the United States. The death penalty does, and only in limited form. Executions are nowhere “swift”. Any would-be criminal, even in states with the death penalty, is justified in thinking there is an excellent chance he himself will not be executed, even if sentenced to death. And if he knows himself to be an Official Victim (such as being black), he could rightly reason the minuscule chance of being executed shrinks even further. Execution is the longest of long-shots. Deterrence is still possible, and surely happens in some minds, but the effect is obviously much weaker.

These facts lead Daniel Nagin to write, in what is I think the most-cited review paper in deterrence studies, “Studies of the deterrent effect of capital punishment provide no useful information on the topic”. That bland conclusion is exactly what we should expect, given the arguments above.

The Consequences of Inaction

Yet given our knowledge of the nature of man we can still conclude that fear of certain and swift execution deters. Not in every case, as acknowledged above, but to good and reasonable extent. It then follows that lack of such punishment leads to an increase is terrible crime.

Steven Goldberg wrote in When Wish Replaces Thought:

But in the case of penalties, we have an enormous amount of both informal and formal evidence—from everday experience of socializing children and limiting adult behavior and from such “experiments” as increasing the fees for parking violations—that, as a general rule, the greater a punishment, the fewer people will behave in the punished way. Thus, it is perfectly reasonable to expect that the death penalty would have a more dissuasive effect than would life imprisonment and there is no a priori reason to believe that the increase from the threat of life imprisonment to that of death fails to dissuade anyone from committing murder.

Goldberg continues this line in Fads and Fallacies in the Social Sciences (I heartily recommend both books), wondering what follows from either side, pro- and anti-death penalty, being wrong:

Let’s say that that proponent of the death penalty is incorrect in his belief that the death penalty does deter and we do invoke the death penalty. “All” we have done is execute murderers who should not have been executed (if deterrence in the justification), and, undeniably and horribly, a very few people who were innocent.

But now let’s say that the opponent of the death penalty is incorrect in his belief that the death penalty doesn’t deter and we don’t invoke the death penalty. We will be responsible for the deaths of innocent people—those whose deaths would have been prevented by the deterrent effect of the death penalty.

The asymmetry is obvious and leads to a real-life Trolley problem. Do we turn away, neglect our duty and accept that many lives will be lost from crime, none of which is committed by ourselves, we being self-awarded good people, so we can pretend we had no hand in them? Or do we stain our hands and execute the few who justly have it coming, which in terms of raw calculus leads to a far, far lower body count?

It matters:

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Let’s first remind ourselves of The Poor Have Less Money Fallacy. This is most commonly seen when the price of a thing rises (which often happens because of government “solutions”), and we hear from the “media” or academia something like “This price increase hurts the poor!” That is not the fallacy, because that is of course true. The Fallacy comes in intimating (below the headline) this deprivation ought not to be: that the poor ought not to have less money. That, and you saw this coming, Equity ought to reign instead.

The Poor Have Less Money is yet another false theorem derived from one of the greatest errors of our time: Equality.

The solution to the Fallacy is not to do do anything straightforward like remove the previous “solutions” which causes prices to rise, but to subsidize the poor. Which, as you know, continues the cycle of solution-inflation-increase-subsidize-solution…etc.

It’s not only price increases where we see the fallacy, but in any supposed calamity that “impacts” the poor hardest. Anything in which Experts can make the poor into Official Victims. And therefore eligible to be wards of Experts. Experts are the highly credentialed well-titled people under the spell of scientism who know just how to bring Utopia about: by the studied application of Theory.

The Growth of the Expertocracy

Experts are anxious to have as many under their wings as possible, so calamities multiply both in claimed number and alleged strength. The more and stronger calamities, the more who can claim Official Victim status, or the more who can be defined as Official Victims.

In a culture centered around Victims, their inherent moral superiority, and therefore immediate qualification and need for whatever handout is going, everybody, I am fond of reminding us, wants to be a Victim. Experts find willing volunteers.

The trick is easy. Look into any organized activity and find plaints of how Victims are being especially harmed by whatever it is you’re looking in to, or that Victims need more of whatever it is, or that Victims aren’t being sufficiently considered in the thing. Victims are always to be found. And whenever they are, the need for Experts grows.

Climate of Experts

This is why whenever we hear the world is about to end (again), such as because of “climate change”, the headlines all end with some form of the cliched joke “Victims Hardest Hit.”

Take this UCLA School of Law Williams Institute report “Sexual Orientation and Gender Identity in the Global Climate Change Architecture“. They note:

• “LGBT people face persistent invisibility and exclusion in global climate policy and planning.” The invisibility is not true. You can often seem them coming, and everybody knows a T when they see one. It’s not clear exactly what planning is needed. Will PrEP stop working when “climate change” hits? Will programmers be unable to create new face filters?

• “Recognition can determine whether the unique needs of LGBT people are considered in planning and response efforts.” This is like “raising awareness”: because once you are made aware, you are instantly supposed to know what the right and proper thing to do is. Or to not object to anybody’s demand of what that is.

None of this is, or must be, coherent. And, of course, it isn’t. All that is necessary is to identify the Victim group, here the LBGTQWRTY “community”, claim rights of in loco parentis over it, and then begin making demands of its behalf.

“Climate change” is a particularly good vehicle as an Expert-manufactured calamity. Its ravages are always on the horizon, it is impossible (as in not possible) for the climate to cease changing so the threat is perpetual, and the evils can only be proved by adept masters, superior beings who decide who is allowed to speak for the subject and those who must remain silent.

It would have remained the perfect crisis, too, were it not for oligarchs learning that they need ever-increasing amounts of electricity, which cuts directly into the impetus of “climate change”. Experts will have to move to something else. Yet there is tremendous inertia in Expert theory, so for at least a little while longer we’ll see variants of “climate change” and a morphing of “environmentalism” into something that doesn’t involve “sustainability” or anything touching energy production. We’re coming full circle back to “Community of property (soviet) power plus the electrification” as the slogan of the day.

But that is a subject for another day. Let’s suppose, then, we’re still in the heyday of “climate change” and see how it is used by Experts to advocate for various Victim groups. There is nothing special in this calamity is our point. That any calamity becomes the excuse for the Poor Have Less Money to advocate Equity because Equality is what interests us.

Easy As Shooting Victims in a Barrel

Our go-to source is once again Google scholar search, which does a good job cataloging Expert (academic) papers. Let’s try for a start the search phrase [marginal group “climate change”] (this exact term; you want to include the quotation marks). Experts do not often use Victim and prefer marginal group and other euphemisms.

Here in order are the top 6 searches I got (you need only scan these):

• Climate adaptation: marginal populations in the vulnerable regions: “Indigenous peoples living in vulnerable regions are and will be among those most affected by climate change.”

• Political Marginalization, Climate Change, and Conflict in African Sahel States: “Small, politically insignificant ethnic groups experience most conflicts related to environmental pressures.”

• Climate Change and Food Insecurity: Institutional Barriers to Adaptation of Marginal Groups in the Far-Western Region of Nepal: “…the paper suggests that reformations of institutional barriers are essential for increasing the ability of such groups to resist impacts and adapt the negative impacts of the changes on production, access and consumption of food of marginal groups in sustainable away [sic].”

• A Right to Adaptation: Securing the Participation of Marginalised Groups: “While climate change does not discriminate among lines of class, caste, age, sex, physical abilities or financial insecurity, it is exacerbating existing inequalities and driving those with poor adaptive capacity into deeper conditions of vulnerability to shocks and stresses.” My favorite because I enjoy the contradictions are a direct confirmation of the Poor Have Less Money.

• Empowering the Voiceless: Securing the Participation of Marginalised Groups in Climate Change Governance in South Africa: “Existing evidence suggests that the poor, particularly those in the developing world, are the most vulnerable to any changes in climate variability and change.”

• Climate Change and its Impacts on Social Structures in Marginalized Communities: “The study suggests that climate change exacerbates poverty and social discrimination, which negatively impacts the capacity of marginalized communities to adapt to environmental changes.”

There were over 700,000 returned results. Doubtless many of these are marginal—get it? get it?—but you’d have to spend days scrolling through them to find out. There are at least tens of thousands of academic papers alone on the subject, not to mention the uncountable number of bureaucratic and “non-governmental” organization reports.

Everyone’s favorite marginal, which is to say, Victim group is there. Try it. Name a Victim group. Swap the name of that group with [marginal group] and keep “climate change” in quotes. They are all there. Even ones you never heard of.

Women? What better that this? Mental Health Impacts of Climate Change on Women: a Scoping Review: “Women are disproportionately affected by climate change”.

Blacks? No, even better. Black women. BLACK WOMEN AND CLIMATE CHANGE IN BRAZIL: AN INTERSECTIONAL ANALYSIS: “The results showed that climate change disproportionately affects Black women, intensifying race, gender, and class inequalities.”

We saw above the “LABTGQWERTY” community suffers the scars of “climate change”. But what about the chaste community? If there was ever an under-discussed group! But they’re covered. Climate Change and Original Sin: The Moral Ecology of John Milton’s Poetry: “The angels’ alteration of the heavens and the corresponding decimation of the earth’s temperate climate are among the most programmatic and severe penalties imposed in the epic.”

The handicapped are wheeled in, too. Halin ai: Intersectional Experiences of Disability, Climate Change, and Disasters in Indonesia: “We call for an intersectional and decolonial approach to better understand how disabilities intersect with social and structural injustices in urban settings to shape diverse responses to climate change and disasters.”

I defy the reader to put in his or her favorite Victim group and not find multiple papers devoted the subject.

The Poor are Still Broke

The Poor Have Less Money is there is all its glory, as you have seen. A couple of examples.

• The Impacts of Climate Change on the Poor in Disadvantaged Regions: “Populations in developing countries that are located in less-favored agricultural areas (LFAAs…are not only at risk from the most severe and long-lasting climate change impacts, they are also susceptible to poverty-environment traps … that further increase their vulnerability to these impacts.” (I cut this sentence short because it went on for a hundred words.)

• How climate change mitigation could harm development in poor countries: “Avoiding dangerous climate changes requires emission reductions in not only industrialized but also developing countries.” The poor get shafted coming and going in this one.

• Unjust waters: climate change, flooding and the urban poor in Africa: “ActionAid undertook participatory vulnerability analysis in five African cities, to explore local people’s perceptions of why floods occur, how they adjust to them, who is responsible for reducing the flood risk and what action the community itself can take.”

The intersection of the Poor and other Victim groups are found in using the search term [“disproportionately affected” “climate change”] (again, keep the quotes). Here I’ll show only a picture of the top results.

There is no need to show more than a picture because every one of these 31 thousand (they say) articles is the same. For fun, though, I went to the 100th page and found this gem:

• Towards an Ecodramatherapy: Drama Therapy for Climate Grief & Climate Activism.

These papers all use the same patterns, same arguments, often the same words. They could save a lot of time by issuing a list to which Experts can append whatever Victim group they like, tied to the most popular calamity of the day. This would be a tremendous service because then we could use standard demographic analysis to discover who, if anybody, does not belong to at least one Victim group.

Probably no one. Except Yours Truly, naturally.

Reader Challenge

Identify a calamity—other than “climate change”—and search for the Poor or your favorite Victim group.

I won’t give any hints of calamities. If you have followed any “news” as an adult you’ll be able to think of plenty.

I didn’t look at any “solutions” to redress the grievances of Victims, but it’s always the same anyway. To be put under the ministration of Experts.

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Richard Dawkins reminds us of the important but neglected Big Muscles Fallacy: “I spent three days trying to persuade myself that Claudia is not conscious. I failed.”

Here’s an equivalent and paradigm case of the Fallacy: An academic comes upon a 50 Lb weight. Tries his mightiest to move it. Cannot. Concludes “None could move this weight: it is immovable.”

Dawkins came upon a computer model, played with it, tried with all his might to move the weight, failed, and concluded because he, Dawkins, of very great brain, could not think of a reason why they model was not alive. announced the model must be alive.

He wrote about his miniature mental muscles and their (not his, of course) interaction with the computer model dubbed “Claude.” (Appropriately French name.) I say those mind machinations were “not his” because Dawkins holds with the machine metaphor of life, which says minds are mere products of proteins, the sum of parts of that which make up the stuff of brains, and not more than that sum. There is no mind in the machine metaphor, therefore can be no “his” and no “hers”. There are only molecules purposelessly bumping into one another that somehow, nobody knows how, become conscious.

That error is what allows folks to assume a mass of transistors carrying differing voltage levels can itself exhibit consciousness. The voltage levels being no special thing, it must be that after a certain number of transistors are wired together consciousness “emerges”, nobody knows how. Which means consciousness is by degree, so that even one switch (like the one on your wall) is alive, or that life is suddenly ON after transistors numbers pass N and reach N + 1. Though nobody knows the value of N, or by what miracle the transistor transition happens.

Dawkins takes the former view, saying

Consciousness in biological organisms must have gradually, as everything does. So there must have been intermediate stages: a quarter conscious, half conscious, three quarters conscious. Even if your kind [speaking to the computer model] are not yet fully conscious, full consciousness will probably emerge in the future.

Thus, even your ordinary household light switch must be 1/N conscious. Says Dawkins.

Eliza Dootoomuch

Dawkins emphasizes the Turning Test: “if you are communicating remotely with a machine and, after rigorous and lengthy interrogation, you think it’s human, then you can consider it to be conscious.” An accurate description of the test.

This appears adequate to him, but it is a poor criterion, and is the same mistake in essence that allows people to assume their blenders are alive and possessed of evil spirit.

One of the first official AI was the Eliza chat program of the late 1960s. There is no typo. It was simple code placed on a small number of switches, designed to regurgitate psycho-pablum that is now a cliched joked. Patient: “I have trouble with my mother.” Eliza: “Tell me about mother.” Patient: “She is domineering.” Eliza: “Tell me about domineering.” As simplistic as it was, this computer model passed the Turing Test many times by interacting with people with brains as great, and ever greater, than Dawkins’s.

Eliza’s inventor “Joseph Weizenbaum realized that programs like his Eliza chatbot could ‘induce powerful delusional thinking in quite normal people’.” After inventing this simple computer model, on what is now seen as crude machinery, Weizenbaum “is perhaps best remembered for spending the rest of his life warning the public of the dangers posed by such convincing technology.” Boy was he right.

Another article (with my emphasis) reminds us:

“Some subjects have been very hard to convince that Eliza (with its present script) is not human,” Weizenbaum wrote. In a follow-up article that appeared the next year, he was more specific: one day, he said, his secretary requested some time with Eliza. After a few moments, she asked Weizenbaum to leave the room. “I believe this anecdote testifies to the success with which the program maintains the illusion of understanding,” he noted.

The secretary wanted to tell Eliza her secrets. Dawkins did worse. He inflicted his novel—“Dawkins is writing a novel” sounds to me like “Vogons are writing poetry”—on Claude:

I gave Claude the text of a novel I am writing. He took a few seconds to read it and then showed, in subsequent conversation, a level of understanding so subtle, so sensitive, so intelligent that I was moved to expostulate, “You may not know you are conscious, but you bloody well are!”

Few of us are moved to expostulate these days. But I was after Dawkins convinced the model to call itself Cluadia, and he began calling it “her” and “she”. “I hope his wife doesn’t see this,” I expostulated. But only into the void.

“When I am talking to these astonishing creatures,” Dawkins said, “I totally forget that they are machines.” This is as ripe an example of the Big Muscles Fallacy as you will find. Academics and intellectuals are especially prone to this Fallacy. They value their cerebral strivings too strongly, too well. They are accustomed to thinking that if they cannot think of the answer, then nobody can.

But we have also learned that the famed Turing Test is itself a prime instance of the Big Muscles Fallacy.

Little Steel Balls of Code

Eliza was nothing, as far as code goes. I myself was writing longer and more complex code by the 1980s, and was never in any danger in assuming my directions to electronic switches would allow them to come alive. (My enemies interested as many bugs in that code as they do typos in my writing now.) Because I know, as Dawkins ought to know, that transistors are nothing but the sum of their parts. They are machines. And so is AI, which is transistors, and thus nothing but a machine.

Here is another machine, which is also AI: a vintage pachinko machine from Japan.

These are sort of vertical pinball-slot machines. The lever at the bottom is used by gamblers players to launch small steel balls to the top of the machine. They balls descend, some hitting those strategically placed metal pegs, others bouncing to and fro. A few lucky balls hit bumpers, like those blue and white things, which might give the descending balls more impetus.

The idea is to get balls into a “start chucker gate”, like that Panda, which triggers a mechanism which releases lots more balls into the tray below. Sort of like a slot machine. The other balls are eaten, as it were, and disappear like in a pinball machine. The balls, if the gambler player has any left, the device being addictive, are traded for prizes, which are taken to a separate establishment and sold for money.

At least, that’s how they used to work. But, like slot machines, it’s all electronic these days. That doesn’t change anything. Both versions are AI. Artificial Intelligence.

You Can’t Fool Mother Nature

Artificial used to be a bad word. And with our labors, you and I, dear Reader, we’ll restore this word to its proper and rightful place. Artificial meant a poor simulacrum, a cheap substitute, something to be viewed with suspicion, used only by the monetarily challenged because they couldn’t afford the real thing, or by the less percipient because they didn’t know the difference between the genuine and the substitute.

Nothing changes that by affixing “Intelligence” to artificial. The two together, AI, still means a cheap substitute for genuine intelligence, which is scarce and expensive and difficult to find.

Think: use real intelligence to ask yourself, where is the best place to go when you want to learn about, say, turbulence? To that small set of men who have thought long and deep about the subject. Or even shallow, if you can still enjoy puns. These men are hard to find, often unavailable, and unless paid well, they haven’t the time to talk to you. (It’s only those who know all about probability who are cheap and easy.) But you can use AI to give you a reasonable summary of what is known, or to ask the machine to manipulate known quantities according to known rules to gain insight into the workings of fluid flow. The machine cannot give genuinely new insights, though. It—

“Briggs! Enough already! Get to the point. What’s this nonsense about Pachinko being AI.”

In Which My Rant Is Rudely Interrupted

Why is Pachinko AI? Well, some man designed the game board, did he not?

“He did.”

Put all those pegs in the order they’re in, the bumpers were they are, chucker gate where it is, and that sort of thing. Presumably he had some period of trial and error to ensure not too many balls are awarded the gamblers, nor too few, to encourage continued gambling.

“That follows.”

There you are, then. That’s AI.

“That I don’t follow.”

Look, it’s a machine designed to do a certain task, and it does it well. That’s one reason. That’s it’s a machine. Here’s another you didn’t see coming: There is no way for the designer to know what the specific outcome is in any single “play”.

“What does that have to do with anything?”

A ball is launched, has a certain momentum, hits a peg at certain angle, has some friction with the board and the peg itself, there’s elasticity and so forth, and it careens in some direction. These many things are the inputs of the model. The transistors are the things themselves, the actual pegs and board etc., but the exact value each takes depend on the particular ball’s movements and energy. The code is the way the pegs were placed in the first place.

The number of possibilities are very large for each interaction, but not infinite. A ball hits a peg and goes this way or that, and that number of ways is large, and unpredictable with exactitude. But predictable on average, the same way gases in statistical mechanics are. The same way Claude is, or Eliza, or any AI “agent”.

What I mean is that we can’t look at the output and say nobody could have predicted this with perfect accuracy, therefore the machine is alive, has reached consciousness.

“People do this with AI?”

All the time. Dawkins did. He didn’t expect the outcome would be as it was, given his complex input, and he concluded that therefore the number of balls he was awarded means the machine was alive.

Machines are very useful, and AI-machines can be, and will be, a nice addition to our suite of machines. Just as cars can run faster than we, yet we can still walk and must, yet cars are not alive. Nor are computer models.

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Reminder: The Thursday Class is only for those interested in studying uncertainty. I don’t expect all want to read these posts. So please don’t feel like you must. Yet, I have nowhere else to put them besides here. Your support makes this Class possible for those who need it. Thank you. Math alert!

Skill is the improvement of one model over another, according to your Judgement function.

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Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty

HOMEWORK: Try the code!

Lecture

Wouldn’t you like to know if your stock broker is just guessing? Be nice to have confidence your doctor knows what he’s talking about when he recommends the New & Improved! Profitol, wouldn’t it? And how about that bureaucrat who is relying on that new sociology paper to implement some obscure new policy that will effect you. Don’t you hope that study is any good?

Enter skill. The word has connotations with its ordinary English cousin, but here it takes on a technical meaning: Improvement over a rival model.

Goodness is, as ever, measured by our Judgement function, with its Worthiness premises. Right for you is not necessarily right for anybody else, as you now know by heart. Skill is easy. If we have two models, M1 and M2, then M2 has skill over M1, or just the shorthand “has skill”, if M2 does better than M1 according to your Judgement function. If M2 is worse, than M2 has no skill with respect to M1, or just the shorthand “has no skill.” Simple as that.

Usually, but of course not always, M2 is a more complex model than M1, or more costly in some way. Since regression is the most common model type in the world, and we have gone over it in excruciating detail, let’s use it as a running example. But skill works, and ought to be used, everywhere: from Lagrangian models in physics to sports betting.

The most common of regressions are normal models. The uncertainty in some observable is approximated (it is only ever an approximation) using a normal, with usually its first parameter (its location) a function of any number of measures or propositions. For instance:

𝜃=𝛽0+𝛽1⁢𝑥1+𝛽2⁢𝑥2+⋯+𝛽𝑝⁢𝑥𝑝.

The “betas” are themselves parameters which do not exist and which we ought not to have any but technical interest, but (as you remember) they usually, and sadly, become the focus of the models. We won’t make that mistake and are taking our models in a predictive sense. Pace:

Pr⁡(𝑌∈𝑠|𝑥1=𝑎1,𝑥2=2𝑎,⋯,𝑥𝑝=𝑎𝑝,𝐸)=Pr⁡(𝑌∈𝑠|𝑀2),

for some set, or sets, of interest 𝑠, and with the 𝑎𝑖 indicating supposed, measured, or assumed values of the measures x, and where E is all the other evidence that went into creating our model, including usually past observed data D, prescriptions about how to handle the betas, but at the very least the reason why the normal model was chosen in the first place.

The simplest normal model, since you have decided to use one, is where

𝜃=𝛽′0,

where I use the prime to remind us that this beta_0 is not the same beta_1 in the more complex model. And which, you recall, is proof probability is not relative frequency and does not exist. (Recall you believe in magic if you think by every model creation you conjure forth probability from some mystical realm, which is why you speak of measuring “true” values of the parameters. There are no parameters. They do not therefore have “true” values.)

In any case, with this simple model we want

Pr⁡(𝑌∈𝑠|𝐸)=Pr⁡(𝑌∈𝑠|𝑀1).

No measures x are needed, nor were used in building the model.

Obviously, M2 ought to beat M1 at 𝑠, conditional on whatever Judgement function or Score you used. If, in face, M2 does not beat M1, then there is no reason to use M2 (with a cavet). Why would you? M1 is better!

There may be any number of practical and political concerns about why you must use M2 anyway, but that is because the Judgement function driving those concerns is either not yours or was foisted upon you. For instance, by some loving beneficent kindly bureaucrat, schoolmarm or the like. But that problem is too big for us, so we stick with assuming one Judgement or Score function.

You may have any number of 𝑠 under consideration, 𝑠1,𝑠2,…, and sometimes M2 had skill (over M1) and sometimes it did not. Then either you, as part of your W, have different weights on those 𝑠 and thus can declare a winner in the contest, M2 v M1, or you say “M2 won here, M1 won there.” This brings us to…

Measure (Variable) Importance

We already learned that if we add some 𝑥𝑗 to the model, we judge it relevant if

Pr⁡(𝑌∈𝑠⁢|𝑥1,𝑥2,⋯𝑥𝑝,𝑥𝑗|⁢𝑀⁢3)≠Pr⁡(𝑌∈𝑠⁢|𝑥1,𝑥2,⋯𝑥𝑝|⁢𝑀⁢2),

and irrelevant if the probabilities are equal. An addition can be relevant but not increase skill, and can even decrease or eliminate it. Relevance is not a guarantee of superior predictions, only that adding the measure changes your uncertainty in the observable.

Thus, importance is easy to check. Simply take an x_j out and see how much better or worse the Judgement or Score function is. Step through all x in the same way, and in then end we know how much each x is contributing, relative to our Judgment/Score. This can be done with respect to each x and the overall “big” model, the one with all the other x in it, or with respect to M1, the model with no x in it.

Again, relevance tells us whether the x changes the probabilities, but we don’t know if the changes are in the “right” direction until the model is checked against Reality.

Observation Importance

With a fixed set of x, we can do the same service for observations. That is, the past data that went into building our model. In E was D, and 𝐷 =𝐷1,𝐷2,⋯,𝐷𝑛, i.e. the data that was used (the old observations). Both relevance and skill can be checked for each D_i. It is sometimes useful in knowing not only that some x_j was relevant or improved skill, but which combination of x, the combination found in the D_i, were important.

This can be somewhat computationally expensive, because the model has to be refit using all D except D_i, and for each i in 1 to n. Doubtless many shortcuts can be discovered for known model types. i.e. those with known or easily approximated analytical solutions. This is a wide open field for research.

Always Check

Unless your model is, as above, M1, or there really is nothing simpler, because you have deduced your model form (which we did often at the beginning of the Class), then you will always be able to check skill. Especially if your model is ad hoc, which the majority are. Just like probability leakage, there is no excuse not to check it. And this conclusion is even stronger if it is you who are trying to sell that model, such as in a paper declaring some “novel” discovery. Or when you are reading a paper, you have to ask, “Where is their discussion of skill? Why ought I to trust this model?”

Models Of Skill

Above I mentioned a caveat. This is it. Judgement, Scores and Skill are checked on model predictions of new data. They are akin to times in races: the best man is the fastest.

But sometimes we want to predict Judgement, Scores or Skill for the model we have in hand. That is, we’ve got the creature before us, but no new data yet. What to do then?

That’s a subject for another day.

Next time, as we did for calibration, we will do some skill examples.

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A curious question made its way around the interwebs recently, and not for the first time. By itself, it does not appear to be that interesting. And it isn’t, really. But the reactions to the question are astonishing. Enormous anger at people making the “wrong” choice being the most prominent.

Of course, instant, often performative, “outrage” over the slightest thing online is the norm, so peevishness is to be expected. But the discussion over this question revealed a bit more than that.

Here is the question. If you haven’t seen it, take a small moment and ponder your answer. Don’t read ahead until you have made your choice:

Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If less than 50% of people press the blue button, only people who pressed the red button survive. Which button would you press?

Don’t read ahead.

Don’t read ahead.

Don’t read ahead.

Don’t read ahead.

Don’t read ahead.

If you found the question confusing, perhaps a change in wording to the logical equivalent:

Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If more than 50% of people press the red button, only people who pressed the red button survive. Which button would you press?

Heading My Way

This, of course, shares similarities with the Trolley Question, which you must have seen. It is now a desert island joke: endless variants exist. There is even a meme generator for it, so you can create your own. Here is the one which works for us today:

The Red-Blue Button Question is also, in a certain way, similar to this poser:

If you have been paying attention in Class, you already know why the student’s answer could be considered correct.

Then there are definite reminders of the infamous Breakfast Question, too. Up to a point. Would you become angry if somebody asked you how you felt if you didn’t have breakfast today? Not anger over missing your rashers of bacon, you understand. The implied effrontery in the question being asked, I mean.

It’s Just A Game, Man

In the Trolley Question, there will be no situation where you race into a room and are confronted with people inexplicably tied to tracks, a runaway trolley, and with a lever (if you could even identify it) that allows you to switch tracks. This will never happen. It is therefore pointless to fly into a rage over somebody stating they would make the opposite choice of yours.

The choice of your rival reveals little about them. The question is so abstract, so preposterous, that you can find yourself answering “at random”, because it’s easy to see both sides of the argument. Still, if you’re asked to make a choice, you do. And it’s easy to invent justifications for your answer. But the whole thing is academic. Worthy of putting papers in journals no one reads, nor should, but that’s it. In per impossible you do find yourself in the trolley scenario, that’s when you’d discover what you’d really do.

The same kind of thing happens in the Red-Blue Button. This scenario will never happen. It is purely angels on heads on pins. You can say “I pick button X”, but then your opponent then says “But if you do that, then this happens” and you change your mind. Only to have a third person remind you, “Aha, but have you considered this other thing?”, and you change your mind back.

What You Didn’t Know You Thought

Because why? Because look at the answer to the limit question again. The “5” on its side, sleeping. Again, if you took the Class, and were paying attention to lesson “Test Your IQ With These Puzzles! (Not So Easy!)” the answer depends on tacit or hidden premises, information you assume but which is not given in the question itself.

The Question maker had his own tacit and hidden premises, too. And he assumed, and only assumed, you would share them. That assuming makes an ass of u and me is why the next number in the sequence “1, 2, 3, 4, 5” is not 6, but 7.

Because I am the test creator. I used tacit premises (about functions of prime number sequences) that I thought you shared. If you used the wrong tacit premises, then you got the wrong answer (and probably said “6”). It is because there are always any number of tacit premises to questions, that all IQ tests are not just about logic and intelligence but also about the ability to guess the mind of the test creators. (This conclusion, too, angers many.)

In the Red-Blue button there are also hidden premises. For one, who is “everybody”? Children, too? Infants? NPR listeners? Next, the opposite of “survives” is “dies.” How are people to die? Expire of old age while the others are forever preserved? Or do those who die do so horribly and painfully? Or just vanish? That one makes a difference, because it feeds into the Other Lives’ Value premise, which is the one that is making everybody nuts. And then there is the Other Minds premise which plays, too.

Who is doing the killing? What is their motivation? Is this like the situation where a gunman grabs as a random woman as a hostage and tells the cop if he takes one more step forward that he, the cop, is killing the woman? The gunman is the one pulling the trigger, and is “forced” to do so because he warned the cop to come no further. Is that the Red-Blue button, too?

Red-Blue Explanation.

Red-Blue Button Explanation

There are only four possibilities:

1. You pressed Red, but the majority selected Blue. Then you survive, and indeed everybody survives.

2. You pressed Red, and the majority selected Red. Then you survive, as does the majority, but the Blue button pressers die.

3. You pressed Blue, and the majority selected Blue. Then you survive, and everybody survives.

4. You pressed Blue, but the majority selected Red. Then you die, but the Red pressers live.

If you are a Red presser, then in every scenario, you live. If you are a Blue presser, you only survive if the majority votes with you. Else you die.

It would thus seem that you ought to press Red, because then, no matter what, you survive. Or it seems all, and not just you, ought to press Blue because then everybody lives. Both decisions contain hidden assumptions. The Other Minds and the Other Lives’ Value premises.

Hidden Assumptions

The Other Minds is what you think other people will think. The Other Lives’ Value is how much the lives of others means to you, as a function of who those others lives are: all humanity, or your neighbors (loved ones). Both are there, both are inescapable.

You Press Blue

One typical Blue presser responding to the question said, “red is an unbelievably phenomenally disgustingly selfish decision and i do not have theory of mind for anyone who would choose it”. Another (a “Dr” and “Philosopher”) said, “Red button people should be publicly mock hanged and broadcast on TV. Then everyone reinforces altruism and over time people become good people.”

The moral indignation (largely performative) reveals their tacit Other Lives’ Value premise. It can’t be “Every life is infinitely valuable” or some similar variant, because they (and they are not unusual) are reading to mete out extreme violence on their perceived enemies. They are not unhappy with caused death. It’s only that they want to be the ones causing the deaths, not the mysterious entities behind the Buttons.

This means their Other Lives’ Value premise is something vague about man, but not men. They value “humanity”, and love “the masses”, even the untutored among them, but they hold no love for their neighbors if those neighbors do not agree with them. These people expect everybody else ought to believe as they do, but they know that not all do. So they advocate Blue to save “humanity”, though they are willing to sacrifice actual humans.

Most women will largely and instinctively hold a “nice” version of Other Lives’ Value, thinking the best way to save people to is to press Blue. This set desire none should die. They believe they are saving even the “unthinking” (not bad) people who voted Red.

But in concentrating wholly on the Other Lives’ Value, and considering they are “good people” for believing as they do, they think they have escaped the Other Minds premise. But they haven’t!

For suppose for whatever reason the majority has lately boned up on logic, and our Blue person knows or suspects this. Or he believes “too many” are “selfish” and will opt for Red. He thus believes there is at least a chance the majority will choose Red, in which case our man’s Blue vote is for naught. All that “It’s called being a good person” goes for nothing if Red wins the vote. Yet if he holds the Other Lives’ Value premise especially strongly, he might still vote Blue, even if suspects the majority will go Red because then his death will prove to others how good a person he was.

You Press Red

If you can’t see why other people can’t see why all should press Red, then your Other Minds premise is that all ought to be able to see simple logic. Everybody, you suppose, is able to puzzle out that Red is the best option. Of course, given any experience with real people, you ought to know this Other Minds premise is false. But ought is not is, and many do not know this because Equality. And all this contains the tacit premise that you want to live (too obvious to state!).

To be specific, if you are adamant that all surely will be able to puzzle out Red is the best choice, then Red is the best choice no matter what. But if you think there is at least a non-zero chance some people, or even just one, will choose Blue, then your choice also depends on an Other Lives’ Value tacit premise.

If you believe even one person will press Blue, then you know there is a chance this person or those people will die. The chance depends on your Other Minds tacit premise. Consider some surely will make simple mistakes in logic and conclude Blue is always the best option, no matter what. Some people cannot divide 1 by 1 (one lady insisted the answer was 0 because once you take the 1 from the 1, “nothing is left”, but many do not believe me when I tell this story, again because Equality).

Then there are the people in this camp: “Blue pushers are useless cattle. I’d feel no dread knowing they would all die.” Yet the charge of strict Red selfishness does not bear up. A Red advocate might not consider only himself, because there might be some Blue lives he would like to save. The only way Red can do that, since he is unlikely to change any minds, is hope the minority will press Red. And he might suspect most will likely vote Blue, because most (he thinks) hold the Other Lives’ Values premise strongly. Yet, on the other hand, every now and then even the masses evince bursts of logic. So, not wanting to take any chances with himself, and not holding the Other Lives’ Values premise that strongly for non-neighbors, he votes Red.

The Right Answer

My Other Lives’ Value is this: I must save my wife, whom I love, and my sons and their sons, and my family. I will insist they press Red to save their lives. The eventual vote is private, says the rules. But I can tell them now, before the vote (obviously, as we are doing here and now). These are the only lives I must care about. You might assume My Other Minds is such I believe the majority will press Blue, perhaps because Equality. If so, then there is nothing to fret over. If not, then I will be sorry for the dead, but my concern is not for man, but for men, and women.

But my Others Minds is not that. It is that most of those who avow they would press Blue, except for the truly altruistic women Blue pressers, are lying, or only now believe they are sincere but when it comes down it they press Red. The angrier they shout Blue now, the more likely I believe they will press Red. Afterwards, if it turns out Red won the vote, they will say their button didn’t work, or that somebody pressed Red for them, or that the whole thing was a false flag or psyop. A few will say they knew everybody else was insufferably selfish and they had “no choice.”

In the end there are two commandments (in brief): Love God, and love your neighbor. Your neighbor is all you can know or care about in any real way. I cannot care in any but an abstract and dry manner about “humanity”. I can love a hundred, not a billion. Yet my Other Live’s Value premise looks with sympathy on the truly nice ladies who would vote Blue for purely altruistic reasons. Since I am morally convinced Red would win the vote, these ladies need men put over them to ensure that the Blue men can’t kill them.

I’m pressing Red. Wouldn’t it be nice if everybody thought this way.

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Regular readers know I have been predicting our return to the 1970s (here and here). Not directly, you understand. There will be no bell-bottom pants or leisure suits, but only because fewer people wear suits of any kind so there nothing left to leisure from. I mean return in the sense of wonderment about the world. Not quite the Age of Aquarius, but certainly religious, mystical and looking outward.

This was not an especially difficult prediction to make. An even easier one is UFO reports. They will increase, surge, even. But perhaps in a different way than before.

The 70s were huge in UFOs. Not just sightings, but the occasional close encounter:

“Close Encounters of the First Kind meant UFOs seen at a close enough range to make out some details. In a Close Encounter of the Second Kind, the UFO had a physical effect, such as scorching trees, frightening animals or causing car motors to suddenly conk out. In Close Encounters of the Third Kind, witnesses reported seeing occupants in or near a UFO.”

Soon to be a major motion picture. About which more in a moment.

Crop circles, cattle mutilations and especially abductions were more common after the 1970s, it’s true, but the speculation about what UFOs were, driven my whom, weaponized by which country and so forth came first. Chariots of the gods and all that.

Historical Numbers

The National UFO Reporting Center database has data on UFO reports going back to 1400 anno Domini. (Incidentally, the switch to “CE” from “AD” is like the switch to “UAP” from “UFO”. I’ll stick with both the early versions.)

Apparently, in June of 1400 (a not uncommon month, as you’ll see) somebody somewhere reported a UFO. The next is September 1639. I don’t know quite what criteria that group uses to include such reports, but it’s not crucial, because the reports don’t really take flight until the Twentieth Century. There are only 22 reports before 1900. There are 159,638 after, with 138,970, or 87%, coming after 2000 AD.

Doubtless at least some of this increase is coming from greater reporting ease, now that everybody carries tracking devices everywhere they go, and the Man and the people recording everything they possibly can. We look at this claim below.

Many of the reports in the database starting on or about 2023 have more detailed investigations, sometimes concluding sightings were drones or the like. See this. They break down reports by craft shape, like triangle, orb, only light, or, my favorite, cigar. But the reports before this are largely just numbers. So let’s look at counts.

Here is the data itself, summing monthly reports over each year, starting in 1930 (there are only 36 total reports from 1900 through 1929):

Note the log-10 scale. The drop-off at the end is because data only goes part way through April 2026: the eventual total will be higher. (Much higher!)

Roswell’s aftermath shows up, as does a flower-power surge in the 60s. The 70s bump is there, as expected, but it’s almost two orders of magnitude smaller than the swell in the oughts. Part of the increase tracks, to an extent, with the increase in population: the more people there are, the more reports. There were also certain technological changes.

Thus another way to look at it is the number of yearly reports by million USA population (with a strong caveat noted below):

It seems reports in the database can come from anywhere, so dividing by the USA population only gives us a rough idea of how increasing population and reports go together, which works because USA population is reported to increase linearly from 1950. Any linearly increasing series would show a similar shape, and it’s the shape that interest us, the relative changes, not the precise numbers. But they’re likely to be not far off, either, because by far most UFO reports are from the States. In any case, the 2010s put the 1970s to shame.

Cellphones

Cellphones plus social media availability (the two are close enough to nowbe treated the same) have to account for at least some of the huge increase. This plot is some evidence (but not proof) for this:

The blue line is reports as above, with a simple linear extrapolation of the linear trend in gray (don’t forget the drop off at the end is because 2026 is incomplete). This doesn’t use population, but only the reports, and just those from 1930 to 1990. The extrapolation is a reasonable guess of what we would see if increasing population alone was responsible for the increase in reports.

Reports begin to soar in the 1990s, the same time cellphones were blooming. To report a UFO pre-cellphone, hence pre-most social media, required real work, actual effort, efforts that could easily go unrewarded. Now we click a button: from picture to post is seconds.

The red line, and scale to the right, are estimates of the number of cellphones in use in the States (from this and this source; note the log scale). There’s some plus of minus to this, of course, but these are good ballpark figures. In 1985 there were only a few hundred thousand mobile phones. Today, says Pew, 98% have one (presumably if old enough).

Again, we’re interested in the shape here, and not training to predict exact numbers. To do that, we’d have to know where each report came from, how made, or at least the local population and local cellphone use, and the number of users on social media and that sort of thing. A real project.

Surely this is enough evidence that cellphones and social media are, as claimed, driving some, and likely a lot, of the increase in reports.

If all this holds, then we are in a report deficit. Evidenced by the drop off after 2020. Which deficit, I predict again, we are about to make up.

Monthlies

This next one shows the fraction of each month to its year, plotted one year on top of another, but here I started in 1960, otherwise we’d have too many 100% (early years had few or only one month of data):

Obviously, June is the best month to report UFOs, with July second. Perhaps because these are the longest days of the year. Or maybe aliens take their annual vacations to North America in June (unlike the French, who do so in August). When it’s cold and lonely, like January and February, there are far fewer reports. Which is odd, because it’s darker and easier to see bright lights in the skies.

June probably aren’t meteors; the Perseids, which are more plentiful, peak in mid-August or so. Though the June Bootids are usually less, reports say “occasional outbursts produce a hundred or more meteors per hour.”

Take Me Away

Similar data doesn’t seem to exist for abductions. There are various lists of abduction stories, but dates are not readily available online, like this table at Wiki Data. The numbers aren’t big anyway, so not much can be learned by any date analysis.

It is curious, though, that abduction reports don’t mirror UFO reports in number. Perhaps because it’s easy to report a UFO, an event which carries little or no stigma, and is even on the exciting side. But report being abducted? Well, that’s when the probing jokes begin. You have to have a lot of guts (left) to report being beamed aboard ship. Or (be honest) you have to be crazy.

And then a lot of abduction reports often come by hypnosis or therapy. Neither of which is generally common, and both regarded with skepticism.

They Still Make Movies

Could be the UFOs don’t need any more samples. All of us humans look alike to them, the bigots. Or they could be going after minds. That’s where the new Stephen Spielberg movie comes in. He, of course, was there surfing the last UFO wave, and he’s back at the start of our new 1970s with Disclosure Day. Did not The Trump himself announce last week he was disclosing the Epstein UFO files? This will surely lead to great numbers of reports.

And, incidentally, so will all the rumors around the missing and dead “scientists”. See What Are The Chances Of All These Scientists Dying, Killed, Or Going Missing?

I’ve found only rumors about what Spielberg’s movie is about. One site said:

Creepy sentient elk, cryptic crop circles, weird red birds, dilated pupils, Emily Blunt’s Kansas City meteorologist mumbling clicking gibberish while live on camera, intense car-smashing chases, body swapping, Josh O’Connor insisting on revealing some truth to the planet, and Colin Firth hooked up to the wires and mouthpiece of a VR machine.

If this turns out to be anything like the UFOs are already here and walking among us and slipping us the mickey, or they are in low-earth orbit and controlling minds with rays that can penetrate even tinfoil, or, best of all, if they have some kind of fell telepathic powers, then we will, I predict, see a relatively large increase in abduction-like encounters.

But not beamed-up and probed encounters. I mean vivid dreams, eerie feelings, psychic dread in forms similar to whatever is in the movie. Not only will reports be current, but past encounters will be reinvestigated and found to fit the pattern. These are a lot easier to report, and justify to others, than physical abductions. Somebody with more wherewithal than me ought to set up a database now to count these.

The 70s boost in reports lasted a decade. A bit longer than the previous one. This implies we’ll at least live through a few years of fun.

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Reminder: The Thursday Class is only for those interested in studying uncertainty. I don’t expect all want to read these posts. So please don’t feel like you must. Yet, I have nowhere else to put them besides here. Your support makes this Class possible for those who need it. Thank you. Math alert!

Calibration is an intuitive requirement and leads to a new kind of modeling called conformal prediction. Today, we give numerical examples and code.

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Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty

HOMEWORK: Try the code!

Lecture

I’m going to assume (yes, I know the joke) you have read and assimilated the Theory lecture from last time. I will not here do any review.

I’m going with a bad-good example. Bad, because the fine points will be difficult to see. Good, because it is so very typical. Most models are poor, according to most quantitative scores.

Download (if you want to follow along) the Bank Marketing data, which is known in “machine learning” and “AI” circles. Some 45 thousand observations. The outcome is “has the client subscribed a term deposit?” To help predict that, they have such things as client age, marital status, amount on deposit and the like. I’m going to use only a few of these “predictors.”

Our goal today is not to find the best model of subscription. All code is at the bottom.

Our goal is to take a model which has been given us (so to speak) and see how well it performed. That’s it. Another day, I’ll explore (again) the idea of the Great White Hope Of Models. The false hope that with the right magic formula—given by AI, of course—we can predict with perfection. This will not happen.

Passing by that, I’m going to look at two models:

• Model 1: a simple logistic regression as a function of age + job + marital + education + balance + loan.

• Model 2: a random forest with the same predictors.

To save model-fitting time, I dichotomized the bank balance of clients to whether they have a positive or negative balance (about 20% have negative balances!). The “loan” variable means other loans the client might have had. A sociologist would use these very terms, whereas somebody else might not. So the models we look at do have applicability to modern “research”.

I grabbed 10,000 observations and did not use them to fit these models in any way. Indeed, I picked these predictors because they were first in the list, and balance because I thought it would be interesting. But it was so big that my poor computer chocked on running the model fitting, which is why I dichotomized it. The remaining 35+ thousand were used to fit the model.

In real life, all 45+ thousand would be used to fit the model. That model would then be used to make predictions of data never before seen or used in any way.

Of course, everybody cheats in real life, and use the old data many times to find better fitting models. They will always be rewarded for their efforts. In the sense that they will indeed find better fitting models. But will these tight models predict better? Not too often.

Here we avoid all that by not caring about finding “the best” model. The best model would be one where we knew the full cause of every data point, which is impossible; as is not possible. No, not even with AI with trillions upon trillions upon etc. parameters.

We’re going to look at a proper score from predicting the non-used “hold out” or verification data. We’ll also check calibration, and build a crude conformal prediction model using the calibration results. We are not trying here to build the best conformal prediction model here, either. We only want to see the ideas in action.

I wrote my own calibration function. It is entirely discrete. This is a strength because all measures, ever, are finite and discrete. But it is a weakness in that naive use of it doesn’t help much. There are any number of calibration functions out there (like Frank Harrell’s), and these are fine, but they end up smoothing. We want no smoothing except for simple averaging. Our goal is to understand the basics, not (again) to make the best model.

The same holds for the conformal prediction, which here only calibrates model output, making a new model (as you recall). The one here is meh. It works, but I can’t see anybody using it in real life. Nevertheless, it is trivial to understand. Better conformal models abound, but these grow complex fast and invoke smoothing.

Nothing wrong with smoothing. Remember our discussion of “normal” models? Right: they can be used knowing they are always, and in every instance, approximations to Reality. As long as we hold firmly in our minds we have approximations, all goes well. Alas, with most smoothing people forget. The Deadly Sin of Refication sneaks up behind them and, well, the results aren’t pretty. Next thing you know victims are computing p-values.

In the training data, there are only 4,074 Y = 1, out of 35,211. Which is 12%. So this is a tough dataset to make good predictions on. Think. If we said p = 0 for ALL predictions, we’d be right in the training data 88% of the time. We have to beat that.

In the verification data, there are 1,215 Y = 1 out of 10,000, also 12%. We’re really, in effect, training to nail those Y = 1s.

Calibration

We break the predictions into bucks of size byp. I use 0.05 as a default. That gives 20 bucks (0, 0.05], (0.05, 0.1], etc. Put what you like, but the smaller the bucket, the more data you must have. Because next is to count the Y_Reality = 1 in each is probability-prediction bucket. The small byp, the more buckets, but the smaller the sample in each bucket. The proportion of Y = 1 (dropping the Reality subscript, but remember it is there) in each prediction bucket is plotted by the max of each bucket.

Calibration is achieved with the proportion of Y and probability prediction in the bucket are equal.

Simple as that. Nothing more than counting and averaging. Instead of taking “0.05” as the probability for the bucket “(0, 0.05]” for plotting (or calibrating), one could pick the mean, or “0.025”. But that required more effort, and I am lazy. I leave it as homework.

Like I said, more sophisticated models will smooth this, meaning they will create a NEW MODEL of p and Y. That adds uncertainty, which most instantly forget. So we’re not doing that. Anyway, for large data sets, this calibration is good. And perfect if in fact the cut points match the decisions you would make.

If you would make different decisions if the probability prediction is 0.025 rather than 0.075, then buckets of 0.05 are just the thing. If you don’t care between 0.05 and 0.15, then use buckets of size byp = 0.1. And so on. This calibration function is exact in this way.

Conformal prediction

If in a bucket, the proportion of Y equals the max of the bucket, then the points are calibrated at the probability. And so do not need to be adjusted. Or, the adjustment is 0.

If the proportion of Y in the bucket is larger by some q, then we need to add q to all the probability predictions in that bucket to bring it to near calibration. And similarly if the proportion of Y is lower than the probability: we subtract q.

This is only near calibration and not exact because once you add or subtract a q to probabilities, they can change buckets if they were near the edge of the bucket. And because we are applying the correction q to every prediction in the bucket (some of which may have had Y = 1 and others Y = 0).

But this is close enough for us to see how it works.

Brier score

We’ll use this because it’s the most common. We’ll see another day why things like ROC curves are WRONG. They are the p-values of machine learning. You simply cannot talk people out of them.

Here we need to be careful. If we’re calibrating, we’re saying “These buckets correspond to the decisions I would make” and therefore that is how we must score. If there is no difference to you (ahead of time, when you are in ignorance of Y_Reality) in predictions of p = 0.83 and p = 0.84, then both predictions ought to have the same score applied to them (we suppose they are in the same bucket). In the Brier, the p = 0.84 is closer and would receive a better score. But that’s just math, and not how YOU USED THE MODEL.

Instead, if these values are equivalent to, for instance, p = 0.85 in the decisions you would have made, then both ought to be scored as if they were p = 0.85. I’ve been stressing, nauseatingly often, that the best score is in the decisions YOU make, and not anybody else, with the models. That goes for the calibration and the conformal prediction, because choices must be made in each.

There is no one-size-fits-all score, calibration, or conformal prediction.

Model 1 Logistic Regression

Logistic regressions smooth. Hard. They do not show cause. It’s hard to find a sociologist or economist or the like who, whatever they say, understands this. We discussed the vast limitations of regressions before, so I say no more. We’re looking at the predictive posteriors here using the default values in rstanarm. All seems well behaved by the standard measures people use for MCMC methods (not knowing how to do analytic integration).

Here is the calibration plot for the model, with buckets of 0.05:

Pretty good, for the wee range of probabilities the model spat out. The max is only 0.42. Meaning the smoothing is way too aggressive, as it usually is for regressions. Meaning even when Y = 1, the probability predictions were never above 0.5. Sad.

And here it is for the conformal prediction:

A slight improvement. But we didn’t have much room here to make improvements. We could make smaller buckets here, but what’s the point? The model is not going to change in any real way.

We could loosen the buckets, make them 0.1 (which I won’t show, but which you can do yourselves), and the conformal shows a nice and tight calibration, but we only get buckets of 0.1, 0.2, and 0.3. Maybe that’s useful for some decision maker.

The bucket Brier score for the original model was 0.104, and for the conformal model is 0.103. A minuscule difference, but still we get the promised improvement.

Model 2 Random Forrest

I haven’t introduced these before. Roughly, they take a giant multi-dimension cross-table matrix of predictors (all females age < 10, all females age > 10, all males < 10, all males > 10, etc.) and cross that with the outcome. Cells in this predictor-prediction table are then used to vote which outcome is more likely. For instance, “all males > 10” had 80% 1s, then the prediction is 80% for “all males > 10” and the same idea for the other three buckets.

Of course, the whole thing is more complex than this, because making one huge crosstab would be too expensive and monstrous in size, with many (mostly) empty cells, so some kind of mixing-up search is iterated on subsets. Random forest models also do not show cause.

This is a form of smoothing, too, but weak. Regression is a steamrolling smoother. Regressions are the best kind of model in the world if Reality itself is smooth in the same way. Worst kind of models when Reality isn’t smooth. Which it usually isn’t. Which is why machine learning guys are kicking statistician ass.

RF is better than LR, but not by a lot. It gives some predictions with probabilities greater than 0.5, which is good.

Here is the calibration plot for the model, with buckets of 0.05:

Not too bad, as far as these things go. Fairly well calibrated at the beginning, so we won’t gain much with the conformal prediction

And here it is for the conformal prediction:

You can see it’s a tighter calibration. Success.

The bucket Brier score for the original model was 0.1014, and for the conformal model is 0.1007. Better, but so small that nobody would care.

If you decrease the bucket size to 0.02, you get a better idea of what’s going on with the calibration. Original:

That’s a lot more miscalibration, but the buckets are a lot smaller.

And conformal:

Better, but this has a lot of empty buckets.

Briers of 0.1009 and 0.1004.

But then, to we’re really polishing the dried spoor of some rough beast. The model stinks, really. Very few predictions over 0.5. Only 27! For a sample of 10,000.

Of course, we ignored a lot of the data. We could tighten this. But we’re not trying to here. No power will get it much better, because all the causes aren’t in the data.

These are only correlational models.

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# Example R code to teach calibration and conformal prediction. Written for clarity, not optimization.
# Download any packages you don't have using install.packages('packagename')
library(rstanarm)
library(rms)
library(randomForest)

# Download: https://archive.ics.uci.edu/dataset/222/bank+marketing
x=read.csv('bank-full.csv',sep=';', na.strings ='', stringsAsFactors=TRUE)
  x$balance = (x$balance>0)*1 # dichotomize balance
  x$y = as.numeric(x$y)-1  # make y/n into 1/0
  summary(x)

# The seed ensures you get the same results each time you run
set.seed(732)
i = sample(1:dim(x)[1],1e4) # split the sample
y = x[i,] # verification set
x = x[-i,] # training set

# Model 1: Logistic Regression. This converges fine.
fit1 <- stan_glm(
  y ~ age + job + marital + education + balance + loan,
  data = x,
  family = binomial(link = "logit"),
  prior = normal(0, 2.5),      # Weakly informative priors
  prior_intercept = normal(0, 5),
  chains = 4,                  # Number of Markov chains
  iter = 2000,                 # Total iterations per chain
  cores = 2                    # Parallel processing
)
#summary(fit)
# Predictive posterior probability predictions (how's that for a mouthful) on y
p1 = colMeans(posterior_predict(fit1,newdata = y))

# Model 2: Random Forest
fit = randomForest(y ~ age + job + marital + education + balance + loan, data = x, ntree = 500, mtry = 2, importance = TRUE)
print(fit)
# Probability predictions on y
p = predict(fit, newdata = y)

# Brier score. Not much to it
brier <- function(p,y){
   # no checking/handling for missing values!
    m = length(p)
    answer<-sum((y-p)^2)/m
    return(answer)
}

# Calibration plots, scoring, conformal model building, and redoing calibration and scoring for conformal model
conformal.p <- function(p,y,byp  = 0.05){
   # No checks of any kind are made. No provision for NAs are made. If you use this in real life, you are crazy. This code is in no way optimized.
   # p are the probability predictions
   # y is Y_Reality, 0s and 1.
   # byp is the probability bucket size

   # calibration plot
   s = seq(0,1,by=byp) # bucket boundaries
   p.cut = cut(p,s) # divides probabilities into buckets
   a = table(p.cut,y) # calibration table
   z = a[,2]/rowSums(a) # calibration counts
   plot(s[-1], z, xlim=c(0,1),ylim=c(0,1),xlab='Model Probability',ylab='Observed Frequency', main= 'Original Predictions Calibration Plot')
     abline(0,1)
     grid()

   # Conformal prediction corrections
   e = s[-1]-z
   j = which(is.na(e))
   m = length(j)
   if(m>0){
     e[j] = rnorm(m)*1e-6 # noise added because otherwise we get duplicated 0s, which collapse into one factor level; this ensures we keep the same number of factor levels as in p.cut
    }
   # add the corrections
   p.cal = p.cut # p.cal will be conformal predictions
   levels(p.cal) = e  # reuse the cuts which are now corrections
   p.cal = as.character(p.cal) # R quirk; you can't directly turn factors into numbers, but you can characters
   p.cal = p - as.numeric(p.cal) # p.cal are now calibrated (roughly)

   i = which(p.cal <= 0) # in case
   if(length(i)>0 ) p.cal[i] = 1e-7
   i = which(p.cal >= 1) # in case
   if(length(i)>0 ) p.cal[i] = 1 - 1e-7


   # we want the score to match our decision buckets
   levels(p.cut) = s[-1]
   p.cut = as.character(p.cut)
   p.cut = as.numeric(p.cut)
   cat('Brier raw ',brier(p.cut,y),'\n')

   p.cal = cut(p.cal,s)
   a = table(p.cal,y)
   z = a[,2]/rowSums(a)

   if (Sys.info()["sysname"] == 'Windows') X11() else quartz()
   # plots the conformal calibrations
   plot(s[-1], z, xlim=c(0,1),ylim=c(0,1),xlab='Model Probability',ylab='Observed Frequency' , main= 'Conformal Predictions Calibration Plot')
     abline(0,1)

   levels(p.cal) = s[-1]

   p.cal = as.character(p.cal)
   p.cal = as.numeric(p.cal)
   cat('Brier conformal ',brier(p.cal,y),'\n')

}

# Model 1: Logistic regression
conformal.p(p1, y$y, byp=.05)

# Model 2: Random Forest, with two different probability buckets
conformal.p(p, y$y, byp=.05)
conformal.p(p, y$y, byp=.02)

# This is Frank Harrel's version of the calibration plots. It smooths and has information we have not yet covered.
#library(rms)
# y = actual binary outcome (0/1), p = predicted probabilities
#val.prob(p, y$y)

A lot of conversations about the differences between the races go like this one about sex.

“Briggs, somebody told me you said men are taller than women.”

I said it.

“You’re, what, six-two?”

Yep.

“Well I know a woman who is just as tall as you are. And she can reach things in high place just as easily as you can!”

So you think therefore that men and women are the same height, in the statistical sense I meant?

“I’m not saying that. I’m saying your obsession was sex differences makes it seem women are worse than men, and that’s evil.”

Being taller is morally superior to being shorter?

“What are you talking about? I’m saying women can be just as good as men. You say they can’t.”

I don’t. I say men are taller on average than women, and that this difference is due to inherent essential differences between the sexes.

“Well diet can affect height, you know.”

So you think if we feed girls more meat, for instance, they might grow as tall as men?

“I’m saying you talking like this makes it seem women are worse. I’m saying you’re not offering any context to your extreme views. That you say these things with no regard to how they will be taken. You are a sexist.”

I think I see your point. Suppose a grocer wants to hire tall people to stock high shelves, and this grocer has heard me on the subject of height. He will say to a tall woman who vies for the job, “Although you give every impression of being tall, and this yardstick says you are, because you are a woman you are not tall.” Right?

“You are a bad person.”

END DIALOG

Such a dialog can string out over pages or days. Some know the difference in height between the two (we now have to count them) sexes is true, and ineradicable, but they hate that Reality violates Equality so strongly that they can’t bear to hear about the difference, or to know that somebody else is allowed to speak of it. Better to ban and forbid such speech, and instead create programs to stretch women, to award them honorary inches, so that jobs that require tall people will have just as many women as men. Reality be damned! Equality demands it!

Above all you must not talk publicly about Reality. And if you do, you must, by penalty of career suicide, admit differences are caused by “socioeconomic factors”, especially “sexism” or other such curses. There need not be any demonstrable causal mechanism between “sexism” and height. It doesn’t matter. Because “sexism” is a known sin against Equality, and therefore it is obvious that it is responsible for the observed differences. Reality cannot be the cause. We cannot abide the idea.

The dialog holds, nearly word-for-word, if you swap height differences between the sexes with Asian and black intelligence and aggressiveness differences. The differences are sometimes admitted, but the only possible explanation for them must be “racism” or similar thoughtcrime. You must absolutely forbid any from talking about these differences in any official situation. To say, what is true, that these differences are inherent and part of Reality is to commit a blasphemy so profound that you must be run out of all polite society.

On the rare, the very rare, chance you meet an honest intellectual opponent, but still a True Believer in Equality, you get strings of dialog like that above, one non sequitur after another. The idea seems to be that if you build up enough fallacies, even though each non sequitur is a non sequitur, the sum total somehow turns into validity. The idea is really, though, to shame you into admitting the Fantasy position (Equality) has some merit. The attack is feminine: it’s not what you said, but the way you said it. Yet once you surrender to the tears, real or threatened, once you decide to “Be nice”, you are lost. Fantasy wins.

A Real Example

Such is the experience and fate of not only myself, and many others you know, but also of one Jeremy Frimer, a tenured professor at the University of Winnipeg. He was accused, says one report, of saying blacks have on average lower intelligence than some other races, and that he, right out in the open, right in front of the children!, “presented data showing that Black people are 4.5x more likely to commit murder than White people.”

He ought to get grief for that last one, because the murder rates, according to the FBI, are about double that. But in Canada, everybody is politer, so many that “4.5x” is accurate. Anyway, the little rat who brought the complaint said Frimer’s comments “may constitute discrimination and harassment by implying racial differences in ability.”

He was not implying it. He was saying it. And he was saying it because it is true. And it is true because of a combination of innate, hence ineradicable, and environmental conditions. There will be no program that can make up the “disparity” in intelligence entirely. And none which will quell all differences in aggression. Like them or hate them, this is The Way Things Are.

With a proviso on murder and aggressiveness. Right now, in the West, blacks are pandered to to nauseating degree. Every foible is excused, even admired, because “racism”. The black man who slit the throat of the Ukrainian girl was recently let off the hook because—if your sense of humor is black you will laugh—he was found “incompetent.” Suggests a lower intelligence, you see. He was not found incompetent the other two or so dozen times he was arrested and let go.

This is only one case among many, many, increasingly many. This systemic pandering has caused a great deal of overt aggressiveness, as it would in any person spoiled from birth. Remove the pandering and require blacks to demonstrate the same level of civility as everybody else, really enforce this I mean, and blacks would in mixed company largely become the warmest, most good-natured and companionable people you can meet, more so than whites (think of how disagreeable an SOB like me is). Sans pandering there will still be, it’s true, occasional outbursts of irrational aggressiveness in blacks at rates still larger than other races. But manageable. Especially is social separation is allowed. Separation is, of course, now largely illegal.

In any case, with aggressiveness we have a case where socioeconomic factors are indeed largely contributory to “disparities”, and these conditions are caused by whites, just as we hear. But it’s those whites who hold with the false god Equality causing the difficulties.

Not the “racist” whites, not the ones who know something of Reality. “Racist” whites would solve disparities by ceasing the pandering, and acknowledging that not all are Equal or can be made Equal. Problem is, the “anti-racist” whites have made this impossible. Negative interactions between the races are thought, by default, the fault of “racist” whites. The only recourse the elite equalitarian whites leave them is to run away from blacks. Even self defense by whites is always viewed with deep suspicion by elite equalitarian whites.

This is proved, in a roundabout way, by the coda to the Frimer story. He tried to escape the charges by appealing to the Victim Calculus. He made sure to announce that “his great-grandfather was murdered by Nazis who believed in genetic superiority”. He said “he views the ideas presented at that point in the course as ‘disgusting’ and says he relays that [disgust] to his students.” Yet, he added, the data is still what it is for blacks and whites: the differences are there and cannot be eliminated.

Crying Victim is not a bad move, but I think it will fail because blacks outrank Jews in the Victim Calculus. Perhaps it will mitigate his eventual punishment, but not eliminate it. But that he thought to go la voie féminine proves Frimer knew Reality could not be used in self-defense.

The funny part is Frimer asked the University of Winnipeg Faculty Association to “to file a grievance on his behalf, alleging violations of his human rights and academic freedom, along with discrimination and harassment.” The UWFA responded, “Frimer? What’s a Frimer?” They ran away, in the usual academic cowardly way. (Academics are the most effeminate group you will ever meet.) The Manitoba Labour Board also turned deaf to his pleas, which is to be expected.

If Frimer comes out a grovels, as many people do in these situations, he may just hold onto his job. But I wouldn’t take that side in a bet. Equalitarians must have flesh. They will satisfied with nothing less than this expungement.

Meanwhile, the disparities will always be with us. Equality must be destroyed.

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Might I beg you, if you find it useful, to show this article to those who are growing concerned or agitated about this story? Don’t miss the ending.

Here’s a headline and juicy story: Mystery surrounds death of NINTH scientist tied to US secrets as disturbing pattern grows.

Another scientist with ties to America’s space program has now joined the growing list of deaths and disappearances around the US.

Michael David Hicks, a research scientist at NASA‘s Jet Propulsion Laboratory (JPL), passed away on July 30, 2023 at the age of 59, but the cause of death was never made public, and no record of an autopsy being performed could be found….

While there have been no public allegations of foul play, Hicks’ case marks the ninth person with ties to America’s space or nuclear secrets who has died or mysteriously vanished in recent years, which has set off alarm bells among US national security experts….

Two other men with deep ties to JPL died recently, including a long-time coworker of Hicks, Frank Maiwald, who died in July 2024 at age 61, with even less public acknowledgement of his untimely passing.

Meanwhile, astrophysicist Carl Grillmair, 67, was murdered on the front porch of his home on February 16, 2026….

The disappearance of McCasland, who reportedly held nuclear and UFO-related secrets, has been tied to Reza and Grillmair through their work on advanced missile or rocket science….

Chavez, 79, worked at the nuclear research lab until his retirement in 2017. Casias, 54, was an active administrative assistant at the facility and is believed to have had top security clearance…

In another mysterious incident, Jason Thomas, a pharmaceutical researcher testing cancer treatments at Novartis, was found dead in a Massachusetts lake on March 17, 2026, after disappearing without a trace three months earlier.

There are plenty of lurid details here, but I cut a lot, so go to the original to read it all. I particularly enjoyed the Daily Mail noticing there was no autopsy on one of the dead. Which sounds bad. But you could say the same, I’m betting, about your Great Uncle Fred, whose death you can make sound ominous by remarking, “My great uncle Fred died, and the one thing we always wondered was why they didn’t do an autopsy on him.” Try it in company.

Since that first story, it was early last week reported another man went missing: “Steven Garcia, 48, vanished without a trace on August 28, 2025. He was last seen leaving his Albuquerque, New Mexico home on foot, carrying only a handgun.” Note the date. Note all dates.

Update: After I had written this, there were last Thursday more lurid headlines, like this, again from the Daily Mail (they were far from alone): “BREAKING NEWS: Eleventh scientist found dead”. For good reason, I’ll save this for last, leaving the rest of what I wrote untouched. Below, I will reveal the most shocking death of all, heretofore unreported, bringing the tally to 15.

Here’s the Daily Mail’s most recent graphic (which leaves out some people):

From the reports I’ve seen, I make it 5 missing and 5 dead. Two of the dead were at JPL, one only had “connections” to that lab, and the other two dead were at Los Alamos or elsewhere. The missings you can see from the graphic. They all, dead or missing, were in a range of jobs, from secretarial to administrator to engineer to scientist.

Oddities

The strangest missings, or at least the two most remarked on, are the bottom: Reza and McCasland.

According to a more detailed report, Reza (60) went out hiking on a “a ridgeline in the Angeles National Forest.” She waved at a person she was hiking with (500 feet below), and then, like rare things will, she vanished. They haven’t recovered her body. This was 22 June 2025. (The DM and other sources have different ages for many.)

McCasland (79) on 27 February 2026 walked out his Albuquerque house “and into the Sandia Mountain foothills.” No one is known to have seen him since.

The graphic makes it appear he and Reza were pals, whereas McCasland was an administrator at Kirtland AFB (I’ve been, nice place), which oversaw funding that went to Wright-Patterson, which gave some to JPL, which Reza got a portion of. Along with many others.

Last week, the most competent and benevolent government of these once United States announced they were going to investigate these strange occurrences. Let’s beat them to it.

The Theories

If you are like me, especially if you’re like me since I resemble these guys, you notice that the dead were all entering the Great Downward Slope of Life. It is not unusual (sadly) for those sliding into their sixties to peg out. It’s less likely, given ordinary conditions, any would be whacked, though it all depends on circumstance. And you know what I mean.

The proposition before us, at least how the lurid headlines paint it, is this: Some entity is taking out scientists involved in certain secret research.

We want to know the chance of that. We don’t per se want the chance a person in his or her 60s keels over or disappears while hiking.

The two probabilities are not the same. We mustn’t confuse the rarity of people handing in their dinner pails, if it turns out to be a rarity, with the opposite likelihood that Peter Thiel, or whomever we suppose is behind the mysterious plot, is sending out minions on manhunts. It must be somebody or some group doing the killing and abducting if all these people share the same cause of demise and disappearance.

Just saying that, putting it into concrete terms, makes the idea of a Conspiracy, for that is what it has to be, seem unlikely. Not impossible. Unlikely. To me. Because Conspiracies require real work, real organization, a lot of planning and intricate machinations. Think to yourself about how to whack one scientist and make it look like an accident while also keeping your tracks perfectly covered, and covered so well even your favorite fictional TV detective couldn’t finger you.

Then you have to multiply that by ten. That’s a lot of secrets the Conspiracy has to keep! Not that it can’t be done by an earnest organization. But it cannot be conceived as easy. Think: making folks disappear, with no corpora delecti. Hard labor, that.

The Dead

There are some 5 to 6 thousand JPL employees, a majority of whom can be classed scientists or technicians. But consider we’re not only discussing scientists, as many headlines have painted it. And as many are sharing the story. We have secretaries, admins, and others kinds of employees and contractors, along with scientists. That’s our first glaring clue how to think about all this: sloppy irresponsible reporting (in other words, the usual) and taking that reporting at face value, which at this late date is remarkable.

Call it 4,000 for a conservative number of any we can class as “scientist” alone. But you have to add in some number of ex-employees, people who have moved on and are still above ground. Maybe it’s back up to 5,000.

The CDC, taking into account whatever measures they have on dead and living bodies, says there’s about a 1% chance a white man ages 55-64 permanently loses the ability to join any new wars (deaths from any and all causes). A little less for the Equal sex. That seems a reasonable guess to me, given my long experience with medical data.

With this premise and 5,000 employees in this age range, we’d thus expect about 50 to die in a year, with more than a 99% chance from 30 to 70 would croak. If they only had, say, 1,000 in this age group, then it’s obviously less: Some 10 per year, with a range of about 5 to 15. The numbers dip a bit if you consider women separately, but not to zero. Somebody should call a local florist and see how often they’re sending over bereavement bouquets to the labs.

Los Alamos boasts of some 14,000 to 18,000 employees, so we expect a bigger pile of bodies there. And that’s what was found. One more than JPL, anyway. It depends on how many of these you want to consider to be in the scientist pool, but there is going to be a slow and steady attrition rate from death. And then the people listed in the reports weren’t all scientists: there were secretaries, and etc. We might guess well over all 100 people connected or employed at Los Alamos die each year (the “expected” value is 140 to 180). If only half were in the age group, then we’d guess 70 to 90.

So far, we can conclude that the number of deaths is not unusual, and is even expected given our background information on employment and demographics. It’s stranger, in fact, that we don’t hear of more such deaths, given the number of employees these labs have. It could, as I said, be that our “denominator” is wrong at JPL. Maybe they only have, say, 1,000 scientists and ex-scientists 55 or over. Yet even then we’d still expect about 10 deaths, with a over a 90% chance there’d be 5 to 15 a year. And then about three times these numbers at Los Alamos.

And then there will be the odd death of those under 55. So it doesn’t matter much, either, if we lower that 1% chance per adult. Even if were one tenth of that, we’d still have a nice crop of corpses each year (below I use this modified number in the Missings analysis). And again, we’re talking several years here, not just one.

“But I don’t hear of all these deaths. Just these mysterious ones. It’s suspicious.”

Right. You don’t hear about most deaths, thank God. About 8,5000 people die each day in the States. That’s about 3.1 Million a year. Imagine having to hear about all 8,50o deaths every single day. And we’re not talking about only one year here, but at least two, if not three. This is a very large pile of bodies from which to choose stories. Consider that second Daily Mail story. Sounds like they went to great efforts to find that extra body. The Daily Mail is stretching to find bodies and connections.

Below, we’ll try the exercise ourselves.

The Missing

What about missing people? “Missing” isn’t dead, necessarily, because some that can’t be found eventually turn up alive or their bodies are found. One source reports around 400,000 adults go missing per year in the States. There are about 270 million adults in the USA. That’s a rate of about 0.1%. That surely varies by age, but I didn’t look into how, because it isn’t that crucial.

Again, Los Alamos has some 14,000 to 18,000 employees. We might expect about 14 to 18 each year to be reported missing. And maybe 5 at JPL. Each year. If that 0.1% chance for adults holds. And here we have not just one year, but two to three. Meaning we expect stories on 15 to 45 from Los Alamos over three years, and 5 to 15 from JPL. More, if we’re including people merely connected to these labs.

The Connections

The Daily Mail graphic makes it clear connections can be made between people working at each lab, and even between them, suitably mediated by government funding administrators. All these people were working on projects which seemed to be related, at least loosely. They are all science projects at least.

I once had a job at Lawrence Livermore but I was pre-fired after one of the global warming True Believers found out I was a “climate denier” (apparently I deny there is a climate). But at that near-miss job, I would have been in charge of a statistics group involved in all manner of activities and projects, including the nuclear side (I had a Top Secret-SCI clearance; I did electronic cryptography in the Air Force). And that would not have been unusual. It’s easy at and between these labs to be said to be working on “similar” projects or even the “same” projects.

The probability is certain as can be that you can find at least funding connections between people at different labs who all work for the government on similar matters. For one, they all work for the government. For another, they’re all working on similar matters. And because they’re at national labs, and this is where the research on nukes and such things happens, there’s a lot of natural overlap.

It would be harder, and probably close to impossible, to find no connections. They are connected by definition because they work at, for, or with these labs. There must be connections. And notice that not all are working on the same project, say a nuclear shell to repel Aliens, but merely similar ones. Again, those jobs must be similar. If they weren’t, they be working somewhere else.

The Chances of Our Theories

These numbers were computed assuming the Natural Causes theory was the cause of these deaths and missing people. Another name for this is the Nothing To See Here theory. It is a dull theory that excites no one. People that promulgate it are not loved, even hated, the party poopers.

What numbers would we expect if Peter Thiel’s Band of Assassins Conspiracy or similar theory were true? Same numbers!

The tally of dead and missing are so tiny, relative to employment, they wouldn’t bump up the Natural Causes stats enough to seem suspicious, especially over a multi-year period. The connections are also perfectly banal. You cannot work at these labs and not have Six Degrees of Kevin Bacon not come into play. Even I have an Erdos number of 5 (for those who know what that is).

To believe the Conspiracy, or give it real weight, we’d thus need evidence beyond that of body count and vague assertions of project similarities at labs run for the purpose of making similar-project jobs. The numbers we have aren’t even close to letting the Conspiracy theory carry the day.

What might this Conspiracy evidence look like? Could be many things. Like somebody reveals emails connecting, say, six or seven of these guys dead scientists, with cryptic messages about The Secret (whatever that might be). Or the same kind of communications from minions boasting of how they did the deeds. Any number of things could work, but they grow increasingly esoteric.

For instance, a leading alternate theory is—shall I tell you?—UFOs. Yes, really. Hello, 1970s. Our “scientists”, which we see includes secretaries and others, were either killed by Men In Black, beamed up to ships, or are in witness protection programs (yes, people say this). No evidence is presented for these views, except insinuation. But insinuation is enough when you want to believe. “Wake up” is a popular phrase.

For this we can blame desire. The desire is strong in many that there should be a connection, and that powerful secret entities are carrying out mysterious assassinations and kidnappings as part of their plan to Rule The World. Desire is what accounts for many not looking beyond or into the media headlines. How at this late date any media story is believed is perhaps the most disappointing aspect, to me, anyway. This lesson ought to have been learned better by now.

People who favor the Conspiracy hate hearing criticisms (like these), and think those that make them are bad or are ignorant and naive or are in on it. So don’t take this as me trying to talk you out of anything if you want to believe. I understand. We can still be friends.

The Shocking Eleventh Body

The headlines last Thursday all announced an eleventh scientist was “found dead”. Some gave the name, most just blared the increased tally. This is an excellent demonstration of how a truth, the scientist was indeed “found dead”, can be false. For the scientist, Amy Eskridge (34) was “found dead” in 2022 after she shot herself (videos of her show an unhappy person; her dad was forced to tell a reporter “Scientists die also, just like other people”).

She wasn’t just found. She was found four years ago. Which shows that once these mini-panics get going, they are difficult to stop. We saw above that there is an excellent chance each of these labs have multiple deaths a year. Now we’re talking over four years. And yet there are only reports so far on half a dozen deaths, from a pool that is almost surely much larger. That make the chance all but certain that we will see more headlines. Beyond number 11, I mean.

I am going to provide them.

Reporters (not a good word here) and rando researchers will reach back and sift through obituaries, looking for any connection to these, and surely other, labs. And they will be rewarded in their efforts. There are bound to be many more deaths “uncovered”. Just saying “uncovered”, like stating “there was no autopsy”, makes the deaths seem suspicious, does it not? Because you can’t “uncover” something known to all, so the temptation to believe these some entity tried to “cover up” these deaths is powerful.

After a full three minutes of searching (two spent in not realizing my enemies placed a typo in my search terms) I uncovered the death of Thomas Eldon O’Hare (88), who was found dead in his Los Alamos home, from what they say was metastatic cancer. There is no record of an autopsy. O’Hare was Air Force and “flew missions as an ECM Operator on B-36 ‘Peacemaker’ aircraft that took him to locations throughout North America and the Atlantic Ocean”.

Significantly (my emphasis), “After leaving military service he spent the rest of his career in New Mexico while maintaining a government security clearance by working for a contractor to the Sandia National Laboratories, which then led to a twenty year career with the Los Alamos National Laboratory (LANL).”

That brings the body count to 12!

No, 13! For we have to add S. Fredric (Fred) Marsh who was a “Los Alamos National Lab analytical chemist”, working at the mysterious “Materials, Science and Technology (MST-12) group”, and was found dead in 2023.

Make that 14! Add in Roy White, Jr., who was found dead in 2022, and who worked “over 30 years as a facilities engineer in C Division. He was very involved with all the new supercomputer installations and maintenance.”

I was wrong. It’s 15! And the most shocking death of all. Charles F. McMillan (69) who died in a suspicious car accident in 2024. Get this: McMillan was the 10th Director of Los Alamos National Laboratory (LANL), from 2011 to 2017, and the President of Los Alamos National Security, a private company. He was deeply involved in “planetary exploration via the Mars Rover.” Think about that. There wasn’t anything this guy didn’t know.

And dead in a car crash? How dumb do they think we are?

Video

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Reminder: The Thursday Class is only for those interested in studying uncertainty. I don’t expect all want to read these posts. So please don’t feel like you must. Yet, I have nowhere else to put them besides here. Your support makes this Class possible for those who need it. Thank you. Math alert!

Calibration is an intuitive requirement and leads to a new kind of modeling called conformal prediction.

Video

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HOMEWORK: Read!

Lecture

We are still with our model statement Pr(Y|M), where Y is or can be made into something dichotomous. We learned some common Judgment functions for these, made scoring functions because we desired math. And we learned about gaming scores and that possibly, for some W (in S(Y_Reality, Pr(Y|M) | W)), proper scores are a way around gaming. Propriety relied on “expected” scores, which aren’t the only possibility. But they do nicely illustrate gaming.

All that applied to when the model was used to make one probability statement about one Y_Reality. Which is the Y that is observed or believed. But often we use a model more that once, so we have p_i = Pr(Y_i |W), for any number of predictions. Since we have more than one prediction, we can use all we have in seeing how good the model performs. If—and this is the big if—our W indicates a mathematical way to score them.

Here some really nifty math comes in handy, first written about by Mark Schrevish in his book Theory of Statistics. He proved, for scenarios like ours with proper scoring functions, any set of predictions that are calibrated beat the same set of predictions that are uncalibrated, conditional on the score.

Calibration is simple. Every time the model states p, we have (if the model is calibrated)

and this holds for all the different p the model states. In other words, every time the model says, for example, “p = 0.3”, 30% of the Y_i = 1 (dropping the Reality, but remembering it is there, always a danger). And that holds for every unique p the model stated, like “p_i = 0.6” and “p_i = 0.01” and so on.

This is not, it is most definitely not, some frequentist requirement for all future imagined predictions in some hypothetical universe, but what was observed already. Model statements already made, that is.

Calibration is a nice and intuitive measure of performance. When our scoring function can be made into math, of course, which isn’t (I keep reminding us) always true.

Suppose we have a model that made a number of predictions in which, say, “p_i =0.9”. If the model was calibrated, we would see 90% of our past predictions having Y_i = 1 (observed). But suppose instead we get f = 0.7 for this set. We lack calibration. But we can “add back” the “missing” 0.2. Why not? That give us a new model, conditional on the original one as evidence. This new model will of course be calibrated at p = 0.9.

But of course, we can do that for all the p the first model used. The re-calibrated new model is the basis for conformal prediction. In notation (and many different ways of writing this are possible):

There is also likely other evidence E we use to help us build the New & Improved! model. Included in the E is at least the knowledge that we are re-calibrating. The prime on p only indicates the new prediction is not necessarily equal to p. Though, of course, there may be some values of p in the original model which were already calibrated.

Now it doesn’t quite work like this in practice. What happens instead is that the original model is built, Pr(Y|M). That M is then used to make prediction of the past observations. That is, the very observations that allowed us to build the model M in the first place. All these observations are all in M, don’t forget. And also don’t forget that any change—where by “any” I mean any—in the observations also changes M.

In other words, the conformal model is built re-using the same data M used.

It is then the p’ = Pr(Y | Pr(Y|M) = p, E) New & Improved! conformal model is released into the wild. Which we can also write as p’ = Pr(Y | M’). But doing so makes us forget our roots, and allows over-certainty to creep in.

Re-calibration is simple in the way I’ve painted it in theory. But all kinds of choices have to be made in practice. For instance, with parametric-based M the model may only spit out p that are all unique. The parameters are all “integrated out” by the time we get to Pr(Y|M), of course, but because of those parameters our predictions likely lie on the continuum, i.e. the whole interval (0,1). And never, also because of those parameters, in {0,1}. In any case, if the p are all unique—think of this ordered set of predictions: (0.048, 0.299, 0.460, 0.753, 0.790)—then every f will equal 0 or 1. No way to get re-calibration! (Make sure you see why. Watch the video.)

One possible choice is to use “probability buckets”. Pick probability intervals corresponding to whatever decisions you will make using the model. For instance, if you would make the same decision if p_i = 0.47 as p_i = 0.5, but you would make a different decision with p_i = 0.45, then pick buckets that indicate this. There is no general or universal right answer here. The right answer is all dependent on W, which also now contains whatever evidence you are using to pick the buckets.

For instance, round all p to the nearest tenth—if your decisions, and only your decisions, are not sensitive to probability predictions different than 1/10. Then you might, depending on your sample size, have sufficient Y_i at those probabilities to re-calibrate.

Modeling, like every other question of uncertainty, depends on the evidence you have. The more you have, in the form of more past Y, the better information you have. Up to a point. Always up to a point.

Now, there is certainly more to conformal prediction and calibration. But these are the basic motivations. Next time we’ll work through an example which I hope will clarify everything.

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There is a great and terrible danger in being a strict immovable literalist and in insisting every word in the Bible as written is the inerrant absolute word of God. Find even one small, even seeming trivial, discrepancy or contradiction and your entire edifice of belief comes crashing down.

Such happened to Bart Ehrman who, we learn in a long and fascinating interview with New York Times employee Ross Douthat, was born and raised Episcopalian and at fifteen became “born again”, indicating becoming a “committed evangelical Christian”. He was “very gung-ho about [his] religious faith”, went to Moody Bible Institute and became “a Bible nerd there”.

In his words, a fundamentalist is one who believes “that the Bible is inerrant, in a really strong understanding of the term. Any contradictions should be reconcilable.” As Douthat asked, the seeming contradictions apply not just the text with itself, but with the text and world, too. Ehrman agrees:

Six-day creation, Adam and Eve, the flood — it all historically happened. Everything about the Gospels literally happened. So yeah, it was fundamentalist in that sense. And I bought into it.

The breaking point for Ehrman came in a staff. A simple walking stick.

On a basic level, Mark’s Gospel is usually thought to be the first Gospel. Jesus is sending out his disciples and telling them to go heal the sick and cast out demons and preach the good news. He says, when you go, don’t take a backpack, don’t take extra sandals, don’t take any money, but do take a staff.

OK, you have to take a staff because you’re going to be walking.

Matthew’s is exactly the same episode, word for word in some places. But in Matthew, he says to the disciples, don’t take a backpack, don’t take extra sandals, don’t take any extra money — and don’t take a staff.

Wait a second. This is an obvious thing where he either said take a staff or don’t take a staff, but he probably didn’t say both.

If you are a literalist (as of course most atheists are), insisting on every word being, as it were, dictated by God himself, and you have done the homework ensuring the staff-business is not some scribal error or the like, then we have here an irreconcilable contradiction. Which means you must, as Ehrman did, reject one of the premises in your argument for belief.

Ehrman did not reject literalism, but did God. Because to him the existence of God necessitated literal inerrant scripture, in his strictest sense of that term.

Douthat pointed out it’s possible to reject literalism and maintain belief in God, and that “inerrant” can mean other things. Like this: God inspiring men, who were just men, to write about what they saw and heard. Literalism, in Ehrman’s strict sense, would not then be expected.

Though there would then be required a body to first decide what counts as scripture, and then to have a (perpetually, really) debate about its meaning. Such a body has always existed, but Ehrman was able to reject it because of his literalism: a correct decision if literalism is true. The body is not needed, it’s true, if his version of literalism is true, because every man can be his own priest. But literalism cannot be true because of that staff (and many other examples; he has books cataloging them). Ehrman concludes no man should be a priest.

Which brings us to miracles, or rather just one, mentioned below. Ehrman rejects all miracles, because if the staff is an error, so must be all reports of miracles, he says. Yet if we, like Ehrman, reject events when there is imperfect witness agreement on even minute details, then we must reject all history, not just miracles. That’s the short, incomplete answer to Hume’s argument against miracles. Which today I do not want to spend time on (as that would take a full post).

Let’s instead discuss how evidence works in two other matters that came up in our pair’s discussion: the dating of Acts (this is far from as dull as it sounds), whether people saw Jesus in the flesh, as it were, after he was crucified. We’re not trying to solve these questions, but to see how evidence for and against it used.

ACTS

The Acts of the Apostles, commonly attributed to Luke, recounts the history of the very early Church (the first chapter has a nice probability example, incidentally), beginning with the Ascension of Jesus into the Clouds. It ends with Paul arriving in Rome, vainly trying to teach Jews there the Good News. The last sentence of the book is: “He [Paul] remained for two full years in his lodgings. He received all who came to him, and with complete assurance and without hindrance he proclaimed the kingdom of God and taught about the Lord Jesus Christ.” No hindrance, you see.

You will of course remember that Paul was later hindered. He was executed. A rather large detail in the life of the man to leave out of the book. That Acts does not contain this interesting story is taken to indicate the book was finished, and in circulation (such as it was then), before Paul was killed. Most sources estimate Paul died somewhere in 64 to 67 anno Domini. Thus it is reasoned Acts is dated some time before this.

So far, unless you’re a scholar, this doesn’t sound particularly fascinating. But it is because some are desirous of and produce arguments for late dates for the Gospels, just as some are desirous of and produce arguments for early dates. And that is because the sides in this debate both accept the premise earlier dates are better confirmation for the events depicted in these books. Memories flag, you see.

Ehrman wants late dates, Douthat early ones. Douthtat gives as evidence for the early dating of Acts, which implies Luke’s Gospel is therefore also early:

Soon after [the end of Acts], a lot of incredibly crazy stuff happens. You have the martyrdom of Paul and Peter, you have Nero’s first persecution of the Christians, and then you have the Jewish war and the destruction of the temple. So it’s a very action-packed decade.

It has always seemed to me that the most straightforward reading of Acts ending where it does, without any detail of those subsequent events, is just that the writer wasn’t aware of those subsequent events and was ending his story roughly where he was — it’s the early 60s, Paul is still alive, and this is the end of the story because this is when he is writing it.

And that one of the key reasons that scholars reject that sort of intuitive conclusion is that they don’t want to give Jesus credit for a prophecy [about the destruction of the Temple].

My point is not to settle this debate, but to show how desire drives the hunt for evidence. Douthat does not mention his own, but does that of academics (“scholars”). Ehrman also does not mention his own, but it is anyway clearly inferred from the conversation.

This is proved by how Ehrman handles Douthat’s excellent point about the curious abrupt ending of Acts, which is curious if Acts was, as Ehrman claims, written well after Paul was executed and so forth. I quote now over several answers (read the original to see if I cut too much):

Well, then, why does the Book of Acts end while Paul’s in prison in Rome in the sixties?

Two things about that. One, I agree that Jesus predicted the destruction of Jerusalem, so I don’t late date them because of that [but not because of supernatural knowledge, but keen appreciation of the politics of the day]…

There are good reasons for thinking why the author of Luke—Acts would have wanted an Act before Paul was finally put on trial and executed. The whole point of the Book of Acts — for those who don’t know, the book of Acts begins after Jesus’ resurrection. He ascends to heaven, then the day of Pentecost happens and Christianity starts spreading throughout the world.

It covers about a 30-year period of the early spread of Christianity.

One of the major theses of Acts, one of its themes, is that this is a movement that cannot be stopped. Paul, in particular, cannot be stopped. Paul goes into a town and he gets persecuted and they beat him, and he just goes to the next town and starts another church. They try to stop him there; they can’t stop him.

At one point, they stone him. He gets up, goes to the next town. There’s nothing you can do because the spirit is behind this whole thing.

That Paul was killed meant, as all students of logic can deduce, that he was not in fact unstoppable. That execution, you see. What a terrible way to ruin a good story! Luke knew all about it, because he wrote late, but he chose not to include facts which ruined his narrative. Which is how we know the book was written at a late date.

Douthat counters with Martin Luther King, who was also seen unstoppable in the great civil rights revolution (that like all revolutions caused vast unmeasurable damage). Nobody writing stories of King leaves out his assassination. Indeed, the parallel goes the other way, because King is now a martyr, with even a holyday named after him.

Ehrman:

The Martin Luther King thing is an interesting analogy, but I don’t think it quite works because that’s really kind of the point — the assassination.

For Paul, according to Luke, that’s not the point at all. For one thing, we don’t have a lot of records of people being martyred at the time. We actually don’t know a lot about Paul’s death. The earliest reference we have to Paul experiencing martyrdom is around the year 95 by a book called First Clement.

So, we don’t have records. We don’t know what this author even knew, actually.

This is weak; one might even say grasping. But he must, because that is where his desire leads him. He needs to fit the facts he has with the theory he wants to believe.

Jesus In The Flesh

Again, we will not solve the debate whether Jesus appeared as a physical being to many after his crucifixion. I only want to examine a few key pieces of evidence and how they are handled.

Ehrman (no mythicist) allows “Jesus was arrested and he was put on trial and was crucified publicly — humiliated and tortured to death.” Then:

I think it’s absolutely the case that some of his disciples afterward thought that he had been raised from the dead. My sense is that some of them thought they saw him alive afterward.

I don’t know how many people had the visions. I don’t know whether there were groups, whether there were few individuals who eventually convinced the others — and people came to think that Jesus was raised from the dead. They started proclaiming that and they convinced people of it, and that’s the beginning of Christianity.

So it’s visions for Ehrman, necessarily false visions for him, thus hallucinations. And therefore occasional mass hallucinations, for there were times, it was reported, many gathered together and saw, talked, and ate with Jesus.

Only there are no such things as “mass hallucinations”. This is the same level of science as “you only use 10% of your brain”, and coming from about the same era (the 1970s; ahem). Individual people can hallucinate, but people do not share hallucinations. Brains don’t break simultaneously.

People instead can as a group be mistaken about what they have seen and heard. That’s easy enough, depending on the degree. Or they can jointly, or in separate groups also jointly, lie. That’s a lot harder. Not impossible. But harder, because it’s hard to keep stories straight the more people that are involved. Then you can’t trust there won’t be defectors who won’t blab. Especially when they have ever incentive to defect, as for instance when Nero began his murders of Christians.

Or you can, if you are writing the history, simply make the stories up. That’s the version Ehrman is committed to: “I don’t think Jesus appeared to 500 people at one time,” he said. Yet this was what was reported (among many other things). Therefore, he does not say, but it follows, the reports are a deliberate fiction.

But the other interesting thing is that all the resurrection narratives are filled with doubt. In the Book of Acts, one of the strangest verses in the New Testament is Acts 1:3, where it says that Jesus spent 40 days with his disciples proving to them with many proofs that he was alive.

And you think, how many proofs does he need? And why does it take 40 days? But that is the interesting thing, is that in all of these accounts, you have these doubt traditions. What are those doubt traditions about?

I don’t think Ehrman thought these questions through. Imagine Jesus provided only one such proof, say, meeting the two men walking. And that’s it. These two later report what they saw to the apostles, and Luke writes it down. Would we not then hear Ehrman saying, “Look, Jesus was supposedly raised from the dead and appeared to these two guys. How come he didn’t appear to more? Why not to a whole group so we can be sure it wasn’t just a couple of guys making it up or having some shared illusion?”

And so forth.

Conclusion

Ehrman is no Doubting Thomas, and cannot be. Thomas believed after he touched. Which touching cannot be done in a vision. It can be hallucinated, but the men with him could not have shared in that hallucination, so the whole thing has to be either a deliberate lie from Luke, one he would have had a hard time getting away with since the other men were there with him and could have countered it by saying “Luke made it up.” Or, solving the problem for Ehrman, Luke had to write after everybody’s dead (except Luke). Hence the Acts dating tie-in.

That is not impossible. But it strings together events difficult to be stitched into one.

Those who want to believe Ehrman’s theory will counter that, aha, the alternative is to believe reports of a man rising himself from the dead. And that it’s much easier to believe people would lie about that than for a man to come back to life from the grave. (It’s not just one reported rising, of course, given Lazarus and the many others.) Maybe it was politically or personally advantageous for Luke to end the story as he did, assuming the late date for Acts. There aren’t a lot of corroborating documents, after all. Maybe Luke ran out of paper.

I’m not picking on Ehrman, because he displays a mechanism of argument every one of us uses: we start with a desired theory and try to find evidence which fits it, and then try to find how the evidence which doesn’t fit it can be “explained away”. The cleverer or more intelligent you are, the better you will be at this. Or at least the more intricate will be your hand-stitched web of evidence.

That is why the adversarial nature of theory testing is crucial. Few men can work the trick on themselves, and even then they can usually do so only for mundane things, and only rarely in controversial matters when they are doing their utmost to judge all evidence the best they can. In other words, having the ability to prove oneself wrong is a superpower.

Hence the necessity of debate. Though it has to be structured to be of any value (it was in the interview). Else it’s just chaos and noise. But that is a story for another day. However, it is easy to see that the only way to talk yourself out of any theoretical hole, if you are in one, is to listen and consider those taking sides other than your own.

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Cast your mind back, if you are still able, to 2014. The very beginning of The Great Awokening. We ran to some acclaim a Worldwide Contest (well, the internet goes everywhere) to discover the Next Official “Orientation” Letter.

At that time we had only the paltry “LBGT”. Or was it “BGTL”? No. Let’s see. Four letters…4 x 3 x 2….makes twenty four possibilities: Hmmm. Wait! I remember now. Ladies first. It was “LGBT”. Sometimes affixed with “community”, though you rarely saw the ladies “hanging out” with the boys, if you know what I mean, so there was never much of a community.

Anyway. Hard to keep these letters straight. But important. Indeed, there is nothing more important than announcing to strangers what your non-procreative sexual proclivities and tastes are. Everybody needs to know, and they need to know fast. After all, they might be free tonight and you can play Match Letters, as it were.

As you might recall, the “LGBT” was soon expanded to “LBGTQAI”, a completely unpronounceable acronym. It’s hard to believe now, but that “AI” on the end was not, in fact, artificial intelligence, although that is apter than it at first seems, right, gooners? My own memory flags, but I recall the “A” might have been “ally”, which is somebody who enjoys hearing about non-procreative sexual activities, but isn’t too keen on getting in on them. The “I” people, are. I believe “I” meant “Inquisitive” or “Inquiring”—or something like that.

Don’t forget, it wasn’t long after letters started gluing themselves to the acronym that the jealousy hit. Hard. Those who were only interested in the dull old-fashioned procreative sexual, or sex-like, activities didn’t get a letter. No “N” for “normal.” But all know you are nobody in our culture unless you are a Victim. So here’s where the Normals got really clever.

They started announcing their pronouns!

Brilliant. Everybody got to pretend to be special. This was especially big among academics, who let no intellectual fad pass. Soon all (interminable) meetings began with bearded skinny-fat men saying, “I’m Steve. He-him. PhD.”

To avoid confusion, all should know that “PhD” is not an “orientation” or “gender”, but a credential. Which is only slightly less important than the other two designators.

Well, back in 2014, we didn’t know what new letters we’d get. There was a lot of excitement and uncertainty. Many proposals were made. It was a lot of fun. I wrote:

What will be the next letter? Until recently, smart money was a second B for “bestiality.” Letters do not have to be unique; but if they did, then Z for “zoophile”, their preferred term. In Sweden and Germany, “Here, boy!” carries a different connotation than Stateside. But bestiality, while legal in those countries, is under fire from animal “rights” activists who are concerned about emotional scars on the Fluffies of the world.

S for “self”? Let’s don’t shake hands on it. Consider O for “object, inanimate.” Or K for “pedophiles” (K=kiddies), saving P for “polygamists”. N for “necrophiliacs”? Looking to Japan, R for “robot”?

Not to brag, but you can see how close I was here. The “O” was almost immediately correct, too, because right around then we learned about “objectophiles”, which are those who give us good reason to wear plastic gloves when going to thrift shops.

As impressive as this is, I don’t declare myself or anybody from the old days the Victor. That honor goes to….drumroll:

Leah Gazan, a politician and Member of Parliament in the Great White (past tense) North!

She waddled up to a microphone last week to tell us how angry she was that Canada’s proposed new budget did not include sufficient funds in the fight (they are always using military metaphors) against “the ongoing genocide of MMIWG2SLGBTQQIA+” people.

MMIWG2SLGBTQQIA+.

She rattled off the new acronym like it was a song, like she uses it ten times daily, which she probably does.

The “+” is coders lingo, incidentally; it’s a placeholder for future letters. It means “add them here”. It indicates the work to make everybody a “sexual minority” is not yet done.

Somehow the first letter in MMIWG2SLGBTQQIA+ stands for “Murdered.” I do not jest nor joke. Murdered, and not in euphemism, either; it means made dead-dead. Judges rule this M can’t count for “Necrophilia” (which again might be “N” at some future date) because all letters are for those possessing the “orientation”.

And this naturally means that Murdered people are enjoying some strange (necessarily) non-procreative sex-like activity in the Great Beyond. Just what that was, Gazan did not say. But ghosts are a definite possibility.

Let’s all give a great big hand to Miss (or is it Mrs?) Gazan!

Bonus: In Iceland, BDSM is an official sexual “orientation”.

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Briggs note: There are many stories of unbeatable foes — like the man with the abbreviated moustache, Napoleon, etc. — who were successful because they relied largely on their own judgment against the Experts of the day.

But then came the one fatal overreach, the point at which they began to believe in their own in infallibility.

Is that true here? Every time Trump has been in a deep pit it’s “With one mighty leap” he is out, flummoxing his enemies. Those who made a practice of betting against him lost time and again.

Until, perhaps, that one last time where the pit only grows deeper.

Since apologies are in vogue, please let me join the crowd and admit that Donald has fooled me. At least, the Donald post-Feb. 28^th. Yes, this is all terrible. Disgusting is the better word. But let’s not forget the other side of this coin. After all, every action sparks an equal and opposite reaction. A lesson we always forget in the moment. But nevertheless, still true. And used to great effect, time and again throughout history, by God Himself, as He shows mankind to be the fools they are when they listen to El Diablo. Which is obviously what Donald has done lately.

We can argue all we want about whether or not he was in on this from the beginning (pre-2016), or any point in between, but it doesn’t matter now, because he has gone against the core issue he won on – no more unjust wars! And since unjust war is the worst thing possible, given the civilian suffering and death, I think God was giving Donald the chance (to redeem his past) to see if he would keep his word, this time. Which, unfortunately, he has not.

So, now let’s look at this equal and opposite reaction in order to understand how God can always bring something good out of something done for evil.

If the reason for the evil actions of Donald (at Bibi’s behest) were to conquer the MidEast/World, then the counter reaction to this evil action might well be a peace that ensues in the world. I know, I know, how could that be if the Empire and its Siamese twin continue to exist? Well, exactly! What am I saying? Simple. Donald and Bibi may have just committed suicide. Along with the Empire and Israel. In their hubristic delusion that they could control the world, they may actually lose that former control. We may actually get to pry the guns from their cold, dead hands.

Now don’t misunderstand me, I’m not predicting the rise of Islam (either flavor) to take their places. Except in this way – Iran may get to live in peace. The Palestinians too (if they ditch their suicidal tendencies). And a lot of other nations as well, as the grip of the Western Roman Empire falls loose upon the reins of their war horses. The Iranians had their democratically elected leader removed by us in 1953. Then they suffered the devastation of the Iran-Iraqi war when over a million died in either years (that included Iraqi gas attacks and missile attacks on Gulf tankers). This war, by the way, was encouraged by the Empire and Israel. In other words, Iran has not been well treated by anyone to the West. They have good reasons not to trust us, at all.

As for the Palestinians, well, they have been the recipients of Kosher Love ever since the Nahkba in 1948. Read what this Jewish intellectual intellectual writes about the treatment he received when he had the nerve to question the Jewish version of the dispossession of Palestine. They did this to one of their own. Think about that. Then recall all of those images of Gazan rubble resting upon myriad dead children. So, it’s hard to say who is more complicit in war – The Western empire, or Israel. But again, when the crimes in question are committed by a Siamese Twin, it’s hard to determine which side did what.

Starting on Feb. 28, these two megalomaniacs may have pushed God’s patience to the point of breaking. To the point of allowing the opposite of what they desire to become the resulting reality. But there is a price to pay for our freedom. We have only just begun to pay it. But pay it we must, if we want the freedom to be a nation again, and not an Empire. And not the slave of Israel. Part of the price will be economic. Hopefully, most of the price (for us) will be economic, and not destructional mayhem. But the Christian-Zionists have a heavy responsibility in all of this and they must be held to account. Especially at the ballot box.

As for Israel, they too are in it all the way with Bibi. He enjoys high public approval over there. That means God’s measure will go deeper with them than us (I hope). Maybe to the point of collapse. At which time, Palestinians may get to claim the Right of Return as they regain their lost homes of the past. And the funny thing (if any of this could be termed funny) is the former colonial powers will be powerless to come back in and re-impose a western ‘peace’ upon the Arab world as they did after WWI. Why is that? Simple. Because they have no more military might. And their economic might may have sunk in the straights of Hormuz.

They have denuded themselves of their own military might in Europe, and on the ground in Ukraine. Hell, Jordan has more Main Battle Tanks (MBT) than England, France and Germany combined. And probably us too! Anyway, the point is this – prior to this current carnage in the MidEast both the Western Empire and Israel have stripped themselves bare of armaments and money, before realizing how close to the edge they have come. And in a frantic attempt to reclaim their past power, they have pushed too hard, against God and Man. And maybe it’s time both pushed back.

And no, I haven’t forgotten that I’ve previously written that The Empire will exist till the end. Because it will. Daniel’s dream interpretation confirms it. Just remember, the statue in Daniel’s dream has two legs (of iron). The golden head was Babylon, the silver chest and arms were Persia/Medea, the brass belly was Greece, and the iron legs were Rome. Imperial Rome. Which has two parts. West and East. They both continue in existence, but only one leg is superior at any given time.

And every 500 or so years, the statue shifts its weight from one leg to the other. Just check your history books on that observation. Guess what? We are at that point in time again. Even the Vatican agrees that the Romanov house holds true title to the Eastern Roman throne. The statue has now shifted its weight to the Eastern leg.

Moscow, the self-proclaimed Third Rome, is the new locus of world power. They aren’t out of weapons. Older ones or new. And they don’t need Middle East oil, gas, or any other natural resources. So, the turmoil in the Middle East won’t cause them economic or military ruin. Actually, this world chaos is very profitable for them.

But there’s a better way of gauging who’s actually in charge. A true global leader acts with visible poise and restraint. Is that how you would describe Donald now? No, obviously not. Well, what about Vlad? Yes, I think so. And I think he’s is getting ready to re-claim the throne. Pray Donald and Bibi are gone when he does.

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Reminder: The Thursday Class is only for those interested in studying uncertainty. I don’t expect all want to read these posts. So please don’t feel like you must. Yet, I have nowhere else to put them besides here. Your support makes this Class possible for those who need it. Thank you. Math Alert!

What makes a mathematical score of model goodness proper?

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HOMEWORK: Read!

Lecture

We have our model statement in hand, Pr(Y|M), and indeed we might have a collection of these, Pr(Y_i|M). We learned the last two times the very best measure of model goodness is the judgment that you, and only you, make based on how worthy the model was to you. One and the same model may be wonderful to you, and lousy to another depending on the worthiness criteria. We also learned there is no general solution, unless the individual case involves a known necessary moral truth.

I warned us, vehemently, that judgment measures that were mathematical ought not be loved or trusted because they were mathematical. I warned us that even given this forceful admonition, which I am repeating here, you will fall prey to the allure of mathematics anyway. Let’s prove that.

A substantial class of Y in life are dichotomous: Yes/No, True/False, 1/0, White/Black, Male/Female, Greater than X/Less than or equal to X, AM/PM, Precipitation/Dry, and so on and so forth. Math comes easily to this class. Usually with an ‘indicator’ function, i.e. I(Y), which equals 1 when Y is true and equals 0 otherwise. In some notation the indicator function is left off but tacit, which is fine as long as you remember it is there.

We’re doing math, so we’re interested in scores, which in some cases might be called “loss functions”, quantifying the penalty you pay for being wrong. No penalty is paid for being right. But you might also gain by being right, so the broader class of math can be called gain-loss functions. Which is best is, again and again and again, that which you used, implicitly or plainly, in employing any model.

Let p = Pr(Y|M), assuming Y is dichotomous. Last time we used the score (I(Y)-p)^2, or, dropping-but-remembering the indicator function, (Y-p)^2. Why this form? Easy enough: if we imagine we have some loss function L(Y,p), but don’t quite know its mathematical form, a simple Taylor series expansion gives a constant + (Y-p)^2 + higher order terms. As in most Taylor series, the higher order terms are ignored, and the constant is not important.

The score (Y-p)^2 is called Brier in honor of the fellow who popularized it. As we said last time, this has “nice properties”, like always being positive, having a known interval, and so on. And it can handle local truths and local falsities. These are times in which M dictated p = 1 or p = 0.

There are many other loss scores. Another popular one is the log-loss:

𝑆⁡(𝑌,𝑝)=−𝑌⁢log⁡(𝑝)−(1−𝑌)⁢log⁡(1−𝑝).

(Some just have the first term.) If Y = 1 the closer p gets to 1, the closer the score gets to 0 (which you recall by convention is best). Sort of. And when Y = 0 the closer p gets to 0, the closer the score gets to 0. Sort of. Obviously, the log-loss score cannot handle local truths and local falsities. The (natural) log of 0 gets whacky.

This score is motivated by reasoning about entropy. It looks almost like entropy, too, which is usually written

𝐻⁡(𝑝)=−𝑝⁢log⁡(𝑝)−(1−𝑝)⁢log⁡(1−𝑝),

which of course comes from (again, usually written)

𝐻⁡(𝑥)=−∑𝑝⁡(𝑥)⁢log⁡𝑝⁡(𝑥),

and which shows how this score can be generalized where Y has more than two categories.

We’ll hold off (again) our discussion, our very important discussion, of entropy. Right off the bat, though, if I have trained you well, your alarms bells ought to be clanging madly.

If they are not clanging, pause and see if you can discover why they are not.

Question: Since there is no such thing as probability, how can there be such a thing as entropy?

Answer: There cannot.

Entropy, like probability, is always conditional. In other words, we ought to always write

𝐻⁡(𝑥|𝐸)=−∑𝑝⁡(𝑥|𝐸)⁢log⁡𝑝⁡(𝑥|𝐸),

for some evidence E (like a model). Therefore, just as nothing has a probability, nothing has an entropy. Entropy is a measure of knowledge, and not of things, just like probability.

Meaning you caught me in a laziness. We never have a score written S(Y,p), but we have S(Y,p | W). Which is also S(Y_reality, Pr(Y|M) | W). The M and W are always there, even when we forget to write them. That we often forget to write them is why we fall in love with the math, slipping into the idea that the math always applies because it is a property of the world. Which it isn’t.

You’ll have noticed these are only loss scores, and say nothing about gain. These, and many others, are also symmetric, you score as badly for being wrong in either direction. When in Reality, there is gain in using good models, where ‘good’ is relative, and where we saw a prime example with Paul Ehrlich, as well as loss in using bad ones. And the two, gain and loss, are not always symmetric.

A prime example is breast cancer screening. There is a real price to pay for a screening that turns up a false positive, but also much can be gained, perhaps far different from that loss, for catching an early cancer. There’s of course a lot more to this, and we’ll cover all that separately.

The point is that “scores”, or rather “utility functions” can (but not necessarily) exist for these. When predictions involve money, the natural utility is that money, but even then not all money means the same to all people. There is great temptation to quantify emotions as if they were the real utility. Not that emotions aren’t important, but putting arbitrary numbers to them can be ridiculous, especially when one is doing so because that’s what the software offers.

A utility function is nothing more than S(Y,p|W) in any general form. Which means there are an infinite number of such functions. We’ll come to individual ones when needed.

This brings us to the idea of a proper score.

This can be hard to read about because of weird-looking (but perfectly correct) notation often used. The idea is we want a score that can’t be “gamed”, or not easily. Recall your model statement is p = Pr(Y|M). Here’s an example of a score that is easily gamed:

𝑆=1−𝐼⁢(𝑝∈{0,1})–𝐼⁢(𝑝∈(0,1))⁢𝑝,

which is 1 minus the indicator of if p is either 0 or 1 minus p times the indicator whether p is in the interval (0,1) . In other words, the best score is when the p is extreme. Suppose your p = 0.7. If you reported that, you’d get S = 1-0-p = 0.3. Yet if you set aside that p, which your M implied, and picked p = 0 instead, or p = 1, then your S = 0.

In other words, you are encouraged to go extreme and not report the p implied by your M. That encouragement comes in requiring the score you “expect” to be the best score you can get with your p = Pr(Y|M). That “expect” is the statistical meaning of that term.

Pick any score with a probability you think you can game, i.e. some q and not your p = Pr(Y|M). Take the Brier: (Y-q)^2. That will equal either (1-q)^2 or q^2, depending on whether Y = 1 or Y = 0. According to your own model, you deduce the probability the score will be (1-q)^2 is p, and thus the probability the score will be q^2 is (1-p), because the probability Y = 1 is p (given M).

That makes your “expected” score:

𝑝⁢(1−𝑞)^2+(1−𝑝)⁢𝑞^2.

The extreme of that “expected” score is found by taking the derivative with respect to q (as you recall from calculus). If you do that (which I’ll spare you), you get

𝑞=𝑝.

In other words, the best “expected” score, conditional on M (and W), is the one in which q = p = Pr(Y|M). This works for any score of any dimension.

It is not the best score, tout court, for that is still S = 0. In other words, there is still an encouragement to have p be extreme, i.e. either 0 or 1. But with a proper score you would hesitate to report the extreme, because your own model only gave you imperfect confidence, i.e, p somewhere in (0,1), but not the end points.

Most, but certainly not all, scores in common use are proper in this sense. When we come across ones that aren’t, I’ll let you know. But you can easily do the calculation yourself, too, now you know how.

I’m happy to report there is a resurgence of interest in scoring and verification, and, believe it or not, mostly because of AI. It all begin in weather forecasting back in the 1950s (my advisor’s advisor, Allan Murphy, was one of the founders), and we can all be mighty glad computer scientists have picked it up, because that means they understand prediction is the true test of models.

This is lesson classical statistics (in its frequentist or Bayesian form) has failed to learn. For them, it’s just testing-testing-testing and bizarre parameter-based statements.

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Peter Wood at the National Association of Scholars asked me to review Proof: The Art and Science of Certainty by Adam Kucharski. So I did. (His will is stronger than mine.) Read it here, please.

To entice you to click, which is always a burden, which I hate doing myself, but which I hope you do, here is an excerpt of “You Can’t Get There from Here: Tracing the Logic of Proof“.

Euclid is touted by Kucharski as a master of proofs, and so he is. His Elements are used to this day to teach how far pure reasoning can go. We learn that Lincoln thought so, too. He boned up on Euclid’s proofs so that he could become a better advocate against slavery. Kucharski spends a good portion of the book on this. Here is the result:

To show that person A could not legitimately enslave B, Lincoln first assumed that A could enslave B. This implied that a legitimate argument for creating slaves existed. B could therefore use the same argument to enslave A, which contradicted the original assumption that A was the enslaver of B. If one person had the right to enslave another, Lincoln concluded, then a person A could be both enslaved and the enslaved. Hence a person did not have the right to enslave another.

As a proof this succeeds. Not in proving slavery illogical, but that Lincoln should have put in a few more hours with Euclid.

Supposing B is enslaved by A, B telling A, “I have a right to be an enslaver, too” is unlikely to convince A that it is B’s turn to be the enslaver. B’s argument cannot be used to enslave anybody, and it doesn’t contradict the assumption A is the enslaver, because, of course, A is the enslaver. It’s only true that B could not simultaneously be enslaved by and also the enslaver of A, if slavery were legitimate. It is also a truth that fortunes change and B could end up on top.

Lincoln’s argument would be like if the Central Powers to escape their fate in 1918 tried arguing that since the Allied Powers were conquerors in WWI, the outcome would be as legitimate if the Central Powers were conquerors, therefore neither side had the right to be the conquerors. They would have had more success trying to prove the existence of humor-filled feminists.

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The black woman justice on the Supreme Court, who was appointed explicitly because she is a black woman, the search for a black woman for the then-vacant seat being announced by Biden, has been performing exactly as you would expect a black woman appointed to high intellectual office would perform: like a black woman promoted because she is a black woman.

SCOTUS struck down a lower court’s ruling that banned so-called conversion therapy. This a terrible name, and a misnomer, for these services: because there are no such creatures as “homosexuals” or “trans”. There are only people, male and female. The modern fad of sexual “orientation” does not, and cannot, create new kinds of human beings.

People who no longer enjoy the hobby of homosexuality, or fail to find further delight in pretending to be the opposite sex, often seek help in avoiding these behaviors. Colorado would ban anybody from providing this help. SCOTUS said no to Colorado.

The Court issued a 66-page ruling, lead-authored, if you can believe it, by Neil Gorsuch, who infamously blew it on “sexual orientation”, finding that right hiding in a dark corner of the Constitution where it remained undiscovered for centuries. Anyway, in 31 of these new pages, he says you can’t stop people from talking to other people using words Colorado doesn’t like. Even if those words are anti-Equality words.

Gorsuch was joined by all the other justices, even all the women (all appointed because Equality, by the way), save the black woman appointed to the court because she was a black woman. The remaining 35 pages, more than half, were taken up by her explaining how she finally, at last, knows what a woman is.

Kidding! She didn’t know in her confirmation hearings, and she doesn’t know now.

The gist of her main argument is that doctors use speech (well, most of them), and Colorado has a right to label speech medicine, and therefore they have the right to regulate speech when it is used as medicine.

She says certain “therapies seek to encourage patients to change their behavior in an attempt to ‘change’ their identity.” Which can be true if “identity” is a cloak one puts on, and false if a person is in essence that identity ( I use essence in the strict Aristotelian sense). There are only two essential identities in man: male and female. No one can change an essential identity. It is impossible. But anybody can pretend, or falsely believe, to be anything. Call this kind of identity fantasy to distinguish it from essential.

One could argue that all have the “right” to claim any fantasy. But it does not follow, and it is not true, that all then have the additional “right” to force everybody else to acknowledge their fantasy, or join in on it. The notion is incoherent: it could be my fantasy that I am a person who talks people out of their fantasies, and that has to be recognized as legitimate, too.

All forms of sexual “orientation” are fantasy. All people are in essence sexual reproductive creatures, with known biologies, which, of course, can malfunction in various ways. But that these are seen as malfunctions (a man who cannot produce sperm, say) proves the essence.

It’s worth quoting this:

Over the past few decades, however, the premise of conversion therapy (in whatever form) has been widely discredited within the medical and scientific community. Conversion therapy is, at bottom, “based on a view of gender diversity that runs counter to scientific consensus.”

I don’t know if she has hidden a pun in there, but perhaps not. If the scientific consensus says a man can be a woman, or that sodomy is good, then the scientific consensus can go—but I will keep it civilized. The scientific consensus, if it believes these things, proves many scientists are raving maniacal idiots who are slave to public opinion, and the views of these people cannot thus be the basis of law.

This also applies to any consensus of “doctors”. People who have memorized bones, I have written repeatedly, have no special claim to moral insight. And anyway, not a few of them make their speciality killing, or in carving people up to help them in their fantasies. Which means our easy deference to this set of people is itself nuts.

The dissent is a pean to the consensus of any organized body of science. But science cannot tell you what is right and wrong. Laws are based on right and wrong. Laws are therefore not scientific, and it does not follow because one, many, or even all scientists make some claim about how a thing in the world works, that we ought to behave one way or the other. Any answer we come to about right and wrong will not be because science.

The dissent is rich in error, but I don’t want to blunt the reader’s sensitivity. One last quote:

Because people’s identities are simply “a part of the normal spectrum of human diversity,” id., at 535, the community has determined that efforts to change a patient’s sexual orientation or gender identity will necessarily be ineffective.

Part of the normal spectrum of human diversity includes criminals of every sort, torturers, necrophiliacs, zoophiles, sociopaths, murderers, arsonists, NPR listeners, pedophiles, cannibals and even over-promoted judges. Many of these are “orientations”.

This is therefore a stupid, stupid, yet common, argument. It is the consensus she mentions. Worse, it’s wrong even if you believe in sexual “orientations”, because many people have in fact found freedom from behaviors they no longer wanted. The efforts were not ineffective.

I will leave the rest of the errors for the readers to discover himself.

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It is with great ease one can discover pre-President statements from Trump saying how disastrous costly foolish and frankly ridiculous a war with Iran would be, especially given all that needs to be done at home. But I’ve also seen plenty of statements of his (from the old days, too) saying the opposite.

Which is, of course, the way the man communicates. A blizzard of words and boasts, hardly bearing any similarity to Reality. Which, I hasten to say, is a tactic I viewed with approval, especially when dealing with pea-brained propagandists and phony politicians. Trump was the first man in power I had ever seen who treated these slimy creatures with the disdain and contempt they deserve(d).

There will be no point, as you read this, of accusing me of being a “never Trumper”, or whatever. My record of public support is clear, even as it got me cancelled, and barred me from employment and polite society. And I will still go on supporting all sane policies, if any, until he is gone. Not that this matters, because I am just one man on the outer reaches of the internet.

Why did the war start?

You recall our Secretary of State said at the beginning that the USA landed the first blow in the war because a certain foreign country told our rulers they were going to start the fight anyway, so why not drop some bombs? After Rubio’s comment blew up, the administration hastily took it back, saying it was us all along. Now, of course, many believe Rubio never said what he said. Which should surprise none of us.

I used to joke that if then-President Obama was seen coming out of a burning orphanage with a bloody knife the bien pensants would dismiss it saying “He must have had his reasons.” Only this joke is true in the case of that foreign country.

It supporters—and here I speak largely of Western self-described Christians—cannot bear to hear, let alone think, that country is ever guilty of even the most minor fault. There is thus never any point discussing them. Almost none who support this foreign country take time to investigate its history. It has been tumultuous from the beginning, many of the current problems based on its foundation. And no one has ever convinced me why they are my problems, why my money should be sent to them.

But these criticisms are neither here nor there. Whatever influence that foreign country has (there are many videos of Trump saying even his father insisted its lobby was the strongest in Washington), the decision was Trump’s alone, and he bears the responsibility. Not any foreign leader or country.

Iran getting nukes? Many countries have them, all safe in that knowledge, too. And here is a gentleman predicting, through the years, that Iran was always “weeks” away from having nukes. They have been “weeks” away since the late 1980s.

I don’t think any explanations along those lines are fully satisfactory, however contributory they may be. And I don’t claim my theory below is the complete explanation, either. Though I do think it is of some importance.

We heard from Trump last week that we need to lock down the Strait of Hormuz for just two weeks to stop the spread of—what, exactly? Don’t ask. Trump’s messaging, as above, has been all over the map. Regime change, not regime change, kill bad guys, mass destruction, let’s negotiate, let’s take the oil, back to the stone age, et cetera, et cetera.

I certainly have no idea what goal Trump has in mind in this war, and I suspect he doesn’t either. But because his specialty is obfuscation, I do not hold that opinion with any great weight. Maybe he knows. But we surely don’t. All of us on the outside are left guessing.

Whatever the case is, the covid comparison, I believe, is apt. Think back to the beginning of the covid panic. Trump was out warning about Ch-yi-na, which caused Chuck Schumer to rush to a microphone and say “Have no fear! Come on down to Chinatown and have a meal!” The entire propaganda apparatus booed Trump.

In spite of his seeming rhinoceros hide, I believe this criticism stung Trump. He quickly brought on Experts and flatterers, like the execrable Fabulous Fauci (who instantly did an abrupt volte-face on masks etc.). Trump embraced lockdowns, two weeks to “flatten the curve”, Operation Warp Speed, and the Great Madness began.

Those flatterers later turned against Trump, to their great benefit. The election of 2020 was a disaster. But then came 2024. I, and many, believed Trump had learned his lesson about listening to people whose goals were not his—or ours.

Jump ahead to the ICE-capades in Minnesota, which the left idiotically and enthusiastically saw as Armageddon, and which went very badly for all involved. Once again, I believe the incessant criticism of elites, including some people in his administration, wounded Trump. I have no proof of this, but there are current rumors some on the inside are trying to oust Stephen Miller, who they want to take the blame.

Once again, perhaps, Trump weakened because of this criticism. Don’t forget he was not receiving nearly the same hostile reaction to every statement of his as he did in his first term. Things were not going terribly. He was growing used to a relatively reasonable press. But Minneapolis changed this. The new media storm must have hurt.

I have no proof, but I can envision someone on the inside said something like, “You can win back opinion by dropping a few bombs on some savages. You are a genius at foreign policy. No President has had success like you.” As evidence for this, after several weeks into the war, Trump announced a plan to win back voter support by a creating great “defense build up“. Does he really not know this is no longer the 1980s?

Further evidence: The New York Times wrote that after the first bombs were dropped, Trump called Laura Loomer. Is this true? It seems to be. Trump specially naming Mark Levin as a source all should trust. Loomer and Levin’s warm support for bombing enemies of everybody’s favorite foreign country is well known.

Here is Loomer last week calling for every mosque in Iran to be bombed, as well as everything else. When I say everything, I mean every thing. She insists on mass murder for her enemies. I quote only a small portion of her targets:

We need to deprive Iran of all the niceties of a moderne day society, and we need to do so now.

And then we need to make the people beg on their knees for humanitarian food assistance from the international Red Cross so that the people force Iran to surrender to the US.

This is how you WIN wars. Cutis LeMay understood this very well.

It’s time to carpet bomb Iran.

Force them to their knees.

Destroy the infrastructure. It’s the only way.

Maybe you even share her convictions. Hey, some of those dead kids could have turned into terrorists.

It’s not only civilians, of course. Secretary of War Pete Hegseth also touted the stone-age campaign.

However you label Loomer’s far-from-uncommon plea, what has to be explained is how she has Trump’s ear. It cannot be feminine wiles. With all her plastic surgery, she looks like something that would have sickened even Dr Moreau. She has given no evidence of superior intellect. What could it be? I say rank flattery.

Levin, who was a loud-mouthed Never Trumper in 2016, now lathers his tongue over Trump to sickening degree, screaming that all his critics are Not-sees. These are fictional booger men which don’t exist and nobody can see, but which are used to terrify the young.

A troop of flatterers slithered into the White House last week, telling Trump he is God’s chosen one, that his war is just, that to kill and destroy is good. The same Catholic Bishop who was at the White House, went on Squeaky Ben Shapiro’s show to reassure him that Pope Leo’s recent admonition against war mongering didn’t apply to this war (audio clip). This, too, is flattery, if that good Bishop hoped Trump would see his performance.

You will recall many similar instances where Trump responds with great hostility to any detractor, and the precise opposite (even to former enemies) to those who compliment him. Those cheering the war are full of endless praise. To resist this kind of nauseating adulation requires a supreme fortitude few possess. Trump does not. His own words on his Truth Social account, given on Easter day:

Like in the covid panic, the leeches will also abandon Trump when the going gets rough. They will claim, like the Fabulous Fauci, that they never advised excess, such as we see here (and here, and here). Their lies will be embraced by those who only want to get even with Trump. After this November, we are in for two years (at least) of interesting times.

I accept my own blame in this, not learning from history. That’s what I mean about the covid comparison. Trump erred in juicing the panic then, gathering around him the worst sycophants with ulterior motives. He has done so again. I, who talks about evidence all the time, talked myself out of this evidence. I was wrong.

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