This reminds me of pre-calculus class, where at the close of 10th grade, the teacher said, "If I had known how dumb all of you really are, I´d have spent the whole semester telling jokes!"
Absolutely interesting lecture, William! Your unique twist has breathed new life into this age-old topic. I look forward to more of the same. There's a lot of hand ringing out there about what Jaynes is saying about probability and statistics. I love the theory but in application is see nothing but rubbish so I'm inclined to side with him. Thank you for doing this.
BTW, it seems that it is your screen and not your PC that is going to sleep (since the video does not stop recording). If you are using a Windows 11 PC, you can change that by going to Settings--System--Power & Battery, then under Power you will see "Screen and Sleep". I have those set to "Never" on my own PC.
We can use this syllogism introduced in the lesson to solve the homework:
((A -> B) & !B) -> !A
For the homework we are given this:
A -> (B is more plausible)
Using the syllogism I mentioned, we can rearrange what we are given to get the following:
!(B is more plausible) -> !A
We also have the trivial observation that:
B -> (B is plausible)
We can combine all the facts we have together:
A -> (B is more plausible)
!(B is plausible) -> !A
B -> (B is plausible)
B
---
A is less plausible
Which works because we have identified a situation where B is plausible, and therefore ruled out one of the things that would imply that A is false.
The train of logic is that:
1. We have B
2. Because we have B, we know that B is plausible
3. Because B is plausible, we know that the condition !(B is plausible) is not met, and therefore that particular proposition is unable to imply A be false.
4. We have removed a proposition which would imply A be false, so there are less things implying A be false, therefore we think A is more likely to be true.
Just a thought, but if you like to talk to people while you’re teaching, why not make it a live Zoom class? Although admittedly, the logistics of that can quickly become a nightmare.
Oh, no! Then he might start taking attendance, so I’d have to get a cardboard cut-out me to sit in when I couldn’t make it. (My ex tells me he’d never suspect.)
So about the homework. It kind of seems like this to me: It seems as though the plausibility of A is conditional on the plausibility of B. This is kind of weak since we do not know anything about the plausibility of A or B actually. It could be many things make A or B true. All we can know is that if B is true that’s one less possibility that makes A true and likewise we do not know that B being true was from A. It's just one less thing that could have cause B to be true. Oh, I get it....to B or not to B that is the question! HAHAHA.
Good lecture. I have a question about your statement,
If A is true, then B is true.
A is false.
Therefore, B became less plausible.
What about the special case in which B happens to be something that is always true? We cannot say anything about the plausibility of B by examining any other premise.
Regarding the assigned homework for this first class, imagine this background condition of reality:
A is 10% of the sole causes of B (which satisfies "If A is true, then B is becomes more plausible.")
C is 20% of the sole causes of B
D is 30% of the sole causes of B
E is 40% of the sole causes of B
100% of the causes of B have been identified, and now we proceed ...
------------------
...
B is true.
Therefore, A because more plausible.
------------------
But when B is true, A isn't any more plausible than C, D, or E. When compared to the 3 other sole causes of B, A actually becomes "less plausible" when B becomes true. Whether A can exist without causing B appears to matter for the answer. This is true of the other 3 sole causes of B as well.
Given B, the relative proportion of causes covered by A (10% of them), along with the relative proportion of instances of A which do not actually result in B, along with those same two kinds of proportions for those other 3 sole causes of B would tell you the answer.
It could be this:
99% of instances of A do not result in B (1% do)
67% of instances of C do not result in B (33% do)
33% of instances of D do not result in B (67% do)
1% of instances of E do not result in B (99% do)
With those values, A is many times more likely to exist without having caused B than with having caused B.
This reminds me of pre-calculus class, where at the close of 10th grade, the teacher said, "If I had known how dumb all of you really are, I´d have spent the whole semester telling jokes!"
Absolutely interesting lecture, William! Your unique twist has breathed new life into this age-old topic. I look forward to more of the same. There's a lot of hand ringing out there about what Jaynes is saying about probability and statistics. I love the theory but in application is see nothing but rubbish so I'm inclined to side with him. Thank you for doing this.
If you're using a newish Mac you can turn off auto display dimming under system settings then 'Lock Screen'. There's a control for it there.
You will know the truth and the truth will set you free! Thank you Mr W M Briggs
For everyone wanting to learn some more about the truth
https://youtu.be/dWU-2w0L-9o?si=7ktDtfC3sETkA3ND
Good stuff! Makes my brain hurt, but it's a good pain.
Thanks.
BTW, it seems that it is your screen and not your PC that is going to sleep (since the video does not stop recording). If you are using a Windows 11 PC, you can change that by going to Settings--System--Power & Battery, then under Power you will see "Screen and Sleep". I have those set to "Never" on my own PC.
We can use this syllogism introduced in the lesson to solve the homework:
((A -> B) & !B) -> !A
For the homework we are given this:
A -> (B is more plausible)
Using the syllogism I mentioned, we can rearrange what we are given to get the following:
!(B is more plausible) -> !A
We also have the trivial observation that:
B -> (B is plausible)
We can combine all the facts we have together:
A -> (B is more plausible)
!(B is plausible) -> !A
B -> (B is plausible)
B
---
A is less plausible
Which works because we have identified a situation where B is plausible, and therefore ruled out one of the things that would imply that A is false.
The train of logic is that:
1. We have B
2. Because we have B, we know that B is plausible
3. Because B is plausible, we know that the condition !(B is plausible) is not met, and therefore that particular proposition is unable to imply A be false.
4. We have removed a proposition which would imply A be false, so there are less things implying A be false, therefore we think A is more likely to be true.
Just a thought, but if you like to talk to people while you’re teaching, why not make it a live Zoom class? Although admittedly, the logistics of that can quickly become a nightmare.
Oh, no! Then he might start taking attendance, so I’d have to get a cardboard cut-out me to sit in when I couldn’t make it. (My ex tells me he’d never suspect.)
So about the homework. It kind of seems like this to me: It seems as though the plausibility of A is conditional on the plausibility of B. This is kind of weak since we do not know anything about the plausibility of A or B actually. It could be many things make A or B true. All we can know is that if B is true that’s one less possibility that makes A true and likewise we do not know that B being true was from A. It's just one less thing that could have cause B to be true. Oh, I get it....to B or not to B that is the question! HAHAHA.
“If A is true, then B is true.
B is true.
Therefore, A because(sic) more plausible.”
Why not “…A is plausible?”
The “more” seems excessively 😁 redundant. And I found it a bit confusing.
Maybe it has heuristic value? I did have to think more about this case because of it.
Where do I get the texts?
Is there a source for the Jaynes book that isn’t pushing $100.00?!
Thx
https://bayes.wustl.edu/etj/prob/book.pdf
Thank you.
(I purchased you “uncertainty” back in …I think 2017.)
Good lecture. I have a question about your statement,
If A is true, then B is true.
A is false.
Therefore, B became less plausible.
What about the special case in which B happens to be something that is always true? We cannot say anything about the plausibility of B by examining any other premise.
Loved it. Can't get enough. :)
HW: let C be (B is more plausible)
we deduced if A -> C and C means A is more plausible. But B->C, since if B is certain it is surely more plausible. So B -> C -> (A is more plausible)
Regarding the assigned homework for this first class, imagine this background condition of reality:
A is 10% of the sole causes of B (which satisfies "If A is true, then B is becomes more plausible.")
C is 20% of the sole causes of B
D is 30% of the sole causes of B
E is 40% of the sole causes of B
100% of the causes of B have been identified, and now we proceed ...
------------------
...
B is true.
Therefore, A because more plausible.
------------------
But when B is true, A isn't any more plausible than C, D, or E. When compared to the 3 other sole causes of B, A actually becomes "less plausible" when B becomes true. Whether A can exist without causing B appears to matter for the answer. This is true of the other 3 sole causes of B as well.
Given B, the relative proportion of causes covered by A (10% of them), along with the relative proportion of instances of A which do not actually result in B, along with those same two kinds of proportions for those other 3 sole causes of B would tell you the answer.
It could be this:
99% of instances of A do not result in B (1% do)
67% of instances of C do not result in B (33% do)
33% of instances of D do not result in B (67% do)
1% of instances of E do not result in B (99% do)
With those values, A is many times more likely to exist without having caused B than with having caused B.