So, what you're saying is, Cathy, that neither coin flips nor perfectly crafted dice can ever be "perfectly" random because the act of flipping or tossing them is a part of the *cause* of how they land, and that action is never the same, however incalculable it may be to the human observers?
Makes sense.
When I need a random number I phone up a Hollywood celebrity and ask them "what number am I thinking of?"
Which prompts a question: would it be worth engineering a perfect coin tosser and seeing if starting heads up, tails, up, or edge on, affects the outcome ratios? Ditto for dice?
Probably easier to do in simulation software than in hardware.
The more I think about it (which means I should probably slow down) isn't there an ontological problem with the concept of randomness?
If some event were truly random, we shouldn't be able to determine whether it was random, because we need to know the cause of something in order to explain how it so happened. What am I missing?
If the “black box” operates via “unknown properties”, why not suppose some alien living in the 11th dimension isn’t just messing with us dumb humans? “Hey Quarg, watch this!”
Interesting that Renner’s perfect certainty about perfect uncertainty was imperfect. Is the real question then what is the criteria for a sufficient amount of certainty regarding a sufficient amount of uncertainty?
It seems to me that "perfect symmetry" destroys randomness. Take a set of binary keys. Symmetry would demand that once the first bit is selected, that all subsequent outcomes are determined. (Same with "symmetry must exist with in a range".) If the metadata is symmetrical, it is NOT random. An encryption key of a specific length, is Not Random, it is convenient.
That said, to my mind, random is simply "unknown causes", and there are a nearly infinite ways that causes can be unknown.
What they did was basically "whitening", using a different method than usual, one that may be less reliable than the usual way. Good hardware RNGs are essentially free these days, one of the many features built into the cheapest (<$0.60) microcontrollers. These usually work by having e.g. 4 high-value resistors, with the current running through each highly amplified to produce white noise, then the voltage compared between pairs, producing a 1 if A has a higher voltage than B, a 0 otherwise. Any one of these 4 resistors' exact voltages would be at least as unpredictable as rolling dice thousands of times per second, but now we have two bitstreams even more unpredictable than any of the 4 resistors. Then we digitally compare the two bitstreams with an XOR, giving a 1 if the inputs are different (01 or 10), 0 if they are the same (00 or 11). The same can be done with more resistors and stages, or many other methods. This should be good enough, but then they do "whitening", which uses the output as a series of seeds for a deterministic hardware (shift-register-based bit-shuffler) pseudorandom number generator, which even if you fed in just a single seed number would not repeat itself for some truly astronomical number of bits, but it's changing the seed with every bit it gets from the resistor circuit, so its output bitstream is so ridiculously unpredictable that no practical or even impractical improvement in its randomness is possible. But if you feel like it, you can run it through another whitener, throw away half the bits by XORing it with itself, run it through the microcontoller's built-in encryption engine using most of the bits as keys... all of the above, whatever. No one will be able to tell rhe difference by any means.
Now, if you took a quarter or maybe 50 quarters and split each exactly in half from the edge, would the head side be equal in weight to the tails side? Would each be slightly different or all the same? Maybe there would be a difference in weights meaning that the head side is slightly heavier or vice-versa. Might this affect the outcome? Does it matter from which side the coin is placed in the machine?
I think I get it that using the machine takes away the randomness to a point. Anyway, how many football games have been superficially rigged by the coin toss? Not all the coins used would be exactly the same. The forces affecting each toss would be different from game to game and stadium to stadium.
Bravo! My father, a nuclear physicist who studied under Fermi, told me that there are no truly random sources of numbers, but the best they could come up with at the time was strings of solar particle emissions...Roulette wheels aren't truly random, but Martin Armstrong said that in players' estimation, certain numbers actually follow the croupier....I'm a Bayesian, it saves effort..
The problem is that information, like energy, does not have a good definition.
If information is defined as a known or knowable state of a system, its evolution is normally governed by time-reversible equations both in quantum and classical mechanics. Hence the initial state can be inferred from the knowledge a future state. In this view information is preserved.
If information is defined as a state of a system to be passed from a sender to a receiver, then the sender time and receiver time define what is passed. In this view information is created and destroyed.
Other definitions exist based on bitrates.
Your discussion avoids the issue of initial and final observation times. Are they or are they not necessary to infer where one is in the sequence of states ?
I think I will have a second random cup of coffee before my head explodes.
So, what you're saying is, Cathy, that neither coin flips nor perfectly crafted dice can ever be "perfectly" random because the act of flipping or tossing them is a part of the *cause* of how they land, and that action is never the same, however incalculable it may be to the human observers?
Makes sense.
When I need a random number I phone up a Hollywood celebrity and ask them "what number am I thinking of?"
Which prompts a question: would it be worth engineering a perfect coin tosser and seeing if starting heads up, tails, up, or edge on, affects the outcome ratios? Ditto for dice?
Probably easier to do in simulation software than in hardware.
The more I think about it (which means I should probably slow down) isn't there an ontological problem with the concept of randomness?
If some event were truly random, we shouldn't be able to determine whether it was random, because we need to know the cause of something in order to explain how it so happened. What am I missing?
We are looking for an uncaused thing...
If the “black box” operates via “unknown properties”, why not suppose some alien living in the 11th dimension isn’t just messing with us dumb humans? “Hey Quarg, watch this!”
Interesting that Renner’s perfect certainty about perfect uncertainty was imperfect. Is the real question then what is the criteria for a sufficient amount of certainty regarding a sufficient amount of uncertainty?
Connoisseur.
It seems to me that "perfect symmetry" destroys randomness. Take a set of binary keys. Symmetry would demand that once the first bit is selected, that all subsequent outcomes are determined. (Same with "symmetry must exist with in a range".) If the metadata is symmetrical, it is NOT random. An encryption key of a specific length, is Not Random, it is convenient.
That said, to my mind, random is simply "unknown causes", and there are a nearly infinite ways that causes can be unknown.
What they did was basically "whitening", using a different method than usual, one that may be less reliable than the usual way. Good hardware RNGs are essentially free these days, one of the many features built into the cheapest (<$0.60) microcontrollers. These usually work by having e.g. 4 high-value resistors, with the current running through each highly amplified to produce white noise, then the voltage compared between pairs, producing a 1 if A has a higher voltage than B, a 0 otherwise. Any one of these 4 resistors' exact voltages would be at least as unpredictable as rolling dice thousands of times per second, but now we have two bitstreams even more unpredictable than any of the 4 resistors. Then we digitally compare the two bitstreams with an XOR, giving a 1 if the inputs are different (01 or 10), 0 if they are the same (00 or 11). The same can be done with more resistors and stages, or many other methods. This should be good enough, but then they do "whitening", which uses the output as a series of seeds for a deterministic hardware (shift-register-based bit-shuffler) pseudorandom number generator, which even if you fed in just a single seed number would not repeat itself for some truly astronomical number of bits, but it's changing the seed with every bit it gets from the resistor circuit, so its output bitstream is so ridiculously unpredictable that no practical or even impractical improvement in its randomness is possible. But if you feel like it, you can run it through another whitener, throw away half the bits by XORing it with itself, run it through the microcontoller's built-in encryption engine using most of the bits as keys... all of the above, whatever. No one will be able to tell rhe difference by any means.
Impractically predictable squared. Wheee.
Now, if you took a quarter or maybe 50 quarters and split each exactly in half from the edge, would the head side be equal in weight to the tails side? Would each be slightly different or all the same? Maybe there would be a difference in weights meaning that the head side is slightly heavier or vice-versa. Might this affect the outcome? Does it matter from which side the coin is placed in the machine?
I think I get it that using the machine takes away the randomness to a point. Anyway, how many football games have been superficially rigged by the coin toss? Not all the coins used would be exactly the same. The forces affecting each toss would be different from game to game and stadium to stadium.
Bravo! My father, a nuclear physicist who studied under Fermi, told me that there are no truly random sources of numbers, but the best they could come up with at the time was strings of solar particle emissions...Roulette wheels aren't truly random, but Martin Armstrong said that in players' estimation, certain numbers actually follow the croupier....I'm a Bayesian, it saves effort..
Your dad and I would get along great.
I think random means “not knowing the cause AND not caring to know the cause. “
Thank you for underlying the distinction between random numbers and maximally unpredictable numbers. I have always confused the two.
What underlies your article is the principle of conservation of information. Is it a valid principle ? Is not information created and destroyed ?
I’m not sure. Can you tighten that principle?
The problem is that information, like energy, does not have a good definition.
If information is defined as a known or knowable state of a system, its evolution is normally governed by time-reversible equations both in quantum and classical mechanics. Hence the initial state can be inferred from the knowledge a future state. In this view information is preserved.
If information is defined as a state of a system to be passed from a sender to a receiver, then the sender time and receiver time define what is passed. In this view information is created and destroyed.
Other definitions exist based on bitrates.
Your discussion avoids the issue of initial and final observation times. Are they or are they not necessary to infer where one is in the sequence of states ?