The human mind and random numbers

[QuietMan]

Nova had a show I believe was called "The Case for ESP" several decades ago where they had a really intriguing experiment. It used a mildly radioactive source for a random number generator that would be heads/tails every ½ seconds. This was fed into a simple 8 light wheel with only one light lite. If the result was heads the light would move clockwise, if it was tails then it would move counter-clockwise. Normally it would balance, but with some people it would rotate one way or the other when they focused on it. Even a 2% deviation was very obvious with this setup. The really weird part is with some people it went the opposite of where they wanted it go.

I would like to repeat this experiment, the only hard part is the random number generator. For it to be valid I think it would need to be something like a mild radioactive source, this puts it in the realm of telekinesis if it were real. A computer interface would be needed too, for later analysis. It would also be a great way to measure the real randomness of the device too.

 

[duffy]

For Pi I used the closest approximation I could find quickly 355/113 then then used the good old method of long division where the remainder is returned.

I'm afraid that one's a little more complicated than that. There are many ways to derive [LATEX]\pi[/LATEX], but the one you are talking about involves forming a definite integral with some eighth-order terms. Specifically:

[LATEX]\pi = \frac{355}{113}-\frac{1}{3164}\left \int_{0}^{1} \frac{x^8(1-x)^8(25+816x^2)}{1+x^2}\,dx\right[/LATEX]

There's just no way to do this one piecewise, and getting more than a few decimals out of it is going to be a real bear - your best approach would probably be to do an iterated summation to approximate that integral with as much precision as you have patience to code and wait for, and then evaluate the rest of it and get your digits on the final day.

But there are many other, simpler ways to do it. You might find one on this page that could be adapted to work in Actionscript without too much pain -
https://mathworld.wolfram.com/PiFormulas.html
In particular, look at the Gregory series - the one referenced as "slow to converge". So long as you move your dot several steps behind the current iteration, you could do this one piecewise, with accuracy, for as long as you want.

And it's worth the effort! I've never seen a study comparing the bias of transcendental natural constants to pseudorandom generators, and it seems like it could be a profound insight.

 

[nsaspook]

Nova had a show I believe was called "The Case for ESP" ...

https://www.youtube.com/watch?v=k-dXhHQ__Lk
https://www.youtube.com/watch?v=SbwWL5ezA4g&feature=related

 

[QuietMan]

I was more interested in the experiment that was a> reproducible, b> impartial, c> interesting.

If it worked it would not be a trick. If it didn't, well that goes under reproducible.

 

[jpanhalt]

Normally it would balance, but with some people it would rotate one way or the other when they focused on it. Even a 2% deviation was very obvious with this setup. The really weird part is with some people it went the opposite of where they wanted it go.

That reminds me of the experiments to test the power of prayer on healing. Some have shown a small positive effect. Others have shown a small negative effect.

There are at least two interpretations of those results:
1) There is no net effect; or
2) Prayer has an effect; you have to be careful who is doing the praying.

As applied to the rotating wheel experiment, unless someone has a new twist to the experiment or more sensitive robust measures of non-randomness, I see little scientific value in repeating it. However, as a means to break the ice at a party, it might be great fun.

John

 

[QuietMan]

Testing is easy, you let the computer sample it with no one there. If there is a deviation when someone there it is significant, no matter which way it goes. I'm not a believer, but I do like to experiment.

 

[jpanhalt]

That design needs a better control and needs to be blinded. It is like testing a drug vs. no treatment. In that case, a better design would be a placebo or the currently best available therapy in a double-blind, crossover design.

Specifically in the case of a spinning wheel, why does the subject need to be in the same room? If distance is a variable, then that should be controlled for and/or assessed in the design. Maybe have several identical, random spinning wheels. The subject will write down on which wheel he is concentrating before seeing any of the wheels. The experimenters will not know that choice until after all data are analyzed. You could also consider replacing the live human with another species or even a cadaver. One could go on and on. Needless to say, many scientific experiments that were done by honest, well-intentioned researchers later have been shown to be flawed in design, which led to faulty conclusions.

John

 

[DerStrom8]

How is "randomness" even measured? How can something be more or less random than something else? In my experience, "randomness" does not exist in the real world. It is like the concept of infinity. Does it really exist? There is no way to measure either, because they are each only theoretical. Nothing in the universe is truly random--everything depends on something else that, theoretically, can be "decoded" using mathematics. Knowing how everything works and being able to do the math would eliminate our concept of "random" because there is no way to define it (we would always be able to know the outcome). So how can studies say that machines can generate strings of numbers that are more random than other strings of numbers? It just does not make sense to me. I would like to know how they determine the "randomness" of these numbers.

Der Strom

 

[DJDAudio]

How is "randomness" even measured? How can something be more or less random than something else? In my experience, "randomness" does not exist in the real world. It is like the concept of infinity. Does it really exist? There is no way to measure either, because they are each only theoretical. Nothing in the universe is truly random--everything depends on something else that, theoretically, can be "decoded" using mathematics. Knowing how everything works and being able to do the math would eliminate our concept of "random" because there is no way to define it (we would always be able to know the outcome). So how can studies say that machines can generate strings of numbers that are more random than other strings of numbers? It just does not make sense to me. I would like to know how they determine the "randomness" of these numbers.

Der Strom

I am not a mathematician but In my humble opinion 'random' is any data set that shows no sign of correlation. For in my program, any deviation from 0 would show a 'trend' or correlation of 'value' to one side or the other.

But I do agree, it is very hard if not impossible to define such as irrational numbers, we know they exist, but have no way of explaining them as a whole, only in part.

For like in astrophysics, there is no absolute speed. There is only comparisons between moving bodies. Same I feel with 'random' there is no absolute random, there is only more or less a comparison of what we perceive as 'random' events.

 

[DerStrom8]

I am not a mathematician but In my humble opinion 'random' is any data set that shows no sign of correlation. For in my program, any deviation from 0 would show a 'trend' or correlation of 'value' to one side or the other.

But I do agree, it is very hard if not impossible to define such as irrational numbers, we know they exist, but have no way of explaining them as a whole, only in part.

For like in astrophysics, there is no absolute speed. There is only comparisons between moving bodies. Same I feel with 'random' there is no absolute random, there is only more or less a comparison of what we perceive as 'random' events.

That is exactly what I'm talking about--there will always be some sort of correlation between values, because they all depend on something else. Remember, I am speaking of the real world, not of theory. I understand the theoretical aspect of "random". I just don't know how they can say something is "more random" or "less random" than something else. How do they measure that if there is no such thing as random in real life?

 

[DJDAudio]

I was able to find one of my old Phi programs!!!

**broken link removed**

I love to watch this one.

Each run it increments the Fibonacci sequence watch how my system of displaying the numbers will allow you to spot number patterns many hundreds of decimals long!

If you let it run long enough it will get closer and closer to true 'Phi' (1+(SQRT(5))/2 or more 'random' if you will.

 

[DJDAudio]

This one runs a bit faster,

**broken link removed**

 

[nsaspook]

How is "randomness" even measured? How can something be more or less random than something else? In my experience, "randomness" does not exist in the real world. It is like the concept of infinity. Does it really exist? There is no way to measure either, because they are each only theoretical. Nothing in the universe is truly random--everything depends on something else that, theoretically, can be "decoded" using mathematics. Knowing how everything works and being able to do the math would eliminate our concept of "random" because there is no way to define it (we would always be able to know the outcome). So how can studies say that machines can generate strings of numbers that are more random than other strings of numbers? It just does not make sense to me. I would like to know how they determine the "randomness" of these numbers.

Der Strom

There are devices that generate bits that are mathematically truly random. https://www.idquantique.com/true-random-number-generator/products-overview.html
and there are ways to produce truly random signatures for devices. https://en.wikipedia.org/wiki/Physical_Unclonable_Function

 

[DerStrom8]

There are devices that generate bits that are mathematically truly random. https://www.idquantique.com/true-random-number-generator/products-overview.html
and there are ways to produce truly random signatures for devices. https://en.wikipedia.org/wiki/Physical_Unclonable_Function

That isn't physically possible. A computer uses data, and each bit of data depends on another. It cannot actually generate truly random numbers. The output is dependent on the program. There will ALWAYS be a pattern.

 

[duffy]

Nothing in the universe is truly random--everything depends on something else that, theoretically, can be "decoded" using mathematics.

If you have a theory. There is no theory predicting the moment a particular radioactive atom will decay. Statistically, a group of them can be said to behave with such-and-such a decay rate, but individual events aren't influenced by heat, light, vibration, gravity, or anything anyone knows of. So a radioactive decay random number generator has an outcome that can't be predicted by theory, because there isn't one.

 

[DerStrom8]

If you have a theory. There is no theory predicting the moment a particular radioactive atom will decay. Statistically, a group of them can be said to behave with such-and-such a decay rate, but individual events aren't influenced by heat, light, vibration, gravity, or anything anyone knows of. So a radioactive decay random number generator has an outcome that can't be predicted by theory, because there isn't one.

I don't agree. Theoretically, this could be predicted. The rate of decay MUST depend on something. Otherwise it wouldn't happen. And since it depends on something, then its rate, theoretically, could be predicted, though I'm sure it would take a real genius to do it. I understand your point of view, considering Heisenberg's Uncertainty Principle. The principle is based on the fact that one cannot measure the motion of a particle without altering its path, and hence cannot predict its future movement. However, its path still depends on something. Therefore, it is not truly random.

 

[nsaspook]

That isn't physically possible. A computer uses data, and each bit of data depends on another. It cannot actually generate truly random numbers. The output is dependent on the program. There will ALWAYS be a pattern.

The source of the randomness is not the computer program. The origin of the randomness is the quantum state of particles being measured or in the case of a small uC the random 0 or 1 of sram bits when powered up. When each chip is made small process variations slightly change the bias in each static memory cell to be a 1 or 0 when power is applied. These variations are random in nature and have many different origins during the many process steps it takes to produce a chip. With a little processing it's possible to isolate that bits that randomly flip from those that usually stay the same.
Here is a simple demo program that uses that randomness of sram bits to produce a seed for a PRNG in C18.

https://code.google.com/p/pic18-puf/

 

[DerStrom8]

The source of the randomness is not the computer or program. The origin of the randomness is the quantum state of particles being measured or in the case of a small uC the random 0 or 1 of sram bits when powered up. When each chip is made small process variations slightly change the bias in each static memory cell to be a 1 or 0 when power is applied. These variations are random in nature and have many different origins during the many process steps it takes to produce a chip. With a little processing it's possible to isolate that bits that randomly flip from those that usually stay the same.
Here is a simple demo program that uses that randomness of sram bits to produce a seed for a PRNG in C18.

https://code.google.com/p/pic18-puf/

My point is that this is not truly random. There are factors that determine the state of the bits upon startup. If there were no factors to make them change, they wouldn't. Don't you see? Everything happens for a reason--not only philosophically, but also physically. My whole point is that if something didn't have a reason to change, it wouldn't. Therefore, it depends on different factors, and that means it is not random. Your example is only quasi-random, meaning it is "random" enough to work in some mathematical cases, but is not perfect. There is no such thing as random in the real world. Period.

 

[Sceadwian]

So a radioactive decay random number generator has an outcome that can't be predicted by theory, because there isn't one.

This is not true; it can be predicted, because although given an individual event can't be known, over time a statistical likleyhood will present itself which can define the probability cloud and from that point the possible values can be reverse engineered.

In order for information to be encoded there has to be information to start with, information can't be destroyed therefore it can always be reconstructed by some method. The best encryption methods available to mankind simply exploit this by requiring a 'key' that is so long that it's practically impossible to brute force decode the key itself, some of which have fallen pray to flaws in the algorythms which allow the key itself to be decoded given enough data (early and some current wifi specs)

Even the highest of high hopes of the future of Quantum encryption/computing (synonymous with random numbers) is the ability to detect if between a source and a target the data streem was intercepted. Simply KNOWING that the link was altered by another source is better than encryption.

 

[duffy]

This is not true; it can be predicted, because although given an individual event can't be known, over time a statistical likleyhood will present itself which can define the probability cloud and from that point the possible values can be reverse engineered.

Not even wrong.

First, that's like saying you can predict a coin flip because over time it will average out to half-heads, half-tails. If you believe that, you need to go look up the "Gambler's fallacy".

Second, with the coin you could theoretically look at the physics involved - force, acceleration, wind resistance, etc. Can't do that with nuclear decay.