Tuesday, February 15, 2005

*WEAK* Law of Large Numbers

So recently someone forwarded this RedNova News article to me:

Can This Black Box See Into the Future?

It actually refers to a real project going on at Priceton:

Global Conciousness Project

Now, the RedNova article does a pretty poor job explaining what's going on at Priceton, so this blog is going to appear to be poking fun at Princeton (and in some small amount it is), but it's mainly making fun of the idiots at RedNova.

For one, if the REG was generating 0's and 1's and adding the next flip to the sum of the previous flips, there's no way the line could hover around zero. Neither 0 nor 1 is negative, so it cannot ever decrease! (also note that the REG is man-made, so it will never be truly random)

So I'm assuming they meant the REG was generating a discrete uniform distribution taken from the support set {-1,1} and logging the cumulative sum of those flips (that sum would thus be a random process). Now, this random process IS NOT SURELY CONVERGENT. RedNova is trying to use the law of large numbers to illustrate what's going on, but they don't realize that they're just using the WEAK law of large numbers here. In reality, as time goes on, the probability that this random process converges to 0 actually DECREASES.

So I decided to generate some examples. I simulated this random process (using MATLAB's uniform random number generator) three times for 5000000 trials each. Since each of their trials is a second long, this corresponds to what you might expect to see if you ran this random process for about 58 days straight. Notice that these plots are not flat lines, do not stay near zero, and have lots of strange trends that should not be interpretted as some blip in the global consciousness. Pay attention to the scale too. These are not drifting a little; they are drifting by thousands of points each realization. Note though that if you bin the values coming from the random vector generating this process, it's almost perfectly uniformly distributed on {-1,1}.

Does this mean something really big is about to happen?

Anonymous said...

Right angle: different subject..

What are the chances that the world's collective unconscious is encrypted?

http://arxiv.org/PS_cache/nlin/pdf/0502/0502026.pdf

"In the present work, we propose a new scheme of chaos-based symmetric encryption and, using the proposed cryptosystem both as symmetric encryptor and pseudo-
random-number (PN) generators, design a prototype for public channel cryptography. In the new cryptosystem, the outputs are extremely sensitive to the secret key. Any detectable mismatch of the secret key, of the order of the
computer precision, will induces a totally different set of outputs. Hence this scheme not only overcomes the basic problem of ”continuity” met in chaos-based encryptions, but also extends the definition of the secret key to
all real values in the key space. Borrowing the concept of ”Merkle’s Puzzles”,we further construct a new
model for public channel cryptography where all blocks
are endowed with spatiotemporal chaos. In comparison with conventional methods, the new model is found to be more effcient and flexible in some aspects."

Theo said...

I don't really see how that's relevant here. It's not difficult to detect encrypted messages. It's not difficult to differentiate between an encrypted message and background noise. It's just difficult to decode and decrypt that message.

Simply finding that autocorrelations in a random process are themselves correlated with future events in time is a significant enough result (even if we can't figure out what those correlations actually mean).

Finding the message is the important part.

Additionally, I think it's a stretch to suggest that the "collective consciousness" COULD be "encrypted." It's certain that such a phenomena would be very hard to interpret and process. By it's very nature, it would be just like decrypting an encrypted message, regardless of whether it was "encrypted."

I guess what I'm saying is... What would a collective unconsciousness that WASN'T encrypted look like? Is there a difference?

Anonymous said...

I guess my point was that if the collective unconscious (the current winning theory in the Global Consciousness Project) was affecting the EGGs in some manner of statistical importance correlating to mass “thought events”, and if we assume the study is not compromised by man made random number generator machines or the apophenia/ pareidolia of the observers/interpreters, then the data collected would be similar to background noise infused with synchonious “messages” pertaining to such “thought events”. Certainly, the detection of such phenomena is of significance, and the fact that the results imply correspondence with future events even more so. The article I attached was read in rapid succession from a link found though the Princeton page and made me think in terms of this analogy. If the world’s collective unconscious is a public channel without the benefit of complete spatiotemporal chaos (background noise), then it is not the message (or its “decoding”) that I find most interesting, but rather the fact that the “thought events” are detected right before, during and right after actual events. This implies that the “message” can be detected close to a point in time, and the collective unconscious has some proximity parameters to the actual event (or to the actual observation). Otherwise, why would it detect a train crash in India and not D-Day or World War 5? As they are also significant “thought events”, is it merely their distant proximity to current time that renders them chaotic and unobservable? To answer your question about “what would an “unencrypted” collective unconscious look like, I would like to gift the following quote and suggest we ask some artists (any artists in the house?):

Incisive changes in history are generally attributed exclusively to external causes. It seems to me, however, that external circumstances often serve merely as occasions for a new attitude to life and the world, long prepared in the unconscious, to become manifest. Social, political, and religious conditions affect the collective unconscious in the sense that all those factors which are suppressed by the prevailing views or attitudes in the life of a society gradually accumulate in the collective unconscious and activate its contents. Certain individuals gifted with particularly strong intuition then become aware of the changes going on in it and translate these changes into communicable ideas. The new ideas spread rapidly because parallel changes have been taking place in the unconscious of other people. There is a general readiness to accept the new ideas, although on the other hand they often meet with violent resistance. New ideas are not just the enemies of the old; they also appear as a rule in an extremely unacceptable form.
Jung, "The Psychological Foundations of the Belief in Spirits" (1920)

Theo said...

Sure sure. And I think it's perfectly reasonable that if such a consciousness or unconsciousness exists, there may be a great lag between its inception and its effects in nature.

In general, nature itself may be a complicated nonlinear time-varying filter acting on that unconsciousness.

And I think the Princeton folk are aware of all of this. That's why I think they're probably concentrating on finding deviations form the expected autocorrelation of that process (or those processes) first. After that, they can start to explain what might be causing it, and that should lead to the topic of lag.

And who knows. Maybe they'll prove the matrix really does exist. Personally, I'm not holding my breath.