randomness versus noise

Ten years ago today my father passed away from complications with lung cancer after a 3 month battle. I remember the feeling, not only of the events, but of the kind of person that I was then. I feel so much older now. Really really old. And I miss my father. Every year I get this email from Amazon. I feel a little uncomfortable. All my thoughts from here will be scattered.

Is some information always better than no information? What if the information is 100% noise, or even 50% (enough to make it impossible to distinguish the signal from the noise)? For example, I tell you that there is an oxygen molecule exactly 4 feet in front of you and 2 feet to the right and 1 foot up. I tell you how fast it's moving, what color it is, which plant made it, and the current stock prize of Amazon. And you're trying to find out whether or not there's enough oxygen in the sealed container to live for another hour. Are you better off?

I think that some information isn't always better than none. Information is useless until it fits a pattern of some sort... until it crosses the threshold into potential generalization. The generalization-level of information is the first point at which information is useful, and then it's only marginally useful and requires that you be highly skeptical of the patterns you're seeing. But anytime before that, it's noise. Until you have some certainty that there's a fairly good chance that what information you haven't isn't completely irrelevant to the situation as a whole--until it fits a possible pattern of larger behavior--it's not good at all, in fact, by even looking at it you could slightly bias your ability to make further decisions, swayed by its information-ness.

What is the difference between randomness and noise? When things happen randomly they often still adhere to some predictability. Like, I'm slowly coming around to believe, the balance of heads and tails while flipping coins repeatedly will slowly become normalized the more you flip. What you're wading through, in order to get towards normalization, statistical significance, is noise. And you'll have to wade to infinity to get rid of all noise. Noise is more insidious than pure randomness because it is completely unpredictable. It is that which makes randomness unpredictable while it is... you can't tame it, all you can do is reduce it. If the flipping of a coin was completely random, with no noise, it might go: heads, tails, heads, tails, heads, tails, heads, tails, etc, forever. Noise makes it do otherwise. A single flip of a coin is always 50% noise, because it should land half-heads half-tails, and it can only do one or the other.

Or maybe not. Math friends, please correct me if I'm wrong. I have the feeling that a single statistics class would've rendered unnecessary all this talk of randomness. Sorry for the redundancy. I need to keep thinking about it because it still doesn't make sense.

If you know you're guilty of something, is it worst to deny the guilt or to not care about the guilt or to admit to the guilt? Of those three, which is the worst? I think I'm guilty of the worst.

I realized today that my recent actions (of which I have not mentioned) make complete sense if I think about them in the context of a clunky machine that is trying to solve a certain problem that it can smell but not yet formulate. First, it has to move to the location of the problem (have it typed in by events, coincidences, and conscious moves), and then it has to solve the problem. Right now, I'm moving closer to the location of the problem.

Genius : The Life and Science of Richard Feynman of course mentioned Feynman. Another book I was reading at the time, Fooled by Randomness: The Hidden Role of Chance in the Markets and in Life, mentioned Feynman which was less likely. It also happened to mention Monte Carlo Simulators, used to map the distribution of possibilities given certain assumptions (not in the context of Feynman though). The third book I'm reading now, The Broken Dice, and Other Mathematical Tales of Chance mentions Feynman as well (odd) and also Monte Carlo Simulators. I've walked into a pool of books that all reference the same ideas. The more they talk about the same thing from different angles, I think the closer I get to understanding whatever it is they are trying to say.

Nanowrimo starts in a little over one day. Okay. Okay.

Comments

[Lewis Brown]

Randomness
Erik, it seems to me that some of the problems you're wrestling with are to do with the difference between statistical randomness (behaviour in the infintely-long-term) and "pointwise" randomness. The idea of pointwise randomness helps to answer the question "how likely is it that this sequence of heads and tails was produced completely at random?" without using statistical tests. It's part of the field of algorithmic information theory, and Kolmogorov complexity. I can't find a good non-mathematical introduction to it, but this link is close.

The basic idea is to work out what is the shortest computer program that could generate a given sequence of heads and tails (for example). The shorter the program, the less "random" the sequence. For example, a sequence of 1,000,000 coin-throws which alternate heads and tails does not have a high degree of pointwise randomness, because a computer program that printed out alternating heads and tails would be quite short. By contrast, a sequence of a million throws with no discernable pattern has a high degree of pointwise randomness because the shortest computer program to generate it might just be one that contained a copy of the sequence (all 1 million characters) and instructions to print it out.

[Lewis Brown]

Oops, the link I added above went missing somehow. It was meant to point to http://szabo.best.vwh.net/kolmogorov.html

[Mats]

Nice formulation!
>>What you're wading through, in order to get towards normalization, statistical significance, is noise. And you'll have to wade to infinity to get rid of all noise. >> I think this is a very nice formulation of the law of large numbers. But here:
>>Noise is more insidious than pure randomness because it is completely unpredictable.>> I don't really follow. Maybe Lewis comment above could help. At any rate, Lewis comment is I think really what solves the problem I was working with under the headline "Statistic Teacher's Fallacy"

http://blogofpandora.blogspot.com/2003_08_01_blogofpandora_archive.html#106192715588179871

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