h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Randomness - A847000
Author: GammaRay - U205749

Well it's my first try, but nontheless a good one, so lets see what people think!

I think this is a fairly interesting entry, but I think that as it stands it isn't suitable for the edited guide, as at the moment it appears to be more like a stream of consciousness, rather than a well ordered, informative, entry. There are also some bits that either don't seem to make much sense (to me at least), or are wrong in my view.

The easiest way to do this is probably to go through it section by section, and criticise as we go.

Firstly, in the first paragraph, you introduce Collin's English Dictionary's definition of randomness. This would be fine, but you don't always seem to be using that definition. For example, in the bit about cats and dogs, you seem to using a definition of randomness which including, or implies, not being caused. Also, the haphazard, aimless', definition doesn't really cover what mathematicians mean when they talk about randomness, when they mean that think operate according to some set of probabilities, so there are difficult possibilities, with different likelyhood, but no outcome is certain to happen (except in certain cases, when the probability is 1).


Randomness

Randomness, then. Collins English Dictionary (Comprehensive but Concise) describes it as made, done etc in an aimless, or haphazard way. But, I hear you cry, is this the real deal? Possibly.

So what is Randomness All About, Then?

Ah, a "how long is a piece of string" question. A pedant would argue that the length of a piece of string is the perpendicular distance from one end of the string to the other. Yet no such pedantic wit can be applied to randomness, because it cannot be measured, though many theories of measurement do claim to exist. These theories express randomness as infinity; anything divided by zero, or just simply ties it down to chaos theory (this theory is widely supported by many undergraduate physicists at the union bar). The beauty of randomness, however, is that if it eclipses all probabilities at one time or other, all the theories must be wrong, and yet, occasionally right. Think about it.

So what is Randomness All About, Then?

In this section, there are a number of problems. There is the fairly minor 'though many theories of measurement do claim to exist', which seems to suggest that theories are doing the claiming, rather than people claiming the theories exist. Then you seem to be suggesting that there are only two types of randomness, and these are division by zero, and chaos theory. I would dispute both of them as randomness. Division by zero doesn't produce randomness, it merely makes no mathematical sense. Also, chaos theory is not really about randomness either, as I understand it, but is about entirely determistic situations, where small changes can lead to large consequences. You can get unpredictability, in the sense that any approximation in your values eventually leading to your predictions being useless, but that's not really the same thing as randomness.

Then the last bit I don't really understand 'The beauty of randomness, however, is that if it eclipses all probabilities at one time or other, all the theories must be wrong, and yet, occasionally right. Think about it'. It isn't really very clear here what you mean by that.

This One's a Hard nut to crack...

There is a similar problem here with
'What we have is an all probability-encompassing device, which could, theoretically be applied to anything, to either refute it or prove it', which I don't think you have really explained very well. It is also not really clear to me what you mean when you say '", because, although you would be correct in that observation, you would, as we have already proved, be very much wrong'. The problem being how can you be wrong and correct about the same observation.

So, Randomness doesn't exist, does it then?

Here, there are some problems too. 'In theory, it works, but so does raining dogs, so that’s not much to go on' is one but that doesn't really make sense to me. In what sense does 'raining dogs' work in theory?

Then, you talk about predictability in human behaviour, meaning that there can't be randomness involved. This is wrong IMO. Randomness can lead to predictability, usually at the large scale. The simplest example being tossing a (fair) coin, (say) 500 times, and getting fairly close to 250 most of the time, whereas predicting each coin toss would be a futile exercise. This works when we talk about the coin toss being randomly either a head or tail. If predictability in human behaviour is similarly predictable in the large scale, this could be a result of something similar.

Further on, you talk about Pi being random. This could apply if as you say random means haphazard, but not if you mean random in the sense of being able to talk about probabilities. Each digit is a result of applying some formula to calculate it, so the digits aren't random in that sense.

Also, you seem to be ignoring Quantum mechanics, which I gather to be based on probabilities to some extent, rather than on certainties, so could be said to be random.

So what about people who claim to be Random? Not so Random now, are they, eh?

I am not sure here, whether someone's bizarre behaviour can be described as random, neccesarily. They may be just operating on some other model of reality or sensibility, as it were. We may appear to be similarly 'random' to them. There doesn't seem to be a very well defined idea of what haphazardness means in this context. I also don't think there are people who call themselves random either.

Let’s correct the abuse of the word “random”, then!

Here, I am not sure what ENIGMA code-breaking (a profession not really in demand now, I reckon ) has to do with randomness. Also, you talk about 'pure mathematical randomness' without really defining it, or giving any idea of what you mean. In my encounters with randomness, in maths, they always seem to be about randomness within set parameters, if I understand you correctly. For example, the classic dice roll cannot be just any old value, but a head or tail (or 0 and 1).

Also, in general, this entry seems to be a pressentation of an argument, rather than an unbiases treatment of the subject, and therefore, I don't think at the moment it is suitable for the edited guide, which likes more unbiased approach.

Also, you seem to be ignoring how the idea of randomness can be useful even if things are really deterministic. For example, I gather that the theory of particules is based on the ideas of particles moving randomly, but with a tendency to go in certain directions, to understand the large scale properties, such as liquids boiling, solids melting and the like. There may be other examples, but I can't think of any others off-hand.

Anyway, that's what I think, I'm sorry if I've been a little harsh, but I hope my comments have at least been useful.

Silverfish

I liked this bit: "Not genuine random, I grant you, but to the best of their ability, they’re trying Bless 'em."

But I agree with the above, not for the edited guide. I think an entry on randomness would have to include some discussion of, at least: the concept of randomness as a fundamental part of reality (quantum physics), the concept of randomness as disorder (Chaitin's information theoretic definition of randomness), the concept of randomness in the mathematical theory of probability and its connection with reality (rationality in the face of incomplete information).

Well, thank you. I'll revise it and try to improve it post haste!

Did you use big fonts or is it just my monitor?

There are some first person bits towards the end of the Entry. That's one of the bigger EG (Edited Guide) no-nos.

Apart from that I got the impression that the thoughts compilated in this Entry are a bit fuzzy at the moment. Could be improved.... Try to think about: What is the key message I want to send across? Cos I didn't quite get it...

The section about pi being a random number is very intriguing / interesting (at least for a like me: Can a natural constant be something random? Or is it just the sequence of digits. Then again, is a sequence random if it has already been published? I am particularly ga-ga about pi because two weeks ago in our lab we had the contest to see whose birthday date appears first in the pi sequence (try it out, birthday dates are almost ALL within the first 10M digits - incredible. Then try out finding the longest sequence of zeros, you'll be surprised, and telephopne numbers... I tell you folks pi is quite spooky, all's in there). There's a page where you can download pi to 100M or even more digits (hold it... ah here it is: h[Broken link removed by Moderator]

There's also another chap I found who actually TRADES ans SELLS random numbers. It is actually not easy to generate real armor-plated random numbers... I know that because one of our guys here is involved in dynamic simulations, and he's constantly p*ssed at his random generator)

Enough for now,

HELL

Hell, are you using a random alpha/num sequence generator when you're posting links to external sites?

When people say that pi is a random number they usually mean that its sequence of digits passes all known general tests for randomness. It may also (but it hasn't been proved) be a "normal" number (it is known that almost all numbers are "normal" but no particular number is known to be "normal"). A "normal" number is one in which any given sequence of n digits occurs infinitely often in the decimal expansion, and that all sequences of digits (of the same length) occur equally often (in a strange mathematical sense of the word which I probably shouldn't try and go into here). This is sort of what you'd expect of a random number and in some sense captures the idea of there being "no pattern" in the decimal expansion of pi.

Oops, sorry for that broken link, I'll try to repost that one monday, meanwhile you can google-search "pi 10M digits"

So sorry,

HELL

Hi everyone...

Firstly, yes, the font seems to be a bit weird. Having taken a peek at the code, I'd bet it's got something to do with the at the beginning .

"Randomness can lead to predictability, usually at the large scale... If predictability in human behaviour is similarly predictable in the large scale, this could be a result of something similar."

Reminds me of Isaac Asimov's "Robots" series of books...



"So we can give it a human connotation that it needs to be something more than just a wild theory in the minds of the ENIGMA code-breakers and deranged mathematicians."

"Here, I am not sure what ENIGMA code-breaking (a profession not really in demand now, I reckon ) has to do with randomness."

Well... I guess that the author's talking about the Enigma cipher-breakers' goal of finding something in the plaintext that could be predefined so that they could use it to decrypt stuff.

Enigma, and one-time pad encryption, are only truly secure as long as none of the plaintext can be predicted and the encryption key is random. If you can obtain either, you can (eventually) decrypt the message (don't ask me how).

Anyway, it does have /something/ to do with randomness. If you didn't understand what I just said, take my word for it .



If I wanted to be really annoying, I'd go through the article and point out everything, but being as I don't, here's a few tips:
* Use ' to quote things, instead of "
* The article is a bit too "jumpy" for my brain: consider turning each paragraph into a section by explaining each point more. At the extreme, this could turn into a Uni project, but double the length'd probably do it justice.

Apart from that, and a few other small things, the article covers a lot of the important points. Like I said above, just try and expand a bit, and tidy up some of the loose ends!

Metaki

The article just seems a bit jumpy to me... but that has been covered. I have only one issue with the article besides things which have been named, and that is calling pi a random number. This is probably just the mathematician inside me, but pi is not a random number. It is a defined relationship between a circle's circumference and its diameter. Pi is an endless number, but you cannot say its sequence is random because the sequence comes up the same every time. Also, pi can be expressed via radians as an exact number (pi radians = 180 degrees).

Moving away from that, I thought it was a pretty interesting article, if a bit brief on some things.

Reminds me of a fantastically funny Dilbert Cartoon:

"Over here we have our random number generator ..."
"Nine Nine Nine Nine Nine Nine ..."
"Are you sure that's random?"
"That's the problem with randomness, you can never be sure."

at Dr M,

Could this be arbitrarily slung from PR? Shirley not?

My favourite thing about this piece was the answer to the question about the piece of string.

Hey GammaRay, you there?

Coooo-ey! Gamma!

Hope it works now. Pi:

http://www.hepl.phys.nagoya-u.ac.jp/~mitsuru/pi-e.html

The discussion about pi being a random number: Pi isn't *A* random number, I think one number alone cannot be random, only sequences of numbers can be random or not... IIRC the sequence of digits (decimal basis) is (so far) thought to be random - I don't like the denomination either, IMO it should be 'the digits are randomly distributed' but what the hey... Ransom... errr Random theory is a big fascinating chunk of maths, along with number theory - ie the stuff that goes into cryptography and prime numbers and all that... Fascinating. Too bad I don't know more about it.

On the other hand, maybe that's why I think it's so fascinating...

Cheerio,

HELL

BTW: "Nine, nine, nine..."

There's a sequence of six nines at position 762 in PI.

And seven threes at position 710100

So, has anybody found the ascii codes for, say, the 10 commandments or the Declaration of Independence somewhere within the pi sequence?

Are you seeing those EYES Bossel?

Scouting with Anna Banana...

HELL (Did you try to find something in pi, BTW?)

I don't think signifant long texts, such as the declaration of independence, and the ten commandment, but this website:
http://users.aol.com/s6sj7gt/picode.htm
, outlines some of the things that can be found in Pi.

The title of the page (The Pi Code), is a reference to the Bible code, which was an attempt to find hidden meaning in the bible, by looking at every nth letter in turn. This seems to be inpart a parody of that.

I've also found this website:
http://www.geocities.com/thestarman3/math/pi/RandPI.html#PATS which gives some information on some of the oddities in Pi.

It also links to this webpage:
http://www.angio.net/pi/piquery.html#likely, that lets you check whether any given sequence (up to 120 digits), is in Pi (or rather the first 100 million digits of Pi).

You can alternatively ask ME , I have downloaded the first 500M digits onto my computer (the link can be found in the backlog)...

HELL

Sadly, can I propose a move to the FM? The author seems to have popped ut for a ham sandwich...

Just two minutes: seconded!

HELL