Russell E. Rierson

The basic argument seems to be "Randomness vs. Teleology" <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />

(1.) What is randomness, really?

(2.) What is Teleology, really?

Probability distributions and "probability formulas" can be used to approximate the percentage of an event ocurring.

P{A and B} = P{A} x P{B|A}...joint probability

P{A and B} = P{A} x P{B}...independent events

P{A or B} = P{A} + P{B}...mutually exclusive

P{A or B} = P{A} + P{B} - P{A and B} ...not mutually exclusive

etc...

Populations, standard deviations, percentage, samples...Formula after formula is employed by the discipline called "statistics".

Teleology basically explains that reality exists for an "ultimate purpose".

Randomness cannot be the complete explanation. Hopefully the mathematical formalism for "teleology" will be discovered.

Randomness and teleology could be two sides of the same coin.

Russ

RufusAtticus

That doesn't mean it is right.

Why not? But before you answer, specify what you mean by "randomness." Is your "randomless" without trends?

Russell E. Rierson

Yes, what exactly is randomness???

Here is a link:

<a href="http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html" target="_blank">http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html</a>

Algorithmic Definition
The new definition of randomness has its heritage in information theory, the science, developed mainly since World War II, that studies the transmission of messages. Suppose you have a friend who is visiting a planet in another galaxy, and that sending him telegrams is very expensive. He forgot to take along his tables of trigonometric functions, and he has asked you to supply them. You could simply translate the numbers into an appropriate code (such as the binary numbers) and transmit them directly, but even the most modest tables of the six functions have a few thousand digits, so that the cost would be high. A much cheaper way to convey the same information would be to transmit instructions for calculating the tables from the underlying trigonometric formulas, such as Euler's equation eix = cos x + i sin x. Such a message could be relatively brief, yet inherent in it is all the information contained in even the largest tables.
Suppose, on the other hand, your friend is interested not in trigonometry but in baseball. He would like to know the scores of all the major-league games played since he left the earth some thousands of years before. In this case it is most unlikely that a formula could be found for compressing the information into a short message; in such a series of numbers each digit is essentially an independent item of information, and it cannot be predicted from its neighbors or from some underlying rule. There is no alternative to transmitting the entire list of scores.

In this pair of whimsical messages is the germ of a new definition of randomness. It is based on the observation that the information embodied in a random series of numbers cannot be ``compressed,'' or reduced to a more compact form. In formulating the actual definition it is preferable to consider communication not with a distant friend but with a digital computer. The friend might have the wit to make inferences about numbers or to construct a series from partial information or from vague instructions. The computer does not have that capacity, and for our purposes that deficiency is an advantage. Instructions given the computer must be complete and explicit, and they must enable it to proceed step by step without requiring that it comprehend the result of any part of the operations it performs. Such a program of instructions is an algorithm. It can demand any finite number of mechanical manipulations of numbers, but it cannot ask for judgments about their meaning.

The definition also requires that we be able to measure the information content of a message in some more precise way than by the cost of sending it as a telegram. The fundamental unit of information is the ``bit,'' defined as the smallest item of information capable of indicating a choice between two equally likely things. In binary notation one bit is equivalent to one digit, either a 0 or a 1.

We are now able to describe more precisely the differences between the two series of digits presented at the beginning of this article:

01010101010101010101
01101100110111100010
The first could be specified to a computer by a very simple algorithm, such as ``Print 01 ten times.'' If the series were extended according to the same rule, the algorithm would have to be only slightly larger; it might be made to read, for example, ``Print 01 a million times.'' The number of bits in such an algorithm is a small fraction of the number of bits in the series it specifies, and as the series grows larger the size of the program increases at a much slower rate.
For the second series of digits there is no corresponding shortcut. The most economical way to express the series is to write it out in full, and the shortest algorithm for introducing the series into a computer would be ``Print 01101100110111100010.'' If the series were much larger (but still apparently patternless), the algorithm would have to be expanded to the corresponding size. This ``incompressibility'' is a property of all random numbers; indeed, we can proceed directly to define randomness in terms of incompressibility: A series of numbers is random if the smallest algorithm capable of specifying it to a computer has about the same number of bits of information as the series itself.

This definition was independently proposed about 1965 by A. N. Kolmogorov of the Academy of Science of the U.S.S.R. and by me, when I was an undergraduate at the City College of the City University of New York. Both Kolmogorov and I were then unaware of related proposals made in 1960 by Ray J. Solomonoff of the Zator Company in an endeavor to measure the simplicity of scientific theories. During the past decade we and others have continued to explore the meaning of randomness. The original formulations have been improved and the feasibility of the approach has been amply confirmed.

End quote.

This "algorithmic definition" is very interesting...

Russ

RufusAtticus

Yes, but what exactly does it have to do with natural processes? For example, does the movement of an electron exhibit this randomness?

It seems to me that you are equivating randomness with trendlessness. If that is true then the natural process are not "random" as you have designated it.

wade-w

That is an interesting argument, Russ.

Rufus, the more usual definition is in terms of probability. Basically, the concept is that given a set of n objects,if the probability of selecting any particular object is the same as any selecting any other object in the set, i.e., the probability of selecting an arbitrary object in the set is 1/n, then we call that random.

RufusAtticus

wade,

Yes that would be a system with a discrete uniform distribution. However, not all random distributions are without trends. Evolution is stocastic and thus random, but selection ensures that it is not trendless and thus not "random" in some usuages of the word. That is what I'm trying to elucidate from Russell.

Is his randomness trendless?

Keith Russell

Greetings:

Russell E. said:
"Hopefully the mathematical formalism for "teleology" will be discovered."

Why, because you cannot bear the idea that randomness is reality?

Some people say things like 'I hope they find 'God', because this can't be all there is."

Because they again fear that an unconscious universe is reality.

Things are as they are.

You can hope for whatever you want, but if you wish, hope, or pray for the unreal, you're going to be sincerely disappointed.

Keith.

Principia

Only to those who insist that randomness implies an antithesis to teleology. Just what is this topic in relation to anyways?

wade-w

I'd have to say yes. In a strictly mathematical sense, if something displays a trend, it can't be characterized as random.

Another way to look at it is given a sequence, there is no way to predict the value of the next member of the sequence. In this sense, mutation can be considered random. However, mutation is not all there is to evolution, so is the process as a whole really random? It seems to me that it isn't, at least not in the mathematical sense.

Doubting Didymus

Has this got something to do with evolution that I am missing somehow? Sounds like philosophy to me.