Random versus Non-Random

Post of the Month: January 2011

by

Subject:    | Random vs. non-random  Re: Fermi Paradox
Date:       | 08 Jan 2011
Message-ID: | ig8dvi$spk$1@reader1.panix.com

"Random" is a very misunderstood word. Colloquially, random is taken to describe a situation where there are, say, three choices and all are equally likely.

Technically, "random" is far broader than that. The example above is certainly an example of technical randomness, but what about this case: There are three choices, the first has a 50% chance of happening, the second a 33% chance of happening, and the third, a 17% chance of happening. Is this a random situation.

The answer is yes, it is. The choices do not have to be equally likely in order to have a random situation.

Evolution can go in a huge number of directions, some far more likely than others, but the choice is random.

What does this really mean? The technical definition of a random set of events is that one cannot predict the next event from the past events. That does NOT mean that all possible events are equally likely, it just means total unpredictability.

Another example: a die has five one spots and one six spot. Shaking it reveals that a one comes up roughly 5/6 of the time, the six 1/6 of the time. The number coming up on the next throw is random.

When John wrote:

"Replication Rules are not random in the sense that, say, Heisenberg's Principle of Uncertainty or quantum mechanics is sometimes supposed to show the fundamental randomness of reality. They are merely random with respect to natural selection. Natural selection is not random: it is the determinate result of sorting processes according to relative fitness. It is stochastic, in the sense that better engineered features can fail for reasons of probability (they may meet accidents unrelated to their fitness), but that poses no greater threat to the scientific nature of evolution than it does for, say, subatomic physics or information theory."

in the article cited above he was not being technically correct with regard to "random". He's also not using "determinate" in a technical matter -- at least not as technical people use it.

What I think he means when he writes

"Natural selection is not random: it is the determinate result of sorting processes according to relative fitness."

is that the result of natural selection is not equally likely outcomes. Instead the outcomes are weighted according to relative fitness. That makes the replication rules not equally favor any old change, but they are still random in the sense of unpredictable.

Here I'll get a bit more technical: Associated with randomness are *distributions*. A simple example results if we plot a graph with the possible outcomes along the x-axis and their chance of occuring along the y-axis.

The common usage of "random" means that all outcomes have the same chance. That makes the graph flat. This distribution is called a "uniform" distribution.

Another common distribution is the "normal" distribution. Its graph is a bell-shaped curve. There are many many other named distributions and an infinite number of unnamed ones.[1]

Another is the exponential distribution which is actually a negative exponential distribution. The graph of amount of a radioactive material versus time on the x-axis is such a distribution.

Each of these distributions can characterize a random process. Radioactive decay is thought to be random. It is characterized by the negative exponential distribution.

The result of throwing a single fair die is a random process resulting in a uniform distribution.

The popular view accepts only the uniform distribution as truly random. Any other distribution, the populace would say, favors some outcomes over others. That is correct. But as long as the next choice cannot be exactly predicted from any or all of the past choices, the choice is random.

So once again I come back to what John was saying: his point was that there is a non-uniform distribution of evolutionary outcomes under selection. And that is, of course true. But the outcome is still random.

Sorry to be so long winded, but this is a slightly complex subject. And sorry to be so pedantic, but it comes from years of working in the random field... ;-)

[1] Find a use for an unnamed one and perhaps it will be named after you.