Perry Marshall: What is Random?

[swamidass (S. Joshua Swamidass)]

@Perry_Marshall

In the post Are Evolutionary Mutations Random? Or Are They Engineered for Success? (which I have posted here several times)

Yes, and you have also refused to quote relevant portions and refused to engage in discussion here about it. Why not? I still don’t understand.

@Perry_Marshall

I will engage further once Joshua provides his definition of the term randomness. His definition and mine appear to be far apart.

So you will engage further here if I repeat my definition (again) of random? I hope so, as an inordinate amount of time is being spent talking about talking.

Perry Marshall’s “Random”

Let’s start by noting your definition. Your definition is not consistent with the field of probability and statistics. You write,

“Random” means absence of pattern and purpose.
(Random vs. Stochastic Evolution)

This is an idiosyncratic definition. I’m not sure it is even possible to construct a random variable without a pattern. Every random feature I know about follows a pattern of some sort or another. I’d honestly like to know where you came up with this definition. You offer no citations. I can’t mathematically make sense of your definition.

“Random” In Statistics and Probability

As for my definition, there is no surprises. I’ve already given my definition several times @Perry_Marshall. On both this thread, and on those that have spin off from it. I’ll give it to you again, quoting form wikipedia to demonstrate that my definition is not idiosyncratic.

@swamidass

In probability and statistics, a random variable , random quantity , aleatory variable , or stochastic variable is a variable whose possible values areoutcomes of a random phenomenon.[1] More specifically, a random variable is defined as a function that maps the outcomes of unpredictable processes to numerical quantities (labels), typically real numbers. In this sense, it is a procedure for assigning a numerical quantity to each physical outcome. Contrary to its name, this procedure itself is neither random nor variable. Rather, the underlying process providing the input to this procedure yields random (possibly non-numerical) output that the procedure maps to a real-numbered value.

A random variable’s possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the possible outcomes of a past experiment whose already-existing value is uncertain (for example, due to imprecise measurements or quantum uncertainty). They may also conceptually represent either the results of an “objectively” random process (such as rolling a die) or the “subjective” randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself but is instead related to philosophical arguments over the interpretation of probability. The mathematics works the same regardless of the particular interpretation in use.

This, of course starts to raise questions about your distinction between stochastic and random. They are the same things.

I also emphasize that mutations (like all random variables) have patterns and can be the consequence of purposeful intention. Mutations, also, are not independent of fitness, even though they are still random. I’ve given several examples that demonstrate just these facts.