Thank you. It looks like we are getting somewhere.
My definitions non-idiosyncratic. They are standard definitions from the dictionary, Philosophy of Statistics and Gregory Chaitin’s famous paper in Scientific American. I defined them at the outset and referenced my chapter “All About Randomness” in Evolution 2.0.
You can review my definitions at It’s Time to Tighten the Definition of “Random”
“I’m not sure it is even possible to construct a random variable without a pattern.”
Let’s put some parameters around this. You can go out and buy a hardware random number generator like this one
and we can use it to generate random numbers between 0 and 1.
Our probability distribution is: no outputs less than zero; no outputs greater than one; and equal distribution for all numbers between 0 and 1. In other words there is as little pattern as possible in the distribution of those numbers.
Chaitin points out that if, within those parameters, it is impossible to describe the output with an algorithm that’s simpler than the data itself, then the pattern is random. That is the most rigorous definition of “no pattern.”
A phenomenon may have other nuances and still be considered random. It could be white noise or pink noise. But it is still noise. If converted to audio or video looks and sounds like a TV between stations. You can the bass and treble controls up and down, you can tweak the color filters, but it’s still random.
Joshua, your definition is not as clear as one might hope. Now, I do believe I understand what you mean when you say a completely deterministic system is a random variable with entropy of zero.
It appears to me that you modeling EVERYTHING as a random variable. But then some of your variables are 0% unpredictable (deterministic) and others are 100% unpredictable (high entropy) and other variables are somewhere in between.
OK, you can do that. I believe I follow your logic. I do understand that while the roll of dice is random, they are only capable of producing numbers between 1 and 6 and yes that is a pattern.
But this misses the point. The point is NOT that dice are restricted to 1-6 or that random numbers are restricted to a range of 0-1. The point is that within stated parameters, the system is unpredictable.
Yours is an unconventional, idiosyncratic way of using the term random. With your definition we have to go a step forward and also define how much entropy is in your random variable. Because until you do that, your statement that something is “random” doesn’t give us any information. In your usage, everything is random.
That is not helpful. One should always prefer precise definitions over vague ones.
The real problem comes when you criticize people like Shapiro and Noble for saying that “mutations are non-random”. You are judging their statement according to your use of the term, not theirs. It is wrong of you to do that. You need to use the terms the way they define them. It’s only fair.
Denis Noble is abundantly clear in Was the Watchmaker Blind? Or Was She One-Eyed? that many things in physics and biology are random. But he then provides many examples in this paper of organisms 1) actively harnessing stochasticity to obtain favorable outcomes; 2) exhibiting sophisticated systematic responses to threats, damage, etc including repair, re-arrangements of coding sequences etc; He also shows 3) that these responses are contextual and depend on the nature of the threat.
Shapiro has also documented this exhaustively - this paper for example https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5745447/
When they say “random,” they mean the same thing I mean. They mean there is little or no pattern, and within stated parameters, randomness resembles noise.
And when they say transposition or horizontal gene transfer or other natural genetic engineering mechanisms are non-random, they are saying that those changes are systemic responses that follow discernible rules. The organism is orchestrating those changes to maintain homeostasis and adapt. They are saying that transposition, epigenetics and HGT are not accidental and not purposeless.
I debated this issue with PZ Myers: Memo To PZ Myers: Damage is Random. Repair is Not. PZ said mutations that generate evolutionary events are random. McClintock showed that they are not. She won the Nobel Prize for determining what the patterns are.
In physics & engineering, the word “random” invokes a continuum:
Random = little or no pattern < —————— > Non-random = systematic, deterministic, predictable
In evolutionary biology, mutations were long believed to be random with respect to fitness. Today, as you have pointed out, we know this is not true. In keeping with this, Shapiro and Noble are saying that evolution is not random events, it is systematic response to random events. They document this thoroughly.
My time is limited. I do not have the bandwidth to explain their work in detail here in this forum. But fortunately the papers cited above make their case quite clear. My book Evolution 2.0 offers a condensed and simplified account of the Extended Synthesis.
I know some people will object to various claims I have made about biology and mutations. I suggest they read these papers with great care.
To me what is important in all of this is that, contrary to popular books by Dawkins, Coyne etc., the mutations that generate evolution are not random, purposeless or accidental. And they are most emphatically not “copying errors.” Cells have a capability of altering their genetic sequences that is truly impressive. There is much we can learn by studying it.