A Mathematician's View of Evolution

The Mathematical Intelligencer ^ | Granville Sewell

[TASMANIANRED]

Smart deer would be really ticked off that it didn't have hands.

[TASMANIANRED]

The problem is that a deer could have the intelligence of Einstein and it would be useless.

No hands..

[Virginia-American]

If you try to say evolution is random then evolutionists will say no, because natural selection is the acting force on those mutations.

so far, OK

... But when you try to say evolution is NOT random (IE, designed or something) ...

"not random" isn't the same as "(IE, designed or something)". It's just not random; some combinations of genes favor survival and reproduction, and some don't. "The race is not always to the swiftest, but that's the wy to bet."

... they'll say no, because the thing natural selection acts on is random mutation. ...

True enough. Evo itself has both random (genetic combinations, mutations) and nonrandom (some are better adapted to the environment than others) components.

Is a casino a random process? To the gamblers it is; to the owners it's completely predictable business. See, it can depend on the scale at which you're viewing the process.

It's a cute little catch-22!

Nope. Catch-22 was a contradiction in the Army's rules; the fact that life has both random and deterministic facets is not a contradiction, it's a fact of life.

[Virginia-American]

alterkaker: Huh? Peanuts are not nuts, they are legumes. I don't believe that there is any taxonimical controversy over their classification.

sittnick: The world is a lot bigger than taxonomy, which is a man-made construct. Nutritionally they are regarded as nuts, and are nutritionally classified in the meat group. Taxonomical categorization is only ONE way of thousands to categorize things. It is often impractical and dopey to insist on taxonomical

But not in a discussion about evolution.

[Alamo-Girl]

Thank y'all so much for the ping to this fascinating sidebar!

In the end, it seems to me that focusing only on material and efficient causes puts Neo-Darwinism in a situation where it's letting the tail [of its desire] wag the dog [of its science]: its methodological materialism precludes it from recognizing that formal and final causes actually do operate in nature. I think science -- especially physics and mathematics -- is increasingly aware that an absolutist materalist reductionism may be creating a false picture of reality.

So very true and well said. That is exactly the point which troubles me - there cannot be a complete picture when half of it has been shoved off the table (two of the four causes.) To say that it is a complete picture is a delusion, a second reality. It's not "real."

[CarryaBigStick]

[Virginia-American]

... (If an archeologist in the year 20000 AD came upon a poodle and rottweiler skeleton, not knowing of the existence of either because they died out, he would likely conclude they were different species) ...

I would argue that domestic dogs are in fact a ring species. Consider a thought experiment or two:

Procure an island with lots of game, water, shelter, etc, but no dogs. Introduce 100 male teacup poodles and 100 female great Danes. Come back in 20 years. I predict that there will be no dogs, that the difference in size prevents mating.

Same setup, only this time the the poodles are the bitches and the Danes are the males. I predict the same result.

Same setup, only this time 100 male poodles, 100 female poodles, and the same number of Danes. I redict that when you return to the island there will be two true-breeding populations, and no mutts.

If my predictions are correct, then you have to conclude that the poodles and Danes are different species.

The fact that the poodles can mate with Jack Russells, the Jacks with terriers, the terriers with beagles ... with Danes, shows that they would be a ring species.

[Virginia-American]

... While black rabbits on the snow would not have a chance - still nothing is doing the selecting ...

the predators aren't?

[Thalos]

A deer as smart as Einstein would come up with something better than running and possibly getting caught...

1) Kill a rabbit or other animal, then kick it around while scavenging. When a wolf attacks, kick the rabbit. Hopefully the wolf's prey instinct will get it to chase the rabbit, not the deer.

2) Bathe frequently to get rid of scents.

3) Find and carry a dead wolf.

4) When in a pack about to be chased by wolves, kick one of your fellow deer before running. Not friendly, but no one said our Einstein deer was a good guy.

[RunningWolf]

Fantastic post and I really like this as to the 'Darwinian euphoria'

Darwinian euphoria is the notion that somehow we all emerged from the primordial soup, that a non-existent God was irrelevant to the process (come, come, Catfish, you don't think that Darwin is defended in a vacuum, do you? The enthusiasm stems from the idiot savant belief that evolution disproves God and is therefore a Promethean gift freeing man fron enslavement to mere reality.) If evolution disproves God, voila!!!! Kill whom you will and mistreat the rest all in the name of the "greatest good for the greatest number."

[UndauntedR]

"Stochastic Process" is typically preferred.

It's like a process, an algorithm, that is based on randomness, but still tends to be predictable and reliable.

It's like statistical mechanics, which deals with huge numbers of particles ("events") at the same time. It's unreasonable, and not fruitful, to try and determine what each one will do precisely, but we can still tell you what the entire system (if it's big enough) will do reliably.

Evolution is less predicable since there are so many freakin factors involved. Like a stochastic process, it's unreasonable to try and determine exactly which mutations will happen and will stick around - so we look at the large system instead, typically as allele frequencies of a population, which we can make lots of predictions about without ever referring to individuals.

[UndauntedR]

Ah man, you started out so strong and got me all excited.

Evolutionary algorithms are surprisingly strong... if made correctly. I have alot of experience with them. Of course they've made new things. They've redesigned computer chips by manipulating everything from the layout to the number, type, and sequence of logic gates. I've used them in simplier hypercubic minterm applications as well as condensed matter optimizations. I even worked with a guy who wanted to apply them to make new quantum computing algorithms.

I'm well aware of the problems stochastic algorithms have with local minima in the fitness landscape of the search space. I have two problems with your interpretation:

(1) The search space doesn't have to be bounded. In many applications the actual search space is so buried in abstract mathematics (A fun little section called Matroid Theory) that its unreasonable to describe changes as simply changing parameters within a space.

(1) As many have said, "New" or "New genetic information" is subjective and, as far as I can tell from the rather ambiguous and ever-changing definitions put forward by Creationists, is environment dependent.

Think of the fitness landscape (environment/time dependent) of the genetic search space (which potentially has infinite dimension, but in practice only has a couple of billion dimensions - 750B base pairs in an amoeba is the highest found). First of all, note that all known life is contained (approximately) in this search space. All evolution is doing is changing parameters... there's no "information" involved.

and then you did the turn to "But the results are impossible to construct randomly even though we're talking about a stochastic process (very different)." which was disappointing.

[sittnick]

None of us know all of the creatures that were around three or four or thirty thousand years ago.

Of course we do. We have intact humans from longer ago than that. 3000 years ago was well within the realm of recorded history, in many places.

There you go with the logical fallacies again. I state that we do not know all of the creatures that existed thousands of years ago, and you say we have intact human fossils. I will grant that we certainly had recorded history, and that tells us a lot more than fossils alone. However, it hardly tells us all of the species that existed. We have a significant number of specialists looking for new species, and sometimes they are still found. The fossil record, even from 3,000 years ago is far from complete, much of the historical record is lost, and large parts of the world have no extant history from that era. So, of course we do not know all of the creatures walking the earth 3,000 years ago. There might be a moa or dodo type creature that died out, forgotten to all, with no found remains. There might be more than a handful of such creatures . . . or not. We just don't know.

We certainly don't know what similar looking specimens could mate with others and produce fertile offspring.

No, and without DNA from early Equines, we will likely never know. But we can make a very educated guess, judging from the fact that extant equines (like horses, zebras and asses) cannot normally produce fertile offspring.

Agreed. And educated guesses are not scientific fact.

Peanuts are different from legumes in all sorts of ways.

Name one.

I should have said "other" legumes, though I think you should have know that from the context. The root of the peanut is edible, while the fruit of other legumes are edible. Peas are green and grow in soft pods. Peanuts are light brown and grow in harder shells. In short everything that anybody from a grocer, to a botanist to a four year-old can say that separates peanuts from the other legume of your choice.

I am glad to see that you no longer pretend that the grocer is "wrong" to put the peanuts in with the other nuts in the supermarket. Should grocers pack Swedish Fish in the seafood section too?

If they do, maybe it should go by the imitation crabmeat. Of course, we call peanuts "nuts" nut primarily because the word "nut" is in it. After all, we don't think of coconuts as nuts. Of course, Swedish Fish are manmade, the base of seafood is natural (ditto for candy corn). The grocer puts peanuts in with nuts (with USDA approval) because of their size, edibility out of the shell, texture and general use. Except for a slight remblance to tiny fish, Swedish fish don't pass muster in that regard.

[Tax-chick]

Vehemently vivid verbosity :-).

[sittnick]

Taxonomical categorization is only ONE way of thousands to categorize things. It is often impractical and dopey to insist on taxonomical

But not in a discussion about evolution.

I didn't say that it was. It is certainly not the only category to refer to. In any event, the taxonomical categories are artificial and man-made. Insisting on using only taxonomical categorizations is "begging the question" (e.g. whales are mammals, and therefore evolved from land-mammals), since we are discussing the natural (not man-made) origin of species. Taxonomical categories describe species, but do not tell us whether one came from another. ( whales could have theoretically developed from fish without leaving the water leaving the water, while the other mammals happened to get their systems independent of what was going on with the whales.)

[UndauntedR]

Wow.

I'm a Stanford graduate student right now. I majored in Math, Computer Science, and Physics as an undergrad. I would LOVE to watch you come to Stanford and conduct this little crusade of yours.

There's nothing mystical or contradictory in "materialism". In fact, it all fits together surprisingly well. In all the billions of ways our experiments could have gone wrong and actually contradict each other... none happen. Small discrepancies or "contradictions" are heavily sought after because that means the concepts/theories are premature and new science can be done to see what we missed.

Scientists change their theories to fit the facts.
Creationists change the facts to fit their theories.

Which is better?

[FreedomProtector]

"are surprisingly strong... if made correctly"

if made correctly...if designed correctly...that was the point.

"The search space doesn't have to be bounded."

That is True.


"First of all, note that all known life is contained (approximately) in this search space. All evolution is doing is changing parameters... there's no "information" involved."

Of coarse DNA is not an example of information theory. There is no information involved. (Pardon the sarcasm)

[Red Badger]

Really smart deer would know how to evolve hands.......

[UndauntedR]

You're a Roman Catholic? Boy are you in for a surprise when you die.

Praise FSM, thy one true lord.

[UndauntedR]

if made correctly...if designed correctly...that was the point.

You seem to have a grasp of evolutionary algorithms... unless you mined that information... I'm confounded how you can understand evolutionary algorithms but not understand the natural process the idea came from.

Of coarse DNA is not an example of information theory. There is no information involved. (Pardon the sarcasm)

You said so yourself: "Evolutionary algorithms don't produce anything new, just find different parameters..

x[t+1] = s( v( x[t]) )".

ALL you need to do is let x be an open set (a "population") in the unbound genetic search space, v() be genetic variation (reproduction, mutation, etc), and s() be natural selection. Working in the space, you would not be able to tell me which genotype contains more information... they're all simply points in genetic space. Only the fitness function (which, as you know, is implicitly built into the s() function and, in this case, is completely environment dependent) can give you a sense of "good" and "bad" adaptation - the gradient (slope) of the fitness function (in a billion-dimensional space remember). No "information"... no "new"... Just a simple evolutionary algorithm in an unbound genetic search space with really really complicated v() and s() functions (which are dependent on time and position within the search space).