A Second Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]

Nutters.org ^ | 28-Jul-2000 | Brett Watson

[Southack]

This is part two of the famous "Million Monkeys Typing On Keyboards for a Million Years Could Produce The Works of Shakespeare" - Debunked Mathematically.

For the Thread that inadvertently kicked started these mathematical discussions, Click Here

For the Original math thread, Click Here

[maro]

But don't the physicists say that the "real" world IS the mathematical world? What is the difference between the two?

[maro]

Assuming that's so, I don't see the relevance. It's the a priori probability we're interested in, no? Let's say that a thousand people try to break the bank at Monte Carlo, come hell or high water. With that assumption, the wealth states of these folks might plausibly be predicted to 1 or 0 eventually, where 1 represents the bank. That doesn't change the (daunting) a priori odds of breaking the bank at Monte Carlo.

[Nebullis]

It is relevant to a discussion of transitions between phenotypic expression. That may be a side issue to the main point of the thread, but it's important to show that what is irrelevant is the demand for smooth transitions based on single point mutations.

[Southack]

"You've jumbled mutation rates, epigenetic mutations, teratogenic mutations, and transmission fidelity (which is what I was speaking to) together as if they all have the same probabilities."

Don't be obtuse. Transmission fidelity applies to any mutation that is passed to another organism, and it does not reach a 100% expected or actual real-world statistical success rate.

[maro]

I don't follow you. Please indulge me and spell it out. Let's assume that alleles tend to 1 or 0--therefore, what?

[powderhorn]

But don't the physicists say that the "real" world IS the mathematical world? What is the difference between the two?

Plato tells us that only reason is perfect. The objects that we touch, see, taste and feel can only be expressed objectivly by way of reason. And mathematics is our most able tool for pure reason. But it does fall short in one respect: we still don't know what we don't know. Mathematics does not create knowledge, it only defines knowledge. It is a tool to EXPRESS what we know (or what we think we know) but it doesn't give us answers outside of the calculations that we put to it. If we put in incomplete calculations we arrive at an incomplete answer.

[Nebullis]

I don't follow you. Please indulge me and spell it out.

My best suggestion at this time is for you to reread the thread.

[Nebullis]

Transmission fidelity applies to any mutation that is passed to another organism, and it does not reach a 100% expected or actual real-world statistical success rate.

Sure it does. Surely you can imagine a single mutation which is passed on from one organism to one of its offspring.

[Southack]

Sure, that's 100%, but you're only citing a single instance of a mutation successfully appearing in future offspring (a useless statistic because it is a tautology by definition), not the overall batting average for all mutations in a species surviving and propagating, which is NOT 100%.

The expected value for all mutations (or even the limited subset of "neutral" mutations) to be propagated is simply not 100%.

[maro]

Well, you don't have to answer if you don't want to. I did review as much of this thread (just your posts) as I could bear--this thread is far too long. It didn't pop out to me. Let me recap, and if the recap is pretty simple it's because no one I believe has really answered a very basic question. Let's try yet another metaphor. Think of a significant somatic change (you would say phenotypic expression) as crossing a river. Now, what "significant" means will eventually have to be clarified, but let's not do that yet. That is, the previous state is the west bank, and the next state is the east bank. Evolutionary theory, as I understand it, says that we can get across the river by hopping across rocks in the river, each of which represents a different genetic state a little different from the last. Each of those rocks have some functional difference, so that the improbability of the mutations between Rock i and Rock i + 1 doesn't really matter--given enough time and enough generations, the mutation happens, and once in existence proliferates, setting the stage for the next iteration. One objection to this theory is the implausibility that you can come up with a chain of functional intermediates to which this story could apply. If in fact there is such a chain, and such a chain in every case, of course the objection falls away. By implication, you and others seem to accept at least the possibility that there could not be a chain of functional intermediates. But you have another argument. You say, consider nonfunctional mutations (or as general re once argued introns), which could accumulate, and at some point become meaningful because of a bitflip, or a transposition. (Btw, whether a mutation is literally single point or something fancier like a transposition doesn't matter for this purpose--it's still intrinsically an unlikely event and still just a single change to the DNA.) In the metaphor, you are saying that the rocks don't need to be so close together--if you wait for nonfunctional mutations, in effect the river crosser can construct one-time use stilts that will give him a bigger stride. I say in response, but that approach depends on how probable it is that the nonfunctional mutations could happen just before the next rock needs to be reached. The probability for that is something like P1*P2*P3..PN, by which I mean proportional to the product of the underlying probabilities of each mutation. (Edsheppa pointed out helpfully that the probability of the mutation may not be the same as the proportion of mutants in the population over time, but as long as the latter is a linear time-dependent function of the former, I think the argument still has force.) So in other words, the farther apart the rocks are, the taller the stilts have to be. So does the concept of nonfunctional mutations get you anywhere? And why do we care what the a posteriori populations of alleles are, when in our thought experiment we are on the west bank and thinking in terms of apriori probabilities?

[Southack]

I like the idea of a summary to draw everyone down to fixed, stated positions, but I'm afraid that you're going to find that the Evolutionary crowd will eventually reply that the East Bank in your metaphor doesn't matter as evolution has no fixed objective. Where ever the mutations / rocks take it (East side, West side, around in circles, whatever), then so be it.

Which doesn't help anyone at all, scientifically. What people like you and I want to know is whether or not math supports Evolution, and the argument that Evolution has no fixed objective gets us quite a ways away from math being able to help answer any of the Big Questions.

What Watson did in the original article for this thread was to identify an area where math could show some meaningful probabilities. Because we can calculate the probability of one or more data sets being reached out of some large possible number of permutations, we can use math to calculate the probability of various lengths of sequences of useful or desired data self-forming without intelligent intervention.

With this math, we can see the odds of bases "accidentally" forming a sequence of DNA that could form life, or we could calculate the improbability of useful data forming on a hard drive after a non-intelligent magnetic interference pattern swept over it, or we could calculate the probability of monkeys banging out the first sentence of Shakespeare's Hamlet.

And that math has merit. We already know by definition that the proper DNA sequence for the first life form either had to form with or without intelligent intervention. Now we have the math to show us just how much data could be within the realm of possibility to form a desired sequence (for letters accidentally spelling out an English sentence, up to 96 correct characters could, over 17 Billion years, potentially self-form without intelligent aid). More than 96 correct bites of data is pretty well out of the question, at least without intelligent intervention.

Of course, the calculated probability / improbability for bases sequencing in DNA will be slightly different, and of course it is possible that there are a large number of potential life forms relative to non-life-sustaining DNA sequencing possibilities which will also affect the final probability somewhat, but one can quickly see with Watson's math that we are drilling down to something useful and scientific, and that has the future potential of identifying Evolution's precise improbability / probability.

But even then, there will be those in the Evolutionary camp who cry that life evolving from inanimate matter (i.e., the first step in the whole process of life - AKA "abiogenesis") is not part of Evolutionary Theory. Perhaps there are even those who would cling to Evolution regardless of the math against it, and might be tempted to try many such ruses in order to steer clear of mathematical truths. Due to popular and political considerations of those who refuse to accept the math on natural abiogenesis, it's probably going to eventually take math on the probabilities of mutations forming, surviving, and being successfully transferred to other organisms before anyone can say with certainly if Evolution is or is not mathematically feasible.

On the other hand, if Life can be shown to be formed with fewer than 96 correct sequential bases in a DNA strand, then natural abiogenesis is certainly possible. Compared to the simplist known life forms, however, we're a long way from proving any such thing, while not being too far away from proving that it isn't possible.

[Nebullis]

Let's try yet another metaphor.

Okay. (Why all the metaphors?)

Just for fun let's call the river an entropy barrier, the crossing a fitness barrier and the banks phenotypic spaces. Just as there is a considerable degeneracy between genotype and phenotype, there is degeneracy between phenotype and fitness. As you move up or down the river you encounter widenings and narrowings at the surface as the depth of the river changes. At a few very rare locations, the banks of the river are close enough that the river can be easily crossed.

Neutral mutations allow the organisms to explore the banks (phenotypic space) free of fitness constraints (necessity of crossing the fitness barrier) until a natural river-crossing is found.

[medved]

But even then, there will be those in the Evolutionary camp who cry that life evolving from inanimate matter (i.e., the first step in the whole process of life - AKA "abiogenesis") is not part of Evolutionary Theory.

Why look stupid trying to defend two untenable ideological doctrines (evolution AND abiogenesis) when, if you act arrogant enough about it and get good enough with the ad-hominems, you can get off with one?

Perhaps there are even those who would cling to Evolution regardless of the math against it, and might be tempted to try many such ruses in order to steer clear of mathematical truths. Due to popular and political considerations of those who refuse to accept the math on natural abiogenesis, it's probably going to eventually take math on the probabilities of mutations forming, surviving, and being successfully transferred to other organisms before anyone can say with certainly if Evolution is or is not mathematically feasible.

It isn't.

The big lie which is being promulgated by the evos is that there is some sort of a dialectic between evolution and religion.

That's BS. In order to have a meaningful dialectic between evolution and religion, you would need a religion which operated on an intellectual level similar to that of evolution, and the only two possible candidates would be Rastifari and Voodoo.

The real dialectic is between evolution and mathematics. Professing belief in evolution at this juncture amounts to the same thing as claiming not to believe in modern mathematics, probability theory, and logic. It's basically ignorant.

The biggest group of disbelievers in evolution is, in all likelihood, mathematicians and not Christians. You had a collosal face-off between leading evolution proponents and some of the world's best mathematicians in the late sixties at Wistar; the mathematicians told the evos they were FUBAR and the evos have been in denial ever since.

The Wistar Institute Symposium was a milestone meeting held in Philadelphia in April 1966 to discuss the statistical possibility of Darwinian evolution. The conference was chaired by Sir Peter Medawar, whose work on graft rejection won him a Noble prize. By 1966, computers had progressed enough to determine statistically if random mutations alone could account for the level of evolution seen in organisms after five billion years. After a heated debate and several meetings, the Wistar Symposium deemed this statistically impossible.

Furthermore, many of the scientists at Wistar came forward to state that the fossil record did not support evolution. Few fossils showing transitional stages between species had been found. Arguments also came up about advanced organs such as the eye and that 5 billion years was not enough time for these organs to evolve.

For more details about the Wistar Institute Symposium, see the following links:

• Wistar Destroys Evolution
• The Anti-Darwinian Scientists

[Southack]

I hate to be a wet blanket, especially when someone is trying to agree with me, but a simple internet search on google will reveal that there have been numerous attacks on the Wistar Conference, most notably that only one mathematician, in only one paper, even came close to saying what most anti-evolution sites say was said by the mathematical community at that conference.

That being said, I feel comfortable attacking the myths against evolutionary theory simply because I am so certain of the reality of the real mathematical evidence against Evolution.

[Southack]

Your thought experiment in that last post was one of the better evolutionary metaphors that I've seen. Nice job.

[medved]

One of the urls I provided notes that there were several of these conferences, not just one, and the primary focus was debate and not the production of papers. Nonetheless, Robert Bass, one of America's best mathematicians, notes that:

What the debate is about is whether or not any known or even conceivable chance-mutation based plus natural-selection based mechanism can lead to a radical increase in (or radical transformation of) the information content of the genome of the species in question. (This can be quantified via rigorous mathematics, as in "Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution," published by the famed Wistar Institute of the U of PA after a bunch of the world's greatest mathematicians [including Ulam, the co-inventor of the H-bomb] debated a group of neo-Darwinian biologists.)

Further, the infinite unlikelihood of stochastic increase in the information content of a genome can be proved rigorously as a mathematical theorem in Information Theory (as published by Yockey, who wilfully avoids the theistic implications), which is almost the same as the Law of Increasing Entropy in Thermodynamics (and the hand-waving high-school-level efforts of neo-Darwinian efforts to discredit this creatonist argument are truly pathetic).

Thus, aside from any papers, you have a whole book of proceedings, the general thrust of which is that the standard view of evolutionism is mathematically impossible.

[Southack]

Perhaps I should have simply said that quotes from individual mathematicians may carry more weight than the Wistar Conferences, when one considers the amount of material that exists which attacks those meetings.

[medved]

You'd EXPECT the evos to attack the Wistar findings; the alternative is having to look for another infinitely stupid ideological doctrine, and infinitely stupid ideological doctrines (ISIDs) simply are not that easy to come up with. An essentially infinite sequence of gross violations of probabilistic laws is involved.

[maro]

Yes, that is a nice metaphor, and perhaps better than mine. In your metaphor, the question I would ask is whether the wanderings up and down the bank "looking" for a natural crossing are not inherently limited by the probability of the neutral mutations. I hope you would agree that there is some such limit. From there, it is a question of fact (or modelling) to determine what that limit is, and whether that limit is big enough/not big enough for natural river crossings to found as the evolutionary hypothesis predicts.

[edsheppa]

Your question on the probability needs to take time into account. Assuming the neutral mutations are independent (e.g. must occur at different positions), that the long term frequency of the occurence of any combination would be the product of the long term frequencies of the individual mutations. OTOH the probability that such a combination will occur within G generations approaches 1 as G increases w/o limit (again assuming independence).

So does the concept of nonfunctional mutations get you anywhere?

Where were we trying to go? Selection can't grab hold of neutral mutations so they'll drift randomly with some long range tendency. They can get locked in by a positive change. The fact that they exist is meaningful in terms of the size of the genetic phase space. Anything else?

But that all is still missing the point. It's not generally interesting to talk about the likelihood of some spcific mutation or combination of mutations occuring. If I may be permitted my own analogy, suppose you are playing poker. You'd be silly to consider only the likelihood of a royal flush in spades; all combinations need to considered for a good analysis.

Continuing the analogy, you must consider process too. Among all the combinations of hands in draw poker, about half are a pair or better. With the draw however, the odds are very sigificantly increased so ignoring the draw (selection) would be a very bad error. Taking the point a bit further, an analysis of a poorly understood process doesn't make for a convincing argument.