Surprise! There’s no satisfactory mathematical model for macroevolution, at the present time.
In 2006, Professor Allen Macneill acknowledged that macroevolution is not mathematically modelable in the way that microevolution is. He could have meant that macroevolution is not mathematically modelable at all; alternatively, he may have simply meant that macroevolutionary models are not as detailed as microevolutionary models. If he meant the latter, then I would ask: where’s the mathematics that explains macroevolution? Surprisingly, it turns out that there is currently no adequate mathematical model for Darwinian macroevolution. Professor James Tour’s remark that “The Emperor has no clothes” is spot-on.
Evolutionary biology has certainly been the subject of extensive mathematical theorizing. The overall name for this field is population genetics, or the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. Population genetics attempts to explain speciation within this framework. However, at the present time, there is no mathematical model – not even a “toy model” – showing that Darwin’s theory of macroevolution can even work, much less work within the time available. Darwinist mathematicians themselves have admitted as much.
In 2011, I had the good fortune to listen to a one-hour talk posted on Youtube, entitled, Life as Evolving Software. The talk was given by Professor Gregory Chaitin, a world-famous mathematician and computer scientist, at PPGC UFRGS (Portal do Programa de Pos-Graduacao em Computacao da Universidade Federal do Rio Grande do Sul.Mestrado), in Brazil, on 2 May 2011. I was profoundly impressed by Professor Chaitin’s talk, because he was very honest and up-front about the mathematical shortcomings of the theory of evolution in its current form. As a mathematician who is committed to Darwinism, Chaitin is trying to create a new mathematical version of Darwin’s theory which proves that evolution can really work. He has recently written a book, Proving Darwin: Making Biology Mathematical (Random House, 2012, ISBN: 978-0-375-42314-7), which elaborates on his ideas.
Here are some excerpts from Chaitin’s talk, part of which I transcribed in my post, At last, a Darwinist mathematician tells the truth about evolution (November 6, 2011):
I’m trying to create a new field, and I’d like to invite you all to leap in, join [me] if you feel like it. I think we have a remarkable opportunity to create a kind of a theoretical mathematical biology…
So let me tell you a little bit about this viewpoint … of biology which I think may enable us to create a new … mathematical version of Darwin’s theory, maybe even prove that evolution works for the skeptics who don’t believe it…
I don’t want evolution to stagnate, because as a pure mathematician, if the system evolves and it stops evolving, that’s like it never evolved at all… I want to prove that evolution can go on forever…
OK, so software is everywhere there, and what I want to do is make a theory about randomly evolving, mutating and evolving software – a little toy model of evolution where I can prove theorems, because I love Darwin’s theory, I have nothing against it, but, you know, it’s just an empirical theory. As a pure mathematician, that’s not good enough…
… John Maynard Smith is saying that we define life as something that evolves according to Darwin’s theory of evolution. Now this may seem that it’s totally circular reasoning, but it’s not. It’s not that kind of reasoning, because the whole point, as a pure mathematician, is to prove that there is something in the world of pure math that satisfies this definition – you know, to invent a mathematical life-form in the Pythagorean world that I can prove actually does evolve according to Darwin’s theory, and to prove that there is something which satisfies this definition of being alive. And that will be at least a proof that in some toy model, Darwin’s theory of evolution works – which I regard as the first step in developing this as a theory, this viewpoint of life as evolving software….
…I want to know what is the simplest thing I need mathematically to show that evolution by natural selection works on it? You see, so this will be the simplest possible life form that I can come up with….
The first thing I … want to see is: how fast will this system evolve? How big will the fitness be? How big will the number be that these organisms name? How quickly will they name the really big numbers? So how can we measure the rate of evolutionary progress, or mathematical creativity of my little mathematicians, these programs? Well, the way to measure the rate of progress, or creativity, in this model, is to define a thing called the Busy Beaver function. One way to define it is the largest fitness of any program of N bits in size. It’s the biggest whole number without a sign that can be calculated if you could name it, with a program of N bits in size….
So what happens if we do that, which is sort of cumulative random evolution, the real thing? Well, here’s the result. You’re going to reach Busy Beaver function N in a time that is – you can estimate it to be between order of N squared and order of N cubed. Actually this is an upper bound. I don’t have a lower bound on this. This is a piece of research which I would like to see somebody do – or myself for that matter – but for now it’s just an upper bound. OK, so what does this mean? This means, I will put it this way. I was very pleased initially with this.
Table:
Exhaustive search reaches fitness BB(N) in time 2^N.
Intelligent Design reaches fitness BB(N) in time N. (That’s the fastest possible regime.)
Random evolution reaches fitness BB(N) in time between N^2 and N^3.
This means that picking the mutations at random is almost as good as picking them the best possible way…
But I told a friend of mine … about this result. He doesn’t like Darwinian evolution, and he told me, “Well, you can look at this the other way if you want. This is actually much too slow to justify Darwinian evolution on planet Earth. And if you think about it, he’s right… If you make an estimate, the human genome is something on the order of a gigabyte of bits. So it’s … let’s say a billion bits – actually 6 x 10^9 bits, I think it is, roughly – … so we’re looking at programs up to about that size [here he points to N^2 on the slide] in bits, and N is about of the order of a billion, 10^9, and the time, he said … that’s a very big number, and you would need this to be linear, for this to have happened on planet Earth, because if you take something of the order of 10^9 and you square it or you cube it, well … forget it. There isn’t enough time in the history of the Earth … Even though it’s fast theoretically, it’s too slow to work. He said, “You really need something more or less linear.” And he has a point…
Professor Chaitin’s point here is that if even a process of intelligently guided evolution takes, say, one billion years (1,000,000,000 years) to reach its goal, then an unguided process of cumulative random evolution (i.e. Darwin’s theory) will take one billion times one billion years to reach the same goal, or 1,000,000,000,000,000,000 years. That’s one quintillion years. The problem here should be obvious: the Earth is less than five billion years old, and even the universe is less than 14 billion years old.
In 2006, Professor Allen Macneill acknowledged that macroevolution is not mathematically modelable in the way that microevolution is. He could have meant that macroevolution is not mathematically modelable at all; alternatively, he may have simply meant that macroevolutionary models are not as detailed as microevolutionary models. If he meant the latter, then I would ask: where’s the mathematics that explains macroevolution? Surprisingly, it turns out that there is currently no adequate mathematical model for Darwinian macroevolution. Professor James Tour’s remark that “The Emperor has no clothes” is spot-on.
Evolutionary biology has certainly been the subject of extensive mathematical theorizing. The overall name for this field is population genetics, or the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. Population genetics attempts to explain speciation within this framework. However, at the present time, there is no mathematical model – not even a “toy model” – showing that Darwin’s theory of macroevolution can even work, much less work within the time available. Darwinist mathematicians themselves have admitted as much.
In 2011, I had the good fortune to listen to a one-hour talk posted on Youtube, entitled, Life as Evolving Software. The talk was given by Professor Gregory Chaitin, a world-famous mathematician and computer scientist, at PPGC UFRGS (Portal do Programa de Pos-Graduacao em Computacao da Universidade Federal do Rio Grande do Sul.Mestrado), in Brazil, on 2 May 2011. I was profoundly impressed by Professor Chaitin’s talk, because he was very honest and up-front about the mathematical shortcomings of the theory of evolution in its current form. As a mathematician who is committed to Darwinism, Chaitin is trying to create a new mathematical version of Darwin’s theory which proves that evolution can really work. He has recently written a book, Proving Darwin: Making Biology Mathematical (Random House, 2012, ISBN: 978-0-375-42314-7), which elaborates on his ideas.
Here are some excerpts from Chaitin’s talk, part of which I transcribed in my post, At last, a Darwinist mathematician tells the truth about evolution (November 6, 2011):
I’m trying to create a new field, and I’d like to invite you all to leap in, join [me] if you feel like it. I think we have a remarkable opportunity to create a kind of a theoretical mathematical biology…
So let me tell you a little bit about this viewpoint … of biology which I think may enable us to create a new … mathematical version of Darwin’s theory, maybe even prove that evolution works for the skeptics who don’t believe it…
I don’t want evolution to stagnate, because as a pure mathematician, if the system evolves and it stops evolving, that’s like it never evolved at all… I want to prove that evolution can go on forever…
OK, so software is everywhere there, and what I want to do is make a theory about randomly evolving, mutating and evolving software – a little toy model of evolution where I can prove theorems, because I love Darwin’s theory, I have nothing against it, but, you know, it’s just an empirical theory. As a pure mathematician, that’s not good enough…
… John Maynard Smith is saying that we define life as something that evolves according to Darwin’s theory of evolution. Now this may seem that it’s totally circular reasoning, but it’s not. It’s not that kind of reasoning, because the whole point, as a pure mathematician, is to prove that there is something in the world of pure math that satisfies this definition – you know, to invent a mathematical life-form in the Pythagorean world that I can prove actually does evolve according to Darwin’s theory, and to prove that there is something which satisfies this definition of being alive. And that will be at least a proof that in some toy model, Darwin’s theory of evolution works – which I regard as the first step in developing this as a theory, this viewpoint of life as evolving software….
…I want to know what is the simplest thing I need mathematically to show that evolution by natural selection works on it? You see, so this will be the simplest possible life form that I can come up with….
The first thing I … want to see is: how fast will this system evolve? How big will the fitness be? How big will the number be that these organisms name? How quickly will they name the really big numbers? So how can we measure the rate of evolutionary progress, or mathematical creativity of my little mathematicians, these programs? Well, the way to measure the rate of progress, or creativity, in this model, is to define a thing called the Busy Beaver function. One way to define it is the largest fitness of any program of N bits in size. It’s the biggest whole number without a sign that can be calculated if you could name it, with a program of N bits in size….
So what happens if we do that, which is sort of cumulative random evolution, the real thing? Well, here’s the result. You’re going to reach Busy Beaver function N in a time that is – you can estimate it to be between order of N squared and order of N cubed. Actually this is an upper bound. I don’t have a lower bound on this. This is a piece of research which I would like to see somebody do – or myself for that matter – but for now it’s just an upper bound. OK, so what does this mean? This means, I will put it this way. I was very pleased initially with this.
Table:
Exhaustive search reaches fitness BB(N) in time 2^N.
Intelligent Design reaches fitness BB(N) in time N. (That’s the fastest possible regime.)
Random evolution reaches fitness BB(N) in time between N^2 and N^3.
This means that picking the mutations at random is almost as good as picking them the best possible way…
But I told a friend of mine … about this result. He doesn’t like Darwinian evolution, and he told me, “Well, you can look at this the other way if you want. This is actually much too slow to justify Darwinian evolution on planet Earth. And if you think about it, he’s right… If you make an estimate, the human genome is something on the order of a gigabyte of bits. So it’s … let’s say a billion bits – actually 6 x 10^9 bits, I think it is, roughly – … so we’re looking at programs up to about that size [here he points to N^2 on the slide] in bits, and N is about of the order of a billion, 10^9, and the time, he said … that’s a very big number, and you would need this to be linear, for this to have happened on planet Earth, because if you take something of the order of 10^9 and you square it or you cube it, well … forget it. There isn’t enough time in the history of the Earth … Even though it’s fast theoretically, it’s too slow to work. He said, “You really need something more or less linear.” And he has a point…
Professor Chaitin’s point here is that if even a process of intelligently guided evolution takes, say, one billion years (1,000,000,000 years) to reach its goal, then an unguided process of cumulative random evolution (i.e. Darwin’s theory) will take one billion times one billion years to reach the same goal, or 1,000,000,000,000,000,000 years. That’s one quintillion years. The problem here should be obvious: the Earth is less than five billion years old, and even the universe is less than 14 billion years old.
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