This is simultaneously peer reviewed, a rant, and as crazy as any Science Fiction novel by Greg Egan, Rudy Rucker or Vernor Vinge – but in a good way! I’m not including the URLs at arXiv.com nor MIT, but do go look! This might deserve a thread of its own in Shtetl-Optimized.

The Mathematical Universe

Authors: Max Tegmark

(Submitted on 5 Apr 2007)

Abstract: I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel’s sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. Comments:

28 pages, 5 figs; more details at this http URL

Subjects:

General Relativity and Quantum Cosmology (gr-qc)

Cite as:

arXiv:0704.0646v1 [gr-qc]

Vasily, you are wrong on this point as well. If you think that darwinism was an “integral part” of soviet ideology, you may be confusing it with Lysenkoism, which you can read about on wikipedia if you’d like to educate yourself.

]]>Additionally, scientists, especially experts, are not so quick to judge that the earth is warming or cooling or whatever it will be, but in the face of massive and growing evidence, and consistent predictions from 19th, 20th and 21st century physics, it’s a bit hard to stay agnostic. At minimum the atmosphere is changing in makeup at an alarming rate, and likely these changes will cause problems for very simple to understand reasons. This is equivalent to a no-go theorem for the skeptics.

]]>The most outrageous example is darwinism. The whole theory is based on assumption that evolution is driven by random mutations.

You are conflating evolutionary biology with the narrow model for historical reasons called the darwinian model. But even this narrow model is more than “random mutations”. The smallest model is variation (independent of selection), selection and hereditary of characteristics. Variation of itself doesn’t work fast, it is the direction which selection gives that enhances evolution.

By adding up some of the earliest known evolutionary mechanisms (now there are many more), an evolutionary biologist described it in a mathematical simile:

“Science educators need to help their students gain a better understanding of how powerful selection operating in nature can be. One of the pedagogical strategies that educators can use involves simple mathematics. The four genetic consequences of selection operating in nature can be represented in mathematical terms.

[…]

(1) The SELECTIVE ELIMINATION (subtraction) of harmful traits, that is, the removal of maladaptive genetic information;

[…]

(2) The SELECTIVE ACCUMULATION (addition) of new adaptive genetic information in the form of new mutations each generation.

[…]

(3) The SELECTIVE MULTIPLICATION of adaptive genetic information each generation brings about an EXPONENTIAL increase in the frequency of adaptive genes in a population. (multiplication)

[…]

(4) The SELECTIVE RECOMBINATION of adaptive genetic information each generation. (division and selective addition)”

( http://scienceblogs.com/evolvingthoughts/2007/04/what_makes_natural_selection_a.php )

Why don’t you require a mathematical model that demonstates the claims of darwinists?

Turning from the simple simile, there are plenty of real mathematical population models that describes the outcomes of the above processes when we include later genetics to describe hereditary. Statistician and evolutionary biologist R.A. Fisher laid much of the groundwork. He has been described as “the greatest of Darwin’s successors”. (Wikipedia.)

Btw, I think it is a remarkable fact that evolutionary biology gives the greatest precision of all natural sciences. The basic structure that common descent with variation predicts is the phylogenetic tree. There are many ways to arrange these trees, yet analysis can pick out a small subset of likely candidates for later confirmation.

“Nevertheless, a precision of just under 1% is still pretty good; it is not enough, at this point, to cause us to cast much doubt upon the validity and usefulness of modern theories of gravity. However, if tests of the theory of common descent performed that poorly, different phylogenetic trees, as shown in Figure 1, would have to differ by 18 of the 30 branches! […] However, as illustrated in Figure 1, the standard phylogenetic tree is known to 38 decimal places, which is a much greater precision than that of even the most well-determined physical constants.” ( http://www.talkorigins.org/faqs/comdesc/section1.html#independent_consilience )

]]>Here we can add a remark by I.M. Gel’fand: there exists yet another phenomenon which is comparable in its inconceivability with the inconceivable effectiveness of mathematics in physics noted by Wigner – this is the equally inconceivable ineffectiveness of mathematics in biology

End quote

This is an excerpt from article by V.Arnold, “On teaching math”, which is very interesting by itself, and can be found

here

In this article, you can find a lot of stuff related to the subject of this thread. ]]>

Vasily, I took a course in evolutionary biology last semester, and it was almost entirely math-based. Most of what working evolutionary biologists do these days requires a lot of math.

“Why don’t you, complexity theorists, explain to public that the statement of randomness is meaningless?”

Or perhaps you could explain it to us? Since have considered this carefully, please explain in what sense mutations are non-random.

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