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Bharath chand
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Gödel and the conspiracy to suppress Leibniz's universal language

Leibniz dreamt of a characteristica universalis: a universal language that could express any scientific concept.  He didn't get too far - nobody was interested.   But it involved a strange idea.  Basic concepts would be encoded as prime numbers.  More complicated ones would be encoded by multiplying these numbers.  So, you could see which basic concepts a complicated one contained, just by factoring it!

When I heard this I immediately thought of Gödel numbering.  This is a much better-worked out idea which Gödel used to encode statements of arithmetic as numbers.  It also uses primes, but in a smarter way.

Did Gödel get his inspiration from Leibniz?  I haven't been able to find out.   But I discovered that he was obsessed with Leibniz's characteristica universalis!   Gödel became paranoid in his later years: after his wife died, he starved to death because he didn't trust food from anyone else.  That may help explain this strange passage in Wikipedia:

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Gödel alleges conspiracy

Because Leibniz never described the characteristica universalis in operational detail, many philosophers have deemed it an absurd fantasy. In this vein, Parkinson wrote:

"Leibniz's views about the systematic character of all knowledge are linked with his plans for a universal symbolism, a Characteristica Universalis. This was to be a calculus which would cover all thought, and replace controversy by calculation. The ideal now seems absurdly optimistic..."

The logician Kurt Gödel, on the other hand, believed that the characteristica universalis was feasible, and that its development would revolutionize mathematical practice.  He noticed, however, that a detailed treatment of the characteristica was conspicuously absent from Leibniz's publications. It appears that Gödel assembled all of Leibniz's texts mentioning the characteristica, and convinced himself that some sort of systematic and conspiratorial censoring had taken place, a belief that became obsessional. Gödel may have failed to appreciate the magnitude of the task facing the editors of Leibniz's manuscripts, given that Leibniz left about 15000 letters and 40000 pages of other manuscripts. Even now, most of this huge Nachlass remains unpublished.
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Biology's Birthday present for Alan Turing: Father of computer science and artificial intelligence, mathematician, cryptographer and…..biologist? 60 years after Turing published a hypothesis for pattern formation (such as zebra stripes) in biology, using math and simple diffusion, scientists have found evidence to support it. Like the yin and yang of Eastern philosophy, Turing proposed interactions between an activator (working over a short range) and an inhibitor (working over long range).

In a paper published in Nature Genetics, researchers discovered that two morphogens worked as an activator-inhibitor pair to develop striped ridges in the roof of a mouse’s mouth. Consider the reaction in Image 2 : A + B react to form C + D, where the product C feeds back autocatalytically to speed its production. C also activates an inhibitor, X*, which inhibits the reaction. Suppose these factors can regulate the genes that make skin pigment, then this interaction can give rise to the Turing patterns shown in the image.

To understand, look at Image 3: As the tissue expands,levels of the inhibitor diffusing from the stripes fall below a threshold (dashed line) so that the activator now gets back to work and produces a new stripe (dashed bar). The other panels show real data from the Nature Gen paper. Notice the appearance of the new stripe r3, first between r8 and r2 and then another (r4) between r8 and r3 both in the excised tissue and in the animal (in vivo). If diffusion of the inhibitor is blocked by making a cut next to the stripe, a new stripe emerges.

Image 4 shows the wonderful range of patterns that can be generated: A) Zebra stripes. B) Fish skin patterning. C) Phyllotaxis (leaf positioning). D) Developmental fields of leg segmentation in Drosophila. E) Cardiac arrhythmias (spiral/scroll waves).

What a neat 100 year birthday present for Alan Turing!

Sources: 1) Nature Genetics Abstract (image 3): http://www.nature.com/ng/journal/vaop/ncurrent/full/ng.1090.html

2) A good free read (images 2, 4): http://www.fasebj.org/content/17/1/1.full

3) Turing’s 1952 paper: http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf

Excerpt from Turing's Abstract : “The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts.”
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