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I have tried to cross this gap with articles available from my web site publication list

http://www.groupoids.org.uk/publicfull.html

try numbers 75, 101, 111, 130, 136, 140.

Ronald Brown

Emeritus Professor Bangor University

FLSW

The commonalities of those sciences are more about asserting a Euclidean space. That is where that shared logic comes from. Machine learning happens only in Euclidean space. If the data is taken from hyperbolic space it has to be converted into Euclidean pace before it can be learned from, and then those lessons have to be converted back to hyperbolic space. This is changing, but we are barely there right now.

The asymmetries you mentioned are typical. When you need to learn something, your sample is small, so the asserted normal distribution is skewed and kurtotic. After you learn something, your sample is larger and it fits the asserted normal distribution better. A standard normal exists in Euclidean space. Those skewed and kurtotic, not yet normal, aka pre-normals are in hyperbolic space. After any distribution has actually been normal, its sigma goes up and the data is in spherical space. Those three spaces have very different logics and maths.

Collaborate by knowing what you need and want. A mathematics might be constructable to that end.

When I read “Wetware” years ago, I was shocked that the Kreb’s cycle does not exist. It appears to happen, but it is the result of filters and spaces.

]]>With my limited understanding of mathematics and biology I’d agree on the notion “In biology we can’t even start bridging the gap”.

For what it’s worth, the even sadder reality is that all 3 disciplines Mathematics, Physics, Biology share fundamental underlying, underpinning _logic_ principles:

– Absolute incompleteness

– Relativistic choice

which are imbedded in the trio per the following:

– Mathematics: “satisfaction-is-not-absolute”.

– Physics: Uncertainty principle.

– Biology: assumed(phenotype) ⇒ unknown(genotype).

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http://jdh.hamkins.org/satisfaction-is-not-absolute/

“Many mathematicians and philosophers seem to share this perspective. The truth of an arithmetic statement, to be sure, does seem to depend entirely on the structure (N,+,.,0,1,<), with all quantifiers restricted to N and using only those arithmetic operations and relations, and so if that structure has a definite nature, then it would seem that the truth of the statement should be similarly definite."

"Nevertheless, in this article we should like to tease apart these two ontological commitments, arguing that the definiteness of truth for a given mathematical structure, such as the natural numbers […] does not follow from the definite nature of the underlying structure in which that truth resides."

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https://en.wikipedia.org/wiki/Uncertainty_principle

"asserting a fundamental limit to the precision with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions."

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assumed(phenotype) ⇒ unknown(genotype).

]]>When I hear that IT is busting silos, I take it amateurs trying to encode knowledge across silos by ignoring much of the knowledge in those silos. It’s sad that we can only get software written at the 101 level. But, that’s the best programmers can do given that they don’t capture requirements these days. There were other reasons why requirements capture or elicitation led us down a path. Requirements elicitation is the big unsolved problem in programming methodologies and in artificial intelligence.

These functional cultures show up in the technology adoption lifecycle when we have to sell an engagement built on top of discontinuous innovation. We do this to advance the adoption of that discontinuous innovation. We sell it to the early adopter that happens to run a vertical function in a corporation. That vertical function is one of many in a value chain that all share work in a single conceptual model or a functional culture.

It turns out that in philosophy, functional cultures are called epistemic cultures. I discovered this many years after coining the term functional cultures.

That value chain can be found in the industrial classification tree. Mathematics would be one branch, and Biology another. Their conceptual models diverged at some point merged at other points and found discontinuous innovation that built a layers structure that shares only the intractable problem that continuous innovation could not solve. The discontinuities there are dielectric. The separate layer becomes traversable only after a time. At first, the old-new rhetorical contract doesn’t exist. The old is reframed into the new, aka the new-old rhetorical contract is built.

Your discontinuous innovation is the carrier for the value proposition sought by the early adopter. The vertical business gets captured. The epistemic culture gets embedded into the application, and the value proposition succeeds. The developers have to learn the epistemic culture of the early adopter’s firm if they are to succeed in advancing the adoption of their underlying discontinuous innovation.

]]>Thought experiment: replace some of the math jargon in the obituary with words like “enzyme” or “chromosome”. This would be acceptable to nature and a lot of pretty fair scientists would have only a vague working idea of exactly what these things are and what their precise structure is.

The Grothendieck obituary was remarkably elegant and compassionate and should resonate with anyone who has solved a quadratic equation in high school? It is above all a celebration of intellectual integrity.

]]>There was a misprint in my web site url!

]]>There is more to be said on this (see my teaching and popularisation web page). I have found biologists very interested in new concepts in mathematics, though not necessarily interested in the “famous problems in mathematics”, a topic on which I have a view expressed on that page.

That is all for now!

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