[Fis] FIS discussions. Units

Pedro C. Marijuan pcmarijuan.iacs at aragon.es
Thu Oct 31 14:06:29 CET 2019

Dear List,

Some brief responses to Jerry and Karl.

> Q4: Does an informed path exist which logically organizes the 
> inanimate into the animate?
> Q5: What are relationships between the inanimate objects and the 
> animate objects?
> Hypothesis: If two independent forms (parts) are copulated (linked, 
> conjoined, connected, bound) together, a novel interdependent informed 
> whole is formed.
> Hypothesis: A set of atomic numbers can be composed into an animate 
> object by copulating the set of parts into a natural sort or kind (an 
> organized whole).
> Pedro: Do these assertions add any light to you critical quation about 
> possible relationships between units,  the animate and the inanimate? 
>  Is any simpler scientific mathematics possible?
Thanks for the abstraction effort, Jerry. Your whole questions set is a 
very good discussion guide although enormously difficult to be answered, 
at least in the biological realm. Even for a very simple cell, eg the 
prokaryote (bacteria), the way its components are coupled and the 
relationship they keep with their environment has not been properly put 
in informational terms yet, as far as I know. A couple of years ago I 
made a pretty complete catalogue of the "signaling parts" of E. coli, 
and the result was surprising for me (see Marijuan et al., BioSystems, 
2017). In a few words, "nothing was eaten that had not been previously 
recognized by some signaling apparatus". It is literal, for in the order 
of 200 'receptors' of all sort could check for 300 or more different 
types of 'food' molecules. Putting in another way, the "energy flow" and 
the "information flow" of the living cell are completely interrelated. 
And the result of their 'logical' coupling is the systematic emergence 
of a life cycle that includes reproduction --Spinoza's principle of 
conatus. What kind of elegant informational/logical synthesis could be 
made (beyond the ensuing Darwinian Dogma)?

Responding to Karl, I was surprised to find, some posts ago, a critique 
of the equality sign. His idea, well argued from his multidimensional 
partitions argument (equality hides from view the many possible variable 
distributions of qualities inside the number's sumands), has been 
coincidentally developed by other mathematicians in a different field: 
"infinite categories". See the abstract below, (courtesy of Malcolm Dean).

*With Category Theory, Mathematics Escapes From Equality
*/Two monumental works have led many mathematicians to avoid the equal 
sign. Their goal: Rebuild the foundations of the discipline upon the 
looser relationship of “equivalence.” The process has not always gone 
Kevin Hartnett, Senior Writer
Quanta Magazine, 10 October 2019
/The equal sign is the bedrock of mathematics. It seems to make an 
entirely fundamental and uncontroversial statement: These things are 
exactly the same./
/But *there is a growing community of mathematicians who regard the 
equal sign as math’s original error*. They see it as a veneer that hides 
important complexities in the way quantities are related — complexities 
that could unlock solutions to an enormous number of problems. They want 
to reformulate mathematics in the looser language of equivalence. “We 
came up with this notion of equality,” said////Jonathan Campbell 
<http://www.jonathanacampbell.com/>////of Duke University. “It should 
have been equivalence all along.” The most prominent figure in this 
community is////Jacob Lurie <https://www.ias.edu/scholars/lurie>//. In 
July, Lurie, 41, left his tenured post at Harvard University for a 
faculty position at the Institute for Advanced Study in Princeton, New 
Jersey, home to many of the most revered mathematicians in the world. 
Lurie’s ideas are sweeping on a scale rarely seen in any field. Through 
his books, which span thousands of dense, technical pages, he has 
constructed a strikingly different way to understand some of the most 
essential concepts in math by moving beyond the equal sign. “I just 
think he felt this was the correct way to think about mathematics,” 
said////Michael Hopkins <http://www.math.harvard.edu/~mjh/>//, a 
mathematician at Harvard and Lurie’s graduate school adviser. Lurie 
published his first book,/////Higher Topos Theory/ 
in 2009. The 944-page volume serves as a manual for how to interpret 
established areas of mathematics in the *new language of “infinity 
categories.”* In the years since, Lurie’s ideas have moved into an 
increasingly wide range of mathematical disciplines. Many mathematicians 
view them as indispensable to the future of the field. “No one goes back 
once they’ve learned infinity categories,” said////John Francis 
<https://sites.math.northwestern.edu/~jnkf/>////of Northwestern University./

So... very good point by Karl! Could new mathematical ideas provide the 
bio-mathematical (informational) synthesis needed?
Best wishes to all,

Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group

pcmarijuan.iacs at aragon.es

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