<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p>Dear List,</p>
<p>Some brief responses to Jerry and Karl.<br>
</p>
<blockquote type="cite"
cite="mid:1B044336-AA57-469A-9FC3-71D3EF554770@me.com"><br>
<div class=""><font class="" size="3">Q4: Does an informed path
exist which logically organizes the inanimate into the
animate?</font></div>
<div class=""><font class="" size="3">Q5: What are
relationships between the inanimate objects and the animate
objects?</font></div>
<div class=""><font class="" size="3"><br class="">
</font></div>
<div class=""><font class="" size="3">Hypothesis: If two
independent forms (parts) are copulated (linked, conjoined,
connected, bound) together, a novel interdependent informed
whole is formed. </font></div>
<div class=""><font class="" size="3">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). </font></div>
<div class=""><br class="">
</div>
<div class=""><font class="" size="3">Pedro: Do these assertions
add any light </font><span style="font-size: medium;" class=""> </span><span
style="font-size: medium;" class="">to you critical quation </span><span
style="font-size: medium;" class="">about possible
relationships between units, the animate and the inanimate?
Is any simpler scientific </span><font class="" size="3">mathematics
possible?</font></div>
<br>
</blockquote>
<p>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)? <br>
</p>
<p>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). <br>
</p>
<div class="gmail_default" style=""><b>With Category Theory,
Mathematics Escapes From Equality<br>
</b><i>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 smoothly.<br>
</i></div>
<div class="gmail_default" style="">Kevin Hartnett, Senior Writer<br>
<div class="gmail_default" style=""><font style=""><a
href="https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/?utm_source=Quanta+Magazine&utm_campaign=388bce3947-RSS_Daily_Mathematics&utm_medium=email&utm_term=0_f0cb61321c-388bce3947-389912677&mc_cid=388bce3947&mc_eid=9dd29ead65"
style="">https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/</a><br>
</font></div>
<div class="gmail_default" style="">Quanta Magazine, 10 October
2019</div>
</div>
<div class="gmail_default" style=""><i><span style="color: rgb(26,
26, 26);">The equal sign is the bedrock of mathematics. It
seems to make an entirely fundamental and uncontroversial
statement: These things are exactly the same.</span></i></div>
<div class="gmail_default" style=""><i><span style="color: rgb(26,
26, 26);">But <b>there is a growing community of
mathematicians who regard the equal sign as math’s original
error</b>. 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</span></i><i><span
style="color: rgb(26, 26, 26);"> </span></i><i><a
href="http://www.jonathanacampbell.com/" target="_blank"
style="background-color: transparent; box-sizing: border-box;
text-decoration-line: none; color: inherit;">Jonathan Campbell</a></i><i><span
style="color: rgb(26, 26, 26);"> </span></i><i><span
style="color: rgb(26, 26, 26);">of Duke University. “It should
have been equivalence all along.” The most prominent figure in
this community is</span></i><i><span style="color: rgb(26, 26,
26);"> </span></i><i><a
href="https://www.ias.edu/scholars/lurie" target="_blank"
style="background-color: transparent; box-sizing: border-box;
text-decoration-line: none; color: inherit;">Jacob Lurie</a></i><i><span
style="color: rgb(26, 26, 26);">. 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</span></i><i><span
style="color: rgb(26, 26, 26);"> </span></i><i><a
href="http://www.math.harvard.edu/~mjh/" target="_blank"
style="background-color: transparent; box-sizing: border-box;
text-decoration-line: none; color: inherit;">Michael Hopkins</a></i><i><span
style="color: rgb(26, 26, 26);">, a mathematician at Harvard
and Lurie’s graduate school adviser. Lurie published his first
book,</span></i><i><span style="color: rgb(26, 26, 26);"> </span></i><i><a
href="https://press.princeton.edu/books/paperback/9780691140490/higher-topos-theory-am-170"
target="_blank" style="background-color: transparent;
box-sizing: border-box; text-decoration-line: none; color:
inherit;"><em style="box-sizing:border-box">Higher Topos
Theory</em></a></i><i><span style="color: rgb(26, 26, 26);">,
in 2009. The 944-page volume serves as a manual for how to
interpret established areas of mathematics in the <b>new
language of “infinity categories.”</b> 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</span></i><i><span
style="color: rgb(26, 26, 26);"> </span></i><i><a
href="https://sites.math.northwestern.edu/~jnkf/"
target="_blank" style="background-color: transparent;
box-sizing: border-box; text-decoration-line: none; color:
inherit;">John Francis</a></i><i><span style="color: rgb(26,
26, 26);"> </span></i><i><span style="color: rgb(26, 26, 26);">of
Northwestern University.</span></i></div>
<div class="gmail_default" style=""><span style="color: rgb(26, 26,
26);"><br>
</span></div>
<div class="gmail_default" style=""><span style="color: rgb(26, 26,
26);">So... v</span><span style="color: rgb(26, 26, 26);">ery
good point by Karl! Could new mathematical ideas provide the
bio-mathematical (informational) synthesis needed?<br>
</span></div>
<div class="gmail_default" style=""><span style="color: rgb(26, 26,
26);">Best wishes to all,</span></div>
<div class="gmail_default" style=""><span style="color: rgb(26, 26,
26);">--Pedro<br>
</span></div>
<pre class="moz-signature" cols="72">--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
<a class="moz-txt-link-abbreviated" href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a>
<a class="moz-txt-link-freetext" href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a>
------------------------------------------------- </pre>
<div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br /> <table style="border-top: 1px solid #D3D4DE;">
<tr>
<td style="width: 55px; padding-top: 18px;"><a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank"><img src="https://ipmcdn.avast.com/images/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif" alt="" width="46" height="29" style="width: 46px; height: 29px;" /></a></td>
<td style="width: 470px; padding-top: 17px; color: #41424e; font-size: 13px; font-family: Arial, Helvetica, sans-serif; line-height: 18px;">Libre de virus. <a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank" style="color: #4453ea;">www.avast.com</a> </td>
</tr>
</table>
<a href="#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" width="1" height="1"> </a></div></body>
</html>