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<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
style='font-size:11.0pt;font-family:"Lucida Sans Unicode";color:navy'>Dear All,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
style='font-size:11.0pt;font-family:"Lucida Sans Unicode";color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'>This note contains some very useful notions and references. It
seems to me that there are very familiar ones which have not received
discussion here: one is the obvious greater than > or less than <. The
sign for non-equality is simply the negation of = and doesn’t bring much
new.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'>The relation that might be much more important is implication c. Its
use is standard in logic, for ‘material’ implication, but I think
this can be extended to a concept of implication as a process of causation in ‘real
matter’. Any takers? Does it correspond to Pedro’s First Hypothesis,
since “novel whole is formed” can be read “new entity emerges”?
Can this sign be used to imply distributions of qualities in real, non-number
systems?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'>Best,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face="Lucida Sans Unicode"><span
lang=EN-GB style='font-size:11.0pt;font-family:"Lucida Sans Unicode";
color:navy'>Joseph<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<div>
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face="Times New Roman"><span lang=EN-US style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabindex=-1>
</span></font></div>
<p class=MsoNormal><b><font size=2 face=Tahoma><span lang=EN-US
style='font-size:10.0pt;font-family:Tahoma;font-weight:bold'>From:</span></font></b><font
size=2 face=Tahoma><span lang=EN-US style='font-size:10.0pt;font-family:Tahoma'>
Fis [mailto:fis-bounces@listas.unizar.es] <b><span style='font-weight:bold'>On
Behalf Of </span></b>Pedro C. Marijuan<br>
<b><span style='font-weight:bold'>Sent:</span></b> jeudi, 31 octobre 2019 14:06<br>
<b><span style='font-weight:bold'>To:</span></b> fis@listas.unizar.es<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Fis] FIS
discussions. Units</span></font><span lang=EN-US><o:p></o:p></span></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Dear
List,<o:p></o:p></span></font></p>
<p><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>Some
brief responses to Jerry and Karl.<o:p></o:p></span></font></p>
<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt' type=cite
cite="mid:1B044336-AA57-469A-9FC3-71D3EF554770@me.com">
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Q4: Does an informed path exist which logically organizes the inanimate
into the animate?<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Q5: What are relationships between the inanimate objects and the
animate objects?<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Hypothesis: If two independent forms (parts) are copulated (linked,
conjoined, connected, bound) together, a novel interdependent informed whole is
formed. <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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). <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Pedro: Do these assertions add any light </span></font><font
size=4><span style='font-size:13.5pt'> to you critical quation about
possible relationships between units, the animate and the inanimate?
Is any simpler scientific </span></font>mathematics possible?<o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</blockquote>
<p><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>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)? <o:p></o:p></span></font></p>
<p><font size=3 face="Times New Roman"><span style='font-size:12.0pt'>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). <o:p></o:p></span></font></p>
<div>
<p class=MsoNormal><b><font size=3 face="Times New Roman"><span
style='font-size:12.0pt;font-weight:bold'>With Category Theory, Mathematics
Escapes From Equality<br>
</span></font></b><i><span style='font-style:italic'>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.</span></i><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Kevin Hartnett, Senior Writer<o:p></o:p></span></font></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><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">https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/</a><o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Quanta Magazine, 10 October 2019<o:p></o:p></span></font></p>
</div>
</div>
<div>
<p class=MsoNormal><i><span style='color:rgb(26,
26, 26)'><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;font-style:italic'>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></span></font></i><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><i><span style='color:rgb(26,
26, 26)'><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;font-style:italic'>But
<b><span style='font-weight:bold'>there is a growing community of
mathematicians who regard the equal sign as math’s original error</span></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><font
color="#1a1a1a"><span style='color:#1A1A1A'> </span></font><a
href="http://www.jonathanacampbell.com/" target="_blank" style='box-sizing: border-box;
text-decoration-line: none;color:inherit'>Jonathan Campbell</a><font
color="#1a1a1a"><span style='color:#1A1A1A'> of Duke University. “It
should have been equivalence all along.” The most prominent figure in
this community is</span></font><span style='color:rgb(26, 26,
26)'> </span><a
href="https://www.ias.edu/scholars/lurie" target="_blank" style='box-sizing: border-box;
text-decoration-line: none;color:inherit'>Jacob Lurie</a><font color="#1a1a1a"><span
style='color:#1A1A1A'>. 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></font><a
href="http://www.math.harvard.edu/~mjh/" target="_blank" style='box-sizing: border-box;
text-decoration-line: none;color:inherit'>Michael Hopkins</a><font
color="#1a1a1a"><span style='color:#1A1A1A'>, a mathematician at Harvard and
Lurie’s graduate school adviser. Lurie published his first book, </span></font><a
href="https://press.princeton.edu/books/paperback/9780691140490/higher-topos-theory-am-170"
target="_blank" style='box-sizing: border-box;text-decoration-line: none;
color:inherit'><em style='box-sizing:border-box'><i><font face="Times New Roman">Higher
Topos Theory</font></i></em></a><font color="#1a1a1a"><span style='color:#1A1A1A'>,
in 2009. The 944-page volume serves as a manual for how to interpret
established areas of mathematics in the <b><span style='font-weight:bold'>new
language of “infinity categories.”</span></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></font><a
href="https://sites.math.northwestern.edu/~jnkf/" target="_blank"
style='box-sizing: border-box;text-decoration-line: none;color:inherit'>John
Francis</a><span style='color:rgb(26,
26, 26)'> </span><font
color="#1a1a1a"><span style='color:#1A1A1A'>of Northwestern University.</span></font></span></font></i><o:p></o:p></p>
</div>
<div><span style='color:rgb(26, 26,
26)'>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
<br>
<o:p></o:p></span></font></p>
</div>
</span>
<div><span style='color:rgb(26, 26,
26)'>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>So... v</span><font color="#1a1a1a"><span style='color:#1A1A1A'>ery
good point by Karl! Could new mathematical ideas provide the bio-mathematical (informational)
synthesis needed?</span></font><o:p></o:p></span></font></p>
</div>
<div><span style='color:rgb(26, 26,
26)'>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Best wishes to all,</span><o:p></o:p></span></font></p>
</div>
<div><span style='color:rgb(26, 26,
26)'>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>--Pedro<br>
<br>
<o:p></o:p></span></font></p>
</div>
</span><pre cols=72><font size=2 face="Courier New"><span style='font-size:
10.0pt'>-- <o:p></o:p></span></font></pre><pre><font size=2 face="Courier New"><span
style='font-size:10.0pt'>-------------------------------------------------<o:p></o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Pedro C. Marijuán<o:p></o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Grupo de Bioinformación / Bioinformation Group<o:p></o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'><o:p> </o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'><a
href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a><o:p></o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'><a
href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a><o:p></o:p></span></font></pre><pre><font
size=2 face="Courier New"><span style='font-size:10.0pt'>------------------------------------------------- <o:p></o:p></span></font></pre>
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