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<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Dear All,</span><span lang="EN-US" style="font-family:"Avenir Book""><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">What a fitting conclusion to our current discussion on formal systems and beyond, which also opens up new questions. Below is my interpretation of the assertions made.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Lou's made the following two fundamental claims:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Mathematics does not rely solely on formal systems; it is propelled by the pursuit of unsolved problems.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Science transcends formal procedures; it is driven by our inquiries about the world.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Markus’s reading of the above differentiates between two modes of knowledge production, normal science vs. paradigm shifts.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">During the paradigm shift:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">The advancement of mathematics does not rely solely on formal systems; it is propelled by the pursuit of unsolved problems.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">The progression of science transcends formal procedures; it is driven by our inquiries about the world.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">During the period of “normal science”, some form of formal system seems to apply.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">It appears that these fields in their standard modes assimilate historical paradigm shifts, weaving them into a fabric of formal systems.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Some problems, or questions about the world that remain unanswered by normal science, require new approaches and lead to the development of new formalisms.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">In the transitional phase from an established system to a new one, no single formal system can encapsulate both. They coexist. Like Einstein's theory of general relativity, and Newton's
law of universal gravitation.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">The history of the concept of force in physics is quite interesting
<a href="https://urldefense.com/v3/__https://en.wikipedia.org/wiki/Force__;!!D9dNQwwGXtA!RsqQdNq3h61D7dpfdBx3YnucK8szGlKENYPC-gfa5RURSNGermLOgxDUxjMkKjvXgkSz9tVE1MEbSKXUHIJcToJsjXFLPg$">https://en.wikipedia.org/wiki/Force</a>.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Could it be that conceptual changes integrate shifts in perspective, providing an impression of continuity?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Marcus suggests 'information' as a concept that goes beyond the "normal science" and “paradigm shifts” transcending scientific and formal domains, in normal science and paradigm shifts.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">It is conceivable that the transition to a language of information might constitute such a paradigm shift in itself, as it brings a new dimension of an observer in the picture of knowledge,
as information is always relative to an observer. „Everything said is said by an observer.“, Maturana H. R.*
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<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">Gordana<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Avenir Book"">*In: Thompson W. I. (ed.) (1987) Gaia: A way of knowing. Lindisfarne Press, New York: 65–82.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-family:"Calibri",sans-serif;color:black">From:
</span></b><span style="font-family:"Calibri",sans-serif;color:black">Fis <fis-bounces@listas.unizar.es> on behalf of Marcus Abundis <55mrcs@gmail.com><br>
<b>Date: </b>Tuesday, 27 February 2024 at 06:22<br>
<b>To: </b>Louis Kauffman <loukau@gmail.com><br>
<b>Cc: </b>fis <fis@listas.unizar.es><br>
<b>Subject: </b>Re: [Fis] "express matter and energy in terms of information"<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt">Interesting points . . . what I think I see reflected in recent posts (Alex, Pedro, Karl, Joe, and Louis) is that Material Reality holds two key 'formal aspects'.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt">First is the REGULAR FUNCTIONING that sustains most daily events (viewed via conventional 'science').<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt">Second is the ADAPTIVE LOGIC (creativity) needed to contend with eternal dynamism that arises as an aggregate effect (*shifting* simple-to-complex reality) of the first.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt">Differences between the two leave us with an unreconciled 'psychological problem'—where *currently* science is our best way of depicting (consistently measurable-and-repeatable) 'most set things'.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt">But creativity differently holds rather ambiguous 'shifting things', and demands another means of presentation. Related, a truly complete INFORMATIC presentation must hold both, equally, while also detailing
interrelations (a de facto 3rd aspect).<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt">My earlier post to Krassimir in 'defining information' frames only the first aspect, via generic terms O-S-O (regular functioning). But not covered in mx post to Krassimir is my framing of S-O-v (adaptive
logic, creativity), and shifting functional degrees of freedom (DoF) to map FUNCTIONAL TRANSITIONS (which Krassimir tries to address in GIT?). Interestingly, all three roles are partly covered by Signal Entropy's logarithmic base (X^n), if viewed from the
right 'meaningful' perspective.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt">Lastly, this psychological problem is perpetuated by the silo effect of current disciplines. For example, even just within the area of Physics . . .
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt">I have found that if I try to speak to someone about four fundamental forces of the Standard Model—they want to respond with a discussion of Newtonian physics and F=MA, which leads nowhere.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:18.0pt">Marcus<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Tue, Feb 27, 2024 at 4:15<span style="font-family:"Arial",sans-serif"> </span>AM Louis Kauffman <<a href="mailto:loukau@gmail.com">loukau@gmail.com</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal">Excellent Karl. <o:p></o:p></p>
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<p class="MsoNormal">Thank you.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">The point about good theorems about limitations is that they show us exactly what produces the limitations. <o:p></o:p></p>
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<p class="MsoNormal">Thus if you insist on using one formal system and it is consistent and can do arithmetic, then it is definitely incomplete.<o:p></o:p></p>
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<p class="MsoNormal">We can actually see how this happens. But that does not mean that we are limited. We are limited if we insist on one system.<o:p></o:p></p>
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<p class="MsoNormal">We are not limited in the Goedelian way if we are evolving new systems over time. That is in fact what mathematics does.<o:p></o:p></p>
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<p class="MsoNormal">No one has proved that there are utterly unsolvable problems, just that if you insist on living in a box then you will not be able to see what is outside <o:p></o:p></p>
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<p class="MsoNormal">the box. And remarkably, we find very challenging problems that push us to find out how we are boxed and push us to get out of that box.<o:p></o:p></p>
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<p class="MsoNormal">The problems come both from within mathematics (like Riemann Hypothesis or Collatz problem) and from outside mathematics (like the problem of understanding biology, or the problem of unifying gravity and quantum theory). Mathematics is
not based on formal systems. Mathematics is based on unsolved problems.<o:p></o:p></p>
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<p class="MsoNormal">Science is not based on formal procedures. Science is based on our questions about the world.<o:p></o:p></p>
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<p class="MsoNormal">Best,<o:p></o:p></p>
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<p class="MsoNormal">Lou<o:p></o:p></p>
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