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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I’m enjoying talking about God and math and all, but it this too off-topic for this list? If so, I’ll shut up. (Like Bugs Bunny, I’m very good at shutting
up.)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">All math can be reduced to logic. As David Hilbert is reported to have said, “</span>One must be able to say at all times--instead of points, straight lines,
and planes--tables, chairs, and beer mugs.” Math can be done without any numbers. Numbers are one of the most successful applications of math. But, if you’ll permit me another quote, this time from Einstein, “As far of the laws of mathematics refer to reality,
they are not certain; and as far as they are certain, they do not refer to reality.” In other words, when you protest that the universe may not be either discrete nor continuous, you are talking about applications of mathematics, not about mathematics.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Science is only the second most reliable body of knowledge we possess.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">There is a famous article “The Unreasonable Effectiveness of Mathematics” that remarks on how astonishingly successful imperfect human beings have been in applying perfect mathematics to a recalcitrant physical universe. But to me the
question of the universality of mathematics come down to the question I asked about A implies B.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">As for math continuing to grow, that is (I’m glad to say) true. There are many conjectures that are not yet theorems. And, of course, people sometimes make mistakes. And sometimes mathematicians argue about the philosophy of mathematics,
and about whether we create mathematics or discover mathematics. But there are no mathematicians I know of who “doubt” the Pythagorean Theorem.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Rick Norwood <br>
<br>
<span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""><br>
<b>Sent:</b> Friday, October 10, 2014 11:24 AM<br>
<b>To:</b> The Urth Mailing List<br>
<b>Subject:</b> Re: (urth) barrington interview<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Actually, math *doesn't* require numbers as such. All of number theory can be reduced to set theory.<o:p></o:p></p>
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<p class="MsoNormal">On Fri, Oct 10, 2014 at 6:09 AM, Lee <<a href="mailto:severiansola@hotmail.com" target="_blank">severiansola@hotmail.com</a>> wrote:<o:p></o:p></p>
<p class="MsoNormal">>Gerry Quinn: All mathematics can be encoded entirely inside the standard arithmetic<br>
<br>
>of the natural numbers, or simple geometry on a plane.<br>
<br>
<br>
A nice summation of my point. Math requires numbers. Numbers describe the<br>
<br>
universe in terms of discrete, countable units. I find it quite possible that there<br>
<br>
are places/times in geography and history of the universe in which the concept of<br>
<br>
numbers was meaningless.<br>
<br>
<br>
"A theoretical mathematician may feel he/she is working purely in the realm of symbolic<br>
<br>
logic and reason but it cannot be so."<br>
<br>
<br>
>Brandon Fuchs: This is one of those wild statements that calls for an example. If mathematicians<br>
<br>
>are not working with symbolic logic, but merely expressing some imperfect brain mechanics.....<br>
<br>
<br>
Let's stop there. My statement was that mathematician cannot be doing PURELY symbolic logic.<br>
<br>
All thoughts within a human brain are animal thoughts with inherent animal biases installed from<br>
<br>
the material world during evolution and development. (the assumption of the validity "numbers"<br>
<br>
being one of them). Of course the human brain can work with symbolic logic. We invented it.<br>
<br>
<br>
But the suggestion that our brains can work purely with symbology with no impingement from<br>
<br>
the material world is unsupportable. There are no human brains which have been entirely shielded<br>
<br>
from the material world. (Something like Severian's Mandragora? But of course even that brain<br>
<br>
had telepathic input affecting it).<br>
<br>
<br>
>....then surely there should be some mathematical statements that different groups of<br>
<br>
>mathematicians are convinced have been demonstrated to be true, while others are convinced<br>
<br>
>they have been demonstrated to be false, and are unable to come to an agreement on the matter.<br>
<br>
<br>
Aren't there? I am not a mathematician but I was under the impression it is an evolving discipline.<br>
<br>
<br>
But even in the unlikely event that every mathematician in history were in perfect agreement on<br>
<br>
every mathematical permutation of the field, it would not demonstrate true universality. It would<br>
<br>
only demonstrate congruence among one group of people from one species on one planet.<br>
<br>
<br>
Just because a human astronomer on earth collects data from the Andromeda galaxy it does not<br>
<br>
mean they are from Andromeda or even that they have been to Andromeda. It just means<br>
<br>
data from there has been plugged into a human matrix of understanding here on earth. If an<br>
<br>
Andromedan came here using math, I would consider that evidence that math is universal. But even<br>
<br>
then, I would prefer a sample size greater than two before I'd be willing to grant the hypothesis<br>
<br>
"math is universal" anything like scientific theory status.<br>
<br>
<br>
Again, my opinion is not that math isn't universal. Only that we have no means of determining such<br>
<br>
a thing. We are stuck in the narrow perspective of one species on one planet and have no means for<br>
<br>
stepping outside it . Before I have confidence in the universality of math, I need to hear from the rest of<br>
<br>
the universe.<br>
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<p class="MsoNormal">-- <br>
Dan'l Danehy-Oakes <o:p></o:p></p>
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