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<body class='hmmessage'><div dir='ltr'><p class="MsoNormal">I must clarify my position because I believe though I have
made several points, I have not explained the reason for having made them.</p><p class="MsoNormal"><br></p><p class="MsoNormal"><br></p>
<p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><!--[if !supportLists]-->1.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->Mathematics is a developing body of knowledge,
technique and application that is by no means closed at this point and cannot </p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;">be talked about as though it is a fully-known “thing”.</span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">As has been pointed out by several posters,
math has been growing and changing </span></p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;">radically in its power and scope from
Euclid, through Pythagoras, on up to Newton, Russell, Gödel, Turing, and
beyond.</span><span style="font-size: 12pt;"> </span></p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;">No doubt it shall continue to
grow as the mysteries we encounter beg to be solved and those investigating
craft stunning and </span></p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;">hitherto unknown methods that allow their depths to be
plumbed.</span></p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;"><br></span></p><p class="MsoListParagraphCxSpFirst" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><span style="font-size: 12pt;"><br></span></p>
<p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><!--[if !supportLists]-->2.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]--> I agree
that the intellectually honest individual is probably obliged to be agnostic
about the universality of mathematics </p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1">(or the existence of God) while also
allowing for a person to profess a belief that is in violation of this seemingly
forced agnosticism </p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1">for the sake of Faustian striving if nothing else.</p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p>
<p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><!--[if !supportLists]-->3.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->I do not however agree that one is likewise obliged
to be agnostic about the existence of areas of the universe that are not
subject</p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"> to mathematical understanding.</p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p>
<p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><!--[if !supportLists]-->a.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->This is because if there are such areas of the
universe, and they are not susceptible to our present set of mathematical
tools, </p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1">nor susceptible to additional mathematical concepts and techniques that
may be developed, then we shall at all times remain in the </p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1">dark about their
existence.</p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p>
<p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><!--[if !supportLists]-->b.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->If we are in the dark about their existence,
then they must have no influence over the portions of the universe that we are
aware </p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1">of, and if that is the case, I feel obliged to call their existence, “existence”.</p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p>
<p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><!--[if !supportLists]-->c.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->If however, they do have an influence over the
portions of the universe we can comprehend, experience, and probe with </p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1">mathematics,
then they themselves must be subject to comprehension through mathematics, but
perhaps mathematics that is yet to be invented.</p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p>
<p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><!--[if !supportLists]-->d.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->If some sentient being is operating in the same
universe that we are such that we might one day have interaction between</p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"> ourselves and them, then there is a means by which our understanding of the
universe through mathematics and their understanding </p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1">of the universe (through
whatever system they have developed) can be translated one into the other.</p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p><p class="MsoListParagraphCxSpMiddle" style="margin-left:1.0in;mso-add-space:
auto;text-indent:-.25in;mso-list:l0 level2 lfo1"><br></p>
<p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><!--[if !supportLists]-->4.<span style="font-size: 7pt; font-family: 'Times New Roman';">
</span><!--[endif]-->What everyone initially started talking about
was whether there was a single, correct reading to a Gene Wolfe story, which
could </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">probably best be answered “yes and no”: “yes” in that authorial intention
is a correct reading if it can be recreated from the text and </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">given the
approval of the (presumably non-mendacious) author and “no” in that text is
slippery and even where there is a distinct authorial </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">intention (not always the
case) it is prone to the interpretation of those who get hold of it (with almost
no rules that can be agreed upon to </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">govern the process). This led to the discussion of mathematics,
with the universe being the true meaning of the work, mathematics being the </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">text, and the human race as the reader.
This analogy, though obviously capable of stirring spirited debate, is a
poor one. Human language </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">is a group of
concepts that need not have any objective manifestation in the world for us to
understand them and as such, they are prone to </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">shades of meaning, words in
languages that are “untranslatable”, and imperfect and widely varying
translations when in fact they are deemed</p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1"> translatable. I am assuming based on the statements made in
this debate that everyone agrees at least that the universe itself is an
objective </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">reality and we are just debating how one is able to understand that
reality. This is the difference between
a short story or a novel and the </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">universe (not the only one I suppose). Because there is an objective ground to the study
of the universe, those who come up with different </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">ways of reaching that ground
should be capable of finding some kind of isomorphic operation to translate
from one to the other, or perhaps </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1">a synthesis of the two into something else
altogether, but which both participants in the collaboration can agree
upon. </p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p><p class="MsoListParagraphCxSpLast" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><br></p>
<p class="MsoNormal">Therefore to make my position explicit I do not believe that
we know what the full scope of mathematics is and probably never will be able </p><p class="MsoNormal">to say that we have closed it for good.
I withhold ultimate judgment on whether it is universal but proceed as
though it is because of the present </p><p class="MsoNormal">evidence and the uselessness of not making
that assumption at this point. I believe
that texts are both capable of a “correct” interpretation that is </p><p class="MsoNormal">in one-to-one
agreement with authorial intention and agree that that same text has several
other “correct” interpretations that appear in spite of </p><p class="MsoNormal">the authorial
intention. I believe that the areas of
the universe that we know nothing about and cannot understand with our brains
may as well </p><p class="MsoNormal">not exist because we can know nothing about them, they cannot
influence us, and we can do nothing with the idea except talk and write about
it </p><p class="MsoNormal">(and as Magritte and others have somewhat obviously pointed out, the symbol
is not the thing).</p> </div></body>
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