<div dir="auto">The last thing Doug said to me on Facebook was, "Growing old gracefully is an oxymoron."<div dir="auto"><br></div><div dir="auto">Sorry about the munged part of the constructivist proof. It looked fine in my mail client when I sent it.</div><div dir="auto"><br></div><div dir="auto">By the way, who was evicted for non-payment of rent? I lost the context.</div><div dir="auto"><br></div><div dir="auto">Frank</div><div dir="auto"><br><br><div data-smartmail="gmail_signature" dir="auto">---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, May 21, 2020, 12:17 PM Steve Smith <<a href="mailto:sasmyth@swcp.com">sasmyth@swcp.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<p>Frank -<br>
</p>
<blockquote type="cite">
<div dir="ltr">Clinicians often call that "being oppositional". <br>
</div>
</blockquote>
<p>I think "oppositional" is one *motive* for contrarianism, and
maybe contrarianism is one *mode* of being oppositional? I'm far
from up on the clinical definitions, and my own *contrarianism*
tends toward nitpicking and hairsplitting (this is an example of
that?), for what *I perceive* to be removing minor occlusions
incurred by the specific point of view that a specific word
(especially drawn from a highly specialized lexicon like DSM2?)
creates. <br>
</p>
<p>I don't remember if you were actively tracking/participating
"back in the day" when Doug was (hyper?) active here and his last
words were (probably paraphrasing mildly but I hope capturing the
essence) "Glen, you can be SUCH an a****** sometimes!" which
shocked but did not surprise me. (these were, I'm pretty sure
literally his last words on the list, but not his last words in
life, which I hope I can get out of Ingrun someday, though it will
probably involve sharing a full bottle of scotch... a taste all
three of us shared, but with differing levels of quality/price
amongst us... anecdotes abound). <br>
</p>
<p>Back to the anecdote at hand... *I* didn't find whatever Glen
had said (it is all in the record but I have a sort of
anti-nostalgia that keeps me from digging it out) as him "being an
a*******" but rather simply being *contrarian*.... Doug (IMO)
was generally pretty *oppositional* himself (if my read on the
term is at all appropriate) so Glen's contrarian style (which is
only one of his modes) was received by Doug *as* oppositional (in
the extreme?). *I* thought Glen was just sparring with Doug in
the mode I think he spars with everyone here from time to time. I
didn't get the word for some weeks after that incident, but it was
Ingrun who shut down his FriAM access (not literally). She put
her German foot down that Doug had "done his time" with his LANL
Blogs which were probably more of an outlet than an irritation. I
don't know what she threatened him with, but I'm sure it was the
same tone of voice I'd heard more than a few times, and it started
with a slightly elevated in volume, but pitched slightly lower in
tone "Douglas! .... " He went back to gaming the stock market,
talking to his birds and cats, gathering peacock feathers from
their property in Nambe, having his knees replaced, riding his
motorcycle, playing Sax with one or two bands in town, and rigging
up media servers from Raspberry Pis.<br>
</p>
<p>FriAM was definitely a source of morbid (irritation) fascination
for Doug, from our private conversations... It is definitely a
morbid fascination for me as well, but not particularly irritating
nor frustrating (with a few very minor/fleeting exceptions). I
never learned to play well with others as a child (or a teen)...
I learned to move semi-fluidly between cliques and "pass" in most
of them if needed, but I almost always had to either minimize my
engagement or eventually "fire myself" from the clique because I
could feel the cognitive dissonance/mismatch. My cohorts through
12th grade probably remember me as a mildly "odd duck" but not to
the extreme some of you here probably find me. Here, I trust
that most can (and do) simply click <next> or <delete>
and that a few choose to skim, while others find a germ of
interest if not truth in my ramblings. For the more
sophisticated, there are mailtools that would automatically route
me to a spam (or similar) folder.<br>
</p>
<blockquote type="cite">
<div dir="ltr">
<div>You say that I've known authorities. I was just talking to
John Baez about my advisor Errett Bishop, often called the
inventor of constructive mathematics</div>
</div>
</blockquote>
One of the great boons of this list for me is to flesh out (in my
mind) the intellectual/social networks of influence that impinge
here. You and I have shared our "Erdos" numbers which I understand
to be nearly irrelevant by many measures, but nevertheless "of
interest" in *this* regard. Your Erdos number of 1 (as his
habitual bouncer from the UCB library in grad school?) is similar to
a friend of mine whose Bacon number is 1 because his old pickup
truck was enlisted on-set for the bad SciFi movie "Worms", and
Bacon's stunt double wasn't on set (and Kevin couldn't drive stick)
when the director was ready to film the scene, so my friend
*played* Bacons character for a few seconds as his old pickup
careened through a scene. I in turn "stood in" in a play my
friend's wife wrote and directed in which he *also* stood in while
trying to develop it as a film. I believe the film *was* finally
made (not a major release or even screened at any indie festivals
except maybe here in SF) so when pressed I like to claim a Bacon
number of 2 (thin as it is).<br>
<blockquote type="cite">
<div dir="ltr">
<div>. Here is a constructive proof, with no use of the
excluded middle, of the irrationality of sqrt(2) that I found
in Wikipedia. Apologies to those who don't care:</div>
<div><br>
</div>
<div>
<p style="margin:0.5em 0px;color:rgb(32,33,34);font-family:sans-serif"><font size="1">In a constructive approach, one distinguishes
between on the one hand not being rational, and on the
other hand being irrational (i.e., being quantifiably
apart from every rational), the latter being a stronger
property. Given positive integers <span><i>a</i></span> and <span><i>b</i></span>,
because the <a href="https://en.wikipedia.org/wiki/Singly_and_doubly_even#Definitions" title="Singly and doubly even" style="text-decoration-line:none;color:rgb(11,0,128);background:none" target="_blank" rel="noreferrer">valuation</a> (i.e., highest
power of 2 dividing a number) of <span>2<i>b</i><sup style="line-height:1">2</sup></span> is odd, while the
valuation of <span><i>a</i><sup style="line-height:1">2</sup></span> is even, they
must be distinct integers; thus <span>|<span style="padding-left:0.1em;padding-right:0.1em">2<i>b</i><sup style="line-height:1">2</sup> − <i>a</i><sup style="line-height:1">2</sup></span>| ≥ 1</span>.
Then<sup id="m_-5159135418316031714gmail-cite_ref-17" style="line-height:1;unicode-bidi:isolate;white-space:nowrap"><a href="https://en.wikipedia.org/wiki/Square_root_of_2#cite_note-17" style="text-decoration-line:none;color:rgb(11,0,128);background:none" target="_blank" rel="noreferrer">[17]</a></sup></font></p>
<dl style="margin-top:0.2em;margin-bottom:0.5em;color:rgb(32,33,34);font-family:sans-serif">
<dd style="margin-left:1.6em;margin-bottom:0.1em;margin-right:0px"><span><font size="1"><span style="display:none;overflow:hidden;width:1px;height:1px;opacity:0">{\displaystyle
\left|{\sqrt {2}}-{\frac {a}{b}}\right|={\frac
{|2b^{2}-a^{2}|}{b^{2}\left({\sqrt {2}}+{\frac
{a}{b}}\right)}}\geq {\frac {1}{b^{2}\left({\sqrt
{2}}+{\frac {a}{b}}\right)}}\geq {\frac
{1}{3b^{2}}},}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/641b9e87f603636755874eee6c5d85875f907483" alt="{\displaystyle \left|{\sqrt {2}}-{\frac
{a}{b}}\right|={\frac
{|2b^{2}-a^{2}|}{b^{2}\left({\sqrt {2}}+{\frac
{a}{b}}\right)}}\geq {\frac {1}{b^{2}\left({\sqrt
{2}}+{\frac {a}{b}}\right)}}\geq {\frac
{1}{3b^{2}}},}" style="border:0px;vertical-align:-4.505ex;display:inline-block;width:50.681ex;height:8.509ex"></font></span></dd>
</dl>
<p style="margin:0.5em 0px;color:rgb(32,33,34);font-family:sans-serif"><font size="1">the latter inequality being true because it is
assumed that <span><span style="display:inline-block;vertical-align:-0.5em;text-align:center"><span style="display:block;line-height:1em;margin:0px 0.1em"><i>a</i></span><span style="width:1px;height:1px;overflow:hidden">/</span><span style="display:block;line-height:1em;margin:0px 0.1em;border-top:1px solid"><i>b</i></span></span> ≤
3 − <span>√<span style="border-top:1px solid;padding:0px 0.1em">2</span></span></span> (otherwise
the quantitative apartness can be trivially established).
This gives a lower bound of <span><span style="display:inline-block;vertical-align:-0.5em;text-align:center"><span style="display:block;line-height:1em;margin:0px 0.1em">1</span><span style="width:1px;height:1px;overflow:hidden">/</span><span style="display:block;line-height:1em;margin:0px 0.1em;border-top:1px solid">3<i>b</i><sup style="line-height:1">2</sup></span></span></span> for
the difference <span>|<span style="padding-left:0.1em;padding-right:0.1em"><span>√<span style="border-top:1px solid;padding:0px 0.1em">2</span></span> − <span style="display:inline-block;vertical-align:-0.5em;text-align:center"><span style="display:block;line-height:1em;margin:0px 0.1em"><i>a</i></span><span style="width:1px;height:1px;overflow:hidden">/</span><span style="display:block;line-height:1em;margin:0px 0.1em;border-top:1px solid"><i>b</i></span></span></span>|</span>,
yielding a direct proof of irrationality not relying on
the <a href="https://en.wikipedia.org/wiki/Law_of_excluded_middle" title="Law of excluded middle" style="text-decoration-line:none;color:rgb(11,0,128);background:none" target="_blank" rel="noreferrer">law of excluded middle</a>; see <a href="https://en.wikipedia.org/wiki/Errett_Bishop" title="Errett Bishop" style="text-decoration-line:none;color:rgb(11,0,128);background:none" target="_blank" rel="noreferrer">Errett Bishop</a> (1985, p. 18).
This proof constructively exhibits a discrepancy between <span><span>√<span style="border-top:1px solid;padding:0px 0.1em">2</span></span></span> and
any rational.</font></p>
</div>
</div>
</blockquote>
<p>This is the chewy nougat of FriAM for me... stuff outside my
specific interest but within the liminal boundaries of my ken
otherwise. <br>
</p>
<p>I don't read FriAM because it feeds the things I am most
interested in, I read it because it expands the things I am
interested in (or reminds me of things I forgot I was interested
in). <br>
</p>
<p>- Sieve<br>
</p>
</div>
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