<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Tue, Dec 27, 2016 at 12:28 AM, Stuart LaForge </span><span dir="ltr" style="font-family:arial,sans-serif"><<a href="mailto:avant@sollegro.com" target="_blank">avant@sollegro.com</a>></span><span style="font-family:arial,sans-serif"> wrote:</span><br></div><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"></blockquote><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>This is a straw man argument. Nobody claimed the brain is an analog<br>
<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>computer. Rafal simply asked that if mathematical infinities are real,</blockquote><div><br></div><div><div class="gmail_default"><font face="arial, helvetica, sans-serif"><font size="4">Well that's the big question, are </font></font><font size="4">mathematical infinities real? I don't know, all I know is that so far nobody has found a infinite number of anything in the physical world.</font></div></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>as<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>experimental evidence supports both with regard to the reality of the wave<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>function </blockquote><div><br></div><font size="4">Schrodinger's wave is continuous but it's not something that can perform calculations or even be directly detected, to do that you need to take the square of the absolute value of the <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">wave </div>function<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> of a particle at a point </div>, and even then you only get <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">the</div> probability<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> not a certainty<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> of finding the particle at that point</div>.</font></div><div class="gmail_quote"><br></div><div class="gmail_quote"><font size="4">So maybe the wave is just a tool humans have invented to help us calculate things, like the lines of longitude and latitude are useful tools for calculating position on the Earth's surface but have no physical reality. After all Schrodinger's wave isn't the only way to calculate probabilities, Heisenberg's more abstract matrix method can do it too and was actually discovered a few months before<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Schrodinger<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>found his wave. On some problems Heisenberg's<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>method is easier to use although usually Schrodinger's<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>is more convenient,<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>but both work.</font></div><div class="gmail_quote"><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>and the lack of granularity in space-time,</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">I think most (but not all) physicists would say </font></div><font size="4">space-time<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> must be granular, and if it happens at the obvious place, the Planck level, then it's not surprising there is no experimental evidence of it. </div></font></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>then might not these<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>infinities allow the brain to generate a continuum of mental states<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>instead of finite number of discrete mental states?<br></blockquote><div><br></div><div><div class="gmail_default"><font face="arial, helvetica, sans-serif"><font size="4">A computer that can be in a </font></font><font size="4">continuum of states is the definition of an Analog computer, and by that definition nobody has ever built a true Analog computer. People stopped making sudo "Analog" computers in the 1950s, and even the best one couldn't be in as many discernible states as a $9 digital hand calculator can. </font></div></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"></blockquote><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">>> </font></div><font size="4">There are an infinite number, in fact an uncountabley infinite number,<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div><span class="gmail-">of maps that can be drawn on a flat square, but only 4 colors are needed<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">to keep all the countries on the map separate. This was proven by a<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">computer way back in 1977, but to this day nobody can prove it without<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">a computer.</span></font></blockquote>
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>No actually it was proven by some mathematicians that used a computer to<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>prove their theorem. The computer didn't even understand the problem it<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>was trying to solve.</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">And human mathematicians </font></div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">don't understand the proof the computer provided, they must just take it on faith that what the computer is telling them is true. </div></font></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Inductive reasoning seems really hard for computers<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>but seems second nature to us.</blockquote><div><br></div><div><font size="4">Inductive reasoning<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> isn't only second nature to us it's second nature to a snail too; Evolution invented it more than 500 million years ago but deductive reasoning is much more difficult, it only managed to come up with it about a million years ago. </div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div>Inductive reasoning<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> just makes use of a simple axiom to predict the future, namely "things usually, but not always, continue".</div></font></div>
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<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>During the Victorian era, when clocks and and analog pocket-watches were<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> [...]</div><br></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div><font size="4">There is no such thing as an analog pocket<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>watch<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">.</div> The hands on those watches were connected to a finite number of gears and ratchets, and those gears and ratchets<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>had teeth on them, a finite number of teeth. So the watch could only be in a finite number of states.<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> So it's not analog. </div><br><br><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>John K Clark</font></div><div><br></div><div> </div></div><br></div></div>