<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Mon, Jul 10, 2017 at 4:37 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"><br></div><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"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​>​</div> I don't see why calculus should work on physical<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​ ​</div>systems if space-time is discrete.<br></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">​We already know the amount of electrical charge a object has is ​discrete, and yet calculus does a excellent job approximating what the electrical field produced by that discrete charge is like. If space and time are discrete the chunks are probably at the Planck level, and that is very very small making for very very good approximations. </font></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">
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<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​></div>If infinities exist ontologically, then space-time is a continuum. In<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​ ​</div>which case classical computers would have difficulties with irrational<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​ ​</div>numbers.</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​<font size="4">I know this is a bit heretical but perhaps irrational numbers really do have a last digit. ​If the computational resources of the entire universe is insufficient to calculate the 10^100^100^100 digit of PI, and given that there are only about 10^81</font></div><font size="4"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​atoms in the observable universe that seems like a reasonable assumption, could the ​</div><span style="font-family:arial,helvetica,sans-serif">10^100^100<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​^100​</div> digit of PI<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​ even be said to exist?​</div></span></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>They will never understand what makes perfect circles perfect<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">​ ​</div>regardless if perfect circles actually exist or not.</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><font size="4">​If ​<span style="font-family:arial,sans-serif">perfect circles don't exist is there anything about them to understand?</span></font></div></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><font size="4"><span style="font-family:arial,sans-serif"><br></span></font></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><font size="4"><span style="font-family:arial,sans-serif"> John K Clark</span></font></div><div><br></div><div><br></div><div> </div></div></div></div>