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On 2015-09-06 05:37, spike wrote:<br>
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<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span><span
style="color:#1F497D">>…</span>As one of our locals once
said, "pluralitas non est ponenda sine necessitate" - do not
add extra stuff to your theory unless you need it. But the
*kind* of stuff can be strange: extra dimensions are not
stranger than other kinds of matter or negative numbers. But
simpler, less extravagant stuff is of course always preferable<span
style="color:#1F497D">….</span>Anders Sandberg<o:p></o:p></p>
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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">Ja.
I wasn’t there when it happened, but visualize what it was
like when Heron and later Bombelli introduced the notion
of imaginary numbers. Plenty of the grumpy old professors
must have dismissed the whole idea as silliness, just some
kind of useless game. It was probably a lot like
postulating an additional dimension.</span></p>
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<br>
Indeed, *negative* numbers were regarded as problematic. As Francis
Masers said in 1759 (!), they "darken the very whole doctrines of
the equations and make dark of the things which are in their nature
excessively obvious and simple". Of course, at that point most
people were actually fine with them and Masers was one of the last
holdouts against calculus and other stupid newfangled concepts.<br>
<br>
I like calling the imaginary numbers vertical. I learned to count
using a thermometer, so negative numbers are just cold numbers
(blue) and positive numbers warm (red). Then I realized one could
count stuff to the sides of the line (windy numbers? :-)<br>
<br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University</pre>
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