tag:blogger.com,1999:blog-264226589944705290.post630236785205435305..comments2021-12-14T05:53:12.175-08:00Comments on God Plays Dice: Worms doing calculus?Michael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-264226589944705290.post-91072514777854997812008-08-07T01:00:00.000-07:002008-08-07T01:00:00.000-07:00Saying "worms do calculus to find food" seems a bi...<EM>Saying "worms do calculus to find food" seems a bit disingenuous to me, though."</EM><BR/><BR/>Perhaps the above statement is too "harsh." I think that when we use calculus to model any phenomenon, we don't assume or imply that the phenomenon somehow "obeys" the laws of calculus; it only means that the phenomenon <EM>allows</EM> or <EM>permits</EM> itself to be modeled by calculus.<BR/> <BR/>Maybe the worms use their own "internal calculus" (perhaps honed by millions of years of evolution) which gives results identical or similar to the ones obtained by using the calculus we are so accustomed to.<BR/><BR/>Anyway, I guess the larger point that I am trying to make is that calculus is an approximation tool! This is discussed by Alexandre Borovik in his post, titled <A HREF="http://dialinf.wordpress.com/2007/12/17/commented-out/" REL="nofollow">Commented Out</A> (which sounds a bit unusual!) in which he makes a methodological point about calculus:<BR/><BR/><EM>"Vladimir Arnold forcefully stated in one of his books that it is wrong to think about finite difference equations as approximations of differential equations. It is the differential equation which approximates finite difference laws of physics; it is the result of taking an asymptotic limit at zero. Being an approximation, it is easier to solve and study."</EM><BR/><BR/>To conclude, the worms in their search for food are perhaps using some kind of mechanism, which can be modeled quite well by our approximation tool, <EM>viz.</EM>calculus!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-89088222487661306292008-08-06T23:07:00.000-07:002008-08-06T23:07:00.000-07:00"Apparently this first appeared in blogs a couple ..."Apparently this first appeared in blogs a couple weeks ago..."<BR/><BR/>You got that <A HREF="http://rocksteg.blogspot.com/2008/07/complete-invalids-guide-to-calculus.html" REL="nofollow">right!</A><BR/><BR/>:D<BR/><BR/>It's too great of a story to let alone!Rocket Stegosaurushttps://www.blogger.com/profile/18392640284912482674noreply@blogger.com