Erwin Marquit: Engels is not arguing that imaginary numbers should not be used. He is arguing against their mystification. In my view, the complex plane (real and imaginary axes) has a one-to-one correspondence with a two-dimensional vector space, so their logical structure is identical, which is why the complex plane can be used for
mathematical derivations of the properties of physically real systems, Erwin ^^^ CB: Exactly ! Demystification came to me this morning as I was thinking about this The book you have at Marxist Educational Press is _Marx demystifies calculus_ On Jan 14 2009, Charles Brown wrote: >Erwin, > > >Do you have any response to the below ? > >Charles > >Natural Science and the Spirit World[1] > > > -------------------------------------------------------------------------------- > >To: a-l...@xxxxxxxxxxxxxxxxxxx >Subject: Re: [A-List] Natural Science and the Spirit World[1] >From: Jim Farmelant <farmela...@xxxxxxxx> >Date: Mon, 12 Jan 2009 19:15:50 -0500 > > > -------------------------------------------------------------------------------- >ï > > >On Mon, 12 Jan 2009 14:34:47 -0300 Nestor Gorojovsky <nmg...@xxxxxxxxx> >writes: >> Dear friend and comrade Jim Farmelant: >> >> I am afraid that Engels did not poke fun, as you say, at >> multidimensional spaces or imaginary numbers themselves, but at >> their >> usage as a "proof" that there exists Another World. >> >> In this sense, you are unfair with him. > >The way I read Engels's essay, he did indeed make >fun of imaginary numbers in the following passage: > >"It is the same with mathematics. The ordinary metaphysical >mathematicians boast with enormous pride of the absolute >irrefutability >of the results of their science. But these results include also >imaginary magnitudes, which thereby acquire a certain reality. When >one >has once become accustomed to ascribe some kind of reality outside of >our minds to v-1, or to the fourth dimension, then it is not a matter >of >much importance if one goes a step further and also accepts the spirit >world of the mediums. It is as Ketteler said about DÃllinger[7]: âThe >man has defended so much nonsense in his life, he really could have >accepted infallibility into the bargain!â " > >As I said before, Engels's grasp of mathematics left something >to be desired (Marx, on the other hand, seems to have had >a better handle on that subject including what were then >the latest developments in the foundations of the calculus). >Having said that, Engels did have a very exceptionable >grasp of the natural sciences of his time, such that >the Harvard philosopher of science, Hilary Putnam, >used to call Engels the "most learned man of the nineteenth century." > > >Certainly, one of the other essays included in *The Dialectics >of Nature*,"The Part Played by Labor in the Transition from Ape to >Man," >is deservedly revered as a work of genius, despite the fact that >Engels >cast his reasoning in Lamarckian terms. > >Stephen Jay Gould in his book, *Ever Since Darwin*, wrote: > >"Indeed, the nineteenth century produced a brilliant exposà from a >source >that will no doubt surprise most readers - Frederick Engels. (A bit of >reflection should diminish surprise. Engels had a keen interest in the >natural sciences and sought to base his general philosophy of >dialectical >materialism upon a 'positive' foundation. He did not live to complete >his >'dialectics of nature', but he included long commentaries on science >in >such treatises as the Anti-DÃhring.) In 1876, Engels wrote an essay >entitled, The Part Played by Labour in the Transition from Ape to Man. >It >was published posthumously in 1896 and, unfortunately, had no visible >impact upon Western science. > >"Engels considers three essential features of human evolution: speech, >a >large brain, and upright posture. He argues that the first step must >have >been a descent from the trees with subsequent evolution to upright >posture y our ground-dwelling ancestors. 'These apes when moving >on level ground began to drop the habit of using their hands and to >adopt a more and more erect gait. This was the decisive step in the >transition from ape to man.'" > >"Upright posture freed the hand for using tools (labour, in Engels' >terminology); increased intelligence and speech came later." > > >> As to his critique of empyricism, I will read HumeÂs essay and >> answer later. >> >> EngelsÂs criticism was that without rising to dialectics and what >> the >> empyricists consider "metaphisical nonsense", it is not possible to >> dismiss paranormal phenomena. Witness, in this sense, the fSU and >> the >> permanent resurgence of "scientists" who tried to grasp that >> paranormal >> behavior. This may well be one of the most important pointers to the > >> >> abstract and utilitary role that "Diamat", that is the barbarized >> and >> schematic "dialectical materialism" that was taught there, played in > >> the >> self-defined "Marxist" discourse of the USSR. >> >> But canÂt go ahead without reading Hume. >> >> farmela...@xxxxxxxx escribiÃ: >> > Engels was, course, quite right to debunk belief >> > in ghosts and mediums. In fact there were some >> > political reasons behind this. At the time that >> > Engels wrote this, spiritualism was quite popular >> > within the IWMA, especially in the US and UK. >> > In the US, one of the leading figures in the IWMA, >> > Victoria Woodhull, was also a famous medium, whom >> > both Marx & Engels very much disapproved of (perhaps >> > unfairly). >> > >> > On the other hand, it should also be pointed out that >> > Engels does go off the rails on a few points in his >> > essay. Engels poked fun of the idea of a fourth >> > dimension. But even in his day, n-dimensional >> > geometries were already quite well established >> > and respectable. Later on, physicists like >> > Albert Einstein would show that such geometries >> > could be useful for understanding aspects of >> > physical reality. Engels poked fun of the notion >> > of imaginary numbers, that is numbers that were >> > derived from the square root of -1. But both >> > imaginary numbers and complex numbers were already, >> > in Engels's time, a quite respectable part of >> > mathematics. And physicists and engineers were >> > already using them in analyzing such things as >> > wave phenomena, for instance. >> > >> > While Engels generally had a good grasp of the >> > science of his day, he was behind the times in >> > his understanding of mathematics (he was also >> > deficient in his understanding of the latest >> > work on the foundations of the calculus) >> > and that led him to making a few whoppers >> > in his writings. >> > >> > His assertion that empiricism was lacking >> > the intellectual resources for battling >> > belief in the paranormal is open to question too. >> > Probably the most important critique of belief >> > in miracles ever written was David Hume's >> > essay, "Of Miracles," >> > (http://www.bartleby.com/37/3/14.html). >> > Hume, of course, was an empiricist philosopher. >> > If Engels wished to show the inadequacies of >> > empiricism as a basis for refuting the paranormal, >> > then he should have discussed Hume's essay and >> > showed where Hume went wrong. >> > >> > Jim Farmelant >> > >> > -- "Charles Brown" <charl...@xxxxxxxxxxxxxxxxxxxxx> wrote: >> > Engelsâ Dialectics of Nature >> > http://www.marxists.org/archive/marx/works/1883/don/ch10.htm >> > Natural Science and the Spirit World[1] >> > T >> > >> > _______________________________________ > > > > > This message has been scanned for malware by SurfControl plc. > www.surfcontrol.com _______________________________________________ Marxism-Thaxis mailing list Marxism-Thaxis@lists.econ.utah.edu To change your options or unsubscribe go to: http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
