When I read a “historical introduction” in a physics textbook there are almost always significant deviations from the actual history. When physics authors write a “historical introduction” they always end up doing the very thing that Mark Twain described. Human memory is fallible human memory is prone to restructuring memories to suit the belief system. It is the job of journalists and historians to correct that.” “In the real world, nothing happens at the right place at the right time. There is a quip by Mark Twain that goes as follows: It’s just: the true history of complex numbers is totally *not* the story to illustrate that. Now, I share the concept of child-like openness that Frenkel professes. Then he enthousiastically gives the Cardano-centered version of the story of complex numbers to illustrate his belief. Over time mathematicians came to see the root of a negative number something on par with other mathematical concepts.įrenkel comes to the story of complex numbers from musings of how important it is to retain a child-like willingness to consider things that appear to make no sense.
Over several generations of mathematicians there was a gradual lessening of suspicion. I infer that at that stage the root of a negative number was admitted, but only in cases where it is seen to drop out of the calculuation. Bombelli noticed that if you allow that root of negative number then there in the cases with obvious root that factor subsequently drops out of the calculation, and then it all works out. There are cubic equations that obviously do have a root, but the Cardano formula involves the root of a negative number. While Cardano’s contribution is vital, it is historically wrong to attribute complex numbers to Cardano. According to Merion Cardano avoided the class of cases that would involve considering the square root of a negative number.
‘A Short History of Complex Numbers’ Author: Orlando MerinoĬardano’s contribution to the overall history consisted of developing a systematic method for finding the roots of cubic equations. My information source for the story of complex numbers:
Generally, what tends to happen in physics/mathematics is this: there is a concept that has many contributors, and as succesive authors retell the story, relying on old memory only, the attribution gets shifted more and more to one persion. (It’s not necessarily the case that Frenkel is at fault there it may be that that is how the story had come to Frenkel.) The version of the story of complex numbers that Edward Frenkel gives is historically incorrect, and significantly so.
0 kommentar(er)
