Re: [math-fun] Complex modulo function?
Tomas Rokicki <rokicki@gmail.com> wrote:
Can't its last digit also be 7?
No, that's the last digit of -i. :-) I did say, "Or vice versa if you prefer." The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped. In quaternions, perhaps my i, j, and k are your j, k, and i, respectively. I've long been fascinated by such symmetries, in both math and physics. How can we know whether the Peano postulates are really referring to the integers rather than to, say, sevenths? How can we be sure we haven't gotten positive and negative charges swapped? Or that what we think is an E field isn't actually a B field, and vice versa; maybe magnetic monopoles are ubiquitous, and it's electric charges that don't exist. Brian Aldiss's novel _Cryptozoic_ had the premise that we're mistaken about the direction of time, i.e. that what we think of as the future is actually the past, and vice versa. If aliens are picking up our TV signals, how can they be sure they don't have left and right swapped? Maybe they've been watching all those "I Love Lucy" broadcasts backwards, and will have to go back and watch them again the right way around.
Thanks for the helpful responses! Kerry On Sat, May 16, 2020, 10:55 AM Keith F. Lynch <kfl@keithlynch.net> wrote:
Tomas Rokicki <rokicki@gmail.com> wrote:
Can't its last digit also be 7?
No, that's the last digit of -i. :-)
I did say, "Or vice versa if you prefer."
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
In quaternions, perhaps my i, j, and k are your j, k, and i, respectively.
I've long been fascinated by such symmetries, in both math and physics. How can we know whether the Peano postulates are really referring to the integers rather than to, say, sevenths?
How can we be sure we haven't gotten positive and negative charges swapped? Or that what we think is an E field isn't actually a B field, and vice versa; maybe magnetic monopoles are ubiquitous, and it's electric charges that don't exist.
Brian Aldiss's novel _Cryptozoic_ had the premise that we're mistaken about the direction of time, i.e. that what we think of as the future is actually the past, and vice versa.
If aliens are picking up our TV signals, how can they be sure they don't have left and right swapped? Maybe they've been watching all those "I Love Lucy" broadcasts backwards, and will have to go back and watch them again the right way around.
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Note that what is "E" and what is "B" depends on your reference frame. That is why it is called "electromagnetism" Maxwell's equations were fully relativistic before Relativity--in fact, were the motivation for the thought experiments that led to Relativity. --R On Sat, May 16, 2020 at 2:19 PM Keith F. Lynch <kfl@keithlynch.net> wrote:
Tomas Rokicki <rokicki@gmail.com> wrote:
Can't its last digit also be 7?
No, that's the last digit of -i. :-)
I did say, "Or vice versa if you prefer."
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
In quaternions, perhaps my i, j, and k are your j, k, and i, respectively.
I've long been fascinated by such symmetries, in both math and physics. How can we know whether the Peano postulates are really referring to the integers rather than to, say, sevenths?
How can we be sure we haven't gotten positive and negative charges swapped? Or that what we think is an E field isn't actually a B field, and vice versa; maybe magnetic monopoles are ubiquitous, and it's electric charges that don't exist.
Brian Aldiss's novel _Cryptozoic_ had the premise that we're mistaken about the direction of time, i.e. that what we think of as the future is actually the past, and vice versa.
If aliens are picking up our TV signals, how can they be sure they don't have left and right swapped? Maybe they've been watching all those "I Love Lucy" broadcasts backwards, and will have to go back and watch them again the right way around.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On May 16, 2020, at 1:54 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
I’m curious, what’s the *first* thing? It’s actually very cool that the Galois automorphism i <-> -i is co-opted by physics in the time-reversal transformation. The real numbers turned out to be incomplete in a very real sense! -Veit
The first thing people ask (I think) is “What is i?” But this question actually has many shades of meaning. It takes on extra piquancy after one realizes that the definition of i as the square root of -1 doesn’t distinguish i from -i, and that this ambiguity undermines the use of the word “the” in the definition. So I think one natural sequence of questions is “What is i?” “Okay, but what is i, really?” “How can we tell i from -i?” “How do I know that my i isn’t your -i?” “Wait a minute, so what is i again?” Jim Propp On Tue, May 19, 2020 at 8:55 AM Veit Elser <ve10@cornell.edu> wrote:
On May 16, 2020, at 1:54 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
I’m curious, what’s the *first* thing?
It’s actually very cool that the Galois automorphism i <-> -i is co-opted by physics in the time-reversal transformation. The real numbers turned out to be incomplete in a very real sense!
-Veit _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
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James Propp -
Keith F. Lynch -
Kerry Mitchell -
Richard Howard -
Veit Elser