This is where folk tales are wonderful. Out of all the complex clutter of daily life among all the different people, they recognize a big question and put a marker on it by wrapping it in a small story or metaphor, which turns out to have staying power as a meme, because it resonated with what really was a big question.
Are the Celts (or even more specifically, the Irish?) the only ethnicity that had a specific meme equivalent to a pot of gold at the end of the rainbow? Or did it convergently evolve in several cultures?
> On Aug 4, 2020, at 2:02 AM, uǝlƃ ↙↙↙ <
[hidden email]> wrote:
>
>
> I know I've posted this before. I don't remember it getting any traction with y'all. But it's relevant to my struggles with beliefs in potential vs actual infinity:
>
> Belief in the Sinularity is Fideistic
>
https://link.springer.com/chapter/10.1007%2F978-3-642-32560-1_19>
> Not unrelated, I've often been a fan of trying identify *where* an argument goes wrong. And because this post mentions not only 1/0, but Isabelle, Coq [⛧], Idris, and Agda, I figured it might be a good follow-up to our modeling discussion on Friday, including my predisposition against upper ontologies.
>
> 1/0 = 0
>
https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.hillelwayne.com%2fpost%2fdivide-by-zero%2f&c=E,1,JxsXytueRHA0GCfR0UOa_3uDRb1upQSgWOk-Xn9W0El902gHmLp9YG0abXsverWIfnV9N-7WHZnF5x4UojpbFdwztwOiAwefuhlrHNfbWDzzwCA,&typo=1>
> Here's the (really uninformative!) SMMRY L7:
>
https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fsmmry.com%2fhttps%3a%2f%2fwww.hillelwayne.com%2fpost%2fdivide-by-zero%2f%23%26SM_LENGTH%3d7&c=E,1,ojb4vUe5aPs24YNNGQSrZVPwWP0D69QletaevbLEpj0OxdCjjavwpY9GtAJu5a2Mc1d5Sv4p18nm2y0FjBAFLDAm8jUY5swj5w4XCY72UHrz&typo=1>> Since 1 0, there is no multiplicative inverse of 0⁻. Okay, now we can talk about division in the reals.
>>
>> So what's -1 * π? How do you sum up something times? While it would be nice if division didn't have any "Oddness" to it, we can't guarantee that without kneecapping mathematics.
>>
>> We'll define division as follows: IF b = 0 THEN a/b = 1 ELSE a/b = a * b⁻.
>>
>> Doing so is mathematically consistent, because under this definition of division you can't take 1/0 = 1 and prove something false.
>>
>> The problem is in step: our division theorem is only valid for c 0, so you can't go from 1/0 * 0 to 1 * 0/0. The "Denominator is nonzero" clause prevents us from taking our definition and reaching this contradiction.
>>
>> Under this definition of division step in the counterargument above is now valid: we can say that 1/0 * 0 = 1 * 0/0. However, in step we say that 0/0 = 1.
>>
>> Ab = cb => a = c but with division by zero we have 1 * 0 = 2 * 0 => 1 = 2.
>
>
>
> [⛧] I decided awhile back to focus on Coq because it seems to have libraries of theorems for a large body of standard math. But still NOT having explored it much, yet learning some meta-stuff surrounding the domain(s), I'm really leaning toward Isabelle. I suppose, in the end, I won't learn to use any of it, except to pretend like I know what I'm talking about down at the pub.
>
> --
> ↙↙↙ uǝlƃ
>
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