32:50 - error in your math, 1 + 7 + 3 = 11, meaning the sum would not be zero. The number should be a 2. So the final answer would be reversimal (287)3.
After the recent video on Egyptian arithmetic, I have been trying to understand their fraction representation using sums of the form 2/(odd)=1/a + 1/b .. , and also the Babylonian approach which doesn't fix the positional indicator in any particular place in the representation of numbers. The p-adics certainly do seem potentially fundamental to arithmetic and to polynomial representations. This video was posted 10 years ago -- has anyone done the major project of a rigorous description of reversimal arithmetic since then? It is thrilling to see an expression of number which folds negative quantity into the expression of rational numbers! No wonder the (so-called) roots of unity are involved in the more recent work on p-adic geometry (Peter Scholze). What is the relation of p-adics to logarithms!? I think I like the sense of wonder caused by these questions and the dawning of a new realm of possibilities, which I have to intuited but in all likelihood would not have come up with on my own in pragmatic terms, as much as the joy that comes from a solid understanding of specific algorithms. Many thanks Professor! I may not be much of a mathematician, but I am a huge fan.
demonstrations.wolfram.com/GoldenIntegers/ is a demo of a p-adic value for the golden ratio. There is no 10-adic (Revercimal) representation for phi, because of the (deep) reason that 10-adic numbers have factors of zero. I was inspired to look at p-adic numbers by this vid. Thanks, njw
The first p-adic video I've seen that explains it's primary purpose; to make it easier to do calculations with repeating numbers. Thanks.
32:50 - error in your math, 1 + 7 + 3 = 11, meaning the sum would not be zero. The number should be a 2. So the final answer would be reversimal (287)3.
I just got to that point and saw the same error. So I looked through the comments to see if anyone else had noticed the same error. Et voila!
Even masters mess-up
Best teacher ever after 3 years just now i found out
Thank you this will stay for eternity
Vow. One is starting to get a feel for all the gobble-dee-gook on p-adics on wikipedia. They're just reversimals in base p. Thank-you.
Thank you very much professor! What a beautiful introduction!
Absolutely fantastic, what a service to the strange beauty or maybe beautiful strangeness of mathematics. Thank you Professor!
You are very welcome.
After the recent video on Egyptian arithmetic, I have been trying to understand their fraction representation using sums of the form 2/(odd)=1/a + 1/b .. , and also the Babylonian approach which doesn't fix the positional indicator in any particular place in the representation of numbers.
The p-adics certainly do seem potentially fundamental to arithmetic and to polynomial representations. This video was posted 10 years ago -- has anyone done the major project of a rigorous description of reversimal arithmetic since then?
It is thrilling to see an expression of number which folds negative quantity into the expression of rational numbers! No wonder the (so-called) roots of unity are involved in the more recent work on p-adic geometry (Peter Scholze).
What is the relation of p-adics to logarithms!?
I think I like the sense of wonder caused by these questions and the dawning of a new realm of possibilities, which I have to intuited but in all likelihood would not have come up with on my own in pragmatic terms, as much as the joy that comes from a solid understanding of specific algorithms.
Many thanks Professor! I may not be much of a mathematician, but I am a huge fan.
Thanks Hani!
Wow, this is really interesting. You have a wonderful teaching style!
These are really great lectures. Thanks so much.
Also great video, I much enjoyed it, thank you for posting all of these
demonstrations.wolfram.com/GoldenIntegers/
is a demo of a p-adic value for the golden ratio. There is no 10-adic (Revercimal) representation for phi, because of the (deep) reason that 10-adic numbers have factors of zero.
I was inspired to look at p-adic numbers by this vid.
Thanks, njw