Today, a long overdue foray into the realm of VORTEX MATHEMATICS :)
00:00 Intro
04:16 The vortex
08:10 The maths of remainders and digital roots
13:25 Demystifying the vortex
16:30 A matter of base. The 8 fingered Tesla.
19:21 Explanation why the digital root is the remainder on division by 9
24:01 Tristan’s challenge
24:44 The magic of modular multiplication maths
25:19 Intuition for multiplier - 1 petals
28:23 Thank You!
Coding competition:
My wish list for the modular times table diagram app:
-Being able to color line segments according to length.
-Indication of the “direction“ of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :)
-different loops in different colors.
...
Here is the prize, a copy of my and Marty’s new book.
That early Mathologer video featuring the modular times tables
Times Tables, Mandelbrot and the Heart of Mathematics
A really nice article about various ways to generate the cardioid by Dave Richeson
Nice debunking/demystifying article about vortex math by “Professor Puzzler“
For a growing pile of implementation of modular times table diagrams see my comment pinned to the top of the comment section of this video.
Simon Plouffe’s website
Articles by him relevant to this video can be found in this directory
See in particular the files
The shape of b^n mod
La forme de bn mod
What I am talking about in this video is really just the tip of a bizarre mathematical iceberg that most mathematically minded people are completely unaware of. Have a look at this presentation by Marko Rodin on vortex math (beware serious nutty and at the same time truely beautifully presented numerology ahead :) A LOT more than is usually reported on in popular YouTube videos.
In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look:
Today’s music: Aftershocks by Ardie Son
Enjoy!
Burkard
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