# The All Common Ancestors Generation

This project is a simulation of how many people can stem from the same ancestor, something Simon has learned from James Grime’s “Every Baby is a Royal Baby” video on Numberphile. In this simplified version, there’re only 6 people per generation. Simon was throwing two dice to determine who the two parents were for every person (in the case when both dice came out to be the same number, this was considered “virgin birth” or simply that the father had come from outside the limited sample Simon was working with).

# On Incompleteness

Simon is enchanted by Gödel’s incompleteness theorem (that he has learned about from Numberphile) and keeps talking about it:

“There’re problems that we just can’t solve. But if we prove that we can’t prove them, then we prove them! We can’t prove that we can’t prove that we can’t prove, and so on… Quirky! Standard math doesn’t really accept that because the statement goes on forever: you’ll just never get to what we can’t prove. What follows from Gödel’s incompleteness theorem is that that statement is actually true!”

The same evening, Simon is also bothered about the lies pupils are told in school. He repeatedly quotes James Grime that it’s a big lie that mathematics is about numbers. — “What is mathematics about? Mathematics is actually about proving! But there’s one more lie that even professional mathematicians don’t know. It’s that it’s about logic. Actually, mathematicians are a lot more creative!”

# Simon’s little slide rule

Simon has crafted his own tiny slide rule that he carries around rolled up in an elastic band and calls his “toy”. The two strips of paper aligned together in certain ways can give answers to multiplication and division problems. Simon distributed the numbers on them according to a logarithmic scale.

# A new tour of Simon’s sketch book

The fertility formula, to predict the population the following year:

A fake number (called “Wau”) to imagine infinity (via Numberphile):

Drawing a square root of 5 (via James Grime):

Pebbling a Chessboard (via Numberphile):

Kolakoski Sequence:

Proof for probabilities in a Wythoff’s game

Probability that everyone will be eliminated simultaneously in Simon’s “Hat Game” (a card game he invented):

Finite List of Primes:

Creating consecutive numbers by using various operators to connect four fours:

# How to draw the Golden Ratio (Phi)

Simon shows how to draw a segment that is Phi times longer than a unit segment. He learned from a video by James Grime how to draw the square root of 5, and worked out the rest on his own.

# Random Field Card Trick

Simon has invented this card trick using a random field of cards and allowing him to predict nearly the whole path through the field. You can play along as a viewer and see how Simon will nearly guess your card (the card that your finger will end up on at the end of the trick), narrowing his final guess down to just a couple of cards (three in this case).

This trick is a version of Kruscal Count. Simon learned about random fields and Kruscal Count from a video by James Grime on the Singing Banana channel.

# Romantic Mobius Origami

Inspired by the videos by Matt Parker

and James Grime:

Simon also made the Borromean rings:

And cubes (which Simon now uses to practice juggling!)

# Rational vs. Irrational

Simon discusses the infinities of rational and irrational numbers, how they relate and the infinitesimal, using a mind boggling problem about a tree orchard as an example.

Inspired by a Numberphile video and by James Grime’s tutorial about infinities (also on Numberphile).

# Liva Stream #13. Math Puzzle: Logic.

In this live session, Simon works a little on his 15s puzzle redo that he started in his previous live session: https://www.youtube.com/watch?v=ixkLFYcb0T0 and programs a math/logic puzzle, checking whether the statement “Every card with a T on one side has a 3 on the other” is true or false. The original puzzle comes from an old video by James Grime, recorded before Simon was born (the fact that Simon finds particularly funny):