Simon working on his proof of the Fundamental Theorem of Arithmetic (he got stuck and then searched for existing proofs online).

# Category: Simon’s sketch book

# Computers of the Future: How Far Do We Need to Go?

How many bits will computer operation memory have and how many do we need to have to link every single particle in the Universe to the internet? And how useful are quantum computers?

# Larger than Graham’s number!

Simon explains strong and weak tree sequences and reveals the greatest finite number used in mathematics: TREE(3), a lot larger than Graham’s number. The TREE sequence is a fast-growing function arising out of graph theory.

Simon comments: “What is you make TREE(TREE(3))?”

Inspired by:

http://googology.wikia.com/wiki/TREE_sequence

https://www.youtube.com/watch?v=3P6DWAwwViU

# L-Systems

Simon loves various L-Systems, sets of rules transforming letters into geometric structures. He used to program these, this time he recreated some by hand.

# Simon differentiating 3tan(2x)

To solve the problem, Simon chooses not to look up what the derivative of a tangent is but work everything out from scratch. He generally doesn’t like rote learning but prefers to gain deep understanding of how and why.

# Electromagnetic Spectrum and the Opponent-process Theory

Simon has been fascinated about theÂ Opponent-process theory (suggesting that color perception is controlled by the activity of three opponent systems, three independent receptor types which all have opposing pairs: white and black, blue and yellow, and red and green). He has been complaining that all the papers on Opponent-process Theory he has managed to find online were too superficial.

# Graham’s Number

# Doing maths at a Parisian cafĂ©, looking for various ways to derive Pi

# Simon’s desk. 31 December 2018.

# More quantum physics: quarks hit by photons and what does a z boson do?

Simon told me about strong force and what happens to a quark inside a nucleon if a high energy photon hits it and pushes it outside the nucleon: a new quark and antiquark are created.

But what if the photon was so strong that it pushed the quark even further? It would create another quark and another antiquark.

Then Simon switched over to drawing Feynman diagrams to show how a w boson emitted by a quark or a changes that quark or lepton (charm to strange, bottom to top, electron to electron neutrino, etc.) “We don’t know what the z boson does” , Simon says. “Maybe it’s there for no reason!”