“Mom, I have the feeling I’m the Ramanujan or Paul of the 21st century”.
Simon showing math magic tricks at Easter celebrations with extended family and Dad’s colleagues:
Simon: The expression of the probability that A wins includes the probability that A wins.
Me: Aren’t you getting a headache from this?
Simon: I’m used to this recursive stuff. Mathematicians sometimes actually love infinity.
Working out the odds in another coin flipping game, applying infinite series, eventually converging to two thirds:
Playing with sis:
Inspired by a Numberphile video, where Simon learned the technique to express the Fibonacci sequence in musical notes.
This weekend Simon told me he came up with this rule that if you take two denominators that make rational fractions when you divide one by those denominators and you multiply them together, you always also get a denominator that makes a rational fraction:
Note: See the update at the bottom of this post!
Simon’s game is online at: https://simon-tiger.github.io/Game_SteeringBehaviorsEvolution/SteeringBehaviours_EvolutionGame_p5/
In the videos below Simon shows how he made the game. It’s an ecosystem type of genetic algorithm (with no generations), where the organisms (autonomous steering agents) clone themselves. The autonomous steering agents evolve the behavior of eating food (green dots) and avoiding poison (red dots). Simon added two invaders into the game, one giving food and the other randomly spreading poison. The player can control the “good” invader by moving him and making new food. The goal of the game is to make the agents survive for as long as possible.
The Processing (Java) version:
The thinking behind the game (Simon explains everything at the whiteboard):
In the last video, Simon talks about his problem with the p5 element.
Evolutionary Steering Behaviors game seek algorithm part 1. DESIRED equals TARGET minus POSITION:
Evolutionary Steering Behaviors game seek algorithm part 2. STEERING equals DESIRED minus VELOCITY:
UPDATE: When Simon saw Daniel Shiffman’s comment on Slack this morning (Daniel saying Simon did a fantastic job and that he might even include Simon’s game in the next Live Stream), he sat down and applied the bind function as suggested by his older peers above – without any incentive on my behalf! And it worked! I think we’ve hit a true milestone again. Simon has this growing feeling that he’s got friends out there, his tribe, who understand and who are ready to help.
One day later: Simon had another chat with his friends on Slack and got a lot of help with the last remaining small bug in his game (the New Game button didn’t start a new game if the player had chosen to play with no timer but jumped to Game Over instead). In the video below, Simon shows how that problem got solved:
Simon told me about two butterflies trying to mate: “One is attracted to the other one and the other one is repelled from it!” He added that he’d already built a similar simulation before.
Simon talking to himself in English, lying on the floor under his desk, his chair upside down next to him: “Am I also 4D? Probably, because I live through time…”
Originally in Russian, very excited: “Mom, did you know it’s a geometrical progression? The A in the first-lined octave is 440Hz, in the second-lined octave it’s 880 Hz and in the third-lined octave – I don’t remember exactly, but how much is 880 times 2? Yes! 1760 Hz!”
Funny how, even when training some pretty straightforward (and boring) arithmetic or Dutch reading, Simon tries to introduce more complex notions like here,
the floor, ceiling and round functions while solving a simple arithmetic word problem:
and lexicographic order, while sequencing Dutch story sentences: