Featuring Neil Sloane from the Online Encyclopedia of Integer Sequences (OEIS). Lunar Arithmetic (aka Dismal Arithmetic)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the OEIS: https://oeis.org
Lunar Primes: https://oeis.org/A087097
Lunar Squares: https://oeis.org/A087019
The original paper on lunar arithmetic (formerly dismal arithmetic) by David Applegate, Marc LeBrun, and Neil Sloane: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf
Sloane's Gap: https://youtu.be/_YysNM2JoFo
Six Sequences: https://youtu.be/VDD6FDhKCYA
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As expected many people ask "what is the point of this"... And fair enough.
Rather than answering everyone individually, here is my view (I am just the film-maker, not a mathematician)
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope not!!!)... But neither is it just throwing ALL rules out of the window... It is creating a new arbitrary set of rules and seeing what happens...
What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
And if you think this is just child's play - read the paper: https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.pdf