Here’s a game I’ve been trying to make for a while.
For a while I’ve had a hunch that there’s fun to be had in moving between numbers by using something related to the prime numbers.
Over the years I’ve tried out a few different ideas, but none of them ever worked out – they were either too easy, too hard, or just not interesting. This time, I think I’ve found something close enough to the sweet spot that I’m happy to publish it.
Prime Run is a game about adding and subtracting prime numbers. You start at a random number, with a random target. Your goal is to reach the target, by adding or removing any prime factor of your current number.
A while ago I made myself a calculator. I don’t know if anyone else uses it, but for the particular way I like doing calculations, it’s been really good. You’d think that if a calculator does anything, it should perform calculations correctly. But all calculators get things wrong sometimes! This is the story of how I made my calculator a bit more correct, using constructive real arithmetic.
One thing you need to think about when making a calculator is precision. How precise do the answers need to be? Is it OK to do rounding? If you do round, then it’s possible that errors accumulate as you compose operations.
I’ve always wanted to make a calculator that gives exactly correct answers. This isn’t strictly possible: there are more real numbers than a finite number of bits of memory can represent, or a digital display can show, no matter how you encode them. But I’m not going to use every real number, so I’ll be happy with just being correct on the numbers I’m likely to encounter.
At the 2021 UK MathsJam Gathering, I gave a talk on a subject that has bothered me more than is reasonable: the graph-theoretic layout of the narrative of the baby’s book Each Peach Pear Plum, by Janet and Allan Ahlberg.
It’s one of my son’s favourite books to fall asleep to. It was his older sister’s favourite, and mine and my wife’s when we were little. I agree with the quote on the back cover, that it’s “the perfect first book”.
My son was born last September. While he doesn’t hate sleep as much as his sister did, he still needs a bit of help to drop off.
I’m not at all musically inclined, and I seem unable to remember more than a couple of lines from wordy songs (my version of “Papa’s gonna buy you a mockingbird” rapidly veers into nonsense as I try to think of a rhyme for the next line), so when the girl was little I hit upon the strategy of singing counting songs to lull her off to sleep.
My aim is to collect examples of conventions in mathematical notation that lead to ambiguities, inconsistencies, or just make you feel yucky. This is largely a result of me wishing I had something to point to whenever I see $\sin^2$ or one of those viral “puzzles” relying on BODMAS.
My aim is to describe conventions, without prescribing a correct notation. Whenever I tweet a question about a notational convention, my aim is to find out the range of different opinions that people hold about it. I often get replies arguing authoritatively for a particular correct answer, usually followed up by an equally certain reply from someone else arguing for the opposite. Like all language, mathematical notation is just something we make up to help express our ideas, and opinions, abuses of notation, lapses in memory and convenience all work against consistency and clarity.
I’d like the site to collect all these difficult aspects of notation, so that they don’t trip up someone who thought they might have an easy day doing maths.
So, have a look, and if you can help to build it out, I’d be very happy!