In the early 1990s, Solipsys Limited was founded to cover a range of various activities. Over time these have evolved primarily into a selection of talks and workshops covering a range of mathematical ideas.
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Some time ago I gave a talk in which I showed that something unexpected happened with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. I computed (an approximation to) $52!$ (52 factorial) by hand. It's not so hard - you just…
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
This is a new thing for me - I'm hosting a blog post by a colleague/friend - James Tanton. You can find James' original post here. One reason it's being re-hosted here is because Medium is apparently blocked in some countries: Egypt Malaysia ..... possibly others. It is astounding to me that mathematics - of all…
A word of warning ... I'm presenting here something called an analogy. It's not perfect, it has problems, it's not exact, but there are ways in which it can aid your thinking. I'm giving a way of visualising high-dimensional spheres, a way that has its limitations, but which can help avoid making mistakes based on…
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
Sieve of Eratosthenes animation Source: Wikipedia[0] One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be…
Recently I've been discussing the details of measuring the size of the Earth by watching a shadow descending a wall at sunrise, or ascending at sunset. The sums are easy enough if you do it at either Equinox, and at the Equator, and you can read about it here:
You may feel like you've seen this before. If you have, skip to the end where I talk about a formula, and discuss the relevance to parameters in computer hashing algorithms. In particular, I'm going to talk about how large hash spaces should be to avoid collisions with a given level of probability. If there are just…