Tag: mathematics

Trusting the world of floating point
A lot of the everyday calculations we rely on depend on “floating point arithmetic” – in other words an approximation of accurrate mathematics and not actual accurate mathematics. For the last six weeks or so I have been working on bring floating point arithmetic to “Riscyforth” – my assemblybased implementation of Forth for RiscV “single […]

A book recommendation
Lying in the bath this morning – relaxing into the Christmas holiday (despite the raging epidemic of omicronvariant Covid that is currently rampaging through London in an increasingly frightening manner), I had thoughts about several blog posts to write over the break, and this is the first… It’s a book recommendation: Ian Stewart‘s Concepts of […]

Coin tossing conundrum
This is from The Mathematics of Various Entertaining Subjects: Research in Recreational Math. It left me so puzzled it took me a while to get my head around it. It’s game – Flipping Fun – and the idea is that participants pick a set of three coin tosses (eg THH, HHH, THT and so on) […]

What’s the evidence your numbers are faked?
Currently reading: Ten Great Ideas About Chance. It can be a bit of a frustrating read – a lot of the chapters about gambling and judgement appear to be poorly explained to me – especially if you’ve ever actually placed a bet on anything (I am far from a regular gambler – I’m not sure […]

The Sleeping Beauty Controversy
I am reading “The Best Writing on Mathematics 2018” and amongst the various fascinating articles is one on “The Sleeping Beauty Controversy” by Peter Winkler. the problem (Here’s a video link – which examines the problem but isn’t related directly to Peter Winkler’s piece) To steal Professor Winkler’s own description from the article: Sleeping Beauty […]

Mathematicians: please help!
I am still stuck with a problem with the M/G/1 queue: not quite the same as my original problem (discussed here) as I understand that now – but the next stage really – involving some manipulation of Laplace transforms. I won’t post all the details here, because you can read them here instead and, if this […]

Puzzle about an M/G/1 queue
I am deeply puzzled by a question about the behaviour of an M/G/1 queue – i.e., a queue with a Markovian distribution of arrival times, a General distribution of service times and 1 server. I have asked about this on the Math Stackexchange (and there’s now a bounty on the question if you’d like to answer it there – […]

Reviving this blog … with a question about binary trees
Work changes and a determination to actually finish my PhD mean I really should make a bit of an effort here and so I will. Here is a puzzle that has been bothering me about binary trees which has come from my PhD research… In that research I am investigating how to implement virtual memory […]

From “The Foundations of Mathematics”
This is a fragment of a question from the first chapter of “The Foundations of Mathematics” (Amazon link): Record whether you think the following statements are true or false: (a) All of the numbers 2, 5, 17, 53, 97 are prime. (b) Each of the numbers 2, 5, 17, 53, 97 is prime. (c) Some […]

Could someone explain this contradiction to me?
Reading on with Julian Havil’s Gamma: Exploring Euler’s Constant and inspired by his discussion of the harmonic series, I come across this: Havil calls this a “nonlegitimate binomial expansion” and it seems to me it can be generalised: as And, indeed if we take we get: at the limit. But if we have it is […]