Tag: mathematics

Further thoughts on Forth (and Riscyforth in particular) and Life
It’s now two years since I began my Riscyforth project of writing a Forth for RISCV single board computers. But it wasn’t until yesterday that I wrote my first serious/useful (if you like this sort of thing) program for it, a version of Conway’s Game of Life. (This program wasn’t as long as the unit…

The unreasonable ineffectiveness of arithmetic with floating point numbers
Eugene Wigner’s wrote a famous short essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” in 1960. To be honest I find it slightly underwhelming: to me mathematics is the abstraction from physical reality and not – as might be implied by Wigner – that our physical universe is a concretised subset of a…

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…