On 5th October 2010, eight years ago this week, I sent a tweet from a Twitter account I had registered on behalf of the British Society for the History of Mathematics (BSHM). I was on BSHM Council at the time and, mindful of the Society’s charitable aim to develop awareness of the history of mathematics for the public benefit, I proposed starting a Twitter account. I thought a good way to generate a background level of activity for the account was to tweet a daily mathematician, taking my lead from the MacTutor website facility. So I set up @mathshistory and sent the first tweet, announcing the anniversary of the birth of Bernard Bolzano.
I am preparing to teach our new final year module ‘Game Theory and Recreational Mathematics’. So I’m thinking about game typesetting in LaTeX (texlive-games is useful in this regard). I was looking for an easy way to display multi-pile Nim games. Usually, I find searching “latex thing” finds numerous options for typesetting “thing” in LaTeX, but here I was struggling.
Nim objects could be anything, of course, but conventionally sticks or stones are used. There are various types of dot in LaTeX that might look like stones, but somehow a line of dots didn’t seem satisfactory. There are various ways to draw a line (not least simply typing ‘|’), including some tally markers (e.g. in hhcount). My problem with these (call me picky) is that they are all identical lines, and a ‘heap’ of them just looks very organised. Really, I want a set of lines that looks like someone just threw them into heaps (though probably without crossings for the avoidance of ambiguity). So I wrote my own.
I made a silly joke, and it made me think.
You may be aware that our own Christian Lawson-Perfect is running the Big Internet Math-Off here at the Aperiodical, a single-elimination tournament with sixteen competitors. I was knocked out in round one by the brilliant Alison Kiddle. I joked that if Alison went on to win, then I’d be joint second.
I’ve been mulling this over and I felt there was something there in thinking about the placement of the non-winners in such a tournament, so I had a play.
This week’s episode of More or Less on the BBC World Service answered a question that involved estimating big numbers: Are there more stars than grains of beach sand?
This claim was famously made by Carl Sagan in the seminal programme Cosmos.
The cosmos is rich beyond measure. The number of stars in the universe is larger than all the grains of sand on all the beaches of the planet Earth.
More or Less come to a fairly standard answer, that Sagan was correct. This sort of problem, which involves approximating unknowable numbers based on a series of estimates, is called a Fermi problem. I’ve written about Fermi problems here before. The More or Less approach to answering this raised a question from a reader of this blog.
Alright, actually Paul is one of the writers of this blog, rather than a reader. Even so, are his concerns warranted?
Do you remember Paul the Octopus? During the 2010 World Cup, in what his Wikipedia page calls “divinations”, Paul was offered boxes of food labelled with different competitors. Whichever box he ate from first was considered his prediction for the match, with some success.
Yesterday morning, my son and I did something similar with our cat, Tabby. This is in response to Matt Parker’s latest initiative, Psychic Pets. Matt is hoping to get thousands of pet owners to make predictions, in order that the odds are good a pet can be found which predicted all prior results for both teams in the final. The good news is it’s fairly straightforward to take part.
I gave a talk on Fermi problems and a method for approaching them using the approximate geometric mean at the Maths Jam gathering in 2017. This post is a write up of that talk with some extras added in from useful discussion afterwards.
Enrico Fermi apparently had a knack for making rough estimates with very little data. Fermi problems are problems which ask for estimations for which very little data is available. Some standard Fermi problems:
- How many piano tuners are there in New York City?
- How many hairs are there on a bear?
- How many miles does a person walk in a lifetime?
- How many people in the world are talking on their mobile phones right now?
Hopefully you get the idea. These are problems for which little data is available, but for which intelligent guesses can be made. I have used problems of this type with students as an exercise in estimation and making assumptions. Inspired by a tweet from Alison Kiddle, I have set these up as a comparison of which is bigger from two unknowable things. Are there more cats in Sheffield or train carriages passing through Sheffield station every day? That sort of thing.