Described on The Math Less Traveled
You're reading: Columns
Putting all the world’s water in buckets
Following this pair of tweets about water:
A bucket full of water contains more atoms than there are bucketfuls of water in the Atlantic Ocean
— The QI Elves (@qikipedia) February 5, 2012
.@qikipedia There are 10,000× more molecules per pint of water than pints of water on earth. (3×10^21 pints/earth vs 2×10^25 molecules/pint)
— Matt Parker (@standupmaths) February 5, 2012
The obvious question is, at what point are the two numbers the same? Or,
If you put all the Earth’s water into containers of the same size so that each container carries as many atoms of water as there are containers, how big is each container?
Click here to continue reading Putting all the world’s water in buckets on cp’s mathem-o-blog
Paper light shades by Lazerian
Paper light shades by Lazerian:
Cubes "portraits" by daha mobilier
Cubes “portraits” by daha mobilier:
Newcastle MathsJam January 2012 Recap
January’s MathsJam was a bit massive. It’s now a week later and I’ve only just gathered enough thoughts together to do this writeup.
There were nine of us this month, all but one of whom either maths students or lecturers. A major theme of the night was of professional mathematicians or nearly-professional mathematicians forgetting basic high-school methods. This led to quite an intense session of puzzling and proving.
Things didn’t start out that way, though. A few weeks ago I found the website of a mathematician in Illinois called Alan Schoen, and his page about Lominoes. They’re a pretty interesting set of shapes!
Click here to continue reading Newcastle MathsJam January 2012 Recap on cp’s mathem-o-blog
Why do we enjoy maths history misconceptions?
I don’t think I have come to a conclusion from my previous blog post about historical accuracy and popularisation, though there were some interesting points in the comments (relating less to my comments about the ‘errors which may be gently corrected’ and more to the ‘demands of the narrative’).
George Jelliss and Thony C. both read the famously inaccurate Men of Mathematics by E.T. Bell in their youth and were inspired to mathematical lives as a result.
Will Daniels suggests I should hold different standards for different people, so those writing historical research are held to a higher level of accuracy than those writing for a popular audience. I’m not sure this feels right. Thony asks a really interesting question:
is it possible to achieve the inspiration generated by Bell’s book and be historically accurate at the same time?
I think this is at the heart of the matter. If it is possible to inspire through popularisation while remaining completely accurate then I can safely hold everyone to this high standard. However, if inspiration requires a little showmanship, if telling a good tale means not getting lost in minor distractions and sub-clauses, then we have our double standard.
This brings me to a final, anonymous comment that includes the following statement:
I am a great believer in the wisdom of stories, regardless of their provenance. If some stories persist despite being disproven, there must be a reason.
My first reaction on reading this is that it is preposterous. If you start presenting stories you know to be disproven you are in the realm of historical fiction. Historical fiction is fine, but these are now just stories and have no place being presented as real accounts of historical mathematics and mathematicians. Then today I was struck by something relevant.
I was listening to Paul Dirac and the religion of mathematical beauty on the Royal Society Library podcast while wrangling with the washing machine. This recording, of a talk given in March 2011 by Graham Farmelo, covers the life of Paul Dirac. Farmelo talks about how Paul Dirac is considered to be the theoreticians’ theoretical physicist, yet he had a very practical schooling and took a practically-focused engineering degree. Farmelo says (15:40):
Let’s get one thing right, he was a very practically-minded person. Completely different from the image that he has among most theoretical physicists.
This is as so often the case; the established fact isn’t just slightly wrong but completely wrong. This is the case in the story that Einstein did poorly at school, a misconception that Thony C. tells me is not as well known as I thought it was when I used it as an example in my previous post.
Do we really want to believe Dirac is a theoretician with no practical sense, that Einstein was a terrible student made good? Is there really some “wisdom” in these stories that causes them to “persist despite being disproven”?
Rather than necessarily being wise, I think we are drawn to certain types of story. The Dirac perception reinforces the view of a flawed genius; a theoretical physicist with no sense of the real world. The Einstein story perhaps speaks to a desire for the plucky underdog to win out in the end.
Aren’t these classic Hollywood ideas? Do other common misconceptions fit into the Hollywood-style? (Galois’ heroic struggle against the odds to invent Galois theory in a single night before the dual springs to mind. What others?) Do, in fact, stories that deviate from historical record and persist deviate when the story fails to fit a certain sort of narrative?
Perhaps more importantly, are there correct historical stories which fit a classic Hollywood narrative? (I’m thinking, for example, of George Green teaching himself advanced mathematics “in the hours stolen from [his] sleep”.) Perhaps stories of this type are the key to achieving Bell-like inspiration while maintaining historical accuracy.
Puzzlebomb – February 2012
Puzzlebomb is a monthly puzzle compendium. Issue 2 of Puzzlebomb, for February 2012, can be found here:
Puzzlebomb – Issue 2 – February 2012
The solutions to Issue 2 can be found here:
Puzzlebomb – Issue 2 – February 2012 – Solutions
Other issues of Puzzlebomb, and their solutions, can be found here.