I listened to the second episode of A Brief History of Mathematics on Euler yesterday. I was quite taken with a quote from Euler which, to me, says something of the potential dangers of the application of mathematics to the real world. The relevant section of the programme is:
You're reading: Columns
- after-math: A lot of words started out being abbreviated before being accepted as words in their own right. In some old books you see “to-day”. Anyone still use “e-mail”? Anyway, aftermath was used like this, and a lot of results for “math” are really for “after-math”.
- math: a Welsh word meaning “kind” or “sort” (so, “math o” means “kind of”). Welsh/English dictionaries are full of this term. A number of the results are dictionaries and commentaries on Welsh texts.
- Math: a King or Lord from Welsh mythology who rests his feet in the lap of a virgin in one of the Four Branches of the Mabinogi.
- Abbreviation for a name in plays with characters named like “Matheo” or “Mathias”, for example in Marlowe’s The Jew of Malta.
- Abbreviation of Matthew in biblical quotations.
- There are a number of results for “M’Math”, a form of “McMath” in Burns’ Epistle To The Rev. John M’Math.
- Math – a monastery in India.
Cosmic-Ray Research Centre and Cold War Helter-Skelter in Secret Cave City
Samuel Hansen directed me to this article: “The secret cave city under Nottingham“. The article is highlighting The Nottingham Caves Survey, who offer:
The Nottingham Caves Survey is in the process of recording all of Nottingham’s 450+ sandstone caves. The project is now underway and we are surveying caves even as you read this. Keep checking the website for newly- surveyed caves! You can read more about the caves, see photographs, watch fly-through videos and take virtual tours.
The survey is producing some interesting images, such as the following (credit: Trent & Peak Archaeology / The University of Nottingham; click to enlarge):
Laser-scanned image of King David’s Dungeon, below Nottingham Castle. King David II of Scotland was reputedly held captive here in 1346.
Laser scanned orthographic plan of the Goose Gate caves, Nottingham. These caves include a medieval malt kiln, 18th-century brewery cellars and a 19th-century butchery.
And some very compelling videos:
I’m not sure about the use of the phrase “secret cave city” and the talk of the Survey using techniques to “reveal elaborate cave systems under the town of Nottingham” (in the post, not used by the Survey itself). I am pleased that the Survey is producing detailed scans of these caves, it’s interesting business and nice to see them being made accessible through multimedia, but the caves were not previously secret. In my experience, the existence of widespread caves under Nottingham is fairly well known. The Survey knows this and is specifically scanning those caves that are physically accessible (although perhaps not all open to the public).
Nottingham is referred to by a biographer of Alfred the Great in 868 as “Tigguo Cobauc” which you see translated as “House of Caves,” “Place of Caves” and “City of Caves”. A book on the history of Nottingham I have has the following:
“Entering the town at the beginning of the seventeenth century, Bishop Corbett exclaimed: ‘Why, the people live not in howses but are earthed in holes!’ If a man was destitute, explained one writer in 1639, ‘he has only to go to Nottingham with a mattock, a shovel, a crow or an iron, a chisel or a mallet, and with such instruments he may play the mole, the coney, and work himself a hole or burrow for his family where over their heads the grass and pastures grow, beasts do feed and cows are milked.’ The caves in the area of the castle have been used as mushroom farms, cockpits, gambling dens, privies, drinking cellars and burial vaults. During World War II, some factories enlarged them as air raid shelters for their workers. Today the caves house social clubs, a rifle range, store-rooms and a cosmic-ray research centre. From time to time somebody gets even more exotic ideas for them – such as linking them together for a Tube railway or turning them into atomic shelters, to be reached quickly by people sliding down on mats as if on a helter-skelter. Builders, of course, regard them as a nuisance and a hazard, and refuse to give a firm quotation for work in the centre of Nottingham. But the tours of underground Nottingham run for the 1972 festival proved so popular that the city has woken up to its subterranean history as a tourist attraction. The thirteenth-century tannery (the only underground one in Britain) revealed in the multi-million pound Broad Marsh development, has been spared”
(Portrait of Nottingham by E. Bryson, 3rd ed. 1983, p. 26).
I reckon there’s a good alternative history story in those imagined subterranean Thunderbirds-esk helter-skelter cold war bunkers.
The quote above is all interesting but the phrase “cosmic-ray research centre” in particular catches my eye. There is a paper ‘The Absolute Intensity of Muons at 31.6 hg cm^-2 Below Sea-Level‘ by Crookes & Rastin (Nuclear Physics B 58 pp. 93-109, 1973) which describes an experiment in a cave under the Castle:
“A cave in bunter sandstone of uniform composition lies below Nottingham Castle, and this provides an experimental site at 43.0 hg cm^-2 from the top of the atmosphere. The apparatus used by Crookes and Rastin to measure the absolute intensity at sea-level in both the vertical and inclined directions was therefore used to provide similar data at this underground location” (p. 96).
The first picture above shows some of the caves under the Castle and it seems some of them provided an experimental site for detection of cosmic rays for physicists from the University of Nottingham in the 1970s.
Math/Maths in Google Books Ngrams
Google Books Ngram Viewer is a Google labs product for comparing terms in books between 1500 and 2008. The idea seems to be to track trends in language. An interesting idea.
Anyway, both Christian Perfect (@christianp) and Daniel Demski (@dranorter) sent me the Ngram comparing “math” with “maths”. Christian observed: “bad news: it looks like ‘math’ outdid ‘maths’ for a lot of history”. Daniel observed: “Apparently the term maths is pretty recent? “.
Here is the graph for math and maths from 1700-2008 (click to enlarge).
So from these data it seems math has been much used through history, earlier and to a greater extent than maths. I have no preconceptions about which came first; what seemed surprising to me was how early either was used.
The Google Books Ngram Viewer info page seems to claim that “British English” is a subset of “English” limited to books published in Britain, but if you look at the “British English” version of the graph from 1600-1700 there’s some activity for “math” that doesn’t occur using the English corpus. Latin was used as the language for writing science into the 1700s, so it seems unlikely people would be publishing works with “math”, “maths” or “mathematics” during this period.
Use of “math” and “maths”
Anyway, let’s look at some of the use of “math” and “maths”.
In abbreviations
You do see both “math” and “maths” used as abbreviations of mathematics, or at least for “mathematica”, in university course catalogues (e.g. Annual Report of the President of Harvard College, 1863 and The Oxford Ten-Year Book, 1863). I’m discounting these though, because you see a lot of terms abbreviated in such catalogues that aren’t used as words on their own. In these documents you see “Hist.” for history, “Rhet.” for rhetoric, “Eng.” for english and many more, yet you don’t hear people referring to history as “hist”.
A similar example you still see today is in the abbreviation of journal titles. For example, you see “Proc. Lond. Math. Soc.” for “Proceedings of the London Mathematical Society”, just like you see “Proc. Roy. Soc.” for “Proceedings of the Royal Society”. Since we don’t commonly see “Lond” used for London, I am discounting this use of “math” for mathematics.
Other words
Sometimes the use of math simply refers to another word, brought into the search due to lack of semantic meaning. For example:
Incorrecly coded data
Some books are marked with the incorrect date, for example: “ICT for Primary Maths” by Jill Clare (1904) (actually early 2000s) and Business week issues 2652-2660 – 1934 (actually 1980)
Otherwise, some words are just incorrectly OCR‘d, e.g. “Mach.” in Macbeth or “wrath” in “An Exposition with Practicall Observations Continued Upon The Eighteenth, Nineteen, Twentieth, and twenty-one Chapters of the Book of Job” by Joseph Caryl (1658).
Etymology
The Online Etymology Dictionary says:
math: Amer.Eng. shortening of mathematics, 1890; the British preference, maths, is attested from 1911.
I haven’t been able to find these cases, but it’s true that around the early 20th Century the use of “math” and “maths” moves out of the sorts of abbreviation-in-a-list-of-abbreviations cases above and what I would consider to be use of these terms in normal sentences to mean “mathematics” starts to be seen in the results.
For “math”, there are some interesting titles but without online previews of the whole book, such as ‘Patented blocks for teaching math with geometric forms’ (1925). Boys’ Life, November 1926 (pp. 14-15) carries a story in which there is a certain amount of concern over who will pass their math exam, and an advert in Popular Mechanics magazine, June 1944 (p. 51) suggests math is in common use, offering the chance, using a slide rule, to “Become a MATH Wizard!” and solve “the toughest math problems in a flash!”.
On the “maths” front, we have references to “swatting up” on “these beastly maths” in These Lynnekers by J.D. Beresford in 1916 (p. 43) and the far more appealing “Aren’t maths beautiful? Is there anything more beautiful than a sphere?…” in The Strangers’ Wedding: The Comedy of a Romantic by W. L. George in the same year (p. 23).
Intros to the Math/Maths Podcast
Could you record an introduction to the Math/Maths Podcast? In recent weeks you’ll have heard intros by Matt Parker, James Grime and Alex Corner. We’re going to cycle through them each week but I’m keen to increase the number of these, particularly from listeners. The basic format is:
“This is Fred {from wherever(.com)}. You’re listening to the Math/Maths Podcast with Peter Rowlett and Samuel Hansen brought to you by Pulse-Project.org”
but feel free to play with it as long as you end up around 30 seconds and hit the key points: “Math/Maths Podcast”, “Peter Rowlett”, “Samuel Hansen” & “Pulse-Project.org”.
Send recordings to samuel@acmescience.com.
MathsJam Nottingham
MathsJam is “a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting.”
Regular events take place in London and Manchester and now also in Nottingham. Events provisionally take place on the second to last Tuesday of every month.
I hope that those involved with teaching mathematics will find ideas and inspiration to enrich teaching and encourage mathematical thinking. I hope students will find they develop techniques to approach problem solving in their studies. I hope everyone will find it a fun, stimulating event to connect with maths as fun!
If you want to find out when and where MathsJam events are taking place in Nottingham City Centre please send an email to nottingham@mathsjam.com.
400 words in 30 minutes on zero
I am bad at writing concisely. I am not great at writing to a deadline. In order to practice both skills I make this pledge: 400 words researched and written in half an hour on a mathematical topic, weekly. I may not keep this up but we will see. It is for my benefit but if you also enjoy reading it that is good. I make no promises about the content except that it will be related to mathematics, so expect some variety and no pattern. I will think of a topic outside of the half hour, and sometimes I may have some prior knowledge of it, but generally I will research and write each piece very quickly. Corrections welcome in the comments. For the first entry, let’s begin where things begin, from zero.
∞
When you don’t have any apples you have zero apples, right? Zero is a natural concept and easy to understand. However, zero is a relative newcomer to the mathematical world and its introduction caused a shake-up in what mathematics can do.
In ancient Babylonian mathematics, the lack of a numeral in expressing a number was indicated at first by a blank space and later by a punctuation mark between numerals. This would be like us writing 2011 as “2\11”. However, this was not our zero because it was not used alone.
All over the world – notably in Greece, China and South America – different cultures used symbols for zero. Some, like the Babylonians, used this as a placeholder but others began to understand zero as a number itself.
In 9th century India, decimal zero was used as we might use it today in practical calculations. The symbol for zero was incorporated in Hindu-Arabic numeral system, which comes to us through the Islamic mathematician al-Khwārizmī. This system of numbers was brought to Europe in the 12th century, particularly by Fibonacci, and so zero was brought into modern mathematics.
But why is zero important?
Zero plays one role in helping to distinguish numbers. Take the number 101: this means one hundred, zero tens and one unit. Without the zero, we would struggle to use this shorthand to represent 101, 1001 and 11.
Apart from this, zero serves as a number in its own right. If you subtract any number from itself, you get zero. This opens up all sorts of possibilities. For example, if rather than just having nothing you can consider yourself to have zero of an item then this opens up the possibility of being owed items as debt. If you allow zero you then get on to negative numbers, and the idea that you can have, say, -3 apples. This means that if someone gives you 3 apples, you will return to the default state of having zero apples again. This idea is very important in trade and economics.
In mathematics, zero plays an important role as an identity element for addition. This means that when you add zero to any number, you get the number itself. This fact is important in group theory, which underpins much of mathematics and must be left for another time.
∞
Performance: not great first time out. 393 words in 38 minutes. At 30 minutes I was about 70 words over.
Math/Maths LIVE from Greenwich!
You’ve seen the promos.
You were promised a monster truck rally, a fight, an intervention, a sci-fi battle and a miracle cure. To find out what really happened on Wednesday 17th November 2010 at the University of Greenwich, you can listen to the Math/Maths Podcast Live from Greenwich!