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Posts from the ‘miscellaneous’ Category

“minus” and “negative”

December 24th, 2008


In the past I have commented on the QI forums that the difference between “negative” and “minus” was a good one and worth keeping*. I didn’t mean it to come across as self-congratulatory psuedo-intellectualism, though I’m aware that this is how it might have come across.

Listening to Stephen Fry’s ‘podgram’ on language, it appears that Mr Fry does not agree that pointing out the difference between “less” and “fewer” is worthwhile. To him, sadly, I am a pedant, attempting to impose a sort of lingustic-conservativism on the world.

Frustratingly, I agree with the majority of what Mr Fry discusses in his podgram; which is that language is a rapidly changing thing, and that what is aberrant in one generation will become established in another. Obliquely he suggests that language is ‘evolving’ though I am scared off that word having read John Gray‘s Straw Dogs, and I think rightly so. The problem with calling something ‘evolving’ is that it somehow implies progress, and I do not think that this is the case for language all of the time.

My reason for believing that “minus” and “negative” should be more clearly demarcated in language is really for its utility in mathematics classrooms, and it is there where I believe the demarcation should be expressed and preserved. There are two separate concepts here: one an operation over two numbers to express (as a directed number) the difference between the two numbers; the other to express the direction of a number, ie whether postive or negative. They are difficult ideas, to be teased out. We tease them out poorly, and need to improve. They would be teased out more successfully if their use wasn’t so interchangeable.

If I am right, then the interchangability of “minus 5” and “negative 5” should not be considered part of the great evolution of language. Wittgenstein is right to an extent, when he claimed that the limits of my language are the limits of my world, and if I lose the ability to use two words for two separate concepts, I lose the ability to differentiate the concepts.

I do not wish to be a pedant, but I think that linguistic conservativism is the bathwater to a good many conceptual babies whose protection is worthwhile.

Maths Education and the Metric System

September 7th, 2008


The following conversation in Metric Views catches the attention both for the interesting article and the subsequent comments.

Metric Views: Are our schools entrenching the ‘very British mess’?

The gist is that our schools reflect our current social muddle by teaching both imperial and metric measures and their relative magnitudes in school. In the article it is argued that the time and cost wasted on this is horrifying.

I have no love of imperial measures; I find it frustrating to have to remember how many pounds are in a stone, or ounces in a pound, or yards in a mile, and struggle to do so. I also find it difficult to convert between anything other than kilometers and miles. I know my weight in stone, but not in pounds, and certainly not in kilograms. I know my height in both metres and feet-and-inches. I am not sure that I can estimate volume in any unit with any degree of accuracy. It’s a horrible, muddy, confusing mess; that is undeniable.

I think my misgivings about the article are about the underlying idea that we should stop teaching both measures to achieve a feat of social engineering; by removing from the minds of the youth any conception of imperial measures, we would hasten the demise of imperial measures, which would be a Good Thing.

My difficulty is that feet-and-inches is such a good measure of height. I am 1.83m or 183cm, but neither is as satisfying as being 6′ tall, and neither is immediately conjourable in my mind. I don’t like Americans’ removal of ‘stone’ as a measurement either; 13 (and a bit) stone is much easier to remember than… whatever number of kilograms or pounds I am.

Feet, inches, stones and pounds are good measures because they are useful. They give us a scale rooted in humanity and the measurement of humans, and allow us to compare ourselves with others accurately. I am not convinced that the removal of these measures in classrooms will remove their common use.

I should not be confused with someone in defence of a curriculum which monitors and assesses the knowledge of different weights and measures and their conversion. Conversion is a fairly dry arithmetical topic. However, there might be problems that involve imperial or metric measures (or even their conversion) which may contain some good mathematics. I would not want that potential to be excluded from the curriculum any more than I would want their being taught made compulsory.

Exact Sine and Cosine Values

May 1st, 2008


Dr Ron Knott in the Department of Mathematics at Surrey University is not a name I recognised, but reading his resume, I now realise that I have heard him talk a few times about Mathematics on Radio 4, both on Simon Singh’s 5 Numbers series, and in Melvyn Bragg’s In Our Time podcast.

I was looking for some information about exact values of trigonometric ratios, and came across his most informative site. I was extremely pleasantly surprised to discover that for some values the trigonometric functions give exact solutions in terms of phi, the golden ratio, among other information.

For example, did you know that the cosine of 27 degrees is exactly a half of the square root of (two plus the square root of (two subtract phi)). (One day when I finish writing my own equation display movies, I’ll write that out in a prettier way, Dr Knott’s website tries a little harder than I do). I love that the number 27, which clearly wants to be prime so much it tricks generations of children into thinking it is, the square root of two and the golden ratio are connected inextricably through the circle-based cosine function. Fantastic!

The whole page, indeed the whole of his site in general, is steeped in extremely interesting, and relatively accessible mathematics with Fibonacci numbers, Egyptian Fractions and so on and so forth. It’s mostly a site for KS4 and beyond (14 years old +), with most material for the older students. Some of it is not for the faint-hearted. However, it is a valuable resource for mathematicians of all hues, and well worth a look.

Free eBook about Martin Gardner & Other Free Maths Resources

April 18th, 2008


I recently stumbled upon Mr Barton Maths page of Essential Freebies, where I was delighted to discover Furbles was one of his essentials.

However, the real gem of the collection in my opinion is the free online PDF of a tribute to Martin Gardner, who was a spectacular mathematical puzzler, without whom the mathematical world would be much the poorer. You can download the ebook at