What’s your favourite number?

Chalkdust

25 June 2015

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Between Saturday 27th June and Sunday 5th July, Newcastle University, in association with the Institute of Mathematics and its Applications (IMA) and The Great North Maths Hub will be holding a Numbers Festival, during which they will be asking people what their favourite number is and why. Favourite numbers for many are linked to birthdays or anniversaries, or the number worn on the shirt of a favourite footballer. Below is our modest contribution to the Numbers Festival, perhaps with a slightly different take on their question…

12 (Adam Townsend) 

It’s unfortunate that we ended up with five fingers on each hand, because 10 is surely a terrible number to base a counting system on. A prime number doubled?! Sure, we can split it in two, but thirds or quarters? Forget it. In a perfect world we would all be talking my favourite number: 12.

Twelve is the base number civilization grew up with. It’s the highest number in English (coming from old German) that has its own special, monosyllabic name. It’s the ultimate canonical times table, and divides beautifully into halves, thirds and quarters. Why would you not want 12s in your life?

The unstoppable march of metric measures and base 10 want to hide the wonderfulness of 12. But it’s still fighting! Although it’s lost the battle of money (12 pence in a shilling), and is losing the battle of length (12 inches in a foot), it still hangs on in time (12 hours on a clock; 12 months in a year) and music (12 semitones in an octave). If only we counted in base 12.

0.20787957635… (Matthew Scroggs)

Whenever a real number is squared, the answer is positive. To get around the problem of square rooting negative numbers, mathematicians represent $\sqrt{-1}$ with the symbol $i$. My favourite number is 0.20787957635…, also known as $e^{-\frac{\pi}{2}}$ (where e and π are the widespread mathematical constants), because it is equal to $i^i$. I like this number because I am amazed that multiplying an imaginary number of imaginary numbers together somehow leads to a real number.

Dunbar’s Number (Rafael Prieto Curiel)

My favourite number is just an approximation because I like to measure our confidence and our degree of certainty in what we say. In other words, I’m a statistician. By analysing the size of a primate’s brain and the size of their social groups, the anthropologist Robin Dunbar estimated in the 1990s that humans can maintain around 150 social contacts: this became known as Dunbar’s number and has been used in politics, epidemiology, urban design and social networks. Of course, Dunbar’s Number is just an estimate: statistically speaking, the number of social contacts a person has should be considered as a distribution that varies from person to person. Dunbar’s number is an approximation to the mean of that distribution, with some uncertainty attached.

0 (Pietro Servini)

Brahmagupta

The Sumerians were amongst the first to develop a written counting system over 4,000 years ago but they, like their Babylonian descendents with their sexagesimal system, only saw zero as a placeholder rather than a number in itself. They represented it by a space or two wedges between two other numbers and never used it alone or, more bizarrely, at the end of a number. The Greeks were probably the first to introduce the modern symbol for zero but even they, despite their mathematical knowledge, could not comprehend the concept of representing nothingness with something.

It was the Indians who, by the 7th Century AD, discovered zero, or sunya – Sanskrit for ‘emptiness’ or ‘void’. In 628 AD Brahmagupta attempted to define the properties of 0, although he claimed that a number divided by 0 is a fraction with 0 in the denominator and that 0 divided by 0 is 0. The knowledge of 0 then travelled from India to the West via the great Islamic and Arabian mathematicians; allowing us to find first the negative numbers and then the imaginary numbers and thus revolutionise science.

1003 (Matthew Wright)

Personally, I’m a bit fed up of everything being so interesting, so my favourite number is going to be the most boring one I can find! I don’t want to choose a number too big, as any arbitrary big number is usually as boring as any other arbitrary big number. Now Wikipedia has plenty of interesting facts about individual numbers, so how about I search for the lowest positive integer without a Wikipedia page?

I was disappointed to find that the first 1000 numbers all have their own Wikipedia page: I’m sure there are some numbers below 1000 that are pretty dreary. But I don’t want to trawl through each page looking for them. So I’m going to go above 1000. Wikipedia lists on its page for 1000 the properties of interesting numbers in the 1000s. 1000 is obviously interesting. 1001 is a sphenic number (7 × 11 × 13), pentagonal number, and pentatope number. 1002 is again a sphenic number, Mertens function zero and an abundant number. All these are far too interesting. Next up: 1003. Wikipedia has nothing. So I looked at its page on Wolfram Alpha and asked: what properties does it have?

These all seem fairly boring and arbitrary properties: I think I’ve found my favourite number! However, is being the lowest boring positive integer in itself an interesting property? Alas, maybe 1003 is interesting after all? But if so it will lose the very property that made it interesting. I seem to have trapped myself in Russell’s paradox…

We’d love to hear about your favourite or most interesting number (or otherwise!). Just get in touch with us via Facebook or Twitter or send us an email (contact@chalkdustmagazine.com)