Science Geek

I like to think of myself as a prolific reader but I’m not sure what metric to judge myself against. I’ve kept a record of every book I’ve read since I started reading at university – there wasn’t a lot else to do – that was 30 years ago. I’m currently up to 674 which is 22 per year. For the last few years I’ve also been recording my reading on Goodreads.com and it shows that I’ve read an average of 39 per year in that time.

I read fiction at home and non-fiction on the train to work. Most of the non-fiction books are about science and maths and when I get to work I bore my colleagues with the wonderful things I’ve learnt.

I like science books with good long chapters that describe the topics in detail – I don’t like those books with short snippets of information detailing why penguin’s feet don’t freeze and why elephants can’t jump.

I’ve read so many that it’s getting hard to find books with topics that I haven’t read about already. I’ve just finished reading Things to Make and Do in the Fourth Dimension by Matt Parker and it was a mix of things I’ve come across before such as the proof of why there is an infinite supply of prime numbers, where to find non-Euclidean geometry and details of a 4D object that can exist in our 3D world.

But it contained quite a lot of stuff that I haven’t read about before such as knot theory, the sausage conjecture and how to make a computer out of dominoes.

The latter must be interesting because instead of the usual tolerating nods from my colleagues at work I got a ‘that’s cool’ response. I agree it is cool too, but not very practical because it took Matt and his team over six hours to construct a computer to add a pair of three digit binary numbers together and worse still it could only be used once. If it didn’t take that long to construct it would be a great tool for teaching kids how computers work, but as it is it’s nothing more than a curiosity.

If you look up the sausage conjecture you will see that it refers to arranging multi-dimensional spheres or hyperspheres into a shape that can be wrapped using a minimum amount of paper. However, for those of us who can’t visualise more than three dimensions, this problem can be considered in three dimensions as how to arrange oranges for wrapping.

It turns out that lining the oranges up in a line (a sausage shape) is the best arrangement for 56 or less oranges and a cluster (or haggis) is better for 57 or more. I haven’t been able to find anything that tells me why the transition should happen at 57. I think I could do the maths for the surface area of the sausage but not sure how to work out the surface area of the non-sausage shape. It must have something to do with Pi I guess.

If you are wondering about the other things I’ve mentioned (you’re probably not) I will elaborate:

A non-Euclidean geometry is one that doesn’t comply with Euclid’s five postulates (rules) and the easiest one to visualise is the one that removes the fifth postulate – the parallel postulate. Consider the lines of longitude on a globe, at the equator the lines look like they are parallel but when you extend them north or south they meet and are therefore not parallel. These geometries defy everything we learn at school, if you draw a line between too points on a globe the shortest distance is not a straight line (it’s a curve) and if you draw a triangle the inner angles do not add up to 180 (it will be larger).

The 4D object is a Klein bottle. It is a bottle that only has one surface i.e. it doesn’t have an inside and an outside. It can only truly exist in 4D but if you cheat and allow the surface to intersect itself you can construct one in our three dimensions.

I love the proof that there is an infinite supply of prime number because it is so simple – if you can accept that all numbers can be constructed by multiplying prime numbers together e.g. 8 = 2 x 2 x 2, 75 = 3 x 5 x 5 that is.

Let’s assume that there are only 3 prime numbers in the world – 2, 3 and 5. If we multiply these together (2 x 3 x 5 = 30) and then add 1 we know that we can’t now construct that number from the known primes because it doesn’t divide by any of them (the +1 ensures that). Therefore, there must be another prime. A proof like this is called “reductio ad absurdum” i.e. prove that something is not correct to show that the converse must be correct.

I’m not sure what I learnt about knot theory other than it’s difficult to comprehend and that we are all tying our shoelaces inefficiently. Matt describes a way of constructing a pair of loops, passing them under each other and pulling to create the same knot as usual without going around the tree.