Helen Czerski does temperature on BBC4

Dr Helen Czerski is doing a series on tmeperature on BBC4 at the moment. I enjoyed the first programme. The link will be valid for a month or so http://www.bbc.co.uk/programmes/b09rzq05

Joseph Black

I hadn't come across Joseph Black before I stood in front of his portrait, but I've been teaching his ideas for years. It turns out he was the person who came up with latent heat and found that different materials have different specific heats. It started with the discovery that if you heat ice at its melting point, its temperature does not go up until all of the ice has melted and become water.

Aeroplanes over High Pike again

Ah! The joy of going up High Pike again in the company of a smart phone owner. When first spotted the Airbus was at 31000 feet and over Ullswater.

By the time I took this photo it was down to 29000 feet.and half way between us and the motorway. 29000 is 9.4km. Half way to the motorway is about 10km. By Pythagoras, that about 14km away. The plane is about 70m long. Angle subtended is 70/14000 = 0.005 radians. That's 0.3 of a degree. If my finger is worth 1 degree, then the plane is worth ... well, I've blown up the image and it is 2/12 = 0.2 of a degree. Not too bad.

Cross Fell: Singing gatepost at Kirklands

The wind was blowing across the hole in the gate post on the way up Cross Fell. It was oscillating between a low note that we thought was around middle C and a much higher note. So which type of stationary wave was being formed. Both ends of the top are closed so let's try the idea that there is a node at each end like on a guitar string. The wave is then a single loop and the wavelength is twice the length of the tube. The tube was about 1 metre long so wavelength = 2m. Speed of sound in air is approximately 340 metres per second. So frequency = wave speed/wavelength = 340/2 = 170Hz. The other alternative is a node at one end and an antinode at the hole which is a quarter of a wavelength and might be worth 70cm. So wavelength = 2.8 metres and frequency = 121 Hz. Middle C is 261 Hz. I'd say first mode is most likely. The higher note would be the second harmonic at 340Hz.

Identity matrix in Dirac notation

I have been working through Leonard Susskind's book Qunatum Mechanics: The Theoretical Minimum. I have decided that I like Dirac notation. I have always found matrices easy to understand so I have been translating Dirac notation into my language. I decided to work in the ordinary 3D Cartesian space. This illustrates what is going on although it is not proof that it works in any coordinate system (basis). So here is the x-axis unit vector. I've called it i. Dirac writes it as |i>

 But there is also a line vector version. This is called the DUAL. Dirac writes it as . Dirac called this bracket notation because of the outside brackets, or bra-ket notation. The dual is called the ket. The inner product gives just a number.

 I then multiplied them the other way round and found out that I got a matrix. This is called taking the OUTER PRODUCT. In quantum mechanics, a matrix is called an OPERATOR. I did it with all 3 basis vectors for x, y and z coordinates.

 When you add the three matrices together you get the identity matrix I. It is like the number 1 for matrices. If you multiply any matrix by I, you get the same matrix back. I did it for the limited case of 3D Cartesian space but here is the general result for any orthogonal basis. This is what I was trying to understand. More on orthogonal later but in 3D space it means the vectors are at 90 degrees to each other.

Lord Kelvin

I met Lord Kelvin in Edinburgh. I was surprised to find later that he was yet another Cambridge graduate! I knew about his work on the Laws of Thermodynamics but I hadn't realised that he had been heavily involved in the project to lay the transatlantic cable to America.

Penrose Tiling Phone Case

I was shown this wonderful phone case by Will. It's a Penrose Tiling. I confess to having never heard of them but here's the explanation https://en.wikipedia.org/wiki/Penrose_tiling I think they will take some investigation and might make a good patchwork project. The case is an example of P2 tiling. My new ambition is to see the floor in the Maths Institute at Oxford.