Dork Scratchings

This post will attempt to explain a strange phenomenon in nature.  If you look into a sunflower, daisy, cactus or fir cone you always see a spiral pattern like the one shown above.  If you look carefully you in fact see two: one spiralling clockwise and the other spiralling anti-clockwise.  And, bizarrely, if you count the number of spiral arms of each you always find they form a consecutive pair from the Fibonacci sequence. To recap, the Fibonacci sequence is the sequence you get if you start off with $F_1 =1$ and $F_2 = 1$ and then iterate using $F_{n+2} = F_{n+1}+F_n$.  So: $$ (F_n) = 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,... $$ This all seems highly contrived, but somehow turns up in seed and leaf patterns.  How? The answer has to do with Phyllotaxis.  This is the manner in which new leaves or seeds are formed.  Imagine a long stem plant growing upwards and generating new leaves as it grows.  The tip of the plant is known as the bud ...

This letter from Einstein to Roosevelt is kept at the Hiroshima Peace Memorial Museum.  (See here for transcript.) Dated 2nd August 1939, it outlines the feasibility of both nuclear power and nuclear weaponry, and points to the evidence that the Germans were also investigating these. (It turns out the Japanese were too.) 6 years and 4 days later Little Boy was dropped, killing around 80,000 on the first day. One of the survivors, Sadako Sasaki (佐々木 禎子), just two years old at the time, feel ill with leukaemia years later. A saying went that if you folded 1000 paper cranes you would be granted a wish, so she started making paper cranes furiously and reached 1300 cranes, but died anyway in 1955. Today, schoolchildren from around the world send paper cranes to the peace park in tribute. The picture below is a photograph of her memorial in the Hiroshima peace park The final death toll was at least 140,000.

Little thank-yous Seen Kanazawa, Japan

These are ubiquitous now in Japan. Technology good => more technology better!?

When the 2nd law of thermodynamics was discovered a lot of theorists were understandably suspicious.  It said that entropy always increases with time, or $\frac{dS}{dt} > 0$, but this seems to go against time reversal symmetry, which is a feature of all physical laws. (Okay... in QM you also have to reverse charge and parity in the system too....)  Amongst those who challenged the new theory was James Clerk Maxwell (he who shed light on light) and he did so with a thought experiment.  Imagine you have a box full of air at a given temperature, and it is divided into two parts.  Between the two is a little door which can be opened and shut by a daemon.  This daemon watches the air molecules speeding towards the door and if the molecule is faster than average and on the LHS he opens the door briefly to let it pass through to the right hand side.  Conversely if the molecule is slower than average and on the RHS the daemon will open the door to let is...