Dork Scratchings

Imagine you were a hamster in a hamster ball living on a hilly surface.  Base camp is surrounded on all sides by high summits, but you have a powerful catapult there that can fire you to the top of any of them.  Once fired you can influence your trajectory, but it's hard work and you don't have much energy in your little legs.  Suppose you know where you want to end up beyond the hills.  What's the best strategy for getting there?

ESA/Rosetta/NavCam – CC BY-SA IGO 3.0 In November 2014 the Philae lander touched down on 67P.  As I tried to imagine what was happening there now, I realized that "there now" doesn't really have much meaning when "there" is 30 light minutes away.  And maybe "what's happening" doesn't have much meaning either, given that the region of spacetime outside of one's light cone provides the sort of causal isolation quantum computing engineers would kill for. In a lapse of character brought on by mental fug I penned a poem On Everett's Peak  Rosetta, Philae, half an hour away if you're travelling light Packed with meters, big and small And a single transistor failure could ruin it all Cosmic ray, beta decay, a single gamma misplaced State changed, plan deranged, non-redundant memory defaced It hasn't happened yet, at mission control, as far as it is known At mission control, it hasn't happened yet, anyti

The following equation can be viewed in a couple of ways $$ action =  \int_{\Omega} \mathcal{L} (\phi_a, \partial_{\mu}{\phi_a}) d^4x $$ 1. Classically Every physical law can be written in terms of an Action Principle .  An action principle states that measurable values $\phi_a(\mathbb{x},t)$ over a region of spacetime $\Omega$ will be such that the action is stationary.  Or to put it another way, if you infinitesimally deform the $\phi_a$ then either  however you do it the action will increase, or  however you do it the action will decrease. There is an important caveat though: the action is stationary because we only consider deformations of the $\phi_a$ that preserve its values on the boundary $\partial \Omega$. This is an alternative to the differential way of describing the universe, in which only a single point of spacetime is considered.  In the differential formulation, instead of being told the values of $\phi_a$ on a boundary of a region of spacetime, and asked

I would be glad to know your Lordship's opinion whether when my brain has lost its original structure, and when some hundred years after the same materials are fabricated so curiously as to become an intelligent being, whether, I say that being will be me; or, if, two or three such beings should be formed out of my brain; whether they will all be me, and consequently one and the same intelligent being. —  Thomas Reid letter to Lord Kames , 1775 If only nature could provide some way to distinguish between identical and the same  then one could answer Thomas Reid's question.  If a reconstructed Thomas Reid were the same being then that being would be him; if it were an identical being then it would merely be a person with the same memories, but without any continuity of experience linking it to the original Thomas Reid.  Incredibly, it turns out that nature does provide a way! A well known feature of modern physics is that if you perform the same experiment t

COBE CMB fluctuations. Original Source: NASA All tortoiseshell cats are female.  Males can be black, or ginger, but never tortoiseshell.  The reason for this is that the mechanism by which tortoiseshell cats get the patterns on their coats depends on having two X chromosomes.  This is all described beautifully in Chapter 7 of "Junk DNA", by Nessa Carey . Females have twice as many X chromosomes as males, which on the face of it should result in 100% more expression for the genes on that chromosome.  This should lead to much greater differences between males and females than we actually see.  To put this in perspective, Down's syndrome is caused by individuals having 3 copies of chromosome 21 instead of 2.  But this is a far smaller chromosome than X and the difference is only 50%, rather than 100%.  (The fact that chromosome 21 is so small is the reason Down's syndrome is more common than syndromes in which there are too many copies of more important chromosome

How much can you make the top Jenga brick overhang the base by stacking them together? Surprisingly, you can go as far as you want. Suppose your bricks are length $l$ and you have one brick (not including the base).  Obviously you can overhang by $\frac{l}{2}$ without the centre of mass being unsupported.  What if you have two?  Now you have two conditions The centre of mass of the top brick is supported The centre of mass of the top 2 bricks are supported A quick calculation gives us that if the top brick is displaced (relative to the one below) by $\frac{l}{2}$ then the one below could be displaced by at most $\frac{l}{4}$ (relative to the one below it). Now suppose you have $n$ bricks (not including the base), then  you have $n$ conditions.  Let's guess the answer based on the result for $n=2$ and let's set $d_k = \frac{l}{2}\frac{1}{k}$ where $d_k$ is the displacement relative to the brick below and $k$ is the brick number starting at the top.  Then the centre

  Original Image: Mariuswalter CC BY-SA 4.0 I've just finished reading "A Crack In Creation" by Jennifer Doudna and Samuel Sternberg.  Doudna is the co-creator of CRISPR, the gene editing tool that genuinely is a Cracking Creation.  (I don't think the pun was intended since the word Cracking is not used much outside of and Wallace and Grommit appreciation societies, however, it would have been incredibly apt if it were!) If you are interested in How-Things-Work then this is a book for you.  I knew next to nothing about cell biology before starting it and now I feel like a pro.  The authors' writing style is incredibly clear, but what really saves you from the sense of drowning in acronym soup are the excellent illustrations throughout the book.  So, if you have heard the terms: DNA, RNA, base pair, ribosome, amino acid, protein, phage, virus, prokaryote, ... and so on, but aren't really sure what these things are or how they relate to each other then

A review of Our Mathematical Universe (Max Tegmark) Our Mathematical Universe was my summer holiday reading this year.  But it turned out to be much more than just something to keep me occupied while lounging on the beach.  This book has changed my conception of reality.  The themes in the book are similar in nature to those in The Fabric of Reality by David Deutch - another one of my favourite books.  However, instead of restricting the argument to the parallel universes predicted by Everett's Universal Wavefunction, Tegmark takes us on a tour of four levels of multiverse.  More than this, he provides an overarching theoretical framework for understanding them based on what he calls "the A-word" (because using its full name is guaranteed to get your paper rejected). The argument goes like this.  Whenever we find Nature appears finely tuned to make self-aware life possible, then there are 3 possible explanations It's a fluke! It's design! (by an intel

It occurred to me the other day while looking at a set of LED traffic lights that they could be improved quite easily.  The layout of the LEDs in all the ones I've seen seems to favour some radial directions over others and/or result in a higher concentration of bulbs at some radii than at others. My solution involves placing LEDs a increasing distances from the centre and as each LED is placed rotating by the golden angle .  This ensures that no radial direction is preferred over any other.  In addition to this, setting $r_n = \sqrt{n}$ ensures that each bulb covers a roughly similar area. By "area covered" I am referring to the portion of space which is closer to that bulb than to any other.  This is the Voronoi cell generated by a point belonging to a set of points.  The picture above shows the Voronoi cells generated by a set of LEDs placed in the manner described, and the code below shows how I obtained it.  I think it would make a pretty stain glass

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 and embryonic leaves known as primordia

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 pass to the left hand side.