Impressive 3D optical illusion

Hello world,

This illusion is interesting if you haven’t seen before. I am noting an explanation at the end, but do tickle your brain a little before reading it.

Our brain thinks that face is always convex. If you change angle of view, you expect certain facial features to become ‘hidden’. So if no features go out of sight it implies that the face is following your angle of view. This dragon’s face is painted on concave surface – so  you can see the whole face over very wide range. Which the brain misinterprets as the movement

An interesting occurence of undersampling

Hello world,

I was checking out the burst mode of my digital SLR on a ceiling fan, and incidentally captured a nice demonstration of the effects of undersampling. Those who are from the digital signal processing area will find nothing new in the following video of a ceiling fan picking up speed.

(Updated video is now embedded.)

Those who are still thinking why the fan seems to start rotating in one direction and then reverses the direction, read on:

The world around us is analog (i.e. continuous in space-time),  but most of the storage equipment digital (i.e. discrete space-time + discrete values). In going from the reality of continuous space-time to stored bits, we perform analog-to-digital conversion.  The first step in this conversion is the discretization or ’sampling’ of the analog information. In this particular case, the DSLR is sampling the motion of the fan in time.  We are clearly losing lots of information in going from continous time to discrete time. But how much information can we lose, and still be able to observe the features of interest? i.e., what is the slowest sampling frequency that will let us have faithful representation of the signal that represents the event. Harry Nyquist discovered that for avoiding loss of information during discretization of continous signals, one needs to sample the value of the signal atleast two times faster than the rate at which the signal changes.  This idea came to be known as Nyquist sampling theorem.

When I switched on the fan and started capturing the burst of images using the camera, the camera was fast enough to capture the movement of the fan. Or I should say, the fan was slow enough such that its movement could be captured faithfully by the camera’s shutter speed. Nyquist theorem was satisfied and we meausred ‘true’ direction in which the fan was rotating.  However, when the fan picked up the speed, the camera shutter was no longer fast enough. More specifically, at some point after the fan was turned on, the fan’s speed of rotation (measured in rotations per second) exceeded twice the value of the speed  of camera’s burst mode (measured in number of exposures per second). This led to ‘false’ measurement of the direction in which the fan was rotating. This effect is called aliasing of information. This was incidental but intriguing occurrence of undersampling.

My micro-eureka moment of today.

Well, make it nano (or pico (or femto)) if you want. I have not discovered a new principle as Archimedes did, but have come to realize a mathematical beauty that exists in the nature’s design.

I have realized that genetic code is a many-to-one function that transforms a sequence of nucleotide into sequence of amino acids. Because this function is many-to-one, it can not be inverted. In terms of genetics it means that – if you know the sequence of nucleic acids in a particular gene, you can always say what protein would it produce; but it is not possible to know the gene that has produced a particular protein (which is a sequence of amino acids).

Sounds foreign? Let me explain.

The right question to ask is: How does a gene control protein manufacture?

Genes are particular sequence of nucleic acids (A,T,G,C) with defined pattern. Every triplet (termed codon) in this sequence encodes an amino acids. Proteins are nothing but a peculiar series of amino acids. When a gene is activated, its sequence is copied to mRNA (messenger RNA). Messenger RNA then carries this genetic information to the place where codons are read and amino acids encoded by them strung togeather. When amino acids are strung togeather, they assume particular chemical and structural properties that in turn govern their functional properties. Proteins are work-horses of cells – they do most of the work.
The code that matches genetic codon with a particular amino acid is uniform, degenerate and unambiguous. What this means is:

• Unifromity: All organisms use the (almost) the same genetic code. (Isn’t it amazing – it really shows we really have grown out of amoeba!)
• Degeneracy: More than one codon can represent any given amino acids (by the way, in humans there are 20 of them)
• Unambiguity: Every codon represents one and only one amino acid.

So if you consider genetic code to be a function (call it ‘g’) maping a set of codons (call it ‘C’) to a set of amino acids (call it ‘A’), we can see that g: C -> A maps every member of the set C to a single but non-unique member of A. Thus, function g is many to one.

Now, it is a mathematical truth that many-to-one function cannot be inverted. Hence, you can never ever get a nucleotide sequence out of protein structure.(edited thanks to Johan’s comment) Hence, eventhough you can infer what nucleic acid sequences may give rise to certain amino acid sequence, you can never be sure which one actually did.

I am Wired!

These days, I am participating in an amazing research carried out by Psychology department of NUS.
They wish to relate the responses given to stress (physical and psychological) by certain populations with their genetic makeup. I am all instrumented these days. I had started writing out the theme, but just towards the end; I realized that I may be violating non-disclosure terms by divulging their method of research.
So for time being, I have just uploaded a pic of me with wires all around.