I cannot help but think that this is a pivotal moment in history. Not only does Internet's resume already appear impressive, it also promises to be that tool which might usher in true accountability and democracy. And it would do it precisely by being messy and arbitrary. Sure it is strife with stupid pictures of cats and an endless barrage of memes but in its frivolity it gives voice and even legitimacy to the ideas of the next generation - the only ideas which are worth anything when it comes to the question of the future. As the Internet expands to subsume more and more facets of social interaction, the youth which would be the primary participant would start to have more and more say in the proceedings. And from the looks of it, it appears to be a good idea because then the important decisions would be made based more upon the views of a population which would be more educated and informed than it has ever been. Things start to rot when power gets concentrated in the hands of a few. They really start to stink when the powerful also start controlling the flow of information. Although democracy is expected to treat these ills, it's often merely a rigmarole where the elected end up being influenced by the powerful few and they perpetuate their stay at the top by keeping the population uneducated, uninformed, and divided on any number of lines. And in a traditional society they manage to do that because they control the flow of information. But democracy still is the best solution because it at least has the potential of being fair and fruitful. It just requires a mechanism where the elected can be kept on a short leash with the provision of a prompt whipping if they are found to be not performing according to their duties. The Internet, with its deep reach and immense integration across pointless divides, promises to be that short leash.

These are fun times to live through. The old guard seems to have absolutely no clue as to how to control the thoughts and opinions of people on the net. They have tried to make pathetic little attempts only to be promptly wrapped on the knuckles. And with every little victory which the netizens score, it seems that the old economy, old government and the old way of doing business loses another creaking support. I believe that the traditionalists will learn to respond better to the new challenges. There would perhaps be more legislative attempts at limiting the democratic and free exchange of information on the internet. We might even see internet lobbying becoming a trend in the future. Religion was said to be the opium of the masses but that observation is already dated in the modern world whose blind religion, I think, is popular entertainment as dished out on traditional media. As more and more people spend more and more of their time on the net, I believe that further attempts would be made to 'tame' the passion. But given the participatory nature of the net, I think that it's going to require much more ingenuity on the part of the powers that be to pull it of. For now they can only look incomprehensibly at this incongruous mechanism and wonder how much of a transformation they will have to undergo in order to be able to compete in this game whose rules already appear to have been changed.

Both sound and light travel as waves through the air. I may now resort to writing the equation of a traveling wave but that would do nothing but cloud the issue. What is important is that if a disturbance travels as a wave through a medium, like sound and light do, then it is possible to make a measurement of that wave at more than 1 location and say something about the location of the source of the wave. That is why we have two eyes and two ears because if we had only one of each then we would not have been able to determine the location of sources of sounds or the depths of objects. The accuracy with which the location of the source can be determined depends upon the distance between the points at which the measurements are made. In general, the closer they are to each other, the more inaccurate the assessment of the location. Now it is not hard to see how the accurate and efficient evaluation of sounds and objects would have been a winning and desirable strategy in the game of evolution. Therefore nature, being the brilliant designer that she is, has separated our two eyes and two ears by a considerable distance. To my limited biological knowledge, it appears true with all other species but I would be interested to know if this assessment is not correct. In fact, I would go as far as saying that if a sufficiently evolved alien specie were to be discovered on another planet and if it had auditory and visual sensors, they would most probably be in pairs (if not more) and that they would be separated on the 'face'.

This brings me to the point of this post. Smell doesn't travel through air like a wave and, therefore, its source cannot be as easily located in space as the sources of sound or light. The only way in which the source location problem can be tackled for smell, it appears to me, is by using its intensity and this is an inherently more inefficient way than by using the phase information for sound or light waves. Intensity processing also doesn't require measurements separated in space. It appears, therefore, that nature could do only so much for smell localization. It bestowed upon its creatures more sensitive noses but their nostrils were packed together because there is no inherent advantage in having them spread apart. And now the final picture emerges. If only smell traveled through space like sound and light do, our nostrils would most probably have been spread apart and what a ghastly scene that would have constituted! With twice the number of independent facial fissures humanity would surely have been a trainwreck, and for all we know it may just be possible that that quintessential fuel of the evolutionary machinery, mating, may have been resolutely refused by all. It would really have been a nightmare!

and I remember those days when I would go to the beach and stand on the shore, looking at the crimson sunset and the ocean surface upon which it melted into a golden denoument, and the flock of birds in pristine geometric patterns wading across the sky in inky silhouettes against a backdrop of clouds in all hues of orange. I would hear the distant sound of the crashing waves and interspersed within it the faint notes of people patiently looking, waiting for that one moment when sky and the water are separated by the final breath of the dying Sun. I remember being so completely taken by the grandeur of it all that I would feel overcome with an overwhelming weariness and an intense inertia against the idea of being at any other place except that. And I would look on long after the evening's empire had returned into sand having taken with it all of my energy and all my purposes.

I have often wondered what is it about Dylan's 'Tambourine Man' which I love so much and perhaps it has to do with the immediacy with which his lines capture some of my fondest emotions. That a beautiful sunset evokes in me a heavy, even sad feeling more than it evokes fascination is something I could never have been aware of, had I not read it in someone else's words. The final paragraph of the song is the most poignant ode to freedom I have ever read. Freedom not in its parochial sense but in its deepest, most intense form. So fundamental that it escapes both a coherent definition and also the root of its own rebellion but is gracefully manifest in the images which the lines provoke - like the credits of a movie, like a swan song, like the final page of a great book, an afterthought of a dot below an elaborate signature - an ending silent, aloof and contented:

Yes, to dance beneath the diamond sky with one hand waving free
Silhouetted by the sea, circled by the circus sands
With all memory and fate driven deep beneath the waves
Let me forget about today until tomorrow.

I believe that this is one of the foremost purpose of art. To make life presentable. To free it from its sorry drudgery, to liberate it from its already penned down certainty. Love stories are a dime a dozen but good love stories are few and far between. Human struggle is a mighty boring subject unless it's narrated by a good raconteur. There is no limit to which I would not go in order to avoid listening to the heartbreak of love but if it's the story of Swann, ah, that's a different thing. Reading literature for the story sounds unappealing to me. Reading it in order to gain some life perspective out of it is a positively disgusting idea. I love reading for the style of it and for the fact that through its misty vague glasses the jagged edges of life appear smooth, its torn troglodytic appearance seems presentable, even beautiful, and because life in its original unadorned form is too crude, too uncivilized, and too vulgar to be a satisfactory subject of cogitation.

Then I started thinking about how the Greek alphabet is used by non-Greeks to express mathematics. It seemed to me that there exists an automatic and unsaid hierarchy of mathematical symbols in academia and one is expected to catch on to it without ever being explicitly told. People in academia tend to use Roman letters (a, b etc.) only to represent trivial things. Roman letters are likely to be used in a construction like, 'if a+b is 2 and a is 1 then what is b.' Such a construction is obviously primitive and no self respecting academician would ever accept to knowing the answer! The only people who still think seriously about such constructions are number theorists and that's only because they make the problem a tad more respectable by bringing in $\epsilon$ in the mix. Now I do this too. I do tend to use the lower case Roman alphabet for the most trivial of things - well mostly explanatory text. Then come the capitalized Roman letters which, on their day, may be used for vectors. But when it comes to higher order tensors it's got to be Greek alphabets. Lower case Greek alphabets for the garden variety $4^{th}$ order tensors but upper case ones for the most hardcore of equations which, as a corollary, must always be taken with a grain of salt.

Sometimes I wonder what the human society would have done without the invention of these symbols. This alphabet which is the mathematical equivalent of 'Here, now take me seriously,' has had a constant presence in most if not all serious scientific papers in the fields of maths, physics and engineering. I wonder how the Greeks actually deal with this problem. I asked this to my Greek friend and she thought for a bit and replied 'we use the Greek symbols for all the trivial stuff and the Roman numerals for some of the serious things.' 'Do they also walk on their heads?' I thought. I was completely stunned at this final revelation and was left reeling at the thought of reading one their papers. It would be a bit like the story of the boy who cried wolf. There was a boy who mischievously cried 'wolf' one too many times for others to believe him on the one time when he cried honestly. And there may very well be a Greek who mischievously said things were important one too many times for me to believe him on the one time when things actually may have been important.

It's not that I have been spending all my time here just going to technical talks, although doing that and thinking about the talks has occupied a much larger percentage of my time than it ever used to be the case. During the last week, I also had wide ranging discussions with Ali and came to the conclusion that he knows more about everything under the Sun than I'll ever be able to know and that he has the extremely rare talent of combining his encyclopedic knowledge with an acutely analytical mind.

I also came across a lot of interesting characters who seem to inhabit this world, which I have come to associate with a certain logic, with a rationale completely at odds with mine. But I like to listen to them with genuine curiosity, trying to find in the scales and notes of their lives, the missing song which is my own world view. I try to find in the colors of their palette, the antithesis of my own colorless (largely logical) existence. I am absolutely fascinated by the stories and experiences of such people and the cities of Santa Fe and Taos seem to throw them up with more regularity than any other place that I have visited. It's not that I necessarily want their lives for my own, but I appreciate that they have interesting stories to recount and that they lack the skepticism to believe in a fantastic, beautiful, and imaginative reality. I can listen to such people in rapt attention for hours whereas I almost instantly shut down whenever someone starts teaching me how to invest my money and hedge my bets so that I can have a comfortable retirement. Therefore, I am thankful for all those individuals who made this little trip interesting. While I don't necessarily agree with them, I am very appreciative of the fact that they exist and make life more colorful and more non-utilitarian. There was Ryan, the barista of the Santa Fe cafe 'Father sky and Mother Earth' who narrated to me his journey across the US, his experiences with meditation and the mystical traditions of the native Indian people of New Mexico, and his belief in the apocalypse of 2012. Then there was Bobby, the guitarist of the band HN88 who gifted me a CD consisting of a collection of his songs. Marianne was the barista of the great 'World Cup' cafe in Taos and told me about her transition from DC to SF to Taos and I ended up adding to the cafe's collection of foreign currencies by donating a 100 rupee note. There was a German (I forget the name) who has spent the last 20 years of his life in the little town of Taos and described himself as a starving artist. He was trying to convey to me his vision of the world as a conceptual artist but I guess my brain has ossified under the influence of logic to an extent where it's not flexible enough to appreciate orthogonal logic. Annamelia was the singer and Matt was the forest officer and finally Johnny was the ex-physicist from Los Alamos who has been collecting obscure memorabilia relating to the automobile and the transportation industry for the last 20 years.

So  I was thinking about the simple spring mass system the other day and was quite pleased with the fact that one can explain the 'complicated concept' of natural frequencies in terms of purely physical intuition. Think of a spring which is attached to a wall at one end and a block which is free to move back and forth at the other end. The spring is made up of a material whose weight is much smaller than the weight of the block (assumption of massless spring) and the whole assembly is placed on a very slippery surface (assumption of frictionless surface.) Let's call the initial location of the block which corresponds to zero stretching in the spring,  'S'. Now we take the block and pull it so that the spring stretches by say 5 cm. and leave it. If one has ever held a spring in hand he knows that it takes effort to stretch it. In fact, it becomes progressively more difficult to stretch the spring to larger lengths. The same it true with compressing it - so the spring has a tendency to force itself to an unstretched position. Therefore, in our spring block system, the spring pulls the block back and keeps pulling it till the spring reaches its unstretched position. But by this time the block has attained a velocity so it doesn't stop and starts compressing the spring. The spring tries to stop this compression but it takes a certain amount of time before the spring is able to bring the block to a stop. By that time the block has already compressed the spring by a certain distance and that distance is exactly equal to the initial stretching of the spring (5 cm. in this case.) So our initial stretch has been completely converted into an equivalent compression. Now that the block is at rest again, the spring starts pulling it back until it crosses 'S', starts stretching the spring due to its speed, and stops when the spring is stretched by 5 cm. This whole cycle of stretching-compression-stretching takes a certain amount of time and now we ask ourselves a question, is it possible for this time to be any less than what it is? We also put the constraint, for the time being, that the amplitude of vibration (5 cm. in this case) has to be the same. For that to be the case, the block would have to travel at a higher speed on average and stop faster. This also means that it will have to be traveling at a higher speed when it crosses 'S'. But if that is the case, the spring will not be able to stop it within 5 cm. If the spring wants to stop it within 5 cm., it will have to be a stiffer spring but that is not allowed in our current thought experiment. Now let's relax the constraint that the amplitude of vibration has to be 5 cm. But that is again problematic because now the block has to travel a larger distance to complete one cycle. So even though it may be traveling at a higher speed on average, it will still take the same amount of time due to the larger distance it has to cover in each cycle.

This brings us to the conclusion that as long as we do not change the spring and the mass, we cannot change the time the system takes to complete one cycle - and this precisely is the natural frequency of the system - a constant for this simple system! In fact, as argued above, it is possible to complete the cycle in a faster time (higher frequency) if the spring is stiffer. It's even possible to do it with the same spring if we decrease the weight of the block - because it's easier to stop lighter objects than heavier objects. So the frequency of our system (number of cycles in a second) seems to increase with increasing stiffness and decreasing mass. Well, that's about how much we can deduce without mathematics! The exact relation is frequency=C*{k/m}^.5, where 'k' is the stiffness of the spring and 'm' is the mass of the block (C is a constant.)

The pendulum is a very analogous system where the effect of the spring is replaced by the pull of gravity. In fact, a lot of systems in the real world are walking this tightrope where there exists a certain force which wants to pull them back to a rest position. In a more complicated way, they all display preferences for certain 'frequencies'. They all want to complete their cycles in a certain time. It's all very drab and academic when a spring-mass system does that but it's all so artistic and cultured when a violin does the exact same thing!

In the movie Raincoat, Shubha Mudgal pines 'Piya tora kaisa abhiman (My lover, why do have this pride),' and it's one of those beautiful moments when a part of this arbitrary reality has been shocked into submissiveness and it presents itself melted along the beautiful contours of the artist's sensitivity. Just a few words, and one feels the infinite desperation of the lover with a poignancy which would only have been reduced, had an effort been made to explain it away. She sits there waiting for him and he doesn't arrive. And as time slips through her fingers like heartless grains of sand, she can only wonder, in mute resignation, what pride prevents him from coming to her. His actions are incomprehensible to her and yet, as the lines almost give away, she is trying hard to understand and would do all that is within her means and more, if only he came back and talked with her. But he doesn't come and she can only wonder...

This reminds me of another beautiful line from Ghulam Ali's 'Chupke Chupe raat din which goes,

Berukhi ke saath sun-na darde dil ki daastan

Wo kalaai mein tera kangan ghumana yaad hai

(I remember how you were fiddling with your bangles, when I was trying to tell you the story of my heartbreak)