Elegance, a quest.

Have you ever noticed your math teacher exclaim about how elegant a solution was? Have you ever exclaimed in joy when you managed to cut through the sordid, confusing muck in a problem and found a solution that was simply brilliant!

If you’re an Engineer, or want to be one you know what I mean.

But what’s the big deal? Why is elegance so important? Perhaps we need to see what its really about:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry – Bertrand Russell

OR perhaps this rather vague one by the late great Paul Erdős -

 "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."

I don’t know about you. But to me they don’t really seem to know what they’re talking about do they? There, done, now bear with me for a moment, before you condemn me to the pits for such sacrilege.

Look at those two statements, look at the words they use and the feeling they seek to evoke. Its ill defined and nebulous at best. And that, I feel is because they’re tapping into one of those poles that define human thought. They aren’t able to explain what it is that they’re talking about because it isn’t possible to do so. Other things are defined in relation to our need for elegance. It, itself is a part of out minds as much as ‘wonder’ is.

We seek elegance in all things. And unlike so many of the other things that define what it is to be human, its a very concrete thing. Elegance can be seen and felt. It can be crafted and imagined and built. Of course, I refer to the elegance of simplicity. The elegance in which the form that is defined by function is in itself a beautiful thing. The faux notion of elegance – the one so often applied to fashion doesn’t appeal to me. It might to you, but to me it doesn’t carry anything like the primal weight that accompanies the elegance sought after by the sciences.

Elegance is simplicity. Elegance is where everything falls into perfect place with the least effort. Elegance is economy without any loss of efficacy. Elegance.

So much of mathematics is driven by our primal desire to seek elegance. So much of physics is driven by our desire (unfounded though, it may be) to define the universe in elegant terms. Indeed, the LHC was built, in a large part to satisfy our hunger for elegance – our current understanding of the universe (the standard model) is about as far from elegant as physicists could stand to be.

And it has an obvious origin. Elegance, as I said, is economy. And when economy and efficiency is the difference between being a meal and catching one – as it surely would have been to our ancestors hunting the Pleistocene savannah, it pays.

The quest for elegance among engineers is probably closer to that primeval need than the desire that drives mathematicians and physicists. In engineering, an elegant solution is often intuitive. And and intuitive solution is easy to verify. It matters in a physical sense too – a simple solution is often much cheaper than a complex one (but don’t let your intuition fool you – this is not often the case) and it is usually much easier to debug.

But its mostly some combination of economy of effort (read: laze) and economy of expense that drives us engineers towards elegance.

So where is this heading? Nowhere for now. I just wanted to set the stage for an argument I intend to post here soon (or at least as soon as is feasible).

They aren’t bullet-proof Mr Creedy

Creedy: [desperately shooting at the approaching V] Die! Die! Why won't you die?... Why won't you die?
V: Beneath this mask there is more than flesh. Beneath this mask there is an idea, Mr. Creedy, and ideas are bulletproof.     [sourced via IMDB]

I loved V for vendetta. It was a perfect blend of mindless action and flowing thought. It was powerful, yet exciting. I’d easily rate it among the best movies I’ve ever seen.

One of the many, many great dialogs in the movie is the one I’ve quoted above. It was beautiful. The injured V staggering on despite his wounds. The terrified Mr Creedy’s true colours showing through. Beautiful.

But Is that really true? Are all ideas bulletproof? Equally so? Can an Idea be killed, stamped out and erased from history’s memory? I’d wager they can. Its been done before and its being done now. I know this. I’ve seen too many dreams and ideas worn down to nothingness by the grinding machinery of apathy to say otherwise. This post is about that idea – that ideas and dreams are not bulletproof and that need constant support and help to keep from falling apart.

I’m from the National Institute of Technology, Tiruchirapalli. Its supposed to be one of the best schools of engineering in India. And accordingly, each year, a batch of India’s finest minds (or nearly so – the very cream is taken by the IITs) enrols there with dreams of changing the world and doing great things. But, for the large part, they don’t. Most seem to take up paid jobs. Some Join the IIMs, doubtless drawn by the huge salaries and comforts of corporate life.

But do they join with that in mind? Does the average NITTian or IITian join with aspirations of a decently paid job at a multinational or does he (and it seems to be overwhelmingly ‘he’ with women a small minority in these institutions – but that sad fact is material for another post) enter with dreams of changing the world in one way or another? I’d wager its the latter, if only in an un-expressed, back-of-the-mind sort of way.

But then something goes wrong. The vast majority of these people seem to loose interest in the path they believed would be theirs and stray towards something more comfortable. Why? Is it perhaps because age and maturity (! lol) have changed their outlook? Perhaps. Is it because they feel that it is their responsibility to earn well and keep their families happy at the expense of their dreams? Perhaps, but I doubt it is so in many, many cases.

Apathy. A state of indifference, or the suppression of emotions such as concern, excitement, motivation and passion – Wikipedia.

It can be induced.

An organization with any power – be it a College administration or a national government has the ability to bring about a situation in which there are enough restrictions and wrongs to prevent the people it has a hold over from truly realizing their full potential. It can create an atmosphere where the effort needed to do the simplest of things is so great that people just don’t do them. You don’t bother reading that article on the web because it is so annoying to go all the way across campus to reach a PC with internet access. You don’t bother voicing your opinion on an idea of some importance because the threat of litigation over some perceived wrong in your words is just great enough.

You just don’t bother.

The one thing you have to note is that there is always a way to actually do whatever you want. It is theoretically possible to do all the work you want on that piece of new equipment in the lab because a procedure actually exists to acquire permission. Or fight off the blatant attempts at silencing descent because the law is actually on your side. But the machinery of apathy is just strong enough that you don’t bother doing anything in the first place.

And that is how ideas and dreams are killed. By exerting just enough pressure to strangle them without actually alerting them to the fact they they are being killed…

The Palaeontologist’s muse

There are two types of forces in the world. There are the explosive, fast forces like volcanoes, earthquakes and thermonuclear fusion weapons. And then there are the slow ones – the rivers that cleave mountains and the seas which batter entire land-masses into submission. In our brief, fleeting, lives we tend to recognise the fast shapers as superior in some way. But take a look at the Grand Canyon or the Himalayas – they were shaped over thousands of years (by water erosion and tectonic plates moving against each other respectively) by the slow powers that be.

The process of science parallels this aspect of nature. There are the moments of extreme insight – the ‘eureka’ moments where we make giant strides in fleeting instants. And then there is the slow process of chipping away at the barriers nature places between us and knowledge. Where we batter down the obstacles we face and achieve our ends inches at a time. This post is dedicated to that inexorable movement. For though the sprint may get us over a hill, it is the march that moves armies over continents.

I mentioned in ‘Our little friends to be’ that I’d spent the winter (of 08-09) in the US. I stayed in Washington DC for the entirety of that trip (except for two awesome days in New York). And as any geek worthy of that title would have done, I spent more than a few days running around the Smithsonian(s) grinning in delight. They weren’t as great as I thought they would be. Don’t get me wrong, they were brilliant. But they seemed to fall a way short of expectation – the dinosaurs didn’t seem as big and the sabre-toothed cats not as menacing as I thought they would in my imagination. But a few parts stood out. One of them, in the palaeontology section is what’s inspiring this post:

They had this glass room in which the palaeontologists who prepared the fossils worked. You could watch them work like any other exhibit at the museum. The room was brightly lit and the hallway outside quite dark. So, I guess, to someone inside it would seem like the quiet labs they were used to. People knocking on the glass, however, might’ve be a problem. But the hilarious sign I’ve photographed above seemed to stop most of that!

A palaeontologist digs up fossils. Fossils can be pretty large – the fully preserved hip of a brachiosaur for example. But I’m given to believe that most are small – teeth, bone fragments and the like. In any case, Palaeontologists dig them up and clean them with instruments like toothbrushes (only for heavy duty work!), paint brushes and other stuff like that. Imagine the patience it takes to sit in the mid-day heat of a desert and dig out a five tonne piece of mineralised bone embedded 20 meters up a cliff-face with a fine sable! What madness drives them!?! But scientists and engineers do that all the time. We seldom rely on leaps of intuition.

There are hundreds of famous examples of this in the history of science. Men and Women have so often made thousands of models and millions of calculations before they got things right. I myself have spent weeks varying values in a circuit trying to find an optimal configuration.

But the effort is almost always worth it. Look around you. Look at that plane overhead or the cell phone you hold in your hand. They almost surely took a massive effort to design and build. But ask an engineer who creates them or a scientist who discovers the principles they rely on and they’ll tell you that the sheer joy of seeing their work come alive is worth every drop of sweat and ever hour lost in thought.

I know this joy. And I suspect almost every creator of things does too. It is our reason. It is the thing that binds us to our lab-benches and drives us. It is our muse. The muse that inspires the palaeontologist within us all to chip away at his problem one layer of dirt at a time.

The nature of will. On the forces that drive.

I once wrote a post titled: ‘To live or not to live. That isn’t really a question’ for my old blog: http://oftheforge.blogspot.com. I dealt with the idea of the human desire to exist, live and fight for his or her life when all evidence points to the magnificent insignificantness of our existence. I came to the conclusion that we live simply because we want to live. And that those bloodlines who didn’t would quickly be weeded out by natural selection. Here I’m going to try and talk about the (related) idea of ‘will’.

The next few paragraphs will be dreary and serious. Bear with me. They are important.

As an added note: these are my ideas alone. I haven't taken the trouble to read through more than Wikipedia or talk to someone who’s devoted any amount of time and study to this. Well, here we go:

A person who chooses not to steal because the Ten Commandments said so would be exercising free will because it was their choice to follow the Ten Commandments Someone who independently forms their own moral system or who composes a musical composition pleasing to themselves. however, would be exercising an act of will. –Wikipedia, on Nietzsche’s perspective

Nietzsche clearly felt that will was something that made us act in a certain way. That something was his higher ‘an act of will’ when it was somehow internally motivated. I disagree. I believe that his perspective is an abstraction of my more general principle:

Will is the ability/practice to put/of putting a larger long term gain* ahead of a smaller short term gain*.

-*Gain is some tangible, visible or perceived benefit whether internal or external. It should be applied in the broadest sense possible, applying to both the trivial and the grand. Also, it is important that the idea of ‘larger’ and ‘longer term’ be applied very liberally. A situation where someone does B instead of A or C, where A is the most immediate and easiest option, B is the middle choice and C the ultimate ‘best choice’ is still exercising ‘will’ as defined above. In this case C is simply disregarded and B is taken as the more ‘difficult’ yet ‘better’ ‘longer term’ ‘gain’ according to that person’s inner reasoning when compared to A. – Me.

Starting with that first principle, we can derive Nietzsche as follows: In the 10 commandments case the smaller, short term gain was the wealth the theft would bring him. The longer term gains (of not doing so) are several – the internal tangible benefit of not having to deal with his conscience, the visible benefit of not being caught and punished and the perceived benefit of being admitted to heaven having lived a virtuous life. The second case is more interesting. For this we must analyse the concept of ‘pleasing to themselves’. I believe that the idea of satisfying oneself can be looked upon as a combination of a  sense of achievement, as simple pleasure and as a stepping stone to something bigger (such as acquiring a mate or future success). All these are, I believe, things our minds trick ourselves into doing as they increase the probability that our Genes will survive. In this sense, my definition holds as the composer is giving up the small gain of lazing around and having fun for the perceived greater, longer term goal of becoming a more eligible mate and more successful person in all. Do note that it is not required for this process to be carried out entirely consciously. Our minds trick us with abstractions. Thus, we simply note that an extra helping of Kesari (a sweet from south India, which you’ll love!) is ‘bad’ rather than trace its effects on our health and thus our eligibility as mates and our efficiency at doing other, advantageous things before denying ourselves it.

One important thing to note is exactly what I have intended to do with my definition of will. I wanted a definition that would apply to all scenarios, especially, situations where a person could be called ‘strong willed’ for doing something instead of some other thing. In the second case I have not actually reconciled Nietzsche's idea of free will with mine. I have simply explained how my definition satisfies an act of free will (i.e. the motivation to do something like that) but not the specifications of that free will itself. I am separating the concept of free-will, the idea of choice and non-determinism, from ‘will’, the somewhat abstract idea of force and power we associate with the word ‘will’.

Volition or will is the cognitive process by which an individual decides on and commits to a particular course of action. It is defined as purposive striving. – Wikipedia on ‘Volition’

Again, this straddles the line between my ‘will’ and the idea of free will. I have tried to define the kind of will it takes to drive a human against all perceived odds. The kind of will you find possessed by heroes ancient (Hector et all etc) and in modern graphic literature (Batman, say) as almost a power that is as important as super-strength or speed. ‘purposive striving’ is closer to what I’m getting at; obviously, it derives from my definition too – why would you sacrifice your immediate comfort to ‘strive’ unless some greater reward lay at the end?

At this point, having discussed several approaches to ‘the will that motivates’, I have hopefully convinced you that my definition of ‘will’ is a good basis for understanding that aspect of the human psyche. Before I get to the point of this post I’d like to address another point: My definition can act repetitively (recursively if you will… no pun intended). For example: in the example given as an addendum to my definition a person chose B out of A, B, C where they lie in increasing order of ‘gain’ and ‘long term-ness’. Here my definition is ideally applied twice. In the first B was chosen disregarding C. Here the person is ‘weak-willed’ as, in the act of deciding on the ultimate objective the ‘best’ one was given up for something easier. He, however, is still ‘strong-willed’ in pursuing B instead of the immediate comfort that A would provide. I am not specifying any limits to these ideas. A person who gets out of the way of a speeding car is still accounted for because he/she took the effort of moving (effort toward the longer term gain of staying alive) as opposed to the ‘easy’ option of simply staying put. This application might seem weird at first, but I feel that a certain amount of ‘will’ is built into our instincts. Doing something to avoid almost immediate pain and suffering instead of just sitting there and enjoying the even more immediate lack of exertion still counts!

And now to the point of it all- isn’t the idea of ‘will’ beautiful? It is so abstract, so belonging to the realm of grander things. But it is something we experience, within ourselves, every day of our lives. I am exercising my will when I write this. I could have simply slept or played another game of Quake. But I didn’t. Why? Well, I don’t really know. All I get from my head is that I’m doing something ‘good’. What my head thinks It’ll result in is beyond the ‘conscious me’. Doesn’t that intrigue you?

I simply want to peer into that great, dark mystery that is the human mind. And I don’t think that it is very complex in its basis at all. I believe that it is just a few rules (like this one) applied over and over again, in inconceivably complex ways. Each of those rules are simple products of natural selection (Indeed, the idea of ‘will’, especially as I have defined it, is an obvious aid to our survival) yet they have resulted in something so much more impressive than anything else around us. We build ships to the planets and cities that tower above all. Our nearest ancestors, who are supposedly, 98% like us would be lucky to build a misshapen club. How on earth is that possible? I refuse to subscribe to any of the silly ideas (read: supernatural explanations) that many rely to- they answer nothing. I yearn to answer that question; to understand ‘us’, ‘we’, ‘you’ and ‘I’. Because hopefully, one day, I’ll be able to improve upon it.

Our little friends to be

During a recent visit to the US, while roaming around a mall I happened upon a stall of Roombas. A Roomba is a vacuum cleaning robot. It has enough intelligence (and the required sensors, actuators etc etc) to navigate around a room avoiding obstacles like chairs, cables, stairs and cats and use a built in vacuum cleaner to clean the carpets. Once done it makes its way back to the base station and charges itself. It does all this without the any human interference. They cost a couple hundred dollars, that's less than most mid range phones, though I doubt anybody actually uses one as their primary mode of carpet cleaning. I’ve read that they aren’t really all that good at it – they don't work well for multiple rooms, they tend to miss corners and they get stuck from time to time.

Obviously, a Roomba isn’t what we thought we’d have by 2009 way back in the 1960s (say). Back then we thought we’d have intelligent humanoids who could do almost all that we take for granted in humans. And we kinda assumed we’d be far enough along for interesting evening gossip to consist of tales of Mrs Parker’s ‘special’ relationship with her new mark IV (again, say). But then again, we also assumed we’d have rocket ships to Jupiter, ray guns and flying cars. Sadly, as a prudish Victorian would remark at all that (especially Mrs Parker): Alas! Taws' not to be!

So what happened? Where exactly did all those wonderful dreams fall out? Have we just not worked hard enough? Is the KGB responsible for it all? Or did we just hope for a little too much in our naiveté? I’d wager on the last one.

See, building a robot that works in the real world is just not easy. There are too many little things that keep popping up that are so difficult to solve (especially with the constraints current, available, hardware places on us). For example there is the problem of navigation. A four year old can walk from one end of a room to another without bumping into too many things. So can a rat. A million dollar bot though, might still have problems. Especially if you throw a shoe in its way once its off. Now why is that the case? I think its because of the way we’ve approached robotics so far.

When you’re asked to create a robot that can solve a problem we tend to approach it too mathematically. We give it data (or it collects data) and we then try to calculate the best probable path (to take the example of path finding) using that data. But what is the best path? Given a top down look of a room, a sort of God’s eye, view I’m sure there is one. But you never get that sort of view. What you have to work with is a rat’s eye view. From that perspective the only way forward it to make ‘educated guesses’. For example: ‘That's a shoe in front of me. Shoes are small and light. I can move it out of the way or try to go around it.’. As opposed to: ‘Sensor #4 reports obstacle. can’t…move… 01010101. B.S.O.D’. This  first example illustrates how we tend to work. And that's how a robot will need to work in order to get around.

This is where all those interesting terms that scientists love to sprinkle on their papers come it – neural networks, genetic algorithms and the rest. But exactly what are these? Essentially, they are models of how things in nature work – neural networks model brains and genetic algorithms model evolution. They abstract things and give you a solution (all proven mathematically) but don’t tell you exactly how they got there. For example, a neural network might help a robot recognise a shoe even if its placed at an odd angle, is upside down and is actually one of those silly things from Prada  (as opposed to the sneaker it was originally shown and trained to recognise as ‘shoe’) They offer some hope because they work well when brute computation won’t. But they don’t bode well with me.

Why don’t they? Because of their nature – they are black boxes. They give you a solution, but not the same one every time and not always the best one. And that just won’t do. I want my robots to work the same every time; to be quick, efficient and straightforward while still having that ‘intuitive fuzziness’ we ascribe to living things (and which the aforementioned ‘natural algorithms’ may give us). Why? Because that’s what robots are for damnit! To do all the stupid little things that suck up our time and free ourselves from the drudgery we would otherwise otherwise have go through ourselves. Like the laundry,  making that perfect cup of coffee and cleaning out the kitty litter. We do those things well-ish because our brains consist of one huge neural network which can handle things in the real world, unlike a hard coded system. But we don’t do it perfectly for the same reason – neural networks are fuzzy. We can guess that we’ve added just about enough sugar but don’t know for sure. A robot ought to be able to measure that to the microgram.

So what’s the solution? I think it’ll involve some sort of hybrid. A robot that will have a traditional hard coded ‘core’ that can call* on ‘softer’ biologically inspired modules to do specific things (For example: call* an ‘object recogniser’ to figure out exactly what it is that's blocking its path or call* a ‘path finder’ iteratively to figure out how to get to the socket on the wall while not waking the annoying kitty). But that’s just me thinking aloud now. If you want to know for sure just get back to me in a few years. I’ll have it down pat by then :)

Where does that leave us then? Hopefully, in a few years (or decades if you’re pessimistic) we’ll have a model III to weed the lawn, a type 7 to make us meals and a mark IV to... err… well, ask Mrs Parker. And then we’ll finally have enough time and freedom to look at the big picture and contemplate whatever it is we want to. We’ll be free to dream and build and do all that we never could if we had to go through the chore of keeping ourselves alive and ticking.

I for one can’t wait for the day I’ll get to say hello to the plethora of our little friends to be.

Imagine worlds

Do you remember that day not all that many years ago when you stared out of the window just dreaming? It might have been a Sunday or maybe it was one of those convenient government holidays. You didn’t have any work and there weren’t any grownups bothering you with chores. Mom had just given you a bowl of something wonderful to eat. The sun was bright and cheerful but it wasn’t hot. There might have been a breeze that that day; that made the curtains swing and cast an odd drama of subtle shadows across the room. And you were lost in a world of your own. It wasn’t any tiny variation on this mundane world – which we imagine all the time, it’s human nature, project our desires of what was and what we wish were onto a virtual world. No, it was something else all together. The universe was dough for your mind to kneed, there were no rules, no things imposed on that true, pure freedom.

I imagined worlds full of wonderful things and staggeringly beautiful impossibilities. Of factions so strange intertwined in war and life. Of toy soldiers brought to life, following rules so bizarre and of beings my mind can barely think about now. I’m sure you did too. Maybe nothing similar in any concrete terms, except perhaps for their sheer differentness, but I’m sure you did. Our minds were unfettered then. We did not impose any rules upon ourselves.

Think about that. Our imagination can’t be fettered and shackled by anything outside. Not by anything that we have yet built at any rate. We do not imagine what we could because we will ourselves not to. We tell ourselves that it is childish, perhaps. We tell ourselves that it has not ‘purpose’, perhaps (As if all we do is only for some ‘purpose’ – hah!). We tell ourselves that many things that may or may not be either overtly or through some corrupted sub-conscious. But, the thing is, we just truly do not imagine any more.

Take my case: I write and I dream more that most I know. But my worlds are normal. They work and they think the same except in extremes of circumstance and in magnitude. They are just the normal world magnified and stylized in the parts I find interesting. But there is nothing truly new about them. I somehow try (perhaps not ‘try’ but in any case I do it to myself) to limit myself to more normal things.

It is our imagination which drove us to be what we are. The imagination which led some ancient Pharaoh to see pyramids where there are none or an architect to imagine ancient Rome where all he saw was a river bank. We do not forsake our imagination, we can’t – that would be as absurd as forsaking thought itself. No, we bind it and lock it in a cage of our making to serve the bidding we decide is ‘best’ for it. Imagine where we would be if we didn’t.