Category Archives: computation

Moral stories in the age of computers

All of us have been brought up listening of reading some or the other kind of moral stories –  Panchatantra, Aesop’s fables, Bible stories and so on. They are part of our standard training while learning to live in the world. All moral stories are motivated by some ultimate aim of human life, though these are never explicit or overshadowed by talking animals and trees. Our morals do not develop in a vacuum – they are shaped strongly by our socio-cultural and geographical locations, and moral stories are among the more effective means towards our ‘shaping’. Not only that, like everything else in the world, they evolve, though not necessarily in the Darwinian sense of the word. Aristotle and Plato may have condoned slavery, but not Adam Smith and his ilk. Even then, considering that Aesop’s fables and the Bible provide relevant advice even to this day, there seem to be some things that are eternal, like numbers.

From where do we derive our ethical codes? The most abundant source is of course our own history. When viewed from a certain lens (which comes from a certain metaphysical position about man and his relationship with other humans and the rest of the universe), history can give us all the lessons we need. Which is why it is said that people who forget history are condemned to repeat it – not that we have progressed linearly from being barbarians to civilized people, it is just that we are animals with an enormous memory, most of it outside our heads and in books, and preservation or changing of such a legacy necessarily requires engagement with it. Therefore, ethics and epistemology have always gone hand in hand.

Our times are unique from any other in history simply due to the predominance of science in determining what we know – Ancient Greeks or Indians would do physics and metaphysics simultaneously without necessarily putting one or the other on a pedestal. Scientific method and mystical revelation were both valid ways at getting to the truth. Nowadays, of course, the second would hardly be considered a valid method for getting at anything at all, let alone the truth. Hard to say whether this is good or bad – evolution does not seem to have a sense of morality.

The Newtonian and Darwinian revolutions have had important implications for the modes of moral story telling: First, they remove the notion of an ultimate purpose from our vocabulary. Newton’s ideal particles and forces acting on them removed any ideas of the purpose of the universe, and the correspondence between particle<->force of Newton and Darwin’s phenotype<->natural selection is straightforward. Thus, biology or life itself lost any notion of ultimate purpose. Economists extended it to humans, and we get a human<->pain/pleasure kind of model of ourselves (pain/pleasure is now cost/benefit, of course). All in all, there are some kind of ‘particles’ and some ‘forces’ acting on them, and these explain everything from movement of planets to why we fall in love.

Secondly, history is partially or wholly out of the picture – at any given instant, given a ‘particle’ and a ‘force’ acting on it, we can predict what will happen in the next instant, without any appeal to its history (or so is the claim). Biology and Economics use history, but only to the extent to claim that their subject matter consists of random events in history, which therefore cannot be subsumed into physics.

If life has no ultimate purpose, or to put it in Aristotle’s language, no final cause, and is completely driven by the efficient cause of cost/benefit calculations, then why do we need morals? And how can one justify moral stories any longer?

The person of today no longer sees himself as a person whose position in life is set by historical forces or karma, depending on your inclination, but as an active agent who shapes history. Thus, while the past may be important, the future is much more so. He wants to hear stories about the future, not about the past.

This is exactly where computers come in. If we accept a particle<->force model for ourselves, then we can always construct a future scenario based on certain values for both particles and forces. We can take a peek into the future and include that into our cost-benefit calculations (using discount rates and Net Present Value etc etc.,). Be it climate, the economy or the environment, what everyone wants to know are projections, not into the past, but the future. The computation of fairytales about the future may be difficult, but not impossible, what with all the supercomputers everybody seems to be in a race to build.

The notion of a final cause is somewhat peculiar – it is the only one which is explained in terms of its effect. If I have a watch and ask why it is ticking, I can give a straightforward efficient cause saying because of the gear mechanisms. On the other hand, If I ask why are the gear mechanisms working the way they do, I can only answer by saying to make the clock tick – by its own effect. Thus, if we see the future a computer simulates and change our behavior, we have our final cause back again – we can say to increase future benefit, we change our present way of life. The effect determines the cause.

Corporations, Countries, Communities are faced with the inevitable choice of using a computer to dictate their moral stance. However, one can always question the conception of a human being (or other life for that matter) as doing cost benefit calculations as their ultimate goal. If we need a more textured model of a human, writing an algorithm for it remains an impossibility to this day.

For example, one can argue that the ultimate pupose of life is to live in harmony with nature or that we should ‘manage’ nature sustainably. The former does not need (indeed, does not have at present) a computer model, whereas the other does. One is within the reach of every person, the latter is only accessible to a technological high-priesthood. Which should we choose? at a future time, which one will we be forced to choose?

Therefore, in this post-Darwinian world, can we imagine an ultimate purpose for ourselves that will enable us to act on our own, or will we be guided by supercomputers simulating caricatures of ourselves? Time will tell.

Systems modelling: how useful is it ?

Modelling complex systems, be they social, economic, terrorist-ic, environmental, ecological, whatever seems to be all the rage nowadays. Everyone (including myself!) seems to be so intrigued with the future that they cannot wait until it arrives.

But what is a model ? and how can/should it be used ? these are questions which are normally unanswered and can lead to disasters like the current financial circus. A systems model is, at its most abstract, a simplification of reality which can help us to answer questions about the future in a computationally tractable way (since everything at the end of the day gets reduced to number crunching, except maybe philosophy). It focusses on internal variables (state), inputs and outputs of a system that are considered important to understand its behavior. The contribution of a model is two-fold: to understand the underlying (simplified) structure, and to use this to answer questions that interest us.

We have to face that we cannot really understand even moderately complex systems properly, and we make certain idealizing assumptions (like there won’t erupt a World War), to make things simple. We then use an intuitive understanding (sometimes called pre-analytic vision) of the system structure to decide how to build the model. For example, economics models are built using the vision that man wants to maximize something (which makes it easy to use calculus of variations or mathematical programming), atmospheric models have to obey the laws of physics, and so on.

Once we identify a structure which can be represented using available mathematical tools, we put them in a computer and start crunching. If they can be represented using nice equations (called deterministic model), you would use differential equations or some cousin or mathematical programming. If it cannot, then you don’t give up, you simply say that it is random but with a structure and use stochastic models, using Monte Carlo methods or time series analysis or some such thing (Read this for a critique of the latter).

Before one gets immersed in fascinating mathematical literature, one must understand that each model comes with an ‘if’ clause: If such-and-such conditions are satisfied, then things might look like what we get here. Which is why I get irritated with both MBAs who talk about ‘market fundamentals being good’ and environmentalists who predict that I’m going to need a boat soon – neither qualifies results which come out a black box. Even worse, there are those who compare results which come out of different black boxes, which need not be comparable at all, just because they, like the modellers, have no idea what is going on. Atleast the modellers admit to this, but those who use these models for political purposes cannot dare to admit shades of gray.

Different models can take the same data and give you radically different answers – this is not due to programming errors, but the pre-analytic vision that the model is based upon. The reason why climate change remained a debate for so long is because of such issues, and vested interests, of course. Therefore, we see that the ‘goodness’ of a model depends critically on the assumed ontology and epistemology, even more than the sobriety of its programmer (well, maybe not).

Thus, as intelligent consumers of data that models spew out everyday, we should make sure that such ‘studies’ do not over-ride our common sense. But in the era of Kyunki Saas bhi, one cannot hope for too much.

Information and Energy, and Entropy!

What follows is quite incomprehensible if you do not have some idea of maths/physics, but read on anyways :)The question that I have been asking for quite some time is : “What is information?”, from an abstract point of view. Would have hardly expected a physicist to answer this, but they did. Looks like there is a connection between the energy of a system and the information it contains. More precisely, the number of states that a system can take is directly proportional to the information it contains. This was put forward by Boltzmann, who is rightly well known for his huge contributions to physics. Take for example two people, A who sits on a chair the whole day and B who keeps running around the whole day. If someone tells you A is sitting on the chair, you would already know it, so it is nothing new to you. However, news about B’s whereabouts will always be new information to you. Therefore, an energetic system tends to contain more information than a static one.

One could also understand this by looking at a storage cell, which can contain n bits. As n increases, amount of information stored increases, so does amount of energy it contains (Not to be confused with present day memories like RAM, where most power is consumed by resistance and (silicon) crystal imperfections.) Boltzmann stated that if a system can have M mutually distinguishable states, then the amount of entropy is given by \log{M} . Entropy can be called a measure of the randomness in a system, that part of the system’s energy that is unavailable for useful work.

Claude Shannon, founder of practically everything we know (if we exaggerate a bit), generalized Boltzmann’s hypothesis to a case where we have some idea of the probability of a state of the system occuring, i.e, we have a probability distribution of the states of the system. In Boltzmann’s view, the distribution was uniform, and hence there was the \log{M} result. In a probabilistic system, one can only talk of the expected information, and that is what we get: Information entropy is given by I = -\Sigma_x p_x \log{p_x} . Note that this reduces to the previous form if p_x = \frac{1}{x} . Here, since the system behaves in ways we understand, the total entropy has been reduced by a factor I . If the base of the logarithm being taken is 2, the unit of the value is called bit. If natural logarithms are used, it is called a nat. Nat, interestingly,  corresponds to the Boltzmann constant when used to in an entropy context. Thus, we see the beginning of a link between entropy and information. We reduce the entropy of a system by gaining more information about the states in which it can be present. If we know exactly what state it is in, the amount of entropy is effectively zero.

How do we find the distribution of states ? we have to measure. Therefore, what is being implied is that measurement reduces the entropy of a system, or that measurement reduces the uncertainty we have about a system, which seems intuitively correct. If system A measures system B, B’s entropy reduces, whereas the entropy of the system consisting of both A and B does not (from the viewpoint of a system C which has not measured either A or B). The information got via measurement must be stored (and/or erased) somewhere, and this requires energy. This could be seen as the solution for the famous Maxwell’s Demon paradox, which claimed to violate the second law of thermodynamics.

These views have importance in the theory of computation, especially in the lower limits of energy required for computation. Say, I have a system that takes in 2 bits and gives out 1 bit (like an OR gate), then the amount of energy expended must be atleast equal to the difference in information entropy, which is 1 bit. Similarly, if information entropy increases, the system must take in energy. You can read all this and more (especially qualifications) in this paper.