Tag: complexity


Complex data: its origin and aesthetics

June 4th, 2012 — 10:28pm

Kolmogorov complexity is a measure of the complexity of data. It is simple to define but appears to have deep implications. The K. complexity of a string is defined as the size of the simplest possible program, with respect to a given underlying computer, that can generate the data. For example, the string “AAAAAA” has lower complexity than “ACTGTT”, since the former can be described as “Output ‘A’ 6 times”, but the latter has no obvious algorithmic generator. This point becomes very clear if the strings are very long. If no obvious algorithm is available, one has no option but to encode the whole string in the program.

In this case, when writing the “program” output ‘A’ 6 times, I assumed an underlying computer with the operations “repetition” and “output”. Of course a different computer could be assumed, but provided that a Turing-complete computer is used, the shortest possible algorithm is unlikely to have a very different length.

An essential observation to make here is that the output of a program can be much longer than the program itself. For example, consider the program “output ‘A’ 2000 times”. K. complexity has an inverse relation to compression. Data with low K. complexity is generally very easy to compress. Compression basically amounts to constructing a minimal program that, when run, reproduces the given data. Data with high K. complexity cannot, per definition, be compressed to a size smaller than the K. complexity itself.

Now that the concept is clear, where does data with high K. complexity come from? Can we generate it? What if we write a program that generates complex programs that generate data? Unfortunately this doesn’t work – it seems that, because we can embed an interpreter for a simple language within a program itself, a program-generating program doesn’t create data with higher K. complexity than the size of the initial, first-level program. A high complexity algorithm is necessary, and this algorithm must be produced by a generating process that cannot itself be reduced to a simple algorithm. So if a human being were to sit down and type in the algorithm, they might have to actively make sure that they are not inserting patterns into what they type.

But we can obtain vast amounts of high complexity data if we want it. We can do it by turning our cameras, microphones, thermometers, telescopes and seismic sensors toward nature. The data thus recorded comes from an immensely complex process that, as far as we know, is not easily reduced to a simple algorithm. Arguably, this also explains aesthetic appeal. We do not like sensory impressions that are easily explained or reduced to simple rules. On first glance at least, hundreds of blocks of identical high density houses are less attractive than low density houses that have grown spontaneously over a long period of time (although we may eventually change our minds). Objects made by artisans are more attractive than those produced in high volumes at low cost. Life is more enjoyable when we can’t predict (on some level, but not all) what the next day will contain.

The deep aesthetic appeal of nature may ultimately have as its reason the intense complexity of the process that generates it. Even a view of the sky, the desert or the sea is something complex, not a case of a single color repeated endlessly but a spectrum of hues that convey information.

 

Comment » | Computer science, Philosophy

The limits of responsibility

December 23rd, 2011 — 2:26am

(The multi-month hiatus here on Monomorphic has been due to me working on my thesis. I am now able to, briefly, return to this and other indulgences.)

Life presupposes taking responsibility. It presupposes investing people, objects and matters around you with your concern.

In particular, democratic society presupposes that we all take full, in some sense, responsibility for society itself, its decision making and its future.

However, he who lacks information about some matter cannot take responsibility for it. And thus we often defer to authorities in practice. Authorities allow us to specialise our understanding, which increases our net ability to understand as a collective, assuming that we have sufficiently well functioning interpersonal communication.

There are whole categories of problems that routinely are assigned to specific, predefined authorities and experts; for instance legal matters, constitutional matters, whether some person is mentally ill, medical matters, nuclear and chemical hazards, and so on. Fields where some degree of extensive training is generally required. (However, under the right conditions, these authorities could probably also be called into question by the public opinion.) The opposite is those categories of problems that are routinely assigned to “public opinion” and all of its voices and modulating contraptions and devices, its amplifiers, dampeners, filters, switches and routing mechanisms.

Responsibility aside, in order to maximise an individual’s prospects for life, and by extension society’s prospects for life, it seems important that the individual possess just the right knowledge that they need in their situation. Adding more knowledge is not always a benefit; some kinds of knowledge can be entirely counterproductive. Nietzsche showed this (“On the use and abuse of history for life”), and we can easily apply the idea of computational complexity to see how having access to more information would make it harder to make  decisions.

This is especially true for some kinds of knowledge: knowledge about potential grave dangers, serious threats, monumental changes threatening to take place. Once we have such knowledge we cannot unlearn it, even if it is absolutely clear that we cannot act on it and that we do not have the competence to assess the situation fully. It  takes effort and an act of will to fully disregard a threat on the basis of one’s own insufficient competence.

On the other hand, knowledge about opportunities, about resources, and about problems that one is able to, or could become able to deal with, would generally be helpful and not harmful. However, even this could be harmful if the information is so massive as to turn into noise.

Even disregarding these kinds of knowledge, one of the basic assumptions of democracy – that each individual takes full responsibility for society – seems to be an imperative that is designed never to be fulfilled. An imperative designed to be satisfied by patchworks of individual decisions and “public opinion”, and whatever information fate happens to throw in one’s way. Out of a basic, healthy understanding of their own limitations, individuals generally assume that the democratic imperative to know and to take responsibility was never meant to be taken seriously anyway, but one does one’s best to match one’s peers in appearing to do so.

It seems to me that the questions we must ask and answer are about the proper extent of responsibility, and the proper extent of knowledge, for each individual. For the individual, taking on no responsibility seems detrimental to life; taking on full responsibility for all problems in the world right now, here today, would also be an impossibility. There would be such a thing as a proper extent of responsibility. One’s initial knowledge and abilities would inform this proper extent of responsibility, and the two might properly expand and shrink together, rather than expand and shrink separately.

In a democratic society, in so far as one wants to have one, we should ask: what is the proper level of responsibility that society should expect from each individual, and what level should the individual expect from himself as an ideal?

More generally, empirical studies of how public opinion functions and how democracies function in practice are needed. It is inappropriate to judge and critique democracies based on their founding ideals when the democratic practice differs sharply from those ideals – as inappropriate as it is to critique and judge economies based on the presumption that classical economic principles apply to economic practice in the large.

3 comments » | Philosophy

Free will (2): Decision making, cause and effect

May 24th, 2011 — 10:26pm

When we claim that an act was carried out as a decision made freely, we implicitly seem to say that the acting subject is fully responsible for the action at hand. In other words, if I suggest to you that you should buy blueberry ice cream and not vanilla, and you go ahead and buy the blueberry ice cream, it is still your responsibility to have done so, were it to lead to prosecution or adverse consequences. Of course, if I have some important knowledge about the blueberry flavour that I have not disclosed, such as it being poisonous, some of the blame may fall on me, out of convention. In this case we may assume that I have tried to manipulate you into doing something you would not have done, had you had full knowledge.

The act of “making a decision” or “making a choice” is an essential part of the model we have of human beings as individuals with their own will and their own choice. If one disregards situations where people try to betray others in some sense, such as the above example (using a preliminary, intuitive conception of “betray”), the act of making a decision firmly grounds all responsibility in the subject, even though various influences, sensory impressions, emotions and so on may have led to the decision.

But if we look at decision making and acting more closely, we discover that a great deal of our behaviour is not rooted in reasons that we are aware of or understand. If we are aware of the reasons, they may be something else than what we think they are. The thoughts “I am doing this because…” or “He did that because…” only apply to a vanishingly small fraction of everything that we may categorise as Actions.

In fact, causality is a tricky problem in general, and not just in the human mind. The world is a never-ending stream of sensory stimuli, and out of this stream, we isolate things that we call events, objects, individuals, delineations, contrasts, causality. We know, as physicists, that heating water ultimately causes it to boil. But this does not mean that we have identified a causal link between event A and event B, in the way that we can identify an electric current with a measurement device, and say “see, there’s 5 Volts in this wire”. The causal model is our best guess, and clearly, there cannot be a final seal and confirmation that the model is the only true one, and the complete one. It merely stands all the trials we can come up with. Details that remain unchanging in the trials, because we did not think of testing them, or because we are not even aware of them, will not be part of such a model.

Suppose now that we do things, on a daily basis, and the majority of things we do we do not know the reasons for, or if we know the reasons, they are incomplete, falsified, or not revealed to us, because of an inner battle between different aspects of our mind. Suppose also that impressions of different kinds may influence our decisions, possibly in ways that we do not understand. For instance, seeing the color blue may lead us to walk briskly, because of some association we made years ago. It seems clear then, that attributing responsibility to the subject, for all of her actions, is a practical thing to do but not a fair thing to do. It may be that we can in fact subject anyone to a series of influences that lead them to carrying out a certain action, if we know enough about their mind, and we can control the environment sufficiently well. Is this not what artists do with their audiences?

 

3 comments » | Philosophy

Free will

May 17th, 2011 — 12:48am

 

Free will is an important idea in ethics, politics, metaphysics and philosophy of mind, since it allows for many important conclusions and principles to be derived. For instance, the fundamental reasoning of a court (at least on some level, historically) that holds somebody responsible for a crime, is that they had a choice whether to commit the crime or not, and by choosing to commit it, they exhibit their deplorable moral character, warranting a punishment. We can see this in how in modern times, psychiatrists are able to declare someone unfit to take responsibility for their actions, which greatly impacts what kind of punishments may be meted out.

Free will can also be used as support for Cartesian dualism, the idea that the body is somehow essentially separate from the soul. Some people would perhaps argue that “we can perceive that we have a free choice, therefore we have a free will, therefore the soul is separate from the body”.

Without having gone too deeply into the literature about the topic, I will posit an idea. Clearly, it is not the case that the mind is perfectly separated from the body, since physical trauma, drugs, stimulants etc, can influence our thinking. On the other hand, the mind is not immediately joined to the body either. This is in the sense that there is no “happy button” or “sad button” that I can press on my skull, or a phrase I can hear, that immediately provokes the feelings of happiness or sadness. Such feelings come only in response to complex stimuli over time. And the mind may reconfigure its responses to a certain stimuli: we may decide to be brave in the face of fear, or sad in the face of something that used to make us happy. We may find a new understanding of some object. So if two extreme ways of thinking about the will are that it is 1) perfectly coupled with the body/surrounding world, or 2) perfectly decoupled from the body/surrounding world, maybe the most accurate way of thinking about a mind is as decoupled to a very high degree, but not perfectly, from the world.

2 comments » | Philosophy

Assessing research quality

April 28th, 2011 — 4:48pm

Academic research is difficult to evaluate. In order to know the significance of an article, a result or an experiment, one must know a lot about the relevant field. It is probably fair to say that few people read research articles in great depth unless they work in exactly the area the article is in. PhD theses might cite hundreds of articles, but it seems natural that not all of these articles will be read with the same degree of scrutiny by the author of the thesis.

Hence the trouble with obtaining funding for research. In order to obtain funding, you have to communicate something that seems incommunicable without the full commitment of the reader. Grant dispensers want to know a number on a scale: “what’s the quality of this paper between 0 and 1?”, but this quality number cannot be communicated separately from the full substance of the paper and its environs. And thus we end up with keywords, catchphrases that become associated with quality for short periods of time, as a way of bypassing this complexity, an approximate way of indicating that you are doing research on something worthwhile.

This reflects a broader problem in society of evaluating authorities. I cannot evaluate my doctor’s, or my dentist’s, or my lawyer’s work, since I don’t have the necessary competence. Accordingly, I base my trust on the person and some of their superficial attributes, instead of judging the work by itself. It seems that the same kind of thing becomes necessary sometimes in choosing what researchers to fund.

It also points to a faculty that must have evolved in human being since millennia: the capacity for evaluating important properties of things we do not understand well very quickly, for danger, nutrition, etc. Only that this faculty does not translate well to research…

Comment » | Computer science

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