On the futility of science
*The rented ford races through the winding roads near santa fe, new mexico. A brown man sits behind the wheels intensely focussed on the curves ahead. We discreetly dwelve into his mind for ten short minutes. What follows is an uninteresting transcript of his neural chatter...*
he enjoys the sight of green capped mountains in the distance alright. when the green becomes white, he wants to try his luck at skiing. thoughts come and go, one after the other, in a neverending boring pattern like the knocks from the feet of a galloping horse. the car pummels its way towards its destination. nothing happens.
after exhausting pleasant memories of old friends, new friends, extinct girl friends, neat cars, fast cars and other more boring topics, his head sneaks into prohibited areas and begins to ask questions that have tortured philosophers and kings alike. he begins to think about faith and science (no..no.. not the science of faith or the faith in science. merely the contrast between "faith" and "science"):
Science is based on a set of axioms, right? Now, Godel proved in this famous theorem (circa 1920s) that in a system based on a set of axioms, one can always find a question that cannot be logically answered. Thus, no matter how mature science becomes, there will always be unanswered questions. Therein lies the conundrum.
I have heard some people say they pursue science to unravel the mysteries of nature. My point is, by the above agrument, science can never unravel all the mysteries of nature. So its a wild goose chase. So, give it up folks, go pick up your implements and start tending to your sun-flower farm.
Contrast that with faith. It is based on one rule: if something cannot be explained using your puny brain, attribute it to the greatness of God. Finished. Game over. Its a wonderful system which puts people at ease. Imagine this:
Grad student: "Argh Professor, I have been utterly puzzled about the dark matter in the universe"
Prof: "My son, all I have to say is this: Thou shalt find light in your deep faith for the dear Lord"
Thats it. No Hubbles, no research papers, no hours of coding and data crunching, no seminars, no arguments, no fights, no free-food...
Granted, a faith-based system does not provide the detailed evidence or connections that science tries to establish. But once liberated souls put their heart into it and take up faith, nothing really perturbs them. Everything becomes beautiful, complete and begins to have a purpose (to satisfy the divinity's plans, which are obviously not questionable!). All those who completely surrender themselves to a faith based belief system seem to be content and happy, which brings us to the big question: "why pursue science. why not take up faith and simply be done with it all?"
he enjoys the sight of green capped mountains in the distance alright. when the green becomes white, he wants to try his luck at skiing. thoughts come and go, one after the other, in a neverending boring pattern like the knocks from the feet of a galloping horse. the car pummels its way towards its destination. nothing happens.
after exhausting pleasant memories of old friends, new friends, extinct girl friends, neat cars, fast cars and other more boring topics, his head sneaks into prohibited areas and begins to ask questions that have tortured philosophers and kings alike. he begins to think about faith and science (no..no.. not the science of faith or the faith in science. merely the contrast between "faith" and "science"):
Science is based on a set of axioms, right? Now, Godel proved in this famous theorem (circa 1920s) that in a system based on a set of axioms, one can always find a question that cannot be logically answered. Thus, no matter how mature science becomes, there will always be unanswered questions. Therein lies the conundrum.
I have heard some people say they pursue science to unravel the mysteries of nature. My point is, by the above agrument, science can never unravel all the mysteries of nature. So its a wild goose chase. So, give it up folks, go pick up your implements and start tending to your sun-flower farm.
Contrast that with faith. It is based on one rule: if something cannot be explained using your puny brain, attribute it to the greatness of God. Finished. Game over. Its a wonderful system which puts people at ease. Imagine this:
Grad student: "Argh Professor, I have been utterly puzzled about the dark matter in the universe"
Prof: "My son, all I have to say is this: Thou shalt find light in your deep faith for the dear Lord"
Thats it. No Hubbles, no research papers, no hours of coding and data crunching, no seminars, no arguments, no fights, no free-food...
Granted, a faith-based system does not provide the detailed evidence or connections that science tries to establish. But once liberated souls put their heart into it and take up faith, nothing really perturbs them. Everything becomes beautiful, complete and begins to have a purpose (to satisfy the divinity's plans, which are obviously not questionable!). All those who completely surrender themselves to a faith based belief system seem to be content and happy, which brings us to the big question: "why pursue science. why not take up faith and simply be done with it all?"
posted by littlecow at
8:27 AM
12 Comments:
Axiom?
Conundrum???
Err...i like Faith better :)
Very interesting point. A week back three of us at home almost killed each other fighting the ID vs. evolution thing. I can see why Godel's proof is so appealing. However, the Godel space is expandable isn't it? In the sense you can keep growing your set of rules to explain a larger set of problems. However, you are right to point out that there will always be a proposition that will not be satisfied by the current set of axioms. Discovering that proposition is a challenge in itself isn't it?
So scientists will continue doing what they do :) Anyway, there is no point in stopping. It isn't like anything else in life makes much sense anyway.
I guess life is about fooling yourself to death. To each his own way. :)
@kumari: You are in a safe boat just like the generations of moms and grandmoms that India has spawned! R-I-P. :-)
@sanketh: "I guess life is about fooling yourself to death". Right on! :-)
@~a~: yes, but the foundations on which the logic of science stand is in itself very abstract, right? i mean, why should force be proportional to the rate of change of momentum and not to the length of lallu's dhoti or something that is equally absurd?
further, i absolutely disagree with a human being's "sense of purpose" -- do you truly believe that people have a sense of purpose? damn, i don't! and i was talking to two fellows yesterday under a moonlit urbana night and they did not. my father does not, my prof does not, my best friends do not. everyone i have spoken to (other than believers and fanatics) seem to agree that they have not yet comprehended the purpose of it all. so, where is the sense of purpose?!
~a~: "bringing up the issues that are incomprehensible for most brains around": you will have to include me in that list as I don't understand a damn thing that goes around me! Somehow, almost magically, I survive, grow and things turn out to be just fine. On the occasions when I feel really cocky, I wonder, 'if i don't understand no nothing and if i assume i am not that bad, then what about the billion others?'. anyways, i do recognize the brilliance of science and love it. i appreciate how wonderful a construct the whole thing is and i have the deepest respect for the people who built it brick by brick. but my point is that spirituality/faith etc might play a central role in the whole process of understanding. that one should not restrict oneself to a blind belief in science!
Have you read "Angels and demons " recently?. Somehow i could find Dan brown effect in this post!
@anon: Nope! But I take it as a compliment!
Sami. Here are my comments on your original blog entry that I finally read.
"Science is based on a set of axioms, right?"
Presumably so, but not rigorously. This is much unlike mathematics, where from 1925 or so, the study of mathematical logic was formalized. The kind of conundrums that Cantor ran into with the construction of the Cantor set for example were settled satisfactorily by a combination of Gödel's completeness theorem and the two incompleteness theorems in 1931. However, even in mathematical logic, which has a much more rigorous logical structure than science, there are several outstanding issues that are yet to be solved. Having said that, it seems to me that your starting supposition and application of Gödel's theorem (the first incompleteness theorem I think) was ill-defined. So, it is not clear if the conundrum you end up with is a consequence of a real undefined nature inherent to science, or if it is a consequence of an ill-defined question to begin with. However, what you have written is in agreement with some of the popular viewpoints on science. A common misplaced application of Gödel's first incompleteness theorem has been to the study of neuroscience. It has been argued by some (sometime in the 1950s I think) that the pursuit of artificial intelligence is futile since the ability of the human mind limits what is within its grasp and what is not. It is yet another example of an ill-defined application of Gödel's theorem and hence paradoxes arise out of it.
Having said all of that, I will be the first to admit that because of the non-rigrous nature of science it is often not possible to rule out fundamental problems in the way science progresses. So, to me science is yet another faith. I am not talking about "the science of faith or the faith in science", but about science as a faith system. I believe that at some level, there is a mechanistic explanation to the world (belief in the causality of the universe, not in irreversibility of time-flow which is not always true at the sub-atomic level it seems). I also believe that simpler explanations are "better" ones (Occam's razor). Unfortunately, I am not a "pure" member of this religion called science, since I also believe that there are a multitude of approximations to the "truth" that work really well for well-defined contexts (in other words, I commit the blasphemy that some would call as engineering). That approximately defines my faith system, which coincides remarkably well with those of science, hence my claim that science is itself a faith system.
@muddy: You have clearly elucidated the differences between science and engineering towards the end of your paragraph. We will keep it as such and start from there.
Science, as referenced here, is the logical explanation accorded to observed facts using the conclusions drawn from mathematical axioms as support. Thus, the science spoken about here is in fact based on a set of axioms.
As you mention, "even in mathematical logic, there are several outstanding issues that are yet to be solved". This is precisely the point made in the essay. Even in the most rigorous of systems (of which science is a subset or at worst, a degenerate subset), there are anomalies, unanswered questions. Quite often, we put a blind belief in science without understanding the limitations that such a system inherently carries within itself.
I have used Godel's theorem, as applied to the mathematical framework that supports science, to substantiate the claim as mentioned in the paragraph above. Hence, it is not an ill-defined application as you allude to in your comment. Indeed, any critique of the application can only attack Godel's theorem directly and I suspect you are not doing that! Note that the definition of science given at the start is clear and the well-defined question posed is one of 'whether science is the elixir for all the questions of life'. No ambiguities there either.
It is possible that the essay might have conveyed the false notion that any system based on axioms is incomplete. I am aware that this is not so. The purpose of this piece was to elucidate a point, which struck me as important, in support of faith against science and not one of an exposition of Godel's theorem. My capabilities and understanding of the theorem preclude any attempt to do so!
Your final conclusion that science itself is a belief system is agreeable. It almost sounds Feynmanish!
Most of your points taken. The only thing that I still disagree with is the use of Godel's theorem to science. The axioms of modern scientific logic are based on a set of empirical observations, which is unlike the moderm formalism of mathematical logic. Since the axioms are science are empirical observations, there is always the risk that it is "incomplete" leading to a non-applicability of Godel's theorem. On the other hand, mathematical logic is based on mathematical constructs such as say, groups or vector spaces etc, where the axioms are laid out explicitly and constructed external to the system (theorems and other subsequent mathematical deductions) itself.
However, I did get the point of your essay that you are trying to compare science to other forms of religious faith and point out the benefits of the other faith systems in a much more coherent and humorous way than I have typically seen written. Unfortunately, I am a devout member of the religion of science. Hence, I continue to turn a blind eye to faith. But as Hardy (the mathematician) once put it, I will play it safe and be an agnostic at most and not an athiest! [-o<
@muddy: Here are my arguments that support the application of Godel's theorem to science:
As you rightly mention, 'the axioms of modern scientific logic are based on a set of empirical observations'! An axiom according to the dictionary is "A self-evident principle or one that is accepted as true without proof as the basis for argument". Thus, one can assert the existence of any axiom until it is self-evident and no observation contradicts it. To note a few loose examples, F=ma is an axiom and so are Newton's other laws. (Note that the above is only given as a classical example and the effects of relativity/quantum mechanics are not considered. Indeed, if you do want to take them into consideration, the axioms identified will be different but their existence never threatened.)
Now Godel's theorems apply only to systems that allow the definition of natural numbers as a set. That said, it is enough to show that the axioms of science allow the definition of natural numbers as a set to prove the applicability of Godel's first incompleteness theorem. This shall be attempted next. (Ref. 'Misconceptions about Godel's theorems', #2 at Wikipedia)
The definition of science as provided earlier was one that combines both the axioms of physics and those of mathematics to explain observations. It is not only necessary to know that F=ma is true, but also essential to formulate arithmetical operations like +,-,x,I and so on before the physics axioms can be applied for explanations. Now, the arithmetical framework certainly includes the definition of natural numbers and Godel's theorem is applicable here. Thus, Godel's theorem implies that a part of the entire set of axioms used in science to be incomplete and hence the superset is also incomplete. Hence, the applicability of Godel's theorem to science. It is also for this reason that any system built on arithmetical constructs fails to answer every question that is posed within it.
As for your comment, "Unfortunately, I am a devout member of the religion of science. Hence, I continue to turn a blind eye to faith", note that science attempts to build a framework wherein the axioms hold true universally. However, there can be no proof devised that will proove that the axioms are applicable everywhere in space and time. Thus, science itself is faith-based, the faith here being the belief that the axioms are universal in nature! By subscribing to the 'religion of science', you are embracing faith rather than turning a 'blind eye' to it. I suppose then that you meant faith in god or some supernatural power. But then, both these modes of faith are already beginning to show similarities, in being adopted by belief and without a scientific proof! While faith in god does not suffer from a lack of rigor as it does not claim to offer a scientific proof to start with, science does suffer as it contradicts its own basis!
I disagree with way too many assumptions implicit in your attmepted arguments above. I state once again that your statements are not well defined like a mathematical statement would be. Your descriptions are still bound by language that does not have precise and unique defitions for the terms you have freely used.
You applied Godel's theorem to math and of course it works (because you claim that all objects of science can be uniquely expressed mathematically, which is not true). Your claim that there even exist objects such as "axioms of physics" is not true. There exist only empirical observations and laws that are passed off as axioms by some. Nevertheless, the framework of science is by no means as rigorous as mathematics. So, I am not picking on you for using not-well-defined terms, but picking on the nature of science and of human language.
Your presentation of so called inconsistencies in science and the lack of them in other religions is very one sided since by definition, you state that logic is not applicable to other religions since they don't claim to be logical. So, that leaves no room for logic and hence any claims of "greater consistency" in non-scientific faith systems is a moot point. However, I think any claim of infallible rigour in science is fundamentally flawed. In my opinion, only math and music have the luxury of that claim.
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