Sunday, September 08, 2013

The Limits of Science

There’s been some buzz going through the blogosphere, following an essay by Steven Pinker on “Scientism”. On the one side of the debate are those who believe scientism is a higher state of consciousness, and on the other side those who think it’s a scientifically transmitted disease with a symptomatic itch that shouldn’t be scratched publicly. And I think they all failed to address the main point: Where are the limits of science? And how do we find them?

If I read essays by philosophers and social scientists and other academics in what is vaguely considered “soft science” I often can’t but sense a certain ring of panic. The physicists are coming, is what I read, they’re planning to take over with mathematics. Then they rush to ensure themselves and everybody else that no, no, some things can’t be described by mathematics. This appeals to the public because nobody likes to be predictable and many people are afraid of math. The softies line with the masses and end up being the good guys for perpetuating cognitive illusions, while the physicists are marked delusional reductionists. Welcome to the 21st century.

Oh yes, the softies will admit, there are meanwhile many mathematical models in the social sciences, and neuroscience has already made some discussions about consciousness entirely redundant. But look, they’ll say, these can only tell you something about statistics (scary math word). Human behavior can’t be modeled mathematically. After all we’ve got free will (unproved). We understand the models about us (irrelevant). Humans are special (said the human), the brain is complex (whatever that means), and it’s got qualia (defined by being unmeasurable). And, most importantly, humans are not elementary particles. (Always good to finish an argument with a completely irrelevant statement that everybody must agree on.)

The problem with these elaborations, besides making me wonder what these people get paid for, is that we presently know of no reason why some observations, like human behavior, cannot be modeled mathematically. But neither does anybody know for sure that it is possible. What we do know however is that it certainly is not presently possible. And that’s what determines the limits of science: our present possibilities, what we can do in practice, and not unknown and quite possible unknowable principles.

It shouldn’t be relevant to my argument, because I’m telling you what matters is what we can do in practice and not what we can do in principle. But just so you don’t misread me: I don’t believe that everything can be described by mathematics (for reasons I’ve laid out here). I’m just saying that we presently don’t know of any reason why it should not possible to describe human behavior mathematically.

Personally, I think it is possible but useless in that such a model would in the best case be a copy of the real system and would not deliver predictions. It would be like trying to understand the sun by simulating it in true resolution and real time on a computer cluster. Then you can either watch the sun or your computer, but besides this you haven’t really gained anything. If you believe that we live in a matrix as study-objects, then we live here because it was not possible to find a simpler way to analyze behavior of human societies than just creating and watching them.

So much about my beliefs. But these are beliefs because we don’t know whether they’re true, and in any case these limits that might exist in principle are far beyond the limits that presently exist in practice.

And of course science has limits. It has limits because our understanding is incomplete. These limits of science aren’t fixed and they are constantly shifting as we learn more about the world that we live in. In that process, topics that were previously inaccessible to the scientific method become accessible, and that creates friction in the communities.

Imagine the world of knowledge as having a core of hard science, surrounded by a belt of soft science, that goes over into interpretations, narrative, opinions, speculations, and eventually fantasy. The hard core expands as we learn: What once was a matter of interpretation becomes measurable. What once seemed beyond computational possibility becomes computable. What once was merely a story becomes supported by evidence. Problems arise if researchers refuse to use the best scientific methods of the day in their field. Then they are simply acting unprofessionally. And when they notice they’ve missed the boat they panic.

Where are the limits of science right now? That’s the discussion that we should have. And it’s not an easy one.

Let me give you three examples of what’s presently off-limits for mathematical modeling.

One is history. You could in principle imagine that it was possible to create a model about human behavior, say, in war-times, that produces outcomes that we can observe today, for example how people expressed themselves in the literature. Then you could analyze the literature to draw conclusions about the circumstances back then. Needless to say, converting experience into writing is so difficult to model mathematically that nobody can do this, and nobody even knows if it is possible. So instead historians go and read the literature and study the paintings, and try to interpret them by taking into account as much as they know, most notably about being human, something that they can do better than any software or equation. At least for now.

The second one is personal identity. Nobody really knows what it takes for a human brain to create a sense of self-awareness and the experience of being an individual actor in possession of a body. Neuroscience has collected a lot of information on that matter, but we’re far off from being able to mathematically model these processes. Much of the literature on the subject is interpretation of data or case-studies. But wait some decades and I’m sure we’ll know much more about what enables “you” to think of “yourself”.

The third example is politics. One often hears that science can only deliver the facts, but humans still have to make the decisions because they have to take into account “morals” and “values” that are off-limits for science. This is however empty vocabulary. Values and morals are just simplifying concepts that arise in our cultures. They are in the first line words that primarily serve the purpose of communicating opinions. Morals and values change over time, people tend to interpret them individually differently, and they might regard them more or less helpful for their self-expression. But there is nothing – in principle! – that prohibits science from predicting the emergence of certain morals and values. Again though, in practice, nobody can do this.

And that’s why science cannot replace politics. Because when you express your opinion about a possible change, you are projecting yourself into the future and try to find out whether or not it would be an improvement. Or, in the Darwinian mindset, whether you’ll be more or less well adapted to your environment. For this projection you need to know some facts, and these facts science can provide – with errorbars. But what science cannot do is to project you and your experience into the future. The best way that we presently know to do this projection is to ask people to do it themselves. There are pitfalls to this, because we are not actually good at predicting what we will think in ten years from now. But presently it’s the best we can do.

The last example also tells you why it is important to know the present limits of science. Because it raises the question what we know about human decision making and whether we can use that knowledge to make better decisions.

In summary. Science has limits, but they change over time. Knowing where the present limits of science are is important because that’s where opinions and interpretations become relevant to decision making. Excuse me for publicly scratching my itches.


  1. /*..In summary. Science has limits, but they change over time...*/

    As Max Planck once said, in science new truth isn't accepted, until all their opponents will die out. After all, the Holy Church accepted the Big Bang theory at the very end as well. The only question is, if we aren't paying the scientists better than Church priests for more flexible attitude than just for pure Darwinian evolution.

    In addition, in dense aether model every theory, every approach has its limits in less or more wider perspective - you may perceive it as a generalization of Goedel's incompleteness theorem. So that even if the scientists will develop the ideal scientific method, this method will hit to its practical limits soon or later. And because the scientists are just a people, their own methods will become counterproductive even sooner.

    The fundamental source of controversy is, that the scientists do need to achieve the progress in research, but when they achieve it, the research ends. And so what, after then? From this reason the scientists adopted the logarithmic approach and when they became too close to the final solution, they delay its acceptation, as Robert Wilson famously expressed in his famous memo (Physics Today vol. 39, p. 26, July 1986).

  2. BTW The Wilson's memo is here. Because Bee tends to wipe out all uncomfortable posts, particularly these linking the external sources, I'm linking it in separate post.

  3. Because the contemporary community of scientists (physicists in particular) is a remnant of relatively resourceful cold war era and as such overpopulated with respect to its actual utility, the attitudes of common scientists are desperately occupation driven: they tend to support only ideas and finding, which are bringing the grants and money into their community and ignore all findings (like the cold fusion) and ideas/concept (dense aether model), which could make portion of them redundant. In this way the new ideas are accepted in just the speed, which doesn't harm the scientific community as a whole.

    The only question is, if this otherwise logical selfish meme behavior is in agreement with interests of the rest of human society, which is actually paying whole this fun. I'd guess, it isn't.

  4. Therefore the actual problem of scientists isn't, they're overemployed (as the increasing portion of so-called :Duh research" indicates), but that they're actively hindering and boycott the progress in areas, which are of key importance by now - like the cold fusion research. Which is why we have still have no peer-reviewed attempt for replication of experiments, which are over seventy years old already. Because no one of physicists involved actually wants to replicate it. And this is what really bothers me, because we are losing incredible values each day with such ignorant approach.

  5. /* This appeals to the public because nobody likes to be predictable and many people are afraid of math */

    The problem is at both sides of conflict here. For most of people purely formal thinking is not natural and they do want to imagine and understand the things in wider causal context, not just to describe it. As Feynman noted, the atemporal math cannot provide such a understanding by itself.

    The deeper problem is, that with expansion of our scope of view the hyperdimensional reality becomes increasingly complex and the formal models based on low-dimensional classical theories aren't effective for its description anymore. I'm usually explaining it with geometry of surface wave spreading, which is directly analogous to the problem of expansion of observational perspective inside of universe.

    Therefore the contemporary physicists are in ideological crisis: they do want to use the (postulates of) their beloved theories for description of observations, which are apparently violating them. Well, they should learn new stuffs instead of neverending extension of these old ones.

  6. Slightly peripheral but #3 in your list of the currently off limits for science a discussion of polling would have to include the "Nate Silver" effect. ( ) An American Statistician and Author who totally out performed professional pollsters in the last two American elections. I realize that predicting winners is not the same as predicting what those winner will actually do it is rather significant I think.
    He now is employed by ESPN predicting Sports outcomes.

  7. /* we presently know of no reason why some observations, like human behavior, cannot be modeled mathematically*/

    This reason is IMO symmetric to reason, why the N-body system of colliding particles cannot be modeled mathematically (I mean with classical means of analytical geometry and differential calculus) for higher number of particles than five-six. Above this limit the purely numerical iterative methods become more effective. The human brain IMO does the collision of solitons in time dimensions instead of spatial ones, but the whole problem in complexity is otherwise identical. It's too highly dimensional and poorly conditioned problem from perspective of low-dimensional math.

    At the web pages we can find many intriguing numerical simulations of fluids and gases, which would require many years of qualified mathematician for their rigorous analysis. The question is, if the human society really needs such an analysis and if the current quantum field theory couldn't be simplified with the same approach. It's like the development of programs in pure assembly language or machine code in IT industry - it's still possible, but nobody will pay for it.

    This doesn't mean, we should stop with mathematical research, but the gold era of dummy theoretical articles filled with otherwise unsolved equations and analytical models is over. The future of physics is rather in numerical methods based on simplistic assumptions and multiparticle simulations, which couldn't be replicated without computer.

  8. Even specifics beyond the generality that human beings evolved from ape-like creatures with some dozen intermediates in the fossil record may be beyond the limits of science, because information to decide between alternate evolutionary pathways may be permanently lost. A lot of evolutionary psychology and sociobiology may remain plausible stories that violate no scientific principles but are undecidable.

  9. e^[(i)(pi)] = -1 precipitates hysteria; not(not(p or q) or not(p or not(q)) = p is textual blight*. We are saved by psychology mocking statistics and macroeconomics' bankrupt modeling of positive feedback. Rome was prosperous, comfortable, and ever hopeful. Its implosion left penury, filth and dread. DCLXVI years tested faith, whose imposition was justified by its failure.

    Triumph of the congenitally inconsequential is God-given (vida supra). History does not repeat itself, but it does rhyme: 22 July 1209 vs. Obamanation’s Syrian crusade. Redirected stupidity is not intelligence, whatever its talents for presentation. Science is the chocolate of our souls.

    *J. Automated Reasoning 19(3) 263 (1997)

  10. I have been saying similar things for many years. People who believe in science like they believe in religion tend to think that there are no limits to it. But it is just as much a disservice to science to expect more of it than it can possibly deliver as it is to expect too little.

  11. Arun,

    "information to decide between alternate evolutionary pathways may be permanently lost..."

    Ah, no, information can't get lost... :p

  12. This comment has been removed by the author.

  13. Have not read essay yet, but as I read your entry somethings came to mind.

    Demarcation Problem?

    Bee:I’m just saying that we presently don’t know of any reason why it should not possible to describe human behavior mathematically

    Also to me now it seems a bit of a change(you live room for the possible) from what I have read with your thoughts about Tegmark in regards to a mathematical universe?:)

    Will write more later.


  14. Plato, you couldn't have possibly expressed yourself any clearer.

  15. Bee:Plato, you couldn't have possibly expressed yourself any clearer.

    You mean the period, right?:)

  16. Yes.... I was a fraction of a second late.


  17. T. N. Palmer

    "Lorenz, Gödel and Penrose: New perspectives on geometry and determinism in fundamental physics"

    A fresh breeze enters a very stale room.

  18. Two things:

    1. To claim that "soft" scientists are the good guys seems a bit a stretch to me especially when humanities departments are receiving less and les funding and in some cases closing shop altogether. If you equate appreciation of science with funding then in think the most recent trend is towards applicability of research, which punishes humanities and basic research alike.

    2. I think that Thomas Nagel in his paper `What is it like to be a bat?' makes a pretty good case for the limits of science when it comes to cognitive science.

  19. Dr Bee,

    I realize your question relates to any inherent limitations of science in modeling the entirety of world around us. On a practical level, science being a human activity, I would expect its limitations to be as numerous as humans themselves.

    In a nearby town three high-school students were in a camper watching a movie on a TV plugged into a gas powered generator. Now one is dead from carbon monoxide poisoning and two have recovered after time in hyperbaric chambers.

    It is across the moving front of the corporate present moment that our science receives its ultimate test and there it is not uniformly available or appropriately brought to bear.

    And can we actually speak of science as some grand aggregate of things known? Is there a legitimate mathematical operation that can add its diverse parts into a functional whole?

    Perhaps synthesis is an inherent limitation. Scientists of all stripes, lured on by their curiosity, will wander off in diverse directions only to come back having gone native and speaking in strange tongues.

    If we adopt mathematics as the lingua franca then perhaps Gödel has the final word.

    No matter how you come to know truth there will be truth you do not recognize.

  20. I am not sure why you lay so much stress on mathematical modelling, which seems to me to be but an economical form of explanation.

    When you say that it may some day be possible to model the formation of value mathematically, do you mean, model it as a purely physical process, or as a social process?

    The question you have not addressed concerning value seems to be much more important than the degree to which value can be explained either physically or socially. And that is, can any possible observation ever imply a statement of value? I say not, and this would seem to be a clear limit to science.

    cornstalk at columbus dot rr dot com

  21. Mark:

    "can any possible observation ever imply a statement of value"

    I'm not sure what this is supposed to mean. I think you didn't really understand what I was saying. I said that values are simplified and generalized assessments that the human brain uses. You could in principle predict them, provided you'd have sufficient computing power to model all human brains, which is arguably presently practically impossible. If you could do this, could you then ask what the spectrum of values is that humans will assign to certain predictions or 'observations'? Yes, sure you could. Alas, that's beyond the presently existing limits of science, so instead you'll just have to ask people what they value. Best,



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