Computability and Comprehension – Is Science About Prediction?

By: Bruce
December 23, 2010

Science is the process of how we use reason to find patterns in reality and then to explain them in finite explanations of reality that allow us to represent reality via processes that are computable.

In my last post, I introduced David Deutsch’s book, The Fabric of Reality. Deutsch’s main interest is in understanding – and by that he means understanding everything. Deutsch believes that understanding something is to have an accurate explanation of it and that this, in turn, serves as a sort of algorithmic compression of all observational data.

Deutsch’s point of view falls under what we might call Scientific Realism. It’s the idea that science is not just about coming up with clever predictions about the world, but rather it’s about discovering reality’s true nature and comprehending it.

The alternative point of view I throw under the umbrella of Positivism. Positivism comes in many forms. Physicist and author Stephen Hawking describes positivism like this:

Any sound scientific theory… should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Karl Popper and others. According to this way of thinking, a scientific theory is a mathematical model that describes and codifies the observations we make. A good theory will describe a large range of phenomena on the basis of a few simple postulates and will make definitive predictions that can be tested.

If one takes the positivist position, as I do, one cannot say what time actually is. All one can do is describe what has been found to be a very good mathematical model for time and say what predictions it makes. (The Universe In a Nutshell, p. 31) [1]

When stated this way, Positivism sounds rather innocuous. Isn’t it just a truism that our science never really uncovers reality? We know there are often multiple interpretations of the same physical phenomenon. For example, in most cases Newtonian Physics and General Relativity both give exactly the same predictions. Not until you start to approach the speed of light do they diverge. And in the case where the two views do diverge, we favor General Relativity because of its better predictive power. But does that really mean we should pretend that the universe is curved even though common sense tells us it’s not?

In other words does it really matter if science finds some ultimate view of reality? Isn’t science really just about making predictions?

Look at our definition of what science is above. Think of Positivism as concentrating on the ‘computational’ aspect of science and Scientific Realists as concentrating on the explanation side of science.

Deutsch is in the ‘ultimate view of reality’ category, for he believes that science is solely about trying to explain and therefore comprehending reality. The computational aspect just falls out as a matter of course once you understand something.

For even in purely practical applications, the explanatory power of a theory is paramount and it’s predictive power only supplementary. (The Fabric of Reality, p. 4)

To prove his point of view, Deutsch suggests a thought experiment. Pretend that aliens give us poor humans a magic box, an ‘oracle’ so to speak, that can “predict the outcome of any possible experiment, but provides no explanations.” (The Fabric of Reality, p. 4)  In theory this should be a Positivist’s dream. Since we only care about the predictive power of science, we now no longer need science because we can literally predict anything.

The problem Deutsch points out is that we still don’t know what experiments to have the oracle predict for us. So it does us no good to have it without first using science to decide what to try to predict. Deutsch goes on to say:

If we gave [the oracle] the design of a spaceship, and the details of a proposed test flight, it could tell us how the spaceship would perform on such a flight. But it could not design the spaceship for us in the first place. And even if it predicted that the spaceship we had designed would explode on take-off, it could not tell us how to prevent such an explosion. (The Fabric of Reality, p. 4)

So it would seem that Scientific Positivism is fatally flawed. “Prediction – even perfect, universal prediction – is simply no substitute for explanation. …the oracle would not be replacing theories at all: it would be replacing experiments.” (p. 5)

So there is a deep relationship between explanation and computability. But ‘computability’ is subservient, so to speak, to explanation itself. But doesn’t this just make sense? If you comprehend something, like what PI is, you can figure out how to calculate it. But if you know how to calculate it only, you don’t really understand what it is or what to do with it.

Criteria for an “Explanation”

But this does give us a sort of criteria for what is or isn’t an ‘explanation.’ Explanations are deeply related to ‘computable algorithms.’ That is to say, there is no such thing as an explanation that doesn’t also have an attached algorithm. (Though there might be an algorithm that has no attached explanation.) At first this might seem a bit uncomfortable. Is it really true that all patterns in nature are explainable and thus algorithmic? We don’t actually know and can never know that for certain. But we can know that the alternative – that some things in nature can’t be explained at all – is unacceptable. [2] If we were ever confronted by an unexplainable pattern in nature we would never give up trying to understand it via explanation. Unless we could somehow explain why the pattern is unexplainable (via a proof/algorithm, of course), we’d forever insist that it must be explainable and keep seeking for that explanation. [3]

Questions

Can you think of any ‘explanations’ that don’t include an algorithm?

Can you think of any algorithms that don’t include an explanation?

For those that are familiar with Omega already (see note 2 and link) what significance is there that we can define a number that we can’t compute, but that we can compute that we can’t compute it? (Did you follow that?)

Deutsch is hard on “Positivism” because he feels it downplays explanation in favor of prediction. Is this the only way to interpret Positivism? Or is Deutsch being too harsh here?

If you owned an alien artifact that could predict any scientific question, what questions would you ask it? (Note: You have to ask it scientifically specific questions. It won’t understand abstract or general questions.)

Note

[1] It’s interesting that Hawking gives Karl Popper credit for Positivism because Deutsch gives Popper credit for Scientific Realism. After reading Popper, I’m not surprised that both schools of thought trace themselves to Popper. However, Popper claims he is not a Positivist unless you stretch the term well beyond the way people normally understand it. (Myth of the Framework, p. 75)

In a future post, I’ll consider Hawking more recent arguments that there is no “ultimate reality” to find in the first place and therefore Positivism actually represents reality better than Scientific Realism.

[2] Gregory Chaitin’s article “The Limits of Reason” challenges the idea that all things are explainable in mathematics and implies that this might also be true for physics. Within the scope of this one post, I can’t tackle everything he says other than this tiny nod to him. Needless to say, even if that is true, unless it’s something like Chaitin’s “omega number” where we can actually explain why we can’t compute it and compute that we can’t we’d have no basis for no longer seeking an explanation. In other words, we can’t compute his ‘omega number’ directly, but we can explain what this non-computable number is via an algorithm (Godel’s theorem and the halting problem are essentially the same theorem in different forms and are both algorithms.) Furthermore, we can come up with algorithms to figure out what finite portions of “omega” are.  So it’s not strictly true that ‘omega’ can’t be computed but only that there is no hope of computing it in it’s infinity. In any case, ‘omega’ is a carefully tailored exception to what I am suggesting. It’s a non-computable number that we can still explain via an algorithm. So I’m not sure ‘omega’ is, strictly speaking, unexplainable.

[3] Chaitin uses the Goldbach conjecture as an example of a truth (maybe) without a reason. I note here that mathematicians continue to try to find a proof for or against it, unable to accept that there isn’t one. And this is in mathematics, not physics. Oy!

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11 Responses to Computability and Comprehension – Is Science About Prediction?

  1. [...] Comprehension – Is Science About Prediction? December 23, 2010 — Bruce Nielson Check out the next post in my “Reason as a Guide to Reality” series over at Wheat and Tares. Here is a [...]

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  2. FireTag on December 24, 2010 at 10:52 AM

    One cliche about common sense is that it can often be wrong when applied to uncommon situations. Relativity predicts things — likr the fusion of the sun or bar magnets — that are very common, but pre-relativistic physics never thought fit into a single explanation.

    So I’m of the explanation more important than calculation school. And space really is curved.

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  3. Bruce on December 24, 2010 at 6:10 PM

    I wish I could see the curves. It would be sort of cool. ;)

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  4. [...] In my last post I started to discuss the differences between Positivism and Scientific Realism. To over simplify it, Positivism cares only about the predictive abilities of science and does not care about whether or not science is getting ever closer to some underlying truth. Scientific Realism takes all scientific theories seriously as approximations of an underlying truth. [...]

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  5. [...] previous posts I responded (or gave other people’s responses anyhow) to the ideas that science is primarily about prediction, Reductionism, or Holism. In those ideas we found some truth, but not the whole [...]

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  6. [...] In a previous post I previously considered the advantages of Scientific Realism vs. Positivism. (See also here) Both have pros and cons, but Scientific Realism is the clear winner when it comes to generating new conjectures and theories. If one were to solely believe in Positivism one would never actually believe in their own theories enough to think up new questions/problems to solve and test. The end result would be the stagnation of science. [...]

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  7. Gilbert Albans on June 26, 2011 at 11:52 PM

    Explanations are not scientific unless they make_at least_one prediction. You can come up with an infinity of explanations that make no predictions, and they would not be scientific. So Deutsch’s position isn’t scientific if he does not allow for prediction. But, if he does allow for prediction, then his explanations would have to make predictions, and so he is stuck with positivism again.

    But, Popper said, to explain something is to have general laws, and we input some initial conditions, and with the laws and initial conditions, we can deduce predictions. This is the explanation of science, under Popper, and also with Carl Hempel. But if you do the Statistical or Inductive explanation, it is still based on past observations and prediction. Not to mention that science describes what they observe, and make predictions, or describes what happens in their models.

    But there is more. Science works on an empirical epistemology, which means that all scientific predictions must have sensory consequences (with our sight, taste, sound, smell, and touch). What we experience with our senses are phenomena. Science works with phenomena, and predicts what we shall observe with our phenomena. But science is hypothetical, and uses hypothetical propositions like “If X, then Y”. Science can only know the consequent, “then Y”, if the proposition invokes things that cannot be experienced with the senses, which would be “If X”. Popper admitted that science gets more and more abstract, which means further and further away from the senses.

    Now, as science invokes things that can’t be experienced by the senses, then it is only acceptable if it leads to consequences of the senses. So take X as “something beyond experience of the senses”, and Y as “something that we should experience with the senses”. Thus, from our hypothesis, X, we can deduce a sensory consequences, which means make a prediction, then it is science. It’s testable. Thus, it forms the proposition “If X, then Y”. But we can only experience, through experiments, Y. But affirming the consequent is a fallacy, because it could be something other than “X” to cause “Y”. For example, “If a white person, then Johnny Depp. Johnny Depp. Therefore a white person.” The problem is that it could Will Farrell, George W. Bush, Petyon Manning, and etc. So, we can invoke a logical infinity of things that are unobservable, and all have the same predictive power, and also the same explanatory power. Thus, scientific realism is in a serious dilemma, while positivism escapes such dilemma.

    But, explanations are based on principles, and from principles we can deduce consequences. Like we have a law, “All A is B”, and from this we can deduce consequences, and say we explained what we observed because of these principles. This isn’t really an explanation, but a deduction that predicts what happens in that system. So explanation is nothing but prediction.

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  8. Gilbert Albans on June 27, 2011 at 12:07 AM

    As a quick follow up, here are some interesting quotes. And they show how scientific realism is untenable.

    “Our theories of the world are related in various ways to experience. We construct theories partly in order to account for what we have observed and partly in order to systematize and support our expectations for future experience. But what we experience is not sufficient to determine our theories. Different theories may account for our observations equally well.” Lars Bergstrom

    [“If all observable events can be accounted for in one comprehensive scientific theory- one system of the world, to echo Duhem’s echo of Newton – then we may expect that they can all be accounted for equally in another, conflicting system of the world. We may expect this because of how scientists work. For they do not rest with mere inductive generalizations of their observations : mere extrapolation to observable events from similar observed events. Scientists invent hypotheses that talk of things beyond the reach of observation. The hypotheses are related to observation only by a kind of one-way implication; namely, the events we observe are what a belief in the hypotheses would have led us to expect. These observable consequences of the hypotheses do not, conversely, imply the hypotheses. Surely there are alternative hypothetical substructures that would surface in the same observable ways.” W.V. Quine

    “Quine’s thesis of the underdetermination of physics can be discussed quite independently of translation in general and indeterminacy in particular. It presents a problem we are said to face even when we are “at home” in our own language trying to build and confirm scientific theories. The problem is this: even if we had all possible observations in the sense of all the observation reports true of the actual world, still there would be alternative scientific theories that explain those observations equally well but are incompatible with each other. To put it another way, if you were to decide you accept all theories that are unrefutable in experience, you would accept a contradiction. Thus the underdetermination thesis denies the possibility of a confirmation function in the classic sense. The underdetermination of physics is prior to the indeterminacy of translation in the sense in which the existence of empirically unrefutable alternative theories is prior to the impossibility of saying of a person which of the empirically unrefutable alternative theories he holds on the basis of his overt behavior.” Jane English

    Hume clearly demonstrated a kind of “underdetermination” of causes, and Goodman’s paradox reveals an “underdetermination” in all inductive inferences.” Jane English

    Not to mention that there almost no logical difference, since predictions have this form, “If X then Y”, while explanations have this form, “Y because of X”. Thus, since we can’t know the cause of what we observe, and can always have an infinity of other unobservable causing what we see, and thus explain it in contradictory systems, scientific realism is untenable, from a logical and empirical standpoint. It’s wishful thinking.

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  9. [...] case, Armstrong’s view here is bad science, plain and simple. It’s a steering towards the very Positivism that elsewhere she skewers. The proper response to this Positivistic outlook of science is [...]

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  10. » Our Epistemology So Far The Millennial Star on October 2, 2011 at 4:12 PM

    [...] everything we thought we knew about science turned out to be false. Namely, science is not specifically about prediction, nor reductionism, nor holism, nor observation, nor falsification. All of those ideas are important [...]

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  11. [...] exceptions.) To him, what the theory says it true is what we’ll accept as true. There is no positivism in Deutsch’s views of the world. You never just use science as just a way to make convenient [...]

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