Uncertainty in science and the bridge to humanities

Felipe describes in his book "A Foot in the River" how, because so-called hard sciences opened the door to the possibility that there is a limit to our knowledge, it also built a bridge toward humanities, the so-called soft sciences:

At least two positive effects have ensued. First, it no longer seems realistic to demand a predictable cosmos, ruled by definitive, unbending laws and bound by links of cause and effect. The causes may still be there, but are often untraceable. The effects may still there but are often untrackable. Second, science has come to seem more approachable and more intelligible from the perspectives of other disciplines: less hard-edged, more yielding; less cocksure, more flexible; less definitive, more open-ended; less confident of solutions, more entranced by problems. After a long period in which humanities and social studies have tried to be more scientific, science has begun to look more like art. Science has let its hair down and become more arty.

(Chapter 8, "Toward the planet of the apes")

See this old blog post that is relevant to this topic.

Quotes from "A foot in the river" by Felipe Fernandez-Armesto

"Maybe there no causes to know, or, at least, maybe much that happens is uncaused. Anyone who thinks that everything is explicable as the result of something else--who sees causation as the 'cement of the universe', making each event adhere closely to the next--may be the victim of an unwarranted assumption. 'Just-so' explanations may be the only true ones." (Chapter 3)

A quote from early in Chapter 3 where the author starts to develop his theory that future human events might not be predictable, a theory that goes opposite to that of Pierre-Simon Laplace but is in line (albeit for different reasons) with that of Karl Popper.

"Empathy is the heart of understanding" (Chapter 3)

 A quote that summarizes, according to the author, a principle of anthropological field work as well as of life followed by Franz Boas.

Popper's falsification expressed in Bayesian terms

Popper's idea that there is only falsification and no such thing as confirmation turns out to be incorrect. Bayes' Theorem shows that falsification is very strong evidence compared to confirmation, but falsification is still probabilistic in nature; it is not governed by fundamentally different rules from confirmation, as Popper argued.

Eliezer S. Yudkowsky, An Intuitive Explanation of Bayes' Theorem.

Chance and free will

To defend free will was not, of course, to insist on the operation of pure chance. Most thinkers still saw objective chance as virtually impossible, and few were prepared to identify the rational will with it. But at least the connotations of chance had changed. Previously it had seemed impiuous to allow chance a role in the world, as if God did not attend to every sparrow. Now chance stood for the incompleteness of mechanical law, for the possibility of non-material causation.

Gerd Gigerenzer et al., The Empire of Chance, section 2.6. This joins the defense of free will laid down by K. Popper as I noticed in this post and this note. See also this post as well as the work on incompleteness by Gregory Chaitlin.

Not the job of science

"H. Gomperz, Weltanschauungslebre, II/I (1908), p. 63, points out that a piece of the world, such as a sparrow nervously fluttering about, may be described by the following widely different propositions, each corresponding to a different aspect of it: 'This bird is flying!'--'There goes a sparrow!'--'Look, here is an animal!'--'Something is moving here.'--'Energy is being transformed here.'--'This is not a case of perpetual motion.'--'The poor thing is frightened!' It is clear that it can never be the task of science to attempt the completion of such list which is necessarily infinite."

Karp Popper, The poverty of historicism, note 28 of section 23 "Criticism of holism".

Self-reference, once again

"The entity being reckoned is fatally entwined with the entity doing the reckoning. As Douglas Hofstadter put it much later, «The thing hinges on getting this halting inspector to try to predict its own behavior when looking at itself trying to predict its own behavior when...» A conundrum that at least smelled similar had lately appeared in physics, too: Werner Heisenberg's new uncertainty principle. When Turing learned about that, he expressed it in terms of self-reference: «It used to be supposed in Science that everything was known about the Universe at any particular moment then we can predict what it will be through all the future... More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves."

James Gleick, The Information, Chapter 7.

I am still surprised that, although Karl Popper has stated the same thing, there seems to have been little exchange of the same idea between these different scholars.

Has the Universe finite or infinite complexity?

"[L]et's now finally discuss whether the physical universe is like π=3.1415926... which only has a finite complexity, namely the size of the smallest program to generate π, or like Ω, which has unadulterared infinite complexity.
Well, if you believe in quantum physics, then Nature plays dice, and that generates complexity, an infinite amount of it, for example, as frozen accidents, mutations that are preserved in our DNA. So at this time most scientists would bet that the universe has infinite complexity, like Ω does. But then the world is incomprehensible, or at least a large part of it will always remain so, the accidental part, all those frozen accidents, the contingent part.
But some people still hope that the world has finite complexity like π it just looks like it has high complexity. If so, then we might eventually be able to comprehend everything, and there is an ultimate TOE [Theory of Everything]! But then you have to believe that quantum mechanics is wrong, as currently practiced, and that all quantum randomness is really only pseudo-randomness, like what you find in the digits of π. You have to believe that the world is actually deterministic, even though our current scientific theories say that it isn't!
[...]Wolfram believes that very simple deterministic algorithms ultimately account for all the apparent complexity we see around us, just like they do in π. He believes that the world looks very complicated, but is actually very simple. There's no randomness, there's only pseudo-randomness. Then nothing is contingent, everything is necessary, everything happens for a reason. [Leibniz!]
[...]
Or perhaps from inside this world we will never be able to tell the difference, only an outside observer could do that."

Gregory Chaitin, Metamath!, Appendix II.

Notice that the last argument has also been mentioned by Karl Popper in his Open Universe (see my review of his book).

The critical reductionist

[W]e may be faced with the possibility that the origin of life (like the origin of the universe) becomes an impenetrable barrier to science, and a residue to all attempts to reduce biology to chemistry and physics. For even though Monod's suggestion of the uniqueness of life's origin is refutable --by attempts at reduction, to be sure-- it would amount, if true, to a denial of any successful reduction. With this suggestion Monod, who is a reductionist for reasons of method, arrives at the position which, I believe, is the one forced upon us all in the light of our earlier discussion of the reduction of chemistry to physics. It is the position of a critical reductionist who continues with attempted reductions even if he despairs of any ultimate success.Yet it is in going forward with attempted reductions, as Monod stresses elsewhere in his book, rather than in any replacement of reductionist methods by 'holistic ones', that our main hope lies --our hope of learning more about old problems, and of discovering new problems which, in turn, may lead to new solutions, to new discoveries.

Karl Poppper, The Open Universe, Scientific reduction and the essential incompleteness of all science.

Science cannot prove that a theory is true. Is this true?

I would like to discuss the notion, developed by Karl Popper, that science can only disprove a theory. I remember reading somewhere that if a theory is proven wrong, then the complementary theory is actually being proven right, which would then contradict the claim that no theory whatsoever can be proven right.

Let's take an example, the climate, not only because the conference on climate change in Copenhague in on this week, but also because it is the system that I am the most familiar with. Say, a theory states that El-Niño is caused by wind bursts in the western Pacific. As long as observations show that wind bursts do occur before the start of El-Niño, you are only observing the facts that the timing of the events might be related but you are not proving that the wind bursts do cause El-Niño. Each can independently be caused by something else. However, if one year, there is no wind burst but an El-Niño, then you are proving that El-Niño is not caused, at least not all the time, by wind bursts. In this case, we have proven that the theory "wind bursts do not always cause El-Niño" is true.

The difference between the two theories is that the first one is a predicting theory which is supposed to work all the time, while the second is not; in other words, the first one is useful, not the second. To prove a predicting theory, you need to prove that the causation works all the time but because the world is infinite and open to the future, you can never prove it absolutely. The more the theory succeeds the tests, the more likely it is, but that is it, no certainty. However, to prove a non-predicting theory, only one example suffices, which we have done above. And so here is the crux of the argument: Formal definitions of theory do include that a theory should be able to perform predictions. So the second "theory" above is actually not a theory. And so yes, indeed, science cannot prove that a theory is true but it can prove other things!

Comment on reductionism by K. Popper

"As a philosophy, reductionism is a failure. From the point of view of method, the attempts at detailed reductions have led to one staggering success after another, and its failures have also been most fruitful science."

K. Popper, in Scientific reduction and the essential incompleteness of all science, section IX, an addendum to The Open Universe.

See my review of his book.

Free will according to K. Popper

"We are 'free' (or whatever you want to call it), not because we are subject to chance rather than to strict natural laws, but because the progressive rationalization of the world--the attempt to catch the world in the net of knowledge--has limits, at any moment, in the growth of knowledge itself which, of course, is also a process that belongs to the world.

Rational action without foreknowledge--of a scientific, a hypothetical, kind at least---is impossible; and it is this very same foreknowledge which turns out to be so limited as to leave room for action--that is, for 'free' action."

K. Popper, in The Open Universe, section 23.

See my review of his book.

Role of science according to K. Popper

"The method of science depends upon our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification--the art of discerning what we may with advantage omit."

K. Popper, The Open Universe, section 15.

See my review of his book.