In my last post I quoted Stephen Hawking’s defense of Positivism. He even goes so far as to suggest that there is no all encompassing view of reality but instead only “a family of interconnected theories, each describing its own version of reality…” (p. 70)
But accepting Positivism as the true nature of reality has consequences.
A famous real-world example of different pictures of reality is the contrast between Ptolemy’s Earth-centered model of the cosmos and Copernicus’s sun-centered model. Although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true. …the real advantage of the Copernican system is that the equations of motion are much simpler in the frame of reference in which the sun is at rest. (p. 71)
Boy, are you ready to accept this? That the earth is no more revolving around the sun then the sun is revolving around the earth and that the only real reason we believe the earth revolves around the sun is because the math is simpler that way?I confess, there does seem to be a sense in which this is true. Einstein’s General Relativity does not allow for a favored coordinate system. Therefore, it is not strictly true that the sun does not revolve around the earth according to General Relativity because it would always be possible to formulate an earth centric theory that gives the exact same predictions.
This is where the famous – and mostly misunderstood – Occam’s Razor comes in. Occam’s Razor does not claim that the simpler theory is the right one. If I had a dime for every time someone tries to claim that…[1]
Occam’s Razor is at it’s best when it makes a much more modest claim. This claim is that given two theories that make all the same predictions, you should choose to use the one that is mathematically simpler to calculate because it’s the “best” by tautological definition. [2]
Of course, as Hawking points out, “simplicity is a matter of taste.”
Therefore, what is wrong with creating a Positivist view of reality, especially if it might turns out to be correct? (Though presumably we’ll never know that for sure.)
Roger Penrose vs. Stephen Hawking: Schrödinger’s Cat
But it seems that Positivism – if fully embraced – has some negative consequences. As I mentioned in this previous post, Positivism seems to be most useful when you just want to make predictions and aren’t so worried about what those models really mean about reality. The model is reality, if you will. Nothing more.
In an extended debate/lectures between Stephen Hawking and Roger Penrose Hawking said the following:
These lectures have shown very clearly the difference between Roger and me. He’s a Platonist and I’m a positivist. He’s worried that Schrödinger’s cat is in a quantum state, where it is half alive and half dead. He feels that can’t correspond to reality. But that doesn’t bother me. I don’t demand that a theory correspond to reality because I don’t know what it is. Reality is not a quality you can test with litmus paper. All I’m concerned with is that the theory should predict the results of measurements. (Find online here.)
Schrödinger’s cat is a classic physics thought experiment where you put a cat in a box and arrange for a vile of poison to break inside the box depending on whether or not a quantum particle is detected. Since quantum particles are in “superpositions” (i.e. are in all locations at once in some sense) until “observed” then quantum theory predicts that the cat will actually be both dead and alive simultaneously until “observed” (i.e. we open the box) and then it’s “wave function” collapses and it will now be either dead or alive.
Contrary to popular belief, Schrödinger proposed this thought experiment to demonstrate that there is something wrong with quantum theory. But today physics take seriously the idea that until observed the cat is in a superposition of being both dead and alive simultaneously.
So in a sense, Hawking is correct. In fact Quantum theory makes the right prediction about Schrödinger’s cat: it predicts we’ll either see it as dead or alive, but not both.
On the other hand, quantum theory seems to suggests rather disturbing possibility about reality with no real answers to what they mean. Does this, for example, mean that that the cat is actually both dead and alive and there are two conscious versions of ourselves, one looking at a dead cat and one looking at a living cat? This is the infamous ‘many worlds’ interpretation of quantum physics. Or does it mean that consciousness creates reality? If so, why? (And if so, then are photographs conscious, since they count as observations too?)
Penrose’s point is that the theory is incomplete either way. There is some sort of significant explanation gap that needs to be filled. Hawking isn’t concerned about the explanation gap, so he feels no need to fill it.
Hawking’s Inconsistency
It seems to me that Hawking’s Positivist view point is inconsistent at best. Consider the fact that he’s done considerable research into black holes. He has pointed out that according to our best theories black holes should give of radiation? But how is this possible if the black hole, by definition, can’t allow anything to escape from it?
Hawking looked more carefully at what quantum theory tells us about the vacuum of space. It predicts that space is actually full of positive and negative particles constantly appearing and then canceling each other out. This should, according to Hawking’s theories, happen right near the event horizon (i.e. border) of a black hole. The positive particles would thus jump away from the black hole and the negative ones would fall in. The end result would be that the black hole would give off radiation and in fact would shrink or evaporate over time because of all the negative particles falling into it.
This theory disturbed many physicists because it had been believed that quantum information could not be destroyed. But if thing falls into a black hole and then the black hole evaporates (over a seriously large period of time) that would imply that quantum information could be lost.
Now the first thing we should recognize is that we’ve never made any observations of black hole radiation before. It is hard to believe a true full throated Positivist would even bother to make up theories about what black hole radiation is like. What is the point when, by Positivist definition, the model is only “connect[ing] the elements of the model to observations”? What observations are we connecting it with regarding Black Hole radiation?
I would submit that this proves that Hawking isn’t really a full blooded Positivist after all. He is forced to resort to scientific realism to make scientific progress.
And, Of Course, The Model Does Matter
Secondly, there is an alternative to Hawking’s theory that navigates the issues better, at least in some cases. Under the alternative theory the radiation of a black hole is actually caused by p-branes in the black hole forming waves that peak above the black hole’s event horizon. These peaks then become particles and escape. In Hawking’s book, the Universe in a nutshell, he points out that:
The mathematical model of black holes as made of p-branes gives results similar to the virtual-particle pair picture described earlier. Thus from a positivist viewpoint, it is an equally good model, at least for certain classes of black hole. For these classes, the p-brane model predicts exactly the same rate of emission that the virtual-particle pair model predicts. However, there is one important difference: in the p-brane model, information about what falls into the black hole will be stored in the wave function for the waves of the p-branes. (p. 127)
In plain English what Hawking just said is that there are two equally good ways of understanding black hole radiation, but one preserves quantum information and one does not. Since the preservation of quantum information is still (at least according to our current best theories) a hard fast law of physics, this suggests that the p-brane model is superior to the virtual-particle pair model because it fits better with the rest of the laws of physics. (i.e. doesn’t violate them.)
Again, it seems to me that Positivism has come up short. Unless we take a Scientific Realists view, we can’t actually assess the obvious: that these two theories are not equal.
Scientific Realism is Superior – Even If Wrong
Which brings me to my key point. Even from a Popperian / Scientific Realist view of the reality, we can’t ever know for certain if there really is a single all encompassing view of reality or not. For nothing within Popperian epistemology allows us to “prove” a theory to be true.
But Popperian David Deutsch does make a compelling argument, that for me, destroys Hawking’s arguments lock-stock-and-barrel. As Deutsch points out, a Positivist view of reality has no explanatory power. Deutsch, commenting on the deep relationship between Scientific Realism, comprehensibility, and algorithmic compression, argues:
If, for instance, we want to understand why the world seems comprehensible, the explanation might be that the world is comprehensible. such an explanation can, and in fact does, fit in with other explanations in other fields. But the theory that the world is half-comprehensible explains nothing and could not possibly fit in with explanations in other fields unless they explained it. It simply restates the problem and introduces an unexplained constant, one-half. (The Fabric of Reality, p. 351)
Try to wrap your head around that statement for a moment. Then do this: try to refute it. The logic of it is impeccable. Thus we are forced to eject Positivism regardless of whether or not it is true:
To understand our best theories, we must take them seriously as explanations of reality, and not regard them as mere summaries of existing observations. (The Fabric of Reality, p. 350)
It is not that we know the Kuhn / Hawking / Positivist view of reality to be false. That can never be proven one way or another. We eject it because, even if they are right, it explains nothing. Even Hawking is forced into a Scientific Realists view when he wishes to make scientific progress. This is because he still has to come up with theories – conjectures – and then take them seriously and honestly believe that they represent reality. This will lead to criticism, either from ourselves or (more likely) from others. This is the only way we can make scientific progress.
In other words, if Kuhn is right then Kuhn’s theory predicts that we must start with the assumption that Kuhn is wrong.
For me, this is sufficient refutation of Kuhn’s final conclusions of a Positivist worldview. I fully accept that the rest of Kuhn’s theory is basically correct. I do not see most of his theory as at odds with Popper’s. Only in Kuhn’s final conclusion, that Positivism might be a reality, do I object. But even then I primarily object on the grounds that, if Positivism is true, this it is what we might call a ‘useless truth.’ Because the untruth is superior to the truth, we should merely go with the untruth even if it’s wrong.
In other words, I believe in Scientific Realism because it just makes sense to. I have faith in the power of this belief regardless of whether or not it is true. (Though obviously I believe it is in fact the truth.)
Therefore, Scientific Realism is the undisputed winner, at least in the Positivist vs. Scientific Realism debate.
Notes
[1] Real life example: Joseph Smith is a fraud because according to Occam’s Razor, the simplest theory is the correct one and it’s easier to believe he made it all up then real ancient American angels came to him.
Ugh!
Unfortunately even famous scientists get this wrong. Carl Sagan popularized Occam’s Razor in his book (and movie) Contact. Unfortunately he didn’t actually understand it, so he gave it the interpretation above: it’s easier to believe we humans made God up than that God actually exists, therefore there is no God as per Occam’s Razor. Granted, Sagan goes on to then refute this view of Occam’s Razor but without ever pointing out that actually it’s not Occam’s Razor in the first place.
[2] There is more to Occam’s Razor that what I am saying here because any extraneous parts to a theory should then have to be explained. Yet that will not be possible before the two theories being compared start to diverge in their predictions. Therefore the simplest theory is also the ‘best’ in the sense that it has less to explain. But this is a post for another time and isn’t relevant to the current subject.