Wednesday, 11 March 2015

On knowledge, Truth, electric chairs, and quasi-local mass

My last few blog posts have been inspired by a recent fascination with the filmmaker Errol Morris. That all started with the new Stephen Hawking movie, which in turn reminded me of Morris's 1992 film A Brief History of Time. Since then I've watched numerous interviews and discussions with Morris, and several more of his films, including Gates of Heaven, The Thin Blue Line, and his most recent, The Unknown Known, and read a number of his New York Times columns, notably the excellent series of five articles on Thomas Kuhn and the dubious notion of incommensurability. I cannot recommend them highly enough. To discuss an obscure philosophical concept in a major mainstream newspaper is quite a feat; to make it entertaining, and at times even hilarious, is pure genius [1].

But the Morris moment that really dug into me, and started all of this, came from a discussion I found on YouTube. The discussion is about the current state of journalism, although we will see that its concerns range much further.

At the end there are audience questions. One audience member gamely begins his question.

AUDIENCE MEMBER: I've heard a word come up a few times tonight, which is Truth, and it can obviously be argued that there is no such thing as objective Truth, and --

MORRIS: No it can't!

Morris stops the question there. "Whoa, whoa, whoa!" he cries out. He expresses dismay at the notion -- apparently a popular notion -- that there is only subjective truth, "truth for you, truth for me, truth for anybody who really wants to claim it as truth". He asks whether we would maintain this view under the following conditions. You are being strapped into an electric chair. You are about to be executed. You are crying out, "I didn't do it!" To reassure you, a chaplain is brought in to patiently explain to you that all truth is subjective. You have to understand that your innocence is merely your opinion. "So suck it up!"

He finishes by declaring, "I don't know where this nonsense started! But forgive me -- there is such a thing as truth. The Truth!"

And so ends the discussion.

Why should this have impressed me so much? Because it made me ashamed. As a good honest scientist, I thought that I was as much a defender of the notion of facts and truths as anyone. But I realised that I was also infected by the modern disease of relativism: reality depends on our perception, and there is no such thing as a final answer or an ultimate Truth.

I thought I had these ideas clear. Some things can be relative and subjective: aesthetic judgements, and sometimes also moral judgements -- one person's bold act of justice is another's war crime.

When it comes to "hard" facts, like scientific observations and measurements, there is always some uncertainty and error associated with them; we never have an answer with absolute precision. But in those cases the uncertainty is well understood and under control: my 1-metre ruler might in fact be 1.01 metres long, or only 0.99 metres, but it is not seven metres long; of that I can be certain. And the ruler has some definite length. You can try to be clever and bring up quantum uncertainty, but the atomic jiggling of my ruler does not enter its length until about 35 digits beyond the 1.000..., and is therefore irrelevant.

I thought I knew all those things. But somewhere in the back of my mind, there was doubt. If pressed on the real truth, I would prevaricate. There would be qualifications. We are mostly certain, we are very confident‚ but I would not have put my foot down and said, "We know!"

I know of two defences of this position. One is better than the other, although both are utterly wrong.

One defence is a bit of philosophical hand-wringing. We cannot prove that reality is as we perceive it. We could all be brains in bottles. We could be imagining the universe we exist in. We will never know.

This is a silly argument, because even if we are brains in bottles, then there is still a reality out there. There is the reality of the brains and their bottles. There is whatever alien intelligence is involved in regularly cleaning out our bottles and replacing our brain pickle. Just because we cannot know it, that does not mean that it is not there.

Furthermore, all these scenarios are so far-fetched and contrived that the likelihood that they are true is incredibly small. We can never be 100% certain of the reality we measure, but we can be so close that it makes no practical difference. To extrapolate from an infinitesimally small uncertainty to the conclusion that the entire enterprise is futile, is quite ridiculous.

The other argument is that modern physics itself makes us question the nature of reality. Two of the great minds of the 20th century, Einstein and Bohr, were lead by the discoveries of quantum mechanics to argue over the existence of an objective reality, and of course Schroedinger had his cat.

Epistemological musings by scientists are often embarrassing, but we should forgive them. If a smoothly running high-octane intellect makes us cough with a little philosophical exhaust -- well, there are far worse kinds of pollution.

Those were arguments over the interpretation of quantum mechanics, and to some extent they continue to this day. But what was not in dispute was whether there were definite laws of physics that these systems follow, or that we could hope to determine what those laws are. If our precise measurements and probes of reality force us to conclude that a cat can be simultaneously alive and dead (although so far there is no conclusive argument that this is the case), then that is what we would have to accept as reality. In other words, there is a reality that we can know about, and the fact that it is so contrary to our everyday expectations and requires so much definitive evidence to convince us of it, strengthens even more our conviction that this actually is the reality.

Our picture of reality is not one that we chose, or that was dictated by our culture, our religion, or our dietary eccentricities. It was forced on us because it is real.

Again, I knew all that. So why was there that gibbering little indecisive fellow lurking in the back of my brain?

I have realised that it was the other great 20th century theory that was unsettling me: my daily bread, general relativity.

In general relativity we have the problem that the notion of the individual mass of an object is ill-defined. We can unambiguously calculate the total mass and energy of one full solution of Einstein's equations -- i.e., the total mass and energy of an entire universe. If the solution we are considering contains one lonely, stationary, inert black hole, for example, then we know the mass of that black hole: it is the same as the mass-energy of the entire universe, which we can calculate.

But what if there are two black holes? What is the mass of each of them? And how much other energy is there floating about in the universe, in the form of gravitational interaction between them? Now we are stuck. We can formulate approximate measures, and in practice most of these agree with each other very well. But they are not identical. And during a violent event, like two black holes about to collide, where space and time are thoroughly whipped up and distorted, the differences in these measures become more pronounced. Even if they agreed, or remained extremely close, we could not (or at least cannot yet) prove that they truly represent the masses of those objects.

This is an uncertainty I have to deal with every day. If I get up at a conference and make some statement about the masses of two black holes in a computer simulation of their collision, some smart-ass in the audience always can (and, you can be sure, always will), put up their hand and ask, "Isn't your mass gauge dependent?" As much as I would like to smile sweetly and walk over to them and give them a punch in the nose, and as loudly as the rest of the audience may applaud, that would not make me correct. Their point still stands.

If I cannot even be sure of such a basic and simple quantity as the mass of an object, then how can I stand up and defend the notion of reality and truth? I cannot say, "The black hole definitely has some mass, I just cannot accurately measure it." No: I cannot even define what mass is!

All of this may have made me queasy and uncertain, but it need not have.

Ok, so mass is ill-defined in the presence of extremely strong gravitational fields. We can live with that, can't we? In weak fields (as on Earth) our measures all agree so well that the uncertainty is even less of an issue than the quantum uncertainty -- i.e., for all practical purposes, not at all.

If it turns out that some of the concepts we use to study the world around us, like mass, are not meaningful in some extreme environments, that is fine. We have devised tools to help us define concepts that are meaningful in those settings. Considering that those are settings that we will struggle to ever recreate in our laboratories, or to ever observe, and yet we know how to study them anyway, is hardly an argument for the ineffable nature of reality -- quite the contrary.

It may seem surprising that it took a YouTube clip of a documentary filmmaker to drive this home to me. However, this is no ordinary filmmaker (if there is such a thing). As I have described previously, this is a guy with a long history of trench warfare with Truth.

His example was inspired by real experience. His most famous film attempted to overturn the conviction of a man sentenced to death for murder. (It succeeded.) He later made a film about an electric-chair repairman. His example was no mere discussion starter from a moral-philosophy text.

When Einstein spoke about the relativity of motion, sloppy minds extended the idea to morality, and to knowledge, and beyond. If you suspect that I am performing the same crime in reverse, by translating Morris's statements on journalistic objectivity to scientific truth, fear not. Morris is well aware of the wider context of what he says.

You need only read the excellent series of articles I referred to earlier, that recount Morris's encounter with that grand master of philosophy of science, Thomas Kuhn. Kuhn's ideas grew (fertilised by an unlimited supply of others' intellectual manure) into the pernicious notion that science is purely a social construct. Morris began his career with severe doubts about all of this, and he summarises his Kuhn smack-down in those NYT articles. He reminds us that, for all the usefulness of Kuhn's insights, there is also a nonsensical component to them, and we should treat that with the disdain it deserves. When it comes to issues of knowledge and truth, Morris is as genuine an expert as you could ever hope to find [2].

His incredulous cry, "I don't know where this nonsense started!" is an expression of frustration. He knows exactly where it started. What he may not know -- and I certainly do not know -- is why it does not stop.

(The question is at 10:40)

Previously: Career advice I gleaned from Errol Morris, for what it's worth

1. The best joke I have read in a long time is the parenthetical remark in Ref. 19 of Part 2. If you want to enjoy it, too, I am afraid that you will have to read one and a half of the articles first. By that point you should be hooked.

2. I would not be at all surprised to discover that Morris also spent two years at Harvard, on a futile search for a rigourous definition of quasi-local mass in general relativity. It is only a matter of time before someone sends me a preprint of that obscure paper on the Morris-Yau mass.


  1. An interesting read. Thanks for the link to the articles.

  2. I'm a big fan of the quote by John Lennox (an advocate of objective reality):
    "It is probably fair to say that many, if not most, scientists are 'critical realists', believing in an objective world which can be studied and who hold that their theories, though not amounting to 'truth' in any final or absolute sense, give them an increasingly firm handle on reality, as exemplified, say, in the development of the understanding of the universe, from Galileo via Newton to Einstein." (John Lennox, God's Undertaker ch 2)

  3. It seems to me that truth is objective, but our individual, contextual relationship to any given truth is very subjective. Which isn't a posh way of saying that sometime we lie. I think I mean that we understand the elements of doubt around any given fact (your example of the rule is good) and work accordingly. In some spheres - politics, morals - the elements of doubt are large, and it is here that the subjectivity of 'truth' becomes more obvious.

    And then, being intellectually lazy creatures who like simplicity and categories, we put truth in the category "always subjective" because we know that it is sometimes subjective.

    I'm sure this argument needs some work ...

    Great post, Mark

    1. Yes. I tried to think of a more intelligent reply, but all I came up with was: Yes.

  4. I think beating down Kuhn (which is something that among prominent physicists Weinberg has famously been doing for some time), about half a century after he revolutionized Philosophy of Science (which is not Weinberg's field, and it should be fair to say not really Morris's field either), is kind of similar to some non-economist (resp. non-psychologist/non-biologist) bashing Marx's (resp. Freud's/Darwin's) contributions.

    1. Not at all, for a myriad of reasons. Philosophers of science presume to explain the work of scientists. Scientists (like Weinberg) have every right to respond -- and I'm tempted to add that the philosophers should be grateful that their subjects are paying attention. Further, the ideas of philosophy are endlessly discussed and debated, and certainly for much longer than half a century, while the validity of a science like biology is based on experimental facts. Facts trump talk. But with philosophy, talk is all there is, and if you have a coherent argument, it's as valid as anyone else's. Finally, Morris does not "beat down" Kuhn. He is surely well aware of Kuhn's contributions. He takes an interpretation of one of Kuhn's ideas, and offers arguments against it. Both the interpretation and the arguments have come before -- he simply uses them, and some personal recollections, as the basis for a series of interesting, informative and thought-provoking articles. And, all of these ideas being open to interpretation, there is no definitive answer that Morris can be accused of misunderstanding. (In other words, there is a distinction between, say, the filmmaker Errol Morris discussing Thomas Kuhn, and the critic Clive James discussing global warming, as discussed at length in the series of posts starting here and summarised here.)

    2. I agree with most of what you say. In particular, I agree that Morris's articles are a delightful read, and I'm thankful to you for introducing them to me. However,
      i) the same way that Weinberg has every right to respond to Kuhn's work, Freud's patients had every right to express opinions about his; (for the purpose of the conducted research) in neither case the opinion of the subjects is nearly worth attention as that of the investigator; in both cases, I imagine, the investigators would be grateful if the subjects are paying attention;
      ii) one of the main decisive factors for Kuhn's success in Philosophy of Science (and I believe you are well aware of what follows) was his massive introduction of "facts" of history into the subject; I disagree that in philosophy "talk is all there is" (and I'd guess you weren't quite serious by saying that either), but even if "talk [was] all there [was]" in Philosophy of Science up to some point, things were clearly far from that way after Kuhn's work; History of Science became an essential part of Philosophy of Science, providing for it the "data" and "the pieces of evidence".

    3. No, my glib remark about philosophy was not completely serious. However, I am inclined to think that it's easier for a non-professional to take part in a philosophical argument than in a technical scientific discussion. Although I imagine that it's easy to come up with endless examples for exactly the reverse claim.

      I was also sloppy in the post in referring to Morris's articles as a "Kuhn smack-down". I have no idea to what extent the idea that Morris held up to (quite reasonable) ridicule was held by Kuhn, or how many other people have interpreted incommensurability in that way -- it could be such an irrelevant fringe that Morris is batting at a straw man, or there could be hordes of influential thinkers. I have no idea.

      The equivalence of scientists with Freudian subjects is too irresistible to argue with. I could quibble that scientists are highly skilled intellectuals who should be fully able to understand and engage with the analysis of historians, philosophers and sociologists of science, whereas the only pre-requisite for Freud's patients was that they were (sometimes) conscious -- but I won't.


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