Too Big to Know? So What?

The other day someone pointed out an article for me by David Weinberger which appeared in The Atlantic, plugging his new book Too Big to Know. It was a strangely breathless article, but I'm not sure that Weinberger's point is a very interesting one. Essentially, he seems to be saying that we have been developing data sets that are so vast they are beyond what people - with our limited brains and short life-spans - can possibly analyse and understand without the aid of computers. What's more, when we let our computers loose on these huge data sets, the derivation of any new knowledge they come up with (usually by running computer models or simulations on the data) is not accessible to us. To understand why the weather bureau's model predicts a 40% chance of rain in South-East England today would take teams of humans years to calculate by hand using the same rules and the same data. To all intents and purposes, these models might as well be black boxes. Worse than this, there are programs that can derive new mathematical and physical laws and relationships - new knowledge whose creation is forever shrouded in mystery because the cost of understanding how it was discovered is astronomically high for unaided humans. 

While some gasp at the epistemological implications right along with Weinberger, my own reaction is one of puzzlement. After all, isn't this and hasn't it always been how nearly all knowledge comes to us?

At one level, we have been hugely successful at seeing the underlying patterns of the world, without the aid of computers - General and Special Relativity, and the Standard Model reduce everything to a handful of very simple equations and constants. On another level, we have the complexity of chemistry, biology, fluid dynamics, and so on, which, while following the rules of basic physics, have lots of interacting parts that we can only model statistically. That the predictions of some of these statistical models can only be made if they are based on huge data sets and worked out by big, fast computers, doesn't fill me with the same kind of trepidation with which it seems to fill Weinberger. Even the fact that the predictions of many such models are acutely sensitive to their initial conditions is hardly cause for concern (unless you're planning a camping trip and need an accurate weather report).

It's true that the models themselves can be generated or learned by second-order systems and that we do not necessarily have any meaningful way of knowing how they work (something researchers in neural networks have been grappling with for several decades already). But that isn't a particular cause for anxiety either. Such models are in principle analysable, if we should ever want to do that (which, I suggest, removes any hint of scariness). Generally, it is not important to know how a model does its job, as long as we are confident about how it was constructed and have verified its behaviour against the data. If we want to verify their outputs or increase our confidence in what the models are doing, we can always set up a second, third, or nth model to cross-check the first or poll their outputs. (Weather models tend to be run over and over and their results combined, for instance.) The thing is, these models tend to be of systems that do not have the scientific significance of E=mc^2, although they may have ample practical significance for campers and drug companies. 

I used to work in artificial intelligence and I made a particular study of a field called "argumentation". It's all about how and why we find arguments convincing - like a modern Rhetoric. The early pioneers of expert systems understood well the issue this article raises. If you run a system with more than a handful of rules, it quickly gets to the point where you can no longer understand or predict the outputs - not without a disproportionately huge effort to delve into the workings. So they tried to devise schemes for expert system to explain their own reasoning (which boiled down to traces of rule activation - presented with varying degrees of clarity). I worked on some particularly massive rule-based systems and I can attest to the fact that presenting a conclusion is not enough - people need more - but presenting the machine's reasoning is a very difficult task.

However, I believe it is doable. People just haven't put much work into it yet.

There is an example of a massively parallel supercomputer of immense power but which is virtually a black box as far as the question of how it reached its outputs are concerned. In fact there are many such examples. One of the best was Albert Einstein. This processor came up with some astonishing physical laws by a process that nobody understands even a hundred years after they were derived. However, the Einstein processor was able to explain its reasoning and the derivation of its laws in a way that satisfied everyone who was able to understand (and the rest of us have been happy to take their word for it). I've read a few books on relativity now and I must say, the fact that I don't know how Einstein derived it from what was known at the time doesn't bother me at all. The rules are logical, consistent, match the evidence, and (having been shown the way) are derivable by other, similarly-endowed processors.

Certainly machine-derived knowledge raises questions in epistemology and ontology. Does it mean something different to know a physical law derived by a machine, for example, especially where the reasoning processes involved are hidden from us? My argument, already stated, is that it doesn't. In fact, it is similar in all important ways.

The question of how much we can trust machine-derived knowledge is a different kettle of fish. Here, I'm happy to use all the usual methods of improving my confidence - particularly the Gold Standard, empirical testing.

There is a possibility that knowledge could be derived by machine that is so far beyond our human understanding that only other machines of similar capabilities could peer-review it, or understand how to devise and run empirical tests, or interpret the results of such tests. When that day comes, we are put in the position that most of us are in now vis-a-vis the great scientists. Bohr, Pauli, Heisenberg, Einstein and the rest may have been able to understand and devise tests for each others' discoveries in quantum mechanics, but most of humanity could not. To us, it is entirely a matter of trust - even of faith.

It's like the climate change "debate". Here the science is simple enough that any intelligent layman can follow it. You could replicate John Tyndall's experiment that first measured the greenhouse effect in your own kitchen with some pipes and jars and rubber tubing. Yet still, for the majority (especially GOP politicians), it is all incomprehensible scientific mumbo jumbo. They can't grasp the principles. They can't separate out the scientific claims from the denialist obfuscation. They are so far from being able to judge the validity of what the scientific community is telling them, that they can have no confidence in what they are hearing - leaving them free to dismiss it as "scare-mongering" or a left-wing conspiracy to increase government regulation of our lives, or any bizarre rationale they can come up with.

One day, even the brightest of us will probably be in that position, when the machines have taken it all to a new level, way beyond our understanding. Will we look like simple-minded denialists to them when we question what seems to us to be the unfounded gibberish they will be spouting? I think so. Or maybe, being so much cleverer than us, the machines will be rather better than human scientists at explaining what they mean and why they're saying such outrageous things.  

The Great Puzzle of Why the Sun Rose This Morning: Part 2

You may remember I wrote a couple of months ago about a strange conundrum regarding time. I mentioned this post on a number of lists I belong to, hoping that someone with a better grasp of physics than I would be able to explain it to me. I got many, many responses but, sadly, not one seemed to understand what the issue was and the great majority assumed I just needed a quick primer in special relativity (and then proceeded to give me one, often in a most garbled and peculiar way.) Most people were genuinely interested and tried to be helpful. However, one idiot, on a list I didn't even post to, became quite abusive and accused me of inventing a load of nonsense about relativity in order to make more sales of my book! (Now, how would that work, exactly?) He also threw in a garbled account of special relativity, just to be sure I understood what a genius he was.

It was quite a depressing experience all round.

I have been reading more on the subject since then and I think I have actually found the answer. Gratifyingly enough, the answer is almost exactly the one I came up with. In the language of relativity it is couched in much different terms, however, but I believe it amounts to the same thing.

The conundrum is this: even though time passes at different rates for different frames of reference, we do not experience objects moving in and out of existence as our relative positions in time change. I gave the example of the Sun, which, having a much larger mass than the Earth, should be aging ever so slightly more slowly. In fact, over the 4.5 billion year life of the solar system. the Earth should be 71 years older than the Sun. So why aren't we in the Sun's future? Why is the Sun here with us in this moment in time?

The answer, I suggested, was that we do, in fact, all move at the same rate through time, which would mean that time dilation is something analagous to the way the frequency of light changes depending on the relative velocity of its source. As it turns out, I shouldn't have been talking about space and time separately but about spacetime. Because, as it happens, we are all moving at exactly the same rate through spacetime. When we use spacetime metrics instead of the metrics of space and time, it appears that everything in the Universe is moving at exactly the same rate. That light has a constant velocity is a corollary of this. Light having no mass, there is no time dimension to its motion in spacetime, it must therefore always appear to be moving through space at the maximum velocity possible. Time dilation, under this view, is simply an effect of the projection onto space and time of a spacetime 'velocity' for objects having significant relative speed or mass (or acceleration). All the space and time components as well as mass/acceleration are traded off against one another to maintain a constant spacetime motion. Time can therefore appear to be 'red shifted', in the terminology I made up, for exactly the same geometrical reasons that light appears to be.

And we're all together here and now in spacetime. That's why the Sun keeps coming up in the morning!

Aren't you glad I got that sorted out?

Review: Why Does E=mc2? (And Why Should We Care?) by Brian Cox and Jeff Forshaw

(This review first appeared in the New York Journal of Books on 13th July 2010.)

Why Does E=mc2? is one of those questions that educated non-physicists must have been asking themselves for over a hundred years, ever since Albert Einstein derived the equation back in 1905. Now, in this easy-to-read little book from Brian Cox and Jeff Forshaw, we have the answer. The authors are both professors of physics at Manchester University, and Brian Cox is also a well-known TV personality—well known enough to warrant a jacket blurb from Stephen Fry.

The book begins with the traditional approach to explaining the slowing of clocks for observers in motion relative to one another, by examining the geometry of a light beam bouncing up and down in a moving vehicle. The authors demonstrate just how easy it is to get to Einstein’s time dilation formula using nothing more than Pythagoras’ Theorem and the knowledge that the speed of light is capped. But they don’t leave it there. In the first half of the book they consider two more approaches that lead us to the same conclusion. 

Along the way, they very cleverly introduce all the ideas we will need to get to the world’s most famous equation, E=mc². What is more, they focus on the most puzzling part: the question of what c, the speed of light, is doing in there. Very early on, they introduce c as a scaling factor so that we can talk about “distances” in spacetime. Later, by various means, they explain why c has to be the maximum speed that anything can travel. It is a small triumph of the book that Cox and Forshaw make the attempt to show the logical necessity of there being a universal speed limit, and that their arguments are presented so clearly.

Yet, as with any book of this size tackling a subject so enormous, it is not long before the authors start asking us to take things on trust, undermining the comprehensibility of their presentation. The first big one is when they introduce Maxwell’s equations and ask us to believe they demand that the rate of propagation of an electromagnetic field be constant for all observers. Then comes the work of mathematician Emmy Noether and her demonstration that invariance leads to the conservation of quantities. 

These, and many others introduced later, are tough ideas and hard to swallow. The authors introduce them to provide alternative ways into the understanding of relativity and that famous equation. It is to their credit that they do not always hide the complexity nor the long history of ideas behind relativity, but it would have been better, perhaps, to have spent a few more pages on some of these notions. It is also to their credit that they make the case, as Feynman and others have done before them, that, at some level, the weirdness of the universe just has to be accepted, and the only test of physical theories that matters a damn is whether they are supported by actual observation and experiment.

And there would have been many pages to spare for additional background and explanation if, near the end, the book had not wandered into obscure and largely unrelated areas as it tackled a broad-brush description of the Standard Model in an attempt to explain what mass is. It was inevitable that some particle physics had to be discussed and that this would lead to discussions of quantum theory. After all, the book’s sub-title is And Why Should We Care? and the reasons given largely involve nuclear power, chemistry, and cosmology—all of which are helped by discussions at a subatomic level. Perhaps also Brian Cox’s involvement at CERN (he heads a project there to upgrade the ATLAS and CMS detectors for the Large Hadron Collider) meant that a discussion of the Higgs particle was inevitable. Nevertheless, this, and the very brief glimpse of general relativity right at the end, seemed to detract from the clarity and force of the earlier exposition.

It is a curious book that tackles several of the most difficult ideas in modern science in the tone of a friendly, almost patronizing, high-school teacher, trying to ensure that the slow kids manage to keep up with the rest of the class. The tone and the endless asides (did you know that the Sun converts 600 million tonnes of hydrogen into helium every second?) can become a bit wearing, but Cox and Forshaw have to be praised for their unwavering insistence that their subject is accessible to anyone at all who will stay with them and think about it.

In an age when most lay people throw up their hands at the mention of relativity or quantum theory, when religious creation stories and New Age mysticism offer a far simpler, less challenging route for the intellectually overwhelmed, it is hugely important that ordinary people see that physics is not just for the egg-heads, that it can be understood, and that there is a grand beauty in what it reveals about our world. Cox and Forshaw have made an important contribution in this area, one that will help school science teachers as much as it will their students.

Time, Relativity, Time Travel, and the Great Puzzle of Why the Sun Rose This Morning

There's something wrong with my notion of time.

I used to think it was all subjective - by which I meant relative to one's frame of reference, as general relativity tells us. I am more than happy to accept all the experimental evidence that says moving very fast, or being near a large mass, will slow down the passage of time relative to an observer outside your frame of reference. There is so much evidence for general relativity that it would be ludicrous not to accept it. Yet a simple observation of my own tells me that there must be more to the story than that.

And this is it: the Sun rose this morning. I know that because I saw it.

The problem is that it should not have done. The Sun should not be there at all. The Sun and the Earth were formed at about the same time, some 4.5 billion years ago. However, the mass of the Sun is about 330,000 times that of the Earth. Relatively speaking, time will run a bit more slowly for the Sun than for the Earth. But, after 4.5 billion years, all those nanosecond differences will add up. Yet Earth and Sun seem to be here together. We have both arrived at today at the same time.

So my notion of time - and/or my notion of what general relativity is saying - must be wrong. In fact, the same goes for special relativity too. I cannot account for why anything moving fast relative to me doesn't just wink out of existence. Because its time is slowed down, I should move into its future, it should move into my past, and we should not be able to perceive each other in our respective presents. After all, I know from experience that I cannot see the future, or the past.

So, okay, the fact that relative gravitational potential, or acceleration, or velocity, affects the rate at which time passes for different 'observers' seems to have nothing to do with the way time is actually passing for us all. I can live with that. In fact, I've seen something very like it somewhere else. The speed of light is quite similar. This is a constant and, all intuition aside, light travels at the same velocity (c) relative to you, whatever speed and direction you are travelling relative to its source. What does happen to light, though, is that its frequency shifts. If you are approaching a source of light very fast, it still hits you at exactly c but its frequency is shifted higher - towards the blue end of the spectrum. If you are racing away from the source, light still catches you at exactly c, but now its freuency is lower - shifted towards the red end of the spectrum.

What if time behaves like light? What if the rate of passage of time is also constant? Then, whatever we were doing in the Universe, time would always affect us the same way. But, accelerations, gravitational fields, and relative velocities lead to us perceiving a shift in something equivalent to the frequency of time. Let's call it time's 'colour'. A high gravitational potential, shifts time's colour towards the red end of its spectrum.

This notion (although it explains my problem with time) is an intuitively difficult one because what we normally think of as time - that thing that measures the intervals between ticks of a clock - isn't really time at all. It is just the colour of time. Real time, the thing that has its colour shifted and which ensures the continued coexistence of everything in the present, must be something else. Maybe we should call it 'persistence' or (to borrow a word from H. G. Wells) 'duration'?

So time is a kind of universal persistence and what I used think was time is just the colour of this persistence.

Am I happy now? No, not really. For a start, shifting the colour of persistence is analogous to shifting the colour of light (and is effected in exactly the same ways). So, by the same analogy, there can be no time travel. Shifting the colour of light does not affect its speed. The rate of persistence will be constant regardless of relativistic effects on its colour. You can age less (or more) than other things in the Universe by manipulating your speed, acceleration, or proximity to mass, but you do not change your place in persistence with respect to the rest of the Universe. That's why fast things do not blink out of existence for me. We are persisting at the same rate, even though we are aging at different rates. (Even dragging the exit of a wormhole around at near light-speed won't do the trick any more, because entrance and exit persist at the same rate, the exit may end up younger than the entrance but they will still be there at the same point in persistence at the end of it all!)

Are there any physicists out there who can tell me why all this is wrong and also explain why I saw the Sun this morning?