Wednesday, 16 November 2011

Stephen Hawking and Leonard Mlodinow, The Grand Design (2011)


Here are some lines from Hawking and Mlodinow's 'new answers to the ultimate questions of life' book:
Philosophy is dead. Philosophy has not kept up with modern developments in science. [13]
Oh.
A law of nature is a rule that is based upon an observed regularity and provides predictions that go beyond the immediate situations upon which it is based. For example, we might notice that the sun has risen in the east every morning of our lives, and postulate the law, "The sun always rises in the east." This is a generalization that goes beyond our limited observations of the rising sun and makes testable predictions about the future. On the other hand, a statement such as, "The computers in this office are black" is not a law of nature because it relates only to the computers within the office and makes no predictios such as , "If my office purchases a new computer it will be black". [39-40]
This is wrongheaded. Saying 'the sun rises in the east' has exactly the same truth-status as saying 'the computers in this office are black'; viz., a localised one. The sun does not rise in the east on Venus, after all. Just as the 'law' about the colour of the computers is falsified by going to an office with white computers; the 'law' about the sun rising in the east is falsified by going to Venus. Indeed, this Popperian notion of 'falsification' is weirdly absent from the book's discussion of what constitutes 'scientific law'.  Really, not a single mention of Popper in the entire book.
One of [Aristotle's] predictions was that heavier objects should fall faster because their purpose is to fall. Nobody seemed to have thought that it was important to test this until Galileo. [69]
Lucretius and Democritus both disagreed with Aristotle about the nature of weight; Democritus probably and Lucretius certainly thought that unequal weights would fall with the same finite speed in a vacuum; and Simon Stevin showed that two objects of different weight fall down with exactly the same acceleration in 1586, long before Galileo.
The idea that the universe is expanding involves a bit of subtlety. For example we don't mean the universe is expanding in the manner that, say, one might expand one's house, by knocking out a wall and positioning a new bathroom. [159]
No shit, Sherlock.
Eddington visualised the universe as he surface of an expanding baloon, and all the galaxies as points on its surface ... if at some point two galaxies were 1 inch apart, an hour later they would be 2 inches apart. [160]
OK.
It is important to realize that the expansion of space does not affect the size of material objects held together by some kind of force. For example, if we circled a cluster of galaxies on the balloon, that circle would not expand as the balloon expanded. [160]
But you've just a few lines earlier said that the distance between galaxiesthis circleis expanding! There's a problem here. Hawking and Mlodinow want to insist upon this point, because 'we can detect expansion only if our measuring instruments have fixed sizes. If everything were free to expand, then we, our yardsticks, our laboratories, and so on would all expand proportionately and we would not notice any difference' [161]. But the point of the balloon analogy is that spacetime itself is expanding (not, for instance, that the big bang happened in the middle of a cavernous empty space, filling it with matter; but that the big bang created the space as it expanded). If spacetime is expanding, then matter that is coordinated in spacetime would expand too. That gravity and atomic bonds set up a counterforce plays a part here, although there is nothing in the book at all on either dark matter or, more crucially, dark energy.

The boast at the beginning of this book is that it will explain 'not only how the universe behaves, but why'; and more specifically that it will answer the three-part 'ultimate question', viz:
Why is there something rather than nothing?
Why do we exist?
Why this particular set of laws and not some other? [19]
But the answers Hawking and Mlodinow provide are weak. They dismiss theological answers on the (reasonable) grounds that answering 'how created the cosmos?' with 'God' only shuffles the question along to a new term ('so who created God?'). But then they do the same thing with their questions. For example, their answer to 'Why is there something rather than nothing?' is that though 'the total energy in the universe must always remain zero' it is possible to balance 'the positive energy of matter' and 'the negative energy of gravity': 'and so there is no restriction on the creation of whole universes' [227]. But this doesn't explain why there is a balance of energy in the first place, or why the cosmos was pushed into this positive/negative state rather than the default nothingness. They answer their second question by invoking Conway's game of life, which shows that complex forms can emerge without a designer, but says nothing about the why. And they answer their third question by gesturing, rather vaguely, towards the anthropic principle. Bah.

To go back to:
Philosophy is dead. Philosophy has not kept up with modern developments in science. [13]
Dudes! You need to read more widely in contemporary philosophy.

5 comments:

Gareth Rees said...

There are some uncharitable readings in this review (perhaps indicating that the book is not all that clear). When they say "The sun always rises in the east" the authors clearly intend "on Earth", so quibbling about Venus seems rather mean. Similarly, a posited "law" like, "The computers in this office are black" can't be falsified by going to another office, because the "law" doesn't say anything about that other office.

Certainly the passage you quote from pages 39–40 does a very poor job of elucidating the idea of a scientific law. The OED does a better job: "law, n. a theoretical principle deduced from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present." But with the better definition in mind, you can see that the quoted passage makes sense.

You've also misread the section about the expanding universe (again, this is probably the authors' fault for not making their explanation more clear). The point that the authors are trying to make is that some structures in the universe are bound together by gravity or electromagnetism, and these structures do not get bigger as a result of the expansion of the universe. Galaxy clusters are the largest bound objects we know about: as the universe expends, each galaxy cluster will stay roughly the same size, while the distance between galaxy clusters will grow. Eddington, I think, didn't know about galaxy clusters—in his day individual galaxies were the largest known gravitationally bound objects. (So it was unwise of the authors to use Eddington's metaphor of galaxies on a balloon and then follow it up with a comment about galaxy clusters.)

Adam Roberts said...

Hi Gareth. I may be being uncharitable to the authors, but I don't think I agree with your defence of them. The OED definition of a law seems to me to apply equally to the Black Computers in the office as to the sun rising in the east on Earth. What they want to say is 'a law is something extrapolated from a whole bunch of related data, when those data aren't linked by, you know, random or capricious things like whether the office manager prefers Black computers'. But this is conceptually inept. The 'if certain conditions be present' element of the OED definition becomes a get-out-of-jail-free-card for any exceptions that challenge the law -- sunrise on Venus, crows that suffer from albinism, subatomic particles that travel faster than light. Better to abandon the idea that science is in the business of established cut-and-dried absolute laws altogether.

You say: 'some structures in the universe are bound together by gravity or electromagnetism, and these structures do not get bigger as a result of the expansion of the universe.' Do you mean 'some structures in the universe are bound together by gravity or electromagnetism, and these forces act against the larger frame-shift of the expansion of the universe'? Because that's not the same thing.

Gareth Rees said...

Do you mean 'some structures in the universe are bound together by gravity or electromagnetism, and these forces act against the larger frame-shift of the expansion of the universe'? Because that's not the same thing.

I'm not sure I understand the distinction you are making here. (Also, I don't know what you mean by "frame-shift".)

However, there are a couple of ways of looking at the situation. In general relativity, the expansion of the universe is built into the law of gravity. So when we say that an object is gravitationally bound, we already mean, "taking into account the expansion of the universe".

If you prefer to imagine one force (gravity) pulling objects together and another (the expansion of the universe) pushing them apart, the outcome is going to be dominated by whichever of these is stronger.

Let's do a na├»ve back-of-the envelope calculation. The rate of expansion of the universe is about 74 km/s/Mpc. So two objects a million parsecs apart would be moving apart at 74 km/s if they weren't gravitationally bound. The constant acceleration that would have resulted in this velocity if it had been applied over the lifetime of the universe (13.7 billion years) is about 1.7×10^−14 m/s^2. Which matches the acceleration due to gravity between the two objects if they have about a hundred thousand solar masses (say, a small globular cluster). So objects bigger than this are gravitationally bound at this distance, even taking into account the expansion of the universe.

Adam Roberts said...

One of the delights of your comments on my blog, Gareth (I'm speaking absolutely genuinely when I say this; I don't mean to be ironic or sarcastic) is that they stretch and educate me. So I went away and read this interesting Wikipedia entry on the metric expansion of space.

By 'frame shift' (poor phrase, you're right) I meant 'metric'; and my point was the Hubble-ish one that 'observational phenomena overwhelmingly support models that rely on space expanding through a change in metric' ('Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion. Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion').

You say 'The rate of expansion of the universe is about 74 km/s/Mpc. So two objects a million parsecs apart would be moving apart at 74 km/s if they weren't gravitationally bound' [my emphasis], which seems to imply that the gravitational binding means that they aren't moving apart at this rate. But they are -- aren't they? Wikipedia again: 'The acceleration in the expansion of the universe has been measured using redshift as H0 = 73.8 ± 2.4 (km/s)/Mpc. For every million parsecs of distance from the observer, the rate of expansion increases by about 74 kilometers per second.'

If the galaxies weren't moving apart from one another, there wouldn't be any red shift at all, surely.

Gareth Rees said...

Be careful! All distant enough galaxies are moving away from us at speeds that are on average proportional to their distance.

These qualifications are important: some nearby galaxies are not moving away. Take, for example, the Andromeda Galaxy. It's about 0.78 Mpc away, so if it's motion relative to us were due only to the expansion of the universe, it would be moving away from us at about 56 km/s. But it's not: it's actually moving towards us at about 300 km/s. That's because the gravitational attraction between Andromeda and the Milky Way is large enough to overcome the expansion of space. We sum this up by saying that the Local Group is gravitationally bound: that is, the force of gravity between the galaxies in this group is large enough to prevent the expansion of the universe from separating them.

The more distant a galaxy, the more the "Hubble flow" takes over: it's thought that even relatively nearby galaxies (but outside the Local Group) like M83 will be carried away by the expansion of the universe.

So why do Hawking and Mlodinow say, "For example, if we circled a cluster of galaxies on the balloon, that circle would not expand as the balloon expanded"? Because cluster is a technical term for cosmologists: what they mean by a "cluster of galaxies" is a group of galaxies that are gravitationally bound, for example the Local Group.

This technical use of cluster is probably so basic to Hawking and Mlodinow that they didn't realise it needed to be explained here. Effective popularisation is tough, and it sounds as though these authors haven't done a particularly good job.