Leonard Mlodinow

In which we meet yet another first-class scientist who wishes to self-identify as a second-class philosopher and a comedian from the back end of steerage.

Since few will buy A Grand Design for its wit we can forgive Stephen Hawking's appalling attempts to be funny, but it's not so easy to forgive his philosophical ignorance. Certain physical scientists might be better off unacquainted with the modern philosophy of science (though those who know it possess a welcome sense of perspective and show more humility). But not world-renowned cosmologists. Their field continually bumps up against the boundary of what science even is (and it doesn't have a "no-boundary condition", whatever that might be).

So when Stephen Hawking claims that "philosophy has not kept up with modern science, especially physics" it suggests not only a lack of perspective and humility, but that Hawking has been skipping on some required reading. Especially since, having written off the discipline, Hawking seems barely acquainted with it. He mentions few philosophers more recent than Rene Descartes (d. 1650). So it is hard to know who he thinks hasn't kept up.

Particularly when Hawking's first grand pronouncement is "model-dependent reality": the idea that there may be alternative ways to model the same physical situation with fundamentally different elements and concepts. "If [such different models] accurately predict the same events, one cannot be said to be more real than the other." Physics has, apparently, been forced into this gambit following recent failures to get unifying calculations to work themselves out. In any case it isn't quite the neat trick Hawking thinks it is.

Firstly, while model-dependent reality might be news to Stephen Hawking (he seems to think it the fruit of modern physics' womb) the philosophers he hasn't been reading have been talking about it for years, if not centuries, to the constant sound of scientists' excoriations. It is even part of Descartes' philosophical fabric (and, more tellingly, Darwin's , but picking a fight with modern evolutionists, while fun, is a story for another day). That is to say, it sounds like it is the physicists who are finally catching up with the philosophers and not the other way around.

Secondly, in the grand game of philosophers' football that Cosmology has become, the model-dependent reality play is something of a surrender before kick-off. For if it is true that the same phenomenon can be plausibly accounted for in multiple, "incommensurate" (© Thomas Kuhn) ways, then the hard question is not about the truth in itself of any model, but the criteria for determining which of the (potentially infinite) models available we should choose in the first place.

This question is not one for physics, but metaphysics. It necessarily exists outside any given model (© Paul Feyerabend). Here we meet our old friend, Occam's Razor. This isn't a scientific principle at all, but a pragmatic rule of thumb with no intellectual pedigree: all else being equal, take the simplest explanation. Occam's Razor is a favourite instrument for the torture of hapless Christians by grumpy biologists: all your tricksy afterlife wagers and so on fail because evolution is so much less complicated and has so much more explanatory value than the idea that an omniscient, intangible, invisible, omnipotent entity pulling strings we can't see to make the whole thing go.

But, alas, in seeking a grand unification of things that really aren't asking to be unified, cosmology reveals some almighty snags. Unification under Hawking's programme, if it is even possible, involves slaughtering some big old sacred cows. To name a few: causality, the conventional conception of space-time; the idea that scientific theories should be based on observable data and their outcomes testable. It bows to some truly heinous false idols too. For example: seven invisible space-time dimensions, a huge mass of invisible dark matter, an arbitrary cosmological constant, a potentially infinite array of unobservable universes which wink in and out of existence courtesy of a mathematically inferred "vacuum energy"). Hawking doesn't propose solutions to these problems, but seems to think they're a fair price for achieving grand unification.

I'm not so sure: other than intellectual bragging rights, the resulting unified theory has no obvious marginal utility. And it has political drawbacks: believing one's model to be the truth carries potentially unpleasant implications for the suppression of those who don't.

There are practical drawbacks, too. We are asked to reject existing theories, which still have quite a lot of utility, in favour of something that it infinitely harder to understand and work with. The accelerating expansion of the universe without any apparent acting force seems to violate Newton's second law of motion. Without an outrageous end-run, the first nanosecond of the Big Bang (wherein the universe is obliged to expand in size by ten squillion kilometres - i.e. far faster than the speed of light) seems to violate the fundamentals of general relativity. String theory requires seven necessarily unobservable space-time dimensions and/or entirely different universes, and even then doesn't yield a single theory but millions of the blighters, all slightly inconsistent with each other (hence the appeal to "model dependent reality).

From the camp which wielded Occam's Razor so heartily against the Christians, this seems a bit rich. If these are the options, then the razor might slice in favour of the big guy with the beard.

But these aren't the options. We could save a lot of angst, and perhaps could have avoided digging trillion dollar circular tunnel under Geneva, had we employed model dependent reality the way the philosophers saw it and not the scientists (and shouldn't we call a spade a spade and label it cognitive relativism, by the way?). Since it crossed the event horizon of observability modern cosmology has become arcane, stunt-mathematics. If there were a chance that it might deliver time-travel, hyperspace or a tool for locating wormholes to other galaxies or universes then one could see the point in this intellectual onanism. But none of that seems to be allowed. So we should therefore ask the question "but why? What's the point? What progress do you promise that we can't achieve some other way?" No one seems to be able to answer that question.

But if we park it, what's left of Stephen Hawking's latest book is some pretty ropey jokes. show less

"Philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics." From the first page Stephen Hawking destroys some cherished myths. You can read for yourself what he has to say about free will, but it is also somewhat shocking.

In a very short book, Hawking manages to take on the ultimate questions of life, the universe, and everything (the answer is not 42) and while he doesn't completely answer the questions, he makes a case for some answers to the show more "whys" that traditionally have been the realm of philosophers.

While there is no heavy mathematics in the book, it is a challenging read with a lot of topics which require one to think somewhat differently about the universe than most of us are used to. While I never re-read books, I will probably make an exception for this book, and feel that I need to re-read it to glean more understanding of the theories he presents.

All-in-all I highly recommend this book for those who want a greater understanding of modern physics, and the early scientists whose work has been built upon to produce modern physics. It is a concise history of physics with emphasis on the quest for a grand unified theory that will bring together all of the specific theories that apply in limited environments. show less

Leonard Mlodinow is a science writer with a sense of humor. In Euclid’s Window, he tells the story of the development (or should I say, evolution?) of geometry from the pre-Socratic Greeks to modern day.

The Greeks made some remarkable discoveries, among them the fact that the length of the diagonal of a square could not be expressed as a ratio of the lengths of its sides—or, as we would say today, the square root of two is irrational.

Not much is known about the person known as Euclid, show more but he seems to have systematized all that Greek civilization knew about geometry. His work, The Elements, shows how the Greeks had demanded rigor and logic in their approach to mathematics. To them, it was not sufficient to be able to calculate, one had to prove that the method of calculation was demonstrably valid. The entire work consists of many theorems derived from just a few definitions and (he thought) self-evident postulates.

But one of his postulates seemed just a little less self-evident than the others: the so-called parallel postulate, which asserts that parallel lines never intersect one another. For 2,000 years, geometers attempted unsuccessfully to show that the parallel postulate could be derived from the other postulates. Euclid himself may have been aware that there was something fishy about the postulate since he refrained from using it in his proofs of his first 28 theorems. It turns out that the parallel postulate is “true” only in a special kind of space, now called Euclidian space, which is basically a “flat” plane, that may be infinite in extent.

It was not until the 19th century when Carl Friedrich Gauss (and others, independently) figured out that logically consistent geometries could be created in which the parallel postulate was not true. For example, the postulate (and thus, much of Euclidian geometry that depends on it) is not valid on the surface of a sphere, like our planet earth. Nevertheless, Euclidian geometry is accurate and valid for practical purposes unless the objects being studied are large enough to be affected by the curvature of the earth.

Other exotic, but logically consistent, geometries were developed in the late 19th century. They found a practical use when Albert Einstein was wrestling with what came to be his general theory of relativity. He found he could make sense of what we call gravity if space itself was “curved.” He was delighted to discover that curved space geometry that fit his theory already had been worked out.

Geometry has come to play a role in modern efforts to combine quantum mechanics with general relativity. The Uncertainty Principle of quantum theory decrees that certain physical traits form complementary pairs that possess a certain limitation: the more precisely you measure one trait, the less precisely you can measure the other. The value of these complementary quantities beyond their limiting precision is fundamentally undetermined, not merely beyond the scope of our current instruments. And when you apply the uncertainty principle to gravity, you are driven to some rather bizarre conclusions about the geometry of space.

Efforts to make quantum theory consistent with general relativity have led to the development of string theory or M-theory, which are driven by insights of mathematics, not physical principles as Einstein’s theories were. Mlodinow writes:

“M-theory appears to have the property that what we perceive as position and time, that is, the coordinates of a string…are really mathematical arrays known as matrices. Only in an approximate sense, when strings are far apart (but still close on the scale of everyday life) do the matrices resemble coordinates—because all the diagonal elements of the array become identical and the off-diagonal elements tend toward zero. It’s the most profound change in the concept of space since Euclid.”

This can be pretty heady and heavy stuff, but Mlodinow makes it pretty enjoyable. He peppers his discourse with wry asides, for example, he observes:

“In the case of the Crusades, ‘contact’ with the Europeans was about as desirable as contact with the Martians in War of the Worlds.”

Whenever he needs two real life examples to explain a concept, he uses his impish young sons Nicolai and Alexei. When the reader is likely to want a simple answer to a complex issue, he admonishes, “Dream on!”

This book might have been subtitled A History of the Concept of Space. It shows how mathematics as well as science develops by building on pre-existing ideas. It is a well-told tale, well worth reading.

(JAB) show less

One of my favorite books ever. If you are interested in human behavior, and why we sometimes behave irrationally even when we think we're making informed decisions, this book will enlighten you. And I use that word intentionally, because it really did change my perspective on risk. Usually a month doesn't go by that I don't mention or use something that I learned from that book, like the gambler's fallacy or the Texas sharpshooter's fallacy.