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The Big Questions
In The Big Questions, Steven Landsburg ventures far beyond his usual domain to take on questions in metaphysics, epistemology and ethics. Beginning with Plato, mathematicians have argued for the reality of mathematical forms. Rene Thom, for example, once said "mathematicians should have the courage of their most profound convictions and thus affirm that mathematical forms indeed have an existence that is independent of the mind considering them." Roger Penrose put it more simply, mathematical abstractions are "like Mount Everest," they are, he said, "just there."
All this must make Steven Landsburg history's most courageous mathematician because for Landsburg mathematical abstractions are not like Mount Everest, rather Mount Everest is a mathematical abstraction. Indeed, for Landsburg, it's math all the way down - math is what exists and what exists is math, A=A.
Read the book for more on this view, which is as good as any metaphysics that has ever been and a far sight better than most. Moreover, Landsburg's view is not empty, it does have real implications. Since there is no uncertainty in math, for example, Landsburg's view supports a hidden variables or multiple-worlds view of quantum physics.
Speaking of quantum physics, The Big Questions, has the clearest explanation of the Heisenberg uncertainty principle that I have ever read. In fact, this is a necessary consequence of Landsburg's metaphysical views; since it's all math all the way down, the explanation of the uncertainty principle is the explanation of the math and any true uncertainty or mystery is simply a fault of our own misunderstanding.
Turning to epistemology, the theory of beliefs and knowledge, two chapters stand out for me. I learned a lot from Landsburg remarkable clear explanation of Aumann's agreement theorem--and I say that despite the fact that in the office next to mine is Robin Hanson, one of the world's experts on the theorem (see Robin's papers on disagreement and also his paper with Tyler, but read Landsburg first!).
Landsburg's skills of explanation are also brought to bear in a wonderful little chapter explaining the theory of instrumental variables and of structural econometric modeling - and this from an avowedly armchair economist!
Finally for those, like me, who loved The Armchair Economist and More Sex is Safer Sex there is also lots of economics in The Big Questions. Highly recommended.
Posted by Alex Tabarrok on November 16, 2009 at 07:43 AM in Books, Economics, Philosophy, Religion | Permalink
Comments
Maths is a beautiful way of looking at the world, but does Landsberg say there is no uncertainty underlying math? 'Uncertainty'is not an unambiguous term; but unless someone has sneaked in a refutation of Gödel's theorems, maths is not perfectly certain.
I dearly hope that Gödel is unshaken. I have never been able to get my mind around the idea of a logic or a world where anything is absolutely certain; and in my late 70s feel too old to try.
Posted by: David Heigham at Nov 16, 2009 9:18:31 AM
So what is the formula constituting consciousness? Inquiring numbers would like to know.
Posted by: J. Bogart at Nov 16, 2009 9:26:14 AM
I haven't read the book, but your description of his metaphysics reminds me of Plato's theory of celestial movement- of course all the planets move in perfect circles, because that is the most elegant and mathematically perfect way for them to move. It's a shame that reality often does not match our ideas of what it should be like.
Posted by: Jim Clay at Nov 16, 2009 9:53:24 AM
Il n'y a pas de hors-equations?
Posted by: tom s. at Nov 16, 2009 9:55:06 AM
It's a shame that reality often does not match our ideas of what it should be like.
Indeed, it often seems as though symmetry and other mathematical beauty are assumed to be necessary. It is a fairly egregious non sequitur, succumbing to the human brain's desire for rule and consistency - "Einstein, stop telling God what to do!"
Posted by: William at Nov 16, 2009 10:02:07 AM
The book and the author both sound insufferable.
Posted by: jdm at Nov 16, 2009 11:18:28 AM
Look, it's mid November; the question is, how will I enjoy it when I'm a-turkied, a-sherried and a-ported at Christmas?
Posted by: dearieme at Nov 16, 2009 11:32:19 AM
ALthough i liked armchair economist and More sex is safer sex, Steven Landsburg is unable to hide his smug arrogance in this book.
To him the world does boil down to mathematics and arithmetic. I do not have a problem with his position on this, but his "proof" is that he just "knows it to be so". and the only example he really uses to illustrate this is that 2+2 = 4 and not 5, which he repeats and repeats throughout the book. His other favorite expression, which i found not only smug, but incomplete in terms of a proof, is that an explanation he's trying to give would require more mathematics than you (the reader) really want to know. (see his explanation for why ripples in water repeat, but sound waves/ripples do not... a very interesting observation, but his explanation for why he is avoiding an explanation is absurd - perhaps its because he doesn't understand it himself)
overall, his use of logical reasoning is solid, standard Landsburg. He likes to take a set of conditions and really run with them to their logical conclusion. I think this is where he thrives. he also has a deep interest in the physical sciences. i wonder if it weren't for economics, he would probably have become a physicist - and many of his vignettes are indeed interesting.
He doesn't really discuss anything about Behavioral Economics, but i suspect he wouldn't understand much of it. He doesn't appear to be able to navigate through "shades of grey" of any sort.
on a side note, i do not understand Dr. Taborrok's plug that this is the "best" metaphysics ever. What ever happened to comparative advantage. Dr. Landsburg is an economist. He hasn't spent his career thinking through metaphysics, nor trying to explain it in the classroom day in and day out.
At best, BIg Questions is an interesting read - you can get some insight into the inner workings of the brain of a very logical person.
Posted by: Brian at Nov 16, 2009 11:57:34 AM
I have not read the book either, but there are ways besides Godel's
Theorem that math is uncertain. Does one accept the axiom of choice
(not all mathematicians do)? Does one accept the law of the excluded
middle (not all mathematicians do). Now Landsburg sounds like he is
channeling Kronecker with his 2+2=4, with Kronecker having said that
"God made the natural numbers, and man made all the rest." Great. Sure,
and (for real), my father actually proved that 2+2=4 in a book on Logic,
after assuming enough of the right axioms.
Except, of course, even that is not always necesasrily true. It is
possible to construct an alternative arithmetic where it is not true,
although one might argue that it is not a useful arithmetic, and, after
all, there is the old black swan argument, we have never see 2+2 not
equal 4, unless you want to play funny games with funny definitions
in funny places like adding angles according to certain rules on
curved surfaces, or something else possibly rather naughty.
Posted by: Barkley Rosser at Nov 16, 2009 12:38:30 PM
I have never seen Landsburg show any ability to recognize the limitations of his own arguments. Given that his writings almost always contradict the conventional wisdom, this makes him incredibly annoying to read.
Posted by: Barbar at Nov 16, 2009 2:10:06 PM
Barbar said that Landsburg how no ability to recognize the limitations of his own arguments ...
"Never forget that there are a lot of people who know a lot more than you do about a lot of things that are important. Listen carefully to what they have to say. Defer immediately to a good argument. But never defer to mere authority. If you have good teachers, they will encourage you. I hope you read this book someday. When you publish your rebuttal, I'll be first in line for an autographed copy."
That's how he ends, "Fair Play," still my favorite of all of his work.
Posted by: wintercow20 at Nov 16, 2009 3:05:29 PM
When did the "Premium" ad for Landsburg's book show up on MR?
I demand to know, or I will contact the FTC, FCC, and maybe even the FDIC and KFC.
Posted by: tom at Nov 16, 2009 3:38:35 PM
The Big Questions ?
Posted by: Instant sales at Nov 16, 2009 3:56:43 PM
In 1960, the well-known Nobel prize-winning physicist Eugene Wigner noted the "unreasonable effectiveness" of mathematics in explaining our physical universe, and argued that this must reflect some deeper truth.
Nevertheless (and not having read the book), I'm not sure where Landsburg is going with this. His background is in economics; I'd like to hear what top mathematicians and physicists have to say. We can safely ignore the nitwits who would argue that mathematics (and practically all else under the sun) is a "social construct", but perhaps Landsburg seems to be veering too far in the opposite direction...
Posted by: anonymous at Nov 16, 2009 4:19:41 PM
Landsburg's PhD is in Math.
Posted by: wintercow20 at Nov 16, 2009 4:29:16 PM
Wintercow20, great, those are noble sentiments. Meanwhile my actual experience reading Landsburg is that he says something that completely contradicts intuition. I go "huh?" and wonder how it could be possible that everyone's intuition could be so completely wrong. Why, it's simple, Landsburg smugly says -- people just don't understand economics, math, and logic. I take a step back, think things over, and realize that Landsburg gets to his conclusion by completely ignoring something important in his "logical" analysis. Meh. Next chapter, the same thing happens again.
So yeah, more sex is safer sex, and laws against pollution make no one better off, and investors have to overpay CEOs to get good performance, and it's shocking how little lobbying occurs in Washington. Behold the magic of Landsburg! Except of course that there are perfectly sound arguments that can be employed against armchair economics in defense of common sense. Oh.
Posted by: Barbar at Nov 16, 2009 4:31:02 PM
Most of what Landsburg writes is pop-schlop stuff these days. He may be playing in higher levels
here again, after a respite. He apparently has published some in philosophy of science, although
I do not know when or where or on what exactly, and he has an unpublished book on quantum theory
(and he did some time at the Institute for Advanced Study in Princeton). His math pubs seem to
be mostly on K-algebras, dating to the early 1990s.
Posted by: Barkley Rosser at Nov 16, 2009 5:17:11 PM
The determinists are nothing if not determined. It's their inevitable hubris with which I find fault.
Posted by: Thanatos Savehn at Nov 16, 2009 8:03:47 PM
Landsburg supports his argument with an enthusiastic citation of the cosmologist Max Tegmark's recent paper "The Mathematical Universe," which was published in Foundations of Physics and is available on the web as an arXiv pdf. Tegmark's arguments have been around for a good many years now. I have read them as closely as I can without having too much math. I must aver that now, late in life, I am convinced. For me they pass the test of plausibility, so far as such profound speculations can, without decisive experimental and theoretical proof.
Posted by: Richard Lubbock at Nov 16, 2009 8:16:48 PM
Sounds interesting. Mathematically the uncertainty principle falls directly from considering a physical entity to be both particle and wave. Being a wave requires certain fourier transform based inequalities to hold, and being a particle means having a set energy, from which uncertainty falls out. If you want a really good treatment of the subject, Braginsky and Khalili's Quantum Measurement is the book. It's readable if you're decent with math. The focus on the book is the uncertainty principle as a dynamical law, rather than as a statistical law.
All in all, the math will make sense, but talking about a wave propagating without a medium in which to propagate is not intuitive [this is the situation with a photon]. It confused Michelson and Morley 100+ years ago. It would confuse more people now, except we don't think about it as much.
Quantum mechanics is also incomplete. We don't know whether it's paradoxes with measurement can be resolved as from non-locality of interaction, or from irreality - that measurement fundamentally alters the state of the universe/measured object in some sort of special way, rather there being a constant external reality. This is one of the great unresolved debates of physics.
To get back to the topic at hand, Tegmark compares the External Reality Hypothesis to his Mathematical Universe Hypothesis. The first one relates directly to whether non-locality or irreality holds true.
Posted by: David Brown at Nov 16, 2009 9:07:21 PM
We don't even really know if quantum mechanics is a good model. Sure there have been confirming experiments, but with laughably small precision.
Posted by: Andy at Nov 19, 2009 7:52:39 AM
