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.
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.
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.
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!”
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?
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.
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.
The Big Questions ?
Landsburg’s PhD is in Math.
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.
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.
We don’t even really know if quantum mechanics is a good model. Sure there have been confirming experiments, but with laughably small precision.
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…
What I would like to know is how is a theory (and that is being generous) that is rooted in arrogance of self worth anything. Lets use the good for solving the good and not making the bomb.
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