S**C
发帖数: 2964 | 1 http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-univers
IN Mikhail Bulgakov's novel “The Master and Margarita,” the protagonist, a
writer, burns a manuscript in a moment of despair, only to find out later
from the Devil that “manuscripts don’t burn.” While you might appreciate
this romantic sentiment, there is of course no reason to think that it is
true. Nikolai Gogol apparently burned the second volume of “Dead Souls,”
and it has been lost forever. Likewise, if Bulgakov had burned his
manuscript, we would have never known “Master and Margarita.” No other
author would have written the same novel.
But there is one area of human endeavor that comes close to exemplifying the
maxim “manuscripts don’t burn.” That area is mathematics. If Pythagoras
had not lived, or if his work had been destroyed, someone else eventually
would have discovered the same Pythagorean theorem. Moreover, this theorem
means the same thing to everyone today as it meant 2,500 years ago, and will
mean the same thing to everyone a thousand years from now — no matter what
advances occur in technology or what new evidence emerges. Mathematical
knowledge is unlike any other knowledge. Its truths are objective, necessary
and timeless.
What kinds of things are mathematical entities and theorems, that they are
knowable in this way? Do they exist somewhere, a set of immaterial objects
in the enchanted gardens of the Platonic world, waiting to be discovered? Or
are they mere creations of the human mind?
This question has divided thinkers for centuries. It seems spooky to suggest
that mathematical entities actually exist in and of themselves. But if math
is only a product of the human imagination, how do we all end up agreeing
on exactly the same math? Some might argue that mathematical entities are
like chess pieces, elaborate fictions in a game invented by humans. But
unlike chess, mathematics is indispensable to scientific theories describing
our universe. And yet there are many mathematical concepts — from esoteric
numerical systems to infinite-dimensional spaces — that we don’t
currently find in the world around us. In what sense do they exist?
Many mathematicians, when pressed, admit to being Platonists. The great
logician Kurt Gödel argued that mathematical concepts and ideas “form
an objective reality of their own, which we cannot create or change, but
only perceive and describe.” But if this is true, how do humans manage to
access this hidden reality?
We don’t know. But one fanciful possibility is that we live in a computer
simulation based on the laws of mathematics — not in what we commonly take
to be the real world. According to this theory, some highly advanced
computer programmer of the future has devised this simulation, and we are
unknowingly part of it. Thus when we discover a mathematical truth, we are
simply discovering aspects of the code that the programmer used.
This may strike you as very unlikely. But the Oxford philosopher Nick
Bostrom has argued that we are more likely to be in such a simulation than
not. If such simulations are possible in theory, he reasons, then eventually
humans will create them — presumably many of them. If this is so, in time
there will be many more simulated worlds than nonsimulated ones.
Statistically speaking, therefore, we are more likely to be living in a
simulated world than the real one.
Very clever. But is there any way to empirically test this hypothesis?
Indeed, there may be. In a recent paper, “Constraints on the Universe as a
Numerical Simulation,” the physicists Silas R. Beane, Zohreh Davoudi and
Martin J. Savage outline a possible method for detecting that our world is
actually a computer simulation. Physicists have been creating their own
computer simulations of the forces of nature for years — on a tiny scale,
the size of an atomic nucleus. They use a three-dimensional grid to model a
little chunk of the universe; then they run the program to see what happens.
This way, they have been able to simulate the motion and collisions of
elementary particles.
But these computer simulations, Professor Beane and his colleagues observe,
generate slight but distinctive anomalies — certain kinds of asymmetries.
Might we be able to detect these same distinctive anomalies in the actual
universe, they wondered? In their paper, they suggest that a closer look at
cosmic rays, those high-energy particles coming to Earth’s atmosphere from
outside the solar system, may reveal similar asymmetries. If so, this would
indicate that we might — just might — ourselves be in someone else’s
computer simulation.
Are we prepared to take the “red pill,” as Neo did in “The Matrix,” to
see the truth behind the illusion — to see “how deep the rabbit hole goes
”? Perhaps not yet. The jury is still out on the simulation hypothesis. But
even if it proves too far-fetched, the possibility of the Platonic nature
of mathematical ideas remains — and may hold the key to understanding our
own reality.
Edward Frenkel, a professor of mathematics at the University of California,
Berkeley, is the author of “Love and Math: The Heart of Hidden Reality.”
A version of this op-ed appears in print on February 16, 2014, on page SR12
of the New York edition with the headline: Is the Universe a Simulation? | wy
发帖数: 14511 | 2 赞星空王座
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appreciate
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【在 S**C 的大作中提到】
: http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-univers
: IN Mikhail Bulgakov's novel “The Master and Margarita,” the protagonist, a
: writer, burns a manuscript in a moment of despair, only to find out later
: from the Devil that “manuscripts don’t burn.” While you might appreciate
: this romantic sentiment, there is of course no reason to think that it is
: true. Nikolai Gogol apparently burned the second volume of “Dead Souls,”
: and it has been lost forever. Likewise, if Bulgakov had burned his
: manuscript, we would have never known “Master and Margarita.” No other
: author would have written the same novel.
: But there is one area of human endeavor that comes close to exemplifying the
| B******Z
发帖数: 9193 | 3 顾铁：这个问题我说两句。。。
a
appreciate
the
【在 S**C 的大作中提到】
: http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-univers
: IN Mikhail Bulgakov's novel “The Master and Margarita,” the protagonist, a
: writer, burns a manuscript in a moment of despair, only to find out later
: from the Devil that “manuscripts don’t burn.” While you might appreciate
: this romantic sentiment, there is of course no reason to think that it is
: true. Nikolai Gogol apparently burned the second volume of “Dead Souls,”
: and it has been lost forever. Likewise, if Bulgakov had burned his
: manuscript, we would have never known “Master and Margarita.” No other
: author would have written the same novel.
: But there is one area of human endeavor that comes close to exemplifying the
| L******d
发帖数: 2461 | 4 赞星空王座的估计都很年轻，以至于没有看过the thirteenth floor.星空从setting上
来说，并没有任何新意。 |
|
