Why Does 2 + 2 = 4? What Math Teaches Us About Deep Reality | Peter Robinson | Hoover Institution

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- 2 + 2 = 4.
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In all places,
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and for all time, 2 + 2 = 4,
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but why?
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What does math tell us
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about the nature of reality?
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David Berlinski, Sergiu Klainerman
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and Stephen Meyer on
"Uncommon Knowledge" now.
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(upbeat classical music)
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Welcome to "Uncommon Knowledge,"
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recording today in Salzburg, Austria.
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I'm Peter Robinson.
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David Berlinski has taught math,
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philosophy and English at universities,
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including Stanford, Rutgers,
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the City University of New York
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and the Universidad del Peru.
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I hope you like
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that pronunciation, David.
- Perfect.
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- He is the author of books including
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"One, Two, Three:
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Absolutely Elementary Mathematics."
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And his forthcoming volume,
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"The Perpetual Rose."
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A native of Romania, Sergiu Klainerman
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is a professor of
mathematics at Princeton.
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In his own words, his current interests
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include, "The Mathematical Theory
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of Black Holes," more precisely,
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the rigidity and stability.
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I'm reading these words without
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having any idea what they mean.
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"And the dynamic formation
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of trapped surfaces and singularities."
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I'll ask you to explain
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a little bit of that maybe, Sergiu.
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The director of
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the Discoveries Institute Center
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for Science and Culture,
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Stephen Meyer started his
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professional life as a geophysicist.
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He returned to school,
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earning a doctorate from Cambridge
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in the history and philosophy of science,
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he has established himself as
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one of America's leading thinkers
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in intelligent design.
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His most recent book,
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the "Return of the God Hypothesis."
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David, Sergiu, Steve, welcome.
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In the "Return of the God Hypothesis,"
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Steve's latest book,
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he argues that three relatively
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recent developments suggests
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that science needs to return
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to some notion of the transcendent.
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And these three developments
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are the Big Bang,
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the fine-tuning of the universe
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and the discovery of DNA.
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After reading Steve's book,
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a certain very accomplished,
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well-known mathematician,
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took Steve aside and said,
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"You only named three developments
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that suggest a transcendent mind.
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There's a fourth."
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Sergiu, what did you mean by that?
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- Well, first, I should say,
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Steve talked about developments
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and mathematics is forever,
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I mean, has been
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around for thousands of years,
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so it's not quite fair to compare.
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But mathematics, by definition,
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deals with its own reality,
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which is, I claim as objective
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as the physical reality.
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So, for example,
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black holes are like that, right?
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A black hole by definition,
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we have a mathematical theory
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of general activity that predicts
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black holes, but by definition,
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a black hole cannot be seen.
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So nevertheless, we can assert
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its existence, why?
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Because general relativity
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is a consistent theory.
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- So black holes scare
the daylights out of me.
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We'll come back to black holes, I'm sure,
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but my mind already hurts is
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just when hearing about your work
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on the rigidity, all right.
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In layman's terms,
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which is to say for me,
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2 + 2 = 4, is real.
- Correct.
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- That's not a figment,
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it's not an artifact of
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our mind of mental processes,
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of the accidental processes
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that might be going on in our neurons.
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- Correct.
- Whether I think
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it's 2 + 2 = 3 or 5, I'm wrong.
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2 + 2 does equal 4,
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and that is objectively real.
- Correct, right.
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- Therefore, there is a conceptual
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objective reality that exists outside us.
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- Right.
- It's not material.
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- It's not material.
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And this is actually a big deal.
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David shrugs.
- Yeah, of course,
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it's a big deal, I mean,
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2 + 2 = 4, is an interesting example.
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But you can derive that
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biological inference from still
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more fundamental ideas,
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which is an exciting
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and interesting fact on its own.
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You don't have to begin
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by affirming 2 + 2 = 4, there I stand,
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I can do no other, you can say,
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I have derived that from
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still more primitive conceptual items.
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But when you go back
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and back and back and back
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and you ask about the initial assumptions,
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the axioms of the system about arithmetic,
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there is no additional defense
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that you can offer beyond the consistency
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of the whole, which is a very
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interesting position to find oneself.
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- So I'm going to quote to you
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from your book.
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- Nothing better.
- "One, Two, Three."
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I think this is,
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I'm hoping this is the same point
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because that will indicate that
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I have actually understood you, quote,
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"Neither the numbers nor the operations
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they make possible permit an analysis
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in which they disappear
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in favor of something more fundamental.
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It is the numbers that are fundamental.
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They may be better understood,
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they may be better described,
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but they cannot be bettered."
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- I still think that's true.
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Bear in mind when you say,
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2 + 2 = 4, that's an assertion.
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- [Peter] Yes.
- What I'm arguing
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for in that particular passage
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is that when you go back
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to the foundations of arithmetic
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in the expectation or the hope
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that you can get rid of the numbers,
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you are going to be very disappointed
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because they reappear.
- All right.
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I'm going to quote David once again,
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but I put this to the
two of you for judgment.
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I'm assuming he will agree with himself,
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although in David's case,
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this is always a question.
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Again from his book, "One, Two, Three."
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Quote, "Across the vast range
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of arguments offered, assessed,
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embraced, deferred, delayed, or defeated,
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it is only within mathematics
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that arguments achieve
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the power to compel allegiance.
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No philosophical theory has ever
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shown why this should be so.
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It is a part of the
mystery of mathematics."
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So you argue from some
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philosophical point that derives
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some Aristotle and has seemed
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straight, but I can still say,
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"You know I'm not persuaded,"
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but when you say to me, 2 + 2 = 4,
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of course you're right about that.
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Is that the point?
- I can speak to this
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from the standpoint of someone
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who's worked in the natural sciences
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and as a philosopher of science,
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the natural sciences provide
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empirical or observational evidence
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in support of conclusions.
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And scientists will evaluate
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particular theories or hypotheses
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by comparing your explanatory
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power or their predictive power.
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But the logical form of those arguments
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does not render a deductively
certain conclusion.
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You, in the best of cases,
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will make an inference to a hypothesis
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which provides the best explanation.
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- Hang on one second, right?
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Just distinguish deduction
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from an inference for us.
- Right.
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So a deductive argument
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will start with a major premise.
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All men are mortal, a minor premise,
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some fact about the world.
- Socrates is a man.
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- Socrates is a man,
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and then a conclusion, therefore,
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Socrates is immortal.
- Socrates is immortal.
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Right.
- Okay.
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And if the premises are true
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and the reasoning is valid,
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then the conclusion can be
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affirmed with certainty.
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But in the natural sciences,
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you start with facts
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that you've observed about the world
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and you want to infer from those facts
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to either some kind of generalization,
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that would be an inductive argument
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or to some sort of causal process
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that might explain
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what you're seeing around you.
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Those arguments typically
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characterize as abductive,
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the kind of detective reasoning that
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we enjoy when we watch detective shows.
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- Colombo.
- Yeah, Colombo or someone's
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trying to figure out who had done it.
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And so those abductive
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and inductive inferences,
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when you examine the logical forms,
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turn out not to give you certainty.
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They may give you plausibility,
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they may give you comparative plausibility
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where one theory is very much better
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than another, but they don't give you
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the kind of certainty that mathematics
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alone and mathematical logic
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can give you.
- And this is why
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a good scientist will never say
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any more than the theory is X, Y, Z,
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and on the best evidence
it holds up for now.
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Whereas, a mathematician
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feels perfectly confident in saying,
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I've proven, we've proven it.
- It's true for all time.
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- [Peter] We have a proof, correct?
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- When we say proof in science,
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the mathematicians, however,
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are better than we are.
- [Peter] When you say
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you've proved something, you mean it?
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- Yes.
- All right, okay.
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So this, go ahead.
- It could be wrong,
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but somebody will show it to me
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that it's all right.
- Yeah.
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So if this brings us to Sergiu's article,
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an inference, a magazine that you edit,
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David, the articles entitled,
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"Reflections on an Essay by Wigner."
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Now, Eugene Wigner, I have to set this up,
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was a 20th century
mathematician and physicist.
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In 1960, he wrote a famous essay,
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"The Unreasonable Effectiveness
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of Mathematics in the Natural Sciences."
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Wigner noted his surprise
that mathematics,
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which after all goes on in our minds,
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should prove so useful in describing
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and even predicting
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aspects of the physical world.
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Okay, can you give me
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a couple of examples of this?
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I mean, when I think to myself,
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wait a minute, so I have a dream
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in the middle of the night, I wake up
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and it turns out it was untrue,
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but if I do a mathematical equation
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and I wake up, it's still true.
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- Well, Sergiu wrote a brilliant essay,
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and what he showed was that
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you can start with very simple
278
00:10:02,490 --> 00:10:04,680
mathematics and build up to more
279
00:10:04,680 --> 00:10:06,390
and more and more complex forms
280
00:10:06,390 --> 00:10:09,120
of math, essentially deductively.
281
00:10:09,120 --> 00:10:10,770
And then those complex forms of math,
282
00:10:10,770 --> 00:10:11,670
take the calculus,
283
00:10:11,670 --> 00:10:13,320
take differential equations,
284
00:10:13,320 --> 00:10:15,480
they map beautifully onto the physical
285
00:10:15,480 --> 00:10:17,400
world to describe actual processes
286
00:10:17,400 --> 00:10:19,080
that are taking place in nature
287
00:10:19,080 --> 00:10:20,220
so that they provide
288
00:10:20,220 --> 00:10:21,810
very precise descriptions of things
289
00:10:21,810 --> 00:10:23,310
that are going on in nature.
290
00:10:23,310 --> 00:10:25,110
And what Wigner is alluding to
291
00:10:25,110 --> 00:10:27,720
is the mystery that this
292
00:10:27,720 --> 00:10:29,460
or the puzzle that induces
293
00:10:29,460 --> 00:10:30,540
for a lot of physicists,
294
00:10:30,540 --> 00:10:31,980
why should the math
295
00:10:31,980 --> 00:10:33,300
that we have developed through
296
00:10:33,300 --> 00:10:35,310
a series of deductive steps
297
00:10:35,310 --> 00:10:37,830
effectively from our own reasoning
298
00:10:37,830 --> 00:10:39,720
map so beautifully to processes
299
00:10:39,720 --> 00:10:41,880
that we sometimes haven't
even observed yet.
300
00:10:41,880 --> 00:10:43,500
And David has a number of great examples
301
00:10:43,500 --> 00:10:44,333
in "One, Two, Three,"
302
00:10:44,333 --> 00:10:45,960
of mathematical structures
303
00:10:45,960 --> 00:10:47,520
that were developed well before
304
00:10:47,520 --> 00:10:50,970
they had any application to physics,
305
00:10:50,970 --> 00:10:52,860
but then later were crucial and maybe,
306
00:10:52,860 --> 00:10:54,460
he should speak to that.
- Yes.
307
00:10:56,640 --> 00:10:58,080
I mean, Eugene Wigner
308
00:10:58,080 --> 00:11:00,240
raised a very interesting point
309
00:11:00,240 --> 00:11:02,280
and people have been discussing it.
310
00:11:02,280 --> 00:11:04,530
If you look at theoretical physics,
311
00:11:04,530 --> 00:11:07,230
the great structures, Newtonian mechanics,
312
00:11:07,230 --> 00:11:11,010
general relativity, quantum mechanics,
313
00:11:11,010 --> 00:11:13,380
you can't do it without
a lot of mathematics.
314
00:11:13,380 --> 00:11:15,510
You just need a whole lot of mathematics.
315
00:11:15,510 --> 00:11:17,730
And Wigner raised the question, is,
316
00:11:17,730 --> 00:11:19,500
you know we need mathematics
317
00:11:19,500 --> 00:11:21,000
to do quantum mechanics,
318
00:11:21,000 --> 00:11:23,010
but we don't need entomology.
319
00:11:23,010 --> 00:11:24,030
How come the bugs
320
00:11:24,030 --> 00:11:25,770
don't figure in quantum mechanics,
321
00:11:25,770 --> 00:11:26,603
but the numbers
322
00:11:26,603 --> 00:11:28,440
and the complex numbers do?
323
00:11:28,440 --> 00:11:30,300
And that is a rewarding
324
00:11:30,300 --> 00:11:31,680
and a provocative question,
325
00:11:31,680 --> 00:11:32,513
but we don't have
326
00:11:32,513 --> 00:11:34,560
to turn to quantum mechanics.
327
00:11:34,560 --> 00:11:36,180
There is a glass here,
328
00:11:36,180 --> 00:11:37,770
there is a glass here,
329
00:11:37,770 --> 00:11:39,480
one glass, one glass.
330
00:11:39,480 --> 00:11:41,580
How many glasses are in front of you?
331
00:11:41,580 --> 00:11:42,413
Two.
332
00:11:42,413 --> 00:11:44,940
From where do you derive
333
00:11:44,940 --> 00:11:47,220
that assurance that there
334
00:11:47,220 --> 00:11:48,780
are two glasses in front of you?
335
00:11:48,780 --> 00:11:50,880
It's not a physical observation
336
00:11:50,880 --> 00:11:52,460
because nothing in the physics
337
00:11:52,460 --> 00:11:54,630
of the situation reveals the fact
338
00:11:54,630 --> 00:11:56,070
that one and one are two,
339
00:11:56,070 --> 00:11:57,540
that is something someone
340
00:11:57,540 --> 00:11:59,580
would think that's additional.
341
00:11:59,580 --> 00:12:00,510
Now, we can break
342
00:12:00,510 --> 00:12:02,940
that all down into smaller steps.
343
00:12:02,940 --> 00:12:04,440
And that's what logicians
344
00:12:04,440 --> 00:12:06,450
have done in the 20th century.
345
00:12:06,450 --> 00:12:07,440
They've shown us that
346
00:12:07,440 --> 00:12:08,940
the method of proof can be
347
00:12:08,940 --> 00:12:11,580
decomposed into very small steps,
348
00:12:11,580 --> 00:12:12,600
in fact, so small,
349
00:12:12,600 --> 00:12:15,030
a computer can execute them.
350
00:12:15,030 --> 00:12:16,560
And the initial assumptions
351
00:12:16,560 --> 00:12:18,720
can be made so general, in fact,
352
00:12:18,720 --> 00:12:20,370
so general that they encompass
353
00:12:20,370 --> 00:12:23,070
all of mathematics as in set theory
354
00:12:23,070 --> 00:12:25,440
or category theory for that matter.
355
00:12:25,440 --> 00:12:27,270
But we are in all this,
356
00:12:27,270 --> 00:12:30,330
in rather an awkward position.
357
00:12:30,330 --> 00:12:31,470
I happen to be looking out
358
00:12:31,470 --> 00:12:33,810
at a beautiful alpine lake now,
359
00:12:33,810 --> 00:12:35,430
and just imagine, we see somebody
360
00:12:35,430 --> 00:12:36,690
on the other shore who begins
361
00:12:36,690 --> 00:12:38,070
walking across the water
362
00:12:38,070 --> 00:12:40,350
without any assistance whatsoever.
363
00:12:40,350 --> 00:12:41,820
He's just crossing,
364
00:12:41,820 --> 00:12:43,800
walking one step in front of the other
365
00:12:43,800 --> 00:12:46,560
and he's crossing the lake toward us,
366
00:12:46,560 --> 00:12:48,600
and he comes, completely dry,
367
00:12:48,600 --> 00:12:50,610
he appears in front of
the television camera
368
00:12:50,610 --> 00:12:52,860
and we say, "How did you do that?"
369
00:12:52,860 --> 00:12:55,233
And he says, "Well, I
took very small steps,
370
00:12:56,790 --> 00:12:58,440
I took very small steps."
371
00:12:58,440 --> 00:13:00,300
Now, our natural reaction would be,
372
00:13:00,300 --> 00:13:03,720
that's commendable and you got across,
373
00:13:03,720 --> 00:13:05,220
but somehow or other,
374
00:13:05,220 --> 00:13:07,650
it's not the answer to the question.
375
00:13:07,650 --> 00:13:08,970
And we are all in the position
376
00:13:08,970 --> 00:13:09,960
of watching someone
377
00:13:09,960 --> 00:13:12,450
cross a large body of water
378
00:13:12,450 --> 00:13:14,947
and explaining his success by saying,
379
00:13:14,947 --> 00:13:16,830
"Look at my feet, small steps."
380
00:13:16,830 --> 00:13:18,300
That's where we are.
381
00:13:18,300 --> 00:13:21,030
- Okay, so Sergiu, well, wait,
382
00:13:21,030 --> 00:13:22,620
lemme go back to your essay.
383
00:13:22,620 --> 00:13:23,857
I'm quoting you once again,
384
00:13:23,857 --> 00:13:26,220
"The mystery Wigner points out
385
00:13:26,220 --> 00:13:29,340
arises in part from the perennial question
386
00:13:29,340 --> 00:13:32,610
of whether mathematics is a science,
387
00:13:32,610 --> 00:13:35,730
advanced by exploration and discovery
388
00:13:35,730 --> 00:13:37,320
like the main physical theories
389
00:13:37,320 --> 00:13:39,420
or whether it is an invention,
390
00:13:39,420 --> 00:13:43,470
a creation of the human mind.
391
00:13:43,470 --> 00:13:45,630
I argue that mathematics developed
392
00:13:45,630 --> 00:13:47,700
through exploration and discovery."
393
00:13:47,700 --> 00:13:49,053
That is to say,
394
00:13:49,920 --> 00:13:51,660
it is like a nugget in the ground,
395
00:13:51,660 --> 00:13:53,703
you find it.
- Correct.
396
00:13:54,690 --> 00:13:56,820
- [Peter] Okay.
- Yeah, no,
397
00:13:56,820 --> 00:13:57,873
absolutely, I mean,
398
00:14:01,500 --> 00:14:03,450
one image that you could make
399
00:14:03,450 --> 00:14:06,810
is that of an alpinist that is trying
400
00:14:06,810 --> 00:14:08,640
to go on the top of the mountain.
401
00:14:08,640 --> 00:14:09,960
He has an idea.
- Everybody's doing
402
00:14:09,960 --> 00:14:12,420
alpine metaphors today.
- Yeah.
403
00:14:12,420 --> 00:14:14,700
He has an idea where
he wants to go, right?
404
00:14:14,700 --> 00:14:15,630
So that's very important.
405
00:14:15,630 --> 00:14:17,490
That's part of doing mathematics.
406
00:14:17,490 --> 00:14:20,279
It's not just deduction.
407
00:14:20,279 --> 00:14:21,330
- Right, right.
- It's sort of a vision
408
00:14:21,330 --> 00:14:22,260
of where you want to go,
409
00:14:22,260 --> 00:14:23,093
which is very important.
410
00:14:23,093 --> 00:14:25,530
- [Stephen] Inspiration, yeah.
- Right, has something
411
00:14:25,530 --> 00:14:26,496
to do with inspiration.
412
00:14:26,496 --> 00:14:28,830
But then, you know,
413
00:14:28,830 --> 00:14:31,020
you have something very objective
414
00:14:31,020 --> 00:14:31,980
in front of you, right?
415
00:14:31,980 --> 00:14:34,080
The stone is of the Alpines
416
00:14:34,080 --> 00:14:35,760
that you have to take into account
417
00:14:35,760 --> 00:14:37,503
that you are not going to fall,
418
00:14:39,600 --> 00:14:40,680
you have to touch the stone
419
00:14:40,680 --> 00:14:42,300
to know exactly where you are going.
420
00:14:42,300 --> 00:14:44,853
And if you don't, you get into trouble.
421
00:14:45,750 --> 00:14:47,403
So mathematics is very similar.
422
00:14:48,570 --> 00:14:49,620
People have the feeling
423
00:14:49,620 --> 00:14:50,940
that everything is deductive,
424
00:14:50,940 --> 00:14:52,053
it's not, I mean,
425
00:14:54,150 --> 00:14:55,800
it is very similar in that
426
00:14:55,800 --> 00:14:58,140
respect to physical sciences.
427
00:14:58,140 --> 00:14:59,433
Physical sciences also,
428
00:15:02,303 --> 00:15:04,620
you have, let's say, an expectation,
429
00:15:04,620 --> 00:15:05,687
you make a hypothesis.
430
00:15:05,687 --> 00:15:06,540
- Right.
- Right.
431
00:15:06,540 --> 00:15:08,263
The choice of a hypothesis
432
00:15:08,263 --> 00:15:12,120
is not a deductive thing, it's an insight.
433
00:15:12,120 --> 00:15:14,160
And then you try to show
434
00:15:14,160 --> 00:15:16,320
that it fits everything else,
435
00:15:16,320 --> 00:15:17,820
all the other experiences.
436
00:15:17,820 --> 00:15:19,680
So-
- And that's the process
437
00:15:19,680 --> 00:15:21,120
of proving something, right?
- [Sergiu] Correct.
438
00:15:21,120 --> 00:15:23,962
- So you have the processes.
- Right, exactly.
439
00:15:23,962 --> 00:15:24,795
- [Stephen] Once you have
440
00:15:24,795 --> 00:15:25,628
the process of discovery,
441
00:15:25,628 --> 00:15:26,823
but then the process of justification.
442
00:15:26,823 --> 00:15:27,656
- The process of justification.
443
00:15:27,656 --> 00:15:30,180
So mathematics, at the end of the day,
444
00:15:30,180 --> 00:15:33,780
it looks like a chain of logical sequences
445
00:15:33,780 --> 00:15:35,730
that the computer can also, I mean,
446
00:15:35,730 --> 00:15:37,020
once you have the chain,
447
00:15:37,020 --> 00:15:39,267
the computer can go very fast to it
448
00:15:39,267 --> 00:15:41,100
and maybe even check.
449
00:15:41,100 --> 00:15:43,650
So there are yet no computers
450
00:15:43,650 --> 00:15:46,230
that can check launch.
451
00:15:46,230 --> 00:15:47,970
I mean, they can check small proofs,
452
00:15:47,970 --> 00:15:48,990
but not large ones.
453
00:15:48,990 --> 00:15:50,910
In any case,
454
00:15:50,910 --> 00:15:53,130
it's sort of a very good example,
455
00:15:53,130 --> 00:15:54,750
I think that illustrates very well
456
00:15:54,750 --> 00:15:56,370
relations between maths and physics.
457
00:15:56,370 --> 00:15:57,930
Take geometry, so geometry
458
00:15:57,930 --> 00:15:59,520
was the first really theory
459
00:15:59,520 --> 00:16:01,260
of the physical world, right?
460
00:16:01,260 --> 00:16:02,130
I mean, it's what it
461
00:16:02,130 --> 00:16:03,453
describes what we see.
- We going all the way
462
00:16:03,453 --> 00:16:05,850
back to Euclid, is that what you saying?
463
00:16:05,850 --> 00:16:07,890
- Right, so Euclid, obviously,
464
00:16:07,890 --> 00:16:09,180
tried to make sort of
465
00:16:09,180 --> 00:16:11,220
mathematical statements out of.
466
00:16:11,220 --> 00:16:13,080
But it's a physical theory without doubt,
467
00:16:13,080 --> 00:16:15,150
including, geometry is a physical theory.
468
00:16:15,150 --> 00:16:18,090
Then it develops.
469
00:16:18,090 --> 00:16:19,950
So here, comes up something specific
470
00:16:19,950 --> 00:16:22,170
to mathematics, different from physics.
471
00:16:22,170 --> 00:16:24,630
Mathematicians can take a theory
472
00:16:24,630 --> 00:16:27,310
and then develop based on
473
00:16:29,070 --> 00:16:30,810
very different criteria
474
00:16:30,810 --> 00:16:31,800
than a physicist would do.
475
00:16:31,800 --> 00:16:33,540
So, you know, they're interesting
476
00:16:33,540 --> 00:16:34,500
in problems because
477
00:16:34,500 --> 00:16:35,900
they're beautiful or because
478
00:16:39,505 --> 00:16:41,130
they feel that it will lead
479
00:16:41,130 --> 00:16:43,860
to a certain understanding
of something else.
480
00:16:43,860 --> 00:16:46,260
And this freedom really,
481
00:16:46,260 --> 00:16:48,330
in the case of geometry went for,
482
00:16:48,330 --> 00:16:50,370
I dunno, 2,000 years without essentially
483
00:16:50,370 --> 00:16:53,100
no connection back to the physical world.
484
00:16:53,100 --> 00:16:55,590
I mean, Korean geometry was there
485
00:16:55,590 --> 00:16:57,360
to start with, but then,
486
00:16:57,360 --> 00:16:59,310
by the 19th century, you have,
487
00:16:59,310 --> 00:17:00,766
you know, have Gauss,
488
00:17:00,766 --> 00:17:01,675
you have Lobachevskian,
489
00:17:01,675 --> 00:17:04,251
you have Gauss, you have Riemannian,
490
00:17:04,251 --> 00:17:05,640
you have Minkowski at the beginning
491
00:17:05,640 --> 00:17:07,950
of the 20th century.
492
00:17:07,950 --> 00:17:09,240
And then all of a sudden,
493
00:17:09,240 --> 00:17:13,155
all that stuff becomes
an essential ingredient.
494
00:17:13,155 --> 00:17:15,390
I mean, you know, it's
not just the technical,
495
00:17:15,390 --> 00:17:17,220
it's an essential ingredient
496
00:17:17,220 --> 00:17:20,313
of special and general activity, right?
497
00:17:21,210 --> 00:17:22,830
- Comes directly applicable
498
00:17:22,830 --> 00:17:25,020
to fundamental physical theory.
499
00:17:25,020 --> 00:17:25,853
- And I think this has
500
00:17:25,853 --> 00:17:27,522
happened many, many, many times,
501
00:17:27,522 --> 00:17:31,440
and maybe, it's not
very well acknowledged.
502
00:17:31,440 --> 00:17:34,950
- So can I ask, when you, Sergiu,
503
00:17:34,950 --> 00:17:37,080
needless to say, I cannot evaluate
504
00:17:37,080 --> 00:17:38,250
your work on my own because
505
00:17:38,250 --> 00:17:40,800
you have done a 2,000 page proof,
506
00:17:40,800 --> 00:17:44,220
2,000 pages of close
mathematical reasoning.
507
00:17:44,220 --> 00:17:46,860
I could live to 2,000,
508
00:17:46,860 --> 00:17:49,800
I could read a page a
day or a page a year,
509
00:17:49,800 --> 00:17:51,783
and it still would escape me, I'm sure.
510
00:17:52,620 --> 00:17:55,170
And this was on the stability
511
00:17:55,170 --> 00:17:58,110
of some aspect of Albert Einstein.
512
00:17:58,110 --> 00:18:00,990
So may I ask, did you think
513
00:18:00,990 --> 00:18:02,730
you were doing a work of art,
514
00:18:02,730 --> 00:18:04,200
creating something beautiful?
515
00:18:04,200 --> 00:18:07,803
Or did you think you were
interrogating reality?
516
00:18:08,940 --> 00:18:10,500
I'm trying to understand.
- Okay, okay.
517
00:18:10,500 --> 00:18:11,640
- [Peter] What it felt like to you
518
00:18:11,640 --> 00:18:13,860
as a working mathematician.
- Great question.
519
00:18:13,860 --> 00:18:15,060
- It's a very deep question.
- [Peter] Deep, deep,
520
00:18:15,060 --> 00:18:16,440
very difficult problem.
521
00:18:16,440 --> 00:18:17,940
- And the answer is both.
522
00:18:17,940 --> 00:18:20,100
I mean, I would take the problem
523
00:18:20,100 --> 00:18:21,127
in the first place, I'm a mathematician,
524
00:18:21,127 --> 00:18:23,403
I'm not a physicist, right?
525
00:18:24,390 --> 00:18:26,400
I believe that the best mathematics
526
00:18:26,400 --> 00:18:28,650
is connected somehow with physics
527
00:18:28,650 --> 00:18:30,573
in complicated ways.
528
00:18:31,830 --> 00:18:34,050
But there are many problems in physics,
529
00:18:34,050 --> 00:18:37,630
and I will pick the one that satisfies my
530
00:18:39,150 --> 00:18:41,940
aesthetical feeling as a mathematician.
531
00:18:41,940 --> 00:18:44,371
So that's a say, hotspot.
- Your aesthetic feeling.
532
00:18:44,371 --> 00:18:46,440
So explain that, you want something
533
00:18:46,440 --> 00:18:48,600
that's good-
- Something that I feel
534
00:18:48,600 --> 00:18:51,540
is very beautiful, it's very profound.
535
00:18:51,540 --> 00:18:53,740
It gives lots of very
interesting questions.
536
00:18:55,500 --> 00:18:56,880
Okay, so that's one aspect.
537
00:18:56,880 --> 00:18:58,830
But then it has to be the second,
538
00:18:58,830 --> 00:18:59,663
for me at least,
539
00:18:59,663 --> 00:19:00,750
there has to be a second aspect,
540
00:19:00,750 --> 00:19:02,610
which is that it should say
541
00:19:02,610 --> 00:19:04,170
something about the physical world.
542
00:19:04,170 --> 00:19:06,000
And in this case, it does, right?
543
00:19:06,000 --> 00:19:07,980
I mean, the Kerr solution.
544
00:19:07,980 --> 00:19:09,480
So here how it goes, right?
545
00:19:09,480 --> 00:19:10,590
You have general activity,
546
00:19:10,590 --> 00:19:13,090
which was well-formulated by Einstein
547
00:19:14,700 --> 00:19:16,353
at the end of 2015,
548
00:19:17,190 --> 00:19:18,420
1915, excuse me.
- And this was
549
00:19:18,420 --> 00:19:20,430
at the time, a new theory of gravity.
550
00:19:20,430 --> 00:19:23,103
- [Peter] Yeah.
- Massive bodies curve,
551
00:19:23,970 --> 00:19:25,830
what's called, space time.
552
00:19:25,830 --> 00:19:29,220
- And then certain solutions were found,
553
00:19:29,220 --> 00:19:30,300
Schwarzschild was the first
554
00:19:30,300 --> 00:19:33,180
found in 2016, immediately a year after
555
00:19:33,180 --> 00:19:34,740
found a so-called, Schwarzschild solution,
556
00:19:34,740 --> 00:19:37,260
which is a stationary solution
557
00:19:37,260 --> 00:19:39,360
with a lot of symmetries
558
00:19:39,360 --> 00:19:40,710
that you can actually
559
00:19:40,710 --> 00:19:43,800
extract from the serial relativity,
560
00:19:43,800 --> 00:19:46,833
from the answer equations
as exact formula.
561
00:19:47,850 --> 00:19:51,360
And that had led to lots of
562
00:19:51,360 --> 00:19:54,270
issues because it has a singularity.
563
00:19:54,270 --> 00:19:56,883
This is connected later on
564
00:19:56,883 --> 00:19:59,640
with the Penrose Singularity Theorem,
565
00:19:59,640 --> 00:20:01,140
for which he actually got a Nobel prize.
566
00:20:01,140 --> 00:20:02,580
He's the only mathematician
567
00:20:02,580 --> 00:20:04,593
to have gotten a Nobel Prize in physics,
568
00:20:06,900 --> 00:20:08,393
there's nobody else.
569
00:20:08,393 --> 00:20:11,523
- Because the math applied so beautifully-
570
00:20:12,452 --> 00:20:13,530
- Right, or to a question
571
00:20:13,530 --> 00:20:15,540
that was a very important question.
572
00:20:15,540 --> 00:20:16,860
- Yeah.
- It was very good.
573
00:20:16,860 --> 00:20:17,804
And then there was
574
00:20:17,804 --> 00:20:21,630
a second major development by Kerr.
575
00:20:21,630 --> 00:20:23,200
This was 1963
576
00:20:24,240 --> 00:20:27,252
where the Kerr solution was.
577
00:20:27,252 --> 00:20:28,182
Okay, so now you have
578
00:20:28,182 --> 00:20:29,632
a Kerr family, which includes,
579
00:20:29,632 --> 00:20:31,500
Schwarzschild, it's a large family
580
00:20:31,500 --> 00:20:33,360
depending on two parameters.
581
00:20:33,360 --> 00:20:34,710
So these are exact solutions
582
00:20:34,710 --> 00:20:36,399
of the equations, right?
583
00:20:36,399 --> 00:20:39,390
From a mathematical point of view,
584
00:20:39,390 --> 00:20:41,133
they are real because for me,
585
00:20:43,260 --> 00:20:44,880
mathematical reality has to do
586
00:20:44,880 --> 00:20:47,340
with objective fact that
587
00:20:47,340 --> 00:20:49,680
these are solutions of an equation,
588
00:20:49,680 --> 00:20:54,030
which you can write
down, it's conceptually.
589
00:20:54,030 --> 00:20:55,230
- And may I interrupt for just a moment.
590
00:20:55,230 --> 00:20:57,150
So if I understand one
591
00:20:57,150 --> 00:20:58,980
of the remarkable things about Einstein,
592
00:20:58,980 --> 00:21:00,510
by the way, of course, correct me,
593
00:21:00,510 --> 00:21:03,240
jump in, I'm doing baby talk here
594
00:21:03,240 --> 00:21:04,920
because that is the top of my form
595
00:21:04,920 --> 00:21:07,260
when it comes to this material.
596
00:21:07,260 --> 00:21:09,180
Einstein comes up with general relativity
597
00:21:09,180 --> 00:21:12,543
in 1915, and here we are in 2025,
598
00:21:14,700 --> 00:21:15,660
there have been experiments
599
00:21:15,660 --> 00:21:17,610
that have been done over the course
600
00:21:17,610 --> 00:21:18,960
of the succeeding century
601
00:21:18,960 --> 00:21:22,140
as new satellite, new technology,
602
00:21:22,140 --> 00:21:23,550
new experiments.
- Yes.
603
00:21:23,550 --> 00:21:25,113
- And every single time,
604
00:21:26,880 --> 00:21:29,310
the theory of general relativity
605
00:21:29,310 --> 00:21:31,710
is proven out.
- Right, yes.
606
00:21:31,710 --> 00:21:32,823
- That is to say,
607
00:21:33,660 --> 00:21:35,490
this theory that Einstein came up
608
00:21:35,490 --> 00:21:36,970
with on a chalkboard
609
00:21:37,890 --> 00:21:39,750
for a century of experiments now,
610
00:21:39,750 --> 00:21:41,580
it turns out to correspond with
611
00:21:41,580 --> 00:21:44,910
and predict reality and your work,
612
00:21:44,910 --> 00:21:48,540
if we could somehow devise experiments
613
00:21:48,540 --> 00:21:52,110
on black holes, your work would prove out.
614
00:21:52,110 --> 00:21:53,760
It's real to that extent.
615
00:21:53,760 --> 00:21:57,330
- So I like to call it a test of reality.
616
00:21:57,330 --> 00:22:00,150
So the fact that the Kerr solution
617
00:22:00,150 --> 00:22:01,920
is stable, right?
618
00:22:01,920 --> 00:22:03,870
It's a mathematical statement,
619
00:22:03,870 --> 00:22:05,940
but with a lot of physical content
620
00:22:05,940 --> 00:22:08,880
because let's say, if it was not stable.
621
00:22:08,880 --> 00:22:11,820
So it's a solution, a correct solution
622
00:22:11,820 --> 00:22:14,430
of the equation, which starts
623
00:22:14,430 --> 00:22:16,980
with specific initial conditions, right?
624
00:22:16,980 --> 00:22:19,380
So the issue of stability is now,
625
00:22:19,380 --> 00:22:21,000
we make small perturbations
626
00:22:21,000 --> 00:22:22,620
of the initial conditions,
627
00:22:22,620 --> 00:22:23,550
and all of a sudden,
628
00:22:23,550 --> 00:22:24,900
we get something entirely different,
629
00:22:24,900 --> 00:22:25,733
which has nothing to do
630
00:22:25,733 --> 00:22:28,380
with the solution, the Kerr solution
631
00:22:28,380 --> 00:22:31,290
that would be called, instability, right?
632
00:22:31,290 --> 00:22:33,810
So if the Kerr solution would be
633
00:22:33,810 --> 00:22:35,310
unstable, it means, it doesn't
634
00:22:35,310 --> 00:22:36,960
have any physical meaning, right?
635
00:22:36,960 --> 00:22:39,060
Because you know, it doesn't correspond
636
00:22:39,060 --> 00:22:41,670
to anything that you
can recognize in nature
637
00:22:41,670 --> 00:22:43,860
that's corresponding to that, right?
638
00:22:43,860 --> 00:22:47,520
So the issue of stability
639
00:22:47,520 --> 00:22:50,207
is a fundamental issue in-
640
00:22:50,207 --> 00:22:52,680
- [Peter] It's a market for reality.
641
00:22:52,680 --> 00:22:54,763
- I call it, mathematical test of reality.
642
00:22:54,763 --> 00:22:56,163
- What's going on here, Peter?
643
00:22:56,163 --> 00:22:58,260
It's so interesting.
- Explicate for us.
644
00:22:58,260 --> 00:23:01,200
- Well, from a philosophical point of view
645
00:23:01,200 --> 00:23:03,630
here, is that there's a deep assumption
646
00:23:03,630 --> 00:23:05,730
that that which is mathematically
647
00:23:05,730 --> 00:23:08,220
consistent, coherent, stable,
648
00:23:08,220 --> 00:23:10,710
is going to give us a guide to
649
00:23:10,710 --> 00:23:12,480
physical reality as if there's
650
00:23:12,480 --> 00:23:15,480
a rationality built into the physics
651
00:23:15,480 --> 00:23:17,550
that somehow matches the rationality
652
00:23:17,550 --> 00:23:18,877
that's at work when we're doing
653
00:23:18,877 --> 00:23:22,320
this type of advanced mathematics.
654
00:23:22,320 --> 00:23:24,900
And so that's the Wigner mystery.
655
00:23:24,900 --> 00:23:27,510
Why does the reason within
656
00:23:27,510 --> 00:23:30,840
match the rationality of nature
657
00:23:30,840 --> 00:23:32,970
external to us, the reason without.
658
00:23:32,970 --> 00:23:34,530
- All right, so now,
659
00:23:34,530 --> 00:23:36,183
now we move into territory.
660
00:23:37,170 --> 00:23:38,580
I'm already in over my head,
661
00:23:38,580 --> 00:23:40,260
but I continue swimming,
662
00:23:40,260 --> 00:23:41,790
it gets deeper.
- May I offer
663
00:23:41,790 --> 00:23:43,360
a simple thing that might help
664
00:23:44,430 --> 00:23:47,150
because we got the field equations
665
00:23:47,150 --> 00:23:50,340
of general relativity and the solutions,
666
00:23:50,340 --> 00:23:53,310
but Sergiu started initially
667
00:23:53,310 --> 00:23:54,990
talking about geometry.
- Yes.
668
00:23:54,990 --> 00:23:56,850
- And just the idea that
669
00:23:56,850 --> 00:23:59,580
mathematical objects
have stable properties.
670
00:23:59,580 --> 00:24:00,720
This is why mathematicians
671
00:24:00,720 --> 00:24:02,250
regard them as real, you know,
672
00:24:02,250 --> 00:24:05,490
circle has certain basic properties.
673
00:24:05,490 --> 00:24:07,860
So it's got a circumference area
674
00:24:07,860 --> 00:24:09,090
and we can calculate these things.
675
00:24:09,090 --> 00:24:11,160
And those properties are true
676
00:24:11,160 --> 00:24:14,520
for all people who think about circles.
677
00:24:14,520 --> 00:24:15,870
There are stable properties
678
00:24:15,870 --> 00:24:17,760
that that geometric object has
679
00:24:17,760 --> 00:24:19,470
that we can describe mathematically
680
00:24:19,470 --> 00:24:21,060
that's independent of our minds.
681
00:24:21,060 --> 00:24:21,893
- Right.
682
00:24:21,893 --> 00:24:23,460
- And yet, the stability
683
00:24:23,460 --> 00:24:25,230
of those properties is a token
684
00:24:25,230 --> 00:24:26,580
as Sergiu has explained
685
00:24:26,580 --> 00:24:27,750
in our recent conference,
686
00:24:27,750 --> 00:24:30,570
it's a token of reality,
687
00:24:30,570 --> 00:24:32,850
a mind independent objective reality.
688
00:24:32,850 --> 00:24:33,960
And that's why mathematicians
689
00:24:33,960 --> 00:24:34,950
don't think that they're
690
00:24:34,950 --> 00:24:38,430
inventing new mathematical formulas.
691
00:24:38,430 --> 00:24:41,340
They almost universally feel
692
00:24:41,340 --> 00:24:43,110
that they're discovering something,
693
00:24:43,110 --> 00:24:44,730
not inventing.
- Well, there are some
694
00:24:44,730 --> 00:24:46,920
who don't, but what's interesting
695
00:24:46,920 --> 00:24:48,660
is that physicists always refer
696
00:24:48,660 --> 00:24:50,910
to mathematics as being an invention
697
00:24:50,910 --> 00:24:51,743
of the human mind.
698
00:24:51,743 --> 00:24:53,730
That's what Wigner says.
- Yeah, yeah.
699
00:24:53,730 --> 00:24:55,020
- Sorry, Einstein says
700
00:24:55,020 --> 00:24:56,190
an invention of the human mind,
701
00:24:56,190 --> 00:24:58,050
but Wigner says something very similar.
702
00:24:58,050 --> 00:25:01,790
So I'm always surprised to see that...
703
00:25:03,600 --> 00:25:05,760
- Einstein felt he invented the general.
704
00:25:05,760 --> 00:25:07,080
- No, no, no, Einstein feels
705
00:25:07,080 --> 00:25:11,040
that mathematicians invent things, right?
706
00:25:11,040 --> 00:25:13,920
- He actually called it, a free creation
707
00:25:13,920 --> 00:25:15,750
of the human mind.
- [Sergiu] Right.
708
00:25:15,750 --> 00:25:17,700
- So free, which he meant what?
709
00:25:17,700 --> 00:25:19,110
- It's not really clear because
710
00:25:19,110 --> 00:25:21,210
if it's a free creation of the human mind,
711
00:25:21,210 --> 00:25:23,190
why are mathematical propositions
712
00:25:23,190 --> 00:25:25,590
so dreadfully necessary?
713
00:25:25,590 --> 00:25:29,070
I didn't have much choice about 2 + 2 = 4,
714
00:25:29,070 --> 00:25:30,990
and I presume you didn't either.
715
00:25:30,990 --> 00:25:33,750
- But there's a, apologies.
- Kind of at odds
716
00:25:33,750 --> 00:25:36,510
with the notion of spontaneous,
717
00:25:36,510 --> 00:25:39,660
spontaneously reaching an invention
718
00:25:39,660 --> 00:25:41,220
like addition doesn't
719
00:25:41,220 --> 00:25:43,830
seem to be an invention at all.
720
00:25:43,830 --> 00:25:46,140
- But I have a reason why physicists
721
00:25:46,140 --> 00:25:49,110
do that and I doubt that Newton
722
00:25:49,110 --> 00:25:50,460
would have said that.
- [David] No.
723
00:25:50,460 --> 00:25:53,100
- It's a modern physicists
724
00:25:53,100 --> 00:25:55,290
who are materialists, they do believe
725
00:25:55,290 --> 00:25:57,000
that there is just matter
726
00:25:57,000 --> 00:25:59,070
and everything the mind including has to
727
00:25:59,070 --> 00:26:01,770
be determined somehow by that.
- But they can't be right.
728
00:26:01,770 --> 00:26:03,420
So okay.
- Notice what's
729
00:26:03,420 --> 00:26:04,680
in the dialectic here,
730
00:26:04,680 --> 00:26:06,810
the mathematicians who are doing
731
00:26:06,810 --> 00:26:10,620
the math, that are developing the math
732
00:26:10,620 --> 00:26:11,790
typically believe that they
733
00:26:11,790 --> 00:26:14,010
are discovering something that is
734
00:26:14,010 --> 00:26:15,570
real and independent of their mind.
735
00:26:15,570 --> 00:26:17,010
Not inventing something like
736
00:26:17,010 --> 00:26:19,800
an internal combustion engine.
- Exactly.
737
00:26:19,800 --> 00:26:21,060
I mean, any invention has
738
00:26:21,060 --> 00:26:22,560
to have a starting point, right?
739
00:26:22,560 --> 00:26:25,140
So it means that before
that starting point,
740
00:26:25,140 --> 00:26:27,990
that mathematical fact
did not exist, right?
741
00:26:27,990 --> 00:26:29,400
Pythagorean theorem was not true
742
00:26:29,400 --> 00:26:31,500
before Pythagoras discovered it.
743
00:26:31,500 --> 00:26:33,900
It's kind of ridiculous.
- But how can anybody,
744
00:26:36,030 --> 00:26:37,500
there must be complexities here.
745
00:26:37,500 --> 00:26:38,700
I'm sure there are complexities,
746
00:26:38,700 --> 00:26:41,160
I'm not grasping, but 2 + 2 = 4,
747
00:26:41,160 --> 00:26:42,660
is true for me, it's true for you,
748
00:26:42,660 --> 00:26:44,250
it's true for David, no matter
749
00:26:44,250 --> 00:26:45,780
how perverse David may be feeling
750
00:26:45,780 --> 00:26:47,706
at any given moment, it's still true
751
00:26:47,706 --> 00:26:50,400
and has been true for all time.
752
00:26:50,400 --> 00:26:52,443
Therefore, there is something,
753
00:26:54,360 --> 00:26:55,193
doesn't that just
754
00:26:55,193 --> 00:26:56,700
put a stake in the heart
755
00:26:56,700 --> 00:26:59,040
of materialism right there?
756
00:26:59,040 --> 00:27:03,003
Something exists outside us.
757
00:27:03,990 --> 00:27:05,730
Something, we can call it reason,
758
00:27:05,730 --> 00:27:06,780
we could call it platon.
759
00:27:06,780 --> 00:27:08,610
Okay, so let's go to Plato.
760
00:27:08,610 --> 00:27:10,503
If I understand this much,
761
00:27:11,430 --> 00:27:12,270
in the republic,
762
00:27:12,270 --> 00:27:13,590
Plato draws a distinction
763
00:27:13,590 --> 00:27:15,453
between the intelligible world,
764
00:27:16,770 --> 00:27:17,850
the sensible world is
765
00:27:17,850 --> 00:27:20,400
what we can see and touch.
766
00:27:20,400 --> 00:27:21,970
And the intelligible world
767
00:27:26,080 --> 00:27:29,327
is intelligible to us, but-
- Access to the mind, yeah.
768
00:27:29,327 --> 00:27:30,600
- Access through the intellect.
769
00:27:30,600 --> 00:27:32,100
Okay, and so that's where
770
00:27:32,100 --> 00:27:33,930
he places his ideal forms.
771
00:27:33,930 --> 00:27:35,550
There is a circle out there,
772
00:27:35,550 --> 00:27:37,980
there is a triangle out there.
773
00:27:37,980 --> 00:27:38,820
Plato says, it does
774
00:27:38,820 --> 00:27:40,290
have an independent existence,
775
00:27:40,290 --> 00:27:41,868
but he seems to suggest that there's
776
00:27:41,868 --> 00:27:46,440
a realm of ideal forms
someplace out there.
777
00:27:46,440 --> 00:27:50,490
Aquinas comes along 1,500 years later
778
00:27:50,490 --> 00:27:55,490
and says, ideas exist in minds
779
00:27:57,360 --> 00:27:59,370
and something that is true for all of us
780
00:27:59,370 --> 00:28:01,800
and for all time, that is intelligible,
781
00:28:01,800 --> 00:28:05,613
but immaterial exists in the mind of God.
782
00:28:07,050 --> 00:28:07,883
David?
783
00:28:08,820 --> 00:28:09,813
- Yeah, maybe.
784
00:28:11,460 --> 00:28:13,260
- David was never more David
785
00:28:13,260 --> 00:28:14,510
than in that very moment.
786
00:28:16,590 --> 00:28:18,000
- I can't make any sense of
787
00:28:18,000 --> 00:28:20,463
the discussion so far, that's my problem.
788
00:28:22,170 --> 00:28:23,130
There is a problem
789
00:28:23,130 --> 00:28:25,380
to which Wigner was calling attention,
790
00:28:25,380 --> 00:28:27,840
which is a real philosophical problem.
791
00:28:27,840 --> 00:28:31,800
That is, if mathematics is essential
792
00:28:31,800 --> 00:28:34,350
for every physical theory,
793
00:28:34,350 --> 00:28:36,130
it cannot be the case
794
00:28:37,110 --> 00:28:40,110
unless it's a trivial explanation
795
00:28:40,110 --> 00:28:41,850
that there is a physical theory
796
00:28:41,850 --> 00:28:45,090
that physically explains mathematics.
797
00:28:45,090 --> 00:28:47,550
I mean, if a man proposes to catch
798
00:28:47,550 --> 00:28:50,130
a carp by baiting his hook with a carp,
799
00:28:50,130 --> 00:28:52,290
he's engaged in a trivial pursuit.
800
00:28:52,290 --> 00:28:53,880
He has the carp.
801
00:28:53,880 --> 00:28:55,530
If we need a physical theory
802
00:28:55,530 --> 00:28:57,000
that includes mathematics,
803
00:28:57,000 --> 00:28:58,770
to explain mathematics,
804
00:28:58,770 --> 00:29:00,690
we no longer have a physical theory.
805
00:29:00,690 --> 00:29:01,650
We have a physical
806
00:29:01,650 --> 00:29:03,210
and a mathematical theory.
807
00:29:03,210 --> 00:29:04,770
And that's the dilemma.
808
00:29:04,770 --> 00:29:06,030
I think the deep dilemma
809
00:29:06,030 --> 00:29:08,250
to which Wigner is calling attention.
810
00:29:08,250 --> 00:29:09,540
There are certain principles
811
00:29:09,540 --> 00:29:11,670
we'd like to hold onto,
812
00:29:11,670 --> 00:29:14,070
it's part of the cultural imperative.
813
00:29:14,070 --> 00:29:15,690
We'd like to hold onto this
814
00:29:15,690 --> 00:29:18,870
fundamental idea, the world is physical.
815
00:29:18,870 --> 00:29:21,120
We live in a physical world.
816
00:29:21,120 --> 00:29:23,190
I'm not saying this is a commendable idea.
817
00:29:23,190 --> 00:29:25,500
I'm saying, it's a cultural imperative
818
00:29:25,500 --> 00:29:27,540
because it seems so reassuring.
819
00:29:27,540 --> 00:29:29,640
Look, we're faced with imponderables,
820
00:29:29,640 --> 00:29:32,910
the basic fact, the thing is a material
821
00:29:32,910 --> 00:29:34,653
or a physical object,
822
00:29:35,490 --> 00:29:37,980
it is very inconvenient culturally
823
00:29:37,980 --> 00:29:40,290
and intellectually to come to
824
00:29:40,290 --> 00:29:41,730
the conclusion that in order
825
00:29:41,730 --> 00:29:44,010
to understand that physical object,
826
00:29:44,010 --> 00:29:45,270
we need a whole lot of
827
00:29:45,270 --> 00:29:48,450
non-physical facts about mathematics.
828
00:29:48,450 --> 00:29:50,700
And in order to explain a whole
829
00:29:50,700 --> 00:29:53,880
lot of non-physical
facts about mathematics,
830
00:29:53,880 --> 00:29:55,260
there is no conception
831
00:29:55,260 --> 00:29:57,870
of a physical theory without mathematics
832
00:29:57,870 --> 00:29:59,670
that can do the explaining.
833
00:29:59,670 --> 00:30:01,080
So we're left in the position
834
00:30:01,080 --> 00:30:03,390
that if mathematics is as useful
835
00:30:03,390 --> 00:30:05,160
as Sergiu and Steve says,
836
00:30:05,160 --> 00:30:06,810
and they're absolutely right about that,
837
00:30:06,810 --> 00:30:08,910
it's useful in daily life.
838
00:30:08,910 --> 00:30:11,970
There is something fundamentally wrong
839
00:30:11,970 --> 00:30:15,120
with our idea of the world
as a physical cystic.
840
00:30:15,120 --> 00:30:17,730
- Exactly.
- Something cannot be right.
841
00:30:17,730 --> 00:30:19,350
Something has to give.
842
00:30:19,350 --> 00:30:21,810
Either we develop physical theories
843
00:30:21,810 --> 00:30:23,670
with no mathematics,
844
00:30:23,670 --> 00:30:26,310
Feynman conjecture,
something of this sort.
845
00:30:26,310 --> 00:30:28,020
Or we agree that materialism
846
00:30:28,020 --> 00:30:29,820
simply cannot be right,
847
00:30:29,820 --> 00:30:32,880
one of the two, but something has to go.
848
00:30:32,880 --> 00:30:34,830
- But physics will until now
849
00:30:34,830 --> 00:30:36,590
at least have not given up
850
00:30:36,590 --> 00:30:39,480
on the idea of physicality.
- [David] No.
851
00:30:39,480 --> 00:30:41,700
- So that's a issue.
852
00:30:41,700 --> 00:30:42,870
- But they're not reckoning
853
00:30:42,870 --> 00:30:44,070
with the dilemma that David
854
00:30:44,070 --> 00:30:45,690
just described, I think.
- No, not me.
855
00:30:45,690 --> 00:30:46,920
I mean, that dilemma has been
856
00:30:46,920 --> 00:30:48,450
in the literature for at least,
857
00:30:48,450 --> 00:30:49,890
50 years or 60, I mean,
858
00:30:49,890 --> 00:30:51,210
even a hundred years.
- I don't understand
859
00:30:51,210 --> 00:30:52,800
all of you bright people,
860
00:30:52,800 --> 00:30:54,330
if something's been in the literature
861
00:30:54,330 --> 00:30:55,890
for half a century,
862
00:30:55,890 --> 00:30:58,770
which essentially is a stop sign,
863
00:30:58,770 --> 00:30:59,670
saying, wait a moment,
864
00:30:59,670 --> 00:31:01,200
wait a moment, wait a moment.
865
00:31:01,200 --> 00:31:02,430
You have a basic decision
866
00:31:02,430 --> 00:31:04,480
to make here about the nature of reality.
867
00:31:07,650 --> 00:31:09,180
Well, then how can the academy,
868
00:31:09,180 --> 00:31:11,460
how can you academics just ignore it?
869
00:31:11,460 --> 00:31:12,293
- Well, so, okay,
870
00:31:12,293 --> 00:31:13,260
so I don't know why
871
00:31:13,260 --> 00:31:16,260
and like David-
- But I hold you
872
00:31:16,260 --> 00:31:19,468
responsible, Sergiu.
- I don't want to talk about
873
00:31:19,468 --> 00:31:23,100
issues of existence,
ideas, platonic ideas.
874
00:31:23,100 --> 00:31:25,140
Maybe, it's a step too far
875
00:31:25,140 --> 00:31:26,640
and that may be what we agree,
876
00:31:27,476 --> 00:31:31,740
but I have a operational
definition of reality.
877
00:31:31,740 --> 00:31:34,200
So reality is consistency
878
00:31:34,200 --> 00:31:36,750
of representations of a particular object.
879
00:31:36,750 --> 00:31:38,550
I mean, that's true in physics,
880
00:31:38,550 --> 00:31:39,930
and that's true in mathematics.
881
00:31:39,930 --> 00:31:41,850
Mathematical objects are real.
882
00:31:41,850 --> 00:31:43,036
A mathematician who works
883
00:31:43,036 --> 00:31:45,660
on a mathematical problem,
884
00:31:45,660 --> 00:31:47,010
calculates in this way,
885
00:31:47,010 --> 00:31:49,050
calculates in that other way,
886
00:31:49,050 --> 00:31:50,310
always gets the same result.
887
00:31:50,310 --> 00:31:51,990
I mean, there's something so obviously
888
00:31:51,990 --> 00:31:54,900
objective about what we do, right?
889
00:31:54,900 --> 00:31:56,790
That somehow to claim that
890
00:31:56,790 --> 00:31:57,960
these are just inventions
891
00:31:57,960 --> 00:31:59,730
of the human mind is ridiculous to me.
892
00:31:59,730 --> 00:32:00,563
I mean.
893
00:32:02,160 --> 00:32:02,993
- There is a way
894
00:32:02,993 --> 00:32:06,300
to defend any position in philosophy.
895
00:32:06,300 --> 00:32:07,920
I mean, we could argue that there
896
00:32:07,920 --> 00:32:09,570
are inventions of the human mind
897
00:32:09,570 --> 00:32:10,740
because the human mind is
898
00:32:10,740 --> 00:32:12,510
the only thing that really exists.
899
00:32:12,510 --> 00:32:14,070
After all, there's a very noble
900
00:32:14,070 --> 00:32:16,800
tradition going right back to Berkeley,
901
00:32:16,800 --> 00:32:18,757
which makes exactly that case,
902
00:32:18,757 --> 00:32:20,940
"To be is to be perceived"
903
00:32:20,940 --> 00:32:24,750
But there is something that inhibits
904
00:32:24,750 --> 00:32:27,490
a return to Berkeley and idealism
905
00:32:29,132 --> 00:32:31,950
in that it sounds vaguely preposterous
906
00:32:31,950 --> 00:32:35,070
to say the only thing
that exists is a mind.
907
00:32:35,070 --> 00:32:37,680
It doesn't comport with the magnificence
908
00:32:37,680 --> 00:32:39,630
of the physical theories weeped about.
909
00:32:39,630 --> 00:32:41,160
It just doesn't.
910
00:32:41,160 --> 00:32:42,180
That's not an argument,
911
00:32:42,180 --> 00:32:44,070
it's an observation.
912
00:32:44,070 --> 00:32:45,750
But having said that,
913
00:32:45,750 --> 00:32:47,940
we are really in danger of being
914
00:32:47,940 --> 00:32:51,510
reduced to an ever-narrowing ice flow.
915
00:32:51,510 --> 00:32:54,000
The ice flow, as Sergiu just mentioned,
916
00:32:54,000 --> 00:32:57,000
is the consistency of representation.
917
00:32:57,000 --> 00:33:00,210
Well, representations is
kind of an obscure term.
918
00:33:00,210 --> 00:33:02,460
Why don't we get down to basics?
919
00:33:02,460 --> 00:33:05,130
It's the consistency of our theories.
920
00:33:05,130 --> 00:33:06,420
Well, what is the theory?
921
00:33:06,420 --> 00:33:08,340
Well, we can provide an answer to that.
922
00:33:08,340 --> 00:33:11,310
A theory is kind of a
large group of sentences.
923
00:33:11,310 --> 00:33:12,720
And what are sentences?
924
00:33:12,720 --> 00:33:14,820
There are things that make certain kinds
925
00:33:14,820 --> 00:33:16,320
of assertions that can be true
926
00:33:16,320 --> 00:33:18,543
or false enough, they're consistent.
927
00:33:19,530 --> 00:33:21,870
That is about as good as we can get
928
00:33:21,870 --> 00:33:23,730
in terms of the credibility
929
00:33:23,730 --> 00:33:26,820
and commendability of a theory.
930
00:33:26,820 --> 00:33:28,980
So we're reduced now and our ice float
931
00:33:28,980 --> 00:33:31,200
is saying, "Well, we have a representation
932
00:33:31,200 --> 00:33:33,540
or a theory about the physical world
933
00:33:33,540 --> 00:33:36,840
and it's consistent,
but when we examine it,
934
00:33:36,840 --> 00:33:40,680
we find out it is not a physical object."
935
00:33:40,680 --> 00:33:44,220
It invokes non-physical substances
936
00:33:44,220 --> 00:33:45,990
like mathematical objects.
937
00:33:45,990 --> 00:33:47,167
We don't have to say,
938
00:33:47,167 --> 00:33:49,140
"We need not make a decision,
939
00:33:49,140 --> 00:33:50,250
do they exist in the mind
940
00:33:50,250 --> 00:33:51,900
or they exist in the external world,
941
00:33:51,900 --> 00:33:54,033
they exist," that's all we need.
942
00:33:55,080 --> 00:33:56,310
The number two exists.
943
00:33:56,310 --> 00:33:57,390
I don't have to tell you,
944
00:33:57,390 --> 00:33:58,413
it exists in your mind exists,
945
00:33:58,413 --> 00:33:59,280
it exists in my mind,
946
00:33:59,280 --> 00:34:00,810
that's an irrelevant, it exists.
947
00:34:00,810 --> 00:34:03,540
That's the determinative statement.
948
00:34:03,540 --> 00:34:05,310
And as long as it exists
949
00:34:05,310 --> 00:34:08,130
and we acknowledge it's not physical,
950
00:34:08,130 --> 00:34:09,697
then we're left with a position of saying,
951
00:34:09,697 --> 00:34:11,190
"How come our best view
952
00:34:11,190 --> 00:34:13,140
of the physical world incorporates
953
00:34:13,140 --> 00:34:14,460
things that are not physical?
954
00:34:14,460 --> 00:34:15,870
Why is that?"
- Existence is
955
00:34:15,870 --> 00:34:20,830
an autological question, I prefer reality
956
00:34:22,530 --> 00:34:25,860
is something that I can work with.
957
00:34:25,860 --> 00:34:27,330
Well, existence, I don't know.
958
00:34:27,330 --> 00:34:28,500
When it comes to usually existence,
959
00:34:28,500 --> 00:34:29,610
I feel lost, right?
960
00:34:29,610 --> 00:34:31,950
I don't exactly-
- You feel lost.
961
00:34:31,950 --> 00:34:33,900
- I mean, I don't know what existed,
962
00:34:33,900 --> 00:34:35,690
what does not exist.
- What intrigues me
963
00:34:35,690 --> 00:34:37,860
in all this is the idea
964
00:34:37,860 --> 00:34:39,057
that those mathematical objects,
965
00:34:39,057 --> 00:34:42,270
whether it's the quadratic equation
966
00:34:42,270 --> 00:34:45,150
or a circle or more advanced forms
967
00:34:45,150 --> 00:34:49,680
of mathematics, have stable properties.
968
00:34:49,680 --> 00:34:51,030
When they-
- Because this is the
969
00:34:51,030 --> 00:34:53,112
consistency you're talking.
- I'm talking about reality,
970
00:34:53,112 --> 00:34:56,650
yeah, reality and objectivity.
- [Stephen] Yeah, yeah.
971
00:34:56,650 --> 00:34:57,840
Yeah.
- Consistency.
972
00:34:57,840 --> 00:34:59,312
- Yeah, what Sergiu was saying is that
973
00:34:59,312 --> 00:35:01,950
these mathematical structures
974
00:35:01,950 --> 00:35:05,550
or objects have a reality
975
00:35:05,550 --> 00:35:07,530
that's independent of whether or not
976
00:35:07,530 --> 00:35:10,170
I affirm those properties myself.
977
00:35:10,170 --> 00:35:11,940
They're mind-independent
978
00:35:11,940 --> 00:35:14,310
and yet, they're conceptual, essentially.
979
00:35:14,310 --> 00:35:15,660
They're not material, they're conceptual.
980
00:35:15,660 --> 00:35:17,493
So it does raise the question,
981
00:35:18,720 --> 00:35:20,433
where do they reside?
982
00:35:20,433 --> 00:35:22,290
If there are concepts,
983
00:35:22,290 --> 00:35:24,060
and this is where we're moving
984
00:35:24,060 --> 00:35:27,150
in this direction by bringing Plato in.
985
00:35:27,150 --> 00:35:28,560
Plato had the idea that there
986
00:35:28,560 --> 00:35:30,330
are conceptual realities that exist
987
00:35:30,330 --> 00:35:34,350
in some sort of, you know, heavenly realm.
988
00:35:34,350 --> 00:35:36,930
But Aquinas's critique of that was,
989
00:35:36,930 --> 00:35:40,170
that's not consistent with our experience.
990
00:35:40,170 --> 00:35:42,063
Ideas exist in minds.
991
00:35:43,140 --> 00:35:45,810
There are these objective properties
992
00:35:45,810 --> 00:35:47,940
of mathematical structures,
993
00:35:47,940 --> 00:35:49,440
they're independent of our minds.
994
00:35:49,440 --> 00:35:51,300
And if these mathematical structures
995
00:35:51,300 --> 00:35:53,100
are themselves conceptual,
996
00:35:53,100 --> 00:35:55,710
it implies not that they're floating
997
00:35:55,710 --> 00:35:59,580
around someplace, but they originate
998
00:35:59,580 --> 00:36:01,020
or reside fundamentally
999
00:36:01,020 --> 00:36:02,820
in some transcendent mind.
1000
00:36:02,820 --> 00:36:04,485
That's the theistic take
1001
00:36:04,485 --> 00:36:06,750
on the mathematical realism.
1002
00:36:06,750 --> 00:36:10,020
- Steve says, math exists
in the mind of God.
1003
00:36:10,020 --> 00:36:10,957
And Sergiu says,
1004
00:36:10,957 --> 00:36:12,180
"Uh, don't bother me with that,
1005
00:36:12,180 --> 00:36:13,440
I'm a working mathematician.
1006
00:36:13,440 --> 00:36:14,983
All I need is this piece of chalk
1007
00:36:14,983 --> 00:36:17,580
and a blackboard."
- Well, operational
1008
00:36:17,580 --> 00:36:19,560
definition of reality, right?
1009
00:36:19,560 --> 00:36:22,950
And the notion that somehow
1010
00:36:22,950 --> 00:36:23,910
everything that's real,
1011
00:36:23,910 --> 00:36:26,160
it's physical, it doesn't make sense to me
1012
00:36:26,160 --> 00:36:28,801
because mathematical
objects are also real.
1013
00:36:28,801 --> 00:36:30,352
- And I think we're all saying
1014
00:36:30,352 --> 00:36:31,530
you know, where you slice this,
1015
00:36:31,530 --> 00:36:32,580
whether you're a-
- Yeah, I think
1016
00:36:32,580 --> 00:36:33,660
that's absolutely right.
1017
00:36:33,660 --> 00:36:36,540
I mean, even if we adopt
Berkeley's position,
1018
00:36:36,540 --> 00:36:38,270
that to be is to be perceived,
1019
00:36:38,270 --> 00:36:41,040
we wind up at the same position
1020
00:36:41,040 --> 00:36:42,720
that a thoroughly consistent
1021
00:36:42,720 --> 00:36:45,540
and coherent view of the universe
1022
00:36:45,540 --> 00:36:47,550
simply can't be physical.
- [Peter] Yeah.
1023
00:36:47,550 --> 00:36:49,476
- It simply can't be clear.
- We agree, okay.
1024
00:36:49,476 --> 00:36:52,260
That actually strikes even my
1025
00:36:52,260 --> 00:36:55,500
little mind as a really quite profound,
1026
00:36:55,500 --> 00:36:56,910
I'm not going to call it an insight,
1027
00:36:56,910 --> 00:36:57,870
it's a discovery,
1028
00:36:57,870 --> 00:37:01,470
it's a real aspect of reality itself.
1029
00:37:01,470 --> 00:37:02,760
- Can I revert back to something
1030
00:37:02,760 --> 00:37:03,930
earlier in the conversation?
- Sure.
1031
00:37:03,930 --> 00:37:05,809
It's just something from David's book,
1032
00:37:05,809 --> 00:37:08,790
he gave a talk in the
U.S. on this one time,
1033
00:37:08,790 --> 00:37:11,583
and it just was so intriguing to me.
1034
00:37:12,510 --> 00:37:13,447
I think it was from your book,
1035
00:37:13,447 --> 00:37:14,280
"One, Two, Three,"
1036
00:37:14,280 --> 00:37:16,250
when you were talking
about it on the road.
1037
00:37:19,004 --> 00:37:21,180
I think it was the complex variables.
1038
00:37:21,180 --> 00:37:23,310
The complex numbers, remember,
1039
00:37:23,310 --> 00:37:25,680
the square root of negative one from math,
1040
00:37:25,680 --> 00:37:27,570
there's this whole mathematical apparatus
1041
00:37:27,570 --> 00:37:30,060
that's been developed
around complex numbers.
1042
00:37:30,060 --> 00:37:31,140
And it seems like it has
1043
00:37:31,140 --> 00:37:33,240
absolutely nothing to do with anything,
1044
00:37:33,240 --> 00:37:36,120
but there's a whole body of mathematics
1045
00:37:36,120 --> 00:37:37,440
on this, I took a course
1046
00:37:37,440 --> 00:37:40,020
in grad school on complex variables.
1047
00:37:40,020 --> 00:37:41,370
And David showed that this was
1048
00:37:41,370 --> 00:37:42,240
invented something like,
1049
00:37:42,240 --> 00:37:44,340
what was it, 140, developed,
1050
00:37:44,340 --> 00:37:45,269
discovered.
- 140.
1051
00:37:45,269 --> 00:37:47,260
- [Stephen] 140 years before.
- Maybe 200, maybe 200.
1052
00:37:47,260 --> 00:37:48,780
- Yeah, and then lo and behold,
1053
00:37:48,780 --> 00:37:50,550
it's absolutely crucial
1054
00:37:50,550 --> 00:37:51,660
for doing quantum mechanics,
1055
00:37:51,660 --> 00:37:53,220
which is our most fundamental
1056
00:37:53,220 --> 00:37:54,630
physical theory or one of them.
1057
00:37:54,630 --> 00:37:57,750
- No, but if I can.
- Yeah, please correct me.
1058
00:37:57,750 --> 00:38:00,030
- What is fascinating about the history
1059
00:38:00,030 --> 00:38:03,120
of the invention of the number I is that,
1060
00:38:03,120 --> 00:38:07,170
well, it came up in Italy
1061
00:38:07,170 --> 00:38:09,960
around, you know, 14th century.
1062
00:38:09,960 --> 00:38:13,380
- 16th century.
- No, earlier,
1063
00:38:13,380 --> 00:38:14,940
I think, 1450.
- [David] Yeah.
1064
00:38:14,940 --> 00:38:17,370
- Okay, 1450, a bit earlier maybe.
1065
00:38:17,370 --> 00:38:19,920
But in any case, it was based on
1066
00:38:19,920 --> 00:38:21,600
their desire to solve equation.
1067
00:38:21,600 --> 00:38:22,433
So they wanted to
1068
00:38:22,433 --> 00:38:23,490
solve first a quadratic equation,
1069
00:38:23,490 --> 00:38:25,680
there was a formula already.
1070
00:38:25,680 --> 00:38:27,866
The Arabs apparently also knew it already.
1071
00:38:27,866 --> 00:38:29,440
In any case, they went
1072
00:38:29,440 --> 00:38:31,830
to the third order equation
1073
00:38:31,830 --> 00:38:34,020
and they found that
1074
00:38:34,020 --> 00:38:36,360
it based to introduce this symbol,
1075
00:38:36,360 --> 00:38:37,350
square root of minus one,
1076
00:38:37,350 --> 00:38:38,190
which makes no sense,
1077
00:38:38,190 --> 00:38:39,304
you cannot take the square
1078
00:38:39,304 --> 00:38:40,650
root of minus one, right?
- Makes no sense to me.
1079
00:38:40,650 --> 00:38:42,360
- But they just put it there
1080
00:38:42,360 --> 00:38:44,160
and they made this incredible
1081
00:38:44,160 --> 00:38:46,530
observation that you can use
1082
00:38:46,530 --> 00:38:48,690
this number and at the end,
1083
00:38:48,690 --> 00:38:49,950
you are getting a solution
1084
00:38:49,950 --> 00:38:53,250
of cubic equations, which are all reals
1085
00:38:53,250 --> 00:38:54,930
and nothing to do with
those complex numbers,
1086
00:38:54,930 --> 00:38:56,943
but they enter into the formula.
1087
00:38:58,260 --> 00:39:00,750
So this was quite an amazing thing, right?
1088
00:39:00,750 --> 00:39:01,830
So then little by little,
1089
00:39:01,830 --> 00:39:03,330
they got used to using
1090
00:39:03,330 --> 00:39:04,860
square root of minus one.
1091
00:39:04,860 --> 00:39:08,520
And at some point in the 19th century,
1092
00:39:08,520 --> 00:39:10,920
it was even made more formal,
1093
00:39:10,920 --> 00:39:14,577
it was given a geometric definition
1094
00:39:16,050 --> 00:39:17,273
of square root of minus one.
1095
00:39:17,273 --> 00:39:18,840
And you have complex numbers
1096
00:39:18,840 --> 00:39:19,830
and complex functions
1097
00:39:19,830 --> 00:39:21,420
and then the enormous amount
1098
00:39:21,420 --> 00:39:24,030
of applications came out of it.
1099
00:39:24,030 --> 00:39:25,710
So square root of minus one
1100
00:39:25,710 --> 00:39:27,960
is obviously real, it existed before
1101
00:39:27,960 --> 00:39:30,727
it was discovered by-
- That's very interesting.
1102
00:39:30,727 --> 00:39:33,758
(crosstalk)
1103
00:39:33,758 --> 00:39:35,460
- When they introduced negative numbers,
1104
00:39:35,460 --> 00:39:36,540
I stopped paying attention.
1105
00:39:36,540 --> 00:39:37,498
Negative numbers have
1106
00:39:37,498 --> 00:39:38,940
nothing to do with reality,
1107
00:39:38,940 --> 00:39:40,920
but I was wrong then.
- Peter, it's not negative,
1108
00:39:40,920 --> 00:39:42,240
these are complex numbers.
1109
00:39:42,240 --> 00:39:43,770
The square root of minus one,
1110
00:39:43,770 --> 00:39:45,330
the negative numbers of minus one,
1111
00:39:45,330 --> 00:39:47,160
minus two, think of debts.
1112
00:39:47,160 --> 00:39:48,510
We're not talking about debts now,
1113
00:39:48,510 --> 00:39:49,920
we're talking about a complex number.
1114
00:39:49,920 --> 00:39:51,480
But here's the extraordinarily
1115
00:39:51,480 --> 00:39:53,550
interesting point, you got this
1116
00:39:53,550 --> 00:39:55,457
weirdo, Italian mathematician
1117
00:39:55,457 --> 00:39:57,960
in the 15th century who figures out
1118
00:39:57,960 --> 00:40:00,000
that if I introduce the symbol I
1119
00:40:00,000 --> 00:40:02,610
equals the square root of minus one,
1120
00:40:02,610 --> 00:40:05,820
I can solidify a chain of inference
1121
00:40:05,820 --> 00:40:07,500
and come out with the right answer.
1122
00:40:07,500 --> 00:40:09,480
Just absolutely amazing.
1123
00:40:09,480 --> 00:40:12,090
However, when mathematicians
1124
00:40:12,090 --> 00:40:13,590
start to think about it,
1125
00:40:13,590 --> 00:40:15,660
it's entirely possible to get
1126
00:40:15,660 --> 00:40:18,630
rid of the square root of minus one
1127
00:40:18,630 --> 00:40:21,300
in favor of two real numbers
1128
00:40:21,300 --> 00:40:24,180
and a set of rules for manipulating them.
1129
00:40:24,180 --> 00:40:25,140
All of a sudden,
1130
00:40:25,140 --> 00:40:27,930
the square root of minus one is gone.
1131
00:40:27,930 --> 00:40:30,120
You're left with what you began with,
1132
00:40:30,120 --> 00:40:32,670
the real numbers, three and seven
1133
00:40:32,670 --> 00:40:34,410
in a certain order
1134
00:40:34,410 --> 00:40:37,290
and obeying certain rules.
- A multiplication rule,
1135
00:40:37,290 --> 00:40:38,759
which is essential.
- [David] Yeah.
1136
00:40:38,759 --> 00:40:39,690
- So that's the complex number.
1137
00:40:39,690 --> 00:40:40,890
- The complex number, exactly.
1138
00:40:40,890 --> 00:40:43,410
- It's a new multiplication rule,
1139
00:40:43,410 --> 00:40:45,930
which did not exist in the realm
1140
00:40:45,930 --> 00:40:49,380
of what is called, real natural numbers.
1141
00:40:49,380 --> 00:40:50,610
- But that interests
1142
00:40:50,610 --> 00:40:52,680
a very interesting analytical point
1143
00:40:52,680 --> 00:40:57,060
that ontology can be reduced in favor
1144
00:40:57,060 --> 00:41:00,570
of a system of rules and regulations.
1145
00:41:00,570 --> 00:41:01,470
You can reduce
1146
00:41:01,470 --> 00:41:03,960
the ontological burden of mathematics.
1147
00:41:03,960 --> 00:41:06,150
You can say, I'm going to get rid
1148
00:41:06,150 --> 00:41:08,100
of the numbers in favor of the sets.
1149
00:41:08,100 --> 00:41:10,170
I'm gonna get rid of the complex numbers
1150
00:41:10,170 --> 00:41:12,510
in favor of ordered pairs of real numbers.
1151
00:41:12,510 --> 00:41:14,160
I'm gonna get rid of the real numbers
1152
00:41:14,160 --> 00:41:16,680
in favor of convergence sequences.
1153
00:41:16,680 --> 00:41:18,570
I'm gonna get rid of so much.
1154
00:41:18,570 --> 00:41:22,290
But as you reduce the burden of ontology,
1155
00:41:22,290 --> 00:41:26,100
you increase the burden
of your regulations.
1156
00:41:26,100 --> 00:41:28,620
So you actually never get to the point
1157
00:41:28,620 --> 00:41:31,320
where mathematics appears from nothing.
1158
00:41:31,320 --> 00:41:33,003
You never get to that point.
1159
00:41:33,900 --> 00:41:36,510
Like a biologist-
- Ontology just being
1160
00:41:36,510 --> 00:41:37,540
the affirmation of
1161
00:41:38,970 --> 00:41:40,980
something substantially real.
1162
00:41:40,980 --> 00:41:42,870
- I mean, biologists love to say,
1163
00:41:42,870 --> 00:41:44,340
life comes only from life.
1164
00:41:44,340 --> 00:41:46,260
19th century, it's obviously true.
1165
00:41:46,260 --> 00:41:47,580
Life comes only from life.
1166
00:41:47,580 --> 00:41:48,690
And how it might not
1167
00:41:48,690 --> 00:41:51,540
come from life is an utter mystery.
1168
00:41:51,540 --> 00:41:52,440
But it's also true
1169
00:41:52,440 --> 00:41:54,990
that language comes only from language.
1170
00:41:54,990 --> 00:41:56,610
And it's additionally true that
1171
00:41:56,610 --> 00:41:59,160
mathematics only comes from mathematics.
1172
00:41:59,160 --> 00:42:02,010
These seem to be processes with which
1173
00:42:02,010 --> 00:42:04,470
we have a good deal of experience,
1174
00:42:04,470 --> 00:42:07,320
which have no point of origin.
1175
00:42:07,320 --> 00:42:08,310
There is no place
1176
00:42:08,310 --> 00:42:10,380
in which mathematics originates.
1177
00:42:10,380 --> 00:42:13,080
There's no place in
which language originates
1178
00:42:13,080 --> 00:42:16,230
and there is no place in
which life originates.
1179
00:42:16,230 --> 00:42:17,970
They may well be fundamental
1180
00:42:17,970 --> 00:42:20,013
features of the universe itself,
1181
00:42:21,330 --> 00:42:24,630
- But nevertheless,
mathematics has a history.
1182
00:42:24,630 --> 00:42:29,220
And this article...
- But it's infinite
1183
00:42:29,220 --> 00:42:30,893
in the past.
- [Sergiu] Right.
1184
00:42:30,893 --> 00:42:32,130
- It's always been.
- It's a human.
1185
00:42:32,130 --> 00:42:33,210
So there is something
1186
00:42:33,210 --> 00:42:35,010
human about mathematics.
1187
00:42:35,010 --> 00:42:36,330
- There's a history of our discovery,
1188
00:42:36,330 --> 00:42:38,490
but not a history to the realities.
1189
00:42:38,490 --> 00:42:39,572
- Exactly.
1190
00:42:39,572 --> 00:42:41,905
(crosstalk)
1191
00:42:43,080 --> 00:42:44,670
- Okay.
1192
00:42:44,670 --> 00:42:48,780
David, this is a conversation you had,
1193
00:42:48,780 --> 00:42:51,030
I think with Steve in Cambridge.
1194
00:42:51,030 --> 00:42:52,473
I'm gonna quote a passage.
1195
00:42:53,407 --> 00:42:55,470
"Hold up a finger.
1196
00:42:55,470 --> 00:42:56,790
Could this finger be a different color?
1197
00:42:56,790 --> 00:42:57,623
Yes.
1198
00:42:57,623 --> 00:42:58,710
Could it be slightly longer?
1199
00:42:58,710 --> 00:42:59,543
Yes.
1200
00:42:59,543 --> 00:43:00,450
Could it be crooked?
1201
00:43:00,450 --> 00:43:01,410
Yes.
1202
00:43:01,410 --> 00:43:03,180
But could it ever be anything
1203
00:43:03,180 --> 00:43:05,883
other than one finger?
1204
00:43:06,780 --> 00:43:08,910
No, the number is obligatory.
1205
00:43:08,910 --> 00:43:11,040
The number is something
1206
00:43:11,040 --> 00:43:13,977
the finger essentially has."
1207
00:43:16,980 --> 00:43:18,660
All right, so now we're in the realm
1208
00:43:18,660 --> 00:43:20,010
of Aristotle and the difference
1209
00:43:20,010 --> 00:43:23,250
between essence and-
- Essential properties
1210
00:43:23,250 --> 00:43:25,020
and non-essential properties.
- And accidents.
1211
00:43:25,020 --> 00:43:26,220
Essential properties.
- Yes, exactly.
1212
00:43:26,220 --> 00:43:28,004
- And accidents, explain this.
1213
00:43:28,004 --> 00:43:29,676
- Well...
- I feel as though
1214
00:43:29,676 --> 00:43:31,339
I'm tiptoeing-
- You're doing well, Robinson.
1215
00:43:31,339 --> 00:43:32,172
- All right, all right.
1216
00:43:32,172 --> 00:43:33,360
So numbers represent
1217
00:43:33,360 --> 00:43:36,180
an essential aspect of reality.
1218
00:43:36,180 --> 00:43:37,410
That's a big deal.
1219
00:43:37,410 --> 00:43:40,230
- Well, it's a very general statement.
1220
00:43:40,230 --> 00:43:43,380
I much prefer, God forbid me,
1221
00:43:43,380 --> 00:43:45,420
forgive me for introducing Heidegger,
1222
00:43:45,420 --> 00:43:47,640
I much prefer his formulation.
1223
00:43:47,640 --> 00:43:49,680
Heidegger, there are very
1224
00:43:49,680 --> 00:43:51,480
interesting passages in his work.
1225
00:43:51,480 --> 00:43:52,687
I admit it, and he says,
1226
00:43:52,687 --> 00:43:55,290
"Look, when we look at objects,
1227
00:43:55,290 --> 00:43:58,050
we cannot separate the oneness
1228
00:43:58,050 --> 00:44:00,510
of this glass from the object itself.
1229
00:44:00,510 --> 00:44:01,980
But we can change the color,
1230
00:44:01,980 --> 00:44:03,060
we can change the shape.
1231
00:44:03,060 --> 00:44:04,489
It'll still be the same object,
1232
00:44:04,489 --> 00:44:06,870
but we can't say this one object
1233
00:44:06,870 --> 00:44:08,910
could have been two.
1234
00:44:08,910 --> 00:44:10,770
That just doesn't go."
1235
00:44:10,770 --> 00:44:13,920
So when we talk about physical objects,
1236
00:44:13,920 --> 00:44:15,030
we're only talking now
1237
00:44:15,030 --> 00:44:18,630
about physically realizable objects.
1238
00:44:18,630 --> 00:44:22,803
The mathematical aspects
are essential to them.
1239
00:44:24,000 --> 00:44:26,373
What holds for numbers
also holds for shape.
1240
00:44:28,680 --> 00:44:31,080
We don't have to do what Eugene Wigner
1241
00:44:31,080 --> 00:44:33,990
did and say, "Look at quantum mechanics
1242
00:44:33,990 --> 00:44:36,180
and the remarkable fact that Hilbert
1243
00:44:36,180 --> 00:44:38,490
spaces require introduction
1244
00:44:38,490 --> 00:44:40,050
of complex numbers."
1245
00:44:40,050 --> 00:44:41,880
No, just look at the glass.
1246
00:44:41,880 --> 00:44:43,020
The glass requires
1247
00:44:43,020 --> 00:44:45,600
the introduction of a natural number.
1248
00:44:45,600 --> 00:44:46,890
Two glasses require
1249
00:44:46,890 --> 00:44:49,410
the introduction of two natural numbers.
1250
00:44:49,410 --> 00:44:52,710
That is every bit as mysterious
1251
00:44:52,710 --> 00:44:54,930
as the invocation of complex numbers
1252
00:44:54,930 --> 00:44:56,040
and quantum field theory.
1253
00:44:56,040 --> 00:44:57,360
Every bit is mysterious.
1254
00:44:57,360 --> 00:44:59,370
And we don't know quite why.
1255
00:44:59,370 --> 00:45:00,690
- Okay, so all three of you
1256
00:45:00,690 --> 00:45:02,193
are willing to agree,
1257
00:45:03,480 --> 00:45:05,440
all three of you are willing to insist
1258
00:45:06,840 --> 00:45:08,193
that mathematics,
1259
00:45:09,870 --> 00:45:11,310
the existence of mathematics,
1260
00:45:11,310 --> 00:45:13,500
the weird way in which mathematics
1261
00:45:13,500 --> 00:45:14,760
seems to correspond with
1262
00:45:14,760 --> 00:45:16,020
and help us to investigate
1263
00:45:16,020 --> 00:45:18,390
reality in a way that is real.
1264
00:45:18,390 --> 00:45:20,313
I'm using reality over and over again,
1265
00:45:21,300 --> 00:45:25,230
proves that reality is not purely,
1266
00:45:25,230 --> 00:45:26,370
not limited to what
1267
00:45:26,370 --> 00:45:28,500
we can access by our five senses.
1268
00:45:28,500 --> 00:45:29,850
- It's a hint.
1269
00:45:29,850 --> 00:45:31,890
It doesn't prove, it's a hint.
1270
00:45:31,890 --> 00:45:33,120
- Oh, now I've lost deep ground
1271
00:45:33,120 --> 00:45:35,370
even from that all, so
all we have is a hint.
1272
00:45:36,300 --> 00:45:38,100
I think Steve is willing to go,
1273
00:45:38,100 --> 00:45:40,530
now here, I'm putting
words into Steve's mouth.
1274
00:45:40,530 --> 00:45:41,973
Steve is willing to say,
1275
00:45:43,447 --> 00:45:46,041
"We're dealing here with the mind of God."
1276
00:45:46,041 --> 00:45:48,423
And David won't do that,
1277
00:45:49,500 --> 00:45:50,640
I could pin you down
1278
00:45:50,640 --> 00:45:53,100
and you wouldn't.
- I'll give you
1279
00:45:53,100 --> 00:45:55,290
sort of an example of something like this.
1280
00:45:55,290 --> 00:45:58,440
So, you know, immediately after Newton,
1281
00:45:58,440 --> 00:46:00,360
there was Newtonian mechanics.
1282
00:46:00,360 --> 00:46:01,193
The idea was that Newtonian
1283
00:46:01,193 --> 00:46:03,000
mechanics has to explain everything.
1284
00:46:03,000 --> 00:46:06,660
Then came Maxwell, the Maxwell equations.
1285
00:46:06,660 --> 00:46:09,040
And in order to
1286
00:46:10,620 --> 00:46:12,420
adjust the Maxwell equations
1287
00:46:12,420 --> 00:46:13,590
to Newtonian mechanics,
1288
00:46:13,590 --> 00:46:16,410
they needed this notion of ether, right?
1289
00:46:16,410 --> 00:46:19,413
So, you know, ether here is that there.
1290
00:46:21,060 --> 00:46:23,100
I mean, Einstein's great insight
1291
00:46:23,100 --> 00:46:25,140
was, we really don't need it, right?
1292
00:46:25,140 --> 00:46:26,790
So it's the same thing, I believe,
1293
00:46:26,790 --> 00:46:28,410
we don't need this materialistic
1294
00:46:28,410 --> 00:46:29,730
representation of the world.
1295
00:46:29,730 --> 00:46:31,260
Just forget about it.
1296
00:46:31,260 --> 00:46:34,050
Reality means something broader than that.
1297
00:46:34,050 --> 00:46:35,430
- It's inconsistent with the most
1298
00:46:35,430 --> 00:46:38,400
obvious presentation
of mathematics itself.
1299
00:46:38,400 --> 00:46:40,050
It's obvious that mathematical
1300
00:46:40,050 --> 00:46:41,790
properties are not material.
1301
00:46:41,790 --> 00:46:44,910
You can invent a metaphysical system
1302
00:46:44,910 --> 00:46:46,170
that explains that away.
1303
00:46:46,170 --> 00:46:48,030
That's why it's not approved.
1304
00:46:48,030 --> 00:46:49,456
- So nobody proved that ether
1305
00:46:49,456 --> 00:46:51,240
does not exist.
- [Stephen] Yeah, yeah, right.
1306
00:46:51,240 --> 00:46:52,830
- We just get rid of it.
- [Stephen] Yeah.
1307
00:46:52,830 --> 00:46:53,812
- And I think that's what we
1308
00:46:53,812 --> 00:46:55,290
should do about material.
- I think
1309
00:46:55,290 --> 00:46:56,610
I could agree with that,
1310
00:46:56,610 --> 00:47:00,540
but going back to your last remark, Peter,
1311
00:47:00,540 --> 00:47:03,000
I think it's just much simpler
1312
00:47:03,000 --> 00:47:04,680
to say that the mystery
1313
00:47:04,680 --> 00:47:07,590
is just the existence of mathematics.
1314
00:47:07,590 --> 00:47:08,493
It's just that.
1315
00:47:09,360 --> 00:47:11,460
Because it's fundamental.
1316
00:47:11,460 --> 00:47:13,440
We could well say, and of course,
1317
00:47:13,440 --> 00:47:15,990
philosophers have well said,
1318
00:47:15,990 --> 00:47:18,060
we can get rid of the physical world,
1319
00:47:18,060 --> 00:47:19,740
metaphysically, that's not a problem.
1320
00:47:19,740 --> 00:47:21,300
Berkeley showed how everything
1321
00:47:21,300 --> 00:47:23,670
is a perception or an idea.
1322
00:47:23,670 --> 00:47:25,890
External world just disappears.
1323
00:47:25,890 --> 00:47:27,210
But we can't get rid of
1324
00:47:27,210 --> 00:47:28,740
the mathematical world,
1325
00:47:28,740 --> 00:47:31,290
that's ineliminable
1326
00:47:31,290 --> 00:47:33,570
and its existence is a profound mystery.
1327
00:47:33,570 --> 00:47:36,030
What is it doing there?
1328
00:47:36,030 --> 00:47:39,690
Why do we see things
in mathematical terms?
1329
00:47:39,690 --> 00:47:41,130
Now, I'm not asking this question
1330
00:47:41,130 --> 00:47:42,630
because I have a secret answer
1331
00:47:42,630 --> 00:47:45,870
that I'm about to say.
- I was hoping you to wrap up
1332
00:47:45,870 --> 00:47:47,190
the conversation with the answer.
1333
00:47:47,190 --> 00:47:48,840
- I find it a great mystery.
1334
00:47:48,840 --> 00:47:51,330
The sheer existence of mathematics
1335
00:47:51,330 --> 00:47:53,280
is deeply puzzling.
- [Peter] You will agree
1336
00:47:53,280 --> 00:47:55,822
with every word of that.
- Yeah, absolutely.
1337
00:47:55,822 --> 00:47:56,790
- [Peter] And you will agree,
1338
00:47:56,790 --> 00:47:58,590
but can you take it farther?
1339
00:47:58,590 --> 00:48:01,230
- Well, I just am intrigued with this
1340
00:48:01,230 --> 00:48:03,120
kind of argument that I recapitulated
1341
00:48:03,120 --> 00:48:04,650
earlier in the conversation
1342
00:48:04,650 --> 00:48:06,330
that mathematical objects
1343
00:48:06,330 --> 00:48:07,740
have stable properties,
1344
00:48:07,740 --> 00:48:09,210
therefore, they have an objectivity
1345
00:48:09,210 --> 00:48:11,220
that is independent of our minds.
1346
00:48:11,220 --> 00:48:12,420
And yet, they are conceptual,
1347
00:48:12,420 --> 00:48:15,090
which suggests by our experience
1348
00:48:15,090 --> 00:48:17,130
that they must not be floating
1349
00:48:17,130 --> 00:48:19,410
around somewhere in the platonic heavens.
1350
00:48:19,410 --> 00:48:20,880
But rather, it makes more sense to me
1351
00:48:20,880 --> 00:48:22,170
to think that they ultimately
1352
00:48:22,170 --> 00:48:23,640
issue from the mind of God.
1353
00:48:23,640 --> 00:48:25,860
And that that is the deep reason
1354
00:48:25,860 --> 00:48:28,080
for the mysterious applicability
1355
00:48:28,080 --> 00:48:29,163
of mathematics to the physical world.
1356
00:48:29,163 --> 00:48:30,720
- Bear in mind, Steve,
1357
00:48:30,720 --> 00:48:32,130
that you're reaching a position
1358
00:48:32,130 --> 00:48:34,200
very close to Berkeley's position.
1359
00:48:34,200 --> 00:48:35,370
- [Sergiu] To whose?
- To Berkeley,
1360
00:48:35,370 --> 00:48:36,720
Bishop Berkeley.
- [Sergiu] Right.
1361
00:48:36,720 --> 00:48:38,318
- I mean, if you say that
1362
00:48:38,318 --> 00:48:39,480
to be is to be perceived.
- Bishop Berkeley's
1363
00:48:39,480 --> 00:48:41,820
17th century British.
- 18th century.
1364
00:48:41,820 --> 00:48:43,740
- [Peter] 18th century English churchman
1365
00:48:43,740 --> 00:48:47,070
and philosopher who appears possibly
1366
00:48:47,070 --> 00:48:49,440
most famously in
Boswell's life of Johnson,
1367
00:48:49,440 --> 00:48:51,060
when Boswell says-
- I refute Berkeley.
1368
00:48:51,060 --> 00:48:53,040
- Yes, thus Johnson kicking a rock.
1369
00:48:53,040 --> 00:48:53,873
Immaterial of all this material.
1370
00:48:53,873 --> 00:48:55,255
- But the point is,
1371
00:48:55,255 --> 00:48:56,088
Berkeley faced the obvious question.
1372
00:48:56,088 --> 00:48:57,570
If you're not looking at the moon,
1373
00:48:57,570 --> 00:48:59,190
Einstein discusses this too,
1374
00:48:59,190 --> 00:49:01,230
does the moon continue to exist?
1375
00:49:01,230 --> 00:49:03,127
And Berkeley's response was,
1376
00:49:03,127 --> 00:49:04,920
"Yes, it exists as a thought
1377
00:49:04,920 --> 00:49:06,120
in the mind of God."
1378
00:49:06,120 --> 00:49:07,290
Which is very close to
1379
00:49:07,290 --> 00:49:09,240
what Steve was just argue.
1380
00:49:09,240 --> 00:49:11,570
Although, he's certainly not-
- I'm not a Berkeley.
1381
00:49:11,570 --> 00:49:12,660
- You're not a Berkeley.
- I don't think
1382
00:49:12,660 --> 00:49:15,390
the physical world has,
1383
00:49:15,390 --> 00:49:17,370
I think it has an independence
1384
00:49:17,370 --> 00:49:18,810
of our mind and of the mind of God
1385
00:49:18,810 --> 00:49:20,220
who created it, but I think
1386
00:49:20,220 --> 00:49:21,900
the ultimate source of mathematical
1387
00:49:21,900 --> 00:49:23,580
reality may well be the mind of God.
1388
00:49:23,580 --> 00:49:24,720
- But it's interesting that you
1389
00:49:24,720 --> 00:49:27,900
are prepared to go further than I think
1390
00:49:27,900 --> 00:49:29,850
many contemporary analytic philosophers
1391
00:49:29,850 --> 00:49:31,800
are prepared to go in the direction
1392
00:49:31,800 --> 00:49:34,230
of a Berkeley kind of analysis,
1393
00:49:34,230 --> 00:49:36,330
which I think is in this case,
1394
00:49:36,330 --> 00:49:37,890
the only analysis that makes sense.
1395
00:49:37,890 --> 00:49:38,820
- At least for math.
- [David] Yeah.
1396
00:49:38,820 --> 00:49:40,800
- At least for math,
because it is so mysterious.
1397
00:49:40,800 --> 00:49:41,850
- Boys, I'm going to attempt
1398
00:49:41,850 --> 00:49:42,990
for last question here.
1399
00:49:42,990 --> 00:49:43,823
I'm going to attempt
1400
00:49:43,823 --> 00:49:46,770
to introduce one new concept,
1401
00:49:46,770 --> 00:49:49,980
and that is the concept of beauty.
1402
00:49:49,980 --> 00:49:51,960
I have no idea how this will go,
1403
00:49:51,960 --> 00:49:53,100
but here's an excerpt
1404
00:49:53,100 --> 00:49:56,317
from the forthcoming documentary,
1405
00:49:56,317 --> 00:49:58,720
"The Story of Everything."
1406
00:49:58,720 --> 00:50:00,840
(gentle music)
- [Narrator] There's something
1407
00:50:00,840 --> 00:50:03,060
in science called, the Beauty Principle
1408
00:50:03,060 --> 00:50:04,710
that says, true theories often
1409
00:50:04,710 --> 00:50:06,840
convey a mathematical beauty
1410
00:50:06,840 --> 00:50:08,763
or a structural harmony.
1411
00:50:08,763 --> 00:50:11,460
(gentle music)
1412
00:50:11,460 --> 00:50:13,590
Upon looking at their model
1413
00:50:13,590 --> 00:50:15,480
of the DNA molecule,
1414
00:50:15,480 --> 00:50:18,003
Francis Crick was quoted as saying,
1415
00:50:19,237 --> 00:50:21,717
"It's so beautiful, it's gotta be right."
1416
00:50:23,400 --> 00:50:24,720
- Explain that.
1417
00:50:24,720 --> 00:50:27,180
Why should beauty enter into this?
1418
00:50:27,180 --> 00:50:28,530
- We don't really know.
1419
00:50:28,530 --> 00:50:30,420
But it tends to be what's called,
1420
00:50:30,420 --> 00:50:32,317
a heuristic guide in science,
1421
00:50:32,317 --> 00:50:34,020
"A Guide to Discovery."
1422
00:50:34,020 --> 00:50:35,970
And in the section of the film
1423
00:50:35,970 --> 00:50:38,760
that follows, there were maybe perhaps
1424
00:50:38,760 --> 00:50:40,710
even more trenchant comments from
1425
00:50:40,710 --> 00:50:42,090
a couple of the physicists who
1426
00:50:42,090 --> 00:50:45,540
are saying how often their perception
1427
00:50:45,540 --> 00:50:46,980
of mathematical beauty
1428
00:50:46,980 --> 00:50:48,300
had been a guide to discovery.
1429
00:50:48,300 --> 00:50:50,220
I think it was Paul Dirac who first
1430
00:50:50,220 --> 00:50:51,420
said that it's more important
1431
00:50:51,420 --> 00:50:52,391
for the theories.
- Yeah.
1432
00:50:52,391 --> 00:50:53,224
- They're more beautiful
1433
00:50:53,224 --> 00:50:56,433
than to have them
consistent with the data,
1434
00:50:58,770 --> 00:51:00,420
well, because we can be mistaken
1435
00:51:00,420 --> 00:51:02,070
about how we're perceiving the data.
1436
00:51:02,070 --> 00:51:03,900
But there is assumption that
1437
00:51:03,900 --> 00:51:05,430
there's something mathematically
1438
00:51:05,430 --> 00:51:07,260
beautiful about reality itself.
1439
00:51:07,260 --> 00:51:09,742
Intelligibility.
- Dirac was mesmerized by
1440
00:51:09,742 --> 00:51:10,981
somebody-
- [David] I'm sorry, who?
1441
00:51:10,981 --> 00:51:11,814
- [Stephen] Dirac.
1442
00:51:11,814 --> 00:51:13,377
I said, Dirac, yeah.
1443
00:51:13,377 --> 00:51:15,780
Dirac was mesmerized.
- And you said
1444
00:51:15,780 --> 00:51:18,000
a moment ago when you were choosing
1445
00:51:18,000 --> 00:51:20,100
projects on which to work,
1446
00:51:20,100 --> 00:51:21,000
I think you used the word,
1447
00:51:21,000 --> 00:51:22,500
is it elegant, is it beautiful?
1448
00:51:22,500 --> 00:51:23,955
- [Stephen] Aesthetic.
- Of course, yeah.
1449
00:51:23,955 --> 00:51:28,830
The Kerr solution is an incredible object.
1450
00:51:28,830 --> 00:51:30,633
I mean, really beautiful.
1451
00:51:32,152 --> 00:51:33,480
- Are we on another mystery here?
1452
00:51:33,480 --> 00:51:35,470
An aesthetic mystery.
- Beauty
1453
00:51:36,660 --> 00:51:38,070
plays a fundamental role,
1454
00:51:38,070 --> 00:51:39,900
of course, in the way we choose problems,
1455
00:51:39,900 --> 00:51:42,390
but also in the way we are guiding
1456
00:51:42,390 --> 00:51:43,920
ourselves towards the truth.
1457
00:51:43,920 --> 00:51:46,530
I mean, towards a solution of a problem.
1458
00:51:46,530 --> 00:51:49,260
Somehow, we reject arguments
1459
00:51:49,260 --> 00:51:51,390
which are contrived,
which are not beautiful.
1460
00:51:51,390 --> 00:51:52,840
We don't call them beautiful.
1461
00:51:53,820 --> 00:51:56,460
Yeah, I mean, it's mysteriously true.
1462
00:51:56,460 --> 00:51:59,103
And physics, of course
is full of such examples.
1463
00:52:00,450 --> 00:52:02,791
Maxwell, you know,
1464
00:52:02,791 --> 00:52:06,300
the way the Maxwell
equations were discovered,
1465
00:52:06,300 --> 00:52:08,860
it was first Faraday who had
1466
00:52:10,080 --> 00:52:12,420
the three laws of electro minorities
1467
00:52:12,420 --> 00:52:13,830
already discovered experimentally.
1468
00:52:13,830 --> 00:52:15,799
- [Stephen] That's right.
1469
00:52:15,799 --> 00:52:17,790
- But he was not a mathematician at all.
1470
00:52:17,790 --> 00:52:21,840
So he just left it there,
1471
00:52:21,840 --> 00:52:24,630
just stated the laws.
1472
00:52:24,630 --> 00:52:26,190
And it was Maxwell who realized
1473
00:52:26,190 --> 00:52:27,810
that if you put those statements
1474
00:52:27,810 --> 00:52:29,700
within mathematics,
1475
00:52:29,700 --> 00:52:32,220
there's a lack of symmetry,
1476
00:52:32,220 --> 00:52:34,473
sort of guided him towards a force one,
1477
00:52:35,310 --> 00:52:37,233
which led to electromagnetism.
1478
00:52:38,700 --> 00:52:40,037
- And all of the technology
1479
00:52:40,037 --> 00:52:42,360
of the modern world.
1480
00:52:42,360 --> 00:52:44,010
- [Sergiu] Beauty.
- With Maxwell.
1481
00:52:44,010 --> 00:52:46,320
- Your comment about beauty.
- Yeah, I'd like to hear
1482
00:52:46,320 --> 00:52:48,390
from these guys 'cause yeah.
1483
00:52:48,390 --> 00:52:51,033
- I kinda reserve that for my tailors.
1484
00:52:54,540 --> 00:52:56,130
- You know, I can tell you that
1485
00:52:56,130 --> 00:52:58,650
as a working mathematician,
1486
00:52:58,650 --> 00:53:00,300
it plays absolutely a fundamental role
1487
00:53:00,300 --> 00:53:01,770
in everything people do.
1488
00:53:01,770 --> 00:53:02,603
- [Stephen] Really?
- There are very
1489
00:53:02,603 --> 00:53:04,987
few mathematicians who would say,
1490
00:53:04,987 --> 00:53:08,963
"I work on this because
it's just ugly," right?
1491
00:53:08,963 --> 00:53:12,400
I mean, you know, they choose
1492
00:53:13,319 --> 00:53:15,270
the problems, the directions
1493
00:53:15,270 --> 00:53:17,833
based on aesthetic-
- That's just a party line,
1494
00:53:17,833 --> 00:53:19,080
Sergiu, there are all sorts
1495
00:53:19,080 --> 00:53:22,440
of mathematical drabs that we keep hidden.
1496
00:53:22,440 --> 00:53:23,700
Nobody's gonna tell me,
1497
00:53:23,700 --> 00:53:25,620
turbulence is a beautiful subject.
1498
00:53:25,620 --> 00:53:27,300
- Oh, it's a fantastic subject.
1499
00:53:27,300 --> 00:53:29,160
- Fantastic, but not beautiful,
1500
00:53:29,160 --> 00:53:32,910
clumsy, lumbering.
- Well, but
1501
00:53:32,910 --> 00:53:34,770
the expectation is that
1502
00:53:34,770 --> 00:53:39,770
we'll find the beauty in turbulence
1503
00:53:39,780 --> 00:53:42,870
by some discovery.
- Expectations are easily
1504
00:53:42,870 --> 00:53:47,310
purchased, beauty comes at famine prices.
1505
00:53:47,310 --> 00:53:48,240
- All right, kick him
1506
00:53:48,240 --> 00:53:49,840
because he's being perverse now.
1507
00:53:50,850 --> 00:53:52,230
He's being mischievous.
1508
00:53:52,230 --> 00:53:54,960
Last question, Isaac Newton,
1509
00:53:54,960 --> 00:53:57,240
the man who gave us mathematics
1510
00:53:57,240 --> 00:53:59,553
on astronomy, fluid dynamics.
1511
00:54:00,390 --> 00:54:03,270
- The calculus
- And Newton explains a lot.
1512
00:54:03,270 --> 00:54:05,917
Here's a quotation from Newton.
1513
00:54:05,917 --> 00:54:07,980
"A heavenly master governs
1514
00:54:07,980 --> 00:54:12,087
all the world as sovereign
of the universe."
1515
00:54:14,880 --> 00:54:17,010
A recognition of the divine,
1516
00:54:17,010 --> 00:54:19,290
or a mind that transcends our own
1517
00:54:19,290 --> 00:54:22,473
is taken for granted
for thousands of years.
1518
00:54:23,910 --> 00:54:25,920
As recently as Newton,
1519
00:54:25,920 --> 00:54:28,080
and then it gets kicked out
1520
00:54:28,080 --> 00:54:29,100
of intellectual life
1521
00:54:29,100 --> 00:54:31,443
and kicked out of the academy.
1522
00:54:35,010 --> 00:54:39,610
Does the mystery of mathematics suggest
1523
00:54:42,420 --> 00:54:45,880
that the materialist
error was an aberration
1524
00:54:47,070 --> 00:54:51,210
that ought to and may be ending now?
1525
00:54:51,210 --> 00:54:52,950
Are you willing to go that far, Steve?
1526
00:54:52,950 --> 00:54:53,783
- No, of course.
1527
00:54:53,783 --> 00:54:54,750
I think that's exactly right.
1528
00:54:54,750 --> 00:54:56,940
And what Newton illustrates
1529
00:54:56,940 --> 00:54:59,190
so beautifully is this principle
1530
00:54:59,190 --> 00:55:00,270
of intelligibility that we've
1531
00:55:00,270 --> 00:55:03,000
been talking about, that the mathematical
1532
00:55:03,000 --> 00:55:05,400
rationality that can be developed
1533
00:55:05,400 --> 00:55:07,830
by mathematicians without necessarily
1534
00:55:07,830 --> 00:55:11,130
observing nature, does then apply
1535
00:55:11,130 --> 00:55:12,690
to understanding the rationality
1536
00:55:12,690 --> 00:55:13,680
that's built into nature.
1537
00:55:13,680 --> 00:55:15,060
And this was so crucial to
1538
00:55:15,060 --> 00:55:18,210
the period of the scientific revolution
1539
00:55:18,210 --> 00:55:21,360
when the systematic methods
1540
00:55:21,360 --> 00:55:23,190
for interrogating nature,
1541
00:55:23,190 --> 00:55:25,110
for studying nature were developed
1542
00:55:25,110 --> 00:55:27,660
and culminating in figures
1543
00:55:27,660 --> 00:55:29,730
that maybe is no figure like Newton,
1544
00:55:29,730 --> 00:55:32,520
who was so profound in his insight
1545
00:55:32,520 --> 00:55:34,860
and who advanced what was called,
1546
00:55:34,860 --> 00:55:36,360
natural philosophy or science
1547
00:55:36,360 --> 00:55:38,760
so much in one generation,
1548
00:55:38,760 --> 00:55:41,760
even in one year, his fame,
1549
00:55:41,760 --> 00:55:43,890
Annus Mirabilis, where he
1550
00:55:43,890 --> 00:55:48,630
went home during the plague to remediate
1551
00:55:48,630 --> 00:55:51,180
his own deficiencies in mathematics
1552
00:55:51,180 --> 00:55:53,220
and came back having
invented the calculus.
1553
00:55:53,220 --> 00:55:56,583
You know, so.
- A heavenly master, David.
1554
00:56:01,380 --> 00:56:02,253
- What can I say?
1555
00:56:03,090 --> 00:56:04,680
That insight has not been
1556
00:56:04,680 --> 00:56:06,273
vouched safe to me.
1557
00:56:07,200 --> 00:56:08,430
- Fair enough.
1558
00:56:08,430 --> 00:56:10,360
- Sergiu.
- Well, okay, so
1559
00:56:11,430 --> 00:56:14,490
first of all, I think material,
1560
00:56:14,490 --> 00:56:15,540
I mean, materialism is just
1561
00:56:15,540 --> 00:56:17,370
the only explanation of the world,
1562
00:56:17,370 --> 00:56:20,043
it should be put in a ash bin of history.
1563
00:56:20,880 --> 00:56:22,480
And that we both agree.
- Yeah.
1564
00:56:23,760 --> 00:56:26,070
- Bringing God in, sure, why not?
1565
00:56:26,070 --> 00:56:27,300
I mean, that's another way
1566
00:56:27,300 --> 00:56:29,190
of looking at the world.
1567
00:56:29,190 --> 00:56:31,350
If there's something else,
1568
00:56:31,350 --> 00:56:33,030
well, let's find out.
1569
00:56:33,030 --> 00:56:34,800
Maybe, there is another explanation,
1570
00:56:34,800 --> 00:56:36,510
but at this point,
1571
00:56:36,510 --> 00:56:38,100
I don't see any reason
1572
00:56:38,100 --> 00:56:43,100
why you should not look
at that possibility.
1573
00:56:43,290 --> 00:56:46,323
- So God exists.
1574
00:56:47,940 --> 00:56:50,182
And why not?
- Right?
1575
00:56:50,182 --> 00:56:52,920
- Sergiu Klainerman, David Berlinski,
1576
00:56:52,920 --> 00:56:55,620
and Steven Meyer, gentlemen, thank you.
1577
00:56:55,620 --> 00:56:57,273
- It's been our privilege, Peter.
1578
00:56:58,140 --> 00:56:59,280
- For "Uncommon Knowledge,"
1579
00:56:59,280 --> 00:57:02,070
the Hoover Institution and Fox Nation,
1580
00:57:02,070 --> 00:57:03,438
I'm Peter Robinson.
1581
00:57:03,438 --> 00:57:06,855
(upbeat classical music)