Transcript of NPR piece of Principia
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irvanellis
Dec 23, 2010, 1:27:20 PM12/23/10
to Logic-History-Research
National Public Radio had a short piece on C.
The transcript (with a URL for downloading and the audio recording is:
'Principia Mathematica' Celebrates 100 Years
December 22, 2010
Listen to the Story
All Things Considered
[5 min 23 sec] Add to Playlist
Download : http://www.npr.org/2010/12/22/132265870/Principia-Mathematica-Celebrates-100-Years
December 22, 2010
NPR's Robert Siegel talks to math writer Julie Rehmeyer about the
100th anniversary of Principia Mathematica, a landmark work in
mathematical logic. Written by Alfred North Whitehead and Bertrand
Russell, it was their attempt to show that all of mathematics could be
reduced to logic. Rehmeyer writes regular columns for Science News and
Wired Magazine.
Copyright © 2010 National Public Radio®. For personal, noncommercial
use only. See Terms of Use. For other uses, prior permission required.
ROBERT SIEGEL, host:
One hundred years ago this month, Cambridge University Press in
England published a book that lost money, that according to one of its
two co-authors was probably read in full by only six people, but that
influenced the thinking of people who influenced the thinking of other
people, who influenced the thinking of still others, and so on and so
forth.
It was volume one of Bertrand Russell and Alfred North Whitehead's
"Principia Mathematica." Two more volumes of the work would follow.
I am deeply in over my head in these mathematical and philosophical
waters, but Im hoping that Julie Rehmeyer can swim through them a bit.
She writes about math for Science News and for Wired. And she joins us
now from Berkeley, California. Welcome to the program once again.
Ms. JULIE REHMEYER (Science Writer, ScienceNews.org and "Wired"
Magazine): Thank you, delighted to be here.
SIEGEL: And first, describe for us what Bertrand Russell and Alfred
North Whitehead were trying to show in this book that in 1910.
Ms. REHMEYER: They were really trying to rescue math from a deep
crisis of foundations. Mathematicians had found some surprising
results that led them to realize they needed to be a whole lot more
careful than they had been previously.
So, Russell and Whitehead set out to show that math really boiled down
to logic and to define at the very most basic level what mathematics
was, and to show then that all of math was logical consequences from
some very, very simple principles.
SIEGEL: Even if the math they were describing involved things that we
didn't see in everyday life and that seemed to...
Ms. REHMEYER: That's exactly right.
SIEGEL: ...violate common sense.
Ms. REHMEYER: That's exactly right. And in particular, what
mathematicians had found that they were responding to was that they
had discovered non-Euclidean geometries, which are kind of whole
different universes of geometry that are mathematically consistent but
utterly non-intuitive and not at all what we experienced in the
everyday world.
SIEGEL: Where two parallel lines might in fact meet at some point.
Ms. REHMEYER: Well, one version is where two parallel lines might in
fact meet, and another version is where there are lots of different
parallel lines through one point.
SIEGEL: That is a measure of their rigor that Ive read, which is how
long it took them in this work to prove that one plus one equals two.
Ms. REHMEYER: Indeed. It took them well into Volume 2.
(Soundbite of laughter)
Ms. REHMEYER: Eighty pages into Volume 2. And when they proved it,
they have this wonderful little note after it that says: The above
proposition is occasionally useful.
(Soundbite of laughter)
SIEGEL: Now, how influential was this work, or was it simply a big
deal for 1910 and subsequent years but forgotten long after?
Ms. REHMEYER: Well, it certainly has not been forgotten. It's been
very influential. But the interesting thing is it's been influential
in a kind of unexpected and, in some ways, sort of tragic way.
The book kind of laid the seeds for its own undoing. About 20 years
later, a German mathematician named Kurt Godel used what Russell and
Whitehead had done in the Principia to show that it actually couldn't
do what it aimed to do, that it couldn't contain all of math, that
there would be true mathematical statements that were not logical
consequences of the axioms that it set out.
And that really, it was completely shocking, and it completely
transformed our understanding of what math fundamentally is.
So the interesting thing about it is, on the one hand, it kind of
destroyed the whole project, and on the other hand, Godel couldn't
have come to that conclusion without the work of the Principia. So it
kind of ate its own tail in a funny way.
And in a certain way, at this point, one of the biggest contributions
of the book is that it laid the groundwork for computation, even
though that was not in Russell or Whitehead's mind at all. Computers
had barely been conceived of at that point.
CONAN: But you mean the project of writing code for computers?
Ms. REHMEYER: That's exactly right because the Principia is getting
rid of all of the ambiguities of natural language, you know, English
language. And part of the reason that so few people have read is that
it's almost all symbols. It's really almost impossible to read. It's
like sitting down and reading a computer program.
So that process of turning mathematics essentially into code is
exactly what ultimately needs to be done to build computers. And it
had a huge influence on the design of computers that lasts till this
day.
SIEGEL: For us baby boomers who remember Bertrand Russell as largely a
political dissident of the 1950s, this is actually what he was famous
for, is a mathematician, yes?
Ms. REHMEYER: Oh, yeah, absolutely, absolutely. Though, you know, his
political work I think grew out of his mathematical views in many
ways. He saw logic as being fundamental to everything, and his
political beliefs I think grew out of that in many ways.
SIEGEL: Thank you, Julie.
Ms. REHMEYER: Thank you. This was fun.
SIEGEL: Julie Rehmeyer writes about mathematics for Wired Magazine and
Science News. She spoke to us from Berkeley, California.
Copyright © 2010 National Public Radio®. All rights reserved. No
quotes from the materials contained herein may be used in any media
without attribution to National Public Radio. This transcript is
provided for personal, noncommercial use only, pursuant to our Terms
of Use. Any other use requires NPR's prior permission. Visit our
permissions page for further information.
NPR transcripts are created on a rush deadline by a contractor for
NPR, and accuracy and availability may vary. This text may not be in
its final form and may be updated or revised in the future. Please be
aware that the authoritative record of NPR's programming is the audio.
The transcript (with a URL for downloading and the audio recording is:
'Principia Mathematica' Celebrates 100 Years
December 22, 2010
Listen to the Story
All Things Considered
[5 min 23 sec] Add to Playlist
Download : http://www.npr.org/2010/12/22/132265870/Principia-Mathematica-Celebrates-100-Years
December 22, 2010
NPR's Robert Siegel talks to math writer Julie Rehmeyer about the
100th anniversary of Principia Mathematica, a landmark work in
mathematical logic. Written by Alfred North Whitehead and Bertrand
Russell, it was their attempt to show that all of mathematics could be
reduced to logic. Rehmeyer writes regular columns for Science News and
Wired Magazine.
Copyright © 2010 National Public Radio®. For personal, noncommercial
use only. See Terms of Use. For other uses, prior permission required.
ROBERT SIEGEL, host:
One hundred years ago this month, Cambridge University Press in
England published a book that lost money, that according to one of its
two co-authors was probably read in full by only six people, but that
influenced the thinking of people who influenced the thinking of other
people, who influenced the thinking of still others, and so on and so
forth.
It was volume one of Bertrand Russell and Alfred North Whitehead's
"Principia Mathematica." Two more volumes of the work would follow.
I am deeply in over my head in these mathematical and philosophical
waters, but Im hoping that Julie Rehmeyer can swim through them a bit.
She writes about math for Science News and for Wired. And she joins us
now from Berkeley, California. Welcome to the program once again.
Ms. JULIE REHMEYER (Science Writer, ScienceNews.org and "Wired"
Magazine): Thank you, delighted to be here.
SIEGEL: And first, describe for us what Bertrand Russell and Alfred
North Whitehead were trying to show in this book that in 1910.
Ms. REHMEYER: They were really trying to rescue math from a deep
crisis of foundations. Mathematicians had found some surprising
results that led them to realize they needed to be a whole lot more
careful than they had been previously.
So, Russell and Whitehead set out to show that math really boiled down
to logic and to define at the very most basic level what mathematics
was, and to show then that all of math was logical consequences from
some very, very simple principles.
SIEGEL: Even if the math they were describing involved things that we
didn't see in everyday life and that seemed to...
Ms. REHMEYER: That's exactly right.
SIEGEL: ...violate common sense.
Ms. REHMEYER: That's exactly right. And in particular, what
mathematicians had found that they were responding to was that they
had discovered non-Euclidean geometries, which are kind of whole
different universes of geometry that are mathematically consistent but
utterly non-intuitive and not at all what we experienced in the
everyday world.
SIEGEL: Where two parallel lines might in fact meet at some point.
Ms. REHMEYER: Well, one version is where two parallel lines might in
fact meet, and another version is where there are lots of different
parallel lines through one point.
SIEGEL: That is a measure of their rigor that Ive read, which is how
long it took them in this work to prove that one plus one equals two.
Ms. REHMEYER: Indeed. It took them well into Volume 2.
(Soundbite of laughter)
Ms. REHMEYER: Eighty pages into Volume 2. And when they proved it,
they have this wonderful little note after it that says: The above
proposition is occasionally useful.
(Soundbite of laughter)
SIEGEL: Now, how influential was this work, or was it simply a big
deal for 1910 and subsequent years but forgotten long after?
Ms. REHMEYER: Well, it certainly has not been forgotten. It's been
very influential. But the interesting thing is it's been influential
in a kind of unexpected and, in some ways, sort of tragic way.
The book kind of laid the seeds for its own undoing. About 20 years
later, a German mathematician named Kurt Godel used what Russell and
Whitehead had done in the Principia to show that it actually couldn't
do what it aimed to do, that it couldn't contain all of math, that
there would be true mathematical statements that were not logical
consequences of the axioms that it set out.
And that really, it was completely shocking, and it completely
transformed our understanding of what math fundamentally is.
So the interesting thing about it is, on the one hand, it kind of
destroyed the whole project, and on the other hand, Godel couldn't
have come to that conclusion without the work of the Principia. So it
kind of ate its own tail in a funny way.
And in a certain way, at this point, one of the biggest contributions
of the book is that it laid the groundwork for computation, even
though that was not in Russell or Whitehead's mind at all. Computers
had barely been conceived of at that point.
CONAN: But you mean the project of writing code for computers?
Ms. REHMEYER: That's exactly right because the Principia is getting
rid of all of the ambiguities of natural language, you know, English
language. And part of the reason that so few people have read is that
it's almost all symbols. It's really almost impossible to read. It's
like sitting down and reading a computer program.
So that process of turning mathematics essentially into code is
exactly what ultimately needs to be done to build computers. And it
had a huge influence on the design of computers that lasts till this
day.
SIEGEL: For us baby boomers who remember Bertrand Russell as largely a
political dissident of the 1950s, this is actually what he was famous
for, is a mathematician, yes?
Ms. REHMEYER: Oh, yeah, absolutely, absolutely. Though, you know, his
political work I think grew out of his mathematical views in many
ways. He saw logic as being fundamental to everything, and his
political beliefs I think grew out of that in many ways.
SIEGEL: Thank you, Julie.
Ms. REHMEYER: Thank you. This was fun.
SIEGEL: Julie Rehmeyer writes about mathematics for Wired Magazine and
Science News. She spoke to us from Berkeley, California.
Copyright © 2010 National Public Radio®. All rights reserved. No
quotes from the materials contained herein may be used in any media
without attribution to National Public Radio. This transcript is
provided for personal, noncommercial use only, pursuant to our Terms
of Use. Any other use requires NPR's prior permission. Visit our
permissions page for further information.
NPR transcripts are created on a rush deadline by a contractor for
NPR, and accuracy and availability may vary. This text may not be in
its final form and may be updated or revised in the future. Please be
aware that the authoritative record of NPR's programming is the audio.
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