bhhilt.blogg.se

1. #ALFRED NORTH WHITEHEAD INTREST IN MATH FULL#
2. #ALFRED NORTH WHITEHEAD INTREST IN MATH CODE#
3. #ALFRED NORTH WHITEHEAD INTREST IN MATH PLUS#

He saw logic as being fundamental to everything, and his political beliefs I think grew out of that in many ways. Though, you know, his political work I think grew out of his mathematical views in many ways. REHMEYER: Oh, yeah, absolutely, absolutely. 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? And it had a huge influence on the design of computers that lasts till this day.

#ALFRED NORTH WHITEHEAD INTREST IN MATH CODE#

So that process of turning mathematics essentially into code is exactly what ultimately needs to be done to build computers.

It's like sitting down and reading a computer program. And part of the reason that so few people have read is that it's almost all symbols. REHMEYER: That's exactly right because the Principia is getting rid of all of the ambiguities of natural language, you know, English language. Computers had barely been conceived of at that point.ĬONAN: But you mean the project of writing code for computers? So it kind of ate its own tail in a funny way.Īnd 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. 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. 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.Īnd that really, it was completely shocking, and it completely transformed our understanding of what math fundamentally is. The book kind of laid the seeds for its own undoing. But the interesting thing is it's been influential in a kind of unexpected and, in some ways, sort of tragic way. REHMEYER: Well, it certainly has not been forgotten. SIEGEL: Now, how influential was this work, or was it simply a big deal for 1910 and subsequent years but forgotten long after? And when they proved it, they have this wonderful little note after it that says: The above proposition is occasionally useful.

#ALFRED NORTH WHITEHEAD INTREST IN MATH PLUS#

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.

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: Where two parallel lines might in fact meet at some point. 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: Even if the math they were describing involved things that we didn't see in everyday life and that seemed to. 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. 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. REHMEYER: They were really trying to rescue math from a deep crisis of foundations. SIEGEL: And first, describe for us what Bertrand Russell and Alfred North Whitehead were trying to show in this book that in 1910. JULIE REHMEYER (Science Writer, and "Wired" Magazine): Thank you, delighted to be here. And she joins us now from Berkeley, California. She writes about math for Science News and for Wired. 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. It was volume one of Bertrand Russell and Alfred North Whitehead's "Principia Mathematica." Two more volumes of the work would follow.

#ALFRED NORTH WHITEHEAD INTREST IN MATH FULL#

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.