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I don’t mean to derail this contribution, but I want to chat about Principia. I ask honestly and earnestly, how would the Homo sapiens and the cosmos progress a

I don’t mean to derail this contribution, but I want to chat about Principia. I ask honestly and earnestly, how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? I bought the book two years ago but find it terribly difficult to penetrate and understand. I’m looking for motivation on why I should invest time and life energy in the ~6 months it would take me to read and understand it.

lgessler 5y ago
Why do you feel as though you ought to read it? Best to think of PM like any other academic text, I reckon: primarily in conversation with contemporary issues/works, brimming with presuppositions of shared knowledge because of this, and unlikely to be of any great interest to a non-specialist. PM of course is no ordinary academic text, but I don't think it's an exception here.
LudwigNagasena 5y ago
Godel proved the whole endeavor to be futile. Really no point in reading it beyond curiousness.
- schoen 5y ago
  That's not right! Gödel proved that PM couldn't do what people like Hilbert (or PM's authors) hoped it could do. However, we still have * mathematics * formalized mathematics * mathematical research despite the incompleteness phenomenon. All of them are still making progress, even often using approaches that are no more powerful than PM's approach. There are still interesting and important conjectures that can be resolved by a PM-like system, but haven't been resolved yet. I'm sure lots of mathematicians were deeply disappointed when they understood Gödel's result, but it didn't persuade anyone that mathematics was over or that we should no longer work within formal systems!
  - LudwigNagasena 5y ago
    > However, we still have >* mathematics >* formalized mathematics >* mathematical research Yeah, none of them are based on or rely in any way on PM.
    - echopurity 5y ago
      HN can't handle the truth.
- carnitine 5y ago
  That is not even remotely what Goedel did. He showed some inherent limitations to all mathematical formalisation, not that they were useless.
  - LudwigNagasena 5y ago
    Yeah, that’s true, he also showed that the PM project was futile. That’s why no one uses it nowadays, unlike ZFC.
    - drdeca 5y ago
      What are the goals of the project of Principia Mathematica which you are claiming he showed were futile?
      - LudwigNagasena 5y ago
        They are stated in its introduction.
- amw-zero 5y ago
  You don’t understand the incompleteness theorems, that’s for certain.
coldtea 5y ago
>I ask honestly and earnestly, how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? Not much, I'd say. For one, it bears no moral significance. You can be a net negative scumbag and understand Principia Mathmatica. Second, it's a formalization of mathematics. It doesn't necessarily yield relevant new insight to advance homo sapiens beyond it's (quite narrow) scope. Understanding Principia Mathmatica doesn't mean you'll know how to make penicillin, for example. Third, even for pure mathematical work, it's not that interesting in the end. Tons of great math work is being done that has no relation to it.
- schoen 5y ago
  Further to that, there are large ongoing efforts in formalizing mathematics on computers now. https://news.ycombinator.com/item?id=25118372 https://news.ycombinator.com/item?id=25118372 Several of them are getting pretty far, and none of them are directly using PM notation (although all of them ultimately owe something to PM). You can learn more math, or contribute more to math, nowadays by learning one or more of these systems. To my knowledge, all of them are eager for new volunteers to continue formalizing theorems in their respective databases.
- jvvw 5y ago
  Agree, and I suspect only a tiny percentage of mathematicians have read it (I certainly did a degree and doctorate in maths at Oxford and sat the logic and set theory paper in my finals and it never went through my mind to read it). I get the impression that it's one of those books that was very influential in certain ways (Godel read it!) but is more a historical artefact now.
- taneq 5y ago
  Being morally righteous isn't going to teach you to make penicillin either though.
  - coldtea 5y ago
    No, but it's going to improve things for others in several other ways. It's complementary and orthogonal, not a substitute.
skulk 5y ago
The only reason I'd ever read it is as a reference, if I ever wondered "hmm, how did Whitehead and Russell prove this theorem?"
deleted 5y ago
[deleted]
dwheeler 5y ago
> how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? It's important to separate historical importance from importance to understanding by most people. The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. In at least one list, it's one of the most important books in the 20th century. PM shattered any argument that mathematics couldn't have rigorous foundations. PM instead showed that it was possible to start from relatively simple axioms and really prove all the way up to a higher level. PM is NOT, however, important to read or understand itself in detail, as it's been superseded by later works. Syntactically, PM uses a dotted notation instead of parentheses that most people find hard to read & generally undesirable. From a deeper point-of-view, PM uses a set of axioms built on a hierarchy of types. This hierarchy of types was an early effort to avoid various paradoxes. Almost no one uses a hierarchy of types like this today; it's far more common to use Zermelo-Fraenkel set theory with the axiom of choice (ZFC). Even if you wanted to use a hierarchy of types, which is rare, you're probably more likely to use Quine's "New Foundations" which provides a much simpler foundation for mathematics. It's not important to understand PM in detail, but knowing that it's possible has inspired many more recent efforts, and that is more important. I argue in my video "Metamath Proof Explorer: A Modern Principia Mathematica" that the Metamath Proof Explorer (MPE) is a successor to PM. MPE uses modern notation (e.g., parentheses) and ZFC set theory combined with classical logic, so it uses modern conventions, but it also tries to prove "everything" from a very few axioms. Thankfully, we can now use computers to verify every last step (with multiple independent implementations), so we can have much more confidence in the proofs. Here's my video, I think you might like it: https://www.youtube.com/watch?v=8WH4Rd4UKGE https://www.youtube.com/watch?v=8WH4Rd4UKGE That video focuses on MPE, but of course there are several efforts inspired by PM. Understanding the impact that PM had on mathematics is, to me, the important thing.

lgessler 5y ago

Why do you feel as though you ought to read it? Best to think of PM like any other academic text, I reckon: primarily in conversation with contemporary issues/works, brimming with presuppositions of shared knowledge because of this, and unlikely to be of any great interest to a non-specialist. PM of course is no ordinary academic text, but I don't think it's an exception here.

LudwigNagasena 5y ago

Godel proved the whole endeavor to be futile. Really no point in reading it beyond curiousness.

schoen 5y ago
That's not right! Gödel proved that PM couldn't do what people like Hilbert (or PM's authors) hoped it could do. However, we still have * mathematics * formalized mathematics * mathematical research despite the incompleteness phenomenon. All of them are still making progress, even often using approaches that are no more powerful than PM's approach. There are still interesting and important conjectures that can be resolved by a PM-like system, but haven't been resolved yet. I'm sure lots of mathematicians were deeply disappointed when they understood Gödel's result, but it didn't persuade anyone that mathematics was over or that we should no longer work within formal systems!
- LudwigNagasena 5y ago
  > However, we still have >* mathematics >* formalized mathematics >* mathematical research Yeah, none of them are based on or rely in any way on PM.
  - echopurity 5y ago
    HN can't handle the truth.
carnitine 5y ago
That is not even remotely what Goedel did. He showed some inherent limitations to all mathematical formalisation, not that they were useless.
- LudwigNagasena 5y ago
  Yeah, that’s true, he also showed that the PM project was futile. That’s why no one uses it nowadays, unlike ZFC.
  - drdeca 5y ago
    What are the goals of the project of Principia Mathematica which you are claiming he showed were futile?
    - LudwigNagasena 5y ago
      They are stated in its introduction.
amw-zero 5y ago
You don’t understand the incompleteness theorems, that’s for certain.

coldtea 5y ago

>I ask honestly and earnestly, how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? Not much, I'd say. For one, it bears no moral significance. You can be a net negative scumbag and understand Principia Mathmatica. Second, it's a formalization of mathematics. It doesn't necessarily yield relevant new insight to advance homo sapiens beyond it's (quite narrow) scope. Understanding Principia Mathmatica doesn't mean you'll know how to make penicillin, for example. Third, even for pure mathematical work, it's not that interesting in the end. Tons of great math work is being done that has no relation to it.

schoen 5y ago
Further to that, there are large ongoing efforts in formalizing mathematics on computers now. https://news.ycombinator.com/item?id=25118372 https://news.ycombinator.com/item?id=25118372 Several of them are getting pretty far, and none of them are directly using PM notation (although all of them ultimately owe something to PM). You can learn more math, or contribute more to math, nowadays by learning one or more of these systems. To my knowledge, all of them are eager for new volunteers to continue formalizing theorems in their respective databases.
jvvw 5y ago
Agree, and I suspect only a tiny percentage of mathematicians have read it (I certainly did a degree and doctorate in maths at Oxford and sat the logic and set theory paper in my finals and it never went through my mind to read it). I get the impression that it's one of those books that was very influential in certain ways (Godel read it!) but is more a historical artefact now.
taneq 5y ago
Being morally righteous isn't going to teach you to make penicillin either though.
- coldtea 5y ago
  No, but it's going to improve things for others in several other ways. It's complementary and orthogonal, not a substitute.

skulk 5y ago

The only reason I'd ever read it is as a reference, if I ever wondered "hmm, how did Whitehead and Russell prove this theorem?"

deleted 5y ago

[deleted]

dwheeler 5y ago

> how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? It's important to separate historical importance from importance to understanding by most people. The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. In at least one list, it's one of the most important books in the 20th century. PM shattered any argument that mathematics couldn't have rigorous foundations. PM instead showed that it was possible to start from relatively simple axioms and really prove all the way up to a higher level. PM is NOT, however, important to read or understand itself in detail, as it's been superseded by later works. Syntactically, PM uses a dotted notation instead of parentheses that most people find hard to read & generally undesirable. From a deeper point-of-view, PM uses a set of axioms built on a hierarchy of types. This hierarchy of types was an early effort to avoid various paradoxes. Almost no one uses a hierarchy of types like this today; it's far more common to use Zermelo-Fraenkel set theory with the axiom of choice (ZFC). Even if you wanted to use a hierarchy of types, which is rare, you're probably more likely to use Quine's "New Foundations" which provides a much simpler foundation for mathematics. It's not important to understand PM in detail, but knowing that it's possible has inspired many more recent efforts, and that is more important. I argue in my video "Metamath Proof Explorer: A Modern Principia Mathematica" that the Metamath Proof Explorer (MPE) is a successor to PM. MPE uses modern notation (e.g., parentheses) and ZFC set theory combined with classical logic, so it uses modern conventions, but it also tries to prove "everything" from a very few axioms. Thankfully, we can now use computers to verify every last step (with multiple independent implementations), so we can have much more confidence in the proofs. Here's my video, I think you might like it: https://www.youtube.com/watch?v=8WH4Rd4UKGE https://www.youtube.com/watch?v=8WH4Rd4UKGE That video focuses on MPE, but of course there are several efforts inspired by PM. Understanding the impact that PM had on mathematics is, to me, the important thing.