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> It was hard for me to get past that point. Why does it bother you that a logician happens to be religious? I myself am a Christian, and some of the most bril

by dvt 5y ago

> It was hard for me to get past that point. Why does it bother you that a logician happens to be religious? I myself am a Christian, and some of the most brilliant people I know happen to be religious (Christian, Muslim, Catholic, Jewish, or otherwise). In fact some of the most brilliant logicians in the history of the world have been religious (from Avicenna, to Anselm, to Gödel, to Kripke).

lisper 5y ago
Not the OP, but what bothers me is not that Knuth is relgious (but see update below), that is perfectly fine. What bothers me is that he chooses to proselytize his religion in a technical publication. That seems inappropriate to me. Imagine the reaction if instead of glorifying God, he had written instead, "Finally, I hope that this paper may glorify Allah the compassionate and merciful..." [UPDATE] I made a mistake here and assumed that Knuth had written this because I happen to know that he's a Christian, but I was wrong about that. And in retrospect I should have realized that I was wrong because Knuth is actually quite scrupulous about keeping his religious views private. But I stand by the substance of my comment subject to s/Knuth/Tøndering.
- dvt 5y ago
  > Not the OP, but what bothers me is not that Knuth is relgious, that is perfectly fine. What bothers me is that he chooses to proselytize his religion in a technical publication. That seems inappropriate to me. First of all, the quote is not by Knuth, but by Claus Tøndering (the author of the paper linked). Second of all, the "Preface," where the quote is snipped from, is just that -- a preface -- a lot of people thank their moms in there. It's just much ado about nothing and annoying posturing. Why is why I, and I'd assume others, take issue with it.
  - lisper 5y ago
    > the quote is not by Knuth, but by Claus Tøndering Sorry, my mistake. I knew Knuth was religious so I assumed it was his quote. I stand by the substance of my comment though. But I agree with you that it's not a huge big deal.
- Bancakes 5y ago
  Math is made by humans to be learned and applied by humans. There's no need for marketing in the form of pretext formalities. If anything, we should savour the human metadata to math - the last decades before AI takes over.
E-Reverance 5y ago
There is an irony to referring to faith when discussing logic.
- eru 5y ago
  Why? Modern math (and logic) explicitly don't make any absolute claims. They are all just "if you take these axioms as given, then you can conclude these theorems." Math doesn't care where you get your axioms from, or why you take them as given. So faith is just as good or bad a source as intuition or empirical evidence as far as logic is concerned. I'm not religious myself, but compatibility with logic is a really, really low bar to clear for any Weltanschauung. (And you can believe that Knuth and the author of the paper are smart enough to be able to reason away any inconsistencies.)
  - necovek 5y ago
    Wonderfully put! To be honest, I struggle to explain this to mathematicians even: many of them do not grasp the fact that axioms are basically the things you put your faith in. I only claim that the main difference between science and religion, which are both based on faith in unprovable statements, is that science invites you to challenge those statements (easy example is the axiom of parallelism), whereas religion doesn't.
    - eru 5y ago
      In some sense, mathematics is just a game you play. Playing round with different axioms is encouraged. Another view at axioms is that they are like an API: Whenever you find a system (real world or elsewhere in math) that fits the axioms of group theory, you can apply all kinds of already proven theorems to it. Very much like building a library on top of an API spec. In this perspective, faith doesn't come into the picture at all: the axioms of a specific theory are just the shape of the socket that you need to fit your plug in to get already proven theorems for free. (A somewhat similar special case is reductions in computer science: where eg you show that some new problem is at least as hard as one we already know to be NP complete.)
Dylan16807 5y ago
I'm a bit weirded out by the implication that a purely abstract number system could be possible or impossible based on the actions of any entity, even a god. That's the only way I can see for God to be glorified in the way described. Yet that would mean that it would be possible to create a universe that has free-thinking mathematicians but in which surreal numbers could not exist even as a concept. Which is quite a claim.
- idiotsecant 5y ago
  I don't think that's so weird. An omnipotent entity controls the rules of reality. It could construct a universe in which contradictory things are true, or whatever it wanted. This is a bit like the puddle assuming the world was made for it because it fits so well into it - we take the rules of our reality for granted but that need not be the case in this thought experiment.
  - Dylan16807 5y ago
    The rules of reality apply to reality, though. It's easy for an omnipotent power to make physics do seemingly contradictory things. But pure logic is not part of reality. You could talk about how a real-life implementation of some element of math doesn't match the logical version derived from a specific set of axioms, but there's no real-life version of surreal numbers in our universe anyway so that's basically true already.
    - idiotsecant 5y ago
      Are you so sure that logic is separate from reality? A great deal of logic depends on physics. Reversing the arrow of entropy, for example, pretty much breaks 'if x, therefore y' statements.
seventytwo 5y ago
It all depends on which axioms you start with…

by dvt 5y ago

lisper 5y ago

Not the OP, but what bothers me is not that Knuth is relgious (but see update below), that is perfectly fine. What bothers me is that he chooses to proselytize his religion in a technical publication. That seems inappropriate to me. Imagine the reaction if instead of glorifying God, he had written instead, "Finally, I hope that this paper may glorify Allah the compassionate and merciful..." [UPDATE] I made a mistake here and assumed that Knuth had written this because I happen to know that he's a Christian, but I was wrong about that. And in retrospect I should have realized that I was wrong because Knuth is actually quite scrupulous about keeping his religious views private. But I stand by the substance of my comment subject to s/Knuth/Tøndering.

dvt 5y ago
> Not the OP, but what bothers me is not that Knuth is relgious, that is perfectly fine. What bothers me is that he chooses to proselytize his religion in a technical publication. That seems inappropriate to me. First of all, the quote is not by Knuth, but by Claus Tøndering (the author of the paper linked). Second of all, the "Preface," where the quote is snipped from, is just that -- a preface -- a lot of people thank their moms in there. It's just much ado about nothing and annoying posturing. Why is why I, and I'd assume others, take issue with it.
- lisper 5y ago
  > the quote is not by Knuth, but by Claus Tøndering Sorry, my mistake. I knew Knuth was religious so I assumed it was his quote. I stand by the substance of my comment though. But I agree with you that it's not a huge big deal.
Bancakes 5y ago
Math is made by humans to be learned and applied by humans. There's no need for marketing in the form of pretext formalities. If anything, we should savour the human metadata to math - the last decades before AI takes over.

E-Reverance 5y ago

There is an irony to referring to faith when discussing logic.

eru 5y ago
Why? Modern math (and logic) explicitly don't make any absolute claims. They are all just "if you take these axioms as given, then you can conclude these theorems." Math doesn't care where you get your axioms from, or why you take them as given. So faith is just as good or bad a source as intuition or empirical evidence as far as logic is concerned. I'm not religious myself, but compatibility with logic is a really, really low bar to clear for any Weltanschauung. (And you can believe that Knuth and the author of the paper are smart enough to be able to reason away any inconsistencies.)
- necovek 5y ago
  Wonderfully put! To be honest, I struggle to explain this to mathematicians even: many of them do not grasp the fact that axioms are basically the things you put your faith in. I only claim that the main difference between science and religion, which are both based on faith in unprovable statements, is that science invites you to challenge those statements (easy example is the axiom of parallelism), whereas religion doesn't.
  - eru 5y ago
    In some sense, mathematics is just a game you play. Playing round with different axioms is encouraged. Another view at axioms is that they are like an API: Whenever you find a system (real world or elsewhere in math) that fits the axioms of group theory, you can apply all kinds of already proven theorems to it. Very much like building a library on top of an API spec. In this perspective, faith doesn't come into the picture at all: the axioms of a specific theory are just the shape of the socket that you need to fit your plug in to get already proven theorems for free. (A somewhat similar special case is reductions in computer science: where eg you show that some new problem is at least as hard as one we already know to be NP complete.)

Dylan16807 5y ago

I'm a bit weirded out by the implication that a purely abstract number system could be possible or impossible based on the actions of any entity, even a god. That's the only way I can see for God to be glorified in the way described. Yet that would mean that it would be possible to create a universe that has free-thinking mathematicians but in which surreal numbers could not exist even as a concept. Which is quite a claim.

idiotsecant 5y ago
I don't think that's so weird. An omnipotent entity controls the rules of reality. It could construct a universe in which contradictory things are true, or whatever it wanted. This is a bit like the puddle assuming the world was made for it because it fits so well into it - we take the rules of our reality for granted but that need not be the case in this thought experiment.
- Dylan16807 5y ago
  The rules of reality apply to reality, though. It's easy for an omnipotent power to make physics do seemingly contradictory things. But pure logic is not part of reality. You could talk about how a real-life implementation of some element of math doesn't match the logical version derived from a specific set of axioms, but there's no real-life version of surreal numbers in our universe anyway so that's basically true already.
  - idiotsecant 5y ago
    Are you so sure that logic is separate from reality? A great deal of logic depends on physics. Reversing the arrow of entropy, for example, pretty much breaks 'if x, therefore y' statements.

seventytwo 5y ago

It all depends on which axioms you start with…