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“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.” Why is there a tendency to invoke God in

“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.” Why is there a tendency to invoke God in math?

QuesnayJr 6y ago
Because it sounds good rhetorically. It is similar to the tendency to declare someone who's really good at X "the god of X".
gchamonlive 6y ago
I think that would be because God is nature (for those who believe in God) and math is how humans describe nature. That would be the same as saying that nature can't be expressed in its own language any simpler than this.
- unixbeard1337 6y ago
  What aspect of nature does the sensitivity conjecture describe?
  - gchamonlive 6y ago
    What do you suppose is the answer to this question, other than the Conjecture itself? I was talking about nature as in "the universe we live in". Answering that question is just describing the problem itself.
great_wubwub 6y ago
FFS take a few seconds and read the article. "Aaronson and O’Donnell both called Huang’s paper the “book” proof of the sensitivity conjecture, referring to Paul Erdős’ notion of a celestial book in which God writes the perfect proof of every theorem. " and read the article that sentence links to.
- scythmic_waves 6y ago
  I think that's just another example of what OP is referring to. Erdős, a mathematician, invoked God.
  - AnHonestComment 6y ago
    I don’t get the question. Are we asking why some people in a largely Christian society refer to God as a concept? That answer seems obvious. Are we asking why some people playfully refer to quotes from famous people when giving praise? Again, that seems obvious. What, specifically, is being asked? OP hasn’t shown that mathematicians refer to God any more often than society at large.
- the_local_host 6y ago
  It's not a terrible question, and even if the reference to God is via Erdős, there's still a reference. I think it's evident in the sciences as well, e.g. "God does not play dice with the universe."
- yesenadam 6y ago
  > FFS take a few seconds and read the article. Please read the HN guidelines. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
diffeomorphism 6y ago
A) There isn't. B) It is a figure of speech that somewhere there is a book of "perfect" proofs/blueprint of the universe. Presumably whatever concept you call "God" has access to this, just like "Death" has a list of all living things etc..
ColinWright 6y ago
It's a shortcut, they're not literally invoking "God". It's an encoding of: We don't know what the optimum is, but we can imagine the complete set of possible things, and from those there will be one that's best. So that's the optimum, and we want to refer to it. We don't know what it is, but we assume it exists, so let's just call it 'God's solution'
- blt 6y ago
  > we can imagine the complete set of possible things, and from those there will be one that's best. Not necessarily, unless we make some more assumptions about the set of proofs and/or the proof goodness function ;)
  - drdeca 6y ago
    Indeed, but I expect that that for any theorem, that for some level of proof quality which is attained, that all proofs that are at least that good, all have at most a certain finite length. And, as there are only finitely many proofs of any finite length, then the supremum of proof quality over any proofs of that theorem, is attained. (whether there is usually unique proof which attains it, I don't care to guess.)
erdevs 6y ago
Mathematics often deal in abstractions, and "God" may be used as a linguistic abstraction for ideal or perfect knowledge. It's a shorthand in writing casually about the most elegant mathematical insights. Its use is also a tradition via Erdos with "The Book", which Aaronson and many mathematicians pay homage to.
- adamnemecek 6y ago
  I understand what it means, but I still don't like it.
  - AlanYx 6y ago
    If it's any consolation, Erdős himself said in one famous lecture that the "God" part is irrelevant: "You don't have to believe in God, but you should believe in The Book."
- michannne 6y ago
  Right. AFAIK there is no universal Math deity like there is Caissa for chess that can serve as a representation of "perfect math", God is the next best thing.
scythmic_waves 6y ago
I think about this sometimes. I think it's related to my interest in the philosophy of mathematics. From the SEP article [1]: > Bernays observed that when a mathematician is at work she "naively" treats the objects she is dealing with in a platonistic way. Every working mathematician, he says, is a platonist (Bernays 1935). I think that's why. There's a tendency to think of mathematical objects platonically. And given that it would be very odd if platonic, mathematical objects interacted causally with our universe, well, it's a short hop, skip, and a jump over to that meaning they're things a God made. And here I mean "God" in a root-of-all-things sense, not a Judeo-Christian or similar sense. Also, I don't think you deserve the downvotes you're getting. There may be a tone of condescension, and there may not be. But there's a totally charitable way of interpreting that question -- you noting a trend that you perceive -- and that's how I took it. [1] https://plato.stanford.edu/entries/philosophy-mathematics/ https://plato.stanford.edu/entries/philosophy-mathematics/
soledades 6y ago
FWIW, most mathematicians surveyed are "Mathematical Platonists," meaning they believe that mathematical objects exist in a way outside the human mind/the physical universe. This mathematical "realm" is a very natural home for the variety of God a mathematician is likely to imagine. Alternatively, if you like, God is one of the most powerful metaphors we as humans have.
sethc2 6y ago
I think it’s because God is often seen as the infinite, or uncreated, or all that can be known. The something that exists apart from any material existence. Mathematical relationships and patterns have this quality. Really what I wonder is why can’t we all just believe in god again? Even if it was just to recognize the fact that there are things that exist in an immaterial way. That there are things that are good and true and beautiful whose goodness truth and beauty is not quantifiable or reduced to some set of atoms. We might disagree on what things are better physical manifestations of the immaterial things, but we don’t need to disagree on their existence. Though I think it is because so many people have said “god is like this” and then posit some religious thing that affirms their often heinous actions, that people have chosen to say yeah I don’t believe in that. But it seems sad that we can’t just talk about god in the sense of there are things bigger than ourself, even if we don’t know them because they are unknowable. Even if we just acknowledged “God” as the first cause or the existence of things not material (like 2+2=4 is true even if there was no material thing to represent it), I feel like we could go a long way to finding that us humans, usually have more in common than we have not in common. That the things that divide us are actually smaller than the thing that unites us. (I don’t see why your question was downvoted by the way)
GuB-42 6y ago
In most religions, God is an omnipotent, omniscient, and generally perfect being. Mathematicians simply borrowed that definition. For example, Rubik's cube "God's number" is 20. Because, of course, God, as an omniscient, omnipotent perfect being will solve the puzzle in the minimum possible amount of moves. And that number is 20 in the most complex case. Computer science have a similar, more formal concept with oracles. An oracle is a machine that can quickly solve a problem. How it does it is not the question, it can be supernatural, but we simply assume that such a machine exists in order to study some theoretical problems.
- vlowther 6y ago
  The overwhelming majority of religions are not monotheistic and believe no such thing about any given deity. /nitpick
deleted 6y ago
[deleted]

“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.” Why is there a tendency to invoke God in math?

QuesnayJr 6y ago

Because it sounds good rhetorically. It is similar to the tendency to declare someone who's really good at X "the god of X".

gchamonlive 6y ago

I think that would be because God is nature (for those who believe in God) and math is how humans describe nature. That would be the same as saying that nature can't be expressed in its own language any simpler than this.

unixbeard1337 6y ago
What aspect of nature does the sensitivity conjecture describe?
- gchamonlive 6y ago
  What do you suppose is the answer to this question, other than the Conjecture itself? I was talking about nature as in "the universe we live in". Answering that question is just describing the problem itself.

great_wubwub 6y ago

FFS take a few seconds and read the article. "Aaronson and O’Donnell both called Huang’s paper the “book” proof of the sensitivity conjecture, referring to Paul Erdős’ notion of a celestial book in which God writes the perfect proof of every theorem. " and read the article that sentence links to.

scythmic_waves 6y ago
I think that's just another example of what OP is referring to. Erdős, a mathematician, invoked God.
- AnHonestComment 6y ago
  I don’t get the question. Are we asking why some people in a largely Christian society refer to God as a concept? That answer seems obvious. Are we asking why some people playfully refer to quotes from famous people when giving praise? Again, that seems obvious. What, specifically, is being asked? OP hasn’t shown that mathematicians refer to God any more often than society at large.
the_local_host 6y ago
It's not a terrible question, and even if the reference to God is via Erdős, there's still a reference. I think it's evident in the sciences as well, e.g. "God does not play dice with the universe."
yesenadam 6y ago
> FFS take a few seconds and read the article. Please read the HN guidelines. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html

diffeomorphism 6y ago

A) There isn't. B) It is a figure of speech that somewhere there is a book of "perfect" proofs/blueprint of the universe. Presumably whatever concept you call "God" has access to this, just like "Death" has a list of all living things etc..

ColinWright 6y ago

It's a shortcut, they're not literally invoking "God". It's an encoding of: We don't know what the optimum is, but we can imagine the complete set of possible things, and from those there will be one that's best. So that's the optimum, and we want to refer to it. We don't know what it is, but we assume it exists, so let's just call it 'God's solution'

blt 6y ago
> we can imagine the complete set of possible things, and from those there will be one that's best. Not necessarily, unless we make some more assumptions about the set of proofs and/or the proof goodness function ;)
- drdeca 6y ago
  Indeed, but I expect that that for any theorem, that for some level of proof quality which is attained, that all proofs that are at least that good, all have at most a certain finite length. And, as there are only finitely many proofs of any finite length, then the supremum of proof quality over any proofs of that theorem, is attained. (whether there is usually unique proof which attains it, I don't care to guess.)

erdevs 6y ago

Mathematics often deal in abstractions, and "God" may be used as a linguistic abstraction for ideal or perfect knowledge. It's a shorthand in writing casually about the most elegant mathematical insights. Its use is also a tradition via Erdos with "The Book", which Aaronson and many mathematicians pay homage to.

adamnemecek 6y ago
I understand what it means, but I still don't like it.
- AlanYx 6y ago
  If it's any consolation, Erdős himself said in one famous lecture that the "God" part is irrelevant: "You don't have to believe in God, but you should believe in The Book."
michannne 6y ago
Right. AFAIK there is no universal Math deity like there is Caissa for chess that can serve as a representation of "perfect math", God is the next best thing.

scythmic_waves 6y ago

I think about this sometimes. I think it's related to my interest in the philosophy of mathematics. From the SEP article [1]: > Bernays observed that when a mathematician is at work she "naively" treats the objects she is dealing with in a platonistic way. Every working mathematician, he says, is a platonist (Bernays 1935). I think that's why. There's a tendency to think of mathematical objects platonically. And given that it would be very odd if platonic, mathematical objects interacted causally with our universe, well, it's a short hop, skip, and a jump over to that meaning they're things a God made. And here I mean "God" in a root-of-all-things sense, not a Judeo-Christian or similar sense. Also, I don't think you deserve the downvotes you're getting. There may be a tone of condescension, and there may not be. But there's a totally charitable way of interpreting that question -- you noting a trend that you perceive -- and that's how I took it. [1] https://plato.stanford.edu/entries/philosophy-mathematics/ https://plato.stanford.edu/entries/philosophy-mathematics/

soledades 6y ago

FWIW, most mathematicians surveyed are "Mathematical Platonists," meaning they believe that mathematical objects exist in a way outside the human mind/the physical universe. This mathematical "realm" is a very natural home for the variety of God a mathematician is likely to imagine. Alternatively, if you like, God is one of the most powerful metaphors we as humans have.

sethc2 6y ago

I think it’s because God is often seen as the infinite, or uncreated, or all that can be known. The something that exists apart from any material existence. Mathematical relationships and patterns have this quality. Really what I wonder is why can’t we all just believe in god again? Even if it was just to recognize the fact that there are things that exist in an immaterial way. That there are things that are good and true and beautiful whose goodness truth and beauty is not quantifiable or reduced to some set of atoms. We might disagree on what things are better physical manifestations of the immaterial things, but we don’t need to disagree on their existence. Though I think it is because so many people have said “god is like this” and then posit some religious thing that affirms their often heinous actions, that people have chosen to say yeah I don’t believe in that. But it seems sad that we can’t just talk about god in the sense of there are things bigger than ourself, even if we don’t know them because they are unknowable. Even if we just acknowledged “God” as the first cause or the existence of things not material (like 2+2=4 is true even if there was no material thing to represent it), I feel like we could go a long way to finding that us humans, usually have more in common than we have not in common. That the things that divide us are actually smaller than the thing that unites us. (I don’t see why your question was downvoted by the way)

GuB-42 6y ago

In most religions, God is an omnipotent, omniscient, and generally perfect being. Mathematicians simply borrowed that definition. For example, Rubik's cube "God's number" is 20. Because, of course, God, as an omniscient, omnipotent perfect being will solve the puzzle in the minimum possible amount of moves. And that number is 20 in the most complex case. Computer science have a similar, more formal concept with oracles. An oracle is a machine that can quickly solve a problem. How it does it is not the question, it can be supernatural, but we simply assume that such a machine exists in order to study some theoretical problems.

vlowther 6y ago
The overwhelming majority of religions are not monotheistic and believe no such thing about any given deity. /nitpick

deleted 6y ago

[deleted]