The book talked about in the article is on Springer Link. Luckily my University is subscribed to Springer Link, so I just had to login to my University's VPN and I was able to download this book for free; score!
In Search of Proofs from “The Book”
31–40 of 52 posts
Re: In Search of Proofs from “The Book”
#32As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.
It logically follows that any faith that believes God to be a unitary creator is going to attribute math to Him. Your absolutely correct observation about gaps notwithstanding, the driving question for me here is this: why does math work so well? I personally exclude any explanation that doesn't involve the Logos in some form as incoherent, but I don't have a specific answer and probably never will.
>why does math work so well?
This question really really bothers me. Why can I completely describe gravitational attraction (at certain distances) by just solving for f=g(m1*m2)/r^2? It's truly disturbing when you start appreciating this for the first time.
Re: In Search of Proofs from “The Book”
#33As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.
It logically follows that any faith that believes God to be a unitary creator is going to attribute math to Him. Your absolutely correct observation about gaps notwithstanding, the driving question for me here is this: why does math work so well? I personally exclude any explanation that doesn't involve the Logos in some form as incoherent, but I don't have a specific answer and probably never will.
Math works so well because we consistently abandon any math that doesn't work well.
Re: In Search of Proofs from “The Book”
#34Earlier quoted context omitted.
It logically follows that any faith that believes God to be a unitary creator is going to attribute math to Him. Your absolutely correct observation about gaps notwithstanding, the driving question for me here is this: why does math work so well? I personally exclude any explanation that doesn't involve the Logos in some form as incoherent, but I don't have a specific answer and probably never will.
Math works so well because we consistently abandon any math that doesn't work well.
And where the math of reality seems ugly or awkward or contrived, we invent notation to make it look neat and simple.
The reason why math education takes so many years is to learn all the complexity, conventions and abuse of notation. As in speech and image interpretation, the adept cannot see the complexity.
You can make anything simple by inventing a language to state it in. Use custom entities instead of multiplying them.
Re: In Search of Proofs from “The Book”
#35As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.
What kind of gaps do you mean? As someone who studies mathematics, I feel like this is a vague criticism I've seen some make without any concrete justification.
Not the OP, and he/she mentioned "physical observations" so maybe he/she was only referencing hard sciences like Chemistry or, indeed, Physics, but I am of the same opinion to him/her when it comes to the gap between mathematics and social (for a lack of better word) sciences, which social sciences (and the underlying social component behind them, i.e., us, humans) play a very important role in, well, how the Universe runs, or is seen as running.
In other words, mathematics is very bad at modeling and explaining human behavior, be it in economics, history or even political science (even though one of the best political scientists that ever was, Hobbes, wrote his most famous book by trying to imitate Euclid's "Elements"). This is starting to become particularly important now because we try to build some "AI" functionalities that should imitate humans (and even surpass them) based mostly on mathematics (and some underlying data), but it is my opinion that because of this "gap" between how humans are and what mathematics can tell us about how humans are and behave, it is my opinion I say that those "AI" functionalities will never "become" human enough. Stanislaw Lem's "The Cyberiad" does a much better job compared to me at showing this gap between humans and "machines built on mathematics".
Re: In Search of Proofs from “The Book”
#36As a working mathematician, I'm uncomfortable with this apotheosis of 'the proof'. While there's always room for aesthetics, this might support the rather misleading premise that mathematics is about digging up chiseled beauties, when it is really about hours, days and months of flailing around, trying to understand one thing, or even what it means to understand that thing. And it's rarely pretty.
I feel like the article does a good job of addressing this when it talks about the role of "ugly" proofs. It might deserve more emphasis on this; that all pioneering mathematics starts with this, rather than assigning it a space as a "stepping stone" to the "book proof". But it is true that "cleaning up" after the pioneers is a difficult and interesting part of mathematics, that serves to make it easier for new pioneers to get to the end of the paved trail.
> Q: There’s a famous quote from the mathematician G. H. Hardy that says, “There is no permanent place in the world for ugly mathematics.” But ugly mathematics still has a role, right?
> A: You know, the first step is to establish the theorem, so that you can say, “I worked hard. I got the proof. It’s 20 pages. It’s ugly. It’s lots of calculations, but it’s correct and it’s complete and I’m proud of it.”
> ...
> To do these short and surprising proofs, you need a lot of confidence. And one way to get the confidence is if you know the thing is true. If you know that something is true because so-and-so proved it, then you might also dare to say, “What would be the really nice and short and elegant way to establish this?” So, I think, in that sense, the ugly proofs have their role.
Re: In Search of Proofs from “The Book”
#37Earlier quoted context omitted.
It logically follows that any faith that believes God to be a unitary creator is going to attribute math to Him. Your absolutely correct observation about gaps notwithstanding, the driving question for me here is this: why does math work so well? I personally exclude any explanation that doesn't involve the Logos in some form as incoherent, but I don't have a specific answer and probably never will.
>why does math work so well? This question really really bothers me. Why can I completely describe gravitational attraction (at certain distances) by just solving for f=g(m1*m2)/r^2? It's truly disturbing when you start appreciating this for the first time.
It must have been just as disturbing for the ancients to see how one could count the sheep using a sack full of pebbles. (We, modern people, are too used to the wonders given to us by the - quite abstract, in fact - notion of a number and never question our faith in the applicability of arithmetical operations to the real world.)
Re: In Search of Proofs from “The Book”
#38As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.
So, are the natural numbers human? (Kronecker would famously disagree: Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.)
Re: In Search of Proofs from “The Book”
#39Earlier quoted context omitted.
>why does math work so well? This question really really bothers me. Why can I completely describe gravitational attraction (at certain distances) by just solving for f=g(m1*m2)/r^2? It's truly disturbing when you start appreciating this for the first time.
It must have been just as disturbing for the ancients to see how one could count the sheep using a sack full of pebbles. (We, modern people, are too used to the wonders given to us by the - quite abstract, in fact - notion of a number and never question our faith in the applicability of arithmetical operations to the real world.)
You can hear a band play music from a radio, even though there is no band inside your radio. How? Because electrons in a wire will slosh back and forth in near synchronous response to electrons in a different wire far away. We live in an interactive world where the fact that correlations can occur in matter interactions means that communication is possible.
And the ability to count sheep by counting pebbles is just a generalization of the same principles. One antenna can move in sync with another, without literally being the 'same' antenna. This is indirection or abstraction, depending on how you want to slice it.
The point being, there is no question of why arithmetical operations apply to the real world. The real world permits an infinite variety of valid and useful abstractions. I'd wager it is impossible to imagine a reality where this weren't the case.
Re: In Search of Proofs from “The Book”
#40As a mathematician and a believer in God, I get uncomfortable when people start attributing math to God. I see math as being very much a construct of the human psyche and as astounding as it is, there are enormous gaps between mathematical models and physical observations. So in my mind math is to reality as human is to Divine.
I don't think Erdős seriously, let alone literally, attributed the proofs in question to god in the sense you seem to be interpreting it in.