IS Math Real?

[wayfriend]

was it Heinlein story of a corp with the motto "the difficult we do now, the impossible takes a little longer?" or somesuch??

I don't know about that but it is featured in the classic Billie Holliday song "Crazy He Calls Me", as featured on Galaxy News Radio by its host, the inestimable and unparalleled Three Dog.

"The difficult we do at once; the impossible takes a little longer."
-- the slogan for General Technics; John Brunner, Stand On Zanzibar

Awesome book. Wait ... better than awesome. But it's shelf life is almost gone, I am afraid: a book about 2010 written in 1968. Read it while it is still vital, I implore one and all.

[Hashi Lebwohl]

"The difficult we do at once; the impossible takes a little longer."
-- the slogan for General Technics; John Brunner, Stand On Zanzibar

Awesome book. Wait ... better than awesome. But it's shelf life is almost gone, I am afraid: a book about 2010 written in 1968. Read it while it is still vital, I implore one and all.

Damnit I missed that reference and I even read that book. I concur--an amazing book that you should go read if you haven't already read it.

[Vraith]

There's a difference between objective and real.

--A

I think you're saying something similar to what I mean when I say different kinds of real.
There's a difference between subjective and real, too, after all...and there are demonstrable connections/interactions/communicative pathways between the kinds, even though the mechanisms of such isn't fully described/understood as yet. All the theories/descriptions/structures have problems and/or gaps.

Hashi/WF, YES...I could only remember it was older, and someone I read long ago and had written a fair amount of stuff that bugged me as well as some great stuff.
Very often that is Heinlein.
Brunner transformed from derivative/boring to interesting.
I might still have that book in my parent's attic [my mom has, I'm pretty sure, every book I bought between '74-ish and 81-ish in boxes. It's a LOT of books. Someday I'll reclaim them, I suppose.]

[Avatar]

There is, IIRC, a similar line in Heinlein's Friday when she is studying, she tells a colleague that she answers impossible questions at once, but the difficult ones take a little longer.

--A

[Vraith]

Kind of sort of returning to the question of IS math real...[but not really]...
whether it is or isn't, in combination with fast computers and specialized code, math has just gone ultra-postmodern. A couple just released a paper.
About a Math proof.
What the proof is doesn't matter, really...
What matters is the computer has generated the proof...
And it is so damn BIG that people can't check it to see if it is correct.
[at least no reasonable number of people in a reasonable amount of time.]
The proof is larger than ALL of wikipedia.
And, beyond the sheer size, we have no way of knowing whether or not any person is intelligent and skilled enough to comprehend it even if they COULD run through the whole thing.

[Fist and Faith]

That's amazing! And a scifi plot, for sure. At what point do we trust computers to do everything for us?

[Avatar]

Never!

--A

[peter]

Woah! [Surely the thing would only do what it had been instructed to do though - so somebody must have 'kinda' had an idea as to what it was doing/proving?

[Hashi Lebwohl]

So if the proof is of a size and complexity such that it is highly unlikely that even a team of highly intelligent people will be able to digest and understand it all in a reasonable amount of time we are left with a simply choice: we must decide for ourselves whether or not we believe that the proof is true.

Computers are--for now--incapable of stating a falsehood; their very nature precludes the ability to lie. Yes, they may arrive at conclusions which are false if fed inaccurate data but based on what they were given the result is true. This would lead us to the conclusion "the proof is true"...but what if the data fed into it by the researchers contained an error? We should never inherently trust computers or their results. Of course, what happens when computer A generates results and feeds those results to computer B? We have to look at the original data fed into computer A, clearly.
Also, we know from Godel that in any axiomatic system there will be true statements which cannot be proven using the axioms. Computers should not ever be able to discover one of those non-axiom-based true statements since they have no intuition.

Math is still real, though.

[Vraith]

Woah! [Surely the thing would only do what it had been instructed to do though - so somebody must have 'kinda' had an idea as to what it was doing/proving?

They know the methods/approach/axioms that enable it...and they have a question they want answered. But DEFINITELY don't have the time to check it for mistakes/errors, and MIGHT not have the intelligence to discover if something is wrong or not.
It's like...given exactly the same information, some people can calculate Asquared+Bsquared=Csquared, [and/or check someone else's math] but never apply it, some can apply it but never prove [or understand/check the proof] it, some can prove it but never invent it. [that last relates to what H said about intuition. Many...maybe ALL...of the greatest mathematicians [hell, and folk in lots of other fields] leap somehow to "knowing" [or at least strongly suspecting] whether a thing is so or not. But it isn't at all uncommon for it to take other people, and many years, to provide the proof.

And yes, H, there is the incompleteness thing...what I find interesting is that that becomes a topic of discussion quite often. But people very rarely mention the part that interests me...the inconsistency problem.
I think the inconsistency has consequences of much greater significance and importance to human beings than the incompleteness [though they are intimately connected].

[Fist and Faith]

I got a letter a few months ago from the NY Dept of Taxation. It said we owed $320 from 2011. We used H&R Block, and paid $30 for Peace of Mind, so I emailed them copies of the letter and the 2011 Return. They said Yes, we did, indeed, owe the money. They saw the error on the Return, clear as day. But they don't know how the computer program allowed it to happen. It was something fairly simple that shouldn't have been possible to go wrong the way it did.

So do I trust a computer about an unverifiable proof? Not really. But if it's something that will be put into practice somewhere, applied to a real-world thing, we'll find out.

[peter]

Just watched the original you tube link - Very well done!

One point. The guy mentions the idea of new mathematical proofs, definitions either being 'out there' waiting to be discovered [ie the realist position where math exists prior to it's 'discovery'] or alternatively not existing because they have not yet been 'created' by the human brain. Does not the fact that these new maths proofs/definitions/whatever are not arbitrary - ie they have to conform to thr rules, they cannot be demonstated to break the existing rules - ever - imply that the process *has* to be one of discovery rather than creation, and thus settle the argument in favor of MATH IS REAL!

[Vraith]

Nope, nope, nope.
I insist, and no one has yet come up with even a hint, let alone a proof otherwise...the problem is not real/unreal.

The truth is the "third way."
There is more than one kind of "real." And the kinds of "real" share SOME properties/relationships/necessities, but not ALL of those are common to each and that SOME of the properties/necessities EXCLUDE the properties/necessities of the other "reals."

Even utterly ignoring physical/material realness as if it did not exist...there are pure, perfect, ideal Platonic things that, by pure, perfect, ideal Platonic definition EXCLUDE EACH OTHER.

No, the only answer is different kinds of real.

[peter]

Ahh! Definitions, definitions, definitions. Always definitions!

[Fist and Faith]

https://mindmatters.ai/2022/12/our-phys ... thematics/

Just found this a moment ago. Haven't read it yet. But figured this is a good place for it

[sgt.null]

Math, like Australia 🇦🇺 is not real.

[Fist and Faith]

I just looked at the article. There's really nothing to it. Also a couple of short videos. Ah well

[Wosbald]

+JMJ+

I just looked at the article. There's really nothing to it. Also a couple of short videos. Ah well

I read it. Couldn't find anything incisive to say about it, so I sat on me haunches.

Though I'd heard the question raised obliquely before, I'd ever really thought about the reality of math being seriously put to the question. It must be a philosophical residue. Prolly stemming from Cartesian Dualism?

[Fist and Faith]

Z would have more to say about it, having been studying these ideas much more seriously and for far longer. My thought is that there are two overall possibilities.

1) Chaos. Reality does not act in consistent ways that can be described by mathematics. I don't see how life could exist if this was the case. I doubt structure of any significance could exist.

2) Order. Things happen consistently. Structures exist, because the way things combine one time happens the next time, so it builds and builds. Life was able to come into being. Intelligence was able to come into being. Intelligence is the ability to act on that consistency. Consciousness has the ability to recognize, anticipate, plan for, and utilize that consistency.

[Wosbald]

+JMJ+

Z would have more to say about it, having been studying these ideas much more seriously and for far longer. My thought is that there are two overall possibilities.

1) Chaos. Reality does not act in consistent ways that can be described by mathematics. I don't see how life could exist if this was the case. I doubt structure of any significance could exist.

2) Order. Things happen consistently. Structures exist, because the way things combine one time happens the next time, so it builds and builds. Life was able to come into being. Intelligence was able to come into being. Intelligence is the ability to act on that consistency. Consciousness has the ability to recognize, anticipate, plan for, and utilize that consistency.

Sounds related to the so-called "Problem of the Metalaws". I.e. Given the set of — at least, formerly — uncontroversial Set of Universal Laws (e.g. 2nd Law of Thermodynamics and whatnot), what superordinate set of laws ensures the stability of the subordinate Universal Laws?

IOW, what prevents us from waking up one day and finding out the Law of Gravity is inoperative according to the former, ironclad standard?