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Inauguration Day, Inauguration Hooooooraaay!
2018-02-20, 5:38 PM #7521
Quote:
Axioms can't be wrong.


Of course they can.

DId you know that Greek geometry started as an emperical science? It's literally a theory of measurement, and, well, it actually presumes Newtonian physics, because the curvature of space-time is too small to notice.
2018-02-20, 5:45 PM #7522
Originally posted by Reverend Jones:
Of course they can.


They can be improperly formulated, i.e. conflict with previous axioms, but no, a properly stated set of axioms like Euclid's axioms can't be wrong.

That doesn't mean you have to accept Euclid's fifth axiom in all settings, it means when you accept it, in that context you can prove all of the statements that follow.

Originally posted by Reverend Jones:
DId you know that Greek geometry started as an emperical science? It's literally a theory of measurement, and, well, it actually presumes Newtonian physics, because the curvature of space-time is too small to notice.


So what you mean to say is the Greeks misunderstood the relationship between geometry and reality, as in, they took geometry to be a physical science? I'm not sure about that, but if so, then yes, Euclidean geometry doesn't describe reality. For all we know, Minkowski spaces don't either. Mathematics is a structure we impose when approaching the world, and the validity of the model depends on how tightly it agrees with reality. But the mathematics can't be wrong, properly understood, that's absurd.
2018-02-20, 5:50 PM #7523
Quote:
But the mathematics can't be wrong, properly understood, that's absurd.


What's absurd is that you so badly misinterpreted the meaning of Jon`C's post.

All models are wrong, some are more useful than others. Are you that far gone a Platonist to think that math is somehow special and different than other models? Just because two sentient beings can arrive at the same mathematics doesn't mean it exists outside their heads except as the part of some philosophical theory. Which, you guessed it, is also in your head.

Your brain is just a prediction machine, get used to it. Mathematical frameworks can absolutely be wrong if they don't do what they say they do. And Euclidean geometry, as understood the way the Greeks did, is broken for precise enough measurements.
2018-02-20, 5:54 PM #7524
Look, nothing is "wrong" if you're allowed to patch up its interpretation up with further explanation every time a contradiction arises.

"Oh, the bible didn't literally mean that Jesus walked on water. No, that was just an allegory. Don't mind the fact that people probably used to take it as literal."
2018-02-20, 6:07 PM #7525
Originally posted by Reverend Jones:
What's absurd is that you so badly misinterpreted the meaning of Jon`C's post.

All models are wrong, some are more useful than others. Are you that far gone a Platonist to think that math is somehow special and different than other models?


Mathematics isn't a model. Mathematics is the study of how to reach new, interesting conclusion after accepting some basic axioms, and the study of abstract things.

In my view, the origin of mathematical objects is in the a priori forms our consciousness has before understanding the world, and studying mathematics is uncovering the mechanistic parts of consciousness. In other words, it deals primarily with the form of how we are able to even model reality, not with content of the model itself. Physicists care whether Minkowski space or Euclidean space are good models, the mathematician gives no ****s.

You're misunderstanding my post. The mathematical validity of Euclidean geometry, and the validity of the axioms that give rise to it, are wholly independent of any attempt to apply that reasoning to real-world objects. I agree it's a worse model for space, but that doesn't make the axioms "wrong", it makes them "not as good for X purpose". If the purpose is accuracy, they're worse, but accuracy is also far less relevant and misleading when it comes to truth.

Originally posted by Reverend Jones:
Just because two sentient beings can arrive at the same mathematics doesn't mean it exists outside their heads except as the part of some philosophical theory. Which, you guessed it, is also in your head.


I never said math exists outside of our heads. Quite the opposite is my belief, in fact.

Originally posted by Reverend Jones:
Your brain is just a prediction machine, get used to it.


Maybe your brain is just a reductionist stemlord half-baked philosophy.

Originally posted by Reverend Jones:
Mathematical frameworks can absolutely be wrong if they don't do what they say they do. And Euclidean geometry, as understood the way the Greeks did, is broken for precise enough measurements.


Yeah, except, we aren't the Greeks, and what the Greeks thought about geometry has zero impact on how mathematicians understand geometry today. I'm not sure why you're bringing that up, as it's just way off mark.
2018-02-20, 6:09 PM #7526
Quote:
You're misunderstanding my post.


Who cares? I understood the part where you misunderstood Jon`C's post. Everything else is more fodder for you to make this more complicated in order to justify your original mistake.
2018-02-20, 6:10 PM #7527
Originally posted by Reverend Jones:
Just because two sentient beings can arrive at the same mathematics doesn't mean it exists outside their heads except as the part of some philosophical theory.


I guess that depends on what "exists" means?
2018-02-20, 6:11 PM #7528
Originally posted by Reverend Jones:
Look, nothing is "wrong" if you're allowed to patch up its interpretation up with further explanation every time a contradiction arises.

"Oh, the bible didn't literally mean that Jesus walked on water. No, that was just an allegory. Don't mind the fact that people probably used to take it as literal."


Euclidean geometry is 100% as valid today as it was when the ancient Greeks laid it down. They may have been wrong about how to interpret their geometric truths, but that doesn't mean they had to modify the geometry to make it compatible.
2018-02-20, 6:12 PM #7529
Originally posted by Reverend Jones:
Who cares? I understood the part where you misunderstood Jon`C's post. Everything else is more fodder for you to make this more complicated in order to justify your original mistake.


I didn't misunderstand Jon's post, I pointed out that he used axiom incorrectly. He probably knows that and was just speaking carelessly, which is whatever. I have no idea what you're doing now besides making a total ass of yourself.
2018-02-20, 6:13 PM #7530
Read this again and tell me you aren't confused about the intended meaning of the word "wrong" in context.

Originally posted by Jon`C:
Someone else brought up Euclid’s axioms. Which, of course, are wrong. We do not exist in a Euclidean space. We exist in a manifold, a small region of space time that locally resembles a Euclidean space, but is in fact curved. Euclid’s axioms seemed true when they were invented, and for the purposes of useful geometry they might as well be, but in reality there is no such thing as a Euclidean plane.
2018-02-20, 6:15 PM #7531
Originally posted by Reid:
I didn't misunderstand Jon's post, I pointed out that he used axiom incorrectly. He probably knows that and was just speaking carelessly, which is whatever. I have no idea what you're doing now besides making a total ass of yourself.


You do this a lot. You misinterpret people by inserting your own interpretation of the words they use, and accuse them of being "wrong", when all you've done is shifted the epistemic foundation in a way that is inconsistent with their intended meaning.

You can call it sloppiness on their part, but I call it pedantry on your part.
2018-02-20, 6:17 PM #7532
Originally posted by Reid:
I didn't misunderstand Jon's post, I pointed out that he used axiom incorrectly. He probably knows that and was just speaking carelessly, which is whatever. I have no idea what you're doing now besides making a total ass of yourself.


Also, there is a fixed point in your confusion here: the word "axiom" is itself axiomatic. You don't win the argument by changing the meaning of the word axiom.
2018-02-20, 6:21 PM #7533
Originally posted by Reverend Jones:
You do this a lot. You misinterpret people by inserting your own interpretation of the words they use, and accuse them of being "wrong", when all you've done is shifted the epistemic foundation in a way that is inconsistent with their intended meaning.

You can call it sloppiness on their part, but I call it pedantry on your part.


Let me repeat Euclid's axioms, translated from the Ancient Greek:

  • "To draw a straight line from any point to any point."
  • "To produce [extend] a finite straight line continuously in a straight line."
  • "To describe a circle with any centre and distance [radius]."
  • "That all right angles are equal to one another." The parallel postulate:
  • "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."


None of these axioms at all pertain in any way to reality in anyway. They all explicitly deal with only mathematical objects. Calling them "wrong" is therefore a mistake. They aren't describing reality, they're laying out rules for a geometric space.

If one of the axioms said anything about the real world, then yes, they would be wrong, but Euclid never said or did that.

Maybe it was a bit pedantic, and unnecessary. Sure, but being ****ing stupid, pedantic and incorrect about basic mathematical ideas is far worse.
2018-02-20, 6:22 PM #7534
Originally posted by Reverend Jones:
Also, there is a fixed point in your confusion here: the word "axiom" is itself axiomatic. You don't win the argument by changing the meaning of the word axiom.


You're speaking nonsense right now.
2018-02-20, 6:24 PM #7535
OK, have fun talking to yourself, I'm out.
2018-02-20, 6:25 PM #7536
Originally posted by Reverend Jones:
OK, have fun talking to yourself, I'm out.


Try PMing me if you want to have a discussion, instead of acting passive-aggressive and shooting random aggro insults every other page in the thread. It makes you look like a huge *****.
2018-02-20, 6:33 PM #7537
Anybody who wants to understand my point can read my posts.

I still think you took a wrong turn in your interpretation of the word "wrong", so there's not much more to be said (already far too much has been said).
2018-02-20, 6:37 PM #7538
In any case, yeah, pretty much all linear algebra is done over Euclidean space, so named because the geometry of Euclidean space is consistent with the axioms laid out by Euclid.

Obviously, linear algebra has millions of applications to all sorts of things wherein the relevance of Euclidean space to modeling physical space is irrelevant.

Other than that, the specific set of axioms Euclid laid out aren't used very much.
2018-02-20, 6:38 PM #7539
Originally posted by Reverend Jones:
Anybody who wants to understand my point can read my posts.

I still think you took a wrong turn in your interpretation of the word "wrong", so there's not much more to be said (already far too much has been said).


My original post literally said "not sure what you mean by wrong", then went to explain my take on what it meant to help clarify what he was trying to say.
2018-02-20, 6:39 PM #7540
What he wrote was perfectly clear before your attempts to "clarify" it.
2018-02-20, 6:40 PM #7541
Euclid’s axioms are wrong because they purported to be irreducible facts about reality. They aren’t. They describe a particular kind of geometry which exists only within our minds, based on axioms that were chosen to be convenient for us, rather than a faithful representation of something we’ve experienced or something that can be said to have been created by God rather than by man.

This reveals Jordan Peterson’s absurdity. Euclid’s axioms were wholly created by a man, and describe a phenomenon that never existed, that only exists within the imagination of man. Yet those axioms can be used to formulate proofs, something even children are capable of doing. Where is God in this process, in the invention of Euclidean geometry? Nowhere.
2018-02-20, 6:44 PM #7542
And of course axioms can be wrong, just look at the axiom of choice ****show. Mathematicians debate whether axioms should be used or excluded all the time. A lot of the axioms that have been chosen turn out to be equivalent too, so they were never axioms to begin with (like copying line segments in Euclidean geometry).
2018-02-20, 6:49 PM #7543
Originally posted by Jon`C:
Euclid’s axioms are wrong because they purported to be irreducible facts about reality. They aren’t..


I suppose I'm just getting at a semantic distinction, because I don't see any evidence of that in the axioms themselves. I don't doubt that Euclid believed, as in, spoke meta-mathematical commentary on what he believed he was doing, that he was arriving at reality itself, and that the mathematics he laid out were perfect. But there's a gap between the axioms themselves and what one believes the axioms to represent.
2018-02-20, 6:53 PM #7544
Originally posted by Jon`C:
And of course axioms can be wrong, just look at the axiom of choice ****show. Mathematicians debate whether axioms should be used or excluded all the time. A lot of the axioms that have been chosen turn out to be equivalent too, so they were never axioms to begin with (like copying line segments in Euclidean geometry).


Where'd you get the idea that axiom of choice is a "****show"? Accepting the axiom of choice is completely optional, and both branches of accepting or rejecting it lead to wholly valid mathematical systems. There's literally nothing wrong with having two separate versions of mathematics which don't meet in all of the same places.

Like, you can reject the group axioms. You can do tons of mathematics without believing in the existence of groups. There's literally nothing a priori wrong with doing so.

The only reason people might not want to accept the axiom of choice is that accepting it conflicts with meta-mathematical conceptions about what's "right" in mathematics. It creates non-measurable sets and weird "paradoxes", yeah, but nothing that's actually inconsistent or invalid.
2018-02-20, 6:55 PM #7545
Originally posted by Jon`C:
A lot of the axioms that have been chosen turn out to be equivalent too, so they were never axioms to begin with (like copying line segments in Euclidean geometry).


Showing that a statement can be proved as a theorem of other axioms doesn't mean the statement can't be an axiom, it just makes it a pointless axiom.

It's a stylistic concern to try and "cut down" the amount of axioms to the minimum needed.
2018-02-20, 6:56 PM #7546
Speaking of "wrong", holy crap how did I miss this

Originally posted by Reid:
astrophysics or mathematical physics, which are definitely as useless as pure mathematics.


Ever heard of Maxwell's equations? Modern theoretical physics and pretty much all of signal processing can be traced back to the work of Maxwell more than anything else. It's a fantastic theory has stood up well even to quantum mechanics for the most part.
2018-02-20, 6:57 PM #7547
Also, on page 5: read and weep, mathematicians:

Quote:
But the mathematicians of the nineteenth century failed miserably to
grasp the equally great opportunity offered to them in 1865 by Maxwell.
If they had taken Maxwell's equations to heart as Euler took Newton's,
they would have discovered, among other things, Einstein's theory of
special relativity, the theory of topological groups and their linear repre-
sentations, and probably large pieces of the theory of hyperbolic differen-
tial equations and functional analysis. A great part of twentieth century
physics and mathematics could have been created in the nineteenth
century, simply by exploring to the end the mathematical concepts to
which Maxwell's equations naturally lead.
2018-02-20, 7:05 PM #7548
P.S.,

Originally posted by Reid:
live in a world of pure abstraction, we don't care about physics.


at your own risk
2018-02-20, 7:26 PM #7549
Originally posted by Reid:
Where'd you get the idea that axiom of choice is a "****show"?


[quote=Doron Zeilberger]
In my ultrafinitist weltanschauung, the great significance of both Gödel's famous undecidability meta-theorem, and Paul Cohen's independence proof is historical (or as Cohen would put it, "sociological"). Both are reductio proofs that anything to do with infinity is a priori utter nonsense, debunking the age-old erroneous belief of human-kind in the actual (and even potential) infinity. Granted, many statements: like "m+n=n+m for all (i.e. "infinitely" many) integers m and n" could be made a posteriori sensible, by replacing the phrase "for all" (when it ranges over "infinite" sets) by the phrase for "symbolic (commuting) variables (or rather letters) m and n". We have to kick the misleading word "undecidable" from the mathematical lingo, since it tacitly assumes that infinity is real. We should rather replace it by the phrase "not even wrong" (in other words utter nonsense), that cannot even be resurrected by talking about symbolic variables.
[/quote]

In particular:
Quote:
Likewise, Cohen's celebrated meta-theorem that the continuum hypothesis is "independent" of ZFC is a great proof that none of Cantor's א-s make any (ontological) sense.


Originally posted by Reid:
Accepting the axiom of choice is completely optional, and both branches of accepting or rejecting it lead to wholly valid mathematical systems. There's literally nothing wrong with having two separate versions of mathematics which don't meet in all of the same places.


There absolutely is something wrong with a theory that becomes complicated if the ostensible reason for the theory is invalidated by said complexity. I can't remember the name the philosopher who said it, but basically: nothing ever useful in philosophy has ever been said that couldn't be said concisely. If your theory itself is experiencing exponential growth in complexity, it's time to trash the theory itself rather than sit there and rationalize it with further amendments.

Quote:
Like, you can reject the group axioms. You can do tons of mathematics without believing in the existence of groups. There's literally nothing a priori wrong with doing so.

The only reason people might not want to accept the axiom of choice is that accepting it conflicts with meta-mathematical conceptions about what's "right" in mathematics. It creates non-measurable sets and weird "paradoxes", yeah, but nothing that's actually inconsistent or invalid.


It seems you are completely ignoring the role of modelling mathematical theories as an applied activity, within the field of mathematics.
2018-02-20, 7:33 PM #7550
Originally posted by Reverend Jones:
There absolutely is something wrong with a theory that becomes complicated if the ostensible reason for the theory is invalidated by said complexity. I can't remember the name the philosopher who said it, but basically: nothing ever useful in philosophy wasn't said that could be said concisely. If you're theory itself is experiencing exponential growth in complexity, it's time to trash the theory itself rather than sit there and rationalize it with further amendments.


Maybe you don't understand: mathematicians aren't trying to be useful to you, and owe nothing to you. We don't need the stuff we do to be taken the next day and applied in your projects. And in this vein, a huuuuge amount of academic work is not useful to you, most studies won't be useful to you, if it's useful to anyone at all. If mathematicians want to work with physicists or not (they do want to and do work with them), that's not up to you, nor do mathematicians owe it to you.

In case you haven't got it, the point is, your views are irrelevant to what mathematicians do, and no amount of quotebooking is pumping the brakes on that. Mathematicians do what they do because they like doing it, the theories are fascinating and cool, and we derive enjoyment out of them. We don't need you to like it (or be able to understand it) for it to be worth doing.
2018-02-20, 7:47 PM #7551
lol what do I have to do with this?
2018-02-20, 7:48 PM #7552
Originally posted by Reverend Jones:
lol what do I have to do with this?


Many people have an undergraduate phase where they like to dictate to everyone how mathematics should be done. Most get over it by the time they graduate.
2018-02-20, 7:49 PM #7553
You're the one who brought up mathematics. Your point about axioms is still wrong.
2018-02-20, 7:51 PM #7554
I should say, you're the one who introduced mathematics considered as a cloistered academic club. Jon`C was making a very simple and easy to understand point.
2018-02-20, 7:59 PM #7555
PM me if you have anything else you want to discuss.
2018-02-20, 8:00 PM #7556
Why? What are you afraid of?
2018-02-20, 8:02 PM #7557
Originally posted by Reid:
Maybe you don't understand: mathematicians aren't trying to be useful to you, and owe nothing to you. We don't need the stuff we do to be taken the next day and applied in your projects. And in this vein, a huuuuge amount of academic work is not useful to you, most studies won't be useful to you, if it's useful to anyone at all. If mathematicians want to work with physicists or not (they do want to and do work with them), that's not up to you, nor do mathematicians owe it to you.

In case you haven't got it, the point is, your views are irrelevant to what mathematicians do, and no amount of quotebooking is pumping the brakes on that. Mathematicians do what they do because they like doing it, the theories are fascinating and cool, and we derive enjoyment out of them. We don't need you to like it (or be able to understand it) for it to be worth doing.


Incidentally, this is a completely off-topic ad hominem that didn't address a single thing I wrote. But I can't say I'm surprised that you don't understand your mistake if you haven't by now.
2018-02-20, 8:06 PM #7558
For the record, I ****ed up the quote I was trying to paraphrase. I should have said: "nothing ever useful in philosophy has ever been said that couldn't be said concisely."
2018-02-20, 8:07 PM #7559
Originally posted by Reverend Jones:
Why? What are you afraid of?


I'm not afraid of the discussion, but since you're intent on forcing a flame war it shouldn't **** up the forum.

If you want to discuss axioms, I'm willing to do it, but since your level of aggro on me on this forum has been substantial I don't expect you to stay rational for long enough to parse an argument. So go to PM, and maybe instead of desperately trying to win the approval of the other members we can speak like adults.

Originally posted by Reverend Jones:
Incidentally, this is a completely off-topic ad hominem that didn't address a single thing I wrote. But I can't say I'm surprised that you don't understand your mistake if you haven't by now.


You've given plenty of criticisms of how mathematics should be done. You're a pipsqueak, biting at the ankles of giants.
2018-02-20, 8:12 PM #7560
I am perfectly willing to carry on this discussion with you if you try not to take it so personally. Look, you're wrong. Axioms can be wrong. We can agree to disagree on this, because I can see you aren't going to admit your mistake.
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