Do you believe in god or math?

[Categories+Sheaves]

Understanding comes not just from our own crippled viewing point, but also from many others, so that a greater, clearer picture may emerge. I guess this is the essence of the scientific method.

Unfortunately, "understanding" can come from group manipulations, where under pressure, sometimes minor pressure, people will agree they saw something just to "go along".

So our "understanding" will be potentially far better, or worse than our own individual view.

If I drive a tank for the army and I get shot while I'm out taking a piss, does this mean the tank's armor can't stop a bullet?
I mean, when my neighbor says something that I think is false, I should be able to say "no, that's wrong for these reasons" or at least "I disagree, but the reasons for my disagreement aren't immediately relevant right now." The compromises we make concerning our knowledge aren't properties of the knowledge itself, right? If I have an unpopular idea that would really advance the current scientific paradigm... my spinelessness in choosing to withhold the information doesn't have anything to do with the fecundity of my idea, right?

However, you did agree that understanding itself is subjective, and capable of being wrong. Even if we have corrected this viewpoint with as many observation aspects as we can currently find, there is always the chance that the understanding can be invalidated with new observational points. (also the scientific method)

The gaps between what we understand, to what we do not understand are huge, and the greasy little uncertainly in our own subjective position makes it suck a bit more.

Okay. But I was arguing that subjectivity alone doesn't create these gaps. We can have gaps in our understanding because we're unreliable observers, reality seems to be much much more complicated than our descriptions of it, et cetera et cetera.

Hence that thing about subjectively stumbling across some gapless understanding of the world. Or alternatively, if our perception of the world was in some sense objective and completely accurate, we could still fail horribly at understanding what is going on. Even if one exacerbates the other, these two issues are not the same things. None of these teeth are coming from subjectivity. These conclusions are coming from the other things you're throwing into the pot.

[The Grand Nudger]

The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

Ever hear of Dyslexia? Right off the bat you are wrong. Why is it that every kid does not score a perfect 100 on their math? Do your kids?

Hmmm right down to the last detail....

I know you are a rational person, but this is delusional. Numbers/math is shared by every human down to the last detail?
Care to prove this?

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

Again, I can accept the entirety of our experience as an illusion (go as many levels down as you like)...including math and numbers. Nonetheless, our illusory civilization (made up of illusory beings) has made an illusory agreement on illusory concepts (themselves illusory) that have the illusion of concordance between themselves and the rest of the collective illusion,......and we call that math.

What does an argument for solipsism add to our understanding of these concepts? Entirely nothing (unless you count misplaced platitudes).

[Abracadabra]

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

You're talking about utterly simple arithmetic there.

Moreover, 1+1=3 or even 1+1=2 is utterly meaningless until those numbers are actually associated with physical quantities.

Here's an equation for you of the form of 1+1=3 that is actually true.

1 pint of milk + 1 cup of milk = 3 cups of milk.

That's 1+1=3 and it's a TRUE statement.

[Modular Moog V]

The collective subjective then, what would you call that? If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail. There's probably a simpler word for that eh?

Ever hear of Dyslexia? Right off the bat you are wrong. Why is it that every kid does not score a perfect 100 on their math? Do your kids?

Hmmm right down to the last detail....

I know you are a rational person, but this is delusional. Numbers/math is shared by every human down to the last detail?
Care to prove this?

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

Again, I can accept the entirety of our experience as an illusion (go as many levels down as you like)...including math and numbers. Nonetheless, our illusory civilization (made up of illusory beings) has made an illusory agreement on illusory concepts (themselves illusory) that have the illusion of concordance between themselves and the rest of the collective illusion,......and we call that math.

What does an argument for solipsism add to our understanding of these concepts? Entirely nothing (unless you count misplaced platitudes).

No, you said this " If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail."

Lets ask various unfortunate Down Syndrome human beings if they can follow your premise. How about those in a coma? Still humans, I presume.
You never answered if your kids get 100 percent scores on their math tests. Did you?

But to answer your question, the solipsism can only point to where we can never have closure. It is a shadow, yes, but how can you get rid of it?

Perhaps you can illuminate us all as to how we can perfect ourselves from this subjective shadow, and have all knowledge/math be perfect to us all as we breath the information from the universe in and out.

I await your revelation, because that is what it would be, if you know how to banish the shadow of solipsism.

[CliveStaples]

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

You're talking about utterly simple arithmetic there.

Moreover, 1+1=3 or even 1+1=2 is utterly meaningless until those numbers are actually associated with physical quantities.

Here's an equation for you of the form of 1+1=3 that is actually true.

1 pint of milk + 1 cup of milk = 3 cups of milk.

That's 1+1=3 and it's a TRUE statement.

You're using a bad notation system, then, because the first "1" means something different than the second "1".

Math doesn't need to refer to physical objects in order for the logic to work out.

You can just say something like this:

1. There is a collection of objects, call it C.
2. There is a way to associate pairs from C with single elements of C; if (x,y) is related to (z), we write f(x,y)=z, or for simplicity write x+y=z
3. In C there exists an object, call it 0, such that for any object c in C, c+0=0+c=c


And so forth. Arithmetic on the natural numbers doesn't work "because" it refers to physical objects; it works because of how it is defined to work.

[The Grand Nudger]

No, you said this " If numbers or math are a wild hallucination...they are a wild hallucination shared by every human being down to every last detail."

Lets ask various unfortunate Down Syndrome human beings if they can follow your premise. How about those in a coma? Still humans, I presume.
You never answered if your kids get 100 percent scores on their math tests. Did you?

But to answer your question, the solipsism can only point to where we can never have closure. It is a shadow, yes, but how can you get rid of it?

Perhaps you can illuminate us all as to how we can perfect ourselves from this subjective shadow, and have all knowledge/math be perfect to us all as we breath the information from the universe in and out.

I await your revelation, because that is what it would be, if you know how to banish the shadow of solipsism.

The shadow of solipsism changes nothing about our understanding of these concepts, it only adds the word illusory (and obviously, plenty of room for unbelievably thick psuedo-intellectual logorrhea.). Math still works within the illusion if that is what our existence is in reality. This isn't a revelation. Solipsism isn't something that has to be dealt with or gotten rid of. It doesn't change anything about our understanding of anything whatsoever, just adds words which provide no additional insight, I'm so sick of retreats to solipsism. It's a juvenile argument, possibly even unbearably so when it comes to something like math.

Perfect knowledge? Good luck with that. I wasn't aware that this was a requirement for knowledge, if it were all knowledge fails to pass the test. These things we know, (including math) must only be correct as far as we can tell, based on as much evidence as possible....and math definitely passes that test. What more are you honestly expecting?

Yes, I said that. I said that because it's a statement of fact. Again, referring to people with disabilities or invoking test scores has nothing to do with math, and everything to do with people, so why do you persist in this?

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

You're talking about utterly simple arithmetic there.

Moreover, 1+1=3 or even 1+1=2 is utterly meaningless until those numbers are actually associated with physical quantities.

Here's an equation for you of the form of 1+1=3 that is actually true.

1 pint of milk + 1 cup of milk = 3 cups of milk.

That's 1+1=3 and it's a TRUE statement.

Simple arithmetic? Simple arithmetic and theoretical physics are both based on the same well demonstrated principles. "Simple arithmetic" is foundational. If the system that we call math were to somehow change the manner in which it is composed or determined as we get beyond "simple arithmetic"..if 1+1=3 at a higher level then it is not uniform, and someone somewhere is incorrect. Fortunately for us this does not occur.

Meaningless? 1+1=3 is a "statement" utterly comprised of meaning..there isn't a wasted breath start to finish. It is incorrect, as is your attempt to shoehorn it in to fit your argument. 1 pint of milk (2/1)+ 1 cup of milk(1/1) = 3 cups of milk (3/3), as has been pointed out, you used bad notation. You wanted your sum in cups, but you failed to account for the number cups in a pint with your equation, which is why it ended up being incorrect (even though the sum was correct...see, in your head you actually added the cups, used proper math, but you didn't express that in your post, because you're trying to manufacture an argument out of thin air). That's why mixing words with meaning into math is a bad idea, and why language complicates arithmetic whilst numbers simplify it, which I think I mentioned pages ago. If you're going to add pints and cups, you have to use notation which demonstrates each unit of measure in relation to each other (which is why I placed the fractions above in parenthesis). This same "equation" could be leveraged to human reproduction, where 1+1=3+....but that's not an accurate representation of the scenario is it? In both cases math is being used to obscure rather than simplify, and it's being done by leveraging bad notation. This isn't highbrow stuff, I don't see what's so hard to understand here.....

1+1=3 is not a true statement, and never will be. Next?

Look, you can both beat your heads into a wall trying to prove that 1+1=3, or that math isn't "perfect", but the arguments presented thusfar are not compelling, it would probably be better to address whatever concepts you've both settled upon that rest on this mistaken assumption..as I'm entirely sure that a discussion about whatever that is would be more interesting than this one. I've been waiting to hear where this is going for ages, if it isn't going anywhere at all (if we're just on a merry go round of bad analogies and poor arithmetic) then I think I've spent enough time in this thread already.

[Categories+Sheaves]

Blaaaaagggghhhhh. Toothless subjectivity monster strikes again.

But this 1 + 1 = 3 business...

Given how we've defined the natural numbers and the addition of numbers and all that stuffs, statements like...
"Given what we defined '1', '2', '+', and '=' to mean, 1 + 1 = 2 is true"
are tautologies. Which is to say, they are absolutely true, but completely devoid of content. The notion that our numbers can exist as a wholly self-contained system based on axioms is certainly valid. But the numbers aren't going to mean anything until we prescribe some way of relating them to the world in front of us, right?

Because (perfectly rigorous*) statements like "This list of axioms implies that theorem" are tautologies, they are absolutely true, but have nothing to do with our world. When said math is situated in regard to the real world, it may be false, but it has something to do with our world. Our world appears to play (somewhat) nicely with our mathematics, but this sort of tension isn't going to ever go away.
(*yes, I know that's another idealization. But poo-poo-ing the rigor of math within this conversation is like a black hole calling the sun dark)
If you agree with that last paragraph, I don't think there's anything more to discuss. If you disagree with that last paragraph, I'm not very interested in continuing this discussion.

[CliveStaples]

Blaaaaagggghhhhh. Toothless subjectivity monster strikes again.

But this 1 + 1 = 3 business...

Given how we've defined the natural numbers and the addition of numbers and all that stuffs, statements like...
"Given what we defined '1', '2', '+', and '=' to mean, 1 + 1 = 2 is true"
are tautologies. Which is to say, they are absolutely true, but completely devoid of content. The notion that our numbers can exist as a wholly self-contained system based on axioms is certainly valid. But the numbers aren't going to mean anything until we prescribe some way of relating them to the world in front of us, right?

That's what makes it such a powerful system. Once you know that something has the structural properties of this meaningless number/arithmetic system, you know how to work in it.

Because (perfectly rigorous*) statements like "This list of axioms implies that theorem" are tautologies, they are absolutely true, but have nothing to do with our world. When said math is situated in regard to the real world, it may be false, but it has something to do with our world. Our world appears to play (somewhat) nicely with our mathematics, but this sort of tension isn't going to ever go away.
(*yes, I know that's another idealization. But poo-poo-ing the rigor of math within this conversation is like a black hole calling the sun dark)
If you agree with that last paragraph, I don't think there's anything more to discuss. If you disagree with that last paragraph, I'm not very interested in continuing this discussion.

It's not true that "they have nothing to do with our world". It depends on whether that axiom holds in our world; if it does, then the theorems hold, and for the same reason that they did in the abstract/"meaningless" setting: because it can't be otherwise, given the axioms.

[Abracadabra]

Care to "prove" that 1+1=3 for somebody somewhere? Any given persons score on a math test has absolutely no bearing over whether or not math is different, that's a measurement of an individual's aptitude and memory with regards to a system.

You're talking about utterly simple arithmetic there.

Moreover, 1+1=3 or even 1+1=2 is utterly meaningless until those numbers are actually associated with physical quantities.

Here's an equation for you of the form of 1+1=3 that is actually true.

1 pint of milk + 1 cup of milk = 3 cups of milk.

That's 1+1=3 and it's a TRUE statement.

Simple arithmetic? Simple arithmetic and theoretical physics are both based on the same well demonstrated principles. "Simple arithmetic" is foundational. If the system that we call math were to somehow change the manner in which it is composed or determined as we get beyond "simple arithmetic"..if 1+1=3 at a higher level then it is not uniform, and someone somewhere is incorrect. Fortunately for us this does not occur.

Meaningless? 1+1=3 is a "statement" utterly comprised of meaning..there isn't a wasted breath start to finish. It is incorrect, as is your attempt to shoehorn it in to fit your argument. 1 pint of milk (2/1)+ 1 cup of milk(1/1) = 3 cups of milk (3/3), as has been pointed out, you used bad notation. You wanted your sum in cups, but you failed to account for the number cups in a pint with your equation, which is why it ended up being incorrect (even though the sum was correct...see, in your head you actually added the cups, used proper math, but you didn't express that in your post, because you're trying to manufacture an argument out of thin air). That's why mixing words with meaning into math is a bad idea, and why language complicates arithmetic whilst numbers simplify it, which I think I mentioned pages ago. If you're going to add pints and cups, you have to use notation which demonstrates each unit of measure in relation to each other (which is why I placed the fractions above in parenthesis). This same "equation" could be leveraged to human reproduction, where 1+1=3+....but that's not an accurate representation of the scenario is it? In both cases math is being used to obscure rather than simplify, and it's being done by leveraging bad notation. This isn't highbrow stuff, I don't see what's so hard to understand here.....

1+1=3 is not a true statement, and never will be. Next?

Look, you can both beat your heads into a wall trying to prove that 1+1=3, or that math isn't "perfect", but the arguments presented thusfar are not compelling, it would probably be better to address whatever concepts you've both settled upon that rest on this mistaken assumption..as I'm entirely sure that a discussion about whatever that is would be more interesting than this one. I've been waiting to hear where this is going for ages, if it isn't going anywhere at all (if we're just on a merry go round of bad analogies and poor arithmetic) then I think I've spent enough time in this thread already.

You are failing to grasp the deeper concept here.

YES, of course, the equation I gave to show how 1+1=3 is a bit of a "trick". However, it is precisely the fact that this trick can be made to work that illustrates my point.

1+1=2 is a totally meaningless statement until the "units" that are being quantified have been made clear. The actual assumption that these units must all have the same quantitative definition is the flaw in the very idealism of the so-called "pure mathematics".

1+1=2 is actually a shorthand notation that does not express the truth of what is required to fully describe the quantitative situation.

What a person must actually be aware of is that this seemingly short and concise mathematical statement is actually far from complete. It's simply shorthand notation that doesn't contain all the necessary information.

It should read:

One unit of well-defined and recognized concept a specific type of quantitative property combined together with another unit of the same well-defined and recognized concept of a the same specific quantitative property in an operation defined as addition will always result in a collection of two units of the same well-defined and recognized concept of a specific type of quantitative property.

That is what 1+1=2 is actually saying.

That's my whole point.

The problem is that those "well-defined" and recognized concepts of specific types of quantitative properties can (in physics) become quite murky. This is especially true in Quantum Physics where they can actually break down altogether.

In fact, this is what the Theory of Quantum Mechanics has basically taught us. It has taught as that at the quantum level of reality "well-defined" and recognizable specific notion of "quantitative properties" breaks down. And thus so does mathematics!

Because the very formalism of mathematics requires that quantitative properties be "well-defined".

That my whole point.

I mean, if you want to talk about applied mathematics in term of building bridges, airplanes, and such, then sure, our mathematics will work perfectly in those situations because everything we are attempting to quantify can indeed be defined in "well-defined" units of quantity.

However, in the more abstract concepts associated with a deeper physics that's trying to get at the "true nature" of reality those "well-defined" units of quantity may no longer exist (just as Quantum Mechanics predicts).

And thus our mathematical formalism breaks down.

Mathematics may not at all be what it has been cracked up to be.

Applied mathematics may be valid.

Extremely abstract "pure" mathematics where the definition of a unit of quantitative property breaks down may be nothing more than a human pipe dream.

Many scientist have actually suggested this, especially with respect to our pursuit of String Theory. Do we really have any reason to believe that mathematics should still be valid at that level of reality?

According to our "most successful scientific theory yet" (i.e. Quantum Mechanics) mathematics should be meaningless below the Planck scale.

Yet all of String Theory rests on the hope and faith that Quantum Theory is wrong and that mathematical quantitative relationships will continue to hold and be well-defined at sub-Planck levels, even thought Quantum Theory says that they won't.

That's where I'm coming from.

Mathematics may have limitation far greater than scientists and mathematicians are willing to face. Our mathematics may not be as "perfect" as we would like to think. It may be nothing more than a reflection of how the macro world works. Period.

And when it comes to the actual true nature of reality it may become totally useless.

That would be scientists and mathematicians worst nightmare, yet it may very well be the truth of reality. Quantum Theory suggest that it very well may be. "Well-defined" units of quantity may simply not exist below the Planck level. And if they don't then mathematics would no longer be valid either.

String Theory would be nothing more than a "reflection". A mirage. All we would be doing with String Theory is trying to push the quantitative nature of macro reality onto the microscopic world where it can't even apply at all.

Many scientists have recognized this possibility. This certainly isn't unique to me. Although I agree strongly that this does appear to be a very plausible case. I even have some possible solutions to offer in the face of this dilemma but that's a whole other story.

---

I should point out also that my replies in this thread are directly related to the actual thread Title and Topic,...

Do you believe in god or math?

That very question seems to imply that mathematics has some almost mystical, magical, or divine truth in it that goes directly to the core of the truth of reality.

That may not be the case at all.

Our mathematical formalism may be nothing more than a reflection of the "well-defined" quantitative properties of the macro world, and be totally inapplicable to the "True Nature" of any underlying reality that may give rise to the macro world.

That's the point that I'm attempting to make.

Comparing math with God (or a notion of divine knowledge) may indeed be a totally invalid and useless analogy.

[The Grand Nudger]

I'm sorry, 1+1=3 is not a "trick" it's just bad math. You determined the object in question in your equation, cups (when you gave the sum in cups).

1 pint plus one cup does equal three cups, but that doesn't make 1+1=3 true, any more than it disproves 1+1=2.

There is no deeper concept, you have no point.

Belief in math is a prerequisite that you have decided to add (which does not belong) to make a comparison that does not exist.