Large Hardon Collider

[Khamsin]

Hmm, I don't really believe that to be the case.


Language changes all the time, based on how people speak and the way in which they wish to communicate. Math doesn't. The way people use math changes. But the math never does.

Math has changed, in the sense of beginning with basic arithmetic, working its way up to algebra, calculus, differential equations, and such. I doubt the first people of earth dealt much with partial derivatives, although I'm certain they were able to distinguish between one apple and two.

However, it could be said that its simply a slow expansion of the discovery of math. Which suggests we may not know all that math has to offer yet, and some time in the future we may have additional mathematical disciplines beyond what we have today.

[zoobernut]

Math has changed, in the sense of beginning with basic arithmetic, working its way up to algebra, calculus, differential equations, and such. I doubt the first people of earth dealt much with partial derivatives, although I'm certain they were able to distinguish between one apple and two.

However, it could be said that its simply a slow expansion of the discovery of math. Which suggests we may not know all that math has to offer yet, and some time in the future we may have additional mathematical disciplines beyond what we have today.

Math hasn't changed what you are talking about are all things added to math. Math that was discovered hasn't changed and we have just added to our knowledge of math over time.

I still agree with Max, math exists whether or not there is a language to describe it. We just created a series of symbols and languages around it in order to communicate what was already there.

[Max™]

Exactly, these principles exist whether there is a language to describe them, or a Universe to observe them within.

The relationships and axioms of mathematics are not arbitrary or open to interpretation, mathematics is the only system in which you can define an absolutely true statement.

A circle is always produced by rotating a line attaching two points about one of those points. That shape is always 3.14159~ times as long as the twice the length of the line used in it's construction. The relationships between those angles and the lengths involved are always the same, regardless of the labels and names applied to them.

We didn't make circles work like this, we found that every circle anywhere, ever, has worked like this, and can be safely assumed to work like this.

[Kuya]

Yea, but this is all metaphysical talk. Can you prove that numbers exist as a concept without a thinking creature in the equation? No. So it's not empirical. However, as long as we've taken that into consideration then i suppose there's no problem, but talking about it as if it were a fact on the other hand...

[Khamsin]

Can you prove that numbers exist as a concept without a thinking creature in the equation? No.

Is this really a "If a tree falls in the forest, and no one is around to count it..." type question?

[Kuya]

Of course, do you have a problem with the rhetorical question?

I would say, if no one was ever around to see/hear/verify that a tree fell, then the question is pointless. If no one knew that the tree fell, then how did you find out about the tree falling in order to ask me that question?

Saying that numbers exist outside of our understanding is a pointless thing to say. That's not cognisant.

[Max™]

Yes the tree fell, it is ridiculous to argue otherwise.

There is a reality out there independent of your observation, unless you're seriously a solipsist, at which point you're basically a house cat.

All circles possessed diameters which were related by pi to their circumference, before any human lived to notice.

All triangles possessed angles which added up to 180 degrees, before anyone ever drew a triangle.

We discovered these facts, we did not invent them.

[Kuya]

Except that a solid object is not the same as an abstract concept. Not that i should have to point that out.

edit: if you say that the tree fell then that means SOMEONE has infact confirmed that it fell, therefore making the question irrelevant, since the answer is given by the question.

[Khamsin]

Of course, do you have a problem with the rhetorical question?

I would say, if no one was ever around to see/hear/verify that a tree fell, then the question is pointless. If no one knew that the tree fell, then how did you find out about the tree falling in order to ask me that question?

Saying that numbers exist outside of our understanding is a pointless thing to say. That's not cognisant.

It's not entirely pointless when you consider, say, something like astrophysics where numerous calculations are done to determine properties of things you can't even see, based on the assumption that other things you can't see are happening.

How can we look at a distant star and observe its motion and calculate the deviation from its expected motion and determine that another body must be nearby that is influencing it, and then go on to determine the properties of said unseen object using numbers and calculations, without the basic assumption that it's still been having an effect on things around it even if it has never been observed?

Everything influences everything else. A speck of dust a billion miles away still (negligibly) affects our orbit through space, and things would be (negligibly) different if that speck of dust were not there. Our observations of the world around us unknowingly include information about the universe billions of light years away in any direction, whether we are cognizant of it or not, and whether we know how to interpret that information or not.

However, our lack of comprehension of things we haven't seen and may never see doesn't cancel the effect those unseen things have on that of which we are aware.

[Kuya]

You are talking about two separate things. It is one thing to say that something exists because we can detect its effects, and it's another thing completely to say that we calculate the position of an object based on the supposition that it exists and functions according to the laws of physics.

[Max™]

Except that a solid object is not the same as an abstract concept. Not that i should have to point that out.

edit: if you say that the tree fell then that means SOMEONE has infact confirmed that it fell, therefore making the question irrelevant, since the answer is given by the question.

Gotta be trolling.

I'm saying I can observe that the laws of physics hold true in any reference frame, that trees exist, and that from time to time they fall down.

I can therefore state with absolute certainty that there has never been a tree which fell upwards (barring things exploding beneath them and ejecting them into space).


I do not take the observation causes collapse postulate as a serious fact about the Universe. Things do not have a nonexistent state before they are observed, the wave function arguments are just showing that we still do not fully understand quantum physics.

The Moon does not stop existing if I am not looking at it.

If a tree were mysteriously on the far side of the moon and it died, I can say for certain that it fell over, deeper into the gravity well of the moon.

I do not have to observe it to know it happened.


As for concepts, there is very little difference ultimately when you get deep into physics, the only true difference is that concepts appear to exist in a sense which we can not truly say objects possess, due to the limitations of being a part of this Universe on our observations.

If another being in some hypothetical n-dimensional universe considered the geometric properties of a simple 2 dimensional space, they would discover concepts such as pi, if the geometry of their Universe were different they may conclude pi had a different value, but logically they could conclude that in a Universe such as we find ourselves within, pi would have the value we observe for it.

[Khamsin]

You are talking about two separate things. It is one thing to say that something exists because we can detect its effects, and it's another thing completely to say that we calculate the position of an object based on the supposition that it exists and functions according to the laws of physics.

It goes deeper than detecting effects. If you walk outside and look at the way the grass ripples in the wind or the shape of the clouds, everything is the way it is due to the influence of everything else. If a tree fell somewhere and nobody ever finds out or ever becomes aware of it, it still has an influence on the environment. Perhaps the grass rippled a certain way because of it, but when you see it you have no idea what it means. You don't even think about it.

By virtue of you seeing the grass ripple, the wave state has collapsed, the tree has fallen. But due to the impossibility of working backwards from the grass ripple to determine the exact cause, nobody is aware it has happened.

Consider also everything that happened in the universe before you were born, and that the first time you opened your eyes, what you saw was only the way it was because of the last few billion years. Yet, we'll never know exactly what it was that happened. We can make educated guesses based on our current observations and calculations, but we'll never know for sure. However, it has all indeed happened because we've witnessed the distant effects of the events in the environment around us without ever becoming cognizant of what it all means.

If we had the theory of everything, it'd be consistent with everything we can observe, right down to the way the grass ripples. And we'd be able to know a tree fell without ever observing or verifying it or being conscious of its effects, because mathematically it had to have happened that way and we can take it for . We'd also be able to work backwards and determine every unwitnessed event that happened in the universe since the beginning of time.

[Kuya]

Uh huh. Okay.

Let me try this again.

The point in saying that math is universal truth is that math is very very accurate for prediction? I, like Kaylia, don't really get your point, or why you're concluding something like "the universe is math" as fact. I've read the entire argument and alls i keep coming back to is:

"Why?"

[Max™]

I said you could argue that the Universe is made of mathematics.

When you look at it's structure, mathematics emerges naturally, this is saying something which we're not very good at hearing.

I didn't say it was a fact, but I did say that math is not something we made, it is something we found, that is a fact.

We didn't make the logical structures and axioms work, we noticed they work and made a language to describe this, the numbers and symbols which people traditionally think of as "being" mathematics. There is a fundamental truth behind that language though, whereas there is no fundamental truth behind say, the alphabet. It is simply a series of symbols we created to describe other abstractions.

[Kuya]

Fundamental truth. Ugh.

[Khamsin]

Just wait until someone comes up with an entirely different way to describe the universe in the same capacity mathematics does, but without simply being a wrapper for mathematics. That is, not redefined terminology and renamed numbers, or a different base, but a completely different system. One that you could use to design functional electronic equipment and discover new planets without a single number or equation (and there would be nothing analogous to numbers and equations in the new system).

That'll put an end to the discussion.

[Kuya]

I think will just let it slide. This seems like one of those no end in sight arguments, and i'm having trouble taking it seriously. These arguments remind me of how Hume and Kant argued that causuality and contrast (among others) were "fundamental truths" in regards to the human brain/mind. Of course, Hume said that these were in the brain and they imposed themselves on reality (seeing causuality where there may be none) and Kant argued, much like you guys, that causuality is not in the brain, but rather it is a metaphysical and fundamental truth that governs reality.

I never really had a problem with what they said, so i suppose i shouldn't have a problem, but i never took it seriously either.

[Khamsin]

These arguments remind me of how Hume and Kant argued...

Ok, Mr. Hoekstra.

[Kuya]

Yea... That's a good use of meme, Khamsin.

[Kaylia]

said you could argue that the Universe is made of mathematics.

When you look at it's structure, mathematics emerges naturally, this is saying something which we're not very good at hearing.

I didn't say it was a fact, but I did say that math is not something we made, it is something we found, that is a fact.

We didn't make the logical structures and axioms work, we noticed they work and made a language to describe this, the numbers and symbols which people traditionally think of as "being" mathematics. There is a fundamental truth behind that language though, whereas there is no fundamental truth behind say, the alphabet. It is simply a series of symbols we created to describe other abstractions.

Your argument make as much sense as one made by someone who firmly believe that the egg came before the chicken.

Why can't it simply be a language that we made to understand the universe? Can you give me one argument against it, or show me why it makes less sense this way?

Just because you see "number" and "mathematics" in the universe doesn't mean it's something more fundamental. It's a fact that you can build mathematics using the axioms you want. When we work with a strucure made to be similar to the one we observe, we will obviously see that structure in our observation.

Hmm, I don't really believe that to be the case.


Language changes all the time, based on how people speak and the way in which they wish to communicate. Math doesn't. The way people use math changes. But the math never does. People use math incorrectly to describe their topic of conversation, thereby resulting in something that is later proven incorrect, because the information they had of the system was not the entirety, and as a result their theory is overwritten by a new one based on other data acquired at a later date. However, the math used between these two theories did not change. The operands and calculations were exactly the same. The difference is one person communicated the process incorrectly, either due to human error or lack of sufficient data. And of course, the person doing this correction may also be corrected later by another who discovers an error in the math they used to explain their theory. But once again, their use of math to disclaim the other will still follow the same route.

Language, on the other hand, changes with society. The rules of English change all the time, or worse, they're simply ignored. As other societies develop, other languages are lost. We cannot return later to an ancient civilization and know what it was they were attempting to communicate with themselves, and perhaps with us, using our language. Especially in cases where the very structure of our dichotomy is different. IE many languages are currently rooted in Latin, so some crossover is observed between them; yet there are other languages that do not have these roots and one cannot simply assume the meaning of words based on language root, because the roots of the languages are different and the structure in which they're interpreted may not be the same. However, you can examine any concept you desire with math, regardless of how old this concept is or who developed it, without needing a dedicated translation tool in order to understand it. People's theories change, their understanding of how things work change, the world goes roundy roundy and blah blah blah; yet the way in which they explain concepts with math to other people remains the same. That is why math is more fundamental. Now, in your example, where the human race is annihilated and noone is left to explain the math we used, I still feel another race would use the exact same dichotomy of math. The difference would most likely come in the form of the base they used for their math. I believe however the way in which they described the universe with math would still be the same.

No language "change", you simply speak a different (but similar) one every time you use new rules. If you write a grammar, it will be the same grammar no matter where you go, and whoever want to communicate using that language would have to follow the rule dictated in it. It's the same with mathematics, your "true" axioms will be true no matter what.
Anyway, what kind of "universal truth" are you talking about? Can you list the mathematical axioms you use?

Years ago, I would have agreed with you, but after doing topology and scratching mathematical theories, many axioms started feeling more artificial in the sense that we can build interesting structure with different starting point.