Telimaktar

Words do correlate to things and ideas, if not then how could anyone understand anyone else's in these threads and elsewhere. Yes a word isn't real but it can relate to something that is real or abstract. It a a group of symbols that man can see and link to something understood. Whether they understand it the same as someone else is more important.
If someone says dog one can immediately picture a generic shape for that animal. If someone says german shepard then one can refine that image to one that relates far more closely to such a animal in the canine family.


If a plane is not built aerodynamically then it will very likely shake. Yes the materials will play a role but a far smaller one than the shape of a plane.

1 is a very well understood and defined concept, it is an idea amongst many that has helped propel humanity to where we are.

To deny that is to deny so much else that has moved us to where we are.

Herra1

Words are also abstractions just like numbers, that was my point and that i tried to say.
Words are also very facinating, dont you think ?
Speech use words, writing uses words.
Does speech have these spaces like here ornot ?

Shadee

I like the original question, It reminds me of flatworld.
Where the 2D people encounter a sphere moving through their 2D world and prove that what they're seeing is an expanding and contracting circle. Because it follows all the mathematical rules of an expanding and contracting circle for them. In actuality there's much more to it than that ofcourse, but they aren't able to perceive the entire sphere.

So yes, while we can prove things we have to realize that they are only proven under the conditions and theories we are currently able to observe, so there's always a possibility that there's a lot more to the truth than we know.

to_hobbes

Keep in mind, however, that mathematics is not restricted to the domain of things that humans can perceive naturally. For example, if those flatworld people could measure the rate of expansion and contraction of the circle, and plot it parametrically, then they could prove that it was a "3-circle", just like us in our 3-space-dimensional world could plot a "4-sphere", although we would have difficulty envisioning what it would look like in all four dimensions at once.

In fact, a good number of mathematic proofs involve geometries that are multiple dimensional, or even infinite dimensional. As long as we have a consistent mathematic language, then we can prove just about anything, even if our own mind can't comprehend what it means.

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(By the way, it's all in your head.)

Shadee

Our math has been proven to be flawed and fall apart at a larger scale while calculating things in the physical world though. So I'm just saying that our methods of calculation and math might not be flawless or even the only way to go about understanding things. And we are still basing those new 4-sphere type calculations on our math principles. So even though the idea makes sense in our way of doing things doesn't mean it's the way things really work.

As for the flatworld example, they have no point of reference as to what a sphere is because they're not able to observe one. Even if they were to come up with the concept they still wouldn't be able to prove it without a doubt. A zeppelin shaped object could seem like a sphere according to their calculations too if it were to move through their world at varying speeds. Same thing for the 4-sphere. Even if we do end up finding mathematical rules it follows it's still no guarantee that our perception of it isn't somewhat skewed due to other variables we simply aren't able to verify.

Herra1

Why i think it is flawed, is because the only way we can explain 1, is through mathematical language.
It seems 1 has no connection to a real world.

Yes, i know, what is, then, a real world ?
But for argument duration sake, lets assume we all comprehed the idea/bstraction of real world.
Where is one ?

Bible must be correct because the bible says so ?

to_hobbes

When you say "flawed while calculating things in the physical world", I think this does mathematics a disservice.

Physics uses mathematics to model the real world. But the real world is independent of our mathematical models. The models are flawless, but it is the method we use to apply the mathematic models in order to predict the physical world are imperfect. In other words, math is basically perfect, but physics is not so much.
This is a very good point. The flatworld people simply don't have the ability to observe a 3-sphere, anymore than we have the ability to observe a 4-sphere.

The way I see it, the real world is something that is ultimately incomprehensible. I guess what you are saying is, we can't see beyond the dimensions to which we are restricted, and I agree. However, just because we observe things imperfectly doesn't mean our logic can't be perfect.

In my opinion, perfect logic is 1 + 1 = 2. An imperfect application of that logic would be saying "adding two cups of water to this pitcher will make the water level rise two inches". Just because we were wrong about the real-world pitcher of water, doesn't mean "1 + 1 = 2" is flawed.

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(By the way, it's all in your head.)

to_hobbes

One exists as a symbol in your mind, and my mind, and a bunch of other people's minds. How that symbol is written in our mind depends on how we store data in our mind -- that is to say, we don't yet know our brain well enough to know how we store information on the number one.

But one can be stored in computers, and on paper. As long as there exist at least one being which can comprehend "1", then "1" really exists in that being's mind.

This is true for any abstraction. Abstractions exist in the real world as some set of symbols written in some medium. And any symbols which can be translated into another form and communicated to another being simply means the symbols can exist in more than one form. So if you can translate an abstraction in your head into words, and then put those words on paper, then that abstraction can be copied into someone else's head.

I think "abstractions" are actually just as real as anything else.

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(By the way, it's all in your head.)

Shadee

No I really did mean math itself being flawed.
There are a lot of holes it it. A simple one being Zenon's paradox and because of those types of imperfections things get really wacky and inaccurate when you try to apply mathematics to a huge scale. Not to mention calculus with which it is possible to prove that 1+1 does not equal 2.

Yes I agree. And that was exactly my point. We can observe certain events and prove that they are behaving according to our methods of logic and calculation (Just like the expanding and contracting circle in flatworld, because they are right, that is exactly what it looks like and it's following all the mathematical rules too). But the important thing is that we need to realize that as long as we can't observe the entire thing and all the circumstances surrounding it we can't say we know exactly what it is because that would just be speculating which is fine for creating theories but not for generating scientific proof.
So who knows, even things we see in our 3D world might end up looking completely different in another dimension or other state of being which all goes back to the original poster's question.

So in short, yes we can prove that certain things behave according to our logic and math, but no we can't prove that that's all there is to the truth and that what we see might not just be the tip of the iceberg.

romansh

Hi Shadee ... looking up Zenon's paradox ..... it's an improperly framed high school math question ... one can calculate exactly at what point Achilles will catch up the the tortoise just using high school algebra.

Could you show an example or reference where calculus shows that 1 +1 does not equal 2? I have seen improper use of algebra to prove 1 = 2?

thanks

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