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/sci/ - Science & Math

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7172496 No.7172496 [Reply] [Original]

Is Euclidean Space a physical reality or a mathematical model?

>> No.7172502

How can we ever know what objective reality is like? We can only work with models.

>> No.7172513

My question is basically that to describe "empty" space you have to define it by using the word "space" again, which is a tautology and a logical fallacy.

"The space that we inhabit is.. "

>> No.7172517

>>7172496
>Is Euclidean Space a physical reality
We don't know whether the universe is flat or not.
>a mathematical model?
We use Euclidean space to model flat space.

>> No.7172522

>>7172496
Minkowski is a better way of understanding, but Euclidean is okay for most things.
Neither are physically real and both are mathematical models.

>> No.7172526

>>7172517
Okay. Let's say that you wanted to physically describe the space in your room. Would using the x,y,z parameters of its dimensions be the most accurate you can do? Maybe the volume it contains? These are mere measurements and not a physical description of what actually IS the space in your room.

>> No.7172533

>>7172496
Space is space. You need to get out more.

>> No.7172547

>>7172517
Even if you ignore nasty GR stuff, I knoe of no experiment that would falsify the assertion that each point in our universe can be represented by a quadruple of real numbers and vice versa (do not ignore special relativistic effects).

Also, I'm not entirely sure that the term 'euclidean space' entails a choice of some particular metric.

>> No.7172561

>>7172533
I (OP) personally think that space doesn't make any sense without matter or radiation. But that doesn't explain time. Is it also dependant on the same factors as space?

>> No.7172571

>>7172561
Time is tied into three spatial dimensions via Minkowski spacetime. It adds a fourth coordinate, so you then have X = (ct, x, y, z). This effectively allows you to relate any real transformation to a constant, c, and hence have an objective relative transformation w.r.t. another event.

>> No.7172598

>>7172571
I see.

>> No.7172811

>>7172547
It entails the choice of a Euclidean metric. That's the definition of a Euclidean space.

>> No.7172840

>>7172496

It's a model. Space-time is not flat, but this point is moot because Euclidean geometry works in all possible higher dimensions including the 3rd.

What makes Euclidean space a less than perfect representation is the curvature or warping of space-time as evidenced by the relativistic movement of bodies.

If you can imagine yourself in 3d space like you were a ball submerged in water, shifting with the tides and effecting gravitational "displacement", you can approximate an image of the over-nature.

>> No.7172842

>>7172547
>I'm not entirely sure that the term 'euclidean space' entails a choice of some particular metric.
It does, though. Euclidean space implies the Euclidean metric.

>> No.7172844

>>7172840
>Space-time is not flat
What makes you so sure?

>> No.7172848

>>7172844

Look around you.

What can you see in nature that is flat, or demonstrates perfect line?

Not wind, water, earth, or fire. Not plants or animals. Only human structures approximate these perfect lines, and crumble and break down in curvilinear fashion over time.

It is not the nature of things.

>> No.7172876

>>7172848
That's the dumbest reasoning I've ever heard.

>> No.7172880

>>7172848
This is not a proof by any stretch.

>> No.7172887

>>7172561
Radiation is matter. It's small particles moving at high velocities.

>> No.7172889

>>7172887
Define moving

>> No.7172893

>>7172887
Depends on what kind of radiation and what definition of matter.
If by matter you mean things with mass, then electromagnetic radiation definitely isn't radiation.

>> No.7172894
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7172894

>>7172880

Well excuse me for not being of physics genius, but I hold that it is prima facie evident that the fabric of reality is not perfectly represented by the model of Euclidean space.

Can you prove that it is? Do you even know that the burden of proof is actually upon you to prove that Euclidean space accurately represents reality? All I've done is denied it and provided a justification for the denial.

Seriously, the fact that you faggots never get run through a basic primer course in the philosophy of scientific method makes me apprehensive of the future.

>mfw

>> No.7172897

>>7172894
You do realize no one here has said that space is flat, right?
Nor did anyone else say that space definitely isn't flat.

You are the one making claims without evidence.

>> No.7172903

>>7172897

I've pointed to the evidence, and you're rejected it out of hand without any explanation. What type of evidence do you define as evidence?

>>7172517

>We use Euclidean space to model flat space.

>> No.7172919

>>7172840
>>7172848
>>7172894
https://www.youtube.com/watch?v=wKjxFJfcrcA

Space-time is actually flat at cosmological scales. On the other hand, every point in space-time is locally flat (Minkowsky).
In other words, shut you mouth and don't talk about things you don't understand because you are going to look like a retard.

>> No.7172922

>>7172903
>evidence
No, you haven't given any. Evidence means either a mathematical justification or experimental results.
If I am trying to determine whether a man committed a murder, what kind of evidence would I need? I wouldn't accept the fact that other people sometimes murder each other as "evidence."

>We use Euclidean space to model flat space.
Yes, we do; no one ever said it is a perfect model. In fact, many great scientists didn't think it was.

>> No.7172925

>>7172919

lol proves it.

Do you has evindece?

>> No.7172929

>>7172919
>Space-time is actually flat at cosmological scales.
You forgot to say,
>according to our most current evidence.

I'm not the guy you replied to, but space is by no means <span class="math">required[/spoiler] to be flat.

>> No.7172930

>>7172922
>no one ever said it is a perfect model

>>7172919

>space-time is flat
>>We use Euclidean space to model flat space.
>no one ever said it is a perfect model

>what does prima facie mean
>how do I into latin

No one in this thread has provided better evidence than what I have already shown you.

>> No.7172932

>>7172925
1v1 me irl fgt

>>7172929
Of course you are right.

>> No.7172940

>>7172930
Why do you consider the geometry of the universe being non-flat prima facie?

Our experiments show that it is flat.

Isn't the whole point of both philosophy and science to never make assumptions without sufficient data?

>> No.7172943

How Can Vectors Be Real If Our Math Isn't Real?

>> No.7172944

>>7172940

Simple empirical observation suggests at first glance that the Earth is round, and therefore indeed not flat.

>pri·ma fa·ci·e
>based on the first impression; accepted as correct until proved otherwise.

>> No.7172951

>>7172944
>Simple empirical observation suggests at first glance that the Earth is round
Yes. What does that have to do with the global geometry of the universe on cosmological scale?

You are making arbitrary and meaningless connections between two unrelated things.
The Earth being non-flat does not mean that the universe is non-flat.

The proper position for someone with a background in philosophy (as you claim to be) would be to make no assumptions about the geometry of the universe.

>> No.7172952

>>7172944
Are you aware that the earth being round and space-time being flat are two different things? They are related by Einstein equations, but you don't know that prima facie.

>> No.7172960

>>7172951
>global geometry of the universe

That the Microcosm necessarily reflects the Macrocosm, and the laws of physics don't change just because you are examining a mile wide diameter rather than an inch wide diameter?

>The Earth being non-flat does not mean that the universe is non-flat.
>implying the planet isn't part of the universe.

>you don't know that prima facie

Certainly, now can someone please explain how an non-flat object can inhabit a flat space-time, assuming said object's dimensions are necessarily determined by the nature of the space it inhabits?

>> No.7172980

>>7172960
>now can someone please explain how an non-flat object can inhabit a flat space-time, assuming said object's dimensions are necessarily determined by the nature of the space it inhabits
Sure. One example is that a 2-sphere, which is curved, can be embedded in a Euclidean space of dimension greater than 2.
Although the geometry of the Euclidean space is flat, the geometry of the sphere that is <span class="math">induced[/spoiler] by the Euclidean geometry is necessarily curved.
In fact, there is even a theorem in math demonstrating that any manifold, curved or not, can be embedded in some flat space. Take a look:
http://en.wikipedia.org/wiki/Nash_embedding_theorem

>> No.7172989

>>7172980
>a 2-sphere, which is curved, can be embedded in a Euclidean space of dimension greater than 2

ohh ok

>> No.7173301

>>7172919
epic meme video reply /b/ro :DD
upvoted X-DDDD

>> No.7173309

>>7172496
i think all this confusion comes from people not understanding what graphs are showing, especially shit like that gravity well

>> No.7173349

>>7172496
Read Kant.

>> No.7173401

>>7172513
Silly anon, spaces are non empty sets by definition.

>> No.7173516

>>7172496
Why could it not be both?