[castor]

A situation with impossible values will yield an impossible result...

Is it really impossible, or just out of scope of finite beings
I guess the whole universe becomes impossible, if you deny infinities.

[watsisname]

If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.

[QuantumDelta]

Including ourselves

[Col. Fishguts]

If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.

Supeconductors have not infinite conductivity (or zero resistance for that matter), superfluids have also not zero viscosity. Black holes represent a singularity in current physics, as in we don't really know what physics to apply within the Schwarschild radius, but that does not automaticvally mean that there's really somthing inifnite in them.

TL;DR In the real world nothing is infinite (the universe maybe, but we don't know)

[watsisname]

Fair enough, I'll concede the point for black holes, though I will stick with my belief that a singularity does exist within them until physics demonstrates otherwise.

As for superconductors, I ask what is the electrical resistivity if it is not zero?  I've never found information suggesting that, but perhaps you have better information than myself.
Same question for superfluids/viscosity.

[Col. Fishguts]

Superconductors have very low but still non-zero resistance (although Wikipedia falsely states otherwise), as to which effect causes the small residual resistance is still a topic of research IIRC. But since there's still no definitive theory for superconductors, this is no surprise.

For superfluids the situation is similar.

The name singularity for the center of the black hole, comes from the fact that it represents a mathematical singularity when you try to calculate physical properties at the center of the black hole, leading to a theoretical point with infinity density, infinitely bent space-time, etc. Nowadays physicists call it still the singularity, but it's properties are basically unknown.

*waits for Herr Doktor to lecture us all in detail about it*

[Uchuujinsan]

Do you have a source on that claim that superconductors have non-zero resistance?
Given the upper limits for the resistance of superconductors I found during research, it's a little hard to believe that such a low resistance could even be measured.
It's like with quantum teleportation - it's not guaranteed to happen instantly, but iirc there is no proof that it takes more than zero time.

After thinking about arguments for some time I believe that question comes close to religion - we only have a finite accuracy to observe the universe, and as a result can neither prove nor disprove the physical and real relevance of infinities.
(I thought about using Real numbers as an argument against that claim, but you could just evade that by saying that the universe is divided into discrete parts - making this argument useless :/ )

[General Battuta]

If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.

Supeconductors have not infinite conductivity (or zero resistance for that matter), superfluids have also not zero viscosity. Black holes represent a singularity in current physics, as in we don't really know what physics to apply within the Schwarschild radius, but that does not automaticvally mean that there's really somthing inifnite in them.

TL;DR In the real world nothing is infinite (the universe maybe, but we don't know)

Everything you say here is correct.  

Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.

(Although I guess you'd probably say that is a mathematical value, and the fact that it is infinite is why it can't happen in reality...)

Actually, I'm just gonna stick with my original hunch that what you say here is correct. Infinity is very useful in mathematics, and in that sense is very useful for describing reality, but no measurable quantity can be infinite except possibly for things like the number of stars in an open flat universe or the size of said open flat universe.

[blackhole]

no measurable quantity can be infinite except possibly for things like the number of stars in an open flat universe or the size of said open flat universe.

Or the extent of human stupidity

[General Battuta]

Finite and quantifiable. 

[watsisname]

Boy, he really sucked the fun out of that reference. 

[CP5670]

It's easy to make up examples of infinities in real life. Anything that is discontinuous (or more generally, unstable) will have infinite derivatives, for example.

As for infinities that are actually relevant in some way, that depends on the context and is probably a matter of opinion as well.

[Col. Fishguts]

Do you have a source on that claim that superconductors have non-zero resistance?

Nothing easily accessible on the net, since last time I've read about the topic was in research papers a few years back. But to prove I'm not making this up

http://www.nist.gov/eeel/electromagnetics/magnetics/superconductor-characterization-2004.cfm

Scroll down to the 3d plot where they measure the resistance in nano-ohms.

Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.

Read that again and think what you typed here

My point is that current cosmology holds that the universe contains a large but finite amount of energy (including matter), therefore any hypothesis that involves an infinite amount of energy (or an infinitely large force, speed, etc) is damned to remain impossible... even in theory.

As for derivatives, they are a mathematical concept and are as much real as the mean value of something. If I define it exists according to my definition, but that doesn't' mean I can touch it.

Plus, can you give me a real world example of a true discontinuity?

[watsisname]

Isn't a Prandtl-Glauert singularity an example of that?  (The vapor cloud produced by a sudden pressure drop in a shockwave)

http://en.wikipedia.org/wiki/Prandtl-Glauert_singularity

[General Battuta]

Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.

Read that again and think what you typed here

Read my post again.

[Col. Fishguts]

Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.

Read that again and think what you typed here

Read my post again.

Sneaky edit But thanks for the clarification, and in that context you're right.

[General Battuta]

Um, that edit was up before you posted anything. It happened less than three minutes after the post went up.

What's with people lately and claiming I sneak edited my posts? 

[Uchuujinsan]

Do you have a source on that claim that superconductors have non-zero resistance?

Nothing easily accessible on the net, since last time I've read about the topic was in research papers a few years back. But to prove I'm not making this up

http://www.nist.gov/eeel/electromagnetics/magnetics/superconductor-characterization-2004.cfm

Scroll down to the 3d plot where they measure the resistance in nano-ohms.

To quote from that article:

When the combination of field and temperature are low enough, the sample is in the superconducting state and the resistance is zero

(emphasis added)
The same can be seen at the 3D-graph - in the superconductivity state it's plotted as (indistinguable from) zero. (at a maximum of 0,5 tesla or  ~7 Kelvin)

[CP5670]

As for derivatives, they are a mathematical concept and are as much real as the mean value of something. If I define it exists according to my definition, but that doesn't' mean I can touch it.

Anything we can talk about will involve definitions made up by us. As I said, what is physically relevant is a matter of context. A lot of basic things like velocity and acceleration are essentially derivatives.

Plus, can you give me a real world example of a true discontinuity?

That depends on what you mean by real world. The height of your desk surface is discontinuous at its edges. Of course, at the molecular level it's discrete and finite, but it could also be argued that the continuous model of this has more relevance to the real world.

As for instability, any kind of turbulence in fluid flow, such as breaking water waves, is like this. In this case, the map from the initial state of the system to the final one is discontinuous. Whether that operator is physically meaningful or not is up to you.

[TrashMan]

Finite and quantifiable. 

Einstein would disagree with you.

Einstein >>>>>>>>>>>>>>>>>>>>>>>>> You