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[eerr]

How can you have energy without mass?

[Neruz]

How can you have energy without mass?

By being a Photon.

I think I'll stop dividing by zero now.  Everybody seems to prefer arguing against it, rather than help me figure out how to do it.

This is because you can't do it. You cannot divide by zero.

End of discussion.


Complaining about not being able to divide by zero is like complaining about not being able to use a Rocket Launcher in DF Adventure Mode; you are operating in a set of rules constructed by humans with a ridged and unchanging set of things you can and cannot do.

One of the things you cannot do is divide by zero. That's the way the rules work. End of story.

[DreamThorn]

The only reason we cannot divide by zero is because, in the maths mankind invented, it is impossible.

[Innominate]

The only reason we cannot divide by zero is because, in the maths mankind invented, it is impossible.

Which is, like Neruz said, basically the same as saying "The only reason you can't engrave constructed floors in DF is because, in the DF Toady invented, it is impossible."

As it happens, any system with the usual definitions for addition and multiplication is incompatible with division by zero. You have to come up with circuitous and frankly useless workarounds to be able to divide by zero, and it never actually helps anything. Nature doesn't ever divide, but it does tend to solve partial differential equations very well.

[Neruz]

The only reason we cannot divide by zero is because, in the maths mankind invented, it is impossible.

Which, as reasons go, 'it's impossible' is pretty much the best one you'll ever get.

[Il Palazzo]

I think that DreamThorn is a follower of the idea that the body of mathematics, which we currently use, being derived from certain axioms, might in fact not be the best tool towards describing our physical world. After all, it seems logically sound, that one could perhaps choose different set of axioms, and derive an alternative mathematical system, which in turn could prove to be a better tool. Better, as in by comparision, Heliocentric description of planeary motion is better than Geocentric, because it's simplier and previously complex problems become much easier to explain.
I do think, though, that such an invention would have to be more radical that just taking a different approach to divisibility by zero, which is itself, AFAIK, a derivation of axiomatic definitions of multiplication and division.

Actually, Sean Mirrsen seems to be a similarly minded person, trying to find an alternative and simplier explanation of the physical phenomena, only he somehow took the idea to an extreme and thinks that no mathematics is necessary to describe the world at all. At least that's the impression I got.

[Neruz]

Mathematics probably isn't the best tool for describing the physical world. It was never designed as a tool for describing the physical world, so it's asking kind of a lot out of it for it to be the best tool for doing so.

[DreamThorn]

Ah, it seems you understand now.

I've now been looking at the hyperreal numbers.  They are a mathematically rigorous way of handling this kind of thing.  While it is still impossible to divide by zero with hyperreal numbers, at least we have properly defined rules for infinitesimal and infinite values.

I should practice saying 'divide by an infinitesimal value' when I would normally say 'divide by zero'.  Because that is what I actually mean.

[Neruz]

Saying what you actually mean is usually a good way to engage in discussion.

[Starver]

I wouldn't say that this is FTL travel, in any sense of the word. Rather, this is STL travel with a classical velocity that's much greater than the speed of light. [...]

I'd like to know what you're replying to with this statement, because you might be either very mistaken or very profound in a way that is lost to me.

[Starver]

There is no such thing as 'energy', the reason things 'lose' energy constantly is because whenever energy of one form gets turned into another form, inevitably some of that energy is converted into heat, which radiates off into the universe and is 'lost'. So to speak.

I know in some circles, they deplore the idea of generic 'heat' with vibrational energy of atoms (what makes things hot to the touch[1]) being considered the same as radiative heat.  And the previous poster (snipped) also seems to think Entropy is related to 'amount of energy' (in whatever form), when it's more properly to do with the order (or the converse) of the universe.

And I wrote a lot more about that, but kept on finding I needed to add further clarifications to my own explanations as I found myself out-pedanting myself.  A lot snipping has been done.  I think you should consider yourself lucky.



[1] And is responsible also for convection, given that it's the vibration of fluidic masses of molecules that give them lighter densities that moves the hotter molecules and colder molecules around accordingly.

[2] And I shouldn't technically equate Heat and Temperature, but that would need another explanation so for now I'm using the premise that they're proportional in our hypothetical system.

[dreiche2]

I think I'll stop dividing by zero now.  Everybody seems to prefer arguing against it, rather than help me figure out how to do it.

Well, as you didn't want to comment on my example, I do it myself:

sin(1/x) * 1/x  for x -> 0   (let's say for x>0, i.e. coming from the right)

1/X goes to +inf. Sin(1/x), however, oscillates infinitely often between 1 and -1 when going towards 0. That means that the product alternates in between larger and larger values, both positive and negative, for x -> 0. So neither +inf nor -inf can be (by themselves) a limit.

The bottom line is that you cannot consistently define 1/0, because 'different ways of dividing by 0' (i.e. different ways of doing the limit) will give you different or even inconsistent results.

KE = m*(v^2)/2 = gamma*m0*(c^2)/2
.

Relativistic kinetic energy cannot be computed with that formula, even for particles with rest mass.

I think that DreamThorn is a follower of the idea that the body of mathematics, which we currently use, being derived from certain axioms, might in fact not be the best tool towards describing our physical world. After all, it seems logically sound, that one could perhaps choose different set of axioms, and derive an alternative mathematical system, which in turn could prove to be a better tool.

Well, yes, he's a follower of this idea, most of us just disagree with it. Well, in general yes, we probably need better maths or even different maths to describe the universe, but that's not because of division by zero problems. There might be a mathematical construct where you can define division by zero in a meaningful way, but

1) I don't see why one would need it to better the describe the universe ('the universe doesn't divide by zero').

2) It seems implausible, for reasons given, that you could get such a system by fiddling with the real numbers, as you, Il Palazzo, have pointed out. Which is another indication that one probably won't need the system anyway, because DreamThorn's intuition about why one would need it certainly does come from playing around with real numbers.

Edit: typos, typos, typos.

[DreamThorn]

I think the main trouble with your sin(1/x) * 1/x example is that sine is not defined for infinite numbers.

I see your point though.

I was also wondering why a particle does not apply a force on itself.  In fundamental quantum mechanics we were calculating what happens to a particle in a potential field, but the particle itself was not affecting the potential for some reason.  I now realize that this is probably not the whole picture, because there should be bosons involved somewhere.

[Neruz]

Ahh yes, the elusive Biggs Morons. If only we could find the damn things.


Of course, if we can't, then all sorts of interesting theories come crashing down and half the Physicists on the planet will throw massive hissy fits.
The other half will dance around in circles going "Wheehehehe, i was riight!"

[Sean Mirrsen]

Which half is going to be which?