Mass is a physical value. Volume is a physical value. Density is a mathematical ratio - a derived value. No backpedalling is required.
Furthermore, ratios can be as silly as you like - what is the ratio of penguins to unicorns on Earth? When the last dodo died, what happened to the ratio of penguins to dodos?
What about probabilities. We know that quantum mechanics describes the subatomic universe and we know that it is nothing if not at least a partially stochastic model. So there are certainly infinite probabilities to be found in QM which would make those probabilities “physical” in the sense that the OP intended.
Exactly.
Same thing for pi. Pi itself can be said to have infinite digits. But if you’d try to actually write them all down, then the quantity of digits would be a physical value, and that’s just not going to be possible.
“Undefined” is just a technical term meaning, “Hey! You’re breaking the rules!”
Zero and infinity are two sides of the same coin. A fantastically readable book about this is Zero: The Biography of a Dangerous Idea. You can read it at Google Books.
I’d say that just because some ratios CAN be silly doesn’t mean all are.
Yes. I don’t think I implied that though.
Neither are physical things, they are just concepts expressed in numbers. Pi is a finite number with infinite precision–it can’t be written exactly with a finite number of digits. The fraction 10/3 is written in base 10 with an infinite number of digits after the decimal point, but that’s a concept. It is not an infinite quantity, it is an exact number. The reason it has an infinite number of digits is a consequence of the base 10 number system; you could write the same number in base 3 as 10.1 with no repeating digits.
I am not saying you’re wrong, just that it’s not germane to the OP any more than any other arbitrary infinite string, like saying the Fibonacci series is infinite.
I’d think that shrinking to infinitely small would be different than trying to reach infinite size or speed. For infinitely small there’s a definite goal that’s a finite distance away - zero size. Trying to go the other way there’s an infinite way to go to reach infinitely large.
You can get to zero in finite steps just by repeated subtraction. You can’t get to infinity by finite steps of repeated addition.
I think making two mirrors face each other will give you something infinite.
Good point. But is shrinking the same as subtracting? Will have to ponder that a bit (coffee subroutine not up and running yet).
Not in the physical world. You quickly reach a point in which the images shrink to a nonexistent size or the number of photons emitted go below one.
I agree. People are confusing the map with reality, so to speak. For the same reason, coastlines are not infinite.
I also agree that ratios don’t count. Or shouldn’t count.
It seems to me that a physical thing should be considered infinite if (in theory) you could measure it in equal, finite increments forever without completing the task of measuring the thing.
By this definition, I agree that the universe might be infinite.
It seems like time is a good candidate for being infinite, if you think of time as a physical thing. But then again, I am probably confusing the map with reality. i.e. my internal concept of time seems infinite but does not necessarily correspond with reality.
I disagree. At least when it comes to something like density, because infinite density is rather interesting and has real world implications.
I have a box of finite size. How much shit can I take out of it? An infinite amount. I can keep taking shit out of it for eternity. That as mind boggling to me as infinite time or infinite space.
Or, I have a finite amount of shit in a box of zero size. How can a box be of zero size? Thats as mind boggling to me as time or space having a beginning or an end.
Though I suspect infinite density doesn’t actually occur. But I find the concept interesting.
In the middle two paragraphs though, you’re talking about mass and volume - not density.
You might want to look up the definition of implications. Or the definition of density for that matter.
Whatever. A ratio isn’t a physical thing, regardless.
I agree that infinite density is interesting, but I would not categorize it a a physical thing that’s actually infinite.
What’s interesting is that some amount of matter is taking up no space at all.
Anyway, if you include ratios, then there are all kinds of mundane infinities lurking around. As someone pointed out, the ratio of penguins to dodo birds is infinite. Which may be interesting, but what’s actually interesting is that dodo birds are extinct.
Well I would definitely count this as a physical thing which is actually infinite. And in fact it passes the test I proposed a few posts back.
Yes, if mind boggling is the test, then this would pass. But you aren’t really dealing with an actual infinity as I see it.
Me too.
I got two ideas here:
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The subatomic world: as technology allows us to look at smaller and smaller things, we keep finding smaller things to look at.
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One way to define “infinite” is constantly growing or expanding. I’ve had a couple of vines in my backyard that would fit this definition, and would definitely overrun the entire neighborhood if left unchecked. My nominee for an infinite plant would be the banyan tree. This example, if you will notice, is a single tree.
