Because - as I’ve said many times on these boards - the fact that someone (in this case the worldwide physics community) chooses an imprecise non-mathematical term to attempt to describe something in the poorly-equipped English language doesn’t then mean that you can take that term and use it as a basis for reasoning. It’s just a word chosen to try and describe something which the English language can’t describe well, and the further implications of that word don’t apply.
The correct description, unfortunately, is a bunch of math. If you want to apply reasoning to the implications or consequences of a description, that’s the description you have to first fully understand and then work with. Which isn’t something that’s gonna happen on a messageboard thread - or anywhere outside of a very long research paper.
It sucks that the universe is so complicated and that we have to use such imprecise language and poor analogies to describe it outside of the math, but there it is.
We can complain that physicists make it so unintelligible - but they don’t. They do their best to describe what they find in conversational language; and they don’t do a terrible job of it, but that language just ain’t equipped. It’s not their fault.
I’m afraid it’s not. Infinity doesn’t work that way. If it can get bigger, then it wasn’t infinite in the first place.
If it helps, think of the universe like a chess board. There are 8x8 squares. Suppose we increase the “size” of the board to 16x16. We don’t have to make the board “bigger”. We can just make each square “smaller.” In fact, you could make the chess board any size you like; it really doesn’t matter. When you start thinking about these things carefully you realize that all that matters is the number of squares; other than that the “size” of the board is meaningless unless it is relative to something.
You’ll have to expand on that, then, because I don’t know what you mean. I mean, there’s the mathematical idea if infinity, and there’s probably a million different ideas from what different people think it means, and Hollywood infinities, and religious infinity, but in this context we’re talking about the mathematical concept.
The infinity of the reals is a bigger infinity than the infinity of the integers. There are an infinite set of infinities of different sizes.
I don’t think that is really relevant to your point, though. ETA: In particular, when Irishman said “But it’s a bigger infinity”, it wasn’t. It was the same size of infinity.
Yes, there are, but you can’t get from one kind of infinity to another by adding on finite quantities, which is why Candyman74 objected to Irishman’s interpretation that infinity +1 is “a bigger infinity”.
The type of infinity that describes, e.g., the set of integers (or positive integers, or odd integers, or any of the rest of Exapno’s examples) is called “aleph-null”, or “countable infinity”. (Because you can put all the elements of any such set into one-to-one correspondence with the counting numbers, even though you’ll never reach the end of your counting.)
There are higher orders or degrees of infinity. An example, as ZenBeam noted, is the size of the set of real numbers, commonly called “uncountable infinity”.
You can’t make a countably infinite set uncountably infinite by adding a finite set (or even another countably infinite set) of elements to it. So no, countable infinity +1 does not equal a bigger infinity in any mathematically meaningful sense of “bigger”.
Agreed. But that is why non physicists have such a hard time with this stuff. These words come packed with all sorts of inherent assumptions about what they mean and how they work. When a scientist uses a specialized use of the word to convey one element of the concept they are trying to express, it is only natural for the non-specialist to try to extend the concept with all the analogies that come with those words. That is how communication usually works. So when it doesn’t work, it is exceptionally frustrating, and thus leaves the non-specialist think the scientists must be full of it, or are pulling a big prank on the rest of us.
So part of the burden for the scientist trying to use these words to laypeople to explain what they are talking about is the burden to caveat that the words being used are fuzzy approximations to drag out one element of what they mean to convey, and not intended as direct analogues that one can extrapolate with. They must try that much harder to make their examples and analogies and descriptive models limited and precise. Because the layperson cannot be expected to know what you mean by “expanding” when what you mean is not getting larger, but getting less dense.
Understandable, but sometimes they don’t do all that great of a job.
Fair enough, but like I said, that’s one of those “that doesn’t make sense” points.
I guess if they’re selling you a book or something, then they have that burden. And if they don’t fulfil it to your satisfaction, you vote with your wallet.
Other than that, their burden is only to get on with their research and do useful stuff.
Or, if they’re just taking personal time to explain stuff to you on a messageboard, they have no burden at all. They make what effort they feel like.
As a long-time worker in a technology field, I totally get where you are coming from. If the researchers, who are thoroughly steeped in the high-end math and can regale each other for hours—but sound, to the outsider, as if they are speaking Martian—try to reduce their findings to a form comprehendible by the layman, they must, perforce, use analogies, metaphors, models and other simplifying devices. These devices, unfortunately, will always describe only a part of the reality, and that, imperfectly.
The researchers do have, at their disposal, words which precisely describe the concepts they are trying to convey. These are called “Jargon.”
So, the dilemma which the populizer finds him/her self in is this: Use words and ideas the average listener is familiar with, knowing that much of the precision will be lost or distorted; Or use words which exactly describe the reality of their research, but concerning which the lay public is unaware, and resents all this “Gobbledy-Gook.”
If there is a middle road, I am not aware of it being used to any great success.
It is not that the researchers are being intentionally obtuse by relying on the mathematical description—that is the reality. The models and analogies which are constructed cannot be extended beyond their purview without some degree of breakdown. And, it happens all too often that the general public sees a simplified explanation and extends it well past the breaking point, then complains when he catches the researcher in a “contradiction,” which was nothing of the kind.
Witness all the “My problem with Relativity…” action.