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There’s also nothing about the physical universe to suggest that it is finite, or that it cannot contain infinities. It’s simply an open question. > If infinit

by simonh 4y ago

There’s also nothing about the physical universe to suggest that it is finite, or that it cannot contain infinities. It’s simply an open question. > If infinity was an actual number (having a size), it would need to be extrauniversal What does the universe or its physical extent have to do with the nature of numbers? A number is simply a concept, or idea, not necessarily a physical thing. We imagine things that aren’t physical all the time.

ravenstine 4y ago
> There’s also nothing about the physical universe to suggest that it is finite, or that it cannot contain infinities. It’s simply an open question. The only evidence we have is that it's finite. Just because the universe expands does not mean that at any given time it is not finite. > What does the universe or its physical extent have to do with the nature of numbers? The only way to have scientific confidence in an idea is to test it. We can't calculate infinity because, infinity being something that isn't finite, every unit of information in our universe would have to be used to describe infinity. This doesn't work because there is never infinite information space in our universe at any given slice of time. Think of it this way; you can't take a modern video game and get it to perform exactly the same on a home computer from 1996 because it simply lacks the computing capacity. The only way it can work is to reduce certain aspects of the software to make it work at a much lesser capacity. There are no examples of any system that can describe another system more complex than itself with total accuracy. Thus, it makes no sense that a universe in which we are currently only able to describe through finite numbers would be able to support calculating what infinity as well as support the rest of its contents, if it can even do that at all. This is why it's not at all accurate that a set of numbers can be "infinite." It only seems infinite because, for all intents and purposes, we don't have the capability to keep dividing a range of numbers forever. Even if we tried, the inevitable dissipation of heat energy would prevent us from doing so, that is if we don't simply run out of finite resources before then. If there is something that is indeed numerically infinite, we too would have to be infinite in order to make sense of it. We can't actually do that. That would be a contradiction. To illustrate this, go write some code that calculates every single number that exists in the "infinity" between two numbers. You won't be able to. Your software will fail because your computer doesn't support it. That is unless it has infinite bits. A set where there's "infinite" numbers would more accurately be described as being indeterminate. The seeming "infiniteness" of one of these sets breaks down when you realize there's no way to even demonstrate that part of a set is infinite. From a conceptual standpoint, it's similar to how it might seem that a ball will fall straight down when you drop it, and it's generally useful to think of gravity in such a way, but that doesn't mean that it's actually so, just as believing that a set can be "infinite" might be useful, but the use of the term "infinite" for something finite like a set is incorrect. So no, to others who think I'm being off topic. This is entirely on topic. A set being "infinite" gives you the wrong idea. At best, it defines a vector too large for humans or even human computers to find an end to. It's entirely virtual until proven otherwise.
- simonh 4y ago
  I’ve read articles, seen interviews and read book by mathematicians and cosmologists on these issues. None of them agree with you as far as I can tell. Some cosmologists and physicists believe it’s likely the universe is finite, some believe it’s likely it’s infinite, but none I know of believe it’s a settled question. Mathematicians perform calculations that include infinities routinely nowadays. They have sophisticated methods for it, and have discovered powerful tools and useful results from doing so.
  - ravenstine 4y ago
    > None of them agree with you as far as I can tell. Oh really? How about Professor Hawking? https://scitechdaily.com/constraining-the-multiverse-stephen-hawkings-final-theory-about-the-big-bang/ https://scitechdaily.com/constraining-the-multiverse-stephen... > “We predict that our universe, on the largest scales, is reasonably smooth and globally finite. So it is not a fractal structure,” said Hawking. > “We are not down to a single, unique universe, but our findings imply a significant reduction of the multiverse, to a much smaller range of possible universes,” said Hawking. > I have never been a fan of the multiverse. If the scale of different universes in the multiverse is large or infinite the theory can’t be tested. [– Hawking] Not that it particularly matters. Cosmologists believe all sorts of things. Lots of cosmologists treat String Theory as more than a hypothesis despite how it hasn't yet panned out after decades and decades. Same goes for ideas like Dark Matter and Dark Energy, which are actually placeholders for some things we can't actually explain. That doesn't mean either of those things live up to their names or exist in any capacity. Hell, a substantial number of cosmologists profess that there's "got to be" alien life out there, despite no credible evidence what so ever. It's fine to hypothesize about all these things, but that doesn't make them even remotely fact, no matter what a cosmologist thinks. Science and mathematics aren't a majority vote. > some believe it’s likely it’s infinite They can believe that all they want, but that doesn't mean they're correct or that they have evidence. It's highly dubious whether it's even possible for us to verify the presence of infinitude. > none I know of believe it’s a settled question. That's because there are no settled questions. Any scientist or mathematician who professes that a question is settled immediately loses credibility by doing so. The difference between infinitude and finitude is one can be demonstrated and the other has yet to be demonstrated. Guess which one hasn't been demonstrated. Just because mathematics can include a construct that allows describing an indeterminate range of numbers doesn't mean calling it "infinite" is accurate. An actual value that can even remotely be referred to as infinity hasn't been calculated and it's possible that it never will if the known universe doesn't even support calculating it. To do math with "infinity" is to use an indeterminate vector in a way that proves useful. It's no different than when someone uses a phrase like "this is taking forever."

by simonh 4y ago

ravenstine 4y ago

> There’s also nothing about the physical universe to suggest that it is finite, or that it cannot contain infinities. It’s simply an open question. The only evidence we have is that it's finite. Just because the universe expands does not mean that at any given time it is not finite. > What does the universe or its physical extent have to do with the nature of numbers? The only way to have scientific confidence in an idea is to test it. We can't calculate infinity because, infinity being something that isn't finite, every unit of information in our universe would have to be used to describe infinity. This doesn't work because there is never infinite information space in our universe at any given slice of time. Think of it this way; you can't take a modern video game and get it to perform exactly the same on a home computer from 1996 because it simply lacks the computing capacity. The only way it can work is to reduce certain aspects of the software to make it work at a much lesser capacity. There are no examples of any system that can describe another system more complex than itself with total accuracy. Thus, it makes no sense that a universe in which we are currently only able to describe through finite numbers would be able to support calculating what infinity as well as support the rest of its contents, if it can even do that at all. This is why it's not at all accurate that a set of numbers can be "infinite." It only seems infinite because, for all intents and purposes, we don't have the capability to keep dividing a range of numbers forever. Even if we tried, the inevitable dissipation of heat energy would prevent us from doing so, that is if we don't simply run out of finite resources before then. If there is something that is indeed numerically infinite, we too would have to be infinite in order to make sense of it. We can't actually do that. That would be a contradiction. To illustrate this, go write some code that calculates every single number that exists in the "infinity" between two numbers. You won't be able to. Your software will fail because your computer doesn't support it. That is unless it has infinite bits. A set where there's "infinite" numbers would more accurately be described as being indeterminate. The seeming "infiniteness" of one of these sets breaks down when you realize there's no way to even demonstrate that part of a set is infinite. From a conceptual standpoint, it's similar to how it might seem that a ball will fall straight down when you drop it, and it's generally useful to think of gravity in such a way, but that doesn't mean that it's actually so, just as believing that a set can be "infinite" might be useful, but the use of the term "infinite" for something finite like a set is incorrect. So no, to others who think I'm being off topic. This is entirely on topic. A set being "infinite" gives you the wrong idea. At best, it defines a vector too large for humans or even human computers to find an end to. It's entirely virtual until proven otherwise.

simonh 4y ago
I’ve read articles, seen interviews and read book by mathematicians and cosmologists on these issues. None of them agree with you as far as I can tell. Some cosmologists and physicists believe it’s likely the universe is finite, some believe it’s likely it’s infinite, but none I know of believe it’s a settled question. Mathematicians perform calculations that include infinities routinely nowadays. They have sophisticated methods for it, and have discovered powerful tools and useful results from doing so.
- ravenstine 4y ago
  > None of them agree with you as far as I can tell. Oh really? How about Professor Hawking? https://scitechdaily.com/constraining-the-multiverse-stephen-hawkings-final-theory-about-the-big-bang/ https://scitechdaily.com/constraining-the-multiverse-stephen... > “We predict that our universe, on the largest scales, is reasonably smooth and globally finite. So it is not a fractal structure,” said Hawking. > “We are not down to a single, unique universe, but our findings imply a significant reduction of the multiverse, to a much smaller range of possible universes,” said Hawking. > I have never been a fan of the multiverse. If the scale of different universes in the multiverse is large or infinite the theory can’t be tested. [– Hawking] Not that it particularly matters. Cosmologists believe all sorts of things. Lots of cosmologists treat String Theory as more than a hypothesis despite how it hasn't yet panned out after decades and decades. Same goes for ideas like Dark Matter and Dark Energy, which are actually placeholders for some things we can't actually explain. That doesn't mean either of those things live up to their names or exist in any capacity. Hell, a substantial number of cosmologists profess that there's "got to be" alien life out there, despite no credible evidence what so ever. It's fine to hypothesize about all these things, but that doesn't make them even remotely fact, no matter what a cosmologist thinks. Science and mathematics aren't a majority vote. > some believe it’s likely it’s infinite They can believe that all they want, but that doesn't mean they're correct or that they have evidence. It's highly dubious whether it's even possible for us to verify the presence of infinitude. > none I know of believe it’s a settled question. That's because there are no settled questions. Any scientist or mathematician who professes that a question is settled immediately loses credibility by doing so. The difference between infinitude and finitude is one can be demonstrated and the other has yet to be demonstrated. Guess which one hasn't been demonstrated. Just because mathematics can include a construct that allows describing an indeterminate range of numbers doesn't mean calling it "infinite" is accurate. An actual value that can even remotely be referred to as infinity hasn't been calculated and it's possible that it never will if the known universe doesn't even support calculating it. To do math with "infinity" is to use an indeterminate vector in a way that proves useful. It's no different than when someone uses a phrase like "this is taking forever."