Mathematics is more than just arithmetic. Just because its a philosophical question does not bring it out of the realm of mathematics. It is more accurately a mathematics question than a philosophical question. I've heard this area of study both described as "the philosophy of mathematics" and as "the foundations of mathematics". It uses mathematics terminology, and often goes over the heads of most philosophers due to the understanding of mathematics terminology that is necessary.

I presume you missed the part where I said we could both assert exactly what you ended up saying lol. We both know it involves more than arithmetic, hence 'more intertwined (math and philosophy) than not.' I didn't say that to be an ass, as I take mathematics very seriously and respect those who would study it. But this discussion was covered in the most basic of mathematics courses we took as undergrads. My professor who introduced me to proof writing long ago said it more eloquently than I ever did, "axioms aren't truth because we say they are, but rather because we need somewhere to start, a foundation for higher level mathematics, because after this point we won't be doing just calculus."

And who is able to say that the number you posted doesn't represent the number of atoms present in the physical universe. And as the universe expands, add 1 to that number until yournumber+1 exists. I didn't mean to say that we 'may at some point' prove it to be true, but rather it IS true. There are applications to the number you gave, and perhaps a savant out there knows it. But we wouldn't know, would we? or wouldn't you? Maybe because your and my knowledge of math is so basic we don't recognize that there are those who are finding applications to that specific number. Lest we recognize that it'd be a waste of funds better spent on curing breast cancer, because it isn't like 99.9999% of cancers operate the same way.

hehe, it was a fast sketch and my math is a bit under-used. probably ain't done ^ to a number for a decade or two.

jagernacht - when the universe is expanding, its expanding, not increasing in mass

Most axioms are valid to an intuitionist. What intuitionists have a problem with are non-constructive axioms, such as the axiom of infinity and especially the axiom of choice.

Something such as the axiom of extensionality, which states the conditions upon which two elements can be considered equal, is very different from something such as the axiom of infinity.

http://en.wikipedia.org/wiki/Hawking_radiation

how does the radiation escape, but light can't escape?

ugh, why do ask silly questions before i read what's on the link.

yeah dibs i figured, considering you knew what you were talking about... the third one looked right still eh?

ah, correct Rockman, my error hehe. it was early in the morning and I didn't really pay attention lol... yes, if you substitute sq cm or mm for atoms then the analogy holds.

And yes... the fact that it's a non-constructive axiom is exactly why I figured you posted it here. hence why I wish there were more mathematicians present. i always enjoyed conversations degrading into arguments about existence involving almost always the axiom of infinity. none of my peers had brought up this argument before though, so it's interesting. I'm especially interested to see what this discussion leads to.

this is computer doesn't have anything installed on it except the OS. i usually use excel for my scratch pad and to check my math. i only manually do math for my checkbook register.

The "sphere" is used correctly; kinda. The observable universe from earth, today, is a sphere with a diameter of 93bn (not 150 :P) light years, centered on Earth. Tomorrow it'll be a bit larger. That means that anything outside that perfect sphere, even though they might exist we can't observe them directly because the light from them didn't have enough time to reach the earth. Kinda like Rockman's problem... We assume that the universe is infinite but best we can do, today, is to measure distances of 46bn light years in any direction.

need to read through these

ok well basically even if the big distances involved are 95 billion instead of 150 , if the 2 furthest away from "each other" bits of the discernible universe are 95 billion light years apart . then assuming everything else was constant - speed of light - gravity - laws of physics as we know them , then that to my mind questions the original assumptions made by einstien and all the rest of them because that suggests matter moving at least close to twice the speed of light .
now i dont claim to be an physicist or much of a maths wiz , but im questioning why we blindly accept something , just because someone else says it .
my untrained thought is , if you have to change a parameter to make a theory continue to fit , then maybe you need to rethink the theory , my main reason for questioning the speed of light thingy , is that people say you cant go faster than it . my gut feeling is that if the universe has been around less than the 40 odd billion years for the universe to spread out 40 odd billion light years in distance then i still think however you measure the speed of travel , it would have had to have travelled faster than we currently measure light travelling at . and if dumb unorganised matter can do it , im pretty sure we could engineer it to happen eventually.

Its not matter that is moving close to twice the speed of light. It is space itself that is expanding.

Space has no mass, and can therefore move at whatever speed it feels like.


If you want an example, think of a glass of water. There's the volume as defined by the glass (space), and the water (matter). But lets say we can make the glass expand, causing the water to fall to the new bottom of the glass. So, what if we make it expand so fast that the water never reaches the bottom, it just infinitely falls?

Probably a bad example. inb4 rockman

I'm still a bit lost on why anyone has a problem with this... assuming computational power, the philosophical question is easy. Yes, it can be represented. It is only a large number of digits because you are using base 10. I provided a version of the equation in base 32 earlier. But you could just as easily represent it in base 256, given enough unique symbols or another representation scheme as IP addresses are (in base 256).

To the original question, I am liking what Atryn is saying.



I am not sure exactly what you are trying to show, but just because you can pose a problem does not mean it is physically meaningful. If you had a rod 10 light years long and pushed it, the information of your push would not transmit instantly, nor at the speed of light, but at the speed of sound of the rod. I guess the equivalent to your problem is that somewhere you have to have a mass that is causing the water to "fall". Again, I am not exactly sure what you're trying to show.

Arthog, it's wrong to apply distance = velocity * time equation other than for nearby points. For example, a point at the edge of the observable univers, currently is situated around 46bn light years away, using current metric. However, 13bn years ago that point was "much closer", again, using today's metric. Hence the paradoxes: a distance of let's say 6 light years (as of 2011 metric) was covered by light in 13bn years thus much "slower" than c, whereas the 46bn light years distance (as of 2011) is travelled by light in 13bn years thus much "faster" than c.

Detmerp: The example it meant to be simple, and so is meant to mean the glass is on Earth, explaining why the water falls. It's an attempt to describe why space can expand faster than the speed of light, and why matter can't. Water and light have limiting factors (water, since it is falling through another fluid, is limited to a terminal velocity; matter would need an infinite amount of energy). Space is more of a volume though, rather than an actual thing, similar to the space within the glass. So, because space has no mass, it can expand as far and as fast it feels, just like the glass not having some limiting factor, allowing it expand as much as it likes. Practically, the glass would have a limit, but this is hypothetical, and is my interpretation of things. Whether or not it makes sense to you isn't my problem, but it's how I make sense of it.

Following that reasoning space would have already reached infinity since it can travel at infinity distance units/time units. I admit I am not particularly well versed in cosmology but it seems that viewing space as an ever expanding nothing, bounded by nothing, that we would never have any way of ever characterizing its extents, only the extents light and mater have traveled in it.

If a number's too big, just convert from yen to dollars. Porblem solved!

I don't think we blindly accept things otherwise Christopher Columbus wouldn't have set sail for the new world, Einstein wouldn't have bothered with the theory of relativity and Zen wouldn't have experiemented with Ravi in between bathroom stalls. We challenge the norms on a continual basis and rediscover science, math, etc as we go.

As for your question, I believe good ole Albert answered it with relativity--aka the universe (space as we're talking about it) can grow faster than the speed of light. Of course you're thinking of the universe as a place that can be visualized. If you start at point a and and go all the way around and you would in theory end up back there, but many people believe there is still light bouncing around out there from the big bang itself.

Actually Columbus did accept things blindly. He didn't set sail for a new world, he set sail for a well known old world, just that he thought that the circomference of the earth was about 1/4 of its actual size. It was only by luck that he stumbled upon a new continent, otherwise he'd starve to death in his voyage. He didn't even know, nor accept, for the remaining of his life that he discovered a new world; he was sure that he found a route to East Indies. But you're right about Albert! (I can't and wouldn't even atempt to comment about Zen and Ravi though.)

But yeah, that's the big problem we all face. Relativity isn't a concept we can easily visualize.

don't think i accept things blindly. i usually ignore them until i might have to use them, then i check to see if it works.

there was also some program on television the other day where the claim on the show was that in the first 10 minutes of the universes expansion from the big bang it spread to more than 10,000 light years . its funny to think that scientific arguments are used to disprove much of the claims of religion , then expect us to take their theories on faith .

you don't know jack about science.

All i have to so is that numbers do not exist. They are purely a form of measurement.

Well this is a lot like watching a bunch of monkeys trying to fluff a football - except that the football is a perfect sphere with no mass and the monkeys are only an abstraction represented by a numerical constant, and the concept of fluffing is a purely illusionary concept based upon a hypothetical point of reference where it could theoretically exist - but otherwise its exactly like the monkey's and their football.

great thread