/sci/ - Science & Math

>>2616523
Well,
>a) the universe is finite, and
Is likely wrong. The evidence is pretty supportive of a universe with infinite mass and space.

>b) there is a quantum of length
I'm curious if there's any sort of anything that supports this. Citations would be most welcome please.

sqrt2/1000000000

pi is an abstract concept that applies to perfect mathematical circles.

it doesn't matter that perfect circles don't exist in real life.

>>2616542

my post was suppositional, I wasn't proposing that either thing was true.

However I fail to see how the evidence supports a universe infinite in spatial dimension if space is expanding.

There is no end to pi because it is the result of two infinity functions. Two functions of which result from other exact number-line collisions; however, if one were to jump to a conclusion, the only number pi could end with is 0.

>>2616523
>>2616542
>>2616549

Who let the trolls in?

pi is a construct of a perfect circle, if you apply real world conditions such as quantum lengths and the sort, the value you are working out is not pi, but a real world appoximation of pi. Essentially you can never make a real world perfect circle.

You are just designating the a certain appoximation. Same as every math teacher in history chooses to designate 3.14. Yours just happens to me more accurate.

Why is the finite universe necessary? Why not just have "if an infinitely small particle does not exist, Pi has a finite practical length" or something.

OP is a physicist

thinks maths has to have basis in reality

>>2616549

exactly, if the two criteria are true then there is a point past any digits in pi are just abstract mathematical constructions.

>>2616542
>infinite mass

>>2616555

If pi's digits were to end with zero then wouldn't it have ended with the digit before that? Also what two functions are you talking supposing?

>>2616554
>However I fail to see how the evidence supports a universe infinite in spatial dimension if space is expanding.
Not seeing how "expanding universe" is inconsistent with "infinite in spatial extent universe".

Are you one of those people that would ask "What is the universe expanding into?" It's not expanding into anything. That's like asking what's north of the north pole. Space is not Euclidean.

Also:
>'A Universe From Nothing' by Lawrence Krauss, AAI 2009
http://www.youtube.com/watch?v=7ImvlS8PLIo

>>2616560

Because you could make a circle of arbitrary radius in an infinite universe and thus require more digits of pi to calculate the circumference.

>>2616569
>If pi's digits were to end with zero then wouldn't it have ended with the digit before that?

you're forgetting sig figs

>>2616564
I suggest that you learn some modern astrophysics.

>>2616562
all the digits are abstract mathematical constructions

all numbers are

Singularities are perfect circles.

>>2616572
Except the rotating ones.

Unless you mean the the point mass itself and not the event horizon, in which case we're talking about a point, which I guess might constitute a circle by the formal definition, a circle of radius 0.

>>2616575
>thinks you need to construct a circle to calculate pi

HERPITY

>>2616542
>>2616549
>>2616554
>>2616555
>>2616558
>>2616562
>>2616558

If you had a perfect circle, it would measure out to pi. You would need increasingly precise measuring tools to determine that last little bit, infinitely.

And why can't you have a perfect circle?

>>2616570

No, of course not. But a universe that is already infinite in spatial extent cannot have space added to it. Therefore the universe must be finite in extent.

>>2616576
Bitter irony. The total amount of mass/energy of the universe isn't infinite.

>yfw I'm right.

>>2616589
Yep, you are one of those people.

Again, the universe isn't expanding into everything. You can expand an infinite universe. Go see Hilbert's Hotel for some thought experiments about infinity. It demonstrates how easy it is to expand an infinite thing to add more space to it.

>>2616570
Unbounded != Infinite

>>2616576

Infinite universe is fine, but infinite mass?

I'm a mathfag but surely if the universe has infinite mass then we are all in a singularity and the universe doesn't exist.

>>2616597
Whatever. I don't feel like playing those pedantics. I don't see a functional difference.

>implying OP's image is Pi and not 'J[;

>>2616584

No, but you need pi to calculate the measures of a circle. A circle with the radius of the entire universe, if the universe is finite and has a quantum of length, would not require infinite digits of pi to calculate.

>>2616591
The curvature of the universe is likely 0, given the available evidence, and thus the total energy content of the universe is likely 0.

That doesn't mean that the mass is zero. The mass is infinite. It's "canceled" by the negative gravitational potential energy, among other terms.

Pi, in this case, is not a measurement in the real world, it is a study of geometry.

The concept of a circle.

>this thread

>>2616601
If the mass is flying apart fast enough, then gravity wouldn't cause it to collapse.

Then we discovered the increasing rate of the expanding universe, and hence "dark energy", which makes it even "harder" for the universe to collapse into a point mass.

I have a feeling i'm the only person in this thread, and the other 25 posts are all samefag troll.

>>2616615
Actually, I don't see any obvious trolls in here, just people ignorant of modern cosmology, and of course me who strongly refutes the strong version of relativism. Call that a troll if you want.

>>2616569
Plot out a circle which has infinity size. Now look at the properties of the number lines you are using and pretend the graph is actually circular instead of flat.

According to the bible, pi is exactly three.

>>2616619

Not my point, if the universe has infinite mass, that implies that every point in the universe has infinite mass, or the universe is infinite but not unbounded.

Or both? Oo

I thought common thought was that the universe was boundless but finite.

>>2616626

wut

>>2616632
What the hell does "boundless but finite" mean?

Know, the current understanding is that the curvature of the universe is 0, which means infinite space, mass, and zero net energy. Again, see:
>'A Universe From Nothing' by Lawrence Krauss, AAI 2009
http://www.youtube.com/watch?v=7ImvlS8PLIo

>>2616603
is the universe known to have euclidean metric?

i mean 2pi r may not apply?

>>2616625
String cosmologist here. No, the universe is not infinite in mass. Just Google it and find out for yourself, since I'm too busy/lazy to do it for you.

>>2616542
>a universe of infinite mass
The universe has zero mass. To within experimental error.

>>2616643
The evidence is consistent with a 0 curvature universe, so yes in the sense that you're using. Of course local masses with disturb this.

>>2616643
To within experimental error, yes. (to within 0.1%, the universe has no curvature)

>>2616608
very much different

the earth's surface is not bounded, if we don't think of it embedded in 3D, but it isn't infinite.

this analogy applies as, afaik, the universe is not embedded in a higher dimension

>>2616610
READ THIS
IT'S A MOTHERFUCKING GEOMETRIC CONCEPT
GTFO PHYSICSFAGS

>>2616647
String cosmologist? Lols. Let me know when your string theory is actually observationally verified.

Also, no, you are the idiot. So, let's follow my simple chain of inferences here:

The microwave background radiation, specifically the "blotches" and variation therein, plus the age of the universe, allows us to measure the curvature of spacetime. This curvature is approximately 0. If it is 0, or an open universe, then there is infinite space and infinite mass.

Which part are you disagreeing with?

>>2616648

you sciencefags need to stop saying shit like this, one day we're all just going to fucking disappear when some chucklefuck realizes we can't technically exist

>>2616654
Ah, I see, no the evidence indicates that we likely live in a flat, not closed, universe, which means it is boundless and infinite.

If you had a circle, 99.999999999999999999999999999999% accurate, (i would agree that you can't have a perfect circle IRL), stretch the circle out and measure it. You would need more precise measuring tools to measure that extra little bit. And then that will leave a little bit, and so on. Once you reach the exact measurement, increase the accuracy of the circle to 99.9999999999999999999999999999999999999999% and do it again.

Why do people not want to believe in infinite digits? You must believe that the concept of negatively infinite does not exist as well, because if you do then you know things can become infinitely small. Like the significance of pi's digits.

And shit, i've never taken a physics class in my life but i have a feeling i'd do a lot better than a lot of people here.

>>2616683
That's a troll. No current scientist says that there is zero mass. That's trivially provable false. You person has mass, so there.

>>2616639
Objects have multi-dimensional properties. One dimension can infinity value while another is limited. If the universe is constructed with different infinities, you can limit them through definite size. They will continue to stretch infinitely in one dimension while they are measurably not infinite in another.

> 43 posts and 3 image replies omitted.
Successful troll is successful.

>>2616687
Again, I don't see a troll. I see legitimate questions about cosmology mostly. The original question was "Is there a point at which further digits of PI would have no practical impact in describing the natural world?" It was answered, in numerous ways, including my favorite "Forgot about significant digits".

>>2616682
If you had a circle whose diameter was as large as the visible universe - some 90 billion light years - 30 digits of pi would be all that is necessary to calculate its circumference accurately to within one radius of a hydrogen atom.

Pi IS a mathematical construct. No one cares about any figure past the thousandth unless they are pursuing it for the sake of pure mathematics.

>>2616692
mass + gravity = 0

>>2616721
Correct (for the suitable intended meaning). That is fundamentally different than mass = 0.

>>2616721
You, sir, are not longer worth disagreeing with.

Distance = Time

>>2616713

Thanks, quotes.

I heard that. Even though i'm extremely skeptical of it, but that is NOT an argument for pi having finite digits. Not even close, i hope that wasn't what you were trying to do?

>>2616715

nobody cares about any digit beyond the 5th or 6th

you can travel to the fucking moon and build a rocket with that much pi

>>2616680
i'm curious about how this topology is reconciled with the big bang.

we had a much denser, but still unbounded and infinite universe, and before that...?

>>2616751
But can you entangle energy from the sun?

>If:
>a) the universe is finite, and
>b) there is a quantum of length

>then it follows that there is a final digit of pi.

No, it doesn't. It just follows that it is impossible to physically construct an object that is perfectly circular. But then, we already knew that.

Also, [citation needed] for a and b.

>>2616753
We don't know what was before that. We calculated the topology with the big bang as a premise. At the last scattering surface, it was mostly uniform, but mass would start to "clump" together. The clumping depends on the various models of the big bang, and the clumps will have a particular size. By looking at the microwave background radiation, we can see these clumps. The clumps will appear different depending on the curvature of spacetime. The observations made are consistent with a 0 curvature spacetime, with a rather small margin of error.

Again:
>'A Universe From Nothing' by Lawrence Krauss, AAI 2009
http://www.youtube.com/watch?v=7ImvlS8PLIo

Pi is a constant. It does not have to relate to length, it can rather relate to time.

So your proof is null and void.

>>2616751
Really? That is .. surprising at first glance.

>>2616751
>nobody
nobody but mathematicians

and not many of them, its other properties are more interesting than its representation in some number system

>>2616542
The energy of a photon is inversley proportional to it's wavelength, if the energy is too high the photon collapses in on itself, and no infomation can be gained from measuring something using a larger wavelength than itself.

It's called Planck length, look it up.

>>2616784
I really don't follow what you're saying. You said some true stuff, and then said "See? Planck length". I took your advice, and googled it

http://en.wikipedia.org/wiki/Planck_length
>The physical significance of the Planck length, if any, is not yet known.

>>2616771
i think you mean something other than topology, in the sense i mean it.

i wonder how you can change from a point (if that's what there was) to something infinite and unbounded.

whereas one can imagine a point "exploding" to an expanding three dimensional surface of hypersphere (a bounded finite universe), as if you shrink a hypersphere, you get a point. this process is well understood in topology.

>>2616814
Perhaps we are.

Either way, the big bang theory does not say that the universe, or even the current observable universe, once fit into a point mass. That is a fundamental misunderstanding of big bang theory. I don't know if you hold such a misunderstanding, but I just want to be clear on this point.

>>2616523
This is the most retarded thread I was given to ever see on /sci/.
Also the most pathetic trolling attempt.

>>2616542
>infinite mass and space
if the universe is infinite in mass and space then every point in the sky must contain- at some distance- a body radiating energy. if the universe is infinite in mass, this radiation should be infinitely strong. If there is no reason for energy to disappear, it would make sense for the sky to be infinitely bright if the universe were infinite, however it is not. Therefore 1) you're right, but energy isn't conserved at a non quantum level, meaning our understanding of physics is massively flawed, 2) you're wrong, or 3) you have an interesting explanation I look forward to reading

tl:dr
lies, proooooooove it

>>2616856
What is with the hate of this thread? There's very little trolling going on. The OP's question is legitimate, if poorly phrased.

>>2616866
http://en.wikipedia.org/wiki/Olbers%27_paradox

In short, your argument is:
>1- infinite number of stars
>2- infinite number of stars imply infinite night sky brightness
>3- the night sky is not infinitely bright
>4- proof by contradiction: no infinite number of stars

There are two problems with this.

The first is geometric. If you have infinite mass over a "bigger" infinity of space, then that wouldn't make the night sky infinitely bright.

The more important second refutation is this: Light takes time to travel distance, and the universe (as we know it) has only been here a finite amount of time. Combine these two facts, and there are stars out there whose light is still on route to us. Now, at some point in the past, everything was really hot, and shone equally bright in all directions (more or less). This is the final part of the "big bang". Why isn't the sky infinitely bright, or at least bright? Why can't we see this? But we can - it's called the microwave background radiation.

Alternatively, as a play on the first point, with an expanding universe, we will never see light of some stars, for all of time. Space will expand fast enough that the light will never reach us.

>>2616866
Also, please see:
>'A Universe From Nothing' by Lawrence Krauss, AAI 2009
http://www.youtube.com/watch?v=7ImvlS8PLIo

>>2616911
For the second time in this thread:

Unbounded != Infinite

>>2616924
Ok. Sure. This is important, as I don't know.

I was under the impression that 0 curvature meant, or was commonly understood / assumed, to be infinite space. Of course infinite space is consistent with this.

I think I see my error. Thank you. I need to do more research.

>>2616904
and
>>2616911
an infinite number of points, even distributed over an infinitely large space, would still cover every point. the distance between some stars and us would be so large the light from them would take trillions of years to reach us, but it would still do so

it's understandable if the universe has been here for a finite amount of time that not all of the possible light has reached us- I'm not sure how big bang theory and an infinite universe can fit together, though
the video is great, I've already listened once but I'm putting it on again: thanks for the reminder.
also, I'm not >>2616924

>>2616952
>an infinite number of points, even distributed over an infinitely large space, would still cover every point.
Yes, but the light would be so weak as to be almost undetectable. Light spreads out as the distance squared. If the stars are far enough apart, then the sky would indeed have a star at every direction, but that doesn't mean it would be noticable. At least I think.

Still, the better refutation is the finite age of the universe and the finite speed of light.

And don't forget the expanding universe. Due to the expansion of the universe, there will be stars out there whose light will never reach us - the universe expands too quickly and the light will always be on route.

>>2616981
an infinitely large number of infinitely small amounts of light would amount to the most light possible, though. For every point in the sky there would be a correlating beam of light straight from the star to us.
Also, as all of the universe would be recieving infinite energy in the form of light it would also be giving the same level of energy out- in effect, stars a long, long distance away would be so incredibly powerful the distance didn't matter in terms of light intensity

I agree that universal expansion would explain the lack of light, but not that expansion would fit with an infinite universe.

>>2617001
>an infinitely large number of infinitely small amounts of light would amount to the most light possible, though. For every point in the sky there would be a correlating beam of light straight from the star to us.
I think you're making some mistakes. Infinite / infinity does not necessarily equal infinity. It could be infinity, a nonzero finite number, or zero. It depends on the kinds of infinities.

If you have an infinite number of stars over an infinite space, the amount of light which reaches us could be a non-zero finite number. In fact, it could be a very small non-zero finite number.

Let me take an example. Imagine a sphere of light bulbs surrounding the Earth. Depending on the power output, we will see an apparent brightness of the sky. If you take those light bulbs and move them back double the distance, then the power which reasons the Earth goes down by a factor of 4.

This problem is a calculus limit problem.

>I agree that universal expansion would explain the lack of light, but not that expansion would fit with an infinite universe.

I now understand from that other anon that curvature 0 doesn't mean infinite space.

Still, how is infinite space inconsistent with an expanding universe? I don't understand your argument.

>>2617025
Can someone help me phrase that first argument in a better way? I'm pretty sure it's right, but I can't put it into words atm, and I'm not a physicist.

faggot who knows nothing about physics, cosmology, or higher math here:

If the universe is finite then what is the edge of the universe like?

>>2617025
re: first point- however, an infinite number of light bulbs all giving off any amount of energy while surrounding earth would result in an infinite amount of light reaching earth- regardless of the energy output of a single bulb, the matrix of bulbs all passing energy to the others will cause the amount of energy being transferred to be vastly higher than that of a finite number of bulbs. Comparing finite light sources moving further out to infinite light sources further out isn't a valid analogy.

re: the second- Sorry for the ambiguity, I meant that I don't understand how an infinite amount of mass and space could expand from a finite amount of space in a finite amount of time.

>>2617059
good question. As the universe is expanding at the equivalent of something faster than the speed of light, I don't think we'll ever know. It'd probably just be completely black, though.

>If:
>a) the universe is finite, and
>b) there is a quantum of length

>then it follows that there is a final digit of pi.

NOPE.avi
You literally sound like one of those pseudo-intellectuals that has literally no mathematical knowledge at all.

http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

>>2617059
There is no edge. Space would not be Euclidean. If you look far enough in one direction, you would see the back of your own head.

>>2617065
>Sorry for the ambiguity, I meant that I don't understand how an infinite amount of mass and space could expand from a finite amount of space in a finite amount of time.
Ah, again: the big bang theory does not posit an original universe of finite space. That's your problem.

It might have been finite, and it might not have been.

JESUS THIS THREAD IS FULL OF TROLLS.

This video pretty much answers your dumbass question OP.
http://www.youtube.com/watch?v=woySeSNBL3o

/thread

>>2617164
Fuck off and let us have a real /sci/ discussion in /sci/.

>>2617105

if space is infinite then this can't happen, what you just said can only happen in a boundless finite universe.

Unsure if you are the same namefag as before but if so you just contradicted yourself.

>>2617111
touché
so the idea is the universe is expanding in the shifting person in room one to room two, room two to room 4, 3 to 8 sense like that hotel based explanation for the size of infinity?

>>2617181
That was in reply to his question "What if space was finite". I answered in the context of that question.

A 0 curvature universe could be finite in extent or infinite in extent. At this point, I am unfamiliar with good scientific arguments for either possibility.

>>2617185
Yep. Just like Hilbert's Hotel, at least I think so.

>>2616523
While I could agree with you on a and b, as those are my assumptions as well given the evidence that I've seen (however, I don't think the evidence is strong enough for it, and I'm willing to change my belief if strong enough contradictory evidence is found).
As for the pi question, pi is defined for real numbers using euclidean geometry, whatever some universe's geometry and physics is is irrelevant to the value of pi, but the length of a circle in a quantized/digital geometry will of course be a rational number (just draw a cicle on a digital picture), but of course this number will approximate pi (depending on the geometry, if it's close enough to euclidean) to some error.

>>2616776
This is a good point. OP should add c) there is a quantum time.