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Is Infinity Possible

The Sum of Awe

Brought to you by the moment that spacetime began.
I've always had an interest in the philosophical concept of nothingness, but just for a short while I am looking at the concept of infinity. To me it's not near as interesting as nothing, there are so many questions that nothing can bring to the table, but the only question infinity has left me for desert is its reality.

I can't imagine how it would be possible for there to be an infinite amount of things at one time. Some believe that there is an infinite span of space, and less accurately some even believe that about matter/energy.

My thought is, how is it possible for infinity to be represented in physical reality? Really think about it.

I do, however, consider it possible that time is endless and its span therefore is infinite, conceptually speaking. At the same time, though, time is limited and it will always be limited. (Disregarding the idea that time had existed for an eternity previous from this moment, another topic) There may be no end of time, but it can never reach 'infinity'. Nothing can reach infinity, since there is no end to it.

If you think of counting all of the grains of sand on a beach, counting all of the grains of sand on earth, counting how many atoms there are that make up every single sand grain on earth, and then how many atoms there are in the galaxy, lastly the universe, it can seem like there is an endless amount, but doesn't there have to be an exact number?
 

LegionOnomaMoi

Veteran Member
Premium Member
My thought is, how is it possible for infinity to be represented in physical reality? Really think about it.
It is (at least in theory) possible for a system to have an arbitrarily high temperature (regardless of scale). That is, while there exists an "absolute zero" temperature, there is no maximal temperature (there are infinitely many positive temperatures). Yet we can and have prepared systems that are infinitely "hot" (have temperatures that are infinitely greater than any positive temperature).

Nothing can reach infinity, since there is no end to it.
If one allows for any quantity (space, time, etc.) to be continuous, then it follows necessarily that there must be infinitely many "units" of this quantity. For example, if one maintains that spatial extension is continuous (i.e., we can always consider half of some length, area, or volume; actually, continuous technically requires there to be infinitely many more possible measures of such quantities than this infinity), then necessarily there exists physical representations that are infinite in any amount of such quantities (i.e., any particular amount of space or time is composed of uncountably infinitely many quantities of space or time).
Once the infinitesimal is allowed, infinities follow.
 

crossfire

LHP Mercuræn Feminist Heretic ☿
Premium Member
I've always had an interest in the philosophical concept of nothingness, but just for a short while I am looking at the concept of infinity. To me it's not near as interesting as nothing, there are so many questions that nothing can bring to the table, but the only question infinity has left me for desert is its reality.

I can't imagine how it would be possible for there to be an infinite amount of things at one time. Some believe that there is an infinite span of space, and less accurately some even believe that about matter/energy.
Infinity is not a number. In infinity is a conceptual abstraction. ∞ + 1 = ∞. You can divide infinity up and still have infinite sets, such as positive integers and negative integers. Both sets are infinite, and neither set intersects the other. (Infinity is not concrete like numbers are.)

My thought is, how is it possible for infinity to be represented in physical reality? Really think about it.
Since infinity is not concrete (see above.) You might want to explore the physicality of abstractions (wiki link)

I do, however, consider it possible that time is endless and its span therefore is infinite, conceptually speaking. At the same time, though, time is limited and it will always be limited. (Disregarding the idea that time had existed for an eternity previous from this moment, another topic) There may be no end of time, but it can never reach 'infinity'. Nothing can reach infinity, since there is no end to it.

If you think of counting all of the grains of sand on a beach, counting all of the grains of sand on earth, counting how many atoms there are that make up every single sand grain on earth, and then how many atoms there are in the galaxy, lastly the universe, it can seem like there is an endless amount, but doesn't there have to be an exact number?
Now you are trying to apply the concrete to the abstract. You might get more traction if you use other abstractions for comparison, rather than the concrete.
 

LegionOnomaMoi

Veteran Member
Premium Member
Infinity is not a number. In infinity is a conceptual abstraction. ∞ + 1 = ∞. You can divide infinity up and still have infinite sets, such as positive integers and negative integers. Both sets are infinite, and neither set intersects the other. (Infinity is not concrete like numbers are.)
The problem with this description is that some infinite sets are larger than others. Thus there are more irrational numbers between any two numbers than there are integers (or rational numbers). The set of integers and rational numbers are both infinite, but are smaller sets than the set of irrational numbers between e.g., 3 and pi.
 

idav

Being
Premium Member
There seem to be a few definitions for infinity, one of them being without end, in reality would be something akin to continuous.

Typically religion and philosophy use the term eternal for concepts of time with no beginning or end where as infinite sets typically have a beginning.

It seems to me that how math utilizes infinite just aggravates the issue. For example pi is a very useful concept when it isn't infinite, but truly pi is infinite.
 

LegionOnomaMoi

Veteran Member
Premium Member
There seem to be a few definitions for infinity, one of them being without end, in reality would be something akin to continuous.
Not really, at least if you intend by "continuous" something akin to the physical/mathematical notion of continuity. Given physical measurements of any would-be continuous quantity (or description of points on a would-be continuous number line) one finds that there exists numbers, points, or values such that between any two of these kinds of measurements, points, numbers, etc., there exist infinitely many others yet that this infinite set is negligible.
More simply, continuity is not at all what one might think. We intuitively consider a series of points to be continuous if they make up a line, i.e., that one can't find any gaps (between any two points, there exist infinitely many more, making the line "continuous"). The rational numbers are such points: between any two, there exist infinitely many more. Yet the rational numbers are negligible; there are almost none of them in any interval of the number line. Continuity requires greater/larger infinities.
Typically religion and philosophy use the term eternal for concepts of time with no beginning or end where as infinite sets typically have a beginning.
Often the term is used in the context of infinite regress, first cause, and other notions that implicitly or explicitly relate to continuity.

It seems to me that how math utilizes infinite just aggravates the issue.
It does, but only because it clarifies the issues involved. The "issue" is complicated and it is only with the use of mathematics that it can be analyzed. Thus Zeno's paradox was resolved and the use of infinite quantities in fundamental physics made sensible and pragmatic.
For example pi is a very useful concept when it isn't infinite, but truly pi is infinite.
Pi is finite. It is actually infinitesimal. But I'm assuming you mean that its decimal representation is infinite (or that the exact value corresponding to pi requires infinite information for its representation).
 

Deidre

Well-Known Member
It's hard to imagine because there is simply no way to measure all of space...all of time. It could end at some point, but we are not able to answer ''when'' so perhaps there is an assumption that time and space is infinite. From a Christian view, I don't find it hard to believe that.
 

NoGuru

Don't be serious. Seriously
Easy. Divide by Zero, you get infinity.

Now before someone jumps in and says "YOU CAN"T!!!!11!!1", you can't take the square root of -1 either, but we use it in electronics all the time.

How much of "nothing" can I put in a box? Hypothetically an infinite amount.

Look on YouTube for division by zero on a mechanical calculator. It spins and spins trying to tabulate an answer, because the number is infinite.
 

LegionOnomaMoi

Veteran Member
Premium Member
Easy. Divide by Zero, you get infinity.

Now before someone jumps in and says "YOU CAN"T!!!!11!!1", you can't take the square root of -1 either, but we use it in electronics all the time.
You can take the square of negative one because i= sqrt(-1) is true by definition. By definition, division is the inverse of multiplication such that if a*b=c, then a=c/b. As this definition is true for division by 0 only if a, b, & c are 0, division is undefined.

How much of "nothing" can I put in a box? Hypothetically an infinite amount.
If you can put an infinite amount of nothing in a box, you can put a lesser amount of nothing in a box. How much of nothing can I put in a box in order to fill it up half-way?
 

NoGuru

Don't be serious. Seriously
You can take the square of negative one because i= sqrt(-1) is true by definition. By definition, division is the inverse of multiplication such that if a*b=c, then a=c/b. As this definition is true for division by 0 only if a, b, & c are 0, division is undefined.

The definition of a square root is two numbers squared equaling X. No number can be squared to equal -1


If you can put an infinite amount of nothing in a box, you can put a lesser amount of nothing in a box. How much of nothing can I put in a box in order to fill it up half-way?

69d6a2d8071bf57eb179d4ce82911ca1.jpg
 

Tumah

Veteran Member
I've always had an interest in the philosophical concept of nothingness, but just for a short while I am looking at the concept of infinity. To me it's not near as interesting as nothing, there are so many questions that nothing can bring to the table, but the only question infinity has left me for desert is its reality.

I can't imagine how it would be possible for there to be an infinite amount of things at one time. Some believe that there is an infinite span of space, and less accurately some even believe that about matter/energy.

My thought is, how is it possible for infinity to be represented in physical reality? Really think about it.

I do, however, consider it possible that time is endless and its span therefore is infinite, conceptually speaking. At the same time, though, time is limited and it will always be limited. (Disregarding the idea that time had existed for an eternity previous from this moment, another topic) There may be no end of time, but it can never reach 'infinity'. Nothing can reach infinity, since there is no end to it.

If you think of counting all of the grains of sand on a beach, counting all of the grains of sand on earth, counting how many atoms there are that make up every single sand grain on earth, and then how many atoms there are in the galaxy, lastly the universe, it can seem like there is an endless amount, but doesn't there have to be an exact number?
I think of infinity as being a negative quality ie. caused by a lack of boundary in some respects. Time could have an aspect of infinity if it there is no boundary to how far it extends, but it remains bound as a concept of the passage of change. Numbers could also have an aspect of infinite since there is no end to how far one could count. But they are restrained to concepts used for counting. You can't peel your potatoes with them.

The only way that something could be completely infinite is if it lacked all boundaries, in which case nothing else could exist, nor could its existence be differentiated in any way lest we bound it. I call that G-d.
 

LegionOnomaMoi

Veteran Member
Premium Member
The definition of a square root is two numbers squared equaling X. No number can be squared to equal -1
Wrong. The number i can, by definition (much like the way in which because, the rule
gif.latex
, the integral of the function f(x)=1/x would be undefined by this rule but is instead defined via the construction of a new function such that
gif.latex
. In other words, because the product rule for integrals involves division by 0 when the exponent is -1, we can't use the rule in this case. So we define a new function that is by definition the value of the integral in this case.
Also, infinitely many numbers can be squared to equal -1. One simply needs to be working within the proper mathematical space.
 

NoGuru

Don't be serious. Seriously
So how is division by zero not allowed then?

You basically said: The rules we had before said it was impossible (the case for i), so we made up new ones to accommodate. The problem with our mathematical system is it's self proving... using itself. That's like a cult leader with all the answers, because he's making them up. You can't prove him wrong no matter what, because he's winging it, per say. New problem? Give him a few days and he'll have a new rule to solve it.

So if I create a new rule to allow for the division by zero, booya, problem solved right?

Well no... we "don't allow" division by zero because I can then prove that 1=2... everything is equal to everything else and this deteriorates everything we know about our made up system, therefore it's "not allowed." The tell tale sign of an imperfect system is the dis-allowance of dissent.
 

Ana.J

Active Member
I think that infinity is impossible because if everything in the Universe is finite then how it can be infinite?
 

LegionOnomaMoi

Veteran Member
Premium Member
So how is division by zero not allowed then?
It is considered undefinded.
You basically said: The rules we had before said it was impossible (the case for i), so we made up new ones to accommodate. The problem with our mathematical system is it's self proving... using itself. That's like a cult leader with all the answers, because he's making them up. You can't prove him wrong no matter what, because he's winging it, per say. New problem? Give him a few days and he'll have a new rule to solve it.
This is often the nature of mathematics. I can define division by 0 to hold in a manner that is consistent with algebras and other operations/formulations of number systems, but it is so trivial as to be pointless: division by 0 can exist in mathematical frameworks by defining it to hold only in the case that, given a|b=c, all are 0.

So if I create a new rule to allow for the division by zero, booya, problem solved right?
Sure. But we don't do that. I can define pi to be 2, and define multiplication to be subtraction. Indeed, differentiation is defined in terms of an operator acting on functions, the standard elementary calculus epsilon-delta limit definition, the infinitesimal formulation made rigorous by Robinson via hyperreals, tensors, differential forms, etc. My sister's courses on calculus at UPenn relied on a standard calculus textbook: Stewart's. As in many such texts, we are told that dy/dx shouldn't be understood as an actual quotient/fraction. Then later we are told that for differentials we can think of this derivative representation as a quotient (and we NEED to do so for elementary differential equations, in order to make use of separable equations).We are introduced to the differential and integral calculus and told that their is this amazing proof that the two are related, but are not told that
1) They were defined to be so
2) They aren't, in modern integration theory (or at least not in the way generally formulated).

The restrictions on mathematical rules relate to consistency, practicality, and similar concerns. It is possible to define mathematical systems that are consistent, logically coherent algebras, groups, etc., in which everything is nothing. This is trivial. Trying to define division by 0 in a consistent manner yields nothing of value but does introduce pointless nonsense.
 

NoGuru

Don't be serious. Seriously
I think you missed my point, although I'm sure you understand it.

I understand why division by zero is not allowed, it breaks everything else. I understand how rules in math are accepted as rules, they must be consistent.. My simple point was that intellectually division by zero should equate to infinity (a number you can't define). Put on a number line, I'd never get to the answer, just keep walking. So we say it's undefined, not allowed or what have you.

However, I feel strongly that just because it breaks a system doesn't mean it should be left alone. Perhaps the exploration of this will yield a system where we can understand when 1 = 4... and everything else.

"Daring as it is to investigate the unknown, even more so is it to question the known." -Kasper
 

GoodbyeDave

Well-Known Member
Personally, I reject the idea of infinity. If we tell some-one to count to 100, then that is an instruction that can be carried out. But how would we follow the instruction "count to infinity"? By counting and not stopping. Infinity is, so to speak, a direction rather than a destination.

In mathematics, Cantor made infinite sets part of its foundations, and most mathematicians have followed him, but there are exceptions. There is intuitionist mathematics, developed by people like Brouwer and Kleene. One problem with "classical mathematics" is the apparent lack of any foundation, since Cantor based maths on logic, a foundation demolished by Gödel.
 

Ana.J

Active Member
I would agree that it is unlikely that the universe is infinite. You know, I think that we are a small models of the universe...like atom is a small model of the solar system. Everything has it's end and is finite.
 
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