can you go to Infinity...and beyond?

[night912]

Ahh.....infinity...that invinsibility of no existance ! Not correct, I'll explain in my next answer.
That point were nothing exists ! Correct, because nothing exist for an Infinite amount of time.
What direction is it ? Forward. That's the only direction that you can go towards infinity.
Where does the Cosmos end ? The same place where it began.

 

[viole]

"math"

Math is only valid in the material and physical realms like Physics, it leads nowhere in ethical, moral and spiritual realms. Right, please?

Regards

Ethical and moral perceptions are very likely solutions of mathematical game theory applied to a set of cooperating beings. It our particular case, a set of primates whose survival crucially depends on their social interactions.

Or do you really believe they come from a spiritual realm, whatever that is.

Ciao

- viole

,

 

[beenherebeforeagain]

"infinity"

So, kindly let know as to what one understands from the word "infinity", one's own understanding of it, not from a lexicon nor the mathematical term/concept "infinity", please.

Regards

Please re-read what I posted: THAT is what I understand about infinity. Period.

 

[cladking]

There's no such thing as "infinity" in the real world so far as is known.

If a spaceship went infinitely fast how long would it take to reach infinity?

What would be just beyond it and why is the spaceship not there?

Is God so powerful that He can create a stone so large that He Himself can't move it?

 

[sealchan]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

I've always thought of infinity as endless counting...there is, by definition, no end to infinity. That could be an infinity of extent or an infinity of divisibility.

But perhaps whole numbers are, in a sense beyond the infinity of divisibilty such that saying you have five fingers is beyond the infinity of the rational and irrational numbers you can count between 0 and 5.

 

[blü 2]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

Always a fun topic, and one that I've contemplated in the past.

The first point to make is that 'infinity' is simply from the Latin meaning 'unbounded'. So (starting with countable infinities, the elements of the number line) you can define a googolplex, raise any number x to the googolplexth power, and raise the result to the googolplexth power, repeating a googolplex of times. Since the number line is unbounded, the only problem about doing this is notation.

The second point to make is that in examining the physical universe we don't find examples infinities. (Some of the maths models may result in 1/0 or whatever, but no one can point you to an out-there example.) But we indeed have minimum quantities ─ the Planck length, the Planck cube, the Planck time ─ below which, we say, no meaning can be attached to the result. To compare this to the possible infinities of the mathematical imagination, consider (and if you like, check for yourself) this simple sum about reality:

The Planck length is ~ 1.616252 ... e-35 meters.
A Planck cube is a cube the length of each side being 1 Planck length.
There are ~2.368e+110 Planck cubes in a cubic meter.

Now, let's stay with the working assumption that the universe is spherical.
A light year is 9.46 x 10^15 m.
Wikipedia tells me the radius of the universe is 4.7 e+10 light years.
So the volume of the universe is 4.35 e+32 cubic light years.
There are 8.47 e+47 cubic meters in a cubic light year.
There are 2.37 e+110 Planck cubes in a cubic meter.

PUNCHLINE

The volume of the universe (on the basis above, anyway) is, call it, 8.73 e+190 Planck cubes, the smallest possible meaningful unit of real volume.
That's a lot of Planck cubes, but nothing like an infinite number.

Again, using that radius of the universe above, the circumference is

The third point is that there's no coherent concept of ω in reality. The idea that 'infinity' is a point and that therefore there can be a 'lowest transfinite ordinal ω' is fine in the realms of imagination but it doesn't intersect with the real world anywhere.

So being a simple soul, I try to avoid the word 'infinity' because it's accumulated so many woo associations (Cantor hungered for woo in his work) and think of 'boundlessness' instead.

 

[Polymath257]

I've always thought of infinity as endless counting...there is, by definition, no end to infinity. That could be an infinity of extent or an infinity of divisibility.

But perhaps whole numbers are, in a sense beyond the infinity of divisibilty such that saying you have five fingers is beyond the infinity of the rational and irrational numbers you can count between 0 and 5.

What you are talking about here is what used to be known as a 'potential infinity'. It is a process (counting, for example), that can continue forever.

If we want to *list* the whole numbers, in order, that would be a process that would be potentially infinite.

But what mathematicians do now is look at the *collection* of all whole numbers as a single entity. This would be a 'completed infinity' in the old terminology. The idea is that the collection is unambiguously defined: for each object, we know whether or not it is a whole number, so whether or not it is in the collection. For example, we know that pi is NOT in that collection, but that 3,234,134,293,394 is. We don't have to check everything in the set to know whether or not any given thing is in there.

So, the collection of all whole numbers is an infinite set. So is the collection of all fractions, and the collection of all decimal numbers (pi is in the last one, but not in the others). Whether or not there is a process that lists them is irrelevant.

 

[viole]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

Oh yeah, you can run an infinite amount of miles in finite time. At least mathematically.

Many infinite things can be done in finite time. For instance, infinite causality regress can unfold in finite time without having an initial cause.

Ciao

- viole

 

[Polymath257]

Always a fun topic, and one that I've contemplated in the past.

The first point to make is that 'infinity' is simply from the Latin meaning 'unbounded'. So (starting with countable infinities, the elements of the number line) you can define a googolplex, raise any number x to the googolplexth power, and raise the result to the googolplexth power, repeating a googolplex of times. Since the number line is unbounded, the only problem about doing this is notation.

The second point to make is that in examining the physical universe we don't find examples infinities. (Some of the maths models may result in 1/0 or whatever, but no one can point you to an out-there example.) But we indeed have minimum quantities ─ the Planck length, the Planck cube, the Planck time ─ below which, we say, no meaning can be attached to the result. To compare this to the possible infinities of the mathematical imagination, consider (and if you like, check for yourself) this simple sum about reality:

The Planck length is ~ 1.616252 ... e-35 meters.
A Planck cube is a cube the length of each side being 1 Planck length.
There are ~2.368e+110 Planck cubes in a cubic meter.

Now, let's stay with the working assumption that the universe is spherical.
A light year is 9.46 x 10^15 m.
Wikipedia tells me the radius of the universe is 4.7 e+10 light years.
So the volume of the universe is 4.35 e+32 cubic light years.
There are 8.47 e+47 cubic meters in a cubic light year.
There are 2.37 e+110 Planck cubes in a cubic meter.

PUNCHLINE

The volume of the universe (on the basis above, anyway) is, call it, 8.73 e+190 Planck cubes, the smallest possible meaningful unit of real volume.
That's a lot of Planck cubes, but nothing like an infinite number.

Again, using that radius of the universe above, the circumference is

The third point is that there's no coherent concept of ω in reality. The idea that 'infinity' is a point and that therefore there can be a 'lowest transfinite ordinal ω' is fine in the realms of imagination but it doesn't intersect with the real world anywhere.

So being a simple soul, I try to avoid the word 'infinity' because it's accumulated so many woo associations (Cantor hungered for woo in his work) and think of 'boundlessness' instead.

Let's go one better. There is an estimate that the number of fundamental particles in the observable universe is less than 10^81. So the number of possible rearrangements of those fundamental particles among all the different Planck volumes, allowing for multiple particles to be in the same volume is *at most*

(10^191 )^(10^81) < 10^(2*10^83)

While this is definitely a big number, it is still far less than a googolplex, which is 10^(10^100).

 

[cladking]

Let's go one better. There is an estimate that the number of fundamental particles in the observable universe is less than 10^81. So the number of possible rearrangements of those fundamental particles among all the different Planck volumes, allowing for multiple particles to be in the same volume is *at most*

(10^191 )^(10^81) < 10^(2*10^83)

While this is definitely a big number, it is still far less than a googolplex, which is 10^(10^100).

It would require about 4.2 x 10 ^ 799,999 monkeys and typewriters to get War and Peace in one draft.

This is a big number but it pales in significance to the odds of Tolstoy writing it had his life been even the slightest bit different.

 

[paarsurrey]

Please re-read what I posted: THAT is what I understand about infinity. Period.

One's post, as I understand, mentioned only the mathematical connotation/term of the word "infinity", whereas the mathematical connotation of the natural word infinity is a later term and mentions only one aspect of it. The natural word is used for “very large number or quantity” “boundlessness, endlessness” as well and was used for philosophical and theological perspectives also.
Why limit it to its one aspect and ignore its theological usages, please?

Regards

 

[Polymath257]

Why limit it to its one aspect and ignore its theological usages, please?

Well, for one, because the theological and other usages are based on an outdated and confused notion of 'boundedness'.

For example, a line segment is bounded. But it has an infinite number of points. So it is possible to be 'bounded' in one sense and 'unbounded' in another. Typically, the theological and philosophical notions have been too vague about which of many possible senses are being used.

Also, a small bit of experience with partially ordered sets would show many theological arguments to be invalid.

 

[beenherebeforeagain]

One's post, as I understand, mentioned only the mathematical connotation/term of the word "infinity", whereas the mathematical connotation of the natural word infinity is a later term and mentions only one aspect of it. The natural word is used for “very large number or quantity” “boundlessness, endlessness” as well and was used for philosophical and theological perspectives also.
Why limit it to its one aspect and ignore its theological usages, please?

Regards

Because I can at least understand enough of the mathematics I can see that while it may be true of mathematics, I still can't wrap my mind around the actuality that is implied in the math. An infinite series of numbers, etc., I can understand the idea of it, because I can think of a number I do understand, and can add one more to it...

As for the theological uses, I find them to be poorly enough defined that 1) I can't wrap my mind around them, and 2) there is no rational system such as mathematics that seems to apply so that I could even hope to understand why I can't understand it.

Mathematics defines its infinities, and I can see why I can't wrap my mind around them. I have no problem thinking that other humans can comprehend more and/or better than I can, but I suspect that there is limit to what humans are capable of, and that would be far short of infinity.

The human concept of the Omnimax deity does not define its infinities, just appeals to the awe factor, "Oh wow! You are just so huge, Lord. We are all really impressed down here because you're beyond our comprehension!"

Does that make my position clearer for you?

 

[paarsurrey]

Because I can at least understand enough of the mathematics I can see that while it may be true of mathematics, I still can't wrap my mind around the actuality that is implied in the math. An infinite series of numbers, etc., I can understand the idea of it, because I can think of a number I do understand, and can add one more to it...

As for the theological uses, I find them to be poorly enough defined that 1) I can't wrap my mind around them, and 2) there is no rational system such as mathematics that seems to apply so that I could even hope to understand why I can't understand it.

Mathematics defines its infinities, and I can see why I can't wrap my mind around them. I have no problem thinking that other humans can comprehend more and/or better than I can, but I suspect that there is limit to what humans are capable of, and that would be far short of infinity.

The human concept of the Omnimax deity does not define its infinities, just appeals to the awe factor, "Oh wow! You are just so huge, Lord. We are all really impressed down here because you're beyond our comprehension!"

Does that make my position clearer for you?

So, one can't understand mathematical aspect because it is ambiguous and ambiguity is another concept of Mathematics:

The Ambiguity of Mathematics
by Bill Byers
"Abstract: This paper deals with mathematical rigor and the notion of ambiguity in mathematics. It takes the counter-intuitive position that ambiguity is of central importance to the mathematical endeavor—that it is essential and cannot be avoided. In our view, rigor and ambiguity form two complementary dimensions of mathematics—what we characterize as the surface versus the depth dimensions of the subject."
mathambiguity
Right, please?

Regards
____________
Ambiguity - Wikipedia

 

[Polymath257]

So, one can't understand mathematical aspect because it is ambiguous and ambiguity is another concept of Mathematics:

The Ambiguity of Mathematics
by Bill Byers
"Abstract: This paper deals with mathematical rigor and the notion of ambiguity in mathematics. It takes the counter-intuitive position that ambiguity is of central importance to the mathematical endeavor—that it is essential and cannot be avoided. In our view, rigor and ambiguity form two complementary dimensions of mathematics—what we characterize as the surface versus the depth dimensions of the subject."
mathambiguity
Right, please?

Regards
____________
Ambiguity - Wikipedia

Amusing article, but ultimately flawed. The problem is that the 'ambiguity' isn't, in fact, an expression of contradictions. Instead, it shows how our assumptions intertwine and reinforce each other.

So the square root of 2 being irrational doesn't show a contradiction between algebra and geometry. But it does show a potential way to *extend* algebra to encompass more than it did previously.

And *this* sort of growth, where we see similar patterns in widely different areas of thought, it a central part of mathematics. This allows us to push the boundaries of some areas of study in new ways and reaching new insights.

But it is NOT ambiguous in the sense this paper outlines because it is NOT a contradiction.

There *is* more to mathematics that the purely formal. But it is NOT because of ambiguity, but rather in common patterns (metaphor?) in the different areas of thought.

 

[beenherebeforeagain]

So, one can't understand mathematical aspect because it is ambiguous and ambiguity is another concept of Mathematics:

The Ambiguity of Mathematics
by Bill Byers
"Abstract: This paper deals with mathematical rigor and the notion of ambiguity in mathematics. It takes the counter-intuitive position that ambiguity is of central importance to the mathematical endeavor—that it is essential and cannot be avoided. In our view, rigor and ambiguity form two complementary dimensions of mathematics—what we characterize as the surface versus the depth dimensions of the subject."
mathambiguity
Right, please?

Regards
____________
Ambiguity - Wikipedia

No. See @Polymath257 's post #75.

I did not say mathematics is ambiguous, or I don't think I did. And I certainly did not intend to.

Mathematics defines its terms, including various senses of the term infinity. Mathematics is very clear about what 'infinity' means within mathematics. It is very clear about all the terms that it uses.

Theology does not, at least not in any way that can be tested, clearly define what it means by infinity, or pretty much anything else. Theology is mostly, to me, not only ambiguous, but MEANINGLESS.

Saying God has always existed and always will exist is not ambiguous as far as I can tell, but it is meaningless. But saying God is infinitely Good, or infinitely Just, or infinitely Powerful are meaningless, undefined--that is AMBIGUOUS--terms with extreme adjectives used as modifiers, used to overwhelm the faculty of reason. Such declarations of ultimate traits set up philosophical conundrums that cannot be resolved because they are unclearly defined nonsense to start with.

There is no way to say what was before and after or outside of our existence, our cosmos, even though some physicists are attempting to investigate whether or not it is possible to discuss before, after, and outside of the cosmos we know. But what they are doing is at this time speculation. On a somewhat better basis than theologists, as it's rooted in the actual observations of the universe and the testable models we have made to explain those observations.

 

[Thief]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

more than that

if we fail to become as …..light
we are not going anywhere

 

[Earthtank]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

The only problem with going to infinite is that it will take you an infinite to get there.

 

[Polymath257]

The only problem with going to infinite is that it will take you an infinite to get there.

That depends on how you do it!

 

[paarsurrey]

No. See @Polymath257 's post #75.

I did not say mathematics is ambiguous, or I don't think I did. And I certainly did not intend to.

Mathematics defines its terms, including various senses of the term infinity. Mathematics is very clear about what 'infinity' means within mathematics. It is very clear about all the terms that it uses.

Theology does not, at least not in any way that can be tested, clearly define what it means by infinity, or pretty much anything else. Theology is mostly, to me, not only ambiguous, but MEANINGLESS.

Saying God has always existed and always will exist is not ambiguous as far as I can tell, but it is meaningless. But saying God is infinitely Good, or infinitely Just, or infinitely Powerful are meaningless, undefined--that is AMBIGUOUS--terms with extreme adjectives used as modifiers, used to overwhelm the faculty of reason. Such declarations of ultimate traits set up philosophical conundrums that cannot be resolved because they are unclearly defined nonsense to start with.

There is no way to say what was before and after or outside of our existence, our cosmos, even though some physicists are attempting to investigate whether or not it is possible to discuss before, after, and outside of the cosmos we know. But what they are doing is at this time speculation. On a somewhat better basis than theologists, as it's rooted in the actual observations of the universe and the testable models we have made to explain those observations.

Does one think* that nature exists?
Does on think* that one exists?

Regards
____________
*(to believe that something is true)