God is laughing up His sleeve

[Viewscreen]

I bet God, if he exists, which some days I am more inclined to believe than others (believe, not know, I make a distinction!) than he has to be laughing. Laughing and crying at the same time.

 

[Ion]

Ion:

I am very familiar with mathematics. Even Cantor regarded his set theory as the abstraction that it is.

It will no doubt take some time, but I can write out the line of real numbers up to any number you give me the shorthand sign for. But no one can do that for infinity. Not only does an actual infinity not exist in the physical universe, in either direction, but also there would be no space, or place, for more than one infinity - if it could. Furthermore, infinity is an indeterminate.

God bless,
jd

Boundaries is a different problem than infinity.

 

[Ion]

Mathematics is awesome; you simply say “let there be the power set on N” and voila there is in your mind and eventually on paper an infinite of infinite…

 

[JDaniel]

Boundaries is a different problem than infinity.

Ion:

Nevertheless, it is a problem for an actual infinity. Unless, by abstraction, boundaries are imaginatively removed.

Will you show me an actual infinity?

God bless,
jd

 

[JDaniel]

Mathematics is awesome; you simply say “let there be the power set on N” and voila there is in your mind and eventually on paper an infinite of infinite…

Ion:

“In your mind” means “an abstraction.” Not real. Real numbers must be attributable to real things, 100 cows, 1,000 chickens, etc. But, how would you know that you have an aleph of rabbits? (Count the ears and divide by two?)

God bless,
jd

 

[GEddie]

Ion:

Nevertheless, it is a problem for an actual infinity. Unless, by abstraction, boundaries are imaginatively removed.

Will you show me an actual infinity?

God bless,
jd

Why bother? An infinity of anything wouldn’t fit in our finite human heads (or in the aggregate of all living human heads).

So the “knowable” universe will always be finite, even if we are given life everlasting, and even if the cubic mileage does indeed go on forever.

ICXC NIKA

 

[Alberti_Devoveo]

You take an infinite set (ex set of natural numbers N) and then you build the power set of it P(N), then the power set of the result P(P(N)), and so on…
It doesn’t increase N in itself, of course

So infinity does not increase, then. So, going back, JDaniel’s comment was certainly correct that the infinity cannot increase.

 

[Ion]

Ion:

“In your mind” means “an abstraction.” Not real. Real numbers must be attributable to real things, 100 cows, 1,000 chickens, etc. But, how would you know that you have an aleph of rabbits? (Count the ears and divide by two?)

God bless,
jd

Our universe is finite, and has a countable number of particles.

God is infinite, people have believed it by faith.

I don’t say that the math concept of infinite relates to the Holy Trinity.
What I said is that it can be considered as proof of the design of us and of the universe, the same way as morals.

A muslim asked me how can one be three persons? I did explained to him that dividing mathematical infinity in 3 equal parts you get 3 infinities, and combining 3 noncontradicting infinities you get one. He admitted that one can be three…

 

[JDaniel]

Our universe is finite, and has a countable number of particles.

God is infinite, people have believed it by faith.

I don’t say that the math concept of infinite relates to the Holy Trinity.
What I said is that it can be considered as proof of the design of us and of the universe, the same way as morals.

A muslim asked me how can one be three persons? I did explained to him that dividing mathematical infinity in 3 equal parts you get 3 infinities, and combining 3 noncontradicting infinities you get one. He admitted that one can be three…

Ion:

Great answer! I’ll have use it if I get the chance.

God bless,
jd

 

[JDaniel]

Why bother? An infinity of anything wouldn’t fit in our finite human heads (or in the aggregate of all living human heads).

GEddie:

Correct. That’s why mathematics uses a *shorthand sign *in place of anything approaching the possibility of infinity.

So the “knowable” universe will always be finite, even if we are given life everlasting, and even if the cubic mileage does indeed go on forever.

Always. The boundary of our universe is an unknown that, should we reach it by space craft, we would probably bounce off of. Or, return to the continuous (infinite) space that is God. No more fermions, no more bosons, no Higgs boson. Just pure, infinite space, at the implicate level.

God bless,
jd

 

[Ion]

So infinity does not increase, then. So, going back, JDaniel’s comment was certainly correct that the infinity cannot increase.

Infinity is hard to imagine. When you take an infinity and divide in 2 (or 5 etc) you get two equal infinities that are also equal with the infinity they come from. When you combine them you get a result equal with any of the parts you combine.
There are also different kind of infinity.
N, the set of integers, has a infinity wich is lesser than the infinity of the real numbers R, which is richer in elements. P(N) is a richer infinity than N, it is proven to have more elements. P(P(N)) is a richer infinity than P(N) or R.

 

[yppop]

Don’t the Planck minimums for duration of time (tp=5.39X10-44) and interval of space (lp=1.62X10-33) establish that there are discrete finite limits for both?

Peter,
I think they do, but science doesn’t; space and time are still continuous quanties.

Yppop

 

[Alberti_Devoveo]

Infinity is hard to imagine. When you take an infinity and divide in 2 (or 5 etc) you get two equal infinities that are also equal with the infinity they come from. When you combine them you get a result equal with any of the parts you combine.
There are also different kind of infinity.
N, the set of integers, has a infinity wich is lesser than the infinity of the real numbers R, which is richer in elements. P(N) is a richer infinity than N, it is proven to have more elements. P(P(N)) is a richer infinity than P(N) or R.

Infinity as a concept is simple to understand, what is difficult is making the connection that infinity is a mathematical construct that has no physical basis.

For brevities sake,

1. n/2 = n/5 = n cannot exist. It is fundamentally impossible.
2. n < n is equally impossible

Thus: either it is impossible to add, subtract, divide, or multiply infinity, or infinity does not exist.

1. What you are also doing is making a set of a set of a set, but not increasing infinity.
2. You state that each infinity is equal to all others infinities, so it makes zero sense to say that one infinity is ‘lesser’ or ‘richer’ than another

Thus: infinity still cannot increase.

 

[tabycat]

It was a belief up to a few years ago that the universe was infinite and immutable. Even Albert Eintein held.
It was a Jesuite priest that shattered this belief. He expanded on the observations of astronomers that saw some peculiar behaviour in the light they were observing from all the galaxies around us.
As a result of this we now know that the universe is Not Infinite but more importantly that it is not immutable. Science has been able to measure the exact moment that the universe was created. And science also cannot come up with a way to explain this creation without there also being a Creator (Cause/Effect).
So yes I agree with your title on God laughing but only at those that think that “science” will be able to disproof Him.

Fred Hoyel called it the ‘Big Bang Theory’, trying to make fun of it. :whacky::bounce:

PS God does have a sense of humor. Either that or mules, duckbilled platapus, and humans are mistakes and since God does not make mistakes, they must be jokes. kpeople:

 

[Cricket123]

Will you show me an actual infinity?

Sure.

Take a piece of paper and a pencil and draw a one inch line segment.

Now count the number of discrete points in it.

“Hold infinity in the palm of your hand…”

 

[Faithdancer]

The universe being infinite and thus being in principle incomprehensible to humans? I’m not saying you’re wrong, but it sounds to me contradictory to the idea of order in Creation.

Not incomprehensible in principle, perhaps, as an abstraction. But to accept infinity is to accept the possibility of an infinite being, is more my point. Aquinas has painstakingly shown us that there can be but one infinite being which, as Aquinas would say, “we call God.” This being transcends time and space while at the same time being the the Creator of time and space. Infinity itself is only comprehensible, then, when one realizes that there is one infinite being, who is the uncaused cause and the unmoved mover. While Aquinas never said directly (that I know of) that God and infinity are synonymous, infinity is certainly a fundamental aspect of God as expressed in the terms omniscience (knowledge), omnipotence (causation), and omnipresence (in time and space, and infinitely beyond time and space).

Here’s how I’d diagram it for my high school students:

<-------------------------------------------------------------------------------------------------------------->
God and infinity

                                            I>I
                 Time, space, and human understanding

The second and lower “timeline” does not apply to that which is aeviternal, which would be represented by a mark placed somewhere on the upper line of infinitude.

 

[Alberti_Devoveo]

Sure.

Take a piece of paper and a pencil and draw a one inch line segment.

Now count the number of discrete points in it.

“Hold infinity in the palm of your hand…”

The term ‘discrete points’ is vague. You could define the carbon atom as the smallest scale. Or the electron radius. Or the Planck length. All of these are still finite, so a finite number of discrete points is expected.

What you are getting at is one of Zeno’s paradoxes, paradoxes that were resolved centuries ago.

 

[Cricket123]

Well, no… it’s a different problem. If we consider, for example, the segment between 0 and 1 on the x-axis, then each discrete point has its own unique x-coordinate. Obviously there are an infinite number of these.

Yet we can also show a one-to-one correspondence between the points which exist between 0 and 1 and the points which exist between 0 and 2. These are both infinite sets but they are the same size; they have the same cardinality. There are not twice as many points in the second set.

In fact, we can set up the same one-to-one correspondence between a segment of any length and the entire number line.

On the other hand, if we take the set of all integers N, and the set of all real numbers R, we can show by diagonalization there is no one-to-one correspondence between these sets, and that the set R has infinitely more elements than the set N. Thus, R is richer in elements than N.

And of course then there are the power sets P(N), P(P(N) etc which Ion mentioned.

Now I’m not arguing for or against anything theological here… just putting out something I find interesting. For myself, I find the notion of the infinite existing in infinite variety fascinating. Clearly, God imagined an infinity much more interesting than the one I would have imagined. My thoughts are not as your thoughts, and all that.

An infinity of infinities is still too limiting for God, who must exist at, and as, the limit of them all.

 

[Alberti_Devoveo]

Well, no… it’s a different problem. If we consider, for example, the segment between 0 and 1 on the x-axis, then each discrete point has its own unique x-coordinate. Obviously there are an infinite number of these.

This is, more or less, Zeno’s dichotomy paradox. Obviously we are not talking about going a certain distance, but you are still assuming that the line segment cannot counted because there is an infinite series of points between the two.

This is false, the smallest division that can be determined, as Peter Plato and Yppop point out, is the Planck length of roughly 10[sup]-35[/sup] m.

Yet we can also show a one-to-one correspondence between the points which exist between 0 and 1 and the points which exist between 0 and 2. These are both infinite sets but they are the same size; they have the same cardinality. There are not twice as many points in the second set.

In light of the above, this does not follow. Since the smallest distance is the Planck length, which is a finite number, then there must be double the number of points from 0 to 2 than from 0 to 1.

In fact, we can set up the same one-to-one correspondence between a segment of any length and the entire number line.

Again, no you cannot.

On the other hand, if we take the set of all integers N, and the set of all real numbers R, we can show by diagonalization there is no one-to-one correspondence between these sets, and that the set R has infinitely more elements than the set N. Thus, R is richer in elements than N.

As I stated in a previous post, you cannot have that n = n and, at the same time, n > n. This is completely irrational. You cannot have two objects be the same and have one greater than the other at the same time. It goes against logic.

And of course then there are the power sets P(N), P(P(N) etc which Ion mentioned.

Which still do not change the value of infinity, hence their irrelevance.

Now I’m not arguing for or against anything theological here… just putting out something I find interesting. For myself, I find the notion of the infinite existing in infinite variety fascinating. Clearly, God imagined an infinity much more interesting than the one I would have imagined. My thoughts are not as your thoughts, and all that.

I did not posit anything theological, only mathematical. Infinity is not a physical, tangible thing, but a construct with no physical basis and is actually quite irrational if you eliminate the symbol infinity and think about the actual mathematics of it.

 

[Ion]

Since Newton, math and science is impossible without the infinite.