Infinity in Math and Eternity?

[Dave Darling]

Hi everyone,

I got to thinking about the concept of infinity in mathematics and the concept of eternity described in the Bible, I could use some help. I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add. One thing that did come to me- with infinity infinity + any number = infinity. Is there a Godly principal in this? Thanks

 

[FrumiousBandersnatch]

... I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add.

Well, infinity in math means (roughly) numbers without end, and eternity means time without end ¯\_(ツ)_/¯

 

[Occams Barber]

Hi everyone,

I got to thinking about the concept of infinity in mathematics and the concept of eternity described in the Bible, I could use some help. I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add. One thing that did come to me- with infinity infinity + any number = infinity. Is there a Godly principal in this? Thanks

Where you need to be careful is in interpreting 'eternity' as necessarily a Biblical concept. The abstract concept of eternity, along with the word itself, exists outside the confines of the Bible and can be imagined outside of a Biblical context.

The Bible also mentions 'tree' but we don't automatically see 'tree' as a term specific to the Bible.

OB

 

[Friedrich Rubinstein]

Eternity can mean "without beginning and without end", while applying the term infinity to time can only mean "with a beginning but without end". An infinite past (in time) is impossible, so there is a difference between "eternity" and "infinity" in this regard.

 

[jacks]

Maybe it's because both Infinity and Eternity are concepts we accept, but really are beyond normal human experience. That gives them a godlike quality, that is similar.

 

[SelfSim]

Eternity can mean "without beginning and without end", while applying the term infinity to time can only mean "with a beginning but without end". An infinite past (in time) is impossible, so there is a difference between "eternity" and "infinity" in this regard.

Why do you say that 'an infinite past (in time)' is impossible, when you have already conceptualised 'without beginning and without end'?

 

[SelfSim]

Maybe it's because both Infinity and Eternity are concepts we accept, but really are beyond normal human experience.

If they're concepts, they most definitely are (demonstrably) human experiences!
Otherwise, by what other means would you posssibly 'conceive' them?

 

[Occams Barber]

'Eternal' is normally used when referring to unlimited time.

'Infinite' is normally used to describe unlimited space or quantity.

OB

 

[Friedrich Rubinstein]

Why do you say that 'an infinite past (in time)' is impossible, when you have already conceptualised 'without beginning and without end'?

Because the term "eternal" allows for that concept while the mathematical term "infinity" does not. Imagine you were to count backwards from minus infinity to zero. Before you get to 0 you have to count -1, before you get to -1 you need to count -2, before that -3 and so on, back to infinite. You'd have to count an infinite amount of numbers before getting to any number, meaning it is impossible for you to ever get to 0. Saying "eternal" instead avoids this mathematical issue.

 

[SelfSim]

Because the term "eternal" allows for that concept while the mathematical term "infinity" does not. Imagine you were to count backwards from minus infinity to zero. Before you get to 0 you have to count -1, before you get to -1 you need to count -2, before that -3 and so on, back to infinite. You'd have to count an infinite amount of numbers before getting to any number, meaning it is impossible for you to ever get to 0. Saying "eternal" instead avoids this mathematical issue.

I think I get your gist there that there's no formalised definition for 'eternal' in math. Ie: the interval from negative infinity to positive infinity, is still infinite.

 

[FrumiousBandersnatch]

Because the term "eternal" allows for that concept while the mathematical term "infinity" does not. Imagine you were to count backwards from minus infinity to zero. Before you get to 0 you have to count -1, before you get to -1 you need to count -2, before that -3 and so on, back to infinite. You'd have to count an infinite amount of numbers before getting to any number, meaning it is impossible for you to ever get to 0. Saying "eternal" instead avoids this mathematical issue.

The same argument applies for +infinity... But it's a false argument - you can't count from infinity because it isn't a number.

There are various logical counters to temporal finitism, but there is also no physical argument why time cannot extend infinitely into the past. In the 4D Parminidean 'block universe' of Special Relativity, the universe is different from one moment to the next, but ideas of the passing of time and moving through time are just ways of describing our subjective experience of it. As Einstein himself said, “The distinction between the past, present and future is only a stubbornly persistent illusion.”

 

[Bob Crowley]

Infinity in maths is a symbol representing a never ending number system.

Good old Pi takes the cake here in my opinion. We can all draw a circle, but the value of Pi has an infinite number of decimal places. In other words we can't pin it down. So given a certain radius, what is the actual circumference ie. 2 x pi x r?

Whereas eternity in physical life means "never ending" in the sense of time.

We have symbols in maths that have no corresponding reality in real life. We can describe a cube as X^3, but trying drawing the geometrical figure represented by X^10. We can manipulate the math symbols, and usually come up with a real answer. But the process might involve some imaginary and complex numbers in a temporary sense.

 

[Friedrich Rubinstein]

The same argument applies for +infinity... But it's a false argument - you can't count from infinity because it isn't a number.

There are various logical counters to temporal finitism, but there is also no physical argument why time cannot extend infinitely into the past. In the 4D Parminidean 'block universe' of Special Relativity, the universe is different from one moment to the next, but ideas of the passing of time and moving through time are just ways of describing our subjective experience of it. As Einstein himself said, “The distinction between the past, present and future is only a stubbornly persistent illusion.”

Infinity is actually treated as a number in maths. But the argument doesn't apply to +infinity because when you have a starting point you can indeed keep counting endlessly. -infinity is a very different issue, because while +infinity starts with real numbers (and therefore includes them), -infinity does not. -infinity starts with infinity and you never reach any real number.

 

[Tinker Grey]

-1, -2, -3, etc. No problem

 

[SelfSim]

Infinity is actually treated as a number in maths. But the argument doesn't apply to +infinity because when you have a starting point you can indeed keep counting endlessly. -infinity is a very different issue, because while +infinity starts with real numbers (and therefore includes them), -infinity does not. -infinity starts with infinity and you never reach any real number.

Infinity means different things in different contexts. For example you are invoking a context of a counting process and real number sets there.
In some contexts there's only one infinity. For example, the slope of a vertical line isn't negative or positive. It's just infinity.
Then there's separate contexts like something that increases asymptotically has a limit of positive infinity, but something that decreases asymptotically has a limit of negative infinity.
One can also visualise a domain where negative numbers don't apply, such as infinite sets. (You can't have a set with negative infinity numbers in it. You can't even have a set with negative one numbers in it).

The concept of "infinity" can also be visualised as the process of things getting smaller/larger over time, or perhaps about moving in a positive or negative direction, relative to an observer. In this case, it 'starts' with an observation and thus 'negative infinity' is possible .. it just means something different from the numbers and sets context.

Infinity doesn't have to be conceptualised as being a really huge number .. or a set.

 

[Friedrich Rubinstein]

Infinity means different things in different contexts. For example you are invoking a context of a counting process and real number sets there.
In some contexts there's only one infinity. For example, the slope of a vertical line isn't negative or positive. It's just infinity.
Then there's separate contexts like something that increases asymptotically has a limit of positive infinity, but something that decreases asymptotically has a limit of negative infinity.
One can also visualise a domain where negative numbers don't apply, such as infinite sets. (You can't have a set with negative infinity numbers in it. You can't even have a set with negative one numbers in it).

The concept of "infinity" can also be visualised as the process of things getting smaller/larger over time, or perhaps about moving in a positive or negative direction, relative to an observer. In this case, it 'starts' with an observation and thus 'negative infinity' is possible .. it just means something different from the numbers and sets context.

Infinity doesn't have to be conceptualised as being a really huge number .. or a set.

Infinity surely means different things in different contexts, but the context I was talking about was pretty clear.

 

[SelfSim]

Infinity surely means different things in different contexts, but the context I was talking about was pretty clear.

The context is time in Physics .. not numbers in Math/set theory.

 

[public hermit]

Hi everyone,

I got to thinking about the concept of infinity in mathematics and the concept of eternity described in the Bible, I could use some help. I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add. One thing that did come to me- with infinity infinity + any number = infinity. Is there a Godly principal in this? Thanks

If you get a chance, read Nicholas of Cusa's On Learned Ignorance. He uses mathematical/geometrical thought experiments to help you grasp how difficult it is to comprehend an infinite and eternal being. It is a mystical writing, but he thinks these kinds of analogies (?) can aid one in how they think about the transcendent God (and hopefully transcend their thoughts about God altogether-I'm a bit unsure where Cusa comes down on this last point, but he's still in the apophatic tradition, just not extremely lol).

De Docta Ignorantia - Wikipedia

 

[SelfSim]

If you get a chance, read Nicholas of Cusa's On Learned Ignorance. He uses mathematical/geometrical thought experiments to help you grasp how difficult it is to comprehend an infinite and eternal being. It is a mystical writing, but he thinks these kinds of analogies (?) can aid one in how they think about the transcendent God (and hopefully transcend their thoughts about God altogether-I'm a bit unsure where Cusa comes down on this last point, but he's still in the apophatic tradition, just not extremely lol).

De Docta Ignorantia - Wikipedia

Indulgence in illogical thinking .. How that comes about from 'mathematical/geometrical thought experiments', is clear evidence pointing to a grossly inconsistent process.

 

[sjastro]

In maths there many different concepts of infinity;

Infinity is a limit such as in the graph f(x) = 1/x.

x → 0⁺, f(x) → +∞ or x → 0⁻, f(x) → -∞ (→ means approaches, ⁺ ⁻ means above or below respectively).

With complex numbers ∞ is the north pole of a Riemann sphere.

In an infinite set such as the set of real numbers R is an uncountable set, whereas the infinite set of natural numbers N is a countable set.
Furthermore the set of integers I is an infinite set but intuitively I should contain ‘twice’ as many elements than N even though both are infinite sets.

In physics when infinities appear something is seriously wrong with the theory.