Is information the interface between the finite and infinite?

[HowToBe]

This idea occurred to me within the last week or so. When thinking about mathematical things I've noticed how you have finite values and amounts, but then if you follow a process (such as counting) out indefinitely you sometimes end up with an infinite value. Now in mathematics I've read or gotten the sense that many mathematicians do not consider infinity to be an "entity", if that's an okay way to say it. They say, more or less, that infinity is merely a concept, it doesn't actually "exist" because you can never actually reach it. It seems to me that this is a view strongly influenced by materialism - in a sense, they consider infinity imaginary like they consider the idea of any sort of God imaginary. At least the concept of infinity is useful, they might say.

Now, in exploring spiritual and philosophical realms of thought, considering Infinity as a real entity, as real as any countable number (although not a number itself exactly), seems to have more credibility, maybe. Infinity is required to explain how consciousness could exist, it seems, and how the Universe could be more than a machine.

One thing I've noticed in thinking about finity versus infinity is that the two of them don't seem to exactly "mix". If you add a finite number to infinity, it is still infinity just the same, and this is also true if you subtract, divide, or multiply. If you start at a finite number, you can't "count to infinity" without giving yourself infinite "time" to do it. Likewise, if you start from infinity, you cannot "count your way out" and reach the finite numbers. So if the finite and the infinite both exist, how do they interface? Instead of counting forever, it seems like some sort of transcendence is required to "reach infinity". It's not exactly like you cross some line and "suddenly it's all infinite!" It seems more like if this bridging must happen, it would be maybe like a "realm border"; a sort of intangible crossing into another reality.

In any case, we experience a world that seems to be full of "finite" expressions. And certainly we can model the finite within computers, so there is some kind of reality to it. So how does the infinity "behind" consciousness interface with the "finite" material world? I'm wondering if this could be part of an idea as to what Information is. Information could be the interthreading that allows the tangible and intangible to associate with one another.

 

[whitecoast]

Hi HowToBe. I think the question of

I think the question of infinity is best answered by specifying what you mean by number or type of number. If you look at the types of numbers there are, there are natural numbers (1, 2, 3...), whole numbers (0, 1, 2...), integers (-2, -1, 0, 1, 2), rational numbers (integers which can exist as a finite fraction), irrational numbers (integers which cannot exist as a finite fraction), real numbers, imaginary numbers.

I tend to agree with the pop math notion that infinity isn't really a number in the sense of the above number types (whole, integer, rational, etc.) If a number does not exist on the integer number line (-2, -1, 0, 1, 2) then the number cannot be said to be an integer. Similarly you cannot find infinity on a number line anywhere, except as an exercise in limits (i.e. the number line goes to infinity, but never gets there). In this sense infinity is more a descriptor of potentiality and the behavior of numbers.

In any case, we experience a world that seems to be full of "finite" expressions. And certainly we can model the finite within computers, so there is some kind of reality to it. So how does the infinity "behind" consciousness interface with the "finite" material world? I'm wondering if this could be part of an idea as to what Information is. Information could be the inter-threading that allows the tangible and intangible to associate with one another.

I like to think of what you're trying to grasp for as "meta". You're familiar with flatworld right? The land where everything is 2D and everyone flips out because simply by being 3D you you exhibit (what they see as) hyperdimensional phenomena. The only real limits or demarcations are the assumptions about reality the 2D flatworlders construct. So I guess I'm saying it's assumptions that separate the finite from the infinite.

The way we remove assumptions is discovery, and gathering knowledge. It is this exercise which has allowed people who initially only believed in natural numbers to discover zero, and then integers, and then fractions and irrational numbers, etc. Math is the same as any science or endeavor in human understanding, OSIT.

 

[Altair]

.. the number line goes to infinity, but never gets there.

Maybe it's kind of attractor? The number line doesn't go to infinity but rather attracted by infinity/Union with the One (7D) (by means of gravity).

 

[John G]

Instead of counting forever, it seems like some sort of transcendence is required to "reach infinity". It's not exactly like you cross some line and "suddenly it's all infinite!" It seems more like if this bridging must happen, it would be maybe like a "realm border"; a sort of intangible crossing into another reality.

In any case, we experience a world that seems to be full of "finite" expressions. And certainly we can model the finite within computers, so there is some kind of reality to it. So how does the infinity "behind" consciousness interface with the "finite" material world? I'm wondering if this could be part of an idea as to what Information is.

The surreal numbers kind of fit with what you are saying.

https://en.wikipedia.org/wiki/Surreal_number

In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. (Strictly speaking, the surreals are not a set, but a proper class.[a]) If formulated in Von Neumann–Bernays–Gödel set theory, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, can be realized as subfields of the surreals.

The visualization graphic for the surreal numbers in the Wikipedia link looks like a binary decision tree aka it's information-like. I've seen surreal numbers linked to a many-worlds quantum field theory and we and our 3rd density consciousness are certainly stuck more in a single world than higher density consciousness would be.

http://www.tony5m17h.net/surreal.html

 

[kenlee]

In any case, we experience a world that seems to be full of "finite" expressions. And certainly we can model the finite within computers, so there is some kind of reality to it. So how does the infinity "behind" consciousness interface with the "finite" material world? I'm wondering if this could be part of an idea as to what Information is. Information could be the interthreading that allows the tangible and intangible to associate with one another.

I think the mathematician Georg Cantor, if I understand him, spoke of there being different kinds of infinities that he was able to express mathematically (Although I can't understand his mathematics]. I think he even spent time in the 'nuthouse' but, imo, this didn't mean he was crazy it just might have meant that he experienced higher levels of consciousness and was able to translate these higher states into mathematical terms. So his experiencing of these intense higher energy states might have contributed to his "insanity" or depression.

What I was thinking is that these different kinds of infinities that he spoke of might correspond to the levels or kinds of consciousness that is talked about in the Gurdjieff work. There's waking sleep which we experience in our 'everyday' state of consciousness and where everything is seen as separate, finite, and countable, much like the points in a line counting on and on into infinity.

Then there's 'self consciousness' which in this context may be viewed as an expansion of our consciousness where we become more conscious of ourselves being conscious of ourselves being conscious of ourselves...and so on, where our consciousness keeps expanding outward into 'infinity' or possibly what is called 'Cosmic consciousness'. Then we might even go beyond that where we could see things as they are just as the universe sees itself, which possibly is what is called 'objective consciousness'. I might be wrong in my interpretation of this but my main point is that there may be different kinds of infinities or 'higher infinities' that go beyond just 'counting things into infinity' into a kind of pure knowing, where the higher infinities are involved and become more qualitative then quantitative.

Regarding information it might be that our Will, that is, our Real 'I' is connected to that universal infinite string of information that makes it uniquely what it is via a (cosmic) higher energy of some kind but when we deal with the lower energies and the lower states of consciousness associated with it then our awareness of what we see and experience becomes more limited and finite. FWIW, hopefully I made some sense here!

 

[John G]

I think the mathematician Georg Cantor, if I understand him, spoke of there being different kinds of infinities that he was able to express mathematically... my main point is that there may be different kinds of infinities or 'higher infinities' that go beyond just 'counting things into infinity' into a kind of pure knowing, where the higher infinities are involved and become more qualitative then quantitative.

Regarding information it might be that our Will, that is, our Real 'I' is connected to that universal infinite string of information that makes it uniquely what it is via a (cosmic) higher energy of some kind but when we deal with the lower energies and the lower states of consciousness associated with it then our awareness of what we see and experience becomes more limited and finite. FWIW, hopefully I made some sense here!

Yes Cantor infinities may have a nice binary information 2^n power set structure too. Surreal numbers kind of handle the subsets of sets with the same cardinality and different cardinality is kind of different sizes of infinity.

https://en.wikipedia.org/wiki/Cardinal_number

...the set of natural numbers N = {0, 1, 2, 3, ...}... This cardinal number is called N0... Cantor proved that any unbounded subset of N has the same cardinality as N, even though this might appear to run contrary to intuition. The continuum hypothesis (CH) states that there are no cardinals strictly between N0 and 2^N0. The latter cardinal number is also often denoted by c; it is the cardinality of the continuum (the set of real numbers). In this case 2^N0=N1. The generalized continuum hypothesis (GCH) states that for every infinite set X, there are no cardinals strictly between |X| and |2^X|.

The N0 (for natural number infinity size) and N1 (for real number infinity size) are called aleph-null and aleph-one and you can keep going to two, etc. Here's an article mentioning aleph numbers, the power set (2^n) and the surreal numbers:

http://www.rudyrucker.com/blog/2015/08/31/john-conway-and-the-absolute-continuum

 

[obyvatel]

[quote author=HowToBe]
In any case, we experience a world that seems to be full of "finite" expressions. And certainly we can model the finite within computers, so there is some kind of reality to it. So how does the infinity "behind" consciousness interface with the "finite" material world?
[/quote]

One way to think about it is to consider the relationship between possibilities and what actually happens. What happens in reality is the actualization of certain possibilities. The world of possibilities is much much bigger than the world of actual events. We can work it out in our daily activities if we pay attention. If we are aware as we go through our daily activities, we can cognize that what we actually do as well as how we do these tasks can potentially have a lot of variability. We can choose to do something different at a particular time than is our usual habit, and we can choose to do the same thing in many different ways. In this way it is possible to viscerally realize that the world of possibilities is bigger than the world of actual events.

If we treat "infinity" as a relational and multilevel concept, then in relation to the world of actual events, the world of possibilities may represent a kind of infinity. What could act as an interface between these two? Choice comes to mind. We can choose to do something and how to do it. But most of the time, we are not aware of doing much choosing and operate on auto pilot. This is what is referred to in Work terminology as being a machine. We can be largely cut off from the world of possibilities and have a very limited field of experience.

So what facilitates choice? Attention can be a component; first we must be aware of what we are doing and how we are doing it. Then comes knowledge of possibilities. What else could we do? How can we do things differently? Some options are "better" than others - either from a value perspective or from energy perspective. But without going further down this path, as far as the interface between these two worlds of possibilities and real events is concerned, I think choice as a function of attention and knowledge can be a candidate. You mentioned computers - computers are built by men. The designers choose to design the hardware and software in certain ways and not others. The way they do their job depends on their attention and knowledge.

[quote author=kenlee]
Then there's 'self consciousness' which in this context may be viewed as an expansion of our consciousness where we become more conscious of ourselves being conscious of ourselves being conscious of ourselves...and so on, where our consciousness keeps expanding outward into 'infinity' or possibly what is called 'Cosmic consciousness'. Then we might even go beyond that where we could see things as they are just as the universe sees itself, which possibly is what is called 'objective consciousness'.
[/quote]

Self consciousness can be the awareness of the pattern of possibilities that exist for a given individual. If the existence of such a pattern is treated as axiomatic, then the rest of what follows can make some sense. If this pattern is much larger than what one real-izes in life then it can stand as a kind of infinity in relation to the personal life of events. The stronger one's conscious connection to this world of possibilities, more the pattern gets actualized in one's daily life and activities, and its relationship to the world of events changes. For a self-conscious individual, his/her pattern of possibilities is expressed in his life.

Objective consciousness belongs to a different level where one's pattern of possibilities is brought into a relationship with the pattern of possibilities of the bigger whole of which one is a part. Starting from family, society/culture, world, ..... the whole of which one is a part seems like an ever expanding entity. So perhaps, objective consciousness is also a relative and multilevel concept. How does one's own pattern align with the pattern of the "whole" under consideration is a measure of objective consciousness.

Speculations fwiw