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Infinity is infinitely big. Conversely, it also must be infinitely small, almost nonexistent. Because, in order to be infinite, it must contain everything, incl

Infinity is infinitely big. Conversely, it also must be infinitely small, almost nonexistent. Because, in order to be infinite, it must contain everything, including all concepts that are contradictory. So it ends up in the eternal philosophizing of many esoteric schools and religions: Infinity is the ultimate balance, tranquility, that is totally inert and irrelevant to outside because it contains all the contradictions inside itself in a balancing, canceling-out fashion. But... Infinity must also be the total opposite of that in order to be infinite - it must be the total opposite of infinitely balanced too. Again canceling out any description and defying identification. So it all begins and ends in mystery. Then again, it also must not be mysterious in order to be truly infinite, so...

drdeca 4y ago
> Because, in order to be infinite, it must contain everything This is wrong (or at least, using a poor choice of definition of infinite). I don't get why people think this?
- unity1001 4y ago
  > I don't get why people think this? Because, otherwise at least one thing will be missing from infinity, and it wont be infinite in that direction. And that's not the mathematical sense of directions, physics vectors etc. All of them are always limited and they cannot describe infinity. Infinity must be infinite in every way. Its the opposite: A lot of people get stuck at a certain point because they try to describe infinity using mathematical concepts or thinking. Mathematics, which is a framework that is limited in specific ways in order for humans to be able to understand it and calculate through it.
  - drdeca 4y ago
    Ok, so you are just using an IMO mostly useless definition of the term. Fine. That mostly just means you aren’t talking about the same thing as everyone else. Though, what do you call something which isn’t finite then? Or perhaps you define “finite” as “not ‘infinite’” where ‘infinite’ is being used as you use it? In which case, that also makes “finite” mostly useless imo, and I question what you would use to describe something which not only has limits of some kind, but is specifically limited in terms of how much stuff it has, in addition to being limited in terms of what stuff, and specifically, where the “how much” is limited as being less than some natural number.
    - unity1001 4y ago
      > mostly useless Its a philosophical approach. Not a mathematical. It does not have to be one. > what you would use to describe something which not only has limits of some kind, but is specifically limited in terms of how much stuff it has, in addition to being limited in terms of what stuff, and specifically, where the “how much” is limited as being less than some natural number. That's a given set of specific limitations. Quite a mathematical concept. Like 'the set of natural numbers up to a given, large number'. It only makes sense within the given limitations and definitions, a precise mathematical use case. Otherwise if you dive into its details, like how an infinite amount of fractional numbers inhabit even that given large set of natural numbers, things go out of hand there too.
      - drdeca 4y ago
        I don’t think it really is a particularly math-specific concept. I mean, it is mathematical in the same way that “how many fingers am I holding up?” is mathematical, but it isn’t specific to any particular axiomatization of something, and is instead expressed in terms of general intuitive notions. If I have a box, I might ask, “is there some number n such that there are fewer than n protons in this box?”. Well, really, the question would be phrased “are there finitely many protons in the box”, but I’m avoiding the word “finite” because you use the word “infinite” differently. The question of “are there ‘un-split-able ones’ ?” goes way back, and is a question about the world, not about math considered abstractly. Aiui, it was considered philosophically. A question as to whether there is a limit to how much things can be split into smaller parts. The question of “Does this thing have a limit of ‘how much’/‘how many’ ?“ is not a question which concerns only mathematicians, but which concerns anyone who seeks to understand the world.
jerf 4y ago
"Because, in order to be infinite, it must contain everything, including all concepts that are contradictory." No, this is a common misconception but it is false. Consider the set of all even integers. It is infinite, but no matter how long you search you will never find 3. There is no sense in which "infinity" entails "all inclusive". You can define "the set that contains everything", but it is also not terribly interesting that it contains "contradictions". Clearly the set that contains everything contains the propositions "2 is even" and "2 is not even", but... so what? All that implies is that contradictory claims exist, which is not even slightly profound. Prove contradictory claims are somehow both true and now you're cooking with philosophical gas, but the mere fact they can be defined is uninteresting. That is literally nothing more than the observation that both false and true statements exist.
- unity1001 4y ago
  > Consider the set of all even integers Nope, don't: Mathematical approaches to infinity do not work. Because all mathematical approaches are limited. And the infinite cannot be expressed by using the finite. Infinity must contain everything that exists and their antithesis in it. If even one thing is missing, the infinity won't be infinite. > but it is also not terribly interesting that it contains "contradictions" It's terribly interesting. Because: > the propositions "2 is even The infinity must contain the antithesis of a proposition. The antithesis of 2. The antithesis of even. The antithesis of everything involved in making that proposition. If it doesn't, then its not infinite because it is missing something.
  - jerf 4y ago
    So, you have your idiosyncratic definition of infinity. You are welcome to it. But you are making the very common mistake of thinking you can play games with definitions and thereby somehow affect the real world. Along with failing to change anything with your definitions, you also sever yourself from any ability to communicate with anyone else in the world using a more conventional definition. I see this sort of approach a lot. It may give you a lot of warm fuzzy mystical feelings, but it's sterile. It can't go anywhere beyond that. You've locked yourself in a tiny little box with your fuzzy feelings and mixed up definitions, and you think you've got a hold of something amazing, but you're just... locked in a tiny box, with nowhere to go, with nothing allowed to come in and affect you and no ability to put anything out into the world. What's more, if you came out into the greater world with the rest of us, you'd find that your content-free mystical feelings are really just a counterfeit of the wonder that is available in the real world. More complicated, more substantial, more interesting, and as far as I can see, an infinite (heh) vista of things to discover and communicate, rather than a tiny little concept posing as a large one. Throw away your attachment to your idiosyncratic definition and join the rest of us on the real voyage of discovery. It may hurt a bit at first, and it certainly requires more work, but the pay off is worth it.
otabdeveloper4 4y ago
Countable numbers (1, 2, 3, ...) are infinite, in the sense that they never end. However, the information complexity of a program to generate them is finite and only a few bytes long. Information complexity of generating digits of π is considerably more complex but still very finite. So what you really want is the infinity of infinite information complexity, but we haven't discovered such a thing yet.
- unity1001 4y ago
  > Countable numbers (1, 2, 3, ...) are infinite They mathematically are. They are not truly infinite. Because, they are countable and define-able as a set. They are infinite in only one direction. > what you really want is the infinity of infinite information complexity Still falls short. The infinity must contain the antithesis of information. And complexity.
BeetleB 4y ago
Looking at your comments, it seems you are merely defining infinity to what you want it to be. Which is fine. It is, after all, what the mathematicians did. But then taking your definition and insisting other definitions are wrong - that's problematic.

drdeca 4y ago

> Because, in order to be infinite, it must contain everything This is wrong (or at least, using a poor choice of definition of infinite). I don't get why people think this?

unity1001 4y ago
> I don't get why people think this? Because, otherwise at least one thing will be missing from infinity, and it wont be infinite in that direction. And that's not the mathematical sense of directions, physics vectors etc. All of them are always limited and they cannot describe infinity. Infinity must be infinite in every way. Its the opposite: A lot of people get stuck at a certain point because they try to describe infinity using mathematical concepts or thinking. Mathematics, which is a framework that is limited in specific ways in order for humans to be able to understand it and calculate through it.
- drdeca 4y ago
  Ok, so you are just using an IMO mostly useless definition of the term. Fine. That mostly just means you aren’t talking about the same thing as everyone else. Though, what do you call something which isn’t finite then? Or perhaps you define “finite” as “not ‘infinite’” where ‘infinite’ is being used as you use it? In which case, that also makes “finite” mostly useless imo, and I question what you would use to describe something which not only has limits of some kind, but is specifically limited in terms of how much stuff it has, in addition to being limited in terms of what stuff, and specifically, where the “how much” is limited as being less than some natural number.
  - unity1001 4y ago
    > mostly useless Its a philosophical approach. Not a mathematical. It does not have to be one. > what you would use to describe something which not only has limits of some kind, but is specifically limited in terms of how much stuff it has, in addition to being limited in terms of what stuff, and specifically, where the “how much” is limited as being less than some natural number. That's a given set of specific limitations. Quite a mathematical concept. Like 'the set of natural numbers up to a given, large number'. It only makes sense within the given limitations and definitions, a precise mathematical use case. Otherwise if you dive into its details, like how an infinite amount of fractional numbers inhabit even that given large set of natural numbers, things go out of hand there too.
    - drdeca 4y ago
      I don’t think it really is a particularly math-specific concept. I mean, it is mathematical in the same way that “how many fingers am I holding up?” is mathematical, but it isn’t specific to any particular axiomatization of something, and is instead expressed in terms of general intuitive notions. If I have a box, I might ask, “is there some number n such that there are fewer than n protons in this box?”. Well, really, the question would be phrased “are there finitely many protons in the box”, but I’m avoiding the word “finite” because you use the word “infinite” differently. The question of “are there ‘un-split-able ones’ ?” goes way back, and is a question about the world, not about math considered abstractly. Aiui, it was considered philosophically. A question as to whether there is a limit to how much things can be split into smaller parts. The question of “Does this thing have a limit of ‘how much’/‘how many’ ?“ is not a question which concerns only mathematicians, but which concerns anyone who seeks to understand the world.

jerf 4y ago

"Because, in order to be infinite, it must contain everything, including all concepts that are contradictory." No, this is a common misconception but it is false. Consider the set of all even integers. It is infinite, but no matter how long you search you will never find 3. There is no sense in which "infinity" entails "all inclusive". You can define "the set that contains everything", but it is also not terribly interesting that it contains "contradictions". Clearly the set that contains everything contains the propositions "2 is even" and "2 is not even", but... so what? All that implies is that contradictory claims exist, which is not even slightly profound. Prove contradictory claims are somehow both true and now you're cooking with philosophical gas, but the mere fact they can be defined is uninteresting. That is literally nothing more than the observation that both false and true statements exist.

unity1001 4y ago
> Consider the set of all even integers Nope, don't: Mathematical approaches to infinity do not work. Because all mathematical approaches are limited. And the infinite cannot be expressed by using the finite. Infinity must contain everything that exists and their antithesis in it. If even one thing is missing, the infinity won't be infinite. > but it is also not terribly interesting that it contains "contradictions" It's terribly interesting. Because: > the propositions "2 is even The infinity must contain the antithesis of a proposition. The antithesis of 2. The antithesis of even. The antithesis of everything involved in making that proposition. If it doesn't, then its not infinite because it is missing something.
- jerf 4y ago
  So, you have your idiosyncratic definition of infinity. You are welcome to it. But you are making the very common mistake of thinking you can play games with definitions and thereby somehow affect the real world. Along with failing to change anything with your definitions, you also sever yourself from any ability to communicate with anyone else in the world using a more conventional definition. I see this sort of approach a lot. It may give you a lot of warm fuzzy mystical feelings, but it's sterile. It can't go anywhere beyond that. You've locked yourself in a tiny little box with your fuzzy feelings and mixed up definitions, and you think you've got a hold of something amazing, but you're just... locked in a tiny box, with nowhere to go, with nothing allowed to come in and affect you and no ability to put anything out into the world. What's more, if you came out into the greater world with the rest of us, you'd find that your content-free mystical feelings are really just a counterfeit of the wonder that is available in the real world. More complicated, more substantial, more interesting, and as far as I can see, an infinite (heh) vista of things to discover and communicate, rather than a tiny little concept posing as a large one. Throw away your attachment to your idiosyncratic definition and join the rest of us on the real voyage of discovery. It may hurt a bit at first, and it certainly requires more work, but the pay off is worth it.

otabdeveloper4 4y ago

Countable numbers (1, 2, 3, ...) are infinite, in the sense that they never end. However, the information complexity of a program to generate them is finite and only a few bytes long. Information complexity of generating digits of π is considerably more complex but still very finite. So what you really want is the infinity of infinite information complexity, but we haven't discovered such a thing yet.

unity1001 4y ago
> Countable numbers (1, 2, 3, ...) are infinite They mathematically are. They are not truly infinite. Because, they are countable and define-able as a set. They are infinite in only one direction. > what you really want is the infinity of infinite information complexity Still falls short. The infinity must contain the antithesis of information. And complexity.

BeetleB 4y ago

Looking at your comments, it seems you are merely defining infinity to what you want it to be. Which is fine. It is, after all, what the mathematicians did. But then taking your definition and insisting other definitions are wrong - that's problematic.