Infinite-finite

[Kyriakos]

I have been meaning to write a second story about the notion of infinity for some time now. I am as usual very lazy, and i have been hypnotized by the small success with the periodicals, but i really have to get back to work.

The idea for the story was rekindled by a quote of Borges, according to which Kafka had as a precursor the paradoxes of Zeno.

Now this i took to mean that Kafka over-analyzed things, to the point of losing the obvious human ability to make more general thoughts. Thus, like Zeno, he focused on the non-general, hyper-specific examination of a phenomenon, and was being robbed of the mental move of infinity, by which i mean the ability to make a general thought that would give a solution to his trouble.

A few more stuff relevant to this:

In Zeno's paradox of Achilles and the tortoise, Zeno examines the race between the two entities as something that never actually reaches the point where Achilles would overcome the tortoise, for it is examined in an infinite series of broken up parts that come before that very moment.

In Kafka one often sees the examination of something which appears to single out some properties, and negate a fuller picture. For example in The Castle, the character K. endlessly speculates about the nature of the shadowy authorities, by trying to examine the stance the lowest authorities have towards him, the only ones accessible to him. This seems to be a parallel to the paradox of Zeno, in that a small part (in Zeno;s case of time, in Kafka's of a phenomenon) gets endlessly broken up into even tinier parts, and one is lost inside the search for their meaning, which however appears now without any possibility to synthesize all the parts, much like in the paradox you cannot make the general calculation about the point in time in which the hero will have surpassed the tortoise.

Anyway, i am not sure- again, always with this type of thread- if there is any interest, so i will stop here and watch for possible replies.

Sadly i cannot produce a tl:dr ; part of the negation of infinity i am afraid ( ), so you will have to be daring and read the paragraphs. But if you reach this point after reading them then i can make clear that i am asking if you find this sort of subject to be of interest. In a short story of course it will have to be synthesized with other stuff, since this is not an article, but that is the easy part. The main thing is to be examining the subject in a correct way

 

[warpus]

I have a bit of an interest in the concept of infinity, probably because I took a bunch of advanced mathematics courses in University.

What sort of story will it be? Who are the characters, who's the protagonist, villain, and what's the plot? and how will it relate to ifininity?

 

[Kyriakos]

I have a bit of an interest in the concept of infinity, probably because I took a bunch of advanced mathematics courses in University.

What sort of story will it be? Who are the characters, who's the protagonist, villain, and what's the plot? and how will it relate to ifininity?

I too took some lessons in infinity, for my last year in highschool since at the time i was directed towards the hard sciences (changed that the following year). But the story has little reference to actual math (although any idea, theoretically, can have a mathematical explanation/translation) and more to do with riddles.

I am not set on a plot currently, but i pondered having the narrator have to solve a riddle involving the number 8 found in a dream of a second character. Now 8, thrown to the side, is the symbol of infinity, so the dream obviously had some connotation particular to that.

My stories usually do not have villains, and never heroes. Most of the time it is ambiguous just what anyone is - or even if they exist as separate entities.

But the idea is to have a person who has lost the ability to think generally, and is analyzing everything, to the point of being sunk perpetually to lower realms of the mind due to the focus on the focus on the focus on the focus etc of the phenomenon.

An example could be someone who cannot any longer identify a human being as a collection, as a oneness, but instead views it as a sum of infinite separate parts. This person may have serious trouble in understanding that he is one, at any level of existence, and might be seeing such dreams with the inverted infinity, or side-lopped infinity (8).

A basic example of a plot could be that the person is locked in a mental asylum, and a friend of his is visiting, observing the number 8 carved in the room's walls. Later on he finds out about the dream, and from then on tries to piece together the little information he has, with the common past with that person, so as to help him.

 

[Ayn Rand]

There is no contradiction here - the Universe is made up of an infinite number of infinities. Thus, your characters obsession with small detail is in fact an obsession with the infinite complexity that exists at the level of the particular.

 

[Kyriakos]

There is no contradiction here - the Universe is made up of an infinite number of infinities. Thus, your characters obsession with small detail is in fact an obsession with the infinite complexity that exists at the level of the particular.

I agree, however the issue is that one can either be lost in the infinity of the particular, or be able to move past it, by generalizing. Most people do the second, without perhaps realizing the complicated of the action, since it is instinctive (probably acquired from millenia of evolution). But some can lose (or negate) that ability of general thought, and blow up all examined phenomena into their tiniest particles, and those particles breaking up to even more tiny ones, ad infinitum

Best thing is imo to be able to do both in excess or in moderation, both noting the details and the overall picture.

 

[Ayn Rand]

I agree, however the issue is that one can either be lost in the infinity of the particular, or be able to move past it, by generalizing. Most people do the second, without perhaps realizing the complicated of the action, since it is instinctive (probably acquired from millenia of evolution). But some can lose (or negate) that ability of general thought, and blow up all examined phenomena into their tiniest particles, and those particles breaking up to even more tiny ones, ad infinitum

Best thing is imo to be able to do both in excess or in moderation, both noting the details and the overall picture.

Perhaps a digression - but what kind of conceptual schema can be used for ordering the infinitely finite? All of our philosophy consists of mechanisms for - as you say - generalising in some form or another. Got any links?

Edit: Also, have you seen this documentary?


Link to video.

 

[Kyriakos]

I do not think it is possible to actually create a consciousness where you have an ongoing attempt to order the infinitely finite, as you put it (if i am understanding you correctly). An example might be someone who has formed a mental ladder to examine the numbers, or something else, and then breaks up that ladder into infinite parts between each natural number, eg 7 and 8. Surely you can break those parts into an infinity even in smaller particles, and continue to do so, but it seems to be pointless (and dangerous potentially). But my own story would have dealt with a clearly pathological state where the person is unable anymore of general thought, and thus sees every single thought as something that is an infinity of particles.

I am not sure if there has been much philosophy on this issue. Maybe 20th century philosophy of the mind is your best bet?

edit: i will check the documentary Also i thought of this perhaps more striking example of an incapacity to go past infinity: a person who cannot count above 1, since first he has to count all of the parts between 1 and 2. Of course this seems bizarre, but the story will have an analogy to it, involving other mental actions and not numbers..

 

[Kyriakos]

Well i saw the intro of the documentary. Very interesting, fractals are impressive as shapes and afaik have very pronounced uses in computer images too.

I am mostly interested though in another shape, the golden ratio. It appears in many places, from the human body and trees, to the Parthenon. I always instinctively though that if we exist as 4 dimensional objects, then the golden ratio would appear as an even more important shape, and evident in 4 dimensions...

 

[Ayn Rand]

edit: i will check the documentary Also i thought of this perhaps more striking example of an incapacity to go past infinity: a person who cannot count above 1, since first he has to count all of the parts between 1 and 2. Of course this seems bizarre, but the story will have an analogy to it, involving other mental actions and not numbers..

There have been several such people - Georg Cantor was arguably the first and most important. Unfortunately they all appeared to have drove themselves into insane asylums as they drove themselves mad trying to prove these things.

Plus of course, even if you could count all the pieces between one and two, it would not be sufficient to fill the entire gap

However, there is generality here. Unless you are dealing with different types of infinity, then the attempt to count all particles between 1 and 2 is much the same as between 7 and 8, or between 10 and 25, or 0 to infinity - or any other sequence of numbers or indeed, any type of geometry. Even something that specific has something general about it - a commonality with all other attempts of its kind.



A documentary about Cantor and his infinitely complex friends, should you find yourself with time to kill


Link to video.

 

[Kyriakos]

I will definitely check that out, thank you AynRand

Regarding the golden ratio, or φ, much like the π and other such numbers it always seemed to me to be something we fail to see as its true identity due to our 3 dimensional thinking. I cannot accept that such important numbers have such seemingly crude characteristics. We have crude mechanisms, currently, for observing them, but they should be perfect.
Anyway it has been many years since i last ventured in high math, much less into anything research-related, but for a short story one does not really have to show that much, less is more and vagueness can be very forgiving

 

[Crezth]

I too took some lessons in infinity, for my last year in highschool since at the time i was directed towards the hard sciences (changed that the following year). But the story has little reference to actual math (although any idea, theoretically, can have a mathematical explanation/translation) and more to do with riddles.

If you really want to acquaint yourself with an intimate understanding of infinity, you'll need to dive deeper into mathematics. Breaking down preconceived notions of infinity and reconstructing them within a mathematical framework is intensely satisfying and you will walk away with a much better idea of how infinity is related to life, the universe, and everything.

In particular, the Zeno paradox is not exactly a paradox, but was an intellectual frustration born out of the ancient Greeks' misunderstanding of infinity, and the mathematical problem it posed has since been solved with the discovery/invention of calculus by Newton and Leibniz.

I reiterate, though, that polishing off your mathematics education is probably the best you can do for understanding infinity (and, well, everything). I've heard it said that learning your way up to calculus and then stopping there is like reading only half of a really good novel.

 

[Kyriakos]

If you really want to acquaint yourself with an intimate understanding of infinity, you'll need to dive deeper into mathematics. Breaking down preconceived notions of infinity and reconstructing them within a mathematical framework is intensely satisfying and you will walk away with a much better idea of how infinity is related to life, the universe, and everything.

In particular, the Zeno paradox is not exactly a paradox, but was an intellectual frustration born out of the ancient Greeks' misunderstanding of infinity, and the mathematical problem it posed has since been solved with the discovery/invention of calculus by Newton and Leibniz.

I reiterate, though, that polishing off your mathematics education is probably the best you can do for understanding infinity (and, well, everything). I've heard it said that learning your way up to calculus and then stopping there is like reading only half of a really good novel.

Maybe mathematics have moved past the problem presented by Zeno in this area, however that does not at all mean that Zeno's thought is no longer existent in our mind. Like anything there exist infinite variations of it, leading upwards to advanced math that overtakes it, and downwards to other issues, such as a schism between the ability to generalize and the ability to synthesize. This is the subject of the story

 

[warpus]

I too took some lessons in infinity, for my last year in highschool since at the time i was directed towards the hard sciences (changed that the following year). But the story has little reference to actual math (although any idea, theoretically, can have a mathematical explanation/translation) and more to do with riddles.

Ahh.. The riddles you posted above (in your op) are actually mathematical in nature by the way. So it's possible that yours are as well, even if you don't realize it.

 

[Kyriakos]

I made provision for this by noting that anything can be translated into maths, given sufficient ability to adapt it in that language of the cosmos

 

[warpus]

I made provision for this by noting that anything can be translated into maths, given sufficient ability to adapt it in that language of the cosmos

What I meant was that Zeno's "paradox" is pretty much just a mathematical exercise converted into a story.

It actually plays a very interesting part in the book "Gödel, Escher, Bach", which I highly recommend btw.. it's more for computer scientists, mathematicians, but I think you might enjoy it

 

[Ayn Rand]

I will definitely check that out, thank you AynRand

Regarding the golden ratio, or φ, much like the π and other such numbers it always seemed to me to be something we fail to see as its true identity due to our 3 dimensional thinking. I cannot accept that such important numbers have such seemingly crude characteristics. We have crude mechanisms, currently, for observing them, but they should be perfect.
Anyway it has been many years since i last ventured in high math, much less into anything research-related, but for a short story one does not really have to show that much, less is more and vagueness can be very forgiving

The golden ratio is probably more famous in Greece than other countries. I'm not sure that it is actually "perfect" in any way - it is simply called that because of its aesthetic properties isn't it? ie it is architecturally "perfect" but not actually perfect, and thus its 4-dimensional importance would necessarilly rely on an evolved sense of perception which happened to find such a ratio to be subjectively pleasing.

Also, having re-read your OP, it seems that your character is dealing with a complete breakdown in his gestalt - or his concept of self-wholeness. That in itself might be very fascinating - except that he would be unaware of just how fascinating his various pieces are, as they have no way of connecting to one another through a unified self. Thus there are some types of interestingness that will forever evade us - and the pursuit of such a form of interestingness would be contradictory and self-defeating as its very creation would have a tendency to forget itself [unless memory can be made to work without a centre]. Quite ironic, don't you think?

 

[Crezth]

Maybe mathematics have moved past the problem presented by Zeno in this area, however that does not at all mean that Zeno's thought is no longer existent in our mind. Like anything there exist infinite variations of it, leading upwards to advanced math that overtakes it, and downwards to other issues, such as a schism between the ability to generalize and the ability to synthesize. This is the subject of the story

Yes, but understanding the nature of the paradox will allow you to give your character a better treatment in your story, rather than looking upon him, askance, as you ponder the meaning of infinity. Better to know what infinity is so that you can get on your character's level.