The Beauty of Bounded Gaps

[The Introvert]

Link here

Discuss.

What does the randomness of prime numbers imply about the randomness of, well, just about everything?

Discordians, take your bows.

 

[SLushhYYY]

Perhaps lower digits exemplify structure and foundation, while larger digits begin to symbolize randomness and chaos, infinite is a pretty chaotic thing if you actually understand it.

 

[The Introvert]

I think the point of it though, was that there isn't a correlation between lower or higher numbers and the amount of prime numbers.

I don't know if I understand infinity or not. I'd like to think I do.

 

[Ex-User (5841)]

What does the randomness of prime numbers imply about the randomness of, well, just about everything?

Discordians, take your bows.

Randomness is necessary to fill the gaps inbetween order. Talking to the free will swarm: "This is a balloon. You can do whatever you want inside of it, dance naked with a watermelon for all I care. The catch is that you cannot see the boundaries." Talking to determinism "Be as you are and encapsulate the force entirely. If it escapes, you will deflate and die."

Determinism is only true because everything that can happen will happen.

Organized chaos. It applies to ALL systems, indeed the only universal law.

The link in the article: http://projectwordsworth.com/the-paradox-of-the-proof/

I don't know if I understand infinity or not. I'd like to think I do.

Multiply the infinite (y axis) by the transfinite (x axis (and z)):

Spoiler

...
-1
0
1
2
3
4.538695486349434394764756175437467561...1
4.538695486349434394764756175437467561...2
4.538695486349434394764756175437467561...3
4.538695486349434394764756175437467561...4
4.538695486349434394764756175437467561...5
5
6
7
8
9
10
...

And you're quickly hit by a brick wall of everything that is...

 

[scorpiomover]

Irreducible elements, the building blocks of the universe, come in matching pairs.

 

[The Introvert]

Randomness is necessary to fill the gaps in between order.

So randomness is everything that isn't already under some sort of classification (be it subjective or objective [if objective classification exists]).

...
-1
0
1
2
3
4.538695486349434394764756175437467561...1
4.538695486349434394764756175437467561...2
4.538695486349434394764756175437467561...3
4.538695486349434394764756175437467561...4
4.538695486349434394764756175437467561...5
5
6
7
8
9
10
...

An infinite amount of possibilities exist even within finite boundaries.

 

[The Introvert]

Really, all numbers are simply a representation of one number. That number is 1. The complete absence of numbers? 0. Is 0 possible? Is the complete absence of everything a possibility? There either is, or there is less (like temperature). Although theoretically possible, Absolute 0 isn't attainable. Is it saying the same thing?

 

[Ex-User (5841)]

So randomness is everything that isn't already under some sort of classification (be it subjective or objective [if objective classification exists]).

An infinite amount of possibilities exist even within finite boundaries.

*pelvic thrust*​

http://www.youtube.com/watch?v=QAt2jfOgqBY

Really, all numbers are simply a representation of one number. That number is 1. The complete absence of numbers? 0. Is 0 possible? Is the complete absence of everything a possibility? There either is, or there is less (like temperature). Although theoretically possible, Absolute 0 isn't attainable. Is it saying the same thing?

What if 0 exists as the isomorphic sum of positive and negative?

 

[The Introvert]

Ok, this is all great and I love thinking about it. But I want to be able to use it for something. It has to be applicable to something, right? There's both a spiritual and scientific use for everything; I understand the spiritual implications, but I want to explore the scientific ones.

 

[Ex-User (5841)]

Ok, this is all great and I love thinking about it. But I want to be able to use it for something. It has to be applicable to something, right? There's both a spiritual and scientific use for everything; I understand the spiritual implications, but I want to explore the scientific ones.

Apply synchronicity. Though there are infinite possibilities, many of those possibilities share common traits (i.e. result in the same behavior or pattern. Say.... grouping/flocking in birds, fish, locusts). These species/populations have about as much in common as prime numbers... the fact that they're prime and little more. Go back to the .gif. What if each number were a different species, possibly with a completely different lineage, but all species of a given color behaved the same? The majority of these "tangential rules" remain undiscovered/undocumented in ecology/biology. I stumbled upon centrifugal organization a while back (last summer) and built upon it to the point where I can now call it fractal organization and say that, for example... Well fuck, I don't have my notes in front of me.

 

[The Introvert]

Apply synchronicity. Though there are infinite possibilities, many of those possibilities share common traits (i.e. result in the same behavior or pattern. Say.... grouping/flocking in birds, fish, locusts). These species/populations have about as much in common as prime numbers... the fact that they're prime and little more. Go back to the .gif. What if each number were a different species, possibly with a completely different lineage, but all species of a given color behaved the same? The majority of these "tangential rules" remain undiscovered/undocumented in ecology/biology. I stumbled upon centrifugal organization a while back (last summer) and built upon it to the point where I can now call it fractal organization and say that, for example... Well fuck, I don't have my notes in front of me.

I don't understand these terms

 

[Ex-User (5841)]

I don't understand these terms

I'm in a visual thinking mood, so beware... All that I see may not make it onto paper.

http://drpaulkeddy.com/pdffiles/CentrifrugalOrganization1990.pdf

Higher trophic levels (at the population level of organization) are structured in the same pattern, so it's really more like this: http://en.wikipedia.org/wiki/Fractal

In a population context looking down on the plant community, things might appear to be flat and centrifugal, but you're actually looking down on a pyramid. the higher the trophic level, the fewer the individuals in a given population; and the further from the center, the smaller the population. (So in the center are large populations that function as keystone species). In terms of energy flow, it's not a pyramid, but relatively solid and stable all the way through the trophic structure because energy isn't contained only within living individuals and leaves through thermoregulation, bodily excretion, etc.

Each population is an agent-based collective that interacts with the local environment as well as surrounding populations, through reciprocal causality.
http://www.intpforum.com/showthread.php?t=12895
http://en.wikipedia.org/wiki/Reciprocal_determinism

When synchronicity is applied in terms of exotic invasions, niches become interchangeable between two species attempting to occupy the same; i.e. both phragmites and native broadleaf cattail can fill a round hole, and both compete directly for that hole. In direct competition, one on one, it's easy to predict (the best species wins and it's over). Any resistance to invasion is actually a systemic mechanism via reciprocal determinism from the surrounding populations and environment.

It's entirely indirect, and can be overcome by invaders regardless of the outcome of direct competition, because the facilitation of other species counteracts the native reciprocal determinism. Other non-native species (aphids, beetles, birds, etc) are able to do this successfully because their intrinsic, evolutionarily/genetically determined adaptive traits are positioned in such a way that they don't align with the shape and volume of the native systemic structure. This trophic misalignment is corrected through entropy (physics!) until a new equilibrium is reached; a stable trophic structure, or alternate stable state.

I think ^this came out in far too many syllables, so a conceptual example: In Ohio trophic niches are squares and far across the globe in Pennsylvania they are hexagons. Each species is a uniquely shaped blob, and all individuals of a given species share the same shape. In this case Ohio species X is shaped like an X and Pennsylvania species U is shaped like a U.

Because niches are always occupied, though not always very strongly, reciprocal causality is constantly in effect. The environment and populations that collectively form the boundaries of the squares in Ohio are collectively predisposed to form an X into a square. When a U appears, the same processes are at work trying to shape the U into a square, but:

-some are ineffective
-some are inefficient
-some do the same
-some are more efficient
-some are super-effective

This produces a different shape (which is locally stable), which in turn alters the boundaries surrounding it and through reciprocal causality, creates its own niche as a self-fulfilling prophecy. The key is identifying the qualities that determine the shape of a given species. If they can be identified, then they can be quantified and thus used as a predictive index.

^This is what explains the lags between initial colonization and epidemic invasion, which occur across a WIDE variety of timescales and are otherwise essentially unpredictable.

(And of course another caveat is a group of different species that add up to form a square of the same dimensions, which brings up the transfinite yet again, as well as the gool ol'd quantum box: http://en.wikipedia.org/wiki/Particle_in_a_box)

 

[The Introvert]

I'm in a visual thinking mood, so beware... All that I see may not make it onto paper.

http://drpaulkeddy.com/pdffiles/CentrifrugalOrganization1990.pdf

Higher trophic levels (at the population level of organization) are structured in the same pattern, so it's really more like this: http://en.wikipedia.org/wiki/Fractal

Still I don't understand what centrifugal organization is (in the .pdf would it be the competition? Is it simply taking one arbitrarily important species [or whatever level of organization you want] and organizing the then qualified important interactions around it?), but:

Fractal organization (in my own words) - is breaking the organization into smaller bits (but still equal in ratio from one bit to the next). So, for instance, you could have interaction between Phrag and aphid being one fractal and then aphid to intestinal bacteria as another fractal, both of which are equal in ratio to the adjacent fractal (say Phrag to aphid = 1.5 and aphid to bacteria = 1.5).

In a population context looking down on the plant community, things might appear to be flat and centrifugal, but you're actually looking down on a pyramid.

So both centrifugal and fractal?

the higher the trophic level, the fewer the individuals in a given population; and the further from the center, the smaller the population. (So in the center are large populations that function as keystone species). In terms of energy flow, it's not a pyramid, but relatively solid and stable all the way through the trophic structure because energy isn't contained only within living individuals and leaves through thermoregulation, bodily excretion, etc.

Cool beans

Each population is an agent-based collective that interacts with the local environment as well as surrounding populations, through reciprocal causality.
http://www.intpforum.com/showthread.php?t=12895
http://en.wikipedia.org/wiki/Reciprocal_determinism

Reciprocal determinism could very easily cause a feedback loop. To be honest it shouldn't be too hard to create a script that models that (simplistically).

Object X = value 1,2,3 when Y =1,2,3
When X = 1,2,3 Z = 1,2,3
When Z = 1,2,3 Y = 1,2,3
(or you could just do X and Y but that's no fun)
Y = 1 = X = 1 = Z = 1 ---> Y=1+1(Z,X), so on

(absolutely no use for me to put that there)

When synchronicity is applied in terms of exotic invasions, niches become interchangeable between two species attempting to occupy the same; i.e. both phragmites and native broadleaf cattail can fill a round hole, and both compete directly for that hole. In direct competition, one on one, it's easy to predict (the best species wins and it's over). Any resistance to invasion is actually a systemic mechanism via reciprocal determinism from the surrounding populations and environment.

Which could ultimately be key in deciding the best species, right? Without other interactions, species A could be better than B, but with common interactions present, the results could be muddier.

It's entirely indirect, and can be overcome by invaders regardless of the outcome of direct competition, because the facilitation of other species counteracts the native reciprocal determinism. Other non-native species (aphids, beetles, birds, etc) are able to do this successfully because their intrinsic, evolutionarily/genetically determined adaptive traits are positioned in such a way that they don't align with the shape and volume of the native systemic structure. This trophic misalignment is corrected through entropy (physics!) until a new equilibrium is reached; a stable trophic structure, or alternate stable state.

Is that what I just said or no?

What's indirect? Resistance to invasion? Reciprocal causality?

How intimately does causality interact with, for lack of a better description, pieces of the evolutionary puzzle (in invasive species) that don't fit exactly into the niche? Surely some have to function, otherwise the organism couldn't survive. How do the non-compliant parts act independently, are are even they acted upon by reciprocal causality? Again, how much?

As for the entropy, would it be possible to predict where the equilibrium will be reached? Can you seriously determine the entropy an invader will introduce into a system, and ultimately figure out where the system will end up? Can I learn to do that?!

I think ^this came out in far too many syllables, so a conceptual example:

I tried really hard, I think I got most of it (hopefully)

In Ohio trophic niches are squares and far across the globe in Pennsylvania they are hexagons. Each species is a uniquely shaped blob, and all individuals of a given species share the same shape. In this case Ohio species X is shaped like an X and Pennsylvania species U is shaped like a U.

Because niches are always occupied, though not always very strongly, reciprocal causality is constantly in effect. The environment and populations that collectively form the boundaries of the squares in Ohio are collectively predisposed to form an X into a square. When a U appears, the same processes are at work trying to shape the U into a square, but:

-some are ineffective
-some are inefficient
-some do the same
-some are more efficient
-some are super-effective

This produces a different shape (which is locally stable), which in turn alters the boundaries surrounding it and through reciprocal causality, creates its own niche as a self-fulfilling prophecy.

IE a feedback loop. KA-CHING!

Spoiler

To shamelessly toot my own horn:
"Reciprocal determinism could very easily cause a feedback loop. To be honest it shouldn't be too hard to create a script that models that (simplistically). "

The key is identifying the qualities that determine the shape of a given species. If they can be identified, then they can be quantified and thus used as a predictive index.

^This is what explains the lags between initial colonization and epidemic invasion, which occur across a WIDE variety of timescales and are otherwise essentially unpredictable.

(And of course another caveat is a group of different species that add up to form a square of the same dimensions, which brings up the transfinite yet again, as well as the gool ol'd quantum box: http://en.wikipedia.org/wiki/Particle_in_a_box)

So, ultimately, the stability of a system is dependent on how snugly the fractal pieces fit, so to speak. If the interconnectivity (not a word) between species is very intricate (multiple levels of organization dependent on one another) then the system is what? More or less stable? I could see an argument from either side:

IF one piece of the puzzle fails, the whole system fails
IF it isn't an intricate system, it would be easier for invasions

Also, though, an invasion could disrupt the system. So I would think that a looser system is actually more stable, because the pieces aren't totally dependent on one another. However, looser systems are more susceptible to invasive species.

Now, in addition to the intricacy of the system, the more pieces a system has, the greater effect reciprocal causality would have, I presume. If organisms are interacting more closely with one another, the actions of any given organism in the system would be more likely to disrupt the immediate surroundings (other organisms, interactions) than a system where there is less connectivity.

Just trying to connect the dots here for you (from fractal organization to reciprocal causality).