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Chaos: A mathematical diversion.


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Hope this isn't too far afield from Glorantha.  

It smells a bit of God Learner...

Here we go...

So I decided to see what the probability of two things emerging from chaos being able to interact.

I start with a very large Chaos Set (CS).  The CS can be anything really, nouns etc..    We then select two large Reality Sub Sets (RSS) then calculate the probability that the intersection of the  RSSs is null.  Assuming the RSSs are the same size and selected without replacement (taking sCS and sRSS as the size of the respective sets). The number of possible first RSS is sCS!/sRSS!/(sCS-sRSS)!, the number possible second RSS is (sCS-sRSS)!/sRSS!/(sCS-2*sRSS)!.  Dividing the second count by the first gives the probability that the RSSs are disjoint. Applying Sterling's approximation and taking a Taylor series on sRSS about zero I got 1-sRSS^2/sCS for the probability of the RSSs being disjoint or sRSS^2/sCS for the probability of a non-null intersection.

 If the Aleph number (size) of the CS is less than or equal to the Aleph number of the RSS then there is a one-to-many or one-to-one map between CS and RSS which would destroy the presumed chaos. For chaos to continue to exist the Aleph number must be less than the Aleph number of the CS which implies sRSS^2/sCS goes to zero (ie all randomly selected RSSs are disjoint).   Therefore randomly selected RSS must be whole and complete upon its creation.

This does not preclude intersecting RSSs, but they require externally applied order.

Our concepts of distance and time can be treated as derived properties of our RSS.  Such a concepts is setup by defining relationships (an element selected from the CS).  In particular our concepts of here & now are subsets of the RSS.

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2 hours ago, Pentallion said:

In Layman's terms.

I'm not clear, but I believe he has asserted "Chaos Gates" -- instant point-to-point transport.

Or possibly this agent of Chaos has actually *built* Chaos Gates via the incantations uttered above...

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On 11/29/2016 at 10:42 AM, Revilo Divad Of Dyoll said:

The chaos set should be infinite rather than very large, so I believe that you're starting with a false premise.

Also, the probability of the reality sets intersecting is not null (see, e.g., the Hidden Greens).

Can you give some references to the 'Hidden Greens'?   I'm not familiar with that.   

The original Chaos Set can be be infinite.   The real assumption here is that the set does have an Aleph number.   "aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets "   -- https://en.wikipedia.org/wiki/Aleph_number

The conclusion that I have drawn from this is that when reality forms out of the chaos;  then the reality that is formed is entire and complete.   What follows from that is what we normally think of as 'chaos' isn't really an intrusion from the chaos set but rather a bit reality we have not discovered yet.    Rephrased:   Intrusions from Chaos Set should not happen and what folks normally call 'chaos' are actually part of the original Reality Set that formed out of the Chaos Set.

 

 

 

 

 

 

 

Edited by ChildOfEru
clarify...
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2 hours ago, ChildOfEru said:

Can you give some references to the 'Hidden Greens'?

When Genert died, his Garden started to drift apart, the broken land fractured and separated. Waha came and tied all of the parts, peoples and things that belonged there into a giant net that Spider Grandmother drew tight and pulled everything back together. The Hidden Greens are parts that Waha missed. They still have an affinity with what is now the Wastes and phase back in and out of reality trying to rejoin what they are part of. They vary from bits of the Green Age to bits of the Great Darkness, the Eternal Battle is a form of one.

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57 minutes ago, David Scott said:

What do feel is the relevance of this to the average Gloranthan or player in Glorantha? (I'm actually interested to hear this).

My joking apart this would be representative of one of many forms of illuminated thinking which in part reconciles what others would see as chaos as part of the cosmos.

The truth of the matter ... shrugs ....  its beyond me.

 

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1 hour ago, David Scott said:

What do feel is the relevance of this to the average Gloranthan or player in Glorantha? (I'm actually interested to hear this).

It is a diversion and I wouldn't be offended if the post was shuffled off to an off-topic board.  On the other hand; I do love tossing around thought experiments. 

Jon Hunter's comment is a good one:  This can be looked on as a form of illumination which argues that chaos is part of the normal functioning of the cosmos.  Like nuclear power ( who do I credit for this analogy?) it is a powerful tool; just don't get any on you.  

 

 

 

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8 hours ago, ChildOfEru said:

... what folks normally call 'chaos' are actually part of the original Reality Set that formed out of the Chaos Set.

This is pretty-clearly a "Lunar" perspective (unless other forms of Illumination also claim to incorporate & sublimate raw Chaos?).

 

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12 hours ago, ChildOfEru said:

Can you give some references to the 'Hidden Greens'?   I'm not familiar with that.   

The original Chaos Set can be be infinite.   The real assumption here is that the set does have an Aleph number.   "aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets "   -- https://en.wikipedia.org/wiki/Aleph_number

The conclusion that I have drawn from this is that when reality forms out of the chaos;  then the reality that is formed is entire and complete.   What follows from that is what we normally think of as 'chaos' isn't really an intrusion from the chaos set but rather a bit reality we have not discovered yet.    Rephrased:   Intrusions from Chaos Set should not happen and what folks normally call 'chaos' are actually part of the original Reality Set that formed out of the Chaos Set.

 

 

 

 

 

 

 

All you had to say was "Vadel was right."  Which we Vadeli have known all along.  At last, an illuminated brother!

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10 hours ago, Pentallion said:

All you had to say was "Vadel was right."  Which we Vadeli have known all along.  At last, an illuminated brother!

Another piece of Glorantha lore I am not familiar with...where can I learn about Vadeli?    A quick google search didn't reveal much.    

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22 hours ago, David Scott said:

When Genert died, his Garden started to drift apart, the broken land fractured and separated. Waha came and tied all of the parts, peoples and things that belonged there into a giant net that Spider Grandmother drew tight and pulled everything back together. The Hidden Greens are parts that Waha missed. They still have an affinity with what is now the Wastes and phase back in and out of reality trying to rejoin what they are part of. They vary from bits of the Green Age to bits of the Great Darkness, the Eternal Battle is a form of one.

And for a slightly more godlearnish perspective, it is a portion of Prax that fades in and out of reality (or impinges on our reality periodically or whatever).  It is referenced in the Guide to Glorantha and various older sources.

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7 hours ago, ChildOfEru said:

Another piece of Glorantha lore I am not familiar with...where can I learn about Vadeli?    A quick google search didn't reveal much.    

Well, normally people avoid "becoming familiar with the Vadeli", if they can ;-)

 

Look at the Guide of course, and Revealed Mythologies (Viymorni and their fall from Danmalastan...)

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I think assuming a fixed Aleph number for your RSS is a mistake. Intrusions of Chaos would indicate an increasing Aleph number.

The irony is that this requires, as you said in your initial post, "an externally applied order". I like the idea that Chaos is attempting to, from its perspective, apply order. (Or would that be "restore order")

Edited by TimurTheMerciful
grammer
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To my mind, one of the foundational mathematical properties of Glorantha is the deep fractal symmetry of its being a world defined entirely by the stories that are told about it. From the ceremonial reenactment of the Myths each sacred time, to the experimental discovery of its denizens and quirks around a gaming table, at every level, it exists because someone, somewhere, has a tale to tell.

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