Tuesday, 25 October 2011

SRH is essence of contradition!

To have a contradiction there must be self-reference since a contradiction is A & –A and so what ever A is must also be negated in –A… that is some quality of A is referred to in both A and negatively in –A. This is not “self” in the usual existential sense of a “thing” but rather self in the sense of “same”.

When we ask whether the hooded man has the same identity as someone we are asking are they the “same” person. To determine whether they are the same person we must, and can only, compare qualities: have they the same name, do both have beards and blue eyes, the same finger prints, the same DNA.

But all this is not sufficient the key thing to establish is that they are never in two places at the same time. It is a joke that because you never see two people together they must be the same person… I believed that for John Sergeant and Jo Brand until they appeared on the same game show. So we can only prove that someone has an identical genetic twins when we have them both in the same room together at the same time. This seems to be the “essence” of identity: the limitation of objects that they can only occupy one space and time.

Yet I use the word “essence”, and we speak of the “same” space and time. Ex: x is at home at 12am GMT on 25th Dec 1850. The location and time-of-location of x are predicates that we apply to the object x, they are things to be said “of” x but they are not x themselves. The idea of “x” as an existing thing necessarily lies outside the realm of description and predication because this is the only way B.Russell can avoid contradiction. If we allow existence as a predicate then we can talk about those things which don’t exist!

I = (x) x does not exist.

Now this creates a set, I, of all those things which don’t exist. So lets take unicorns. Unicorns don’t exist so they belong to the set I. But how can something that doesn’t exist have membership of a set?

Having hermetically excluded all existing things from predication we are safe, but at a cost there is no way to speak about existence: it is a normative assumption of language, that is we use it when we do predicate logic, and we use it when we communicate but only implicitly; a rule of the game.

Thus one wonders whether “existence” is any more than just a rule of the game. Certainly the idea that our “hooded man” is an “existing” individual, separate from others in some fundamentally true way that we can only ever guess at with more and more evidence, is just a vain hope, a faith in the fundamental reality of the world. Let us hope that physics doesn’t continue its path of upsetting this faith much more since little remains already.

So returning to the top, the idea of reference referring to the same existences may be only a rule of the game, in reality any supposed identity is always, and only ever, based upon evidence and predicates of the entities under scrutiny. We have no magical way of ever pulling away the veil of phenomena to look at the underlying things to decide which is which, and what is what, and who is who. Hesperus and Phospheros once thought to be morning and evening stars with evidence and a new model of the skies became the same entity: I wonder what they thought of this after all those years apart ;-)

Maybe then reference is always between predicates and when these predicates are the same then we presume “real” identity or non-identity… until things change and we decide they are different or the same.

Monday, 24 October 2011

Monkey King interpretation

Posted here some time in 2002 I believe.

"Village of the Undead" (Season 1, Episode 22)

"The Matrix" is just a fairy tale compared with Monkey...

Initially it's a basic situation of good and bad. Pigsy the one representing crude desires is powerless and accepts the intoxication of drink and women without struggle. Quickly he renounces the walk to collect the sutras and is reduced to the level of an animal. Sandy is next. His symbolism has always been enigmatic, I believe it to be something to do with abstract philosophical searching: he never has much role, and always offers irrelevant analysis of situations. Fish is often associated with knowledge and intelligence anyway (maybe practically in its dietary effect on the brain). Anyway these are powerful demons and Sandy succumbs readily too. Both desire and intellgence are soon fooled, intoxicated, attached and literally married to the illusion. The demons are now almost in full existence. Only Monkey and Tripitaka remain. For once it is Tripitaka, they acknowledge, who is the greatest challenge for them.

Monkey's response to the evil is opposite is Pigsy and Sandy. As usual he detects its demonic nature, and typically he opposes it and fights it. Monkey is the ego: out of our control, self determined and always jumping around; basically irrepressible but useful because his self assurance is powerful and he looks after himself and his own very well. Being egotistiocal his relationship with those around him is always oppositional (either playfully arguing with foolish Pigsy or aggressively with demons). However these are a different type of demon from those before: if he believes in them (like Pigsy and Sandy) they will exist but by opposing them he is only making them exist all the more strongly. He cannot win, and quickly is given the choice by the girl: give in or run away. He runs away and joins Tripitaka.

Tripitaka (the monk) obviously represents the seed of enlightenment. Never sure up to this point in the series on the correct path, this time he is clear that they can neither fight nor run away. This is beyond a simple case of good and bad. He at least will surrender. Monkey is proud and loyal and follows his. So they are taken prisoner. All 4 now face death.

The demons owe their existence to the belief and imagination of the 4, but as long as they depend upon them they cannot be sure they exist independently. They need to kill them to prove that they exist freely from their captives minds: so in doing they will gain completely free, independent and solid existence.

One of the demons however doubts this and at the last minute she turns upon the demon king and ends the illusion. Everything vanishes and all 4 are free. What does it mean?

Firstly I shall explain very generally. The whole of Monkey and Buddhist teaching is aimed at teaching that it is our "thoughts which create the world" (as said in the narration at the start of every episode), or better it is the Mind which create the world. When it says "thoughts" or Mind it does not mean Monkey (the ego) creates the world. When we think "I am thinking" (Sandy) or "I want to rule Heaven and create the world" or just "I am going to do this or imagine that" (pure Monkey) or "I desire that" (Pigsy) or "I want to learn the Sutras" (Tripitaka) this is Ego (which monkey also generally represents to) not the Mind. The Mind creates all these thoughts listed and more. The Mind (if anything in Monkey) is the narrator himself who with words and pictures creates the stories. Our 4 characters, the demons and the places they find, are all created by the story, aka the Mind. In this episode they are learning not just to revel in their surroundings (like Pigsy) or analyse things (like Sandy) or change the course of events (like Monkey) according to their wishes and desires, but rather to surrender and ignore the demons and obstacles that the story (their mind) throws up. Without belief and attention fueling the illusion it vanishes and the story ends. The mind they will learn is what puts everything together into the problems they encounter each week.

More specifically I now write. All the things of the world are created by our minds, just as everything in the episode is created by the story. The demons represent ordinary things which because they are very attracive to the 4 travelers become an issue and distraction from the goal of gaining the sutras (which represent the achievemnt of truth). Not everyone passing through these place will find these demons - hence why they seem to lie in wait. Actually they are ordinary things, but because the travellers believe them to be attractive and special they become so. Thus they are distractions and become obstacles and the demons come into existence. The illustration is drink, girls and enjoyment to attract Pigsy and Sandy. "What is wrong with enjoying yourself" says one of the girls philosophically to Sandy as he falls under the spell of this hedonism. (A poignant question to todays rational and capitalist world).

Secretly we know that the Mind has created our obstacles. In reality when we become wise for example we get bored of things and they evaporate - forgetting them we normally don't wonder how they changed. Attraction draws us deeper and deeper into our obstacles, and intoxicated we wish they were really existing so we could feast on them and really gain something from them. Soon the belief that the things we like really are likable, gives way to no wish to escape the illusion (the blue pill in the Matrix 'story'). As we give ourselves up to the object of desire we are exchanging our very power to have an attraction and find something attractive for the very attraction itself. We are handing it the power and becoming its slave. This is the way we kill ourselves with desires and this is the strength of the demons. Its no good to reject the things we like either, because this does not stop our like for them. A classic learning curve for most religious people. When we reject things we still believe that the power of attraction is real and separate from ourselves, otherwise we would realise distance can't help. The ignorant run away like Monkey (becoming the subdued puritan here).

It is Tripitaka who has Buddhist teaching already! (strange if he is going to get the sutras) who realises that there is nothing that can be done. If you fight them you will become evil also he tells Monkey, i.e. they will become stronger and beat him. He neither gives into the objects of desires nor runs away. He (and Monkey) is then trapped (again :-)). For ego this is very painful and Monkey is suffering in the vat of acid. The next bit is not woven into the story I don't think. Tripitaka has sowed the seed of the end of the story here because he does not believe the demons fully. He is neither fooled into intoxication nor fearful - just trapped by his mind. The demon power is already weakened. The scene is set to end the story.

Already weakened it is then through the demon who has intoxicated our philosophical fish Sandy that the ray of enlightenment comes. "If we are created by these 4 prisioners how can I exist if they are dead". The very desire which has Sandy's mind transfixed suddenly realises its complete dependency on Sandy and so realises its own emptiness. It kills the king demon and so all the desires and illusion is ended. The obstacle is gone and all are free to pursue Enlightenment.

The narrator ends with the statement "Each day the clever mans learns something, but each day the wise man learns to accept a bit more uncertainty". The point and relevance is that it is our fixation on definite things which begins the path to evil. Rather it is with a mind which gives up definite things, realising that the interest and attraction for specific things, and the rejection and boredom of other things is all set in motion by ourselves. Reality is not a definite thing, it does not come in the shape of good and bad things, demons and heavens, or interesting and boring things, nor does it make sense like a story or even this explaination of the episode! Its just a matter of seeing the Pigsy, Sandy, Monkey and Tripitaka in ourselves, and doing the crazy journey for real (and being a little irrepressible to).

Facebook debate on Wales v France ref decision…

Most interested in the argument that cropped up about not listening to other people. It’s not a valid argument (no-one seems to have noticed) but it raises a point about individuality. If we decide to base our thoughts on what others are thinking, what do we do if they are thinking you shouldn’t do that? Like when Brian—in the ‘Life of Brian’—tells the throng that ‘they are all individual’ what a stupid thing to say because if it’s true then how can you tell them? If they need telling then they already aren’t! Indeed the very fact we can talk about “individuality” at all is proof that it doesn’t exist! Is there an SRH argument here?

In the face of an outrageous ref decision that invalidates the outcome of a game isn't it better for the whole team to just walk off the pitch?
Like ·  · Share · October 15 at 9:26am via mobile
Alva Gosson Even if Wales win the cost will damage the final. Strike!
October 15 at 9:30am · Like

Jeremy Edwards It all depends on which course of action raises the most revenue.
October 15 at 10:02am · Like

Michael Sissons No! They'd be banned from competitive rugby. Not every commentator is agreeing that wasn't a red cardable tackle, either...
October 15 at 10:13am · Like
Alva Gosson Hi Jeremy, sadly I think you're right. I was against rugby becoming professional... yes it means the players have more time to concentrate on rugby and the rugby is better, but it risks people starting to play not rugby but the stupid game of trade and income... which is vacuous and pointless. Sadly too many people spend their lives playing this game. Unlike in football I still believe these guys play rugby.. which is why it is the far superior sport (still).
October 15 at 10:50am · Like
Alva Gosson Hi Mike, well if the IRB decided to back the decision and ban Wales then they would invalidate themselves, and set off a huge political battle. A niche would immediately open up for any group/tournament who would include Wales and other teams would have to decide whether they backed the IRB. The IRB could become isolated and defunct and a new rugby board evolve. I wouldn't let all that stupid politics get in the way of my team walking off. (As a principle it never matters what other people think btw.)
October 15 at 10:55am · Like
Alva Gosson ‎(p.s. reason for that is that if the principle was to base our thoughts on what other people believe, what do we do if other people don't believe that principle ;-)
October 15 at 11:00am · Like
Alva Gosson ‎(p.p.s. absolutely technically for an image processing computer, it was a red card, but I would expect the red card to be for something that was either deliberate or un-professionally sloppy. Being upended on to your shoulders from waist height is utterly trivial... I'll put money on it the famously shifty French played that for all its worth (if the player had leapt to his feet--as he could have--it wouldn't even have been noticed); no risk of injury at all, and nothing more than a fantastic tackle! Shocker!)
October 15 at 11:13am · Like

Cheong Kong Chen I bet u will be seriously torn when both of ur "favourite" teams get into the final. And I wonder if u r going to watch it ;)
October 15 at 11:49am · Like
Alva Gosson Well rugby is the most important bit, how the teams play the second, and who the teams are the third. First two apply to everyone; the third just personal preference. So won't make much difference who gets thru :-) Personally I hope it's NZ because a NZ v France final would be the most unpredictable (given history). Objectively I hope so too because if NZ don't win this the bomb on Hiroshima for the Japanese will be a firework compared to the fall out in NZ! Sadly the final is spoilt because thanks to Alain Roland (hmmm french/irish) the N. Hemisphere isn't fielding its better team for the final so everything is messed up on all levels for everyone. Plus Australia objectively can't win because that makes it 3 WCs from 7 and they're cocky little b*****ds at the best of times ;-)
October 15 at 12:27pm · Like

Jeremy Edwards Rugby, racing & beer ...
October 16 at 8:20pm · Like

The Tortoise and the Hare hold a key truth on rates.

Fig 1: If a journey is split into two halves and the first half S1 travelled at the speed on the x-axis, then the y-axis gives the speed the second half needs to be cycled to get an average of 15mph. Given by this expression:
image

Going slow has a far bigger impact on average speed than going fast! Half the journey spent 3mph off at 12mph requires the other half 5mph faster at 20mph! The effect rapidly diverges as speed slows down. velocity-to-make-avg15

As speed increases the energy required per mile increases with a square (or a cube per second) so to double speed requires 4x the energy. Thus the impact of the above means that total energy used in a journey rapidly increases if we spend time slower than the average we want see Fig 2. (Y axis has just relative units the numbers don’t mean anything.) So spending time at 10mph when we want an average of 15mph will result in us putting more energy in over the journey than were we to spend time at 25mph! vel_energyIf the speed even drops a little to 10.5 it doubles the energy you need to pull the average back! While 4.5mph the other way (19.5mph) only increases energy use by 35%.

The clear message is what I’ve heard from time trial cyclists that its “not the going fast but the not going slow.”

 

 

 

 

Now this is exactly what Aesop was saying. Short periods of spectacular performance are impressive but are highly wasteful and are easily out stripped by a slow but regular approach; the stream over centuries eroding the landscape versus the flood.

This applies to cars too. The car manufacturers would like us to think that cars with spectacular performance will achieve more but such performance will achieve very little if we spend time below the average we want. A Porsche driver wants to travel 100miles in an hour. If he spends 30minutes at 70mph he needs to spend the other 30minutes at 175mph! Or more sensibly we want to travel 60miles in an hour. The Porsche has to get out of an urban area and averages 40mph for 30mins of the journey, they will need to average 120 for the rest! While a car that simply found a route where they could cruise at 60mph the whole way would achieve the same.

The logic applies to any rate. To make money it is not making a few spectacular incomes, but the not ever making a little. Conversely to reduce rates and save money it is the little purchases, or the not buying things, that matters rather than the big buys. In chimps it applies to social status too: success has been shown to lie in saving energy by minimising skirmishes and putting it into big fights.

I think the main difference between working and middle classes lies in this too. The rich buy quality occasionally, while the poor make lots of cheap purchases. The rich work consistently at a reasonable rate, the poor accept low rates and hope to make up the difference by big wins in gambling/lotteries and occasional lucky deals. Capitalists know this and try to encourage us to spend a little often thus sapping our wealth.

Thursday, 20 October 2011

On Time

The suggestion of neutrinos breaking the light barrier finally raises the possibility of time paradoxes. A clock strapped to one of these neutrinos will have moved backwards the next time it is checked, while the neutrino—from the frame of reference of the observer—will have travelled forward in time to a new place. A future cyclotron—using perhaps the gravity of planets—could bend the path of neutrinos so that they return suitable close to the starting point. If a detector position here could signal rapidly enough for the neutrino source to be moved then a very bizarre situation would arise. A clock strapped to the arriving neutrinos would see the change of position of the journey happen before they had set out! So that in fact their arrival would be moving the position back so that they could set out on the original path… has some difficulty saying that!

Anyway got me thinking about the great unsolved question of time.

There is an obvious problem with time. The standard model sees it as having a direction—Past, Present and Future—and somehow the Future becomes the Present which becomes the Past. This change from one to the other is imagined like a river, or an arrow or in someway a movement. Once so established we then use time along with space to relate positions of moving things so that like static frames of a film they may be strung together into a flowing phenomenon of change. But if we wish to explain the movement of an arrow or a river by using static events linked by time, we can’t then use the river or the arrow to describe the flow of time. At root we still (in the 21st century despite millennia) have no way to think about the time apart from the observation that things change. This idea that movement was ineffable was first posed to me by a friend, Andrew Rennie, at college. And being ineffable I have been reluctant to take up the gauntlet for what is 21 yrs now!

It would appear that the standard view of time serves to separate events into film like frames that are static and frozen. These are describable pictures and numbers may enumerate the points in these pictures and the frames themselves. But how they fit together—how the points in space are differentiated from one another, and the frames in time are differentiated from one another is beyond such insight. How they comes to be joined together into a changing phenomenon remains utterly unexplored in this frozen world. Perhaps essentially so since the very process here is to encode and produce in language the phenomenon of change, which is essential to differentiate the sequence of symbols and thoughts of the process.

Returning to the start, phenomenologically, what we begin with is the observation of change. That nothing remains as it is. We may sit and stare at a leaf and, if stationary, we will start to notice that it has movement in the wind, and as the days go by its shape will change as it grows or is eaten or decays. We like sudden changes, but most change is a very morphing from one shape into another and from one state into another. This morphing, refusal to remain what it is, is the essence of Being. We must I assume begin with this idea. It is the flux of Heraclitus, the Power of Nietzsche, that is forever in turmoil undoing what is, and becoming what is yet to be. “Becoming” is what came first, the Become only steps along the journey. Language being entity biased prefers the Become, the established things that have happened, but it forgets that they are only here because they Became, and like the Little Mermaid the cost of having Become is to one day Begone. Unenlightened life, as Buddha taught us, is dominated by fixation on the Become, the Becoming, and the Begone. Enlightened life is the realisation that true reality is built upon the shifting sands the both build and destroy the sand dunes of our minds.

Time travel is a mine field of paradox. As I read once paradox is a sign that something has gone wrong in our language and thoughts since in reality there are no paradoxes. If I was to return to 1859 what assurance have I that it is the ‘same’ 1859 as recorded in History? A paradox requires that it is the same 1859 so that in a century and a halves time I will be building my time machine. But how do I know this? More importantly how could I know this! What even does the ‘same’ time mean? Its normal usage would be concurrent events in different places, but the idea of same place but different time moves the question of same ‘time’ to same ‘place’. The question in 1859 is then is this the same place as in 2011. If I was in Downe House in Kent in 1859 I would be witnessing Darwin putting the finishing touches to ‘On the Origin of Species’. Downe House lies on certain identifiable roads and in relation to certain other places. In 1859 these would remain the same so I could give a normal definition of same place. Likewise I would recognise Darwin, and the house and grounds having seen paintings of him and visited the house, so could give a normal definition of same house and man. But this is deceptive. What if I was visiting an exact copy of the Earth? Crazy but what if I was the visit the area 100,000 years before: how would I find the ‘place’ where the house now stands. I need a point of reference. I could use GPS and make that a point on the Earth’s surface. But what is my 0 position. The rotation of the earth, precession around the sun etc all mean that there is no fixed point 100,000 years ago that I can find to map to the present. I would need to map the current 0 longitude and latitude back through time to find it 100,000 yrs ago. Likewise the whole issue of the English plate moving from the South Atlantic over time to crash into the Scottish plate. 100,000 yrs ago the GPS reading for Downe House would have been in the sea and wouldn’t even refer to the same rocks as today. So same ‘place’ is entirely relative, the problem I have when trying to reference the next sentence clause: it must be relative to a mysterious thing called Here and Now which is always assumed a priori and cannot be defined.

It is that mysterious Here and Now which is the true Place and Time and this remains the same even when we travel back to 1850. It is just another day. True that people carrying future knowledge don’t show up very often. If I was to tell Darwin the impact of his book in my world it would be a very odd occasion for him; and the fact it doesn’t happen suggests that there is something else wrong here. But assuming that it does happen the point is that I would be retelling Darwin of a world that is not in his future as though I was from further down the river than him, nor now is it in my future. The point is that we are both in a new place and time, as ever and the future remains as open to us as it did. If I went and killed one of my ancestors there would be no paradox as my own history doesn’t change, there are simply two ‘pasts’ one before in my memory and one after in my memory.

Sunday, 2 October 2011

On Boredom

Cut from Facebook

Boredom is one of the great sufferings in life (largely unacknowledged I think!). Decided yesterday (after 20yrs of filling my bored moments thinking abt it) that isn't it just a type of greed, coming after an more exciting period of time has ceased?
Like ·  · Share · September 23 at 10:42am via mobile
Weng Leong and Richard Pickles like this.
Alva Gosson The mistake all addicts make is to be motivated to recreate the high when maybe the best approach is just to go thru the withdrawal? Needless add an economic spin to that ;)
September 23 at 10:44am · Like ·  1 person
Alva Gosson Now i got my answer i'm bored ;)
September 23 at 10:46am · Like ·  1 person

Jerry Cloony what about less thinking and more doing Alva !?
September 23 at 12:16pm · Like ·  1 person

Jeremy Edwards Boredom is a state of mind. If something's become boring it's no longer fun. And when it's not fun it's time to stop doing it. One of the one-liners in quality assurance ...
September 23 at 12:53pm · Like
Alva Gosson Hi Jerry I'm sitting on the toilet in the middle of a 60mile cycle how much more doing do you want :) you know i'm only going to think of an answer to that ;) I take a Tao approach at mo that doing is really non-doing if you look closely. Certainly whenever i do anything i realise i depend entirely on other people and the 'doing' wasn't mine anyway + sun 'doing' a gr8 job drying my washing today ... The world goes around thats abt all we can say. + i just 'did' some thinking so done even more :)
September 23 at 3:05pm · Like ·  1 person
Alva Gosson Jerry u just reminded me of my new year resolution which wasn't to 'do' anything spectacular (that is just ego) but rather to harmonise between the worlds around me... Not 'done' that at all! Still 1/4 yr to go!
September 23 at 3:18pm · Like ·  1 person

Jerry Cloony hehehe !!! Just get on with it and don't share you sticky mobile phone with anyone. hahaha !!!
September 23 at 3:37pm · Like
Alva Gosson Eco-friendly home made anti-theft paint ;) Sorry there was a purpose to being so frank it was to highlight the difference between the base nature of reality and doing and the more sublime realm of thought.
September 24 at 1:17am · Like ·  1 person
Alva Gosson Indulge me here this interests me a lot! A visit to the toilet is preceded by some sense of urgency and desire for something, and a process which leads to some satisfaction and the evacuation of something which the digestive processes have made. So it is with thinking itself, tho Socrates prefered the analogy of child birth... At risk of suggesting he was talking shit perhaps, 4 which he was killed anyway ;) anyway was digesting this in bed this morning and now i give birth to these ideas ->
September 25 at 8:09am · Like
Alva Gosson themselves BUT, and this is the point, the process of having these ideas IS NOT the idea itself any more than a baby IS the birth, or a shit IS the pooing -> therefore i can't think abt thought itself as it happens real time! So there is the distinction between what a thought is about and a thought itself and they CAN'T be the same... I call that SRH-it's called Non-Identity in the books. So buddha asks us to go to the toilet and be the pooing not the poo, and be the thinking and not t thought.
September 25 at 8:35am · Like
Alva Gosson Problem with ego, property and Capitalism is that it protects and values the poo more than the pooing, and it is the poo which becomes marketed and fetishised by the customer rather than the industry and the skill of its pooers. So you have worthless shiters in the streets seeking to buy poos that they think are worth something. Bad mistake!
September 25 at 8:41am · Like
Alva Gosson Interesting cos most of the time we think that with enough doing, working, living, shopping, thinking, scientific investigating, pooing we WILL have sometime to show for ourselves when actually we ARE those things.

What makes us happy or sad is not Reality

cut from Facebook…

IF how we think about something determines whether we are happy or sad, then it is our ego that is making us happy or sad. LIKEWISE if there are two sides to a situation that matters to 'us', then that is also our ego making us happy or sad. Reality can only be one way or the other, everything else is ego.
Like ·  · Share · 6 hours ago
Alva Gosson We know when things are Real cos they actually ARE, and they don't need a STORY to accompany them to tell us how they are. Most things aren't real ;-)
6 hours ago · Like
Alva Gosson like this post :-)
6 hours ago · Like
Alva Gosson Qualify that: like what this post says (obviously it can't 'say' anything).
6 hours ago · Like
Alva Gosson I ended up in a situation that was unfair... at least it suddenly occurred to me as such 3 days later which made me unhappy. So I made a decision to deal with it. Everyone i told about is said it was unfair. Then it turned out that the situation I was thinking about hadn't even arisen. All that storm in a tea cup over a story I wrote myself... one that even convinced everyone I told... my mind, my ego, making me trouble :-)

To be constrained, and the constraint.

For a system to be useful it must have constraints. For example a system of N degrees of freedom can be represented in an N dimensional space, however without constraints it occupies that whole space.

The problem is the opposite for a system that is seeking to express itself. It needs freedom from constraints so that it may be large enough to contain all possibilities. The N dimensional space is the ideal system in which to express other systems because it is free from all constraints other than its dimensionality.

For a system to express itself it needs to have less constraints than itself. If it has the same constraints as itself then isn’t its representation the same as itself?

Consistent Networks and Rugby World Cup

Exploring a way of using networks to create means and therefore predictions of missing links in the network.

If a team A plays a team B then a statistic can be formed of their relative strength(RS) r by dividing r=A/B.

If a team plays itself then we would expect its relative strength to be r=1

In a round-robin competition where every team plays every other team a network of RSs exists. Where loops exist it is possible to calculate the score where team A plays team A. For example in the Tri-Nations competition, where 3 teams play, suppose Australia plays New-Zealand with r=2, and NZ then plays South-Africa with r=2. This means that A is twice as good as NZ who is twice as good as SA so we would expect SA to be 1/4 as good as Australia (assuming it is the same Australia we started with). It is this assumption which is flawed as teams are never the same and so can never play themselves! This is a kind of SRH where relationship with oneself once again proves impossible. However holding the assumption that loops multiply to 1 and that such consistent networks reflect  the underlying dynamics of competitions the following calculations can be made.

In a competition of N teams there are N-1 degrees of freedom in a consistent network. So with N=4 teams playing there are 3 unique r values. Imagine the network (a square with diagonals drawn in). Once we know 3 of the sides (a,b,c) the 4th side is simply d=1/(a*b*c). One diagonal is e=1/(a*b) and the other diagonal is f=1/(b*c). Care must be taken to treat these as vectors where direction from A->B always means A/B.

Once real values are known for any of these values the following expression can be used to find the “nearest” consistent network.

network  

If each arc of the network is treated as a dimension then the space of all possible networks between N teams is represented by an N(N-1)/2 dimensional space. However only certain points in this space are consistent networks. The consistent networks obey the loop constraints as discussed so the distance from the real network to a consistent network is given by D. Numerical minimisation of D offers the easiest way to discover the nearest consistent network, that is the consistent network that gives the smallest overall change to the data values.

UPDATE (3/10/2011)
However this method means reducing a score from 1 to 0.5 is considered a smaller change than increasing one from 1 to 2 when actually they are the same change. Instead it makes sense to calculate the difference between log values D, then take Exp(magnitude of D) as the Euclidean distance. This forms each part of the above expression.

Recap on 2011 6-Nations championship

N=6 teams play, with a network of size 6.5/2=15 and N-1=5 degrees of freedom (size of the system). From the final championship scores the following relative scores r were calculated (original actual scores before minimising in brackets):

Eng/Ita=4.08 (4.54)
Ita/Ire=0.35 (0.85)
Ire/Fra=1.44 (0.88)
Fra/Sco=0.99 (1.62)
Sco/Wal=1.04 (0.25)
Wal/Eng=0.47 (0.73)
Sco/Eng=0.50 (0.73)
Fra/Eng=0.49 (0.53)
Ire/Eng=0.70 (3.00)
Wal/Ita=1.94 (1.50)
Sco/Ita=2.02 (2.63)
Fra/Ita=1.99 (0.95)
Wal/Ire=0.68 (1.46)
Sco/Ire=0.71 (0.86)
Wal/Fra=0.97 (0.32)

D=3.15

Tri-Nations 2011

N=3 with 3x2/2=3 arcs and 2 degrees of freedom.

This year only 2 matches were played with the following relative scores and geometric average.

A/SA = 1.65
SA/NZ = 0.51
NZ/A = 1.19

For geometrically averaged r D=0.33!

Geometric because if a team does 4x another on one occasion and 1/4 on the next occasion they are on average the same as that other team!

Very much the teams didn’t play as well as themselves! Also the limited size of the network means it doesn’t hold much information. Both rounds are consistent within themselves (small D), but contradictory between themselves. Since the scores represent how many times one team scored than the other it is perhaps better to use the geometric mean for averaging them.

Rugby World Cup 2011

The first week is done and South Africa/Wales (r=1.06), Australia/Ireland (r=0.4!!) and Australia/Italy (r=5.33) have both played Southern Hemisphere teams. These two games link the networks above and enable a consistent network to be calculated for the top 9 teams.

N=9,full network arcs=36 (not all games will be played),d.f.=8

There are 6 more arcs to add to the 6 Nations network
Aus/SA = (1.65)
SA/NZ = (0.51)
NZ/Aus = (1.19)
SA/Wal = (1.06)
Aus/Ire = (0.40)
Aus/Ita = (5.33)

Numerically minimising the new expression gives the following network seeds from which the rest of the consistent network can be calculated:

D=3.30632

a -> 3.95592, b -> 0.218121, c -> 1.97058, d -> 1.09539, e -> 1.02128, p -> 5.10258, r -> 1.17188, t -> 1.33486

Eng/Ita=3.96 (4.54) [a]
Ita/Ire=0.22 (0.85) [b]
Ire/Fra=1.97 (0.88) [c]
Fra/Sco=1.10 (1.62) [d]
Sco/Wal=1.02 (0.25) [e]
Wal/Eng=0.53 (0.73) [1/(a b c d e)]
Sco/Eng=0.54 (0.73) [1/(a b c d)]
Fra/Eng=0.59 (0.53) [1/(a b c)]
Ire/Eng=1.16 (3.00) [1/(a b)]
Wal/Ita=2.08 (1.50) [1/(b c d e)]
Sco/Ita=2.12 (2.63) [1/(b c d)]
Fra/Ita=2.33 (0.95) [1/(b c)]
Wal/Ire=0.45 (1.46) [1/(c d e)]
Sco/Ire=0.46 (0.86) [1/(c d)]
Wal/Fra=0.89 (0.32) [1/(d e)]

Aus/SA = 1.84 (1.65) [p b c d e/t]
SA/NZ = 0.46 (0.51) [t/(b c d e p r)]
NZ/Aus = 1.17 (1.19) [r]
SA/Wal = 1.33 (1.06) [t]
Aus/Ire = 1.11 (0.40) [p b]
Aus/Ita = 5.10 (5.33) [p]

Using this consistent network we can walk between teams multiplying with the arrows and dividing against the arrows to find the relative strengths of games not played. This provides a ranking of teams.

EvNZ=0.67
EvA=0.78
EvI=0.86
EvSA=1.41
EvF=1.69
EvW=1.89

6 Nations further study

The values of the 6 nations network was evaluated after each game in two ways. (1) the nearest consistent network NCN was calculated each time in one step from the raw data network (2) the NCN was calculated from the last network plus the new dimension of data, i.e. in a series of incremental stems. Version two allowed for teams to gradually improve or weaken during the tournament, while version one assumes that games at the start are as important as those at the end.

Results from 1 step calculation.

The first 5 games do not complete any loops so offer no network with which to work. Team strengths relative to England are given on a Log scale and games mark the x-axis.All teams strengthen against England as the tournament progresses, in particular Ireland who storm ahead in the game against England.

image

Version 2 – Incremental

image

Essentially the same results but changes in teams (i.e. the walk through the Network space) is smoother. Scotland in particular should be happy with the way their team improved the most during the tournament, perhaps however because they started so weakly. France and Ireland take the last two games very seriously.

UPDATE 3/10/2011

Following the decision to work in log space to make 1/4x the same magnitude change as 4x the 6 nations 1 step calculation yields:

D=8.13701 – the large D value is because %increases above 1 are as valuable as %decreases below in this method.

{a -> 1.04727, b -> 0.745217, c -> 1.32598, d -> 1.43158, e -> 0.76705}

So relative to England the teams would score:

E-W = 0.955
E I = 1.098
E It = 1.432
E F = 0.939
E S = 1.245

Using this method there is very little between the teams! England is stronger than Ireland, Italy and Scotland, but Wales and France are the threats.

A General Note on Networks

If one walks a network making sure that no “loops” are formed then after N-1 arcs (where N is the number of nodes) the “seed” arcs will be laid from which all other arcs can represented by an alternative route through the seed network. In other words the number of arcs A = N + R – 1(R=the number of “regions”). However regions are topographical in N dimensional space so that no arcs ever cross. I believe this is a recognised formula … will check.

ToDo
It has also not been fully tested whether deciding which arcs to make seeds (i.e. degrees of freedom d.f.) and which are dependent on the network leads to different minima. Easy to test just try a few variations of network.

Done it: proof that Jewish thinking is limited. Spent most of the day avoiding triggering ChatGPT but it got there.

So previously I was accused of Anti-Semitism but done carefully ChatGPT will go there. The point in simple terms is that being a Jew binds y...