Stock Market Distribution

Well a year late it seems I have my answer. I've already shown that a log/log graph of FTSE day changes is mostly linear. This indicates a scale invariant power law distribution!

Such distributions exist where the more you have the more you get. It implies, as suspected, that the size of a days change is liable to snow ball. Large losses encouraging more and more people to become bearish. Likewise large gains encouraging more and more people to become bullish.

This supports the "speculative" side of the market: that people trade not for long term fundamentals but try to trade in the short term and take advantage, or protect themselves, from current trends.

The question then is the distribution of bear/bull thresholds in the average human population. By which I mean if the number of people turning bearish increases with the size of the down turn there must be a distribution of thresholds beyond which people decide to sell. If there was just one threshold at say 1% then were the market ever to turn below 1% then everyone would sell. This doesn't happen.

Obviously the down turn is different from different people. People buying on that day will see a 1% drop. People who were perhaps 100% up will fall to 98% on a 1% drop. People who bought in after the 1% drop would only see a 1% drop where the market drop further to 2% down. There is a distribution of people going into the market, coming out and the existence of thresholds will need to be wrestled from them.

2Do!

Nature of Flagger/Coward Distribution

A linear function was chosen to describe the number of flaggers in a group, such that the total number of flaggers across all the groups was equal to the total number of cowards.

f(x) = a + x (n-2a)/g , where n is the total number of rabbits in each group, g is the number of groups and a is the number of flaggers in the 1st group. This integrates to ng/2 i.e. half the rabbits. The gradient of the function is given by grad=(n-2a)/g.
Using this as f(x) the expression Gc – Gf (from before) was calculated. This gives the average predator pressure experienced by flaggers relative to cowards for populations of heterogenous groups with varying numbers of flaggers and cowards as described by ‘a’.
Gf – Gc =


Substituting the expression a = (n-g*grad)/2 into the expression enables a clearer expression of heterogeneity.

Results
p=0.5, n=10, g=10

Once the gradient is steeper then 60% then flaggers experience rapidly decreasing predator pressure. This is a distribution with group one having 8 flaggers and 2 cowards, and group 10 having 2 flaggers and 8 cowards a range of {2,8}
For 50 groups (g=50) the graph has the same shape but the gradient only needs to be 12% before flaggers benefit more than cowards. The general rule is that the cut-off is proportional to 6/g.
p=0.5, n=20, g=10


For groups of large size there is little extra benefit to cowards until the groups have a larger range than {5,15}. After which there is considerable advantage to flaggers.
p=0.1, n=10, g=10

If the probability of not seeing the predator is very low (10%) there is range of distributions which benefit cowards very much. Suddenly when the range reaches {0.5,9.5} is benefits flaggers. 0.5 isn’t possible so there are no distributions which favour flaggers in small groups.
p=0.9, n=10, g=10

A simple curve where ranges {2.5,7.5} and steeper benefit flaggers. Flagging strategy is an anti-predator strategy and obviously only benefits where predators are skillful and not easily seen by individuals.
ConclusionFlagging as a strategy depends upon strong heterogeneity in flagger/coward ratios. Low dispersal of offspring i.e. children remaining in the warren will create such a heterogeneity. Sexual selection for flaggers is vulnerable to the evolution of a “slag” gene but may provide a mechanism for heterogeneity also.
Another avenue of investigation is in free markets. The local marginal strategy is always to defect and become a coward. However under certain situations strategies that benefit the group will lead to selection for groups of individuals who do not do this, i.e.e those who abandon local marginal thinking.

Co-operative genetics

On holiday while looking at rabbits was wondering how genes for particular sexual attractions spread in populations. What if there was a gene that made brave individuals attractive. Decided to look at the old area I did at college that of tail flagging in rabbits to warn of predators (assume it’s a warning signal rather than predator visual confusion). If this is in doubt then alarm calls will do as another model. Let there be two genes F and C which cause their bearer to F=flag (or give an alarm call) or C=just run away. Let there be two other genes that cause their bearer to find this behaviour attractive Lf and Lc. I’ll ignore a ‘Slag’ gene that just breeds with anything for now (for good reason since it messes this whole argument up, unless there is another gene which doesn’t like Slags etc). I assume a simple haploid genetics to make like easy.

Cowards and Braves

F = brave flagger
C= coward who saves himself
Lf= find flagger attractive
Lc=find coward attractive

These parents: flag+likes cowards x coward+likes flaggers give the following children:

FLc x CLf –> FLc,FLf,CLc,CLf (in equal proportion)

It can be seen that only 1/4 of FLc and CLf matings are like the parent and 1/4 are FLf and CLc.

FLf and CLc parents however only produce themselves.

The other combinations won’t happen since the very nature of the Lf and Lc genes is to make the bearer look to mate with only flaggers and cowards respectively. So if you are Lc you will only look for cowards to mate with, and if you are a flagger yourself only Lf will mate with you so FLc must mate with only CLf.

As a result the population of FLc and CLf both drop by 75% each generation (assuming that all individuals mate freely). If low density means that it is harder to find a mate then this will be larger.

By contrast FLf and CLc populations replace themselves each generation and get added to by the 25% of the FLc and CLf populations.

CONCLUSION: (without the Slag gene) flagging genes rapidly become associated with genes that mate with flaggers at the exclusion of cowards, and vice versa.

The Population Models

Let p=the probability that an individual does not see a predator. This is the probability the individual will be eaten in some time frame.

Take a group n numbering f flaggers and c cowards (n=f+c). The group comes under attack from an ambush predator looking for 1 individual. To succeed the predator needs only catch the prey unawares, after which it is a certain kill. The probability of being taken P is:

P = 1 / Number of unaware individuals

However the flaggers alert the group so they all need to be unaware at once. If all the flaggers are unaware (prob = p^f) then the total number of unaware individuals is f (since all the flaggers are unaware) + pc (the unaware cowards). The probability of being taken as a flagger is then:

Pf = p^f / (f + pc)

The cowards benefit from the flaggers flagging but also the probability that they are looking too or conversely the probability they are taken is p^(f+1). The probability of being taken as a coward is thus:

Pc = p^(f +1) / (f + pc)

CONCLUSION: Thus as a coward your probability of being taken is always p less than being a flagger. Flaggers because of their relative generosity will decline in number relative to cowards in a given population.

However note that Pc has a maximum value when c==n and a minimum value when c==0.

CONCLUSION: Thus having flaggers around instead of cowards is beneficial to cowards. It is better for cowards to move towards areas with higher proportions of flaggers. However as will be seen this leads to mating problems if there are genes that don’t like cowards.

Model 1

Let the population be spread out in g groups. The predation pressure on the population as a whole can be estimated by looking at the individual average, that is the sum of f*Pf for each group divided by the total number . As a continuous function we therefore need (given that f+c=n so c=n-f),

  for flaggers and

  for cowards

If f[x] is a constant f (as before) then the equations decompose to the equations before i.e. Gf = Pf and Gc = Pc

If f[x]=x i.e. it linearly increases through all the groups so that groups have increasing numbers of flaggers and let there be n groups so that flaggers range from 0 to n, then the integrals to calculate are (where g=n):

Which numerically integrated for p=1, n=10 gives

Gf = 0.1
Gc = 0.1

As expected since the average predation in any number of groups of 10 individuals if they are blind (unable to detect the predator) will be 1/10. i.e. Gf/Gc = 1. For the following probabilities where group size is n=10, Gf/Gc gives:

p=0.25   0.264687
p=0.5     0.295375
p=0.75   0.496825

That is the average predation of flaggers is around 30% that of cowards for lower probabilities and rises relatively as both groups become less vigilant. For larger groups (and a larger range of groups) the effect is ever more apparent so that with groups of size n=30 predation of flaggers is 10% that of cowards.

CONCLUSION
When the ratio of flaggers to cowards varies linearly across all the groups it remains beneficial to be a coward as an individual in any one group. However the flaggers in mostly cooperative groups do better than the cheats in mostly cheating groups so the average globally benefits the flaggers. So while cowards will locally do better than their neighbouring flaggers, globally their population will drop significantly faster.

Model 2

In all groups the rate of reduction of cowards is p less than that of flaggers. That is cowards will therefore come to dominate all static groups and if the group size is limited (as by limiting resources) then eventually flaggers will become extinct in these groups. However it is beneficial for cowards to move to areas of high flagging density.

In reality offspring, likely to carry the parents flagging or coward gene, will disperse around the parents creating pockets of high density. Infiltrating individuals may be excluded by territorial behaviour. It would be in the interests of the cowards to let flaggers into their territory, but not vice-versa.

Sexual selection may also provide a barrier to migration as described above.

2Do
Model that looks at changing rate of populations in cells (with genetics) dy/dx = ry(genetic factors) – pred(y)
Model that looks at changing rate of populations globally (with genetics)

Model that looks at changing rate of populations in a cell (with steady influx of individuals) i.e. like mandelbrot… look to see if there are critical influxes that lead to changes in the cell ratios… then we know any cell with neighb\ours that cause that level of migration will turn themselves into such a cell. i.e. if their outflux goes to the level that needed to promote them.

Examine the shape of distribution of ratios across groups. Population heterogeneity can create incongruent local versus global properties! Apply to markets where marginal action (i.e. to become a coward) is offset by global benefits of being a flagger. Relevance of markets? Conditions where “Invisible Hand of Markets” no longer operates… consider information dispersal through a population as one means to create heterogeneity.

4 Points on Anti-Capitalism

1) Anti-Capitalism doesn't exist. If someone described me as an anti-Nazi I'd attack the term because obv. they were trying to frame the discussion in Nazi terms. Anti-Nazism doesn't exist precisiely because we reject Nazism. No one supports "anti-unicorn believers" because we think there aren't any unicorns! 1st up: rejection of anti-Capitalism and all debate surrounding it (including the illegally biased news coverage). The correct thinking is: there is Capitalism AND everything else. Once the debate is allowed to start "anti-Capitalism" becomes a vast array of "other" views. Science and God-religions offer two huge subsets of "anti-Capitalism"... most "anti-Capitalists" are primarily attacking this fascism that refuses any debate whatsoever on the subject.

2) The problem with Capitalism for me is not itself, but how a society adopts it. Our society is making it the model of all human organisation. That is why scientists should be anti-Capitalist: because it is being adopted by prejudice and not research or knowledge. This is the main criticism of Capitalism. Final 2 points are why it is unsuitable.

3) Capitalism uses "exchange" in a market to value things. It has no other model of value. In a society where value is determined by exchange there can be no friendship, no family and no love. The reason is that when anyone interacts in such a society they keep an account book open of debt and credit. I help a "friend" only because I expect them to help me back. I have a child only because I think they will be useful to me. This does happen--and so does murder--but it is important it is not the only basis for human relationship. This is exacty what religions are teaching against in fact and why religions are "anti-Capitalism". "Real" wealth cannot be counted in account books they argue and the opposite behaviour of deleting account books is recommended (as the EU is being forced to discuss now ironically).

4) Who owns the wealth? This is the most famous "anti-Capitalist" issue. Mr Wheel and Mr Plough (the respective inventors of their namesakes) have brought humans literally untold riches. The human population rose on the invention of the latter alone from 1million to 100s of millions. If they somehow owned the rights to that then 1 family would literally own the world. Likewise if someone invented a single machine that could do all human labour more cheaply (a day that is approaching fast) would they really own everything, and more importantly how can an economy function when all humans are finally put out of work? It is clear to me that Capitalism isn't a complete, or even very well thought out system, all the time old problems remain to be solved... and the elite who are happy with the status quo will do everything to stop them being solved (like ever lasting light bulbs, and cancer cures, and DVD players that work longer than the warranty etc)... which is the greatest truth.

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.

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