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:

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.

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! If 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.

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.

A rational agent can’t know their own probability distribution

If it did then it would be able to construct choices that differ from that distribution.

http://en.wikipedia.org/wiki/Bayesian_probability

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.

  

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.

Version 2 – Incremental

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.