Saturday, April 25, 2015

The health and diet debate heats up

A article chases up both sides after a recent anti-carb study: The BBC takes a different tack on the same anti-carb study: Also this is interesting, not least because it addresses real outcomes not risk factors:

I've changed my mind so often on these health issues that nobody should take much notice of my opinion. For what it's worth here it is.

Firstly here are some facts which seem reasonably likely to be correct:
  • People lose weight on a low carb diet, and reduce their blood sugar levels.
  • People lose weight on a low fat diet, at least if it is low in sugars and other refined carbs.
  • Statistics used to show that being overweight was bad for your health and reduced life expectancy.
  • Statistics now show that being overweight is protective and increases life span.
  • Gluten allows leakage from the gut into the blood circulation. In celiac (and maybe other gluten sensitive folk) this gets to be significant.
  • Emulsifiers may do the same.
  • When obese people have a gastric bypass operation, so the food bypasses the top 1/7 of the gut, then they almost immediately stop having high blood sugars, long before they lose any weight.
  • If you are fit and active you will live longer if you stay overweight.
  • If you are unfit and inactive you will live longer if you are overweight.
  • A very high protein diet (particularly if from mammals) is bad for your health. So you've got to eat carbs or fats or both.
  • Processed food, particularly meats, are generally bad for health.
  • A healthy diet, particularly one low in refined carbs, makes people enjoy being active more.
  • UV (direct sunlight) modifies molecules in your blood, and in some cases (at least one = bilirubin) turns them into something  your liver can deal with better.
So why did statistics previously favour not being overweight? The reason is that most fit active people don't stay overweight. Previously more than half the population were fit and active (and got out in the sun) and these tended to normal weight. Being overweight was highly correlated with inactivity which was the actual cause of the statistical bad outcomes. Now things have changed. Nearly everyone is inactive, and now the health advantages of higher weight show up directly.

We used to think that being overweight caused bad health. So it was assumed that things which lead to lower weight must improve health. All these interventions that address risk factors rather than outcomes are highly suspect, particularly medications.

Kids are rarely overweight until they become inactive. But that doesn't mean that anything that reduces their weight is good. Rather it is a wake-up call on activity levels.

We can see that some significant part of metabolic syndrome is caused by problems in the top 1/7 of the gut. So it makes sense that healthy diets are ones which can't be easily processed and require processing lower down in the gut. I suspect that this includes nearly all fats and proteins, so that is why a low carb diet addresses metabolic syndrome in the same way as a gastric bypass.

However I think it is hard to have a healthy diet unless it is mostly plant-based. Sugars and refined carbs are immediately satisfying because they get processed in that top 1/7 of the gut. So grains, if any, need to be minimally processed. I suspect that people would have a lot less trouble if all gluten, and many similar molecules, were not available for processing at the top of the gut.

TL;DR: Mostly eat vegetables/fruit/nuts/grains. For protein mostly fish and birds (and plant protein, particularly pulses). Mammal meat every 2 weeks. Get active. 15 hours sitting plus 1 hour of activity doesn't do it. Get your heart rate up a few times a day. Get a standing desk and keep moving. Get in the sun but don't get burnt.

I don't recommend my home-made standing desk, but it is cheap (card table plus small angle beams held up with nuts and held on with cable ties):

[update: I should have mentioned that there are important nutrients that you need to get. This ( mentions B6, B12 and Folate. There are others. Selenium is important: brazil nuts often have a lot, depending on where they're grown. Look for brands which specify how much selenium.]

Saturday, April 18, 2015

A simple energy calculation

From we read: "The US uses 4500 TWh of electrical power (and 10 times that amount when currently non-electric transportation and industrial power usage is counted.)". Presumably per year.
So assume a near future world with 10 billion people with average standard of living and energy use that of the current US, which has 1/3 billion people. Total energy is 4500*10*30 TWh/year, which to one significant figure is 1000000 TWh/year.
In we see:

Shale gas padWind farmSolar park
(10 wells)87 turbines,
174 MW capacity
1,520,000 panels,
380 MW capacity
Energy delivered over 25 years9.5 TWh9.5 TWh9.5 TWh
Number of tall things1 drilling rig87 turbinesNone
Height26 m100 m2.5 m
Land area occupied by hardware, foundations, or access roads2 ha36 ha308 ha
Land area of the whole facility2 ha1450 ha924 ha
Area from which the facility can be seen77 ha5200-17,000 ha924 ha
Truck movements2900-20,00078003800 (or 7600*)

So these facilities deliver 9.5/25 TWh/year. About 0.4. So we'll need 2.5 million of them. So if we take the "land area of the whole facility" to be 1000ha for wind or solar we get 2.5 billion hectares total.
Now according to google the world land area is 15 billion hectares. So no problem, right?

Monday, March 30, 2015

The Australian Test Cricket team

My pick for the Australian Test team is: Warner, Rogers, Smith, Clarke(c), Voges, Maxwell, Nevill(wk), Johnson, Harris, Starc, Hazlewood. The list of players unlucky to miss out is huge:
  • Fawad Ahmed. A Test-quality wicket-taking wrist spinner. Australia loves to have one of those.
  • Lyon. The best attacking orthodox spinner Australia has ever produced.
  • Agar. Much improved and a very good bat as well.
  • Lots of competitors for Hazlewood in the 4th fast bowler spot: Cummins, Pattinson (if ever fit), Siddle and more.
  • Watson. The best paid cricketer in the world. Could possibly replace Rogers as opener.
  • Faulkner. A genius with bat and ball. How can I leave him out.
  • Mitch Marsh. Unfairly deprived of the opportunity to play 1st class cricket recently.
  • Shaun Marsh. One of the best batsmen in the world on his day, but so inconsistent.
  • Every other first class wicketkeeper.
Maxwell and Smith (and Clarke and Warner) allow us the luxury of 4 fast bowlers. This is a team that nobody will want to bat against. The tail bats well down to number 11.

[update: Can't believe they've left Maxwell out of the squad. I've been watching Cricket for over 50 years and I rate him as one of the best players of all time.

IF they're going to put the long form of the game on a pedestal, and select people based on 1st class cricket performance.
THEN they have to allow players to say "I'm only available for short form international cricket when there are no 1st class matches I could play in."

It may be that they want Maxwell to play a bit in India (in the A side) and maybe play for a county, rather than touring but not playing much which won't suit his temperament.

In my initial version of this post I put in a different (retired) Peter instead of Peter Nevill. A "senior moment".]

Saturday, March 28, 2015

A peek into the quantum world

In, John Baez discusses the amount of information in a gram of water. In Newton's classical world this doesn't make sense. To describe even the position of just one molecule of the water would take an infinite number of decimal places, and hence an infinite number of bits. But when we get into the quantum world things actually get simpler, and Baez can write:
we see a gram of water holds

4.05 × 10^24 bits

of information.  And amazingly, this is something we know quite precisely!  I've rounded off the numbers, but we could actually work it out to more decimal places if we wanted.
[10^24 means a 1 with 24 zeroes following.]

This makes me feel that I understand a bit more about what the quantum mechanical view of reality is [though obviously nobody should take my opinion too seriously]. Any time you have a very large finite system obeying relatively simple rules then it's going to look like some infinite thing which is philosophically more complicated, but likely to be more tractable mathematically. For example, if you plot the distribution of the result of 10^24 coin tosses then it is going to look indistinguishable from a continuous bell shaped curve (a gaussian distribution).

Will this viewpoint help me the next time I try to understand quantum mechanics a bit? We'll see.

Thursday, February 26, 2015

In-marriage Out-marriage oscillation

Previously (Group Selection of Humans) I convinced myself that humanity finds a balance between in-breeding and out-breeding. I now think that the balance is more like an oscillation, as balances often are. Here’s the story:
There was a discussion about ISIS that seemed to assume that male talk was the full story ( I tried to suggest more real-world reasons for the vigorous opposition to Western values:
An interesting aspect of the IS area is that a lot of marriages are to cousins, preserving family power and status. The great threat to family status is female education and power from merit. I suspect that it would be useful to understand female opinion in the area as well as listening to the cacophony of males talking about arcane knowledge.
Which everyone ignored, except for David Friedman who responded:
"An interesting aspect of the IS area is that a lot of marriages are to cousins"
Any more than elsewhere in the Islamic world?  I've seen figures for Iran, where that is also true, and it's clear in Islamic literature that cousin marriages are favored. Consider, for instance, the farmer who understands the speech of animals in an early story in the 1001 nights, where the fact that his wife is his cousin is clearly seen as a plus.
I thanked him for this:
Thanks, that perhaps explains why pushback against modernity is common in the Moslem world. It is an interesting contrast to Christianity where rules against incest were expanded to cousins for a time (unless you paid the Pope). …
Whether it had much to do with indulgences, there is no doubt that Europe freed itself from the inbreeding which, I’ve argued, was crucial in the development and maintenance of human social behaviour. But human behaviour had recently (on an evolutionary timescale) changed to feature larger culture-based groups (see What is Culture for). At times the inbred extended family groups continued within the larger groups, as we see in the Middle East now. In Europe now we see the opposite, with random marriages meaning there is no genetically coherent groups within the culture based groups. This has immediate advantages in strengthening the culture-based group, as we see in the very coherent European nation states that conquered much of the world in the 19th Century, but there are long term costs.
It changes the evolutionary incentives. Opposition to non-cooperating individuals has a cost. And now there is no direct advantage to an individual’s genes to take those actions. With that opposition weakened, the proportion of people not cooperating will rise. Indeed it will continue to rise until that culture-based group starts to malfunction. It might get to the point of losing in struggles with groups which include those extended family subgroups. But perhaps it doesn’t get that far. Perhaps as society gets dysfunctional, with lots of bad guys causing trouble, then there is incentive for families to try to hang together via cousin marriages.
So we might reasonably expect an oscillation between inbreeding with extended family groups, and outbreeding with individual loyalty going directly to the culture-based group.

I believe that cousin marriages and extended families creates a very conservative environment. In particular they have to suppress individual freedom to prevent random marriages. Freedom and individual initiative has been the most powerful advantage of the West in recent times, and very likely for other successful culture-based groups in the past. But the disadvantage will eventually catch up with us, if we let it.

Monday, February 23, 2015

What is Culture For?

[I've said this stuff a number of times, but there is no obvious URL to point to, so here's a summary]
Seventy thousand years ago humans were very different. Superficially it wasn't that different from more modern hunter gatherers. People lived in groups (quite in-bred promoting cooperation). They made tools. They talked about the weather and the food options and who was doing what with whom. But look closer and there is little to call art or music, and nothing changes over thousands of years.
Then culture started and around 30,000 years ago it swept the world. Most obviously there is art, and there is invention and change in tools and clothing and housing. What I mean by "culture" is things that groups adopt to distinguish themselves from other groups. Groups love to distinguish themselves:
  • "We are the group that dresses like this"
  • "We are the group that speaks and understands this language and these idioms"
  • "We are the group that makes this sort of pottery"
  • "We are the group that plays and enjoys this sort of music"
And these things require skills that take years. Foreigners can't just walk in and blend in.
Culture takes up a lot of brain power and a lot of time and effort. Why was it so successful in displacing the simple lifestyles that preceded it?
Intergroup conflict is a characteristic of our species, and indeed of related species such as chimpanzees. For a graphic discussion of this, see Jared Diamond's book The World Until Yesterday. Before Culture, groups were limited to ones where everyone knew everyone else. Culture allowed us to create groups that were defined by common culture. These could be much larger.
So that's it. Culture allowed us to create big groups that beat up the small groups of pre-cultural humans. At first the pre-cultural females would be absorbed by the victors, diluting the culture genes and slowing things down. But by 30000 years ago the dilution process became insignificant and the takeover of cultural genes went very rapidly to completion.
We love cultures generally and our own particularly. So this is not quite the story we would want to hear. But we need to understand how we got here if we are going to make good decisions about where to go.

Tuesday, February 10, 2015

My mum versus the experts

All 5 of my parents' granddaughters are now married (and what an inspiring quintet (quintuple?) of young women they are). Thinking about my mother I thought I'd mention some of her battles with the (self-appointed, pseudo-) experts.

1. My mum insisted that butter was healthier than margarine, against the "experts" put up by the processed food industry. This has recently been proved right. She was also strong on the importance of other particular foods: brains (from sheep) and liver. Her ideas on these things come down from her ancestors. It is shocking how easily we abandon traditional knowledge these days. Expertise used against traditional knowledge needs a high standard of proof.

2. My mum was a great believer in the health benefits of sunshine. This has been proved right, though the anti-sun propaganda continues to push the damaging zero-sun policy. I should say that my reading leads me to believe that this is not just about vitamin D. The body uses UV to break down toxic organic molecules in the blood. This is extra important for people (like me) whose liver is not working 100%. An example of this, that is not in dispute, is bilirubin that causes jaundiced babies.

3. My mum was a strong believer in fresh air in houses. We are faced with a strong push from the Green movement for housing to be built tight as a drum and heated and cooled with heat pumps. I think my mum will be proved right again. Even if you are not in a Radon area (are you sure?), sealed houses get various sorts of toxic build up. All my life I worked in air-conditioned offices and I'm very pleased to have escaped that.

[update: The point I forgot to make is this: The expert brand is badly tarnished. This needs to be addressed by creating an environment where: (a) There is an open vigorous investigation of facts that are relevant to public policy and people's lives; (b) This needs to include nailing not only false claims, but also identifying those who are trying to deliberately mislead (this has to be seen to be impartial); (c) Identifying the real experts who know the facts and the relevant mathematics.]

Wednesday, December 17, 2014

The Importance of Negative Results

We respect the people who are given the job of dealing with hostage sieges, such as the recent tragedy in Sydney. They have to make tough and quick decisions. We now need to spend some time looking at the process, so that we can do it as well as possible next time.

When we think of lone nut cases with weapons we remember the bad outcomes. The lone gunman at Port Arthur is the one that comes to Australian minds. However that wasn't a hostage situation. The lunatic then was shooting people at a distance that he had not met. Most single person hostage taking involves explosives and the threat of a suicide bombing, or it involves a male with family members. So this was an unusual case.

When a team of hostage takers are involved then the whole thing is more practical. They can take turns sleeping. They are likely to have a plan and specific objectives. They can provide moral support to each other, plus the implied threat of violently punishing any backslider. The whole thing might even be relatively sane, without being less bad for that.

Since there isn't much time when the action starts, we need to have a small number of people in the country who know a lot about these various situations and how they have panned out in the past. The little point that I would like to get through is this:

The people who end up making decisions need to know about good, as well as bad, outcomes from around the world. The good outcomes don't stick in the mind. The good outcomes aren't as well reported. It is an easy mistake to overemphasize the possibility of bad outcomes, and then take overly aggressive action. I'm not saying that is what happened in this case, though my instinct is that someone sane enough to be given parole would find it difficult to shoot people he had been dealing with for many hours.

The importance of negative results has been recognized in medicine where all trials must be registered before they start. This stops drug companies from running multiple trials and only reporting when benefit is shown.

Wednesday, November 5, 2014

Multivector momentum

[update 2014-12-10: This post is definitely not quite right. I'm trying to understand units and torsors better. Also, how then to fit heat/temperature better in with the others. Hopefully I'll write about these things one day, but fixing this post seems likely to remain beyond me.]

I trained as a Mathematician, and I try at times to understand some developments in modern Mathematics. Mostly I do this by following John Baez who writes beautifully so that you imagine that you understand it. I’m only vaguely following his current interest in networks, but I loved this diagram (from for an unrelated reason:

\dot q
\dot p
Mechanics: translation
Mechanics: rotation
angular velocity
angular momentum
flux linkage
pressure momentum
Thermal Physics
entropy flow
temperature momentum
molar flow
chemical momentum
chemical potential
The first row (after the headings) is the familiar fact that a moving body has momentum which keeps it moving in a straight line at constant speed. To change that requires effort: the application of a force. We are equally familiar in life with the fact that a spinning body (such as a top, or the Earth) has angular momentum which keeps it spinning, and you have to put in effort to stop it.
In the 4th line Dr Baez is thinking of liquids in pipes, but I am more interested in unconstrained gases. If you imagine an explosion then that has pressure momentum which will keep it expanding forever. It requires effort to stop the expansion and that effort would be pressure.
I also want another row which might be the same as Dr Baez’s 6th line. At any rate the momentum in this case is heat. Things will keep the same amount of heat unless some effort (heating/cooling) is applied to change it. This might seem different to the others, since the others are about movement, but actually heat is just internal movements within the matter. The temperature of a gas is proportional to the kinetic energy per molecule.
Now I need to take a detour before I can put these together.


A vector is something with magnitude and direction. Speed is just a number, but velocity (and momentum and force) are vectors because they also include the direction. We imagine vectors as arrows in space with the length representing the magnitude of the vector. You can slide them around: they don’t start at a particular place. Our vectors are three dimensional: every vector can be made of a bit of x, a bit of y and a bit of z.
You can combine two vectors to make a bivector. This is called the exterior product. To imagine this we place the 2nd vector so that it starts where the first finishes. This makes a little parallelogram floating in space, and the area is the magnitude of the bivector. However the bivector is not really a parallelogram: it can be any shape in that plane with that area. And there is a natural way of adding bivectors and they are also 3 dimensional: every bivector can be made of a bit of xy, a bit of yz and a bit of zx.
The exterior product of 3 vectors is a trivector. We can visualize this as a bit of volume with the 3 vectors at edges, but once again it is just the amount of volume that counts not the shape. Trivectors are just one dimensional, since each is just a multiple of the 1x1x1 xyz volume element.
There are nice diagrams of all these at Wikipedia’s Geometric Algebra page:
It turns out to often be a useful idea to combine our 3 dimensions of vectors, 3 of bivectors, 1 of trivector plus 1 more for scalars (scalars are just numbers). This makes an 8 dimensional space of multivectors. These are mostly particularly useful when combined with a way to multiply them, but we won’t get to that here.

Momentum types

Ordinary momentum is a vector. It has magnitude and direction.
Angular momentum is best seen as a bivector. The area of the bivector is the magnitude, and its orientation (perpendicular to the axis of rotation) determines the rotational geometry.
Since pressure acts in all directions at once, it is natural to see it as a trivector.
Finally we have heat which is intrinsic to the matter and not involved in directions. It is just a scalar value.
It is easy to combine these together into a single multivector value. The question is how meaningful that is.
One aspect is this: Are there other mechanical momentums that this leaves out? I conjecture that for an infinitesimal amount of matter this is all there is.
Speaking of infinitesimal amounts of matter: It is tempting to think that a small amount of matter can’t have much angular momentum. But actually the smaller matter is, the faster it is able to rotate. Even electrons have significant spin (though the mechanicalness of that might be in some doubt). I wonder if the study of fluid mechanics takes adequate account of small rapidly spinning vortices?


It seems cute, but that is not a justification. It does suggest two lines of investigation:
One is to study fluid mechanics in full generality starting with infinitesimal amounts of matter having these 4 types of momentum. The hope will be that some of the research on Clifford Analysis will turn out to be useful.
The other is to use this in computer simulations of oceans, atmosphere or other fluid situations. These are typically done by dividing the matter to be simulated into little cuboids. The cuboids have some physical characteristics, and the value at the next step is determined from the current value plus the values in neighboring cuboids (plus other forcings, i.e. effort, that may be specified). The hypothesis is that this 8 dimensional value, across 4 types of momentum, is the optimal choice for the value to be stored in each cuboid.

Sunday, November 2, 2014

Saving Test Cricket

It is nice to have the 3 levels of Cricket, corresponding roughly to sprint, middle distance and marathon events in Athletics. However Test Cricket seems to mostly survive on cultural links to the past. I don't have a problem with the duration of the game or the shortage of action, but there are problems which need to be, and can be, fixed:
  • Timeless Tests had serious practical problems that were exposed in the last years of the 1930s. The solution of limiting Tests to 5 days and allowing draws has been worse (though it has produced the occasional exciting moment).
  • Games need a mercy rule so that they don't go longer than necessary when they get one-sided. Teams batting on and on when they already have more than enough runs is bad for players and spectators.
  • The deterioration of wickets through the course of a match gives an excessive advantage to the team winning the toss.
Luckily I have a simple solution to all 3 problems:

The solution is to have the two teams' innings in parallel (as near as practicable). Every 30 overs the teams switch over who is batting. Except that, when one team is behind on runs and has lost more wickets then they are given 2 consecutive batting segments. Here's why this solves all the problems above:
  • The deterioration of the wicket is no longer a problem because it affects both sides equally. In fact it is a good thing because:
  • Wickets can be made to start well but not last longer than 4 days so that wickets fall rapidly from the 5th day onwards. This stops matches going too long, but avoids the need for a time limit. It also encourages teams to score quickly while the wicket is good.
  • This is a perfect mercy rule. The winning team would rarely do more than 30 overs batting beyond what is needed to win the match.
[30 overs is chosen to fit with the natural breaks in the game.]

Saturday, November 1, 2014

group selection of humans

Our species is social, and we have a lot of adaptations designed to support cooperation. The obvious explanation is group selection: groups with those adaptations were more successful than those without. The trouble is that it is very hard for group selection to succeed. Cheating genes, which take advantage of the cooperation of others without reciprocating, seem certain to overwhelm the honest players.

This confused me for a long time, until I read Jared Diamond's "The World Until Yesterday". The key point is the large amount of inbreeding within primitive villages. Most people marry cousins, so that all the people in the village are very closely related. There is some gene transfer with neighbouring villages, but little beyond that.

Group inbreeding potentially creates a situation similar to social insects, where every individual is closely related to everyone else, and in particular to the reproducing females. This allows the group to function as the unit of evolution so that group selection can operate and cooperation evolves. So it seems obvious that this must be the normal (i.e. pre-civilization) human situation.

Of course inbreeding can be taken too far, and we see that it is natural for high status individuals to have the privilege of partnering outside the group. So how much inbreeding is there? Let me guess that a balance is maintained. Groups with too much inbreeding lose from the direct genetic cost. Group with too little inbreeding lose by failing to maintain group selection and being invaded by cheating genes.

This is non-expert speculation. However it is an important area to understand because it has obvious implications for the future of humanity. We have left our traditional lifestyle behind so quickly that the evolutionary effects have not had time to reveal themselves.

[update: "can't"=>"can". A senior moment.]

[update: It isn't that some groups have cooperation and some don't. What evolves to support groups is an inspect to suppress non-cooperation within the group. We hate freeloaders and cheats. But we need groups to be have common genes from inbreeding for us to get value out of those "suppression of non-cooperation" genes. Otherwise we gain by avoiding the costs of that suppression effort. This becomes significant when we move to culture-based groups: see What is Culture for?]

Friday, October 24, 2014

Security versus Privacy

The difference between security and privacy is not that hard. If others can see my bank transactions then I lack privacy. If others can take money out of my bank account then I lack security. However important people think privacy is, they must admit that security is much more important ... Right?

In fact we see an endless stream of postings that seem to be completely muddled about the difference between security and privacy. There are good reasons for that:
  • Security is about the protection of our assets, including life and health. Privacy is the particular asset that is most immediately compromised by security breaches in the information industry
  • Often we use privacy to protect our security. This is most obvious in the way we protect passwords and PINs. Anonymity, an extreme form of privacy, is used as a security mechanism by those doing things, good or bad, that others would, rightly or wrongly, seek to punish.
  • An important information security mechanism is public key cryptography, where keys come in pairs: the public key that is made available to all; and the private key that the owner holds and does not share. In this case the word "private" is to distinguish it from "secret": A secret, and in particular a secret key, is something that is shared.
Still it is hard to understand the confusion, because we see that privacy is something that most people seem prepared to give up very lightly. Most of us enter "customer relationship management" schemes for very little reward, put details of our life on social media, tolerate privacy invading indignities at airports.

I ask people pushing for protection of privacy to address actual privacy issues. If they are actually interested in privacy as an enabler of security then they need to include some evaluation of how effective it is in that regard. When governments lacked the ability to penetrate the anonymity of protesters then it was effective. Would it still be effective if governments said that they would not use their new capabilities to penetrate people's anonymity? Pardon my doubts.

Most particularly I want people to acknowledge that the greatest protection of our security against the government, and against the oligarchs, is transparency and accountability. Transparency is anti-privacy, and that is what we need. People advocating for individual privacy need to be explicit about why it is not going to weaken transparency. People who are not advocating for transparency are not the good guys, and their privacy concerns can be dismissed.

Friday, October 17, 2014

Holes in Networks

Thinking about holes is often the best way to understand what is going on.
The first example we usually encounter is in electricity. Suppose we have a solid with each atom holding its electrons in place. If we add an extra electron it is easy to imagine it flowing towards a positive charge (though that might be an oversimplification). But suppose there is a missing electron. The neighbour that is closest to a nearby negative charge will be the one that tends to move into the hole. This moves the hole closer to the negative charge. And so we imagine a sequence of electrons moving into the hole, so that the hole moves towards the negative charge. Well this is a simplification (since electrons are indistinguishable), and it is not the best simplification. The best simplification for human understanding is that the hole is a positive entity which flows towards the negative charge. And in fact the hole behaves for most purposes very similarly to a positively charged electron.
A rather recent example is in Computer Science. It is that you can do a formal differentiation of a type constructor and get a new type which is a one hole context for the original type. It is, in some sense, the original type but with a hole in one slot that can be filled. Dan Piponi has blogged about this (e.g. The idea might be due to Connor McBride, but I expect that it is known earlier in related Mathematics. Anyway it seems like a very general way of traversing data structures.
It is interesting to think about economics. Consider a job vacancy. That is a hole in some sense. Indeed filling the vacancy might generate a new vacancy somewhere else, and so on, much like the electron example above. This applies to other resources, not just labour. So the need for a resource is like a hole. It increases the price which, in the short term, removes the resource from those who could barely afford it.
Does this have anything to do with differentiation? I don't know, but it is interesting to consider Steve Keene's idea: that a major driver/indicator for the economy is not the rate of change debt, but the derivative thereof. In other words the second derivative of the amount of debt.
I'm also trying to understand cohesion, as in Lawvere's article reproduced at I don't pretend to understand it, but it is interesting the way it talks about distinguishability. This applies to resources too. People have special skills, and the economy works best when people can all be employed maximizing their skills. But we know that when things get bad then people end up in more generic jobs, like driving taxis and labouring, where individuals are less distinguishable. And something similar may apply to other resources where varied and sophisticated use of resources happens more when the economy is functioning well. We can perhaps also consider the case of ecology, where productive ecosystems have high diversity, but weedy general purpose species take over when things are bad.
All this is highly speculative, but why stop there. Here is an analogy between the economy and phases of matter.
  • When things are going well, the economy is like a liquid. In a liquid there is high interaction between the molecules, but also high mobility of molecules. We see a similar thing in the interactivity and mobility of labour and capital in the most successful economies.
  • Feudal systems are like a solid. Labour and capital are stuck in a fixed relationship to each other. This promotes specialization but without mobility the specialization is often non-optimal. Feudal societies were the home of the craft guilds.
  • Anarchic economies, when there is no effective rule of law, have plenty of mobility but too little interaction. This is like a gas.
And, as we know, you need enough pressure to get a liquid. Otherwise things sublimate directly from solid to gas. I leave the economic interpretation of that to the reader.
Anyway, getting back to subject, I think anyone thinking about the dynamic behaviour of networks should think about holes in the network. And I suspect that has something to do with differentiation (in some funny sense) and/or cohesion.

Wednesday, August 13, 2014

safer team ball games

Even the safest ball games involve players running to the same ball. The result is head clashes and boot-head interactions that cause concussions. It would be safer if the access to the ball changed sides in some way. I had an idea.

The idea came from a game I play with one of my grandsons. You just need a ball that bounces on the available ground, and some marked small enclosed area between the players. The players take turns batting the ball with an open palm, and they have to bounce the ball exactly once in the enclosed area or lose the point.

So I thought of players bouncing the ball to their team mates. Call the team in possession the attackers, and the other team the defenders. Until the ball bounces only the defenders are allowed to try to get the ball, and after the second bounce only the defenders are allowed to get the ball. After the first bounce only the attackers are allowed to get the ball, and of course naturally the attackers will bounce the ball deliberately to their team mates. This is perhaps still to easy for the attackers and maybe the attackers have to get the ball after the bounce and before the top of the trajectory after that first bounce.

The point is that the players on opposing sides aren't going for the ball at the same time. It leaves a lot of room for adjustment of other rules to make an interesting game. I would suggest that the player is only allowed to take possession of the ball and then throw it if he is stationary (i.e. no foot comes down between first touching the ball and throwing it). When moving you can only bat the ball with an open hand. A score might involve bouncing the ball to a team mate in the end zone.

Saturday, July 26, 2014

Bridge bidding arithmetic

[I don't suppose any non-Bridge players will read this. But just in case I'll give some info in square brackets at times. In Bridge players partner in pairs who have to cooperate in bidding. The (pseudo-)auction involves bids by the four players (partners opposite) in order 1c,1d,1h,1s,1nt,2c,...7nt. One way to cooperate is a relay where one player always makes the cheapest bid and the other describes their hand. The hand has 13 cards. We say a hand is 3541 if it has 3 spades, 5 hearts, 4 diamonds and 1 club. "Game" is 4h or 4s or 5c or 5d (or 3nt) and scores a lot extra. Slam (12 or 13 tricks out of 13) scores even more.]

After a relay the asker needs to set the suit below game [to allow slam investigation]. We need to do this below 4h, so it can be done starting at 3s, for example: 4d sets spades; 4c sets hearts; 3s sets a minor and responder always bids 3nt after which 4c sets clubs and 4d sets diamonds.

So lets assume for the moment that we are only showing distributions. How many different distributions can each bid now show:

3h: 1
3d: 1
3c: 1
2nt: 2 (asker then bids 3c and responder can bid 3d or 3h with the 2 distributions)
2s: 3 (asker then bids 2nt and responder can bid 3c or 3d or 3h with the 3 distributions)
2h: 5 (asker bids 2s, responder bids 2nt with 2, 3c/3d/3h with others)
2d: 8 (...)
2c: 13 (...)

Which continues to be the fibonacci numbers (each number the sum of the previous 2): 21,34,55,...

So how many distributions are there:

Though the cumulative total goes up linearly and fibonacci goes up exponentially, still we don't have a lot of room to cover low probability distributions. And certainly we can't afford to waste much space.

One can consider what order to show distributions in. A simple scheme is: (a) show more balanced hands first (lower number of distribution points [doubleton=1, singleton=2, void=3]); (b) within that constraint show hands with more major cards (i.e. in decreasing number of hearts+spades); (c) within that constraint show in decreasing heart length.

The reason for showing more balanced hands first is that this makes slam less likely, so asker can often quickly bid game after a lower bid, without relaying it out and telling the defenders more than necessary.

One of the objectives of bidding is to find useful trump fits. [It is desirable to have 8 trumps. Hands without an 8 card major (heart/spade) fit are usually best in 3nt if possible.] Relaying wastes space compared to having both partners contributing. The question of how to best use both partners is a difficult problem. A simple approximation/guess is to use binary search. Here's how that works:

Taking a suit at a time in some algorithmically defined order the bidder cuts the length of that suit in half and bids one step with the higher (or lower) range and otherwise goes up a level and repeats.

Suppose you are playing "Romex" and a 1NT opening is 20+ points [ace=4,k=3,q=2,j=1]. One way to play the responses follows. Note that 1 step is towards the middle, bypass shows more extreme.

At any time by either player: 3s/4c/4d set the suit, as described above.
2c: 0-4 points. Higher bids forcing to game.
2d: 0-3H
2h: 4-7H 0-3S -- beyond this we further breakdown the majors
2s: 4-5H 4-7S
2nt: 6-7H 4-5S
3c: 6H 6-7S
3d: 7H 6S 0C 0D made it with a bid to spare

That worked well because narrowing the range in the majors also narrowed the range in the minors. But in other auctions we can find all 8 card major fits but the minors don' get narrowed down (as much). For example here are continuations after 1n-2s:
4c/4d: setting major with 4, otherwise deny 4
2n: 2-3S (i.e. matching the top half of responders 4-7)
3c: 3H 0-1S (ie hitting top of openers 4-5H range)
3d: 0-2H 1S (hearts eliminated)
3h: 0-2H 0S 4-5C 4-7D -- With 11-13 minor cards can be 47 56 65 or 74.
and a few more.

Given the fibonacci connection it might be better to split unevenly with approximately 38% in 1 step and 62% beyond (1:1.62 = 0.62:1 is the golden ration and consecutive fibonacci numbers tend towards that ratio). But this is not nearly enough and low probability distributions have to be lumped together to make it work when starting at 2d. Realistically one also needs to start lower or start with a restriction on the range of distributions. And indeed that is commonly the case for auctions starting lower than 1nt.