Thursday, May 14, 2015

CANZUK to CANZEWSI

The plan (http://grampsgrumps.blogspot.com.au/2015/05/the-canzuk-solution.html) is to solve a lot of problems at once:
  • Keep Scotland in the fold by making a better fold;
  • Get the UK out of the EU to allow both to move forward separately, because it is increasingly clear that they can't move forward together;
  • Allow a group of nations that are culturally aligned to come together to build something that is more than the sum of its parts;
  • It would be really nice to bring Ireland into the fold as well. Unification is the obvious carrot. That could be ugly, but so might other options that I've thought of.
  • Address Australia's anxiety about being a minnow in a tough local area where we are not well liked.
Previously I picked the CANZUK acronym (and later found that others had done the same). However in my mind the idea is to replace the UK with this new federation, with the nations each having complete home rule for domestic matters. So I like the CANZEWSI acronym better. There might be a better arrangement of letters, but remember to keep "NZ" together.

It is a bit hard to see why Canada would join, but it will be a bit strange without them. Somehow I feel that emotionally they will want to join if the other 6(7) ask them. One carrot would be to put the capital there: maybe Halifax. Another might be support in establishing an Arctic presence and opening up the NW passage.

The widely spread Federation would have good reason to reestablish our ancestors' strong involvement with shipping. The world needs a revolution in shipping to significantly reduce the carbon emissions. Nuclear powered ships are the only plausible solution. The next generation of nuclear power generation will be ideal since it fails safe and is very hard to adapt for weapons. Nuclear powered vessels can produce the energy needed to act as ice breakers over extended periods of time.

The people who had the idea before me are The United Commonwealth Society. There are a couple of reasons why it is probably best not to link the plan to the British Commonwealth.
  • It suggests that other poorer parts of the Commonwealth might be included at some stage. This will not go down well with voters and explicit denials won't get through to all of them.
  • It will probably be best if the chosen name avoids identifying one location (i.e. Britain) over the other parts. Of course British heritage and English language are core unifying factors, but it is hard to get that in the name without annoying some folk unnecessarily.

The importance of proofs

For at least 2 thousand years mathematicians have been constructing proofs, and everyone else has been saying "that is not important to me, I'm only interested in algorithms for real world problems". Now two things are happening: proofs are important; computer software can help us check them and even generate them.

Bug hunting can be a fun intellectual exercise. Here's a nice story if you like that sort of thing: http://arstechnica.com/information-technology/2015/05/the-discovery-of-apache-zookeepers-poison-packet/. What it illustrates is the ubiquity of software bugs. We already knew that because of all the security bugs that hackers (good and bad) love to find.

What we want is that software is proved to be correct to the greatest extent possible. One thing we explicitly don't want is perfection, which is unattainable. The weakness of perfect systems is one of the key discoveries of 20th century mathematics. What we want is to know the axioms that we are assuming, and the things that we expect to be true which we don't yet have a proof for.

So what do we do about assumptions that we don't have a proof for? Use Science. Experiment. In other words: test. Try to disprove it. Testing is expensive and error-prone. The reason for proving as much as possible is exactly so that we know what needs to be tested and to reduce that to as little as possible.

So who is going to build these software development systems incorporating proof technology? We can't trust government research to do it, because governments everywhere are addicted to using software bugs as a vector for surveillance and even for acts of war. It will need to be done by the independent open source community. Doing this will be the 21st century equivalent of defending freedom by bearing arms in a well regulated militia.

Monday, May 11, 2015

We shouldn't always do what we are optimized for

Here's a mistake I made a few years ago. The question I wanted to answer was "How do you decide how much UV you should get?". Now it turns out that your skin colour is correlated with the Autumn UV levels where your ancestors come from. We are optimized for sunlight levels where our genes come from. So I thought that that level of sunlight is what will be best for us.

It was a particularly dumb case to get wrong. The English may be designed to survive a UV-free dull grey winter. But that doesn't mean that it is optimal for them to experience that. It actually seems extremely likely that, however pigmentless your skin, it is a good idea to get some extra UV in some way during winter, or at least take vitamin D supplements. Extremely likely but not certain. Maybe our genes have developed some trick that depends on that break in UV exposure to work correctly.

This error is related to the logic error called Modus Tollens, and humans seem particularly prone to errors of this general type. And we can see why. If there is absolutely no other factor that you can think of then it is a reasonable starting point to assume that what we are optimized for is (arguing backwards) what is optimal for us. Still, as we see, we can nearly always think of other factors.

A case where this style of argument is being used is the Paleo Diet. Maybe we are optimized for a paleo diet. That doesn't mean we can't improve on it. It does mean that we shouldn't reject aspects of it too quickly.

Sunday, May 10, 2015

How to integrate political parties into the electoral process

Traditionally in Australia, political parties were invisible in the electoral process. Suppose you were voting for 5 senators for your state. All you see on the ballot paper is the names of individuals. The voter numbers the squares, and the magic of single-transferable-vote means that you get proportional representation. So maybe the winning party gets 3 senators and the rival party gets 2. But as far as the electoral process was concerned it was just electing 5 individuals.

This beautiful system was difficult for the voters, so the rules were changed. Now political parties are registered and their names appear beside the individuals, or at the top of a list of individuals. I think this is the way it is in other countries. The problem is that it is no longer clear whether we are voting for people or parties. What should happen when an elected member of parliament decides to leave the party which they had claimed to represent? What if the member was expelled from the party?

The answer is that the voters have to be given some reasonable level of control. This can't extend to reconsulting the voters, which is almost impossible for multi-member electorates. Nor may it depend on the political parties having any rational behaviour or even continuing existence. I have a plan.

The idea is that the ballot paper will show a mixture of individuals and parties. Voters can vote for one or the other or in some systems (such as STV) a combination. More detail on this below. The important thing is: what happens when a party wins, rather than an individual.

When a party registers as a candidate for an election it would provide a list of individuals who will be the custodians of that seat should the party win it. There should also be an individual nominated who will be the person to initially hold the seat.

Now suppose the party wins the seat and their representative is installed. At a later time the nominated custodians can send replacement votes to an appropriate electoral authority. If, during the first half of any month, more than half of the nominated custodians request that the elected representative be replaced with some specific willing person, then that nominee will become the new holder of that seat starting from the beginning of the following month. Additionally 2/3 of the custodians can vote to replace some other custodian in the list.

A nice thing about this is that, for seats held by parties there is no need to make any special arrangements should the sitting member become unable or unwilling to continue.

This can work with any electoral system. For multi-member STV electorates, the political party candidate will only appear once on the ballot paper. It can translate into multiple winners if, after preference distribution, it collects multiple quotas. Also parties can endorse individuals to stand in the same election as well, to gather the votes of those who want a known individual who can't be replaced. However this would be problematic in first past the post systems because it would split the vote.

Friday, May 8, 2015

The CANZUK Solution

Three of Britain's prior colonies are substantially populated by people of British descent: Canada, Australia and New Zealand. 150 years ago it was obvious that these colonies were so far away that they needed to become independent. Then 60 years ago it seemed that Britain was close to Europe and needed to find its future there. But now communication technology (particularly the Internet) and air travel have made the world a very small place.
The UK is very dysfunctional, not knowing if it is one country or several. The result of the UK election suggests that the Union is not long for this world. The huge population imbalance between England and the other nations in the union is a significant factor in making the Scots uncomfortable.
Well I have an idea that might solve the UK's problems, and some of Australia's and hopefully some others I haven't thought of. The plan is:
To create a political Union of the current UK nations, plus Canada, Australia and New Zealand.
The Union will have the following features:
  • The separate nations will retain their identity for sporting and many other purposes.
  • The central government will handle foreign policy and defence.
  • There will be a single currency and a central bank with full power.
  • The central government will collect the bulk of the taxes and redistribute wealth to provide balanced service delivery, as happens in all well functioning unions.
  • However national and subnational units will deliver most government services.
This is the way successful unions work, and not the way the EU works. It is possible because all the proposed constituents are about equal in per capita wealth.
I believe this plan will have various benefits:
  • Scotland will be happy to stay in a union in which England has less than half the population.
  • The British people will not be uncomfortable to return to being part of a world-wide entity.
  • Australia will get a nuclear deterrent, and generally beefed up defense. This means we won’t have to suck up to America all the time and go on all their stupid wars.
  • The UK will get help in paying for their nuclear capabilities.
  • One country, with historically good financial regulation, on which the sun never sets (almost), is a natural to dominate the world financial industry.
  • Australia (and NZ) get an operating nuclear industry in case we need to stop burning coal (which we do).
  • I think that all the participating nations will be more comfortable with this union than the various regional groups which they are currently involved in. (Except Quebec will likely be grumpy).

[Update: I did a google for "CANZUK" and found that this is not a new idea. An obvious name, since all the parts have retained the British monarchy, is the "Federated Kingdom of ..." It is a delicate balancing act but it is most likely to work if the individual countries (with England, Scotland and Wales separate) are regarded as independent, so that the FK (and the old UK/GB) doesn't have any sporting teams.]


Saturday, April 25, 2015

The health and diet debate heats up

A news.com.au article chases up both sides after a recent anti-carb study: http://www.news.com.au/lifestyle/health/whats-the-real-secret-to-weight-loss/story-fneuzkvr-1227316009826. The BBC takes a different tack on the same anti-carb study: http://www.bbc.com/news/health-32417699. Also this is interesting, not least because it addresses real outcomes not risk factors: http://www.npr.org/blogs/thesalt/2015/04/11/398325030/eating-to-break-100-longevity-diet-tips-from-the-blue-zones.

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 (http://www.express.co.uk/life-style/health/385884/Supplements-halt-Alzheimer-s-groundbreaking-dementia-prevention-treatment) 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 http://nextbigfuture.com/2015/04/elon-musk-battery-singularity-1000.html 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 http://withouthotair.blogspot.com.au/2014/08/shale-gas-in-perspective.html 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
(chemical)(electric)(electric)
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 https://plus.google.com/117663015413546257905/posts/B16McQB6Vn2, 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 (https://plus.google.com/u/0/117663015413546257905/posts/5DfjTXF5agm). 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 http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/) for an unrelated reason:

displacement:
q
flow:
\dot q
momentum:
p
effort:
\dot p
Mechanics: translation
position
velocity
momentum
force
Mechanics: rotation
angle
angular velocity
angular momentum
torque
Electronics
charge
current
flux linkage
voltage
Hydraulics
volume
flow
pressure momentum
pressure
Thermal Physics
entropy
entropy flow
temperature momentum
temperature
Chemistry
moles
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.

Multivectors

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: http://en.wikipedia.org/wiki/Geometric_algebra.
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?

Implications

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?]