Saturday, July 29, 2006

Allergies and responsibility

Emily Brazelon in Slate misses the point a bit when she likens a case about cutting down a tree to general policies on childhood allergies. Here is the case:
Earlier this month, the city of Milford, Conn., agreed to cut down three 60-feet-high hickory trees because of a 3-year-old's nut allergy. The trees rise over the backyard and swimming pool of the child's grandmother, who helps take care of him. According to the New York Times, he once had to go to the hospital after touching a bowl of cashews. If the trees don't come out, he could die, his family told the town. Neighbors, however, are skeptical: They say the grandmother tried to have one of the trees removed before and is now using the allergy to her advantage.

Who is crazy here—the family that wants the trees felled or the residents who seem willing to put a child at risk? It's hard to tell. That's the dilemma of nut allergies. There are cases of real danger and real death. And then there's the huge circle of caution that often gets drawn around children when, rationally speaking, more modest precautions might do. If every school is already a nut-free zone, the felling of the Milford trees suggests that every block might become one, too. Is this a smart way to marshal our resources to avoid risk, even risk to children?

The issue here is not whether the town should require the trees to be cut down or not but, instead, who should bear the costs if, indeed, it is worthwhile for them to be cut down. Brazelon rightly points out that it is not certain if the risk to the child (or children) is worth the cost of getting rid of trees: not just the physical cost but cost in terms of land values.

Now if the town had no policy but the risk to the child was truely great, the grandmother could go to her neighbours and offer compensation for the loss of the trees. If her assessment of the value of that risk wasn't really high enough, then we can conclude that it probably isn't worth cutting down the trees. However, if the town mandated the trees be cut down regardless, no such assessment would be made. So we would never know.

A better policy would be to give the grandmother a right to ask for the trees to be cut down. This opens up the possibility of negotiation again and that the trees wont be cut down if the risks aren't too large. The difference between that and no requirement is simply who bears the costs of cutting down the trees should that be desired: the grandmother or the neighbours. So in terms of issues such as this, the key is to open up the possibility of fruitful negotiation rather than preclude it.

Now when it comes to policies of schools prohibiting certain types of food, it may seem that a similar issue arises. Here, we trade-off the risk to the child with parental convenience. Here is Brazelon's take on this one:

At the risk of sounding heartless and bratty, though, let me try to make the case for better-calibrated, more-moderated responses to nut allergies. Parents who ask for more accommodation than their kids really need do a disservice, I think, by making the rest of us unsure of when we need to strictly comply. It's a form of crying wolf. Or at least that's how it has felt to me on occasion. One summer, my older son Eli, then 4, got sent home from preschool with a stern note, because the granola bar I'd given him for a snack was made at a factory that processed other products that contain tree nuts. The next day I sent Eli with a plastic baggie full of cheese crackers made by Annie's, the organic pasta company. Their factory stamped out organic macaroni and crackers, I thought—no nuts.

But the father of the boy in the class with the nut allergy wasn't so sure. He asked me to take the crackers home. I'm sure this seemed like a minor concession to him. But to me, it seemed unfair and a little ridiculous. My son and his son didn't sit at the same snack table. They'd never shared food. His son's allergy had never been triggered by airborne particles, and it was no longer particularly serious. And if I couldn't give Eli his crackers, then he wouldn't have a snack. For the second day in a row. So, there was a cost, however small, for doing as asked.

I left the crackers with Eli. They provoked no allergic reaction in his preschool classmate. When I got home that night, I checked the Annie's box. There was the telltale warning: "Produced in a facility that also manufactures products containing peanuts and tree nuts." So, what's the moral of this story—that I'm inconsiderate, or a reasonable risk-taker?

Now in this situation, daily negotiations are not possible. The costs would be too high. Instead, the school needs to have a policy on the foods that can be brought in. When the school knows it has a child at risk, something it would have to manage, it sets the policy accordingly. Because children are hard to manage at a young age, it is not surprising that they might think to control the situation by restricting foodstuffs. Schools do this for so much food brought in from meats (that might get bacteria) to sweets (that might cause hyperactivity and create conflicts).

In this situation, the issue would become whether the child could go to school at all or not. And for many families they may not have the wealth to buy off the convenience costs to other parents. So, in contrast to the trees, there is little scope for an efficient deal to be struck especially on cracker level decisions.

In my mind, the way to think about schools is very simple: social risk pooling. Someone's child may have a nut allergy. Yours may have something else. For instance, they might be poorly behaved and extra teaching resources are required. For all of them, managing the issue may cause inconvenience or cost to others. But the attitude should be, if it were me with that child, would I expect the school to accomodate the issue. If the answer is 'yes' it should be supported.

[By the way, all this analysis borrows from Ronald Coase -- the negotiations part -- and John Rawls -- the put yourself in the place of others part].

Thursday, July 20, 2006

Extreme Lego

Take a look at the Top 10 Coolest Lego Machines. Suffice it to say, if your kids aren't doing this, they aren't getting the most out of your lego investments.

Saturday, July 15, 2006

Negotiated Chess Rules

Today I observed my oldest (7 year old) and her brother (the 5 year old) playing chess. They have the actual rules down but this typically leads to a quick bloodbath by the strategic (7) over the asthetic (5). Strategic play is the intended play of chess: think about how your opponent will react to your moves. Asthetic play is a different sort: move pieces to increase the likelihood that they will make interesting patterns. A good example of the former is the two knight opening move while a good example of the latter is the two knight opening move.

Following the first game, they decided to change the rules. Mr Aesthetic decided on a new layout for the two rows of starting pieces and Ms Strategic saw an opportunity and decided that a flexible starting layout was a good idea. So a new set of rules was agreed upon. All the pieces would move according to the same rules but would start differently.

Ms Strategic continued a defensive posture with pawns on the front row while Mr Aesthetic offered up a mixture led by two rooks in the centre while the King and Queen were placed at two ends on the last row surrounded by a set of pawns. The new rules lasted two moves (well actually, one) before there was a rule change as Mr Aesthetic swept across the board to remove a pawn. That move was 'reversed' when a new rule came up: the 'no taking period' (yes it was called that). This was a period of indeterminant time (actually to the observer but not to Ms Strategic who would announce when it was over) whereby they could move pieces but were not allowed to take anyone else. This resulted in lots of positioning until Ms Strategic got frustrated when Mr Aesthetic wouldn't muck up his King-Queen-Pawn configurations to allow her instant victory when the 'no taking period' finally ended.

This game took some time because Ms Strategic had to wipe out all of the Mr Aesthetic's pieces before he would budge on the protection to the King. It occurred to me through this that this new game was far closer to real warfare than the actual rules of chess. The continued negotiation of the rules through a diplomatic process that required everyone to still want to fight along with the strategic manipulation of that process led to a situation far closer to historical experience.

Anyhow the new rules lasted only one game when Mr Asthetic decided that it would look better if he could use BOTH black and white pieces in his two rows. Ms Strategic was very upset by this notion claiming it would lead to chaos because no one would know whose pieces where theirs. A good point for which Mr Aesthetic countered that the King and Queen would be a common colour and that would define the game. Negotiations broke down at that point and Professor Diplomat (me) was brought in to broker a solution.

I suggested that they take the pieces from yet another BLUE and CLEAR chess set thereby satisfying Mr Aesthetic's desires and Ms Strategic's concerns. Alas, they have taken this to mean that both sets of pieces and now a set of checkers will be on a single board. Suffice it to say they haven't got past the 'laying out period' and, as I write this post, will soon work out that no one can actually move; thus, handing Mr Aesthetic a victory in terms of his preferences.

The game of Meta-Chess is far more interesting than Chess itself. I recommend it highly as a spectator sport.

[Update: the Chess and Checker piece mixture evolved into a hybrid game where the chess pieces were laid out in the normal configuration while the checker pieces filled the remaining rows. (The other Chess set continued as another game played at the same time). First, there was a checkers game in the constrained space until one player lost all of their checkers pieces and could use chess ones to take the others' checker pieces. However, the hybrid involved no change in rules as I observed when a checker piece lept over a knight to take it! Suffice it to say, the chess pieces appear to be at a considerable disadvantage. The goal remains to get the Chess King.]

Saturday, July 8, 2006

The use of Public Holidays

Andrew Leigh argues in the Australian Financial Review that we could use some more public holidays. The argument is based on the idea that public holidays -- being common to all people -- mean that there is more chance for social interaction outside of the home. This is backed up by economic evidence suggesting that time spent on entertainment, meetings and social time rises with the number of public holidays. This leads to an 'obvious' policy conclusion:
In the Australian case, the best time for a new holiday would be in the second half of the year. For example, we might consider making Melbourne Cup Day or Remembrance Day a national holiday, commemorating Sir Henry Parkes’ Tenterfield Oration (24 October) or marking the anniversary of the Eureka Stockade (3 December).
There are alot of assumptions going into this conclusion. The first and most obvious is that the type of public holidays likely matters. If it is a religious holiday or something like ANZAC Day, then the activities spent might be social but if we did not have compulsory public holidays those undertaking those activities are likely to coordinate on them anyway. Remember, what is being called for here is compulsory public holidays. But if there is a focal point (that is a natural reason to choose to take that day of voluntarily), then it doesn't really require a coordinating device.

This suggests that the best public holidays are the more or less useless ones. In this case, the 24th October stands out. It is an excuse for social behaviour. It is not likely that large numbers would have run off to hear Parkes Oration reinactments and it is not likely that we would care if they did. Thus, the compulsory public holidays should be those that do not have a motivating activity. It is only then that we will have less religious or other divisions in our social coordinating chances. Surely, that is what we want.

As a parent, if I had to lobby for a social activity in Australia, it would be Halloween. Halloween is a great and memorable childhood activity in the US that requires coordination. You need broad neighbourhood participation. Without this, you have a bunch of kids dressed up begging for food. How to get that established in Australia is difficult but let's say we took the Henry Parkes Day and spun some tale that linked it to cross dressing and lollies. Then I think we might be in business.

Toddlers unleashed

Scott Adams in The Dilbert Blog wonders why we don't see more toddlers walking around with leashes. He writes:
Yesterday I was trudging the 47-second commute from my office to my home and passed a father taking his two-year old son for a walk. On a leash.

Yes, the man was walking his child like a dog. The leash design was ingenious. It was actually a backpack/harness arrangement featuring a puppy as the backpack, with the leash coming from the puppy’s tail area. The kid seemed delighted with the arrangement as he strained against the leash. And the father had no worries about the kid darting into traffic for at least two good reasons:

1. The kid was on a leash.
2. There was no traffic.

In fact, we were the only people on the street. So in effect, the father had his son on a leash to protect him from me. I would take offense but it probably happens more often than I realize.

My first reaction to the kid on the leash is that it was humiliating and wrong. But the kid seemed happy enough.

The whole leash thing as always struck me as something interesting. After all, we care so much about safety that it seems extraordinary that we let children walk around so freely. We restrict their movements in many more undignified ways (for instance forcing them to walk around with one hand high attached to an adult), but tethering them has always been seen as too far. Moreover, this appears to be something more or less universal across the world. There aren't countries somewhere whether childhood leashing is considered respectable.

Saturday, July 1, 2006

Subtraction before addition

Why Not? is an interesting book by Ian Ayres and Barry Nalebuff that came out a couple of years ago. It suggests some simple things people might do to be more creative. One of the most interesting suggestions is to turn things on their head. For instance, it is commonplace to see tomato sauce bottles now with the lid at the bottom. Actually, all that has been done is to flip the label. Most of us were putting these bottles upside down for years.

The message of that story is to claim that sometimes thinking about doing things in exactly the opposite way to what you do now may lead to improvements. Of course, George in Seinfeld got this idea first.

A few years ago, while trying to teach my then 3 year-old daughter some mathematics, I hopped on a similar Why Not? moment in reversal. She had always been pretty quick with numbers and could easily count to 20 and beyond. So I set about teaching her how to add. Now the way to do this is to make liberal use of fingers. This is all very well when the numbers you are adding are less than 10 but is a problem after that. Then it requires breaking up the problem; a conceptual advance that is pretty daunting for a child. Of course, you could move on to toes as my son is want to do but that involves taking off shoes.

So I thought, stuff this! How about we start with subtraction first? The idea there was that you could take any number up to ten and subtract any smaller number and still not exhaust your finger options. That dramatically opened up the possibilities and, what is more, I noticed how damn easy it was for a child. They were used to having and then not having and seeing what was left. It was a natural part of their day. When they eat, the food on the plate shrinks. When they paint, the clear bits of the canvas get smaller. Subtraction was a far more natural part of everyday life for children.

What is more, within the same session, I was able to easily move on to subtracting from numbers greater than 10. We didn't even need fingers.

I was very surprised at the results so I tried them on any child, 3 to 6, I could find and later on my son. The same thing occurred. Children had no idea how to add, could easily subtract. What is more, once they understood that comfortably, it was easier to reverse the whole thing and shown them what addition meant. Now I have nothing but my own anecdotal experience here, but it seemed to me that the speed of numeric learning was dramatically improved.

Interestingly, we, of course, have the same 'growth' order in multiplication and division. We teach the thing that requires bigger numbers first (how to multiply) before getting on to the smaller numbers one (how to divide). This is where most difficulty with learning mathematics becomes an issue. Most people have an easy time with addition and subtraction but other operations are far more difficult. The same goes for children. It takes years to really learn these even after the rote learning of times tables (and not division tables!) takes on.

So a few weeks after teaching my 3 year old daughter how to subtract and then add, I decided to move on to divide. Talk about easy! Take a group of 20 objects. If we divide it into 4 groups with the same number of objects in each, how many objects are there? No problem, 5. Do this with even numbers less than 10 and you can illustrate division by two using hands.

Now I am not claiming that she could divide in her head but she could work it out. Division is an even more natural part of a child's life than subtraction. They do it all the time when they learn social behaviour. It is all there and worked out. Not surprisingly, it is also something that they have an abstract understanding of too.

Sadly, learning division did not translate speedily into multiplication. That turns out to be a hard concept. 4 years on and we have got it but not at the same depth as other operations.

The problem with all of this is it is dramatically different from the way these things are taught at school. Students are barely allowed to try division until they have 'got' multiplication. Now maybe a proper scientific study will bear out that that order is the best way for most children. But, for the moment, I am not sure. Any teacher I have talked to about this looks at me blankly and is more willing to attribute this to the skill of my children (which is fine) than an overall problem with the way we do things.

Anyhow, there is no harm in trying this out for yourself. Try subtraction before addition and division before multiplication. I would be really interested in your observations. One day if I dump the whole economics business I may set out to examine this more scientifically. For the moment, my casual observation will have to do.