Behind Bolt

Today’s 16-yr-old age group world record holder would have won a bronze medal in the 1980 100m Olympics.

Here’s a graph from the New York Times showing how far other Olympic medal winners would be behind Usain Bolt at the finish line of the 100m:

Usain Bolt Compared to Other 100m Runners

Usain Bolt could run the 100m dash in 9.44s, given the right legal conditions.

The Guardian -v- Addison Lee

I was wondering why the London-based taxi firm, Addison Lee, had so many bad reviews all of a sudden on its iPhone app and so did a little googling. This Guardian article explains part of the controversy*, which concerns a quote by the company’s chairman:

“There has, as we all know, been a tremendous upsurge in cycling … These cyclists are throwing themselves onto some of the most congested spaces in the world … the influx of beginner cyclists is going to lead to an overall increase in accidents involving cyclists.

“The rest of us occupying this road space have had to undergo extensive training.

“It is time for us to say to cyclists, ‘You want to join our gang, get trained….”

The Guardian felt differently however, using as evidence the fact that motorists are responsible for up to 75% of collisions involving cyclists. Their source was an earlier Guardian article which contained this:

The data, which was analysed by the Transport Research Laboratory (TRL) …found that police attributed responsibility for collisions to … the driver solely in about 60%-75% of all cases, [with] riders solely at fault 17%-25% of the time … CTC said the report showed that the government needed to focus more on driver behaviour …”We believe this report strongly supports our view that the biggest problem for cyclists is bad driving.”

I don’t agree that the data supports that the view that the government should concentrate on driers [though this may be true]. The statistics reported relate to the probability that party x caused an accident given that an accident occurred. It can often be useful to analyse something with extreme numbers, so let’s do that.

Imagine there are 1,000,000 motorists, just 4 cyclists, and 3 collisions. Two of the collisions are the fault of the driver, and one is down to the cyclist. So 66% of accidents are caused by motorists, but this ignores the fact that there are relatively more drivers than cyclists (ok, a lot more given the numbers we picked). The bigger picture is that in this version of London a mere 1 in 500,000 motorists cause accidents, as opposed to a massive 1 in 4 cyclists.**

A related stat I remember: you have the same chance of dying on a 200-mile motorbike ride in the UK as you do of getting killed whilst serving for a single day in the British army in Afghanistan (a year or so ago).

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* The actual source of bad reviews seems more likely to be by black cab drivers not taking kindly to their unique privilege of being able to use bus lanes being challenged – a challenge which I think has some merit.

**When I first heard about Monty and his 3 doors I didn’t guess to change door, so happy to receive a challenge on this way of looking at the stats…

Earth to reach boiling point in 400 years

As an ex-physicist who realises later in life that he’d probably rather have studied economics, I’d like to paraphrase from an interesting article by Tom Murphy. It uses fundamental physics to argue that economic growth cannot continue indefinitely, albeit under the assumption that increases in GDP require an increased use of energy*:

US energy consumption has increased by about 3% per year for several centuries.This is partly due to increases in population, but per-capita energy use itself has grown also — our energy lives today are far richer than those of our great-great-grandparents a century ago.

So even if population stabilizes, it’s fair to say we are accustomed to per-capita energy growth.

The Earth has only one mechanism for releasing heat to space, and that’s via infrared radiation. It’s well understood. If we use more energy (it must all end up as heat energy) then more must be radiated away, and the surface temperature of the planet will increase.

This graph, which presumes a constant 2.3% energy increase per year, plots the Earth’s surface temperature over time:

Graph of earth temperature over time at constant energy growth

The upshot is that at a 2.3% growth rate, the Earth would reach boiling temperature in about 400 years. This statement is independent of technology. Even if we don’t have a name for the energy source yet, as long as it obeys the laws of thermodynamics, we cook ourselves with perpetual energy increase. Thermodynamic limits impose a cap to energy growth due to the process of radiating the spent energy away.

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*Under a model in which GDP is fixed, with conditions of stable energy, stable population, and steady-state economy, then if we accumulate knowledge, improve the quality of life, and thus create an unambiguously more desirable world this is a form of economic growth, but one which more normally falls under the title of “development” rather than “growth”.

Let there be light

I’ve come across this a few times over the years, and been meaning to post it the next time I saw the numbers somewhere. And today I have, here:

In 1800, a candle providing one hour’s light cost six hours’ work. In the 1880s, the same light from a kerosene lamp took 15 minutes’ work to pay for. In 1950, it was eight seconds. Today, it’s half a second. In these terms, we are 43,200 times better off than in 1800.

The 1800 number I think is too high (I reckon you can go and find some wood in less than 6 hrs, or buy some for an amount smaller than 6 hrs of labour). Order of magnitude correct though.

I also think it takes less than half a second, by the way, today, plugging in average salary and electricity kw/h numbers for the UK.

But the thrust of the point is clear, we are massively better off than generations before because we have gotten more efficient at producing things. Four of the basic human needs, food, clothing, fuel, and housing, are now far cheaper in terms of the average wage.

And given it’s Easter, remember, stars died so that you could live.

Putting the clocks forward caused 1,000 heart attacks

This article from Sweden (hat tip Åsa) describes some research by the Karolinska Institute analysing hospital records from which they calculate that over the two weeks from putting the clocks forward, there is typically an excess of 30 Swedes dying from heart attacks. Conversely, in the Autumn, there are 10 fewer heart attacks in the period following the clocks going back.

Scaling that up, this gives a rough back-of-the-envelope calculation for 1,000 excess fatal heart attacks across the EU27 each year as a direct result of the stresses caused by getting up an hour earlier.

Flying: weigh more, pay more?

I saw an article earlier discussing whether people who weigh more should pay more to fly. (It reminds me of one of Tim Harford’s ‘Dear Economist articles’ on how to split a taxi fare on a trip home after a night out when a group of friends are going different distances).

The author states that:

Friends with whom I discuss this proposal often say that many obese people cannot help being overweight – they just have a different metabolism from the rest of us. But the point of a surcharge for extra weight is not to punish a sin, whether it is levied on baggage or on bodies. It is a way of recouping from you the true cost of flying you to your destination, rather than imposing it on your fellow passenger.

But I think he may be in danger of missing the woods for the trees. It’s true that the cost of flying is directly proportional to the weight carried, but almost all of that weight is the plane itself: a passenger on a A380 at maximum takeoff weight is about 0.01% of the total. Differences in passengers would run at an order of magnitude less. If you did want to charge according to weight, then the fixed cost of moving the plane itself (from which all passengers derive the same aerodynamic benefit) should presumably be shared equally amongst everyone, and then the smallest of deltas added on for individual weights.

Indeed, the data point given in the article is that carrying an extra 1kg from London to Sydney and back again on an A380 costs an additional… answer at the bottom, under the fold.

I typically fly a few times per week, and my answer to friends who ask what I think about the environmental consequences of this is that at the margin, I don’t think I make any difference. If I didn’t fly, I would be significantly financially poorer, yet the environment in no measurable way any better off. Tens of billions of humans will be responsible for dangerous climate change should it occur (it’s from accumulated excess CO2 in the atmosphere, so you need to add up the contributions of everyone from 1850ish, up to say 2050ish) and I’m going to be an infinitesimal portion of it. Tragedy of the commons, yes. (And it’s only looking at one side of the equation anyway, think about all the benefits accruing to other people from the consulting project I’m working on…hmmm.)

People sometimes take issue about me considering myself to be the marginal passenger, rather than an average one, which is a reasonable point, not withstanding the point above regarding the relative weight of the passenger to the plane. Of course, at some point the lose of one more passenger could cause the  airline to drop the route, and I could [not] be that passenger. I read an article a few years back that suggested that whilst the scenario can play out like this in the US, in Europe typically Airline A might keep operating unprofitable routes in order to tie up take-off and landing slots so that competitors B,C, and D are unable to use the slots to compete on the route/timing that is super profitable for A.

And anyway, wouldn’t the plane not just be deployed on another route? If you want to reduce the contribution to global warming from air travel then you need to stop planes moving, not passengers flying on them. Therefore reduce slots, rather than tax passengers more. I guess that would raise governments less revenue though, all things equal.

And, if you’ve read this far, the cost of carrying an extra 1kg from London to Sydney and back again on an A380 is: Read more of this post

Missing women are not where you think

Typically there are more male births than females, an imbalance which evens itself out by the time a handful of testosterone-fuelled adolescent males have gotten themselves into sticky situations. In some parts of the world, however, there are substantially more men than women – notably in India and China, with tens of millions of ‘missing women.’ This is often put down to selective abortions/infanticide, but the data do not entirely support this theory.

Sources: Review of Economic Studies (2010) 77, 1262–1300, Missing Women: Age and Disease (pdf link); My analysis.

Around half the missing women in both countries are down to the mortality rate from mundane things such as cardiovascular disease being much higher amongst women than in the west (where fewer women than men die from such things). Over half the excess deaths occur within the adult population.

In China, circa 40% of the missing women are down to selective abortions and first year deaths, but this is not the case in India, where the largest cause of excess death is “injuries,” accounting for some 0.25m excess deaths per year, mostly occurring between the ages of 15 to 29.

Related Post: Increased chances of dying if you don’t get on well with your colleagues

Maths question: If a country were to implement a policy so that families had to stop having children once they had a boy, but could have as many daughters as they like until then, what would the male-female ratio be? Answer under the fold.

Read more of this post

The age of reason

Could you imagine getting either of these questions wrong today?

The source presentation is here and the key takeaways are to start estate planning early, and to strongly consider converting capital and assets into annuities that will secure an automatic income to live on, thus avoiding the need to make complex financial decisions at a time when cognitive decline has already set in.

Your friends are more popular than you

Scott Feld’s clever 1991 paper, why your friends have more friends than you do,  shows that if individuals compare themselves with their friends, it is likely that most of them will feel relatively inadequate.

This is rooted in mathematics, and is because you are more likely to be friends with those who have many friends than with people who have few friends.  At the limit, if someone is friends with everyone, then they are friends with you, (and more popular than you); People with just 1 friend are probably not your friend (though they are –  hopefully! – less popular than you. But they’re not showing up in your data). Mathematically, the mean number of friends of friends is greater than the mean number of friends of individuals.

But not only are you less popular than your friends, the ones you do have aren’t really paying attention. This guy decided to regularly alter his Facebook profile so it appeared to be his birthday 3 times in one month (his real birthday was actually 6 months earlier). He got 119 birthday wishes on the first occasion, reducing to 71 on the 3rd fake birthday 3 weeks later. Here’s a graph I made:

Graph of number of facebook birthday messages received

Dunbar’s number is often touted in connection with numbers of Facebook friends, with a figure of 150, but it’s not really applicable. I have more than that, and most of my friends have more than me I’ve noticed (but that’s ok, see above!). His research was into physical group sizes, in particular groups that are highly incentivized to stay together (e.g., a subsistence village, a military troop, a cartload of chimpanzees). He ran a regression between the average group size to the brain sizes of different primates and obtained a forecast of 148 for humans.

It’s fair to say that one’s collection of Facebook friends is not a group that is incentivized to stay together physically, and as the 3-birthdays-a-month guy concludes:

It’s one thing to remember your friend’s birthday because you took him out a decade ago for his drunken 21stbirthday debauch. It’s much lamer to “remember” your friend’s birthday because Facebook told you to. A significant number of Facebookers clearly use the service without sentiment, attempting to build social capital—undeserved social capital—with birthday greetings that they haven’t thought about based on birthday memories of you that they don’t actually have.

And yet my three-birthday July was not completely demoralizing. An encouraging number of my friends—many of them my actual friends—were so socially alert that they cottoned on to my manipulation of the Facebook birthday system.

Daily Mail or the daily espresso in the morning?

An article today on the BBC regarding research into coffee consumption and depression led me to look up what the Daily Mail had published. The BBC headlined with “Coffee may prevent depression”, whereas the Daily Mail opened with “Coffee is good for you“.

The BBC at least mentioned that the 50,000 study participants were all US female nurses and linked to the research article, though neither revealed that the mean age of those involved was 63. The Daily Mail also adds in a bit of science which is just plain wrong, “…caffeine works like antidepressant pills by stopping the production of certain hormones such as serotonin”.

Both give the figure that those who drink between 3 cups per day were 15% less likely to suffer depression without giving the absolute risk difference (there were only 2607 cases of depression total over the ten years in the study.) A rough, back-of-the-envelope calculation gives “Out of 10,000 quite old women, half of which drink coffee, there will be 27 cases of depression amongst the non-drinkers this year and only 24 within the coffee-drinking group.” I guess that’s why I don’t write headlines.

The BBC article mentions other factors in the study, and how the initial headline statistic might come down once they are controlled for. The Daily Mail does not. Neither article considers whether this small difference is casual or correlative (coffee drinkers perhaps being less depressed because the reason they drink coffee in the first place is because they have lots of friends to meet up with at Starbucks).

courtesy of xkcd.com