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.

If you’re not paying for it…

A quote I saw somewhere recently (sorry, I don’t have the link now):

If you’re not paying for something, you’re not the customer; you’re the product being sold.

This is partly why I don’t read free Metro-type newspapers when I come across one. More thoughts on whether you should spend time reading/watching the news here.

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

I, Pencil

I, Pencil“, written by Leonard E. Read some 50 years ago, has been described as an essay which “many first-time readers never see the world quite the same again” after reading. It takes just a few minutes to read, and here is a flavour:

I am a lead pencil—the ordinary wooden pencil familiar to all boys and girls and adults who can read and write.

Simple? Yet, not a single person on the face of this earth knows how to make me … millions of human beings have had a hand in my creation, no one of whom even knows more than a very few of the others.

It’s a simple story implying that economies cannot be centrally planned, yet as Milton Friedman wrote:

I know of no other piece of literature that so succinctly, persuasively, and effectively illustrates the meaning of both Adam Smith’s invisible hand—the possibility of cooperation without coercion—and Friedrich Hayek’s emphasis on the importance of dispersed knowledge and the role of the price system in communicating information that “will make the individuals do the desirable things without anyone having to tell them what to do.”


And a random but related note on the urban legend that America spent millions of dollars designing a space pen that would work in a zero gravity vacuum,  whereas the Russians used a pencil:

Alas, for all its appeal and plausibility, this is not true.  Initially, astronauts and cosmonauts were both equipped with pencils, but there were problems: if a piece of lead broke off, for example, it could float into someone’s eye or nose.  A pen was needed, one that would defy gravity, write in extreme heat or cold, and be leak proof: blobs of ink floating around the cabin would be more perilous than a stray pencil lead.  A long-time pen maker named Paul C. Fisher patented the “space pen” in 1965 (which he had developed at the cost of a million dollars, at the request of but not under the auspices of NASA.)  NASA bought four hundred of them at $6 each, and, after a couple of years of testing, the pens were put into space


You couldn’t make it up

One method that can sometimes be applied to a set of numbers to see if they are genuine or made up is Benford’s Law. I came across it some years ago, and Tim Harford mentioned it this weekend in relation to the data the Greek government supplied for their submission to join the eurozone:

In the late 1990s, eurozone wannabes squeezed and stretched to meet the criteria for accession, including low inflation and government deficits, and moderate levels of debt. The criteria were somewhat irksome, especially for an economy such as Greece, but nevertheless the Greeks seemed to comply…Eventually, it became clear that the Greek numbers did not quite add up.

The law applies to sets of numbers (e.g., lengths of rivers in a country, line items in a company’s cost accounts) that don’t follow any particular statistical distribution, and ideally span several orders of magnitude (i.e., from 5km to 5,000km, or £0.50 to £500,000). It presumes also that the sample you take has no selection effects (see here for a recent catchy BBC headline regarding the London riots that I’m fairly sure contains some stunning selection bias).

Specifically, Benford’s Law has something to say about how many times the digits 1 to 9 should be the leading digit of the numbers in your set. So, items costing £4.00, £412.99, and £4,999.00 all start with the digit 4, and you’d expect around 10% of your set to start with a 4.

That doesn’t seem so remarkable, with there being just 9 leading digits to pick from, of course you’d expect each to appear around 10% of the time. But in fact no, the lower the digit, the more likely you should see it. So, numbers in your set should begin with a 1 around 30% of the time, down to 10% for a 4, and with 9’s only showing up 5% of the time. Here is chart I lifted from Wikipedia, regarding the population of the world’s countries. The red bar is the data, and the black dots are what Benford’s law predicts:

Source: Wikipedia (here is a thought about the number of wikipedia articles from an earlier post)

Using ideas like this to investigate sets of numbers reminds me of a project, at my first employer, from many years ago. A bank had participated in some collaboration with another consultancy, whereby many banks submitted their trade data (number of trades, fees charged, etc). The consultant then calculated some statistics for each bank, such as average cost per trade, and shared them anonymously back with all the participants. That should have been the end of it, except for that the consultant had left more information in his spreadsheet than intended, as data was given to many decimal places, albeit formatted to just show one decimal place. One of the banks came to my company with that, and asked what could be done.

Now, if you’ve got an average cost per trade of £2.08375638201 you can write a VBA programme to automate the process of cycling through all possibilities to back calculate and see which two numbers (an integer which is the number of trades, divided by the total revenue derived as shown in one of the participant’s annual reports and of the format £xxxxx.xx) would have got to that answer. Cute.

Other Posts on Maths/Distributions:

Why your friends are more popular than you

Selection effects and the London riots

God and maths tests

What do people who lose their jobs do with their time?

One number in particular in this study of how American households spend their time caught my eye. It’s an estimate of how the time that would have been spent in work (market hours) is reallocated between housework, home improvements, etc (non-market work), childcare, leisure, etc. when people lose their jobs.

…less than 1% of the foregone market work hours are allocated to job search

That seems too low to me.

The rest of the breakdown is more plausible, and includes:

  • 51% of foregone market work hours are allocated to leisure (including 20% to sleep, 12% to television watching)
  • 30% of foregone market work hours are allocated to non-market work
  • 12% goes towards time investments in their own health care, their own education, and civic activities
  • 6% is absorbed as childcare

Here are how the 168 hours in a week are spent on average:

More motivation

Following on from yesterday’s post I came across this related article on bonus payments.

The payments were up to $50 (AUD) and made to members of sales and sports teams.

While neither sales nor sports teams improved when people were given money to spend on themselves, Norton and his colleagues found vast improvements for those who engaged in prosocial spending.  While they were purchasing a gift for a teammate, they also became more interested in their teammate and were happier to help them further in multiple other ways.




Motivation to go

An article on Pret a Manger on how to motivate low paid staff. Their staff turnover is around 60% per year, compared to an industry average of 200%. Most of their techniques appear to be on rewarding the group rather than individuals.

Some excerpts:

New hires are sent to a Pret a Manger shop for a six-hour day, and then the employees there vote whether to keep them or not. Ninety percent of prospects get a thumbs-up. Those who are voted out are sent home with £35, no hard feelings.

Pret also sends mystery shoppers to every shop each week who give employee-specific feedback. (”Bill didn’t smile at the till,” for instance.) If a mystery shopper scores a shop as “outstanding” — 86 percent of stores usually qualify — all of the employees get a £1-per-hour bonus, based on a week’s pay.

Every quarter, the top 10 percent of stores, as ranked by mystery-shopper scores, receive about £30 per employee for a party.

When employees are promoted or pass training milestones, they receive at least £50 in vouchers, a payment that Pret calls a “shooting star.” But instead of keeping the bonus, the employees must give the money to colleagues, people who have helped them along the way.


World War III insurance premium of €1,000 a year

I came across this quote recently combining physics and economics, nice:

There is no politician who will ignore the laws of physics when building a bridge. But there is a tendency in politics in every country to suppose that the laws of economics are flexible and can be adjusted to political necessity

Quite timely given the events in Europe.

The Treaty(ies) of Rome, signed in 1957, established the EEC.

In a rush to get the ratification process completed, the signing ceremony was scheduled before the agreement was reached:

They signed a bundle of blank pages. The first title existed in 4 languages, and also the protocol at the end. Nobody looked at what was in between – Pierre Pescatore

By 1968 a Customs Union of these founding 6 members – Benelux, France, [West] Germany, Italy – was fully in place.

The overall resultant uplift in GDP 5 years later, apportioned to being from the extra free trade created amongst these 6 contiguous states, was… 0.15% (Balassa, 1975). Small wonder that European integration has been described as being more about political integration, rather than economic integration.

Yet all the while there is a remedy…it is to re-create the European family, or as much of it as we can, and to provide it with a structure under which it can dwell in peace, in safety and in freedom. We must build a kind of United States of Europe – Winston Churchill, 1946

Today, the 27 member states each contribute roughly 1% of their GDP, which is then redistributed around Europe in the form of subsidies, projects, etc. The net benefit, per person per country, in Euros, has Luxembourg – the richest country by far – doing very well, thank you very much:

Net per capita benefit from EU budget


In fairness, these are not easy calculations to do, and it gets trickier for smaller countries where the beneficiary of a grant can be an MNC, with a HQ that happens to be in that country. I’ve seen a figure closer to €2k for Luxembourg in another source.