Mesofacts: slowly changing facts

There is an area of applied mathematics that should be of interest to anyone interested in mesofacts: record progressions and extreme value theory. Record progressions are simply the series of successive records over time, for whatever is being measured. And extreme value value theory explores the probability distributions that describe the upper (and lower) end of a distribution, and are relevant for records over time.

Not much related to examining records over time has been done recently, but in the 1970's and 1980's, this was a fertile area in probability. For example, there is research on how the times between new world records changes as the population size increases (a followup paper here) as well as research into the viability of predicting future performance.

Anyone have any other favorite papers on world records they would like to share? Please feel free to mention them in the comments.

The maximum number of moves required to solve a Rubik's Cube, also known as God's Number, has been recently shown to be 20. A table of progress in this field towards this number is shown on this website, which I have graphed below.

An article from 2006 in the New Yorker by Richard Preston, entitled Tall for its Age (alas, behind a paywall) chronicles the recent discoveries of the world's tallest trees. These trees, with colorful names like the Stratosphere Giant and Helios, are all Redwoods and about 370 feet tall. The tallest is named Hyperion and is over 379 feet tall, and was only discovered in the last few years.

Chess players are often rated according to a methodology developed by Arpad Elo, which is implemented by a number of organizations, including FIDE. According to this system, the ratings of the greatest players has increased over time, making this a mesofact. However, there are many who contend that this is simply a symptom of ratings inflation, and is not necessarily due to a true increase in the skill of the players. This is discussed in detail here.

I have an article in this Sunday's Ideas section of the Boston Globe entitled Hard to find: Why it's increasingly difficult to make discoveries - and other insights from the science of science. It discusses a scientific paper of mine published recently in Scientometrics, which is the journal of the "science of science". The journal article entitled Quantifying the Ease of Scientific Discovery (also freely available on the arXiv), discusses how to think mathematically about how scientific discovery becomes more difficult over time.

Examining three different scientific areas of discovery - the number of mammalian species known, the number of minor planets (asteroids) known, and the number of chemical elements known - I found that their "ease of discovery", as quantified by using size, all have the same mathematical shape. For example, I calculated the average diameter of asteroids discovered each year, and this decreases according to a clear function (for those interested, it's an exponential decay).

Of course, the increased difficulty of discovery within a single discipline should not lead to a state of despondency, where we assume everything than can be discovered already has been. Instead this type of quantitative research can help us to understand the social and technological processes that underlie scientific discovery.

Both the Globe piece and the scientific article were a lot of fun to write, since I got to discuss scientometrics and patterns in science over hundreds of years of discovery. In addition, all the data sources I used are freely available, so you should feel free to play with the data sources.

Here's a figure from the paper, if you're interested (A shows the average size of discovered minor planets, B shows the average size of discovered mammal species, and C shows the average inverse size of discovered chemical elements):

Yesterday, June 28, 2010, marks the 12,000th day of the Voyager 2 mission. Since 1977, Voyager 2 (along with its companion Voyager 1) has been exploring the solar system and pushing the envelope of the extent of our exploration of the universe. How far these probes have gone, and how far humanity has ventured away from Earth (albeit indirectly), are intertwined mesofacts. And the current status is that Voyager 2 is 14 billion kilometers from the sun, and Voyager 1 is more than 17 billion kilometers from the sun. Of course, these are both less than two-tenths of a percent of a single light-year, meaning that we have our exploration cut out for us. In addition, the Voyager probes are not actually the farthest probes; Pioneers 10 and 11 hold that distinction. However, they are no longer operational, and so while they continue to move through space, they no longer actively explore.

An interesting side-note: I learned of this milestone courtesy of Voyager 2's Twitter feed, @Voyager2, which was described as follows:

"12,000 days since launch, & still going strong. Thank you, to all who designed me, put me together, talk to me, & keep me going to this day."

I can only imagine that this is a subtle allusion to the ancient Jewish prayer known as the Shehecheyanu, which is traditionally said to celebrate special occasions. It is translated as follows:

"Blessed are You, Lord our God, Ruler of the universe, who has granted us life, sustained us, and enabled us to reach this occasion."

For further reading about the Voyager probes, I recommend checking out Todd Sieling's wonderful paean to the Voyager mission, showing its effect on a single person.

A few weeks ago, Geoff Nicholson had an essay in the New York Times Book Review entitled The Joy of (Outdated) Facts. Nicholson writes of facts, our obsession with them, and how they change, though there is unfortunately no mention of mesofacts by name. Here is one passage, among many interesting ones:

"Of course, ideas of what’s worth knowing, and even what’s interesting, are constantly changing: The fascination with trigonometrical formulas certainly seems to have receded. But in a world where ever fewer people care about, or even understand the nature of, fiction, where readers and viewers demand facts and reality, outdated books of supposedly impartial information can be a useful reminder of just how slippery facts are — as unreliable as the most unreliable narrator."

The entire article is well worth a read.

Since 1947, the fraction of the economy that is responsible for manufacturing has remained relatively constant. Meanwhile, the fraction of the population employed by the manufacturing sector has fallen drastically. (thanks, Michael)

Wikipedia has an astonishing page entitled List of Statistically Superlative Countries. This page is a veritable treasure trove of mesofacts, from largest spinach producer (China) to most Eurovision wins (Ireland). Read this page often, both for the changing facts and to learn the extent to which countries are the 'best'.

Both the Aral Sea, bordering Kazakhstan and Uzbekistan, and the Dead Sea, bordering Israel and Jordan, are not of constant shape. Their sizes have been shrinking over the past decades. The Soviets diverted water from the Aral Sea for irrigation projects leading to the collapse in size, and the Dead Sea is shrinking due to water from the Jordan River (which feeds into Dead Sea) being diverted.

A NASA website shows the amount the Aral Sea has shrunk since 1960, focusing on the amount it has grown smaller in the past decade.

And here is an animated graphic showing the change in size of the Dead Sea from 1960 to 2007:

However, there has recently been some talk of connecting the Red Sea to the Dead Sea.

(thanks Pete for bringing this topic to my attention!)