## Friday 21 December 2012

### Life expectancy in Middle-Earth: elves and mortality tables

 If Uruk hai drove buses the war of the ring would have been short.
A scary thought: I have an a priori chance of one in a thousand of dropping dead within next time this year (qx) in New Zealand, which is far more likely than winning the kiwi lotto (on a lotto day, 1:4M). Life is unfair, eh?
Luckily, I am not doing anything dangerous nor have any underlying conditions hence the a priori —although, I have not bought a lotto ticket either.
If I were in my nineties the chances change to a one in three or four per year, so the above figure is really low really. The reason is obvious, namely deterioration due to old age.
80% of the probability for young folk to die is due to external causes, which means accidents, homicide, suicide or war. For the elder folk it is due to diseases such as cancer. Boys do much more stupid stuff than girls, therefore for a woman of my age, the chances drop to one in three thousand.
The life expectancy is around 67 years in developed countries, but what would it be if one did not age?

Agerasia is the mythical state where one does not grow old. It is different from immortality as it does not include invulnerability: the probability of external causes still applies. As this probability does not change with age, age of death would follow a geometric distribution (and not a Gompertz–Makeham curve —thanks, Wikipedia!—) and the mean will consequently be 1/p. This means that on average a kiwi male would live 1,300 years, whereas a female 5,500 years.

In fantasy and science fiction, long-lived or agerasic humans and humanoids often appear, but those figures do not match the above…

In The Lord of the Rings, the dwarves had a life expectancy of 250 years or so the web informs me because they age slower than men. The elves do not grow old and lived about 1,000 years —Galadriel (Kate Blanchett) was probably one of the oldest and was a bit over 5,000 years. Middle Earth would just slightly more dangerous than New Zealand, but not by much. (In (ir)reality, elves are hardier than men, so the comparison is slightly unfair.) Possibly unsurprisingly, the US, on the other hand, is slightly more dangerous than Middle Earth.

In Iain M. Banks's Culture novels the folk of the Culture are said to live on average 400 years. The figure is so low because they get utterly bored after a while and kick the bucket, however one chap lived for 10,000 years, but he was rather bonkers.

In the bible, the patriarchs before the great flood lives for a long time. Their age of death are given which is really handy, but there are only ten of them and one, Enoch, did not technically die. Despite the small sample size, they lived on average 912 years, but the numbers are curious as they all died between 900 and 1,000 which is statistically impossible both under a geometric and a Gompertz distribution. The explanation that they get a "millenium crisis" at 900 does not fit as it is written they die of super-old age (which hits all of a sudden). Given that only Abel dies of external causes (1 in 10), it could be deduced that antediluvian Israel was much safer than New Zealand, Middle Earth or the US, but whatever rabbi wrote down the numbers wasn't well versed with statistics, so the bias is too strong for any conclusions.

Sources: Wikipedia, NZ life tables, some bible website, Iain Bank's Hydrogen Sonata and several unutterably nerdy LotR sites…

## Tuesday 16 October 2012

### A map of Britain through a kaleidoscope

Captain Cook and chums may have gone where no white man had gone before, but, despite the romantic nobility of setting forth into the unknown, creativity in naming was not a job prerequisite.
This sentiment is perfectly told in a Mitchell and Webb sketch where a captain calls an bewilderingly new land in Australia after dreary southern Wales.
It does have curious upsides: I proudly told people from Portsmouth, New Hampshire in New England, that I came from Portsmouth, Hampshire in England, which amused me —it bemused them who had never realised the existence of a place without "New" slapped in front of it.
I am perpetually fascinated by the shuffled order that bares little resemblance to the original one. In New Zealand Windsor (in the South Island) is nowhere close to the river Thames (in the North Island), whereas Birkenhead (Liverpudlian suburb) is next to Devonport (Plymouthian suburb) in Auckland.
This raises the question whether on average towns and cities in an English-speaking new world country are geographically more spread out than their British namesakes.
After normalisation that is: the difference in size would bias this figure —after all the concept of "closeness" is seriously warped in new worlders.
On a gut instinct, I would used a simple arithmetic difference, so the final figure would be the number of British kilometers towns are more or less spread out on average, (as opposed to a ratio and geometric mean).
If new world towns were randomly distributed, the difference would not amount to much, but towns are not randomly distributed. The Aussie outback is truly empty and the Otago and Southland regions in New Zealand are one step short of being gàidhealtachd. My guess is that this figure would put British towns as more spread out than their newer namesakes if normalised.
Furthermore, many towns bear local names, such as the sublimely named Wooloomooloo, whereas other are missing: using least square regression the true namesakes of these missing towns could be found, although I have feeling the correspondence would be unidirectional.
However, getting the data for this inane quandary would be more hassle than it is worth, but it would be cool. One day…

## Tuesday 4 September 2012

### Homologues and synonyms

All creatures great and small evolve, but evolution is not limited to the biological realm: languages evolve too and in a similar way.
My interest in languages stems from their ability to evolve with many similarities to enzyme evolution (and in light of not being able to spill the beans on my own research, I seem to post here a lot about words —And this is another!)
The technical words in linguistics differ from those in biology and I have yet to find an enlightening paper on the coevolution of synonyms and the parallels between language and genomes.

In enzymology, protein function and structure are not not always linked. Proteins with different functions can have similar structures having evolved from the same ancestral gene (functionally-divergent homologues) and proteins with different structures can perform the same function (functionally-convergent analogues).
In a language, words can have similar meanings, yet have different origins (synonyms) and words from the same origin can have different meanings.

New genes enter an organism via gene duplication, horizontal gene transfer or gene birth. Similarly, new words enter a language by duplication, loanwords (words of foreign origin) or onomatopoeiae.

English is a really great language for two reasons: it is my mother-tongue and it is a hybrid.
Regarding the latter reason, over a third of the words in the English dictionary were acquired from French due to the Norman invasion of 1066. The grammar and basic vocabulary remained that of Old English, whereas the advanced vocabulary was that of Old French.
A parallel to this can be drawn with the weird and wonderful bacterium Thermotoga maritima, 24% of whose genome is of archaeal origin: the replication and expression machinery is bacterial, but several metabolic routes are archaeal.

A loanword is a foreign word that is adopted in a language thanks to its real or percieved utility, whereas a horizontal gene transfer is an aquisition of a foreign gene in a genome thanks to its fitness benefits. The original spelling of loanwords are gradually lost in favour of a more compatible spelling and similarly the codon and amino acid compositions of trasferred genes also gradually change to match that of the new genome.

Often synomyms of different origins coexist, in English for a while the Old-Norse–originating window (vinauga, wind+eye), the Old-English–originating eagþyrl (eye+hole) and the Old-French–originating fenestre were coexisting, until one won. When French entered into the English language many synonyms died, but many survived in a figurative meaning, for example, enthrall litterally means to enslave, but nowadays it is used figurately, ie. capuring one's attention.
With genes the pressure to remove genes with identical function (be they paralogues, xenologues or analogues) depends on the selective pressure and in Eukaryotes they can coexist for some time.
Some words adopt alternative spellings, which can dissapear or gain different functions, such as the pairs yet and get, passed and past, and especial and special. Gene duplication does the same. In the IAD model of gene divergence, the new function comes before the amplification.

English, French and several other languages use the Latin alphabet to write words down. However, the phonetics of Latin lacks several sounds present in these and work-arounds are done. The letter h is used as a modified in English to make wh, th and ch sounds and vowel combinations allow extra vowel sounds. Old English used to be written with Anglo-saxon runes and then, with Christianity, switched over to the Latin one, bringing with it two heavily used runic letters absent in the Latin alphabet (þ and ƿ). However, as most typesetting letters were produced in France the letters died out. Despite the obvious simplicity they endow, new letters are very rarely added.
The work-around the lack of letters results in coding problems: the th group in Bath, Chatham Islands and Thailand differ, as the former is the fricative, the second is a word fusion (the H is not a modifier) and the latter is a plosive (a “violent” T). The only way to know is to know the exceptions or guess from the etymology, which can be misleading in thyme and Thames.
In protein several non-standard residues can be found. None of these use a recoded codon by itself, but require special sequences or post-transcriptional modifications, so the system differs slightly in that new letters (codons) cannot be added, but is similar in its workarounds.

Many differences exist, however.
Languages have grammar and generally authoritative bodies acting independantly of the evolution of the language (French academy).
Many suffices and prefices are highly constructive, a modularity that is hard to find in genes.
Enzymes have promiscuous function, minor non-physiological functions that can lead to new main activities: a property that is different in words. Words have multiple definitions and some are often confused. The word brothel used to mean prostitute, but it was confused with the word bordel and the meaning of the latter was bestowed on the former. Biannual traditionally means two-yearly, but its continual misuse as semestral means that the word has two discordant definitions, annulling its functionality. Genes have layers of regulation, whereas words don't. However, the metaphor could be stretch to equate grammar to regulation, but that may be wholly in the handwaving realm…