Filling a niche
The ecological repercussions of the Australian government’s plan to eradicate
cats using a poison that doesn’t harm other species may be far-reaching and damaging
(This Week, 3 July, p 5). When a species is introduced to an area, it
can quickly take over ecological niches to the detriment of indigenous species.
But over time these effects lessen and often balance out. At that point it can
be devastating to destroy the introduced species.
In New Zealand, for instance, the government decided to destroy a large
proportion of rabbits, an introduced species, because of their growing numbers
and the incidence of the viral disease myxomatosis. They did so by dropping
poisoned carrots in affected areas. Many rabbits died while other species were
left unharmed.
But because the rabbits were no longer there to feed on the fruit that fell
from the trees, birds began feeding on it instead. This meant that many birds
began to feed on the ground, rather than in the trees. That in turn gave
bird-eating rats, another introduced species, ample opportunity to prey on these
birds, resulting in massive devastation of the indigenous bird population.
Smoke screen
Andy Coghlan describes the high levels of pollution that resulted from iron
smelting in Sheffield during the Second World War
(This Week, 3 July, p 12). As
a teenager I visited relatives in Sheffield during the war years. The smog was
unbelievable, not only because of the iron smelting, but also because of the
intentional burning of oil wastes.
I recall seeing hundreds of special burners lining the city streets, belching
forth a filthy cocktail of PM10 particles. The rationale for this was to
safeguard the city and its vital industry. Being surrounded by hills, Sheffield
forms a natural basin in which the smog settled and cleared only on very windy
days. So from the air the city was almost invisible. In fact, if my memory is
correct, Sheffield was bombed only once during the war.
Digital flop
Your assertion that the late and unlamented Digital Video Express (Divx)
failed because it was beaten to market by DVD
(This Week, 26 June, p 15) is
hogwash. As the article acknowledged, Divx is based on DVD technology, so it
couldn’t have been developed until DVD was already well established.
The reason Divx failed is because it was a wretched and ill-conceived idea.
The gadget fans鈥攖hose early adopters who would have bought into Divx
first鈥攄idn’t like the idea of buying a movie that they would never truly
own no matter how often they paid for it, couldn’t watch on demand if they
couldn’t get a phone connection to the Divx pay-to-play centre, and couldn’t
take from one player to another elsewhere in the house without buying the movie
all over again. On top of that, should the sole hardware vendor go out of
business, or the so-called standard fail鈥攁s it has鈥攖he Divx would
become useless junk.
Telltale numbers
The existence of Benford’s Law, which dictates that the number of numbers
beginning with particular digits follows a specific pattern, is fascinating
(“The power of one”, 10 July, p 26).
But I doubted that such a universal
law鈥攐ne which would affect “even the inhabitants of the Planet Zob, who
measure area in grondekis”鈥攚ould use something with logarithms in base 10.
Why, I wondered, wasn’t this like so many other laws, applicable to the natural
log to base e?
Clearly the law as framed would not work for eight-fingered Zobans, because
they would never have come across the digit 9. I think a fair hypothesis would
be that the universal Benford’s law, applicable even on Zob, has to be framed to
include however many digits you use to count.
If you have eight fingers, you are going to use the base 8 logarithm for your
accounting, rather than base 10. In other words, for organisms counting with
x digits, the proportion of numbers beginning with digit D is log base
x of (1 + 1/D).
This also suggests that in future, rather than having to analyse in full the
books of suspected fraudsters, cyber-VAT inspectors will just run their software
over the computer records of companies they are investigating鈥攚ith the
figures expressed as hexadecimal (base 16) rather than binary numbers.
Charles Arthur is absolutely right. Indeed, not only is Benford’s law base
invariant, but Theodore Hill, the mathematician mentioned in the article, proved
in 1995 that any universal law of digit distributions that is base invariant has
to take the form of Benford’s law (“Base invariance implies Benford’s law“,
Proceedings of the American Mathematical Society, vol 123, p 887)鈥擡d
Letter
I suspected that I could test the validity of Benford’s law by examining a
large set of random numbers each chosen from a random range. I reasoned that to
choose a representative random range I needed to select from a log base 10 of
ranges. This would avoid skewing towards larger collections of digits.
Thereafter, a number could be chosen from each range linearly at random. So I
sat at my UNIX terminal and typed the following single line command:
yes | sed `100000q’ | awk `BEGIN{srand();u=6*log(10)}
{printf”%en”,rand()*exp(rand()*u)}’ | cut -c1 | sort | uniq-c
This tries 100 000 numbers. The lower range limit is always 0, the upper
between 1 and 1 000 000. And it worked! Now I know why the smaller digits always
go first from the house-numbering section of my local DIY store.
Letter
Robert Matthews states that Benford’s law would not apply to numbers such as
the prices of different types of beer, which are constrained by market forces.
Considering the preponderance of 9s in modern sales and marketing strategies, I
would suggest that the law does apply, and that it confirms what we have known
all along: that these sales are frauds.
Spiral processing
Regarding Gereon Fink and John Marshall’s inconsistent findings on the
lateralisation of visual processing
(“Left brain Right brain”, 3 July, p 26), I
have a suggestion. Perhaps they could run their tests with some of the
spectacular navons鈥攊mages made up of a smaller images repeated many
times鈥� constructed during the 1960s.
Psychedelic art contains many layers of local versus global symbolism.
Watching the brain sort them out could be quite amusing and informative.
Letter
I am delighted to read that the split brain garbage has now been dumped. Of
course, I dumped it 19 years ago鈥攊n New 杏吧原创
(“Right brain, left brain”, 11 September 1980, p 790).
It’s high time you realised that I am
always right . . .
Pale imitation
If, as you suggest, the Neanderthal and the Cro-Magnon cultures coexisted in Europe for some time
(“Family secrets”, 19 June, p 42), is it not possible that
the Neanderthals were the origin of the pale skins peculiar to European branches
of modern man?
Surely it makes more sense for white skin to have evolved in caves in glacial
Europe, rather than on a journey from Africa via the Middle East? Other possible
descendants of the Cro-Magnon鈥攖he Dravidians and Andamanese of India, as
well as the Aboriginal Australians鈥攕how no signs of bleaching.
Maybe the time has come for the descendants of the first Europeans to
acknowledge the possibility that while their brains may have come from the
Cro-Magnon of Africa, their looks derive from the Neanderthal of Europe.
Show stopper
The proposal to modify music CDs to prevent them being played on a computer’s CD-ROM drive
(This Week, 10 July, p 20) is surely illegal鈥攁t least in
Britain. For the same reason that some of the early Pentium chips, which could
not do a particular simple mathematical calculation, had to be changed or
modified, a CD that will play on a music system but not on a computer is, under
the Sale of Goods Act, “not of merchantable quality”. In theory, a prosecution
could be brought for each individual CD sold which failed this simple test.