Number of the Month

February   2005

When it was really hot

Ardent number watcher Dennis Ambler found this account of the summer of 1540. No doubt the believers gathering in Exeter this month will make much of the summer of 2003, ignoring, or course, the dramatic and frequently fatal winter of the same year across the Northern Hemisphere, as recorded in part on these pages. In these days of Orwellian rewriting of history, the Mediaeval warm period has been swept away with one wave of a hockey stick: so they must have imagined it.

Intellectual Interlude

Number Watch has come under some criticism for not paying due respect to the academic way of life, allegedly because of its unsavoury obsession with numbers. In order to correct this, Numeric Towers has commissioned a series of lectures by eminent academics. Here is the first from Dr Pietro Punctilio, Professor of Comparative Literature at the University of Much Hadham.


I will take as my text, two versions of a traditional ballad of miscegenation  and violence. First half a dozen lines opening the British version:

A frog he would a wooing go,
"Heigh, ho!" says Rowley.
A frog he would a wooing go,
Whether his mother would let him or no.
With a rowley, powley, gammon and spinach.
"Heigh, ho!" says Anthony Rowley.

 Then, the beginning of the American version

 A frog went a-courtin' and he did ride, M-hm, M-hm.
A frog went a-courtin' and he did ride
Sword and pistol by his side, M-hm, M-hm
He rode up to Miss Mousie's door, M-hm, M-hm.
He rode up to Miss Mousie's door,
Where he'd been many times before, M-hm, M-hm

Let us consider these versions in order. This first line introduces the protagonist and his intention – to wit, to woo. The second line is one of the most significant in the history of English Literature, a vital pre-echo. It introduces a mysterious stranger, the early appearance of a device that would later be used to create an atmosphere of dramatic tension by such great writers as Harold Pinter. This has been misunderstood by many commentators, such as Dr Evadne Pincushion, who devoted much of her working life to a series of essays on Who was Anthony Rowley? The importance of the stranger is not who he is, but what he says! As Chambers Dictionary reminds us, these two simple words form an exclamation expressive of weariness. Are we not forced to accept that this is an astonishing anticipation of the bleak landscape that would be occupied by great writers of the future, such as Samuel Beckett? Thus in one simple line the author has mapped out the whole of the best of twentieth century literature to come. The next line might be considered by the superficial reader to be pointless repetition, but it performs an important purpose as the hook upon which to hang the conditional clause that follows. It is hard for us to understand in these modern times the rôle that parental authority played in the life of the young in those days, but this very work was possibly one of the first to initiate the struggle that has resulted in the liberation of the young adolescent from the stultifying control of the family.

The penultimate line of this stanza is an extraordinary one that has given rise to a whole genre of critical literature. As Dr Rick Blaine commented, “Of all the menu items in all the restaurants in all the world, he picks on these.” Obviously, the selection of these three foods is the result of careful artistic choice, and not just a random tribute to euphony, as some have alleged. Roly Poly is a dessert dough pudding that has largely fallen out of favour, now that we are aware of the dangers of obesity. Gammon is the cured ham of a hog, which was popular before the discovery that red meat is carcinogenic. These two items, however, are there to form a gentle modulation towards the shock introduction of the symbolic vegetable, spinach. Again we marvel at the technique, which was to influence many future artists, such as the film director Alfred Hitchcock. Why has this traditional green become such a potent literary symbol? Is it that creations such as épinards a la crème so often disguise fraudulent substitution of the humble leaf beet for the real thing? Whatever the explanation, there is no doubt as to its symbolic power. The idea was plagiarised in the creation of a lengthy American literary series on the life and times of a Sailor Man, replete with the reprehensible violence endemic to that benighted nation; which all brings us to the American version.

As before the protagonist and his intention are introduced, but there is the addition of a redundant and meaningless locution. Had the writer realised that the scansion had fallen short of the iambic pentameter to which he aspired? But then he gratuitously repeats it. Once it had been created, had the triteness of the pentametric form dawned on him, or is the second occurrence just a sort of literary appoggiatura for the following line? What would a skilful iambologist, such as the Great Bard himself, have made of the same material? The second line is a repetition leading to an unfortunate manifestation of the militaristic and firearm-obsessed milieu from which this version springs. Does this not foreshadow a pattern of behaviour that would one day lead to the invasion of peace loving countries in Asia? There follows a statement of the protagonist’s arrival at the door of the deuteragonist. This is shocking to readers from the old world, where such directness is, to say the least, uncomfortable. In the earlier version it takes the author several stanzas to reach this point in the dramatic narrative. Furthermore, the final line carries the suggestion that this is part of a repetitive behaviour pattern. Had an inappropriate relationship already been established before the narrative began? It would serve no purpose to dwell upon the mechanics of such a liaison, so we shall pass on to purely literary considerations. Now in the next verses…


(to be continued)

Photo opportunity

One of the most depressing pictures of the year was a photomontage taking up half a page of the Daily Telegraph of February 2nd. The night they put the fizz in into physics was the jolly sub’s merry headline. Many of the professional professors of panic who have featured in these pages were there – Professor Colin Blakemore, Professor Richard Peto, Sir Martin Rees, Sir John Krebs – as were the telly dons who make a nice living from the small screen – Dr Adam Hart-Davis, Lord Winston, Raj Persaud. In addition there were every female professor they could dig up, just to add politically correct authenticity to the event. It purported to be a party for the scientists to meet the media, but it was really just another show-biz bash. Alas poor science!


Responses to the above essay


I am shocked that you choose to publish that arrant charlatan Punctilio.  He does not know his trochee from his spondee. My mouse pointer will never hover over your entry button again.

Yours in disgust
Dr David Dactyl
Reader in Rodent-Ranarian Rhyming
Metropolitan University of Nether Wallop


It was sheer anti-Americanism posing as scholarship, and ignorant as well.

Elmer Q Aluminumstein
Associate Professor of Pentametric Poetry
University of Boot Hill

The editorial board have decided to abandon this experiment.

A tale of two conferences

One was a modest affair organised by scientists for scientists. Most participants were there under their own financial steam. The speakers were distinguished real scientists (as opposed to "climate" scientists), who presented evidence -  numbers, charts and photographs. The other was a lavish three-day politically-inspired festival. Such evidence as was presented was highly selective, though most of the claims arose from computer models

The ultimate irony is that the real scientists were subjected to a pre-emptive strike by the man who is supposed to be the nation's leading scientist, in the form of the crude and mendacious ad hominem attack that they were all in the pay of the US oil industry. The scaremongers, on the other hand, all really do make their living out of Global Warming. Global Warming pays the mortgage and feeds the kids. Without it they are on the streets and unemployable. The money is wrested (willy-nilly) from the taxpayer and handed over to them in lavish quantities. Benny Peiser  gives us an account up to the point where he withdrew under the pressure of  the depression that the proceedings induced. He showed more stamina than some of us by actually taking on the task.

Another irony is that the junkfest was organised by the people who cannot tell us what the weather is going to do to tomorrow. It so happens that in this particular week the forecasts have been even more of a joke than ever. The promised dry bright periods turned out to be uniformly dull with intermittent drizzle.

Alas poor science!


Q and A

A new reader of Number Watch, after a few complimentary remarks adds:

However, I'll admit to being concerned about (my interpretation of) your stance on global warming and was wondering if I could get some additional input from you.  Specifically:

1.  Do you dispute the possibility of *any* forward causal relationship between CO2 and temperature?  Or just the way that uncertaincies and other factors have been neglected from the public discourse?

  1. CO2 is a greenhouse gas, but a minor one. It can only be made to look important by invoking feedback in computer models involving the major greenhouse gas, which is water vapour. If you put feedback into a large  computer model you can prove anything.

2.  Do you (in principle) resist any attempt to reduce CO2 emissions?  Or just those that have an unsupportable (via prudent risk analysis) price tag?  Or do you mainly object to Kyoto (which even many on the "left" agree is flawed).

  1. For the reasons given above, the motivation for reducing emissions has not been justified. The Skeptical Environmentalist, though astonishingly credulous in many ways, has demonstrated that the investment could be better placed (for example to give the world clean water and save millions of lives). Kyoto is absolutely meaningless, even if you swallow the whole of the global warming religious message. Use of the term “left” is significant – CO2 stands as a proxy for industry, which is the prime objective of Green attacks. Capitalism is mean and nasty, but it is still the least bad system that humankind has come up with. Environmentally, communism was much worse. If you had seen Frankfurt an der Oder from the Polish Bank in the 1960s, you would know what real pollution is, and perhaps understand the German Kyoto Hoax.

3.  On several of the "green" sites, they attempt to refute the common points raised by skeptics (most of which also appear on your site).  Do you have a response to these?  Or know of a link that does?

  1. First, I would refer you to Langmuir’s Laws of bad science, particularly laws 4 and 5. Second, I suggest a reading of Karl Popper (perhaps followed by Locke and Hume). Experience of engaging with the believers is that it involves one in an infinite and sterile cycle of claim and counterclaim. Scientists of the older generation were taught to be sceptics, only now are they taught to be believers. You cannot prove any theory. Every scientific theory should be exposed to a continuous process of attempts at disproof.

4.  While googling on the subject, I ran across "".  A surface read seems to suggest that these guys are serious scientists with relatively conservative positions (relative to the standard "scare mongering").  However, they do seem to fall into the basic "CO2 -> global warming" camp.  Are you aware of this site?  What is your opinion of it?


  1. That particular web site would appear to be posing under a misnomer. It is more about computer models than the real world. Very little is known about the inter-reactions of variables in the real climate, which makes the modelling all rather a pointless exercise. The site seems to be largely inhabited by supporters of Michael Mann, who devotes a great deal of activity to preventing the publication of “poor” papers (being defined as those that disagree with Michael Mann). Such attempts at censorship have been going on for years. Mann’s Hockey Stick disregards the contributions of literature, history, art, entomology and even musical instrument making. It is based on the erroneous application of a method of linear algebra to systems (such as plant growth) that are demonstrably non-linear. According to his critics, who are pursuing the correct scientific method of attempting to disprove a theory and to determine whether results are in fact reproducible, he got his sums wrong. That continues to be argued, but his attempts to suppress criticism are an outrageous abuse.


The online stats service has drawn attention to the fact that your bending author’s name has been taken in vain in a discussion group. To make things clear, this author does NOT

bullethide behind noms de plume,
bulletrespond to gratuitous insults,
bullettake part in ever-decreasing-circle discussions,
bulletcomment on the intellectual calibre of his attackers.

And a correction

Thanks to Sherlockian work by regular number watcher, John Baltutis, it turns out that our rude correspondent is correct and the first figure in the trends document was in error. By calculation, John determined that there was a left hand point missing in the plot and a subsequent search through the Number Watch archives gave a further clue in the name of the MathCad program, It appears that one of the quirks of MathCad is that, while it automatically inserts the zero value of an index in calculation, it does not do so in the plotting routine. By the time all the calculations and plots were done, your bending author had clearly forgotten that there were originally five points. This has now been corrected by including the point at the origin. Apologies are due to anyone inconvenienced by this error.


 By mistake

OK, hands up, bang to rights, etc. You commit a howler publicly and you don sackcloth and ashes, eat humble pie, face the flak (and mix other metaphors). Erroneously omitting (or including) a zero value in an index is one of the most common errors in scientific papers. It is also one of the most common in computer programming, resulting in frightened old ladies being threatened with the courts for a debt of 0.00 currency units. There are no excuses.

Having said all that, it is nonetheless an interesting error, in that not only the author, but several regular correspondents, could not see it, even after it had been mooted. A likely reason is that they are all professional users of applied mathematics, accustomed to plotting stimulus-response relationships. The point at the origin is always there (you cannot get a response from zero stimulus), even if it is approached asymptotically along one of the axes, but it is rarely marked. It was unfortunate that the point not shown in the plot was the very one that would be restored in the mind’s eye of seasoned experimentalists.

It was also a very modern type of error, one that results from not reading, learning and inwardly digesting all the small print of the software manual.

As we observed last August, the making and correcting of errors is one of the ways that science progresses. It is also a useful route for younger scientists to ease their way into publication. Most of us oldies got our earliest publications from the errors of our elders and betters. That does not make being caught out any more comfortable. In those ancient times it was also done without insult or triumphalism, but science, like cricket, is no longer a game played by gentlemen.


Remember this number - 17

Your cynical author was deeply moved by this opening paragraph from the Personal View column on the back page of the Daily Telegraph:

Headache, high temperature, the shakes, an enlarged spleen and two billion parasites in my liver – that's the price of travelling to Sri Lanka to cover the aftermath of the tsunami.

It was by Roger Bate, who is a health economist with Africa Fighting Malaria. He has long campaigned for the rights of a large proportion of the world’s population not to be slaughtered on the altar of western environmentalism.

In a less important context, back in the last century, he was one of the few people who encouraged your bending author to publish Sorry, wrong number! and wearing a different hat found some money to purchase sufficient copies of the print run to cover the remaining shortfall in funding. The first guest paper published on Number Watch