Feynman, the latter
How would he view modern,
The clever old so-and-so?
Double dactyl, or "Higgledy-piggledy" is a verse form. It is described in a nice Wikipedia entry which gives lots of examples, all of them biographical; and indeed, this seems to be a defining feature, as it is with the clerihew (and the limerick for that matter, at least as popularised by Lear and allowing for imaginary subjects). In its biographical guise the double dactyl was, apparently, 'invented' by the American poet Anthony Hecht in collaboration with Paul and Naomi Pascal, in 1951. Its basic structure is surely much older; consider:
Moses supposes his
Toeses are roses but
For nobody's toeses
Are poses of roses as
Moses supposes his
Toeses to be
made famous by that duet in Singing in the Rain (1952) but presumably traditional.
The limerick is too hackneyed to be worth talking about, or writing except when some special effect is needed. The clerihew is less well-known and to my mind is very difficult: there is hardly room to do more than associate, in a deliberately inane or deadpan manner, the subject with something that he or she is famous for; it is a delicate balancing act. Here is a nice example by the group theorist John Dixon:
Was a remarkable man.
His famous Traité
Is still read today.
Only a Haiku says more with less. (By the way where does this come from:
I think the Haiku
As a verse form is best left
To the Japanese.
I wonder?) Anyway, Higgledy-piggledies, being slightly longer, should allow room to amplify a bit: the best amount to a mini-lecture on the person's life, character or work.
Herr Rektor Heidegger
Said to his students:
"To Being Be True!
This I believe
And the Führer does too!”
Herr Werner Heisenberg
Said "Now Your Honour
It just isn't fair,
Or if I was, then
I can't have been there!"
Those two seem perfect to me. They are a model for the solemn and weighty rules for a Higgledy-piggledy (c.f. this (paywalled) 1967 Time article and echoing more or less those given by Wikipedia for Higgledy-piggledy's close cousin, the double amphibrach):
I will now try and assemble a collection of double dactyls, double amphibrachs and muddled hybrids, one for each theorem posted at www.theoremoftheday.org. A waiver: Rule no. 3, humiliatingly disorientating my lexicographical manoeuvrability, is seldom obeyed!
If anyone would like to choose a theorem and contribute to this pointless endeavour that would be fun! Just email it to me at the address at the bottom of this page, or even write it in the visitors' book.
Higg-le-dy-pig, a dit
Pierre de Fermat:
"For two non-zero nth powers,
n more than 2,
Was proving it true!)
See Theorem no. 9
Found what makes Latin Squares
See Theorem no. 53
Said spheres pack with density,
Pi over root
For close proximity
Which, pending Flyspeck,
Is still a bit moot.
See Theorem no. 101
(Since I wrote that last, the mootness of Kepler is banished, Flyspeck having successfully completed!)
Thus Peter Cameron,
(One might imagine)
Arriving in heaven:
Thus God: "... oh ... gosh! ... about ...
Find out more here. Taking my eye off the ball — that wasn't a Theorem of the Day at all, or not yet anyway.
And having lost my thread, I will digress to mention a sort of triple amphibrach which I wrote a long time ago when I was coincidentally at Goldsmiths College with the much more illustrious Geoff Whitty. In fact I seem to remember I published it in the staff magazine Hallmark, under the pretence of providing a helpful aide-memoire. It was easy to write; much more difficult, as an exended version of "Which witch is which", to speak!
Which Whitty's Which?
"Which Whitty's which?" Goldsmiths College cried,
When faced with the two of them, side by side,
And it's true, it's a difficult thing to decide,
Unless you are very discerning.
Less witty than Whitty is witty, to wit
The wit Whitty's writing concerning
Whitty and which is it wittily witters
And which is the Whitty that's written the wit
About which Whitty's which Whitty, which wit is which.
Of the two, it is true there's a weightier Whitty;
You'll find when you get down to the nitty-gritty,
This Whitty's a twit (but ... 'e's learning)
Anyway, enough of that — time to get back on track!
Trendy and cool:
Slums of topology
See Theorem no. 52
Euclid, like Bourbaki,
May not have actually
Existed as such;
The primes form an infinitude,
I'm not so sure that it
Matters that much.
See Theorem no. 4
Spent her career,
Proving r.e. is D.
Yuri Matiyasevich is
Why she's a personal
Hero of me.
See Theorem no. 43
Coloured three points per quadruple
Blue, the fourth one red,
Design of the Century:
Type B bipartite S(
See Theorem no. 100
John D. Dixon,
Decided a question of
\lim as n \rightarrow
See Theorem no. 49
Peter M. Neumann:
Three cheers for his Maths Gene-
As it obeys his Sep-
See Theorem no. 64
Perhaps this is growing monotonous? Perhaps I am inserting a limerick or two just so I can reuse 'one I did earlier'? Or it's because Higgledy-piggledy doesn't really lend itself to playing fast and loose with form in the way that the limericks does:
The mathematician Lowell Beineke,
Has characterised the graphs leineke
Thus: it is forbidden,
In G, to find hidden
A graph from his set of size neineke.
See Theorem no. 48
From Louis Goodstein the logician
Comes hereditary base-k attrition:
Start his sequence at 4:
It's increased to three-score
In three steps, then some more: ..., 584, ..., 884, ...
(now imagine a long intermission)
..., 2, 1, 0 (done!)
See Theorem no. 73
To KASIMIR KURATOWSKI,
See Theorem no. 24
This last, by Frank Harary, which appears on Theorem of the Day courtesy of the Perseus Book Group, has lured me into the territory of the iambic quadrameter where can be found this, still only too relevant more than a hundred years after it was published:
The Microbe is so very small
You cannot make him out at all,
But many sanguine people hope
To see him through a microscope.
His jointed tongue that lies beneath
A hundred curious rows of teeth;
His seven tufted tails with lots
Of lovely pink and purple spots,
On each of which a pattern stands,
Composed of forty separate bands;
His eyebrows of a tender green;
All these have never yet been seen —
But Scientists, who ought to know,
Assure us that they must be so....
Oh! let us never, never doubt
What nobody is sure about!
From More Beasts for Worse Children, Hilaire Belloc, 1897
The link to the excellent Baldwin Project will allow you to read The Microbe with Basil T. Blackwood's
illustrations from which it must always remain inseparable. Their absence on this page leaves me space to quote from Belloc's no less timeless tease directed at the academy (and even at constrained writing):
Don dreadful, rasping Don and wearing,
Repulsive Don — Don past all bearing,
Don of the cold and doubtful breath,
Don despicable, Don of death;
Don nasty, skimpy, silent, level;
Don evil, Don that serves the devil.
Don ugly — that makes fifty lines.
There is a Canon which confines
A Rhymed Octosyllabic Curse
If written in Iambic Verse
To fifty lines. I never cut;
I far prefer to end it — but
Believe me I shall soon return.
My fires are banked, but still they burn
To write some more about the Don
That dared attack my Chesterton.
Lines to a Don, Hilaire Belloc, 1910
Alors, revenons à nos moutons!
Hegel de Pigalle dit:
A fait l'impossible
Quadrature du cercle:
Sa circonférence par
Des racines carrés pendant
... Deux, trois siècles.
See Theorem no. 102
Cheryl E. Praeger,
With Cameron, Saxl and
Seitz, answered C.
Does `bound' |G_x|
See Theorem no. 65
Hegel de Pigalle dit:
Sophie Germain —
Vos premiers éponymes de quoi
Vaut mieux que vous demandiez à
See Theorem no. 59
What's it all about then, this Hegel-Pigalle thing? Hegel visited Paris in 1827 but at that time Montmartre was not even a part of the city and anyway he stayed in the 6th arrondissement on the other side of the river. So those first lines are complete and utter rubbish, which is as it should be in a double dactyl. (I had a little help from Emmanuel Amiot with those, by the way.)
Beginning her journey at
Jones in 2D,
Analyst's version of
See Theorem no. 108
Appel and Haken,
Announced to the world that "Four
See Theorem no. 1
Kenneth J. Arrow —
Invoked by the ballot box
Pareto Efficiency —
You'll only end up with
A bloomin' dictator!"
See Theorem no. 69
Coloured his triangles
red, blue and green;
Coloured ones were not
The only ones seen.
See Theorem no. 16
Isaac and Isaac
And 'tween this f and
See Theorem no. 2
An ironic abuse of notation since I've used Leibniz's rather than Newton's!
John H. Halton and
See Theorem no. 109
The term 'asymptopia' was used by David L. Applegate in an email to me — it is perfect.
Gale and Shapley,
Leant the estate that is
Not entered lightly,
Pre-emptive advice against
(Nudge, nudge) activities:
See Theorem no. 68
Actually I received from John Drost a very neat haiku on this same theorem which sums the whole thing up in just 8 words instead of 8 lines:
not preferring each other
And having been again seduced from the double dactyl I will venture so far as the iambic heptameter or fourteener, because I cannot resist posting this gem, which my friend Helen Connies-Laing emailed me:
Today I turned my calendar of ‘Theorem of the Day’
And for once I felt an inkling of what the theorem had to say.
You see, I recall a discussion long ago with Dr Rutherford
When she tried quite hard to explain to me why Latin squares are good.
She told me about farmers and planting stuff in fields
Though there’s nothing on the calendar that with agriculture deals….
She didn’t mention Wesley Brown, Fred Cherry or the rest –
In the light of which, I feel that I really must protest.
Has she really got a PhD in Matroids/Combiniatorics?
Is that why our discussions have the same effect as Horlicks?
Because looking at the calendar, today on June’s first day,
Not a sausage corresponds to what Dr Ruther had to say.
I like the pretty colours – though the yellow’s rather loud
And I must admit when I saw the squares I felt a little proud.
You see, it’s very rare I open it and see upon the page
Something – however tiny – with which I can engage.
See Theorem no. 131
An exercise in constrained writing: ...and some unconstrained inventiveness:
If M's a complete metric space,
And non-empty, we know it's the case
That if f's a contraction
Then under its action
Just one point remains in its place.
See Theorem no. 145
See Theorem no. 143
The inventiveness being that of Dilip Sequeira, whose clever verse sparked a scintillating rejoinder from Michael Fryers (in Eureka, nos. 52 and 53, respectively—I am grateful to the Archimedeans for permission to reproduce Sequeira's poem here and both of them in Theorem no. 145 itself).
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