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I doubt that the pointer I put many month ago on Igkt forum raised much interest.
It was about an article published in the New Journal of Physics.
If, but it is rather a IFF, the link is broken then use this link.

You may find on the net video of the breaking of spaghetti !

I did some spaghetti breaking, using small points of colour - water based ink - strategically
disposed to get, in the absence of any high-speed camera, a notion of what was happening.

I may have stumble by pure chance on something that can be use.

"Un mot n'est pas la chose, mais un éclair à la lueur duquel on l'aperçoit"
Denis DIDEROT - Philosophe Français du Siècle des Lumières

“A word is not the thing, but a flash of lightning in the gleam of which it is glimpsed”
Denis DIDEROT - Enlightenment French philosopher.

Well this might very well be the gleam in which to look at this phenomenon.

Most of you must know the coloured hollow plastic "thread"/"wire"/"tube"/"line" used to
make "scoubidoos". Diameter : 1.5mm or  6/100th of an inch.

Well the sort I got hold of behave quite like the under cooked spaghetti but in very slow
motion and let you see what is happening until the last second.

Just try it instead of going on thinking "that is silly".
Compare with a few spaghetti.
You may learn something not previously known by you.

By the way I found one rope maker "MEISTER" who give knots as diminishing by 50%
the strength of a rope but SPLICES TOO.



In History And Science Of Knots
under the editorial supervision of J.C TURNER and P Van De GRIEND
publish in  : Series on Knots and Everything -  Volume 11 - World Scientific is the publisher.
It is a series that leaves you in no doubt about it having the hallmark of academic standards
of publication.

Chapter 13 : Trambles, signed by Geoffrey BUDWORTH .

At the occasion of "trambles" a 'natural' concept formalized by Desmond MANDEVILLE
author evoked with some details the idea of the alphabet in knots that is, "by default",
attributed solely to Desmond MANDEVILLE who is said to have launched it "in the late

It is good form for authors of an academic publication , when writing about a particular idea,
to be thoughtful of mentioning, even if only in the most swift passing manner, the antecedents
of the idea so as not to lead "by default" the  readership into thinking it is its first emergence.
Either this mention has exceeded my capacity of understanding written English or it is too
subliminal for my catching it. I am sorry to raise the point if it is indeed in the printing.

Idea of an alphabet using knots has been in the air since at least the last fourth part of the
19th century.

I had  encountered the alphabet in knots prior to reading M. Budworth piece, in the idea of
David MACHEATH and Robert MYLNE that is mentioned in
Chapter XVI : An Alphabet Of Knots
in his book Knots Ties And Splices - A Handbook For Seafarers, Travellers, & All Who
Use Cordage published by Routledge and Sons in 1884.

Burgess state that
[begin quote]
Many persons have suggested a series of knots for this purpose ( my note : purpose is
"communicating a message apart from the usual pen and ink"), apparently in the ignorance
that such a scheme of knot writing was introduced for the use of the blind many
years ago
, by a teacher named David Macheath, of the Edinburg Blind Asylum, and a
scholar named Robert Mylne. They describe their "string alphabet" as they term it, thus...
[End quote]

I believe that more than three fourth of a century is what can be honestly qualified as
 The more so because it seems that is was not only 'an idea thrown in the air' but a tool for
 blind persons.
It was 'in the air' to invent means of communication.
BRAILLE invented his system for the blind in 1819 taking his idea in the "écriture nocturne"
/ Writing in obscurity invented by Charles BARBIER DE LA SERRE. This Charles was an
Artillery Captain inventor of a system allowing soldiers to trace and decipher messages  in
full darkness using 6 sets of "point saillant"/'raised point to represents phonetic sounds.
BRAILLE published his system in 1829.

Desmond MANDEVILLE's  merit and stature would (could) not have been, still are not,
diminished by the mention of his predecessors in this general line of using rope and knots to
This is 'convergence'.
( khipus, as far as we know, when not letters or sentences but digits and numbers)

I will welcome precise pointer to an antecedent to Macheath and Mylne.



I have read several "short history" of the study of knots by mathematicians.

Some do not even mention the giant K.F. GAUSS (document was found on the Net, ) but none of the non-European (for this topic
UK citizens will not be considered as Europeans, they don't behave like Europeans! They
are just UK citizens)  authors writing in English that I read seems to acknowledge or know
that even the great GAUSS was preceded :

by a French mathematician of the 18 th century.

Karl Frederick or Carl Friedrich GAUSS will follow in 1833, in the first part of the 19th
century, as he was discussing knots with one of his doctorate students (Johann Benedict
LISTING (1808-1882)
) .

It seems it was LISTING that coined the word "topology" to name the new "geometry of
position" (géométrie du placement).
It is the title of one of his published pieces.

It seems that GAUSS himself wrote a few words on knots but that it was LISTING that
"did the work" under the inspirational teaching of Gauss for what was to be "topology" for
his "Vorstudien zur Topologie" , Göttingen  (1848) "Preliminary studies on the topology"

Short note : the MÖBIUS strip ( Moebius if "¨" is suppressed  ) should be the LISTING
strip as it was he LISTING who discovered it two month before MÖBIUS made his find.

As early as 1771, Alexandre-Théophile VANDERMONDE (1735-1796) mentionned
knots in a "Mémoire" written for l'Académie Royale des Sciences ( Paris - France ) with
 the title of :

"Remarques sur les problèmes de situation", (that is "Remarks about placement problems"
or situation problems) pages 566-574.

This .pdf file is a courtesy from Anne Bernard  from
Délégation à l'Information Scientifique et à la Communication
Académie des Sciences
23 quai de Conti
75270 PARIS CEDEX 06
Got an answer in the hour following the reading receipt for my e-mail.

The old typography plus the scanning do not make for easy reading, so I transcripted it with
modern typo ( Word format) .

Style is 18th! just imagine reading a corresponding text in English.

In it there is no mathematical formalism such as prescribed by the  BOURBAKI group
(French group of mathematicians who made many people feeling disgusted with
mathematics  even if it helped to standardize exposition of reasoning. Sometimes too
much is counter-productive)  but clear reasoning.

VANDERMONDE was : musician, jurist, mathematician, chemist, physicist, mechanics,
economist and demographist.

I am told that VANDERMONDE matrix is a tool used every day by mathematicians so
why this "miss" in "short history of knot theory"?
May be I am just playing at  the irate 'Coq Français'.


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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

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