A pretty picture of the Solar System

[Benjamin W. Betts] has made some studies of the Solar System, and endeavoured to find the law by which the intervals between the planets are regulated. He considers that the planets mark points of undeterminateness in the circuit of the polar forces of attraction and repulsion. Gravitation lie considers as the resultant of a proportional relation of these forces and not as an independent force in itself.
He believes the form of the Solar System, by which he means the invisible form of the activities immediately concerned in its production, and of which certain points are marked by the position of the planets, to be a nine-petaled lily similar to the Ond Corollas(1). Every Solar System in the sky he supposes to be the counterpart of some flower at our feet. Our Solar System is an Alpha or male universe. Others he believes may be Omega or female forms. The systems with dual suns he thinks may resemble his diagrams of bi-axial corollas.
(1) The Ond Corolla, or simlply Ond, is the name given by Betts to form such the figure presented here.
Image source: The public domain review
Text source: Geometrical psychology, or, The science of representation - An abstract of the theories and diagrams of B. W. Betts by Louisa S. Cook (1887)
Read also: barin pickings and Dataisnature

Calculating machines

posted by @ulaulaman about the italian exhibition dedicated to #AlanTuring
The Museum of Science and Technology Leonardo da Vinci in Milano was founded 60 years ago on the 15th February and yesterday this birthday was celebrated with a free admission from 14:30 until 23:30. Inside the museum you can participate in various interactive laboratories usually offered to visitors and visit exhibitions presented in the rooms of the Museum. While some of the exhibits are permanent, such as the one dedicated to Leonardo da Vinci, others are temporary, such as the one dedicated to Alan Turing, which centenary was celebrated during the last year.
The exhibit occupies three small rooms, nothing incredibly wide or long to see, but certainly very interesting. The exhibition, in fact, tells about the evolution of calculating machines, starting from pascaline by Pascal until you reach the final room, explicitly dedicated to the great British mathematician and logician, where thanks to some infographics, the life of Turing is telled to the visitors. Meanwhile on the wall a series of videos posted to YouTube and dedicated to the great scientist are projected.
To complete the room there is also an Enigma machine:
Enigma machine
The Enigma machine was patented in 1918 by the German Arthur Scherbius which takes and expand the operating principle of the Italian Leon Battista Alberti's cipher disk.
Created to facilitate the encryption of communications in the financial and commercial, it was officially presented to the Berne International Postal Congress in 1923. Continuously improved, it is adopted first by the German navy and later by the army to make secret military communications. Easy to use, it enjoys a solid reputation as indecipherable that it ensure the wide diffusion.
Enigma is based on the whole system of secrecy of Nazi Germany. The attempt to break the cipher is one of the most famous stories of counterintelligence of the twentieth century. The first attempts are due to the Polish Marian Rejewski but with the capture of the specimen aboard the German submarine U-boat 110, which is able to provide important information to the team of scientists at Bletchley Park, working night and day to this purpose. Alan Turing is among these. Thanks to his skills as a mathematician and cryptographer, Turing can make an electromechanical computer, The Bombs, ables to perform the task with a remarkably efficient. Subsequently he developed a more powerful computer, Colossus, that at the end of the war will be destroyed on the orders of Winston Churchill, and its existence is only made ​​public uprisings years after the end of the war.
In the gallery below there are the photos I took during the visit to the museum:

Proofs without words: the rolling circle

A rolling circle squares itself.

Elsner T. (1977). The Rolling Circle Squares Itself, Mathematics Magazine, 50 (3) 162. DOI:

Extraction of square roots

Oppenheim A. (1955). 2553. Extraction of Square Roots, The Mathematical Gazette, 39 (329) 237. DOI:
At the end of his article on the extraction of square roots(1) Professor Haldane writes:
The methods here given are probably now of no practical importance. Had they been discovered in the 17th century, as they might have been, they would have saved a good deal of computation.
In point of fact Brook Taylor in 1717 gave "A general Series for expressing the Root of any Quadtratick Equation". It will be found towards the end of his paper
An attempt towards the Improvement of the Method of approximating, in the Extraction of the Roots of Equations in Numbers(2).
In modern notation Taylor's solution of the quadratic equation \[xx - akx + akk = 0\] is \[x = k + \frac{k}{c} + \frac{k}{cc'} + \frac{k}{cc'c''} + \cdots\] where $c=a-2$, $c' = c^2 -2$, $c'' = c'^2 -2$, $\cdots$ He gives the example \[1 + \sqrt{2} = \frac{1}{2}-\frac{1}{2\cdot 6}-\frac{1}{2 \cdot 6 \cdot 34}-\frac{1}{2 \cdot 6 \cdot 34 \cdot 1154}-\frac{1}{2 \cdot 6 \cdot 34 \cdot 1154 \cdot 1331714} - \cdots\] and concludes
The Fractions here wrote down giving the Root true to twenty three Places(2)

(1) Haldane J.B.S. (1951). The Extraction of Square Roots, The Mathematical Gazette, 35 (312) 89. DOI: (pdf)
(2) Taylor B. (1717). An Attempt towards the Improvement of the Method of Approximating, in the Extraction of the Roots of Equations in Numbers. By Brook Taylor, Secretary to the Royal Society, Philosophical Transactions of the Royal Society of London, 30 (351-363) 610-622. DOI:

The electric science of Captain Swing

posted by @ulaulaman about @warrenellis comics #electromagnetism #Faraday #diamagnetism
Later that year [1830], there was a spate of riots by farm workers in the south of England who were reduced to starvation by the introduction of machinery that could do their jobs cheply and tirelessly. They destroyed threshers, burned workhouses and sent manifestos of fiery intent to the landlords and magistrates.
These letters were signed: "Captain Swing".
In this way Warren Ellis tells us the main inspiration for his story, Captain Swing and the Electrical Pirates of Cindery Island, drawned by Raulo Caceres: the protests by farmers against the introduction of machinery in country work. But Ellis' graphic novel is not an historical novel, but, first of all, a teslatopia (or a teslapunk novel) or an electrical romance of a pirate utopia thwarted, following Ellis' definition. If you want, from a more simple point of view, the Electric Pirates is a steampunk novel, but it is also a scientific comics. The fil rouge of the novel is, indeed, the electromagnetism research, and the diary of Captain Swing is a source of precious information that the reader could study in deep as soon as the closing of the book.
For example the reader could say himself if a ship could fly thanks to the electromagnetic force, or if the instruments illustrated in the pages of Captain's diary are true or not (in this last case the main source is probably Joseph Priestley's books, see for example The History and Present State of Electricity). Or we could ask if Ellis/Swing is lieing when he writes, for example, the following passage:
Ionic air propulsion(1). Electrostatic levitation(2). Electrogravitics. The Biefeld-Brown Effect and the electro-fluid-dynamics(3). Nothing here is invented. It simply appears to be uchronic, counterfactual, sitting in the break of a time out of joint.
In fact, many of the questions mentioned by Ellis are really studied by physics and electromagnetism.
Electromagnetism is the branch of physics that deals with the study of electric and magnetic fields. As demonstrated by James Clerck Maxwell, the two fields, electric and magnetic, are very closely related to each other and only in a static situation can, with good approximation, be considered separately.
In fact, however, the two concepts of electricity and magnetism were initially separated, and in particular the first observations about electricity date back to the Ancient Greece:
Thales first transcribed the induction of static electricity in 600 BC.
Only about one thousand of years we have a significative progress in the field:
Otto von Guericke built friction-machines for the accumulation of static electrical charge around 1650 AD.
Guericke, a prussian phisicist, is known primarily for his experiments on the air, which actually dates back to 1650 (according to the Britannica). In particular, he realized a famous experiment with a hollow sphere inside which was a vacuum: the horses tied to the two spherical caps that made the ball could not to separate them, thus demonstrating the tremendous pressure exerted by the air on the objects.
The invention cited by Warren Ellis come from 1663, which is the first electric generator in history.
The real high jump, however, comes with 1800s:
Upon thye founding date of the Metropolitan Police, Francesco Zantedeschi discovered electromagnetic induction (although, in this slow world, Michael Faraday would have been unaware of this when he published his more famous discovery of same, a year from now).
A simple experiment of electric induction (in this case electrostatic) is rub a pen on a knitted wool and then see his effects on some pieces of paper. Or you can try to do the same thing with a ball and a rod, using different materials to determine which of these is able to attract the ball after a suitable scrubbing:

We want a theory

We want a theory. An uncommon want
When every year and month sends forth a new one
Till after cloying the gazettes with cant
The age discovers it is not the true one.

Hannes Alfven from On the Origin of the Solar System