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### Extraction of square roots

*Oppenheim A. (1955). 2553. Extraction of Square Roots, The Mathematical Gazette, 39 (329) 237. DOI: 10.2307/3608773*

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 NumbersIn 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^{(2)}.

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: 10.2307/3609330 (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: 10.1098/rstl.1717.0011

### 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.In this way

These letters were signed: "Captain Swing".

**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 propulsionIn 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^{(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.

**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.

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*
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