MAXWELL’S EQUATIONS

HOW THE MODERN WORLD

WORKS

The invention of the phonetic script about three and a half thousand years ago enabled humans to suddenly think about a million times better, and they took off. Likewise the invention of a script for thinking quantitatively, that is to say Mathematics , could lead to thinking of a different kind that is just as powerful. In fact it has already: Maxwell’s Equations (ME).

Some arguments are of a purely quantitative nature. For instance in our post “Civilization and Moonpower” we demonstrated that large cities not dependent on slavery only became feasible once tidal energy was harnessed, as was possible in North Western Europe, where it is far more abundant than elsewhere. Here I talk about the most momentous piece of Mathematics ever done, Maxwell’s Equations.

Maxwell’s Equations describe the interaction between Electricity, Magnetism, Space and Time. They were an attempt to write down the experimental findings of the ‘electricians’ Hans-Christian Oersted (1820) and Michael Faraday (1831) but they led to a totally unexpected insight, and thus to the modern world: “Electromagnetic waves can propagate across empty space at the speed of light”.

Out of that insight (1864) there was to come Radio (1887), Transatlantic wireless (1901), Relativity (1904), Electronics (1912), Broadcasting (1920), Television (1930), Code-breaking (1930’s onward), Radar (1935), Microwaves (1940), The Electronic Computer (1943), Communication Satellites (1960), Space Travel (1969), The Internet (1980), Mobile Phones (2000). … while the Second World War could as aptly be called ‘The Radio War’ because it was started by Radio ( broadcast hate propaganda), controlled by radio (e.g. Churchill and Roosevelt talking to their peoples), won by radar in its many guises both in defence and attack, and lost by code-breaking ( e.g. : the battles of Midway and Kursk). A huge operation like the D-Day landing would have been unthinkable without the command and control made possible by radio.

Einstein is rightly famous for his E=mc2 equation (1905) but in a sense he and others (for he was only one of several) were only adding footnotes to Maxwel’s Equations which in themselves prove that Space and TIme cannot be at all as we had thought them to be.

So what are Maxwell’s Equations? There are 4 of them actually and you can write them out in different ways using rather different vocabularies. Textbooks on Electromagnetism can make them look both galumphing and arbitrary, when, as I believe, they are inevitable; the world couldn’t have been constructed in any other way. I find that both beautiful and totally unexpected. They, and the many stories behind them, are certainly worth having a look at even if you have no ambitions to use them yourself. You can regard them like The Rosetta Stone, as a wonder to behold, though they are far far more remarkable and momentous than that iconic stone. If you don’t believe me look at:

https://mjdisney.org/wp-content/uploads/2021/04/MAXWELLSEQUATIONS.pdf

Yes they do look unfamiliar, even frightening, but that’s probably because you’ve been put off Mathematics by bad teaching.The world is full of Baducation and bad ideas . And one of the most debilitating , which goes back to the Ancient Greeks, is the notion that “Mathematics is Deductive in Nature”, and therefore quite different from our normal everyday Common Sense Thinking , which is Inductive. But that is a complete misconception. It’s as if the Maths teaching profession have mistaken the grocery- bill for the groceries. Don’t take my word for it: Morris Kline, that most eminent Historian of Mathematics wrote: ” “Mathematics is a human activity and is subject to all the foibles and frailties of humans. Any formal, logical account is pseudo-mathematics, a fiction, even a legend, despite the element of reason.” [‘Mathematics, The Loss of Certainty, ‘ OUP, 1986]

So many of us have been put off maths because we’ve been taught it back to front by the maths- teaching profession: deduction first, intuition afterwards. No wonder so many of us rebel. If you look at the following url you can see ‘Pythagoras’ Theorem’ being taught in the two alternative ways so that you can judge which is best for yourself:

https://mjdisney.org/wp-content/uploads/2020/10/dedvindmaths.docx

The consequence of all this innumeracy are fairly tragic. Most of us are innumerate and, in my opinion, innumerate people can never become wise, not any more, not in the modern world( see all the current confusion over Covid vaccination statistics). The great news is that innumeracy is by no means irreversible. Maths is a subject peculiarly suited to self-instruction over the Internet. I suggest that everyone who earns a certificate of numeracy receives an immediate grant of £15,000 while many prestige professions and jobs be reserved entirely for the numerate. Thus a large fraction of a population could become numerate at a trivial cost by comparison with many infrastructure projects. And surely widespread wisdom is more desirable than say more runways. It’s probably no accident that the most numerate people on Earth (the Japanese) are also the wealthiest (UN figures).

The consequences of all this innumeracy are fairly tragic. Most of us are innumerate, and in my opinion innumerate people can never become wise, not any more, not in the modern world ( see all the current confusion over Covid. vaccination Statistics). The good news is that innumeracy is by no means irreversible. Maths is a subject especially suited to self instruction over the internet. I suggest that everyone who can earn a certificate of numeracy receive an immediate cash award of £15,000, while many prestige jobs and professions should be reserved for the numerate. Thus much of a population could become numerate at a trivial cost: Widespread wisdom is surely more desirable than say more runways. It is probably no accident that the most numerate people on Earth (the Japanese) are also the wealthiest (UN figures).http://Baducation

If you would like to see a wide-ranging discussion of numeracy and innumeracy in the British context, taken from my book ‘History of the Brits’ (Amazon 2020) you might like to click on:

If you want to see a wide-ranging discussion of Numeracy in the British context you might like to click on:

https://mjdisney.org/wp-content/uploads/2021/04/HISTORY15numeracy.pdf

Anyway , for those who can appreciate them, Maxwell’s Equations are every bit as beautiful as great music, prose or poetry . They enable us to hear , in Tennyson’s words “…the horns of elfland faintly blowing….”

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