15th July 1912. ‘The Greatest Man Scotland Has Produced’.

Nautilus shell logarithmic spiral.

Nautilus shell logarithmic spiral.

The Nautilus grows in a shell following a logarithmic spiral. In other words in a way that turns by a constant angle along its entire length.

Logs are the inverse operation to the Exponent (power), as minus is to addition, or multiplication to division.

Today in 1912 the Council of the Royal Society of Edinburgh, resolved to commemorate the tercentenary of the publication in 1614 of John Napier’s ‘Mirifici Logarithmorum Canonis Descriptio’, or, ‘the wonderful rule describing logarithms’.(1)

It was the philosopher, David Hume who later glowingly described him, as in the above Title, as nonpareil.

Though Napier’s Logs were different to those used today, and bearing in mind that all development rests on previous work, Napier is regarded as the man whose brilliance led to the breakthrough which later revolutionized mathematics.

Brilliant though he was however, he like many of the thinkers of the time, were involved in the occult; John Napier being known as a wizard, sorcerer and necromancer, which he seems to have acquired from his father, Archibald 7th Laird of Merchiston, near Edinburgh. John’s nephew Richard, indeed, was known as the ‘Warlock of Oxford’.(2)

Logs were to save the time of the then astronomers, who worked with myriads of numbers and helped to limit ‘slippery errors’ of calculation.

In fact Logs were used by Kepler and others, and underpinned much of Newton’s work on Gravity.

Logs in saving time in calculations, was also a step towards the discovery of infinite calculus, the work of Liebnitz and Newton.

Log scales in modern science, have a wide use in the decibel unit, music intervals, quantity of sound pressure and voltage ratios, as well as in pH, which is a log measure for acidity of aqueous soil.




10 power 4=10,000: Log 10 10,000=4

To find a Log of a number we need to find how many of one number (exponent) do we multiply to get another? In Log (2) 8 =?  2x2x2=8. We need 3 so Log is 3.

Exponents are the same as Powers or Indices: thus 2³ is 2 to power 3 or 2 to 3rd power or 2 cubed.

(1) A resulting Congress was held from Saturday 25 July to Monday 27th July 1914, which thoughts were collected in a volume by C. G. Knott (ed), who to paraphrase, said that: ‘within a week, the many of the people there, in an atmosphere of goodwill and friendship, would be on opposite sides in war.’

John Napier (1550-1617) (Napur etc) as his name had many variations.

(2) The Scotsman.com/news/napier.

Ref: wikipedia.org/Image of nautilus.

Ref: mathsisfun.com/algebra/logs.

Ref: maa.org/external-archive/devlin.


Log example: log of 1000 for base 10 =3 because 1000 is 10 to power 3. 1000- 103 = 10 x 10 x 10. Where x = by , then y is log of x to base b, and is written logb (x). So log 10 (1000) =3.


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About colindunkerley

My name is Colin Dunkerley who having spent two years in the Royal Army Pay Corps ploughed many a barren industrial furrow until drawn to the 'chalk-face' as a teacher, now retired. I have spent the last 15 years researching all aspects of life in Britain since Roman times.

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