How Long?

It takes 100 years for an idea to go from inception to general acceptance.
Dijkstra[1]

When I first read this I thought it alarming.

Then I started collecting some historical tit-bits[2]…

Set theory

Cantor invented (or discovered?) Set Theory around 1870.
Modern math started getting taught in American schools in 1960.
One of the new contents was Set Theory.

So a little under 100 years.

Calculus Notation

Leibniz and Newton independently invented the calculus around 1675
Leibniz d/dx notation did not reach England till 1815 when Charles Babbage co-translated the leading European calculus text by Lacroix

Thats about 150 years.

[Yeah thats right: THE Charles Babbage of computer fame]

Added later:  Prof. Mathai Joseph pointed out that strictly speaking one could push the discovery of Calculus to two centuries earlier in Kerala-India.  The notations used then are however hard (for me) to make out.

Roman to Arabic numerals

It seems a no-brainer today to prefer Arabic numerals to the earlier used Roman ones.  It was not so obvious:
eg  5 + 3 is 8 is more arbitrary and unhelpful than V + III is VIII

And the transition took a while…

[From Arabic numerals in Europe]

Al-Khwarizmi described 'Hindu numerals' in 825 AD.

This reached Europe in 976
They came into common use in the mid 16th century

Thats about ½ a millenium of the Europeans knowing of  'Arabic' numerals and sticking to Roman.

Aside

If we count strictly as time it is more than a millennium, counting the first known occurrence in India around 500 AD. I consider this mode of reckoning however as not germane to our inquiry.

Irony 1

His book in Arabic was called On calculation with Hindu numerals.  The world now — starting with the wikipedia page above — calls them Arabic numerals.

Irony 2

Arabic is a right-to-left (r2l) language in which units before tens before hundreds imples units-tens-hundreds must come in r2l order. The Europeans copied the r2l order without seeing that it was wrong for their default order.

Irony 3

And the 'Hindus' re-imported it back keeping the wrong order!

The cure for Scurvy: Discovery to Implementation

In 1601 Capt. James Lancaster placed the crew of one of his four ships on a regimen of three teaspoons of lemon juice a day.  By the half way point almost half the men of the three ships had died of scurvy whereas not a single one of the lemon supplied ship had died.

One would think that lemons as a cure/preventive for scurvy would get adopted??

Yes...

In 1747, a British navy physician, repeated Lancaster's experiments and showed that citrus reversed scurvy — a mere gap of 146 years

And 48 years later — 1795 — the British navy enacted new guidelines requiring citrus and scurvy was eradicated from the British fleet.

The British board of trade adopted this for the merchant fleet in 1865 — ie 70 years later.

So Lancaster's discovery to its general adoption took 264 years[3]

From Flight to Commercial Aviation

The Wright brothers flew in 1903.
The Douglas DC-3 ushered in commercial air travel in 1935.
Peter Senge in the Fifth Discipline deconstructs why these 32 years:
Five components needed to come together synergistically for that to happen.
The earlier year Boeing managed with 4. That was not enough. The five were

• variable pitch propeller
• retractable landing gear
• a lightweight body material called monocoque
• radially cooled engine
• wing flaps

[Boeing had everything except wing-flaps]

Heliocentric Universe

The heliocentric model of the universe that we take for granted took some time to stabilize:

Copernicus 1532 →
Tycho Brahe 1588 →
Kepler 1615 → 
Galileo 1615 →
Newton 1687

Thats 150 years from the beginnings of a revolution to its closure.


Note 1: Copernicus' book gave the word after which came the French and American revolutions — of a rather more violent nature.

Note 2: It is customary to badmouth/ridicule the catholic church round this event. Yes, the church's behavior was condemnable: It took the Church 350 years (Pope John Paul 1992) to accept and correct its error. Even two years before that (1990) Cardinal Ratzinger, the future Pope Benedict justified the church's prosecution of Galileo!  All churches are like that... And the more secular the 'church' the more persistent it is in error.  Its just that the 'secular churches' dont last for millennia. To demonstrate that stupid science is as stupid as stupid religion is a subject for another day...

Sick Visionary or World Teacher

2 millennia ago a certain person who was causing 'law-and-order trouble' to the ruling Romans was chastised at first for his misguidedness and finally given capital punishment – a relatively common practice of that time.

200 years later he had a few thousand followers.
A millennium later his teaching — Christianity — became the dominant religion.

No, this is not about the status and stature of Jesus Christ, but about a more incontrovertible conclusion: Before writing someone off as a sick visionary, do consider waiting for a thousand years.

J. S Bach

lived from 1685 to 1750.  In his time he was regarded as an excellent organist.
Not too many people took his music seriously; he was regarded more as a 'musical mathematician': .
In 1823 by chance Mendelsson discovered his St. Matthew Passion and from there many of his other compositions.

This led to the Bach Gesellschaft being constituted in 1851, which finished publishing all of Bach (that was not lost as waste paper) in 1900.

Where between then and now : "greatest musician of all time" became the generally accepted position regarding the stature of Bach, I cannot say. Putting it at 1900 gives the figure of 150 years.

Likewise

Beethoven

was regarded as a capable musician… when he was a performing musician.
After he became deaf he was considered past his time and his compositions were regarded as the monstrous abortions of German idealist

Perhaps now in the changed scenario 150 years later, we should modify it to:

    the monstrous abortions of an European idealist

given that these abortions became an important factor for the unification of Europe:

Physics

Aristotle wrote physics around 350 BC in which he claimed that heavy bodies fall faster than light ones
Galileo disproved his claims around 1589 AD by dropping two balls from the Leaning tower of Pisa.

That's TWO MILLENNIA of the world preferring proof by authority over proof by experiment!

Geometry

Euclid wrote his elements around 300 BC→
Kant  claimed (18th century) that Euclidean geometry was innate in human consciousness →
Gauss/Riemann/Lobachevski created alternate geometries within the next 100 years →
Einstein used Riemann's version for general relativity 1910 and laid to rest Kant's claim : 150 years.

A quote from Gauss probably dates from his not having the stomach to publish his geometry against the enormous prestige of Kant:

     When a philosopher says something that is true then it is trivial.
     When he says something that is not trivial then it is false.

Parallel Processors

von Neumann machine described his machine in 1945 — the quintessential sequential machine

What about alternative parallel architectures?

• As early as 1955 the IBM 704 had parallel units. Last machine in 1975
• Cray Research was founded in 1972. Its spin-off Cray Computer Corporation went bankrupt in 1994. Cray research bought out by SGI in 1995
• Inmos (behind Occam and the Transputer) founded 1978; Brand name finally discontinued 1994
• Thinking Machines founded 1983; filed for bankruptcy 1994

Unnoticed by these and parallel-ly(!)... Intel introduced

• the superscalar Pentium 1993
• Streaming SIMD (SSE) in 1999

Were these yet considered 'parallel'?

Parallel processing begins to get mainstream:
In 2006, Intel introduced its Core 2 architecture and NVidia released CUDA

How would the parallel computing scene looked if one asked around 1994-5?
After 2006? 

AI

Started with Slip and Lisp in the 1960s
By the 80s what is called the  Winter of AI had set in in which research funding mostly stopped.

1998: a certain company is incorporated in Mountain View that used this 'useless' AI research...

• first for search
• then maps
• then translation
• and much more

I guess some of my readers may have heard of google?

When I started teaching in the 80s I used to tell my students:

    Lisp is a great language; AI is all nonsense

Fact of the matter is that google uses AI everywhere and Lisp nowhere! Not only that it does it all in – gasp – C++!!
But then neither would it be where it is without the 50 years of prior AI research in Lisp-like languages

So...

For an individual to persist in error for over a 100 years somehow does not make much sense... we can say 'for his whole life', thats about it.

Yet the human race habitually persists in error for centuries and often millennia.

I (personally) find it hard to wrap my head round the combination of these two facts…

---

Footnotes:

[1] This is from memory. If someone can find and tell me the exact quote I will be much obliged!

[2] This list started with this exchange on the python list

[3] The Healthcare singularity and the age of Semantic Medicine
    from The Fourth Paradigm by Hey, Tansley and Tolle