Monday 14 September 2020

Poetry: The Non-linear Mathematics of History

Posted by Chengde Chen *

Things are so obvious, why can’t we see them?
We are still obsessed with developing technology
as if we wished to hasten our extinction
This is because history is deceptive
We have no understanding of the mathematics of history
hence are immersed in a linear perception of ‘progress’:
history has proved that man controls technology
so technology must do more good than harm
This has been our experience of thousands of years
thus our unshakable faith and confidence

We, of course, need to rely on history
which seems to be the only thing we have
Yet, history is not a piece of repeatable music
but more of non-linear mathematics
Some histories may be mirrors of futures
while some futures have no reflection of history at all

It is hard to establish such a non-linear understanding
as it’s so different from our intuition
Thanks to the difficulty, as a famous tale relates
Dahir, an Indian wise-man of 3000 years ago
almost made the King bankrupt his Kingdom!

One day, the chess-loving King challenged Dahir
by asking him to play the final phase of a losing battle
As it seemed impossible for anyone to turn the table
the King promised Dahir smugly:
‘If you can win, I’ll meet you a request of any kind!’
Dahir, with his superior intelligence, did win
but he only made a very small request:
‘I would like to have some grain
placed on the chessboard in the following way:
one for the first square
two for the second square
four for the third square
and so on and so forth
so that each square is twice that of the previous one
until all sixty four squares of the chessboard are placed’

What an insignificant request, the King thought
and approved it immediately
He ordered his soldiers to bring in a sack of grain
and to place them in the way requested
When one sack was finished, another was served
Then another, and another…
until they exhausted all the grain in the Kingdom
it was still far from completing the 64 squares
The grains required are such astronomical quantity that
even the amount of grain in today’s world
does not come near it (over 1000 billion tonnes)!
It was the modest figures of the early counting
as well as the linear intuition about ‘history’
that made the King miscalculate the matter completely
He is still in debt to Dahir to this day!

Technological progress is the kind of exponential curve
but it is even more deceptive
It had crawled very slowly for very long in ancient times
but rose quicker and quicker in recent centuries
People, however, have considered the change linearly
assuming the rate of growth the same as the past
Hence a common-sense conviction:
we have always progressed through technology
so through it we can always progress into the future
technology has always become more and more advanced
so with it we can always be more and more powerful

Oh, the linear thinking of progress!
History is not optics
nor is the future a mirror image of the past

In the past man was a small member of the club of nature
while today, we have changed the weather, raised oceans
and created new species, as well as new forms of energy
If we cannot see such a world of difference
we are as miscalculating as the old King was!

We cannot, however, afford to miscalculate
as we would have no time even to be surprised
The surface value of history is its usefulness
The deeper value of history is to prove itself useless

The history in which we controlled technology
was only history, no matter how brilliant it was
The future may mean a ruthless breaking away from it!

Editor's note. The amount required is 2 raised to the power of 64 minus one. Wikipedia offers that the total number of grains is eighteen quintillion, four hundred and forty-six quadrillion seven hundred and forty-four trillion seventy-three billion seven hundred and nine million five hundred and fifty-one thousand six hundred and fifteen (18,446,744,073,709,551,615) and that this is “about 2,000 times annual world production”. 
* Chengde Chen is the author of the philosophical poems collection: Five Themes of Today, Open Gate Press, London. He can be contacted on


Martin Cohen said...

Chengde's poem reminds me of Einstein's famous warning in the wake of the use of the first atomic bomb. A lot of Einstein quotes are made up, but the Bulletin of Atomic Scientists seems pretty convincing on this one:

"In May 1946, The New York Times reported that Albert Einstein had sent a telegram appeal to several hundred prominent Americans, asking for contributions to a fund “to let the people know that a new type of thinking is essential” in the atomic age. Einstein wrote in his telegram: “The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe.”

Keith said...

Yes, Chengde, the doubling of grains from square to square on the chessboard has always been a fun lesson in exponential growth, and of the boggling number that quickly results, catching unsuspecting people off-guard. I enjoyed revisiting the story. I would offer that there’s a modern example of such sobering growth, but with vastly more-dire consequences than that of the tale of Dahir: the early threat of exponential (nonlinear) growth in the number of infections of the coronavirus, if mitigation measures were to prove anemic. The numbers of infections reported around the world at the starting gate were disarmingly small — until they very quickly no longer were.

Chengde Chen said...

Thanks Keith, that's very true!

Thomas O. Scarborough said...

Earlier this year, I had an exchange with Holmes Rolston III. Our ideas differed fundamentally on one point. He felt that we have tools which are powerful enough to address the problems. I felt that we do not.

It is in the very nature of our knowledge today to exclude the whole. In 1973, the philosophers Wilhelm Kamlah and Paul Lorenzen debated whether our knowledge is in itself deficient, and they came to the conclusion yes, it is. They wrote, 'We pay a heavy price above all for the very progress of knowledge itself.'

We do not know the limits of our knowledge. 'Knowledge, wrote Confucius, is to know both what one knows, and what one does not know.' Or as the poet John Dryden wrote, 'How can the less the greater comprehend? Or finite reason reach infinity?'

Martin Cohen said...

"He felt that we have tools which are powerful enough to address the problems. I felt that we do not. "

What tools? What problems?

Martin Cohen said...

Maybe I should say "which" problems... Presumably the 'environment' in some regard…

Thomas O. Scarborough said...

Thank you, Martin. Chengde refers to technological progress, and our belief that it 'must do more good than harm'. He suggests, however, that we may be 'in the final phase of a losing battle', and alludes to things we have introduced to the world, presumably negative: the climate, sea level rise, and so on. '... we are as miscalculating as the old King was!'

I picked up on Chengde's thought that 'we have always progressed through technology so through it we can always progress into the future'. This was my debate with Rolston. He said that 'we cannot understand everything about complex natural systems'. However, 'we are quite capable of understanding enough ...' We have the tools at our disposal.

But it is our very understanding which has brought us to this point, and will continue to take us down this road, until it is game over. Chengde appears to be saying that we are doing something we were not designed for, '... it’s so different from our intuition'. He may also be saying that we can override our intuition.

In short, I see that Chengde is speaking of runaway 'externalities' in a philosophical sense. Neither our minds nor our tools are big enough to assess these externalities or to cope with them. Unfortunately Chengde's poem, while it contains (I think) a sound perspective, is a whistling in the wind, until we understand precisely what we are doing. If we can. We have had dire warnings since the 1960s at least.

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