Time and Hard Sums

I’ve been thinking recently that maybe there’s an elegant way of describing Time simply as difficulty. Mathematicians now have a charmingly naive term, “hardness,” for describing the relative knottiness of a calculation problem. If asked to give an explanation to a layperson, they will often say something like: “Well, suppose you had a perfect computer. A hard problem takes it more time to solve than an easy one.” If you have a problem like the “traveling salesman” puzzle–given n cities, how do you figure out the shortest route by which he can visit all of them–it’s really easy if you have three or even five cities, but if you have a few hundred, no computer in the universe, using the fastest theoretical algorithm, could solve it in less than a billion years, by which time the salesman would long ago have moldered into atoms. These algorithms are called “NP hard.” There are even more difficult problems still, ones that ask, for instance, whether it is possible to prove whether or not a given problem has an algorithm to solve it at all–i.e. problems that can only be solved by the emergence of as-yet-undiscovered further problems that will require unimaginable algorithms of the future if they are to be solved.

If we describe the universe as a computational system–and the fact that all science expresses its conclusions in numerical terms strongly suggests that science “votes with its feet” for that hypothesis–then we can see all entities in the universe as the workings of problem-solving algorithms. The ones that are easily solved have been solved already and have stopped, and constitute the eternal constants of physics that are true at every instant through all time, like the instantaneous coexistence of the probabilistic quantum world described by David Bohm. The ones that are a bit harder but still solvable are the deterministic processes in nature that Newtonian science describes. The ones left over constitute the whole world of change and becoming, ranging from chemical reactions through self-cloning living organisms to ourselves, arranged in a nice pyramid of emergent temporal features as described by the great philosopher J. T. Fraser.

If time is a river, there would be nothing to indicate the passage of time unless some parts of the river were flowing faster than other parts. “Hardness” gives us a nice way of measuring which ones are faster and which ones are slower.

Here’s a nice thought-experiment to prove this idea. The increase of entropy (thermal disorder) is usually recognized by physicists as a reliable marker of the passage of time. Thermal disorder is what we call heat. If I am right, a large amount of local computation should be the same thing as a large amount of local time; and a large amount of time should be correlated with an increase of heat. If you are using a laptop, and it’s actually on your lap, you can feel the heat of computation generating time on your thighs.


A Brilliant Ramshackle Redemptive Book

I’m reading Michael Strong’s BE THE SOLUTION. It’s co-written with the most exciting entrepreneurial thinkers around, like Muhammad Yunus of the Grameen Bank, John Mackey the CEO of Whole Foods, Hernando de Soto the visionary Peruvian advocate of property rights, and others. I don’t usually like how-to books, and this is a how-to book about the whole world’s economy and is insanely ambitious. But this book has the goods. It’s popping with good ideas about do-gooder business, entrepreneurial education, free enterprise zones, prediction markets, microfinance, the rule of law, and poverty. The book blows the usual Left-Right, Conservative-Liberal divide right out of the water, and it has all the audacity of hope. Obama should read it. He’d like it, I think.


Chi and Quantum Gravity

This week I gave a paper at a conference on “Translating China” at the Confucius Institute center at my university, the University of Texas at Dallas. Helped by my wise assistant on these matters, Daisy Guo, I read a few of my translations of the great Tang Dynasty poets.

One of the themes of the conference turned out to be Chinese metaphysics–if that’s the right word. If it means what Aristotle meant, that is, “further reflections on physics (the study of the productive and reproductive process of nature)”, then it could accurately describe this branch of Chinese philosophy. But if it means “the study of the supernatural (that which is not part of nature and temporal processes)”–the usual “Western” meaning–then it would be the wrong word.

Recent developments in cosmological physics implying that if the universe is made of anything, it’s not made basically of matter or static “stuff” but of dynamic feedback, seem to confirm the ancient Chinese (and Heraclitean) notion of harmonic change–CHI–as the origin and foundation of all things. Poetic form is the way feedback is generated in language–if you rhyme and keep to a metrical form, every word affects every other word. Classical Chinese poetry has many such rules, and so it naturally expresses chi. Here are a couple of the poems.

*Farewell, Upon Passing Mount Jin Men
Li Bai (701-762)

And now at length I’ve passed beyond Jin Men
On my adventure to the land of Chu.
The mountains end, the flatlands open out,
The Yangtze meets the vast plains and pours through.

The moon is flung upon its heavenly mirror,
The clouds grow mirages of towers and sea;
But still I love the waters of my homeland
That travel with my boat a thousand li.

A Song of Liang Zhou
Wang Zhihuan (688-744)

The Yellow River climbs away
to far white clouds and sky;
A lonely outpost fortress lies
in mountains ten miles high.

Qiang flute, why must you take to heart
the “Willow” song, alas?
You know the spring wind never blows
across the Yu Men pass.