A Hundred Millennia From Now

[ecosophia]

I need a little help from my readers for a fiction project in the early conceptual changes.

I'm trying to find accurate information about the enduring legacies of modern industrial civilization. Assume that our civilization circles through the normal cycle of decline and fall. Assume that ordinary history continues for the next hundred thousand years or so. Assume that ordinary ecological and climatic cycles, perturbed by our current mess, return to normal in a reasonable period of time and persist for that same very long period. What traces will remain of the earth's first global technic civilization?

What I would like, if any of my readers can point me to this, are some easily accessible written sources by geologists and other people literate in the earth sciences which address this. Yes, I'm beginning to draft a story set in the far future; no, it's not going to be the fake future of so much bad science fiction, in which today's mental and cultural habits remain frozen in place across the ages while technotrinkets lurch into ever more elaborately predictable forms. We never went to the stars, nor did alien space bats ever come to visit us; life has continued to evolve; today's industrial society, the legendary First Technate, is a dim presence long since fallen out of mythology, and recalled only in fragmentary surviving records from less prodigiously ancient societies.

Oh, and there's a new ice age on, though the glaciers are slowly beginning to retreat. Fun times!

If any of you have scientifically based sources to suggest for the long-term destinies of our mines and freeways, dams and tunnels, landfills and miscellaneous waste, I'm all ears.

Comments

[walt_f]

See MONIAC, and also the Russian Water Integrator machines from the 1930s. The mathematics is basically differential and integral calculus, but the devices run cases instead of trying to solve the integrals symbolically. A differential is an instantaneous rate of change (such as a flow rate, that might be changing over time, at a specific moment) and an integral is the cumulative change in a fund/reservoir over some period of time.

This is the same mathematics as most scientific computing today, though. Consider weather modeling. It's all about analog flows (of air, water, heat, etc.) The calculations are done digitally on discrete numbers as a way of approximating the results of the simultaneous interdependent flows defined by the differential equations. This reduces the precision of the results, but analog computers also have limited precision for different reasons. (And the main reason Tuesday's weather forecast is wrong isn't either of those limitations, it's insufficiency and inaccuracy of the current-weather data being fed in.)

[(Anonymous)]

There's a few working MONIACs in the world, including one just up the road from me in Wellington, New Zealand, in the bottom of the Reserve Bank Museum. Bill Phillips of Phillips Curve fame (or infamy) was an NZ economist and invented them.

[ecosophia]

I had both of these in mind. I wonder, though, if a civilization starting from very different ideas about the cosmos might come up with its own wholly different math along these lines.

[walt_f]

I see what you're getting at, but it might just be too difficult to imagine from our perspective, or outright impossible. Mathematicians after all have spent a lot of time developing all kinds of different forms of mathematics. I can see having very different mathematical curricula and very different preferred technological applications, but imagining them resulting in pure math methods very different from what we know is beyond me. (If it weren't... well, think how publishable wholly different math would be!)

If flows or rates-of-change instead of counting was the starting point of your mathematics curriculum, then calculus (perhaps starting with Newton's fluxions) would come much earlier on. But as soon as you want to compare the magnitude of one flow with another (or, equivalently, measure a flow), that's a discrete number. (Or do I only assume that because of ingrained habits of thought? Either way, I can't think of another comparison that's more generally useful, or simpler.) So discrete numbers might not seem inherent in the concept of flows, kind of like how zero or negative numbers might not seem inherent in the concept of counting, but as with zero and negatives you'd run into them before you go past the elementary school level. Going farther, the distinction between integers, rationals, and irrationals might only be of interest in specialist branches. (Today, you don't need to know the difference between rational and irrational numbers, or set theory or what prime numbers are, to do e.g. weather modeling or rocket science.)

If you don't have arithmetic early in your curriculum, and hence widespread, you're going to be developing a lot of analog computation tools instead. How do you buy potatoes at a market? Your currency could be rods instead of coins, valued by length and material; the price is another length that's displayed and is also a setting for the levers-and-cams machine that cuts your rod to the right amount for the price, the deflection of the scale, and the value rate of the particular type of rod you're paying with. In your advanced civilization the value could be an inverse logarithmic function of the length of the rod (twice as long is 10x the value, perhaps) with the devices designed accordingly, and people looking back on the days of primitive linear cash. The use of a general-purpose slide rule would be associated with technical folk, not because of the use of nonlinear analog scales (familiar to all) but to the unusual process of using numbers to set the scale and read the result.

[(Anonymous)]

The potential hydraulic computers you described could be coupled with perturbation methods. I think the emphasis is going to be a lot more on manual simplification than computing, but that's just a guess.

[(Anonymous)]

*Ordinary* differential equations in an analog computer are fine, as long as you have dedicated circuit elements for each variable.

I think contemporary digital computer calculations of *partial* differential equations (which is what you'd need for e.g. weather) rely heavily on random-access memory and the fact that digital memory cells can have their state preserved while being accessed. The machine reads a stencil of adjacent binary numerical values, passes them to the ALU/FPU in some pattern, writes the resulting binary-rounded-off numerical calculated update somewhere, and then slides the stencil over and repeats the process for the next spatial/temporal location. If you tried to do that in a hydraulic computer, then every time a memory cell was read, it would have to be restored, presumably with local circuitry that might gradually go off-spec in a different way than its neighbors. This restoration process would be noisy, the more so the smaller the reservoir in the cell, and that trades off against how easy the cell would be to write. The access path to each cell would also be a potential source of irregularities; it would have to work like the old telephone system with relay-switched connections.

(Maybe you wouldn't have to drain a little of a storage element to read it, if you had some levers connected to a flexible membrane that measured the pressure in the element, like how the middle ear works. Though that might lead to other accuracy problems in amplifying the lever position to a pressure value to send elsewhere in the system.)

It might be easier to do partial differential equations with mass-production of parallel circuit elements, organized in a grid. But that's a lot more expensive, both in manufacture and maintenance, for hydraulic parts than electronic ones. Also the grid geometry wouldn't be easily changed; if you had a simulation region that didn't geometrically correspond to the grid, normally you'd have to just switch off some of the elements as being outside the simulated region. Since the access patterns are more consistent and over better-matched timescales, gradual drift in stored values should be easier to engineer around. At some added expense, you could conceivably even do some tricks with fast-Fourier-transform hard-wired butterfly calculation patterns to go back and forth between space-domain representations and frequency-domain representations, to get a hybrid spectral method, say for simulating systems with a fast-equilibrating more-linear component (e.g. pressure in liquid flows) and a slow less-linear one (e.g. transport of liquid momentum).

Again, this is expensive. The U.S. Army Corps of Engineers built a 320'x400' hydrological scale model of the San Francisco Bay and nearby watersheds in 1957 to test some dam proposals:

https://en.wikipedia.org/wiki/U.S._Army_Corps_of_Engineers_Bay_Model

That must have been cheaper than the analog computers that could have been built at the time, even with electronic components.

Similarly to the Bay Model, rarely solid-state physicists have a quantum phenomenon they want to study that's expensive to calculate, but that they can measure by doing experiments on a sort of scale model in a mathematically isomorphic quantum system that's more feasible to manufacture and measure. In one case, I think this even involved using a holographic principle to pass between a two-dimensional quantum system and a three-dimensional one.

Then there are *stochastic* differential equations:

About ten years ago, there was a startup called Vicarious that was trying to use massively parallel cheaply-manufactured and unreliable circuit elements to do cheap Monte Carlo stochastic sampling of scenarios, such as one might use to get probability distributions from stochastic differential equations. I'm not sure the idea really made sense. Like, if you get a bunch of cheaply made shopping carts whose wheels have carefully-tuned wobblinesses, and run them down a gentle slope, to sample from a Gaussian distribution of total wheel wobbles for where the carts end up (from left to right) when they hit the ditch downslope, you'll get a misleading answer. Some of the shopping carts are still going to pull consistently left on top of their wobbles, and some are going to consistently pull right. If you assume that the wobbliness was all that was happening, you'll end up thinking wobbliness is more powerful than it is. On the other hand, if the distribution of wheel leanings matches the distribution of overarching tendencies in the phenomenon you're trying to statistically predict with cheap shopping carts, then I guess you're golden.

But then, for most problems of interest, the metaphorical shopping carts would still be complex enough that they'd be kind of expensive, either to make or to run up and down the slope, absent electronics, some very specialized biotechnology, or some kind of clever mass-production technique I haven't thought of.

I guess I could imagine a civilization whose ideas of scientific computation were about that kind of matching properties with systems that could be more easily manufactured. A more abstract version of that would be the "new kind of science" that Stephen Wolfram was pointing toward with his book.

[deborah_bender]

Thank you for explaining differential and integral calculus so clearly and concisely. One of the great regrets of my life is that I did not take calculus in high school. To make up the ground later, I would have had to review algebra and trigonometry first.