The Singularity

You may have heard of it: the idea that as science and technology advance, the rate at which technological progress increases will itself increase. In other words, as computers get cheaper, Internet connections speed up, research methods improve, and better engineering technologies are developed, we will be in a better position to further reduce the cost of computers , increase connection speeds, generate research at an even higher volume, and improve production rates. This gives rise to an exponential increase which eventually happens so quickly that predictions about what life-changing invention will come along even as soon as next week will be impossible; life itself will have changed beyond imagining. This hypothetical event is described as the technological singularity. The most outspoken proponents of the idea are probably Ray Kurtzweil and Vernor Vinge, an inventor and a science fiction author.

A rough timeline for innovation throughout the ages. Both the technologies chosen and the vertical axis are subjective; I focused particularly on engineering applications and gadgetry.
A rough timeline for innovation throughout the ages. Both the technologies chosen and the vertical axis are subjective; I focused particularly on engineering applications and gadgetry.

And the idea is easily recognizable as science fiction; a what if proposition about technology and the future. On the other hand, the reasoning behind the singularity is a straightforward extrapolation of trends that have been in effect for the length of human history. In the last 100 years we have seen more technological revolutions than in the 1000 years before that, which in turn have seen more game-changing technologies arise than the 10000 years before that. All we have to do is keep drawing the curve and we can see that before long things will be going too fast to keep up with. Kurtzweil puts that date at around 2045, so… some of you may want to reconsider your life insurance policies.

Or maybe not. Because I can think of three very good reasons to doubt why things will work out this way; in this post I’ll concentrate on just one.


Reason 1: Problems with the graphical approach

The graphical approach is a good one, in that it gives more information than we would have without it. It isn’t a good one in the sense that it always returns accurate results. The graphical approach works better when dealing with a simple or sell-understood system, in areas where higher-order terms are known to have a negligible impact on the outcome. Unfortunately the world and its technological output isn’t a simple system; rather, it has the characteristics of a chaotic one, where subtle changes in initial states can have drastic implications for later states. And not only can slight changes in initial states change the outcome, but often the hidden existence of higher-order terms means that the rules change as a system enters a new regime.

Diverging Series
Two polynomial functions follow indistinguishable trajectories up to x = 1.3, diverging thereafter.

But wait, there’s more: The graph we’re using may be wrong to begin with. Technophiles and futurists may not be terribly interested in history, so it’s easy to see why they might think of progress as slow but steadily increasing in speed. In fact, it hasn’t been as slow as is generally believed. For instance, we can consider:

Ancient Egypt. The Egyptians had key-locks, water clocks, cement, and glass jars. They were also able to manufacture the colossal pyramids to a level of precision that has been described as uncanny, indicating a technological sophistication that cannot currently be gauged.

Ancient China. I mentioned gunpowder above. But the Chinese also had flame throwers, automatic crossbows, and deadly chemical warfare (in the form of bellows, mustard smoke, and lime) before the time of Christ. Less exciting, but arguably much more life-changing inventions, included paper and the compass. Likewise, the Han dynasty’s public education and standardized examinations for selecting civil servants shouldn’t be ignored.

Classical Antiquity. Public education was also a common feature of Greek city-states. Although they are well known for the invention of simple machines, archaeologists have also recovered the antikythera mechanism, an analog computer capable of predicting astronomical phenomena before the time of Christ. The Romans also had high quality cement, aqueducts capable of transporting water hundreds of miles, and possibly even some form of germ theory. There is also good reason to believe that they had effective herbal birth control.

Prehistoric Europe. That Stonehenge served astrological functions has long been known, although the methods for its construction remain mysterious. Even more mysterious is the evidence of brain surgery from healed skulls, evidently with a high survival rate.

What is most telling about these innovations is that many of them disappeared, sometimes for thousands of years, before rediscovery. Europeans during the high middle ages did not have the technological prowess to build pyramids to Egyptian standards, nor elegant astronomical devices like the Antikytheria mechanism, nor paper,  or standardized examinations, nor germ theory, public education, nor even concrete for a Roman-style aqueduct. Given the spotty archaeological record, it is likely that:

  1. We don’t know everything the ancients knew, and,
  2. The possibility exists that we may not even have rediscovered everything that has been forgotten. (This isn’t mere speculation; if the ancients really did have effective birth control, the recent development of the contraceptive pill represents an example of a lost technology that was only very recently rediscovered.)

So progress to this point has not been at all smooth. The fall of Egyptian, Mayan, Babylonian, and Classical civilizations, each time with an attendant loss of information (such as the ruined Library of Alexandria) points to a halting, jagged, increase in knowledge, sometimes characterized by rapid improvements and other times decline and stagnation.

Technology No Singularity
An alternative timeline for innovation throughout the ages, taking information losses into account. Both the technologies chosen and the vertical axis remain subjective; also, some technologies may have appeared at an earlier date than shown. Readers may decide for themselves which of the two graphs seems more accurate.

It would be foolish to debate the fact that we are currently on a technological upswing. Yet some commentators (e.g. Charles Murray) have argued that for the last half-century the rate of increase is no longer increasing, but declining. Even considering the graph at the top of this post, which focuses on Industrial and modern technology at the expense of many earlier discoveries, it is hard to miss the widening time gap between discoveries over the past fifty years. When the Atlantic compiled their list of the 50 Greatest Breakthroughs Since the Wheel, sixteen were introduced from 1900 to the 1970’s, but no technologies of the past 40 years made their list. I chose mobile technology to represent the most recent advance, but its overall impact may not be very high, particularly when compared with inventions such as writing or the transistor.

So the graphical approach, even insofar as it can be relied on to provide an accurate forecast, doesn’t indicate a clear, exponential trend, rising with increasing steepness. Instead what we see is a bumpy graph that rises by fits and starts, with many seemingly “new” technologies having their origins in antiquity, and a slight leveling off over the past forty years.

This is enough for now; next time I’ll look at the issue from another perspective, considering the feasibility of making the discoveries we’d need to see for a singularity to occur.

4 thoughts on “The Singularity”

  1. Yes, the discovery of these little lost bits of technology gives rise to speculation about what hasn’t been rediscovered yet. Tales of Atlantis, or “alien” technology may actually have genuine seeds of truth to them. The fact that so much information was lost during some of the darker ages of civilization means that coming up with precise technological levels for the more ancient civilizations may not be as easy as most experts would have us assume.

    For instance, historians bend over backwards to explain how the ancient Egyptians could possibly have built the pyramids with the rudimentary technologies that they are presumed to have had. I have heard modern engineers claim that they themselves would have difficulty creating the pyramids with the tools that they have available today.

    But what could this mean? To me it seems that either the level of their intelligence must have been so high as to give rise to the ability to use crude technology to build highly technical structures, or more likely, using the principle of Occam’s Razor, simply raising the assumed level of their technology to accommodate the building of the pyramids would be the only reasonable explanations. If either of those conditions aren’t met to some extent or the other, then how can it be explained that the highly educated, computer driven science and minds of today, can’t explain adequately how they did it? Unless we really do want to posit that Anubis granted them 3 gifts.

    1. Which historians bend over backwards to explain how the Egyptians stacked up a bunch of rock? That these rocks were so carefully aligned with the Earth’s rotation does seem interesting, yes, but what exactly about the pyramids should make us think they would be difficult for us to build today?

      1. “Which historians bend over backwards to explain how the Egyptians stacked up a bunch of rock?”
        All of them really It’s their job after all, and some of them spend their lives in the process. Commendable, but I imagine it might make them a bit obstinate when someone comes in and tries to shake up their lives work. Indeed, there is still no agreed upon theory as to how the Egyptians managed it. I personally think that Jean-Pierre Houdin’s “internal ramp” hypothesis, is the most promising, and if you combine it with the cement block theory it seems even more probable.
        “That these rocks were so carefully aligned with the Earth’s rotation does seem interesting, yes, but what exactly about the pyramids should make us think they would be difficult for us to build today?”

        First off, I just want to point out that I am not proposing that building them with modern technology would be impossible. I’m fairly confident that it could be done given enough time and money. I’ll also point out preemptively that I don’t believe aliens came down and gifted the Egyptians with their pyramids either. There is quite a bit of evidence in the form of the failed and collapsed pyramids of the area that show a steady progression in human pyramid building technology. The difficulty I have, is believing that their technology was nothing more than sleds, wedges, and picks.

        Here is a link to what I consider an interesting documentary:
        It has some pretty far fetched conclusions, but that being said, the path they take to get there is pretty interesting, and indeed they raise some valid questions that beg some kind of explanation. I found the interviews with the engineers and scientists enlightening.

        You may call the pyramids no more than a great pile of rocks, but in truth they are massive, very well thought out piles of rock that have withstood earthquakes, weathering, and looting for centuries (really I’m talking mainly of the great pyramid here).

        The sheer mass of the stones (20-80 tons), transported at such distances(500 miles), and then up, up, up 40 stories high, is really amazing all by itself. Then factor in the fact that there were 2 to 2.8 million of the stones, and they were put together with enough finesse to withstand not only their own weight, but also to stand the test of time. And let’s not forget precision. From what I understand, the 13 acre plateau that is the great pyramids base, was leveled with the precision of modern instruments, and the passageways that are cut through the rock of the pyramid are also cut with similar straightness and accuracy, and like the structure itself, line up with various astronomical features. Not an easy task with just hand tools and no room for error.
        Another interesting fact is that the pyramid is actually 8 sided, which can only visually be seen for only a few seconds on the equinox.

        Dare I to mention as well that all of this is estimated to have been achieved in 20 years! In order to do that, they needed to carve out, and move over 2 million giant stone blocks over 500 miles, and place them with high precision and skill too. Even assuming an uninterrupted supply line, you’d need to average at least 1 block, placed, mortared, and finished every 5 minutes, round the clock, over that 20 year period. Yikes, talk about a logistical nightmare!

        Could it be done? Well it’s possible. Here are a couple of modern massive construction projects that the above movie references just as a comparison though:
        Abu simbel temple project 1963-1973 – the reconstruction and quarrying of a temple made of some 2200 blocks some weighing 30 tons using modern trucks and equiptment. It took 5 years.
        Clay Quarri in Forges les Bains, Essonne, France: The size of the great pyramid, it took 12 years to do nothing but fill it with rubble.

        I’ll also add…
        White House 1792 – 8yrs
        Hoover Dam 1831– 5 yrs
        Panama Canal – 33 yrs
        Golden Gate Bridge 1933– 5 yrs
        Twin Towers 1966– 4 yrs

        Wouldn’t it be so much simpler though to posit if not more advanced tools, at least some extra time?! I suppose though that most everyone would agree that when it comes to Ancient Egypt… there’s a little something missing to the picture.

        1. I didn’t look at the documentary you posted yet, but I’ll say that nothing you’ve pointed out looks truly impossible for the level of technology they are known to have. I don’t mind positing technologies beyond those that are commonly accepted—and I think crediting Romans with germ theory went a bit out on a limb—but I don’t see that the fast construction times or precision really *necessitate* unknown Egyptian technology.

          Still, seems to corroborate your claim that the Great Pyramid of Giza was built quickly, with an (apparently unsourced) claim that “the pyramid was built as a tomb over a 10 to 20-year period concluding around 2560 BC.” That’s remarkably fast for people working with hand tools, and I agree that, if true, such a finding is definitely suggestive of missing technology in the archeological record.

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