The thing I notice most in this model is this: the gap between opportunity and implementation used to take centuries and now takes years. Clearly, in the future it will take months, and then days. (Kurzweil was right?)
Maybe! Although see this: https://slatestarcodex.com/2019/04/22/1960-the-year-the-singularity-was-cancelled/
Yes and no.
Strictly speaking, every invention is taking more and more effort to realize. But there is increasing wealth to invest from the reinvestments from previous inventions and energy and information tech and having 8 billion humans many of them educated and so on.
And yes Kurzweil thinks the information tech, which already has led to huge speedups and improvements, with many advanced tools, will itself gain the competence that it will be like instead of 8 billion people available, with some tiny fraction of a percent performing innovation and R&D, most of them not coordinating with each other, it will scale to the equivalent of having all 8 billion people studying problems, coordinating near perfectly. Then 80 billion and 8 trillion and then the computational equivalent of having the biomass of every habitable planet in the galaxy working on R&D or something.
Some absurd explosion. But as the amount of intelligence rises, all the easier problems will be solved almost immediately and you would expect technology to very quickly advance to where the additional compute isn't helping, everything is gated by physical law. Every computer chip is computronium, every machine optimal nanotechnology, every solar panel near thermodynamic limits and so on.
So that "days" period might only last for, well, days.
Epistemic status: thinking out loud
My most-puzzling why-did-this-take-so-long example is the base-ten system for writing numbers, using zero*. Wikipedia tells me this was invented in India in the 7th century AD and spread gradually into Europe after that. But this seems to be millennia late. There were plenty of highly organised empires trying to administer everything from military logistics to tax systems to pyramid-building with Roman numerals or worse. See here for the Babylonian version, for example.
So far as I can tell, once you have writing and some basic concept of writing-down-numbers (I can't describe Roman numerals as mathematical notation), there are no further pre-requisites for the invention of zero. And the existence of the abacus, possibly invented as far back c2,700 BC, presumably helped. And yet, we have circa 3,400 years from inventing the abacus to figuring out how to write down a numerical system that actually made sense.
Why not?! Looking at your list of factors 1. Total number of researchers. 3,400 years times every civilisation across Eurasia that needed to administer a large polity or project. The number of person-hours of people calculating stuff must have been astronomical. 2. Speed of research. OK, this is before the printing press, but still. 3,400 years is an excessive delay. 3 size of opportunity. Just huge. 4 social barriers - I don't think many civilisation treated math as a controversial topic.
*It doesn't have to be base-10, a base-12 or -20 or whatever system would work fine too. Just not freaking Roman numerals!
I suspect it might have to do with (the representation of the thing) and (the thing) tending to blend together in people's minds. Once you've learned to read fluently, seeing a string of writing will make you think of the meaning of the words rather than the underlying letters. And especially someone who is only familiar with one writing system is likely to see things not as a property of the writing system, but as a property of the words themselves. So instead of thinking "this writing system makes this word hard to spell", they'll just think "this word is hard to spell".
In a similar way, I would expect the average person only familiar with Roman numerals to think not "our number system makes it hard to write down numbers efficiently", but just "it's hard to write down numbers efficiently". In order to realize that the difficulty is a property of number system, you first need the idea that it's possible for a number system to represent numbers more efficiently than you are currently doing, which is exactly the idea that you are missing if nobody has invented a better number system yet.
That explanation does still leave it a bit confusing why the abacus didn't work as an example of an alternative number system. The one thing that comes to mind is that the abacus is a device for doing calculations by physically manipulating the beads, while Roman numerals are something that you write down. There are a lot of mathematical equivalencies that seem obvious to us but needed to be explicitly learned - it's not immediately obvious to all children that 2 times 4 and 4 times 2 are the same thing, for instance. Likewise, if a culture doesn't have the abstract concept of "a representational system" yet, it may not be very obvious to them that an abacus and a system for writing down numbers have anything to do with each other. "They're different things for different purposes" may be the default thought.
East Asia used counting rods for calculation for thousands of years. Counting rods use true positional numeral system. It's just that East Asia didn't use it for writing. In other words, there were separate systems, one to calculate numbers which was efficient, and one to write numbers which was traditional. If that sounds weird, consider that we calculate in binary but write in decimal.
It is weird and it’s extra-weird that everywhere from Carthage to Greece to China failed to use an efficient system for writing numbers. It’s not like there was just one outlier which kept a traditional system.
And I wonder if the use of traditional systems for writing delayed the development of calculus and advanced mathematics too.
Would the combination of rifled musket + Minié ball been practical before the 19th century? It's really weird to me that nothing like it was used in the hundreds of years that muskets were used, not even something like the Foster slug, which significantly increases accuracy in smoothbore shotguns.
With long-distance signaling technology, it seems that the challenges were what we might call "cost per channel," "rate of transfer," and "information security."
With a fire or heliotrope network, other nearby light sources would interfere with the signal. So a large land area has to be dedicated to maintaining the communication channel, and somebody had to be watching for incoming signals at all times. It was also easy to interfere with messages, including by sending false messages. An expensive, slow, single-channel, insecure long-distance signaling network would have limited usefulness, and it wouldn't be too surprising to me that the ability to construct more detailed messages on this ultra-slow long-distance network was not a bottleneck for militaries winning battles or governments governing effectively. It seems like delegation was the name of the game, and in fact my impression is that modern militaries continue to focus on delegating authorities to troops on the ground rather than using top-down command and control decision making to the extent that modern communications technologies would theoretically allow.
The advantage of the telegraph and telephone was that messages could be sent faster, with greater security, with the ability to triangulate conversations between specific users, and with far less expense per channel.
So your market-based explanation works nicely here.
Could you explain this please? "In the 1600s it was still frowned upon to create labor-saving devices." 😁
In the records of the society from the 1680s we find evidence of interest in the earliest steam engines and most important, the society was receptive at the time to what was to become a socially revolutionary argument. The fellows discussed the notion that mechanical devices could, and indeed should, save labor, in effect decrease rather than increase employment. At the time of those discussions it was extremely difficult to get a patent from the government for any device if its inventor argued that it would save labor. Indeed until the late 1720s patents may have been rejected if an applicant argued such a case. Yet in the minds of Restoration natural philosophers associated with the Royal Society we can find a mentality discernibly industrial in the modern meaning of that term and, most important, an eagerness to promote their vision of industrial progress whatever the immediate and, from the government's point of view, undesirable social consequences.
Margaret Jacob, Scientific Culture and the Making of the Industrial West
My first highly popular essay was “Why did we wait so long for the bicycle?” I’ve asked the same question of the cotton gin and the threshing machine. Others have asked it of the steam engine and the wheel. Recently Brian Potter asked it about wind power and Anton Howes about semaphore signaling systems. See more examples here.
When asking these questions, we should think about when the question even needs an answer. That is, “why did it take so long” is only interesting if it took an abnormally long amount of time.
Here’s my model for this.
First, an invention is not going to happen at all if (1) it’s not technically possible or (2) there’s no market for it.
Gate (1), technical possibility, could include, for example:
Gate (2), the market, is whether it can be done commercially at a price that anyone will pay. If someone does make an invention there is no market for, it doesn’t go anywhere, and we might not even hear about it, because it is unlikely to make the history books. In any case, it wouldn’t affect the world, because it wouldn’t get distribution, and so it wouldn’t be historically relevant for our purposes. You see examples of this from time to time, such as the Korean movable-type printing press that predated Gutenberg.
Note that the bar inventions have to meet is not just a proof of concept: they have to be sufficiently powerful, efficient, and reliable to be of practical use. Early computing machines were too slow; early threshing machines broke down too frequently; early light bulbs burned out too quickly. These are technically interesting prototypes, but not true inventions. An invention does not merely demonstrate a concept, it solves a problem—the whole problem, not just a part of it, even if it is the most visible or obvious part. An invention has to be practical. (See more discussion of this here.)
Once something is technically possible and economically viable, then the clock starts ticking on how long we “waited” for it. But invention is a human process, and it’s not instantaneous. There is no perfectly efficient market in which an invention springs to life immediately as soon as it’s viable. It takes time, effort, trial and error. People have to decide to do something—they have to get the idea, and be sufficiently inspired and motivated to devote full-time efforts to something unknown, with an indefinite timeline and uncertain rewards. (Only a minority of people even have the temperament for this; in this sense, I agree with Anton Howes that innovation is not simply “in human nature.”) Then they have to get free to do it: at any given time, most inventors will be busy with projects, and only a subset will be looking for something new to do. They may have to acquire resources or recruit help, which takes time. Once they finally get to work, they have to experiment with approaches, discard failures, get new ideas, iterate.
Given the nature of that process, there are several factors that affect the time that elapses before an invention. I have written about many of them before in the context of “flywheels of progress.” Here are some that I would call out specifically regarding the invention process:
You can think about this by analogy to stochastic processes in thermodynamics: the exact path of any given molecule is random, but in aggregate there are predictable patterns, and they are determined in part by macro-level factors such as temperature and pressure. You could think of total amount of R&D effort as like the temperature of a system, and the market size as a kind of pressure in a particular direction. Or in an electronic analogy, speed of communication is like conductivity in a material, a large market is like a high voltage differential, and social strictures are a kind of resistance. (These are rough analogies, not mathematical isomorphisms.)
Given all that, it’s not surprising to me if we “waited” many years for a recent invention, or several decades in the 18th or 19th centuries, or centuries in the period before that. For instance, all of the following seem normal to me:
That’s just how long these things take.
It’s also not too surprising when we wait a long time for something that doesn’t have a billion-dollar market (or the equivalent in the past). I don’t really think we need to scour for explanations or wrack our brains over why it took “so long” to get wheels on suitcases, or role-playing games. These are niches.
And just for the record, I’m no longer surprised by the bicycle, either. I think that case is fairly well explained by materials and manufacturing techniques, overall market size, and the other general factors listed above.
For a while, I was surprised that flag-based naval messaging systems were not in use until the late 1700s. It’s a very simple technology, with a strong, obvious need not only economically but militarily. But after Anton’s recent essay, I think there is much less to explain: telescopes needed to be carried on ships in order to see the details of flags in the distance, and that starts the clock much later.
In fact, I can’t immediately come up with an invention gap that isn’t explained by this model.
Does this render irrelevant the factor of fundamental philosophical attitudes towards progress—the idea of progress itself, and whether it is possible and desirable? No, quite the contrary: the belief in progress affects most if not all of the factors above. A society that believes in progress will encourage its best and brightest to become scientists and inventors, set up networks of communication for them (from the Republic of Letters to arXiv), establish institutions for them to work in, provide plentiful funding for them, and drop its moral strictures against various forms of progress—indeed, there will be honor and acclaim for progress and those who make it.
I hope this model can simplify and condense the discussions and debates about “why did we wait so long.”