Measures of Awesomeness

Epistemic status: exploratory. I’m building out a model.  I know zero anthropology, so my speculations may very well be reinventing some wheel.

A visit to the anthropological wings of the Museum of Natural History can cure you of cultural relativism in a hurry. Some cultures, in some times and places, made cooler stuff than others.  In other words, the concept of “technology level” refers to a real thing.

In the context of looking at ancient pottery or metalwork, a casual museumgoer won’t see anything too strange about that assumption.  But there are a lot of uncertainties smuggled in.  How do we know that this pot is superior to that pot?  Doesn’t that depend on who you are and what you value?  When we look at an object and consider it “primitive”, does that mean anything besides mere cultural chauvinism?

Tech trees

One potential way to make the idea of “more advanced/less advanced” technology objective is to talk about a dependency graph.  If one technology is a prerequisite for another, then the “child” technology can be identified as “more advanced” than the “parent” technology. This concept has been referred to as fabricatory depth.  You need kiln-firing technology before you can produce glazed pottery; therefore kilns are a prerequisite for glazing, and glazing is more technologically advanced than kilns.  If you see people who can only make unglazed pottery and not glazed pottery, then, in that particular respect, those people are lower-tech than their glazing neighbors.

The computer game concept of a tech tree (really, it’s a tech DAG) is a simplified version of this concept. The “roots” of the tree are primitive technologies; applications and advancements on these technologies take you to higher levels of the “tech tree”, which in turn can lead to even higher levels.

This puts a partial ordering but not a total ordering on technologies. Not every pair of technologies is directly comparable.  Which means that it’s more nuanced than categories like “Stone Age” — it’s possible for Culture A to be more advanced than Culture B in one sector, but less advanced in some other sector. We’re not assuming that technologies line up in one single March of Progress; but we are noticing that some technologies are structurally, by necessity, more “foundational” or “basic” or “primitive” than others.

Thinking in terms of dependencies/prerequisites means we can talk about technology level while keeping some distance away from value judgments. Forget what’s more “useful” or “higher quality.”  A high-tech object is just an object that depends on a lot of accumulated technologies.  It’s an object that requires a long chain of skills to produce.

Note that this isn’t quite equivalent to a high degree of skill. It takes very high skill to hunt with a throwing stick. But probably not a long sequence of techniques, each of which produces many applications.  We don’t have to assume that a low degree of technological advancement implies a low degree of effort or intelligence; it just means that, for whatever reason, you don’t have a big stack of technologies that build on each other.

Prowess Metrics

If you stroll through the museum and ask yourself what makes “higher-quality” objects, you’ll notice some commonalities.

Usually, finer, more precise work is intuitively higher quality. Finer brushwork or filigree or carving, smoother carvings, finer textiles with tighter weave, straighter or more symmetrical shapes, etc.

Stronger and more durable objects tend to be higher quality.  Steel is harder than iron.  Glazing makes pottery water- and stain-resistant.

Highly replicable objects tend to be higher quality. Molds and casts and potter’s wheels allow identical objects to be produced with little effort.

More efficient objects tend to be higher quality. Structures that are lighter relative to their strength. Machines that consume less fuel or physical effort.

Bigger objects can be higher quality.  Buildings or sculptures or cities on a colossal scale.

These kinds of criteria are still relevant even in the modern day. The semiconductor industry runs on making finer, more precise circuits. Materials science continues to make glass, ceramics, and other substances stronger, more durable, and lighter.  The software and manufacturing industries run on making objects more replicable.  “Big data” refers to the technologies necessary for handling information at scale.

There seem to be some simple qualities like these which continue to be valued in technologies, over time and across industries.  I’ll call them prowess metrics, inspired by Venkat Rao’s discussion, because they’re usually related to excelling at a single property rather than being very well suited to a market niche.

Human wants are enormously varied; but certain inputs tend to be common among them. At the most elemental level, almost anything anyone could want will require things like mass and energy; therefore mass and energy are close to universally valuable.  Prowess metrics are capacities which permit a wide variety of applications.

As you go up a tech tree, producing technologies that are necessary for technologies that are necessary for technologies, the technologies that have a lot of descendants will tend to be high on prowess metrics.  If you develop a technique for very reliable duplication, or a stronger construction material, there are a lot of technologies that can be derived from it.  In fact, we can even define prowess metrics as the qualities that predict having a lot of descendants on the tech tree.  They are what make a technology “generative”, productive of new technology.  Prowess metrics might also be expected to correlate with being high on the tech tree, which makes sense if you picture a long-tailed distribution of technology — most “chains” peter out early, but if you’ve reached a certain level of technology, that means you’re more likely to continue going to yet more advanced technologies.

Being high on a prowess metric is no guarantee that an object will be useful.  Usefulness is defined by humans and the context in which the object would be used.  The fastest cars in the world are novelty items, because most people don’t actually need or want the fastest cars in the world.  Identifying the usefulness of an object to actual humans is the basic function of marketing, and prowess metrics can’t substitute for that.  Usefulness is about utility and value judgments and all that squishy stuff.

However, I hypothesize, prowess metrics are decent predictors of the utility of objects. If you have a way to make your widget faster, bigger, finer, stronger, lighter, cheaper, etc, it’s at least worth privileging the hypothesis that there’s going to be demand for it.

The Innovator’s Dilemma defines a disruptive innovation as one which satisfices on a bunch of the standard metrics, optimizes hard on a different metric, and finds a new market that really values this new metric. Usually, the examples given in the book of all the above metrics fit the pattern of prowess metrics; things like size, speed, cost, etc.  Which prowess metrics matter depends on the market and the use case. But that prowess metrics matter is not really disputed.

In engineering-focused domains like the excavator industry or the semiconductor industry, the technical performance of the machinery matters a lot to purchasers. As you move “up the tech tree” to higher-level applications and consumer-facing products, technical prowess becomes less obviously relevant, but still in some sense underlies what’s possible.  Computing power still ultimately determines limits on what software applications are available.

Prowess metrics seem to be behind intuitions that look like the labor theory of value.  A worthy or excellent object, you feel, gives you a lot of something you can measure: many tons of wheat, high tensile strength, etc.  Objects that are “merely” well adapted to their context and highly desirable to their users may be perceived as having “fake” or “superficial” value, as opposed to the “real” value captured by prowess metrics.  “I care about the fuel economy of my tractor, not what color it’s painted!”

From a conventional economic perspective, this is exactly backwards: the prowess metric is only a correlate, a proxy,  of the things that really matter, the supply and demand.  And it’s not even always a good proxy!  But it’s an understandable fallacy once you accept that prowess metrics are frequently good predictors of value.  Moreover, prowess metrics tend to indicate something like “downstream” value — they mean that future applications of the technology can go farther and likely be worth more.

This is the intuition behind “We wanted flying cars, instead we got 140 characters.” Getting better prowess metrics on basic technologies (as you’d need to, to build flying cars), is substantial because it tends to open the doors to a lot of future technology and future value. Getting good product-market fit on an app built from off-the-shelf parts is less valuable in the long term because it isn’t causally necessary for as much future innovation.  (Twitter’s not a great example of a non-technological “tech” company, but it’s easy to think of better ones.)

Obviously, a lot of this is influenced by glamour — modern logistics is arguably as big a technological advance as flying cars would have been — but there still may be a meaningful, semi-rigorous notion of a foundational rather than a trivial technological improvement, and it seems to have to do with prowess metrics and going to nodes that have a lot of descendants on the tech tree.


There’s an intuition that a civilization can have a certain amount of motive power or mana or ability to do stuff.  Thriving cultures are increasing it; declining cultures are stagnating or losing it. And of course trying to make this intuition rigorous is hard, and potentially impracticable. You can’t directly rank cultures on how awesome they are.

But an armchair-observer, outside-view perspective might point to a handful of prowess metrics (literacy rates, cost of a loaf of bread, etc) and try to use them to get a rough, multidimensional picture of “ok, how rich and powerful is this society really? How much mana is there here?”

Studying material culture in this way is how, for instance, Kenneth Pomeranz argued that China was richer than Europe until the 19th century.  The Chinese consistently consumed more calories and more meat, had more furniture in their homes, and even read more books, than the Europeans. Comparing the historical “GDP’s” of China and Europe is uncertain and subject to statistical shenanigans; but if the Chinese consistently seem to have more of all the necessities and luxuries of life, then it starts to seem undeniable that, for most definitions of “rich”, they were richer.

The “material culture” approach is pretty similar to the “look at a bunch of prowess metrics” approach.  You make no attempt to have a single metric of “intrinsic value”. You can only make pretty modest claims. You merely observe that if a culture seems to be booming along a lot of highly general and “upstream” metrics, then there’s probably something vaguely positive going on.  This is the heuristic behind the kinds of claims in The Great Stagnation — things like ‘maximum vehicular speed isn’t increasing’ or ‘life expectancy isn’t increasing.’  Taken together, a lot of stagnant metrics paint a dispiriting portrait.

With a tech-tree model, most of the dependencies are unobserved, including (of course) all the future ones.  It’s hard to work with empirically, and even if you did know the structure, it would be impossible to put a single number on “the tech level.” If we can talk about that kind of structure at all, it’ll be with simplifying models — things like prowess metrics that are shared across many technologies and correlate with technological advancement.  You still can’t say much objectively about “how much mana do we have?” — as always, there’s an irreducible element of selection and storytelling.  But this at least, I think, gives us a starting point to concretize the questions and hypotheses.

The Peril of the Sublime

The “sublime”, as defined by writers such as Burke, Kant, and Keats, is an experience of immensity and awe.  “THE PASSION caused by the great and sublime in nature, when those causes operate most powerfully, is astonishment; and astonishment is that state of the soul, in which all its motions are suspended, with some degree of horror.”  We experience the sublime when we see vast mountains, violent storms, towering pyramids, dazzling details of pattern,the infinity of space.

The standard psychedelic or religious experiences are classic examples of the sublime.  The impression of infinite hugeness or infinite smallness, the impression of endless fractal intricacy, the impression of infinite recursion, the impression of vast significance  — these are intimations of infinity.

Indeed, it may be appropriate to simply define the sublime as the subjective experience of infinity.

But what, concretely, is the experience of infinity?

I suspect that it is merely the experience of being unable to measure or count. A person can innately see one or two objects and recognize them as one or two, without counting; if you show her more than seven or so, her first perception is of “many”.  The experience of uncountable multiplicity is the experience of losing count. “And he brought him forth abroad, and said, Look now toward heaven, and tell the stars, if thou be able to number them: and he said unto him, So shall thy seed be.”  Our metaphor for impossibly many is the innumerable stars. We measure the size of infinities by trying (and failing) to put them into one-to-one correspondence with each other.  Countlessness provokes awe.

So, too, does scalelessness: when we cannot estimate size, we become dizzy with vastness, with smallness, with the scale-free multiplicity of fractals. Timelessness provokes awe, with thoughts of “eternity in a grain of sand.”  When something breaks our units of measure, when it appears to go beyond them, we experience that as infinity.

If you think of perception as working through convolutional neural nets, you notice that higher level nodes are averages or invariants over measurements — the same object, independent of position or rotation or color shift.  Allow the neural net to run its outputs into its inputs long enough, and you begin to see the kinds of images that show up in DeepDream — highly multiscale, intricately patterned.  Some of these higher-level invariants are, clearly, being activated very intensely if the network is allowed to “ruminate” on its own contents.

I might speculate that ordinary perception puts something like frames or limits on this kind of recursive rumination.  As an artist drawing a picture first sketches the proportions of the main objects, before filling in details, to make sure nothing is out of balance, in ordinary perception we put objects or ideas in proportion or in context with the rest of our world. They have a finite size, a particular place in time, a finite importance, and so on.  If this ability to gauge proportion is baffled or broken, we get the impression of infinity and sublimity.

The sublime naturally inspires worship. When something appears to be infinitely important, infinitely vast or complex, eternal or beyond time, how can we not ascribe it with huge significance?  We can easily claim that some particular sacred cow is not, in fact, sacred; but to deny the importance of the sublime is tantamount to saying sacredness itself is not sacred.  From the perspective of someone who has experienced raw barefaced wonder, an enemy of the sublime is a desecrator, a dirty vandal, trying to reduce us all to his level of prosaic blindness.

I am not a vandal. But I am a scientist by training. And so, I find myself in a complicated relationship with the sublime.

The danger of worshiping the sublime is that it can all too easily reduce to worshiping one’s own incapacity.  The sublime’s favorite phrase is “I can’t even.”  It is the inability to put things into context and perspective.  To be overwhelmed by a wildflower is a kind of elevated sensitivity and acuteness of observation; but if you can be overwhelmed by anything, then you have a failure to prioritize.  If you perceive “infinity” as simply beyond what you can measure or comprehend, then seeking a sense of infinity is seeking your own ignorance.  You find yourself looking backwards and inwards, towards childhood, towards faith, towards “unmediated” perception, trying to peel back the layers of ordinary reason towards something “beyond” the workaday world.

I suspect that this kind of a backwards mental move is a fundamental kind of error. I’ve done it myself, enough times to recognize the pattern. You remember experiencing something as awe-inspiring and mysterious; you want to recreate that experience; you try to come up with a rational structure that preserves that intuition of mystery, that delicious sublimity; and look! you find you have come to a dead end, and the facts force you to acknowledge failure.

The first and most canonical example of this pattern is trying to prove the existence of God.  I recognize a similar kind of flavor in trying to defend superrationality, trying to refuse the No-Free-Lunch theorem, and trying to argue against digital physics.  There’s a deep appeal in ideas that seem to cut through our finite, parochial, incremental limitations to something “beyond,” but I’ve frequently found those intuitions impossible to justify.

Beyondness is sublime; locality is mundane.  But “beyond” is not a place you can get to.  We always represent infinity in terms of the failure of the finite. “For every N, there exists an n such that a_n > N.”  In other words: every bound will break. This is a temptation towards falling in love with brokenness.

The danger is that in reaching for infinity, reaching for the sublime, you wind up committing a kind of self-harm. Stunting your actual, real-world powers; admitting frank impossibilities into your belief system; seeking not the universe’s bigness but your own smallness.

The universe really is vast and awe-inspiring — it is not an accident that Carl Sagan, our contemporary poet of transcendence, was an astronomer — but to experience awe at the genuinely vast, you have to actually be moving outward along with the scientists, claiming old territory as comprehensible and well-mapped even as you look toward uncharted skies.  There’s a robust, outward-facing experience of the sublime that is dual to the “stolid, prosaic” approach that treats the world as finite and moderate in importance; if you can be cool-headed and proportionate and realistic, you can take on grand adventures and explorations.