Von Neumann's hall of mirrors
Much science done today studies nature by studying artificial models, but do you know how to tell them apart?
When I was a kid, I made a startling discovery. Whenever you faced two mirrors at each other, it opened a magical portal into an infinite corridor.
I could sit and stare down this blasphemous violation of the natural order for hours. Was anyone down there? Had some unlucky soul fallen in and become stuck in this non-world? What unimagined things could be lurking in wait to grab a nosy seven year old?
Turns out the infinite corridor is only an optical feedback loop, the visual equivalent of a screeching microphone held too close to a speaker. No wizards or extra-dimensional monstrosities here. You can explain it all with high school physics, which makes it bo-ring.
What I didn’t know at the time was how much science itself has come to resemble two mirrors facing each other. This was pointed out by real-life super-genius John von Neumann, who helped midwife the computing machines we know and love today. Back in the 1940s he identified out a critical flaw in the matrix which has had lasting and poorly-understood effects on the sciences ever since World War II.
A threshold of complexity
Von Neumann pointed out that with simple machines, it’s easier to say in words what the machine does than to physically build it.
As a machine grows beyond a critical threshold, its structure becomes simpler than a description of its behaviors. It’s infinitely simpler to say how to build such a thing than it is to create a model of its future behavior.
The simplest and most efficient way to describe the behavior of a complex system like the stock market, the local weather, or the human brain is to observe its behaviors in real time.
Since a great deal of science today depends on building abstract mathematical models of complex stuff, the complexity threshold creates a deep puzzle nobody’s sure how to solve.
What’s a model?
A model can be the thing that we build to represent an object, the way a model train is the model of a real-life locomotive.
A model can be the object represented by the man-made item, as when slender women on a runway act as the model for next year’s fashion trends.
Scientific model-builders aren’t always as clear as they could be about what is the model of a natural object and what is the model for their artificial model-building.
And sometimes, due to the problems in describing complex objects, they have to use a physical thing as a model of non-physical logical and mathematical models cooked up by scientists. Spooky.
… almost everything we know about the solutions to these equations [of fluid dynamics] we owe to experiments carried out on the physical systems themselves … now it is the natural object that serves as the model of the mathematical object, rather than the other way around.
Sciences that study complex things, such as living organisms and human mental activity, end up blurring the lines between “natural” and “artificial”.
And that’s a major problem for sciences that claim to study objective reality.
The model isn’t the object.
The whole point of building models is to simplify complexity. But, thanks to the sting in von Neumann’s tale, the model of a complex object doesn’t make it any simpler.
“A mathematical model describing a complex object is itself a complex object,” writes Jean-Pierre Dupuy. Instead of one complex system nobody can understand, you now have two complex systems nobody can understand—and no way to tell them apart.
In the case of a complex object, the mathematical model—an artificial object—loses its status as an instrument of mastery and control because no one knows how to solve the system of equations that constitutes it.
A complex model may have the real object as one of its models. But thanks to the new possibilities opened up by computer simulations, the man-made mathematical object can be treated as if it, too, were a natural object.
Only watching the actual history of behavior allows us to understand the complex object. So what happens when we have to depend on equally complex models to even know what we’re looking at?
In a great and hilarious irony, the self-referential models-modelling-models locates a good portion of modern science alongside the worst offenders of “postmodernism” and “poststructuralism”. There is no world, only symbols.
The more models are involved, even necessary for studying some features of nature, the less part nature plays.
Losing the world in the ideas
The ideal of science sold to us folk in the general public is one of objective studies of objective existence.
The real trend, meanwhile, concerns fooling around with computer simulations that have a vague and poorly-understood relationship to non-simulated objects.
The model, if it is to be faithful to what it represents, must also exceed this [complexity] threshold. But then it will be not only a model of its object but also a model of itself, or rather its own behavior.
If the prestige and authority of science rests on its mythology of describing and explaining The World As It Really Is, what’s left of that ambition in a game of models modelling models?
That thought can spiral off in dozens of directions. The angle I return to time and again concerns studies of mind and society. The supreme paradox is that scientific projects to naturalize the mind are headed by a discipline called artificial intelligence.
Ever since Warren McCulloch got it in his head to build an artificial neuron back in the 1940s, the sciences of mind have been inseparable from human constructions of logic and math. The fatty lump inside your skull is barely involved except as a source of numbers for crunching.
The attempt to restore mind to the natural world that gave birth to it ends up exiling the mind from the world and from nature.
Scientists and materialist philosophers mystify consciousness by kicking first-person subjective experience out of the material world. The alleged “mystery” of consciousness which so preoccupies the cog-sci people is a problem of their own making. They’re blind to this paradox they created, no longer able to tell us what or who did the kicking, despite their confidence that the kicking was done.
It’s like holding up one mirror to another. You get a pretty illusion of depth and distance, but there’s no there there.
In final twist, by showing that descriptions of complex behavior are infinitely more complex than an object’s structure, von Neumann also demonstrated how a brain or a computer could produce mental activities, while ruling out any option of fully explaining their behaviors. That key doctrine that the anti-Free Will determinists depend on is a bit of fantasy.1
The question for you to chew on: What’s left of a “science” trapped in this infinite corridor?
All quotes taken from On the Origins of Cognitive Science by Jean-Pierre Dupuy.
Thanks for reading.
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We’ll have to get into the guts of that claim another time. The short story is that certain results in formal logic, mathematics, and computation theory by Alfred Tarski, Kurt Godel, and Alan Turing in the 1930s proved convincingly that you can’t get semantics (content) from syntax (structure). Every “materialist” who tells you that atomic forces determine the behavior of life and thought has entirely missed this important detail.