Institute Output
What If We Had Bigger Brains? Imagining Minds beyond Ours
Stephen Wolfram
We humans have perhaps 100 billion neurons in our brains. But what if we had many more? Or what if the AIs we built effectively had many more? What kinds of things might then become possible? At 100 billion neurons, we know, for example, that compositional language of the kind we humans use is possible. At the 100 million or so neurons of a cat, it doesn’t seem to be. But what would become possible with 100 trillion neurons? And is it even something we could imagine understanding?
What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?
Stephen Wolfram
Things are invented. Things are discovered. And somehow there’s an arc of progress that’s formed. But are there what amount to “laws of innovation” that govern that arc of progress?
There are some exponential and other laws that purport to at least measure overall quantitative aspects of progress (number of transistors on a chip; number of papers published in a year; etc.). But what about all the disparate innovations that make up the arc of progress? Do we have a systematic way to study those?
Towards a Computational Formalization for Foundations of Medicine
Stephen Wolfram
As it’s practiced today, medicine is almost always about particulars: “this has gone wrong; this is how to fix it”. But might it also be possible to talk about medicine in a more general, more abstract way—and perhaps to create a framework in which one can study its essential features without engaging with all of its details?
Who Can Understand the Proof? A Window on Formalized Mathematics
Stephen Wolfram
For more than a century people had wondered how simple the axioms of logic (Boolean algebra) could be. On January 29, 2000, I found the answer—and made the surprising discovery that they could be about twice as simple as anyone knew. (I also showed that what I found was the simplest possible.)
On the Nature of Time
Stephen Wolfram
Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.
Foundations of Biological Evolution: More Results & More Surprises
Stephen Wolfram
A few months ago I introduced an extremely simple “adaptive cellular automaton” model that seems to do remarkably well at capturing the essence of what’s happening in biological evolution. But over the past few months I’ve come to realize that the model is actually even richer and deeper than I’d imagined. And here I’m going to describe some of what I’ve now figured out about the model—and about the often-surprising things it implies for the foundations of biological evolution.
Nestedly Recursive Functions
Stephen Wolfram
Integers. Addition. Subtraction. Maybe multiplication. Surely that’s not enough to be able to generate any serious complexity. In the early 1980s I had made the very surprising discovery that very simple programs based on cellular automata could generate great complexity. But how widespread was this phenomenon?
What’s Really Going On in Machine Learning? Some Minimal Models
Stephen Wolfram
It’s surprising how little is known about the foundations of machine learning. Yes, from an engineering point of view, an immense amount has been figured out about how to build neural nets that do all kinds of impressive and sometimes almost magical things. But at a fundamental level we still don’t really know why neural nets “work”—and we don’t have any kind of “scientific big picture” of what’s going on inside them.
Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes
Stephen Wolfram
Why does biological evolution work? And, for that matter, why does machine learning work? Both are examples of adaptive processes that surprise us with what they manage to achieve. So what’s the essence of what’s going on? I’m going to concentrate here on biological evolution, though much of what I’ll discuss is also relevant to machine learning—but I’ll plan to explore that in more detail elsewhere.
Can AI Solve Science?
Stephen Wolfram
Particularly given its recent surprise successes, there’s a somewhat widespread belief that eventually AI will be able to “do everything”, or at least everything we currently do. So what about science? Over the centuries we humans have made incremental progress, gradually building up what’s now essentially the single largest intellectual edifice of our civilization. But despite all our efforts, there are still all sorts of scientific questions that remain. So can AI now come in and just solve all of them?