Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes

The Model

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.

OK, so what is an appropriate minimal model for biology? My core idea here is to think of biological organisms as computational systems that develop by following simple underlying rules. These underlying rules in effect correspond to the genotype of the organism; the result of running them is in effect its phenotype. Cellular automata provide a convenient example of this kind of setup. Here’s an example involving cells with 3 possible colors; the rules are shown on the left, and the behavior they generate is shown on the right:

Note: Click any diagram to get Wolfram Language code to reproduce it.

We’re starting from a single () cell, and we see that from this “seed” a structure is grown—which in this case dies out after 51 steps. And in a sense it’s already remarkable that we can generate a structure that neither goes on forever nor dies out quickly—but instead manages to live (in this case) for exactly 51 steps. Continue reading

When Exactly Will the Eclipse Happen? A Multimillennium Tale of Computation

See also:
“Computing the Eclipse: Astronomy in the Wolfram Language” »

When Exactly Will the Eclipse Happen? A Multimillennium Tale of Computation

Updated and expanded from a post for the eclipse of August 21, 2017.

IWhen Exactly Will the Eclipse Happen? A Multimillennium Tale of Computation

Preparing for April 8, 2024

On April 8, 2024, there’s going to be a total eclipse of the Sun visible on a line across the US. But when exactly will the eclipse occur at a given location? Being able to predict astronomical events has historically been one of the great triumphs of exact science. But how well can it actually be done now?

The answer is well enough that even though the edge of totality moves at just over 1000 miles per hour, it’s possible to predict when it will arrive at a given location to within perhaps a second. And as a demonstration of this, for the total eclipse back in 2017 we created a website to let anyone enter their geo location (or address) and then immediately compute when the eclipse would reach them—as well as generate many pages of other information. Continue reading

Computing the Eclipse: Astronomy in the Wolfram Language

See also:
“When Exactly Will the Eclipse Happen? A Multimillennium Tale of Computation” »

When Exactly Will the Eclipse Happen? A Multimillennium Tale of Computation

Computing the Eclipse: Astronomy in the Wolfram Language

Basic Eclipse Computation

It’s taken millennia to get to the point where it’s possible to accurately compute eclipses. But now—as a tiny part of making “everything in the world” computable—computation about eclipses is just a built-in feature of the Wolfram Language.

The core function is SolarEclipse. By default, SolarEclipse tells us the time of the next solar eclipse from now:

Continue reading

Can AI Solve Science?

Can AI Solve Science?

Won’t AI Eventually Be Able to Do Everything?

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?

To this ultimate question we’re going to see that the answer is inevitably and firmly no. But that certainly doesn’t mean AI can’t importantly help the progress of science. At a very practical level, for example, LLMs provide a new kind of linguistic interface to the computational capabilities that we’ve spent so long building in the Wolfram Language. And through their knowledge of “conventional scientific wisdom” LLMs can often provide what amounts to very high-level “autocomplete” for filling in “conventional answers” or “conventional next steps” in scientific work. Continue reading

The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Version 14.0 of Wolfram Language and Mathematica is available immediately both on the desktop and in the cloud. See also more detailed information on Version 13.1, Version 13.2 and Version 13.3.

Building Something Greater and Greater… for 35 Years and Counting

Today we celebrate a new waypoint on our journey of nearly four decades with the release of Version 14.0 of Wolfram Language and Mathematica. Over the two years since we released Version 13.0 we’ve been steadily delivering the fruits of our research and development in .1 releases every six months. Today we’re aggregating these—and more—into Version 14.0.

It’s been more than 35 years now since we released Version 1.0. And all those years we’ve been continuing to build a taller and taller tower of capabilities, progressively expanding the scope of our vision and the breadth of our computational coverage of the world:

Number of built-in fuctions Continue reading

Observer Theory

The Concept of the Observer

We call it perception. We call it measurement. We call it analysis. But in the end it’s about how we take the world as it is, and derive from it the impression of it that we have in our minds.

We might have thought that we could do science “purely objectively” without any reference to observers or their nature. But what we’ve discovered particularly dramatically in our Physics Project is that the nature of us as observers is critical even in determining the most fundamental laws we attribute to the universe.

But what ultimately does an observer—say like us—do? And how can we make a theoretical framework for it? Much as we have a general model for the process of computation—instantiated by something like a Turing machine—we’d like to have a general model for the process of observation: a general “observer theory”. Continue reading

Aggregation and Tiling as Multicomputational Processes

Aggregation and Tiling as Multicomputational Processes

The Importance of Multiway Systems

It’s all about systems where there can in effect be many possible paths of history. In a typical standard computational system like a cellular automaton, there’s always just one path, defined by evolution from one state to the next. But in a multiway system, there can be many possible next states—and thus many possible paths of history. Multiway systems have a central role in our Physics Project, particularly in connection with quantum mechanics. But what’s now emerging is that multiway systems in fact serve as a quite general foundation for a whole new “multicomputational” paradigm for modeling.

My objective here is twofold. First, I want to use multiway systems as minimal models for growth processes based on aggregation and tiling. And second, I want to use this concrete application as a way to develop further intuition about multiway systems in general. Elsewhere I have explored multiway systems for strings, multiway systems based on numbers, multiway Turing machines, multiway combinators, multiway expression evaluation and multiway systems based on games and puzzles. But in studying multiway systems for aggregation and tiling, we’ll be dealing with something that is immediately more physical and tangible. Continue reading

How to Think Computationally about AI, the Universe and Everything

Transcript of a talk at TED AI on October 17, 2023, in San Francisco

Human language. Mathematics. Logic. These are all ways to formalize the world. And in our century there’s a new and yet more powerful one: computation.

And for nearly 50 years I’ve had the great privilege of building an ever taller tower of science and technology based on that idea of computation. And today I want to tell you some of what that’s led to.

There’s a lot to talk about—so I’m going to go quickly… sometimes with just a sentence summarizing what I’ve written a whole book about. Continue reading

Expression Evaluation and Fundamental Physics

Expression Evaluation and Fundamental Physics

An Unexpected Correspondence

Enter any expression and it’ll get evaluated:

And internally—say in the Wolfram Language—what’s going on is that the expression is progressively being transformed using all available rules until no more rules apply. Here the process can be represented like this:

We can think of the yellow boxes in this picture as corresponding to “evaluation events” that transform one “state of the expression” (represented by a blue box) to another, eventually reaching the “fixed point” 12.

And so far this may all seem very simple. But actually there are many surprisingly complicated and deep issues and questions. For example, to what extent can the evaluation events be applied in different orders, or in parallel? Does one always get the same answer? What about non-terminating sequences of events? And so on. Continue reading

Remembering Doug Lenat (1950–2023) and His Quest to Capture the World with Logic

Logic, Math and AI

In many ways the great quest of Doug Lenat’s life was an attempt to follow on directly from the work of Aristotle and Leibniz. For what Doug was fundamentally trying to do over the forty years he spent developing his CYC system was to use the framework of logic—in more or less the same form that Aristotle and Leibniz had it—to capture what happens in the world. It was a noble effort and an impressive example of long-term intellectual tenacity. And while I never managed to actually use CYC myself, I consider it a magnificent experiment—that if nothing else ultimately served to demonstrate the importance of building frameworks beyond logic alone in usefully representing and reasoning about the world. Continue reading