[#18] Singularities as Hints, Unrelated to Reality

[#18]  Singularities as Hints, Unrelated to Reality

By Piet Hut

Predictions of technological singularities are as wrong as predictions of singularities in physics, which have always been the harbingers of new physics.  When any prediction leads to division by zero, we can be sure that new laws or regularities will set in.  What singularities are good for is providing hints that we are on the brink of discovering some kind of new knowledge, but it doesn't tell us anything more than that.

A spherical sheep

In physics, we like to start with oversimplifying.  There is the joke about a physicist being asked to study a cow, starting off with a "spherical cow" as a first approximation.  And there is nothing wrong with that, as long as we are ready to add more detail later, when and where needed.

In fact, it would be overkill to start with a model that would be too detailed.  And a good way to make sure that you are not wasting your time in running a simulation or doing a calculation with too much detail, is to see how far you can simplify a model before it stops being realistic.  You are likely to have read a quote ascribed to Einstein, along the lines of "everything should be made as simple as possible, but not simpler", which is exactly the right attitude of a physicist  (but see the quote investigator for a critical tracing of the history of this quote).

In my career in interdisciplinary studies, the greatest contrast in ways of thinking that I encountered has been that between physicists and biologists.  For whatever historical reasons, biologists tend to refuse even to discuss models of the type that physicists like to start with.

I have been in many a bewildering brainstorming session, in which the following scenario played out, after an initial discussion.  A physicist in the group walks up to the blackboard and draws a simple stick figure with only a few lines and one or at most two arrows.  Then a biologist walks up, and fills the rest of the blackboard with a plethora of lines and curves and arrows of different types and thickness. When they then look at each other's drawings, supposedly illustrating the same topic under discussion, they realize that they effectively live in separate universes.

When asked, biologists will tell you that physicists tend to oversimplify, leaving out essential features, while physicists will tell you that biologists thicken the plot unnecessarily. Both can be right, depending on the context, and what is more, depending on one's willingness to adjust an initial model, when it is seen to be inadequate.

A good historical example is the birth of quantum mechanics. When it became clear that an atom consists of a positively charged nucleus, surrounded by negatively charged electrons, the first model that was proposed took its cue from the way that planets orbit the sun.  However, a quick calculation showed that electrons circulating a positively charged atomic nucleus would emit electromagnetic radiation, thereby losing energy.  As a result, electrons would crash into the nucleus in a very short time, far less than a second.

In that simplest model, both the nucleus and the electrons were represented as point particles.  Mathematically, the model predicts the formation of a singularity, with an infinitely short distance between nucleus and electrons, and an infinitely strong attraction between them.

It was immediately clear that this model was wrong, and nobody was talking about "atoms as singularities" as a realistic prediction.  That would have been absurd.  Instead, over a period of a few decades, with great efforts of the best minds in physics, quantum theory was established, in which a more accurate description was offered, without the original singularities.

Half a century later, when the existence of black holes was predicted and indeed observationally confirmed, physicists talked about the "singularity in the center of a black hole".  The reason for this was that the best available theory of gravity, general relativity, predicts a point-like center of mass with infinite density to lurk in the center of a black hole, hidden by an event horizon, further out, as the point of no return for an infalling observer.

“‘’singularity’’ as a matter of speech”

Of course, physicists know that the word "singularity" is just a matter of speech, shorthand for "the as yet unknown inner core of a black hole that in first approximation seems to show a singularity, but that in a future, more accurate, replacement of general relativity will turn out to not be singular".  However, since it would be very clumsy to repeat such a sentence over and over again, physicists are happy to talk about singularities, as long as the real meaning is understood: a pointer to an as yet unknown new theory.

“physicists are often misunderstood”

The problem here is that, by using that language, physicists are often misunderstood as implying the physical existence of mathematical infinities.  And that in turn invites a similarly wrong usage in other areas.

A glaring example of a misunderstanding of the nature of singularities is the talk about technology running into a singularity some time this century (predictions vary).  Yes, it is true that in various areas of technology we have seen exponential growth, sometimes for a surprising long time (Moore's law is the archetypical example).  But no, you cannot extrapolate such exponentials beyond their range of validity (even Moore's law is now saturating).

A recent antidote to the habit of taking mathematical singularities at face value is an insightful and sobering recent article written by Rodney Brooks, who shook up the world of robotics in the early eighties by coming up with a completely new architecture for building robots, inspired by the behavior of insects.  I first met Rodney more than twenty years ago, during one of my visits to MIT, and I was immediately struck by his deeply philosophical approach to anything that he built.  In addition, he clearly had fun in his work and his life, as caught in the movie made around that time, "Fast, Cheap and Out of Control".

The article I was referring to appeared first on his blog and soon afterwards, slightly rewritten, in a magazine.  If you don't have time to go through the whole article, I especially recommend reading his thought experiment of time-teleporting Isaac Newton to the present, and handing him an iPhone, in his second deadly sin, "Imagining magic".

Piet Hut is President of YHouse (where this blog is hosted), Professor of Astrophysics and Head of the Program in Interdisciplinary Studies at the Institute for Advanced Study in Princeton, and a Principal Investigator and Councilor of the Earth-Life Science Institute in the Tokyo Institute of Technology.