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Chapter Five – The Reality of Abstractions

In this chapter Deutsch makes me reconsider reductionism – sort of. He also makes me reconsider, and ultimately change my mind, on science and morality. Before I get to those, though, I want to discuss how Deutsch shakes me up about the nature of knowledge.

Consider Newton’s vision of gravity. Newton essentially explained Kepler’s Laws by providing a mechanism, the gravitational force operating by the inverse square law. It was a great advance in knowledge – we now had an explanation with enormous reach, an explanation that showed why Kepler’s Laws worked for the Solar System, for the Moon-Earth system, for the Galilean satellites, and in fact for the galaxy itself.

But then Einstein improved Newton’s explanation with his own explanation, General Relativity. In the new explanation, gravity was no longer a force. But wait, was it ever a force? If Newton was wrong after Einstein, surely he was wrong before Einstein, too. As Deutsch points out, this sort of evidence was used to argue that science never actually adds to our knowledge, because new theories wipe out the old ones. If Einstein’s curved spacetime does away with Newton’s gravity, then Newton’s gravity was never there in the first place.

But this is wrong, and here’s why: “it is true that something real (the curvature of spacetime), caused by the Sun, has a strength that varies approximately according to Newton’s inverse square law.” (p 108) Much else was also true in Newton’s theory – or at least approached the truth. Compared to what came before it, Newton’s theory was “more right.”

“Wherever (a theory) made true predictions this was because it had expressed some truth about reality.” (p 108)

Deutsch again states quite plainly why explanations are so crucial to science. “(I)n order to make progress in any field, it is the explanations in existing theories, not the predictions, that have to be creatively varied in order to conjecture the next theory.” (p 109).

So better explanations always approach the truth, but of course never get there. We’re always at the beginning of infinity. The next explanation will correct some of the errors of the previous theory, but it will also preserve the truth inherent in the previous theory. Remember, there are lots of ways to be wrong, but only one way to be right. Therefore, any explanation that correctly models some portion of the real world must have some element of truth to it. It is that element that will be preserved in the next, better, but still infinitely far from perfect, explanation.

Before this discussion, though, Deutsch goes after reductionism. As a committed reductionist, I of course at first reacted angrily. But a closer listening and reading of the section on reductionism convinced me of two things:

1) I’m not really a reductionist, not in Deutsch’s sense (and neither is anyone else who’s given it any thought).

2) He has a very good point.

First, Deutsch says this:

“The behavior of high-level physical quantities consists of nothing but the behavior of their low-level constituents with most of the details ignored.” (p 109)

This is all I’ve ever meant when I say I’m a reductionist. Stop there, and we already agree. But Deutsch’s real beef with reductionists is over the meaning and importance of explanation. As Deutsch points out, good explanations don’t have to be at a low level. His description of Douglass Hofstadter’s domino computer is an effective example. The explanation of the computer is meaningless on a physical level. It only takes on meaning when we understand the point of the program, which is to determine whether or not a number is prime. As Deutsch points out, there’s nothing in nature that insists on good explanations being reductive, and in fact he can show me many (like the domino example) that are not reductive and yet are still good explanations. I can’t argue with that. But, as I said, I’m happy to define my reductionism solely in terms of Deutsch’s first sentence. That’s all it really needs to mean, because this sentence, all by itself, does away with supernatural explanations. That’s all I really was after.

More shocking than the lesson on reductionism is Deutsch’s convincing argument that science is not mute on morality. Of course it isn’t, how could I have ever been so blind? I’ll use the question of race as an example. Before Deutsch, I was convinced that we couldn’t use scientific truth about race to inform our morality. The reason seemed straightforward. Scientific conclusions are always tentative. What if scientific truth changes? Does that mean our morality changes, too?

For instance, scientific consensus says that all humans derive from common ancestors who lived in Africa around 200,000 years ago. What if we discover that this is incorrect, that in fact human races really are genetically separate. Is racism then ok? Of course not!

Here’s where I was wrong. Humans are all people. We’re all universal explainers. We’ve all made the jump to universality. This makes us unique entities, well deserving by any sensible measure of equal treatment as stakeholders in humanity. If this weren’t true (and it might not be if, for instance, we found a living group of australopithecines, or even Homo erectus), we’d need, without question, to reexamine our attitudes about human rights. Morality is absolutely informed by factual knowledge, and if factual knowledge changes, then it is absolutely sensible that morality might (even must) change, as well.

But none of this, of course, is the point of Chapter Five. Instead, Deutsch is trying to convince readers that abstractions are real. He succeeds, but it’s an interesting sort of success. Consider Newton and Einstein again. In Newton’s time, the force Newton called gravity was real, because it was part of the best explanation existent at the time. But Einstein’s better formulation showed that the force Newton called gravity wasn’t real at all. It no longer played a role in our best explanation, and so had to be abandoned. In the same way, any explanation that is replaced by a better one also changes what is real (at least, real to us).

This begins to give a hint at the power Deutsch sees in explanation. Reality is defined by our best explanations. If something, including an abstraction like gravity or curved spacetime, appears in our best explanation, it is real. If it doesn’t appear there, it’s not real. Reality is always changing as our knowledge increases – but how could it be otherwise? For, as Deutsch here so vividly points out, we define reality – and, as the subtitle of the book claims, transform the world – through our explanations.


I found out on Monday that Ray Morrow had passed away. I can’t say that I knew Ray well, but news of his death hit me hard. Ray was a commenter on this blog on occasion, and I loved his frequent e-mails about the wonders and silliness of the “Internets”. Ray was already a COSI icon when I started there in 1993, and I remember fondly his “bat boy” poster and his positive and rational outlook toward work and life. I think back to little snippets of conversation we had – the overblown West Nile Virus scare, the oral poetry of the Harry Potter books, the abilities of Carl Sagan and Joseph Campbell to find wonder in rationality. The world is a poorer place today for Ray’s absence. My sympathies go out to his family, and to those who knew him best. I wish I had been one of them.

Chapter Four – Creation

The brilliant insight in this chapter comes on page 91, when Deutsch makes the following statement:

“Neo-Darwinism does not refer, at its fundamental level, to anything biological.” (p 91)

Knowing that Deutsch is a quantum computer physicist, this statement is perhaps not all that surprising. Dawkins has said similar things when talking about simulating biological evolution in computers, or when thinking about more abstract replicators. But Deutsch made the concept very clear to me when he talked about what makes neo-Darwinism such an excellent (hard to vary) explanation. It’s not what you might think.

Deutsch quotes Haldane again, who said that disproof of evolution would be “rabbits in Cambrian strata.” But this is incorrect. Deutsch tells a convincing story of how rabbit-like creatures might be found fossilized in Cambrian-aged rocks. Such a find would totally change our view of the evolution of life on this planet. But that doesn’t disprove neo-Darwinism. Neo-Darwinism isn’t about the story of life on this planet, nor is it about the biological machinery that makes life possible. Instead, neo-Darwinism is about the creation of knowledge.

Don't get all excited; it's a hoax.

It’s quite a remarkable statement. There are only two ways we know of to create knowledge in the universe. One is through the mechanism of biological evolution (knowledge creation applied to biology). The other is through conjecture, criticism, and testing done by people – the search for good explanations.

So what would disprove neo-Darwinism? Now that we know what neo-Darwinism is, the answer is ridiculously simple. Any example of knowledge that did not evolve and did not come from a person would do the trick. Here are Deutsch’s examples:

– the observation of exclusively or mainly favorable mutations (refuting the idea that variation is random)

– new, complex adaptations that suddenly appear (refuting the mechanism of knowledge creation via selection of favorable random variants)

– complex adaptations that have survival value today, but not in the past (the example Deutsch gives is the ability to hibernate based on internet weather reports)

What all of these point out is how simple neo-Darwinism really is, and how easily it might be refuted if it were wrong. There are only two ways to create knowledge. Either it evolved, or else it was created by people through conjecture, criticism, and knowledge. Find knowledge that could not have come from either, and you have disproven neo-Darwinism. Brilliant!

One crucial point here, and I may as well bring it up now. Supernatural explanations are ruled out. Why? They are always bad explanations. The reason is simple. Any supernatural explanation is infinitely easy to vary. “God did it” says exactly nothing about how it was done. Did God intervene? Then He’s not supernatural, and we can investigate the evidence and find a good explanation. Did God not intervene? Then He could have had no effect. Supernatural explanations are always bad.

Chapter Three – The Spark

This long and varied chapter has so much material it could be a book itself, and it almost is. The chapter centers on two misconceptions, called The Principle of Mediocrity and Spaceship Earth.

I love the discussion of the Spaceship Earth misconception. I’ve been bothered for a long time about the almost mystical reverence people seem to hold for the environment. The reality is that nature is harsh. Unless we save ourselves, the environment will eventually wipe our species from the universe. This is exactly what has happened to the overwhelming majority of species that have ever arisen on the planet. To believe that we are somehow different, unless we make ourselves different, is magical, wishful thinking.

On the other hand, Deutsch’s attack on the Principle of Mediocrity originally left me cold. No, I’m not so concerned with the idea that our place in the universe is special. Sure it’s special. We live on a rare planet in a rare solar system. We live in gravitational and magnetic fields that are both rare and unique. We live near a stable, solitary star in a system with stable, circular orbits. There’s lots about our situation that is far from typical. Of course we’re special. If we weren’t, we wouldn’t be here.

What actually got me was Deutsch’s swipe at Richard Dawkins – specifically Dawkins’ idea that, since our brains evolved in a particular environment for particular purposes, there’s no intrinsic reason to suppose that we should be able to understand everything about the universe. In JBS Haldane’s phrase, “The universe is not only queerer than we suppose, it is queerer than we can suppose.”

Our brains, in this view, are no different from our thumbs, our stomachs, or our eyes. They are parochial adaptations to our environment. But Deutsch makes the convincing argument that this cannot be the case. I think he’s convinced me, and I suspect that he might even convince Dawkins were the two to discuss it.

His argument comes down to this. We know that all possible transformations of material in the universe come in two classes:

1) Those transformations forbidden by the laws of physics – for instance, an object at location “a” cannot move to location “b,” one light year from “a,” in less than one year.

2) Those transformations not forbidden by the laws of physics – for instance, moving an object from “a” to “b” in one year or greater. Any such transformation requires only the knowledge to make it happen. If the transformation wasn’t possible, then there would be a law of physics preventing the transformation.

Note that Deutsch doesn’t claim that humans won’t gain more knowledge. Far from it. Instead, he says that we already have the ability to gather all the knowledge available. In other words, any other people (defined as universal explainers, and therefore universal constructors) we might ever encounter (or build, as in artificial intelligence) will be like us. While they might well have knowledge that we lack, they won’t be qualitatively different kinds of thinkers.

I’m still struggling with this idea. Wouldn’t any advanced race naturally believe that they’d advanced as far as there was to go? But Deutsch’s argument is very subtle. He’s not saying we’ve advanced as far as we can (or will), only that in order to keep advancing we don’t need any ability that we don’t already have. We are already universal explainers, and all universal explainers must be the same.

Deutsch then uses some of his most inspirational language to show the true power of explanatory knowledge. Just one example is supernovae. We observe supernovae all through the universe, and we have very good explanations of how and why they happen. But these explanations make a tacit assumption that there aren’t intelligent beings out there, making transformations that alter the rate of supernovae. Only intelligent beings could do so, and since anything not ruled impossible by the laws of physics must be possible given the right knowledge, it must be possible to alter the rate of supernovae explosions. We could alter that rate. We could alter anything about the universe that we choose to alter. We could be the spark that causes the universe to behave in a new way. If it isn’t impossible, then with the right knowledge we could choose to make it so.

Chapter Two – Closer to Reality

In this small and deceptively simple chapter Deutsch tells the story of looking at stars and galaxies on a photographic plate. When he wonders about one particularly hard-to-classify smudge on one plate, he is told that it is neither a star nor a galaxy, but just an imperfection in the photographic emulsion.

But of course, all the images on the plate are made of the same stuff. Why is one a galaxy and the other just a mistake? Deutsch here reinforces the idea that all observations are theory-laden. There is nothing particularly remarkable about a smudge on a photographic plate. Only by applying the correct theory does the wonder come out. This is an image of a galaxy, hundreds of billions of stars all found millions of light-years away. Without theory to explain it to us, they’re all just smudges.

Good explanations open the world to our sense of wonder. A rock can be just a rock, or it can be the result of hundreds of millions of years of geologic processes, an artifact from our planet’s past. Maybe it contains a fossil, but fossils themselves only become meaningful when placed into context by a good explanation.

At COSI we have a cloud chamber. In looking inside the cloud chamber, one can see either little puffs of smoke, or through a good explanation one can see pieces of atoms flying apart, powered by the energy of radioactive decay, first stored in a supernova explosion billions of years in the past. That’s the sense of wonder that a good explanation can bring.

Chapter One – The Reach of Explanations

What is science? One can hem and haw over a definition that tries to capture all the varied facets of science. But because of Deutsch’s book I have an answer that is at once elegant and simple, and yet also makes a strong statement about the world.

Science is the search for good explanations.

So what are good explanations, and how do we search for them? A good explanation is one that fits all the known facts, and is also (and this is the crux of Deutsch’s book-long argument) hard to vary. A bad explanation, by contrast, might account for the facts, but it is easy to vary, and this is its downfall. Myths and other supernatural tales are easy to vary, because the details of the myth are only superficially linked to the explanation. This makes them, always, bad explanations. Not because they get the facts wrong. One can always alter a bad explanation to fit new facts because a bad explanation is easy to vary. And this is what makes it bad.

By contrast, a good explanation has nowhere to go if facts contradict it. Because the explanation is hard to vary, if a fact comes along that doesn’t fit the explanation, then the explanation is wrong – or at best, incomplete. In this way, good explanations can become bad, because they no longer fit the facts. But bad explanations can never go the other way until they themselves change to become hard to vary.

Where do these explanations come from? They arise from the human mind. We take experience, imagination, snippets of other explanations that have worked elsewhere, stir them around, and come up with an idea, a conjecture. We then criticize the conjecture, molding and shaping it until it fits all the known evidence. If we are creating good explanations, we also mold and shape the explanation in another way, linking the explanation to the evidence in such a way that the explanation becomes hard to vary.

And then something amazing happens. For some, though not all, good explanations, a new property arises. That property is reach. Some good explanations will reach beyond the narrow set of phenomena they were designed to explain. They will explain phenomena that may have seemed unrelated. They might even make predictions about phenomena that have not been observed. Some very few explanations (Newton’s and Einstein’s explanations of gravity are two examples) will have “universal reach.” These explanation will stretch not just far beyond their initial application, but infinitely far.

It is this unexpected reach of good explanations that makes progress possible. And it is this idea that Deutsch will explore through the rest of the book.

I really never thought this would happen. I’ve been affected by many books in my life, many ideas. My intellectual heroes have included, among others, Carl Sagan, Richard Feynman, Joseph Campbell, and most recently Brian Greene. But now I’ve read a book that has forever changed the way I see the world. Upon my first reading, many of the ideas made me angry – I disagreed with them vehemently. But then I thought more, and realized I didn’t disagree at all. In fact, in many cases the writer was correct, and I had been wrong all this time. Other parts I didn’t grasp completely. I’ve read or listened to every part of the book at least four times now, and I’ve gotten more and more from it each time. Of course, there is still much I haven’t grasped. I’m just at the beginning. And that’s an amazing place to be.

Did you think I was talking about the Bible? The Quran? No. The book is “The Beginning of Infinity” by David Deutsch. I was attracted to the book mostly by its subtitle, “Explanations that Transform the World.” As a science educator, I want to know about explanations. I want better explanations. I was curious to find out how they might “transform the world.” Oddly, I was also attracted by the title by the word “infinity” for exactly the opposite reason. I didn’t believe in infinity when I started reading. I didn’t see how infinity could actually exist in the world. Now I am beginning (just beginning) to grasp it. That’s only one of the transformations I went through in reading this remarkable book.

Over the next three weeks I’ll be posting my thoughts on each of the eighteen chapters of this book, around one new chapter each day. I hope the journey for you captures a bit of the wonder I experienced in my own journey through this astounding book – uplifting, frustrating, confusing, enlightening, and, ultimately, forever transforming. Enjoy!

My first book, called The Turtle and the Universe, was published by Prometheus Books in July 2008. You can read about it by clicking on the link above.
My second book, Atoms and Eve, is available as an e-book at Barnes and Noble. Click the link above. You can download the free nook e-reader by clicking the link below.
November 2011
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A blog by Stephen Whitt

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