by Steve Talbott

In "The Limits of Predictability" I tried to show the great distance between understanding a certain lawfulness inherent in events and predicting or explaining the events themselves. Contrary to all current thinking within science, the more uncompromisingly we formulate the precise and determining action of a physical law, the less it tells us about the events it governs. We gain more and more exactness about less and less of the world's concrete expression.

I illustrated this by describing what happens when we release a leaf in a vacuum chamber. The leaf now "drops like a rock". That is, we get a trajectory that seems to be little more than the graphic display of a mathematical expression we call the "law of gravity". To see an event in this way as a mathematical necessity made visible gives us a powerful sense of explanation.

But -- and this was the decisive point -- if we restrict ourselves to the sphere of our mathematical explanation and do not smuggle in qualitative aspects of the phenomenon lying outside the explanation, then we no longer even know whether we're dealing with a leaf or rock! The explanation, in its own terms and despite all its precision, gives us no means to distinguish between the two. We highlight a law equally implicit in both leafy and rocky phenomena by sacrificing everything distinctive in those phenomena to the single, implicit aspect we are looking for.

Truth and Artifice

The experiment is both legitimate and valuable. But perhaps we should explore what it obscures -- namely, the concrete and distinctive reality of the leaf -- as well as what it clarifies through the graphic depiction of a law abstracted from that reality. What is the relation between the gain and the loss?

But the issue is even more serious than this question suggests. After all, when we do look at the fuller reality of our experimental truth -- and thereby recognize, for example, that we are dealing with a leaf rather than a rock -- we see that the experiment introduced a false note: leaves never behave that way in nature. They could not do so and still be leaves. We have obtained the skeletal truth of our quantitative law not only by scraping the flesh off the phenomenon we are observing, but by replacing it with artificial flesh.

If it is important to preserve the truth of the experiment, it is equally important to acknowledge and correct the artificiality. The correction will require us to accept the observable world's lawfulness as it is actually given to us rather than as we have learned to think of it. That is, we will have to accept a lawfulness inherent in, or implicit in, or expressed by full-fleshed phenomena -- not a lawful authority dissolving and falsifying these phenomena or (to change the metaphor) ruling them like some despot lording it over his subjects.

The vacuum experiment can help us understand what gravity has to do with a leaf dancing on a twig or floating and fluttering to the ground -- but only if we first allow our leaf to escape from the vacuum chamber and back into its own world.

But there is no overestimating the hunger for precise, universal, and despotically deterministic laws -- laws that "govern" phenomena rather as algorithms are thought to govern our machines. If we insist on such laws, we will obtain them after a fashion. We will even find experimental vindication for them wherever, through artifice, we can isolate the desired aspect of a phenomenon from all else. But the observable world we started out to explain will disappear from such laws, much as the separate character of rock and leaf disappear into the mathematical law of gravity.

Sorting this out will require some delicate analysis and patience. It could hardly be otherwise when we are dealing with errors and omissions that have influenced our culture's thinking for hundreds of years. But the analysis will yield striking rewards. The gap between the idea of a law implicit in the world's phenomena and a law fully determining or explaining or characterizing those phenomena turns out to be as large as it is subtle -- large enough, we will eventually see, to serve as the misconceived arena within which nearly the entire history of conflict between science and religion has taken place.

The Dream of Determinism

Perhaps you have been thinking that we can get from the gravitational description of a leaf's descent in the vacuum chamber to a full characterization of the individual leaf in all its reality if only we factor in all the other known scientific laws. You will recall that in "The Limits of Predictability" I left open this possibility. More broadly: could it be that if we knew all the laws bearing on phenomena and if we likewise exactly understood the current state of every particle or other entity in the universe, we would be in the position of Pierre Simon Laplace's famous "universal intelligence"? The great mathematician put it this way:

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it -- an intelligence sufficiently vast to submit these data to analysis -- it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes. (1951, p. 4)

Now, you may be inclined to dismiss Laplace's celebrated determinism as outmoded in an era of chaos theory and quantum mechanics. But his way of thinking about law continues to rule the minds of most people -- and even the minds of scientists most of the time. We have by no means surmounted the error it represents.

What is needed, even more than appeals to the exotic and philosophically perplexing results of modern physics, is an ability to recognize how misguided Laplace's opinion already was when he voiced it in the early nineteenth century, at the triumphant height of Newtonian science. I'm convinced that only when we understand the illusions of that earlier, supremely confident era will we begin to penetrate the long-resistant but promising scientific conundrums of our own day.

On Being Precise About Nothing Much

Only a madman would deny that our formulation of quantitative law aids our understanding of the world. It enables us to predict things more or less, even if not in a Laplacean manner. A world without predictability would be a world without order; it would render our existence meaningless and intolerable. Actually, such a world is not even conceivable. What we do find is, in Alexander Pope's words,

Not chaos-like together crush'd and bruis'd,
But, as the world, harmoniously confus'd:
Where order in variety we see,
And where, though all things differ, all agree.

The decisive question is not whether there is predictable order in the world. Nor is it whether mathematically precise laws focus our attention upon elements of this order -- which obviously they do. Rather, we need to ask how, in their strictly quantitative, precise, and unequivocal aspect, laws relate to the world they help us understand.

We can find our answer by exploring all those domains where we have learned to extract one or another sort of lawful syntax -- that is, a purely formal structure -- from the content of the domain. Or, I might say: from the harmoniously confused order and variety of the domain. We do this, for example, whenever we strive to articulate as clearly and unambiguously as possible the logical, mathematical, or grammatical structure of some aspect of the world. I say "unambiguously" because the overriding aim here is always for clarity and exactness, for unqualified validity, for the simplest possible rules with the most universal reach. "A does not equal not-A".

We must aim for this unqualified exactness. At least, we must do so with some of our cognitive energies. But our various syntactic endeavors have taught us two things:

• If we strain toward nothing but syntactic clarity, precision, and universal applicability, then we progressively lose the meaning, or semantic content, that our syntactic constructs were originally intended to elucidate.

• If, on the other hand, we preserve this content and observe how the syntactic rules or laws work within it, we find that these laws no longer have the same ruling or determining character we so naturally impute to a pure, isolated syntax.

As for the first of these points, I do not believe we can ever arrive at a pure and exact syntax that is not the syntax of something, however vaguely conceived. But this does not matter at the moment. We remain intent on pressing toward such empty structure, and we have come close enough to the goal for Ludwig Wittgenstein to say of formal logic that all its propositions "mean the same thing, namely nothing". And close enough for Bertrand Russell to say that formal mathematics is "the subject in which we never know what we are talking about, nor whether what we are saying is true". And close enough again for contemporary linguists, following Noam Chomsky, to imagine the possibility of a pure grammar that is not the grammar of any particular content ¹.

Nothing here is terribly difficult to see. In assigning universal validity to "A does not equal not-A", we say that it is true of everything -- every A -- in the universe. But, unavoidably, what is true of everything without qualification doesn't tell us much about anything in particular. Having emptied our terms of their concrete and qualitative content in the hunt for universal validity, we find that we can say nothing much about the world, but we can say it with absolute precision and certainty! ²

But now our interest is more positive -- not how we tend to lose the content we are investigating when our single-minded concern is to abstract an unqualified lawful syntax from it, but rather: if we are willing to keep the content in view, how do we discover its lawful syntax living in and informing the content?

If we want to understand the world and not merely the abstract revolutions of our own minds, then this is the decisive question. What is the relation between syntax, on the one hand, and semantics (content or meaning) on the other?

Speech and World

In a certain way we are all as intimate with the answer as with our own speech. We are, after all, experts at producing meaningful content informed by lawful -- that is, logical and grammatical -- relations; we do so every time we speak. And there are two things to say about this accomplishment. One is that our speech could not have any coherent or meaningful content if it lacked the sort of ordered, syntactic relations we have learned to distill through logical and grammatical analysis. Imagine speech with no lawlike structure whatever and you will be imagining gibberish.

In the second place, however, the lawful syntax of our language does not in any absolute sense govern our speech as a meaningful whole, does not fully explain its content, and never allows us to predict with certainty what the next words of a speech or text will be. While there must be lawful order, it is an order implicit in and growing out of this content, not controlling or determining it. The content reveals itself as the source, significance, and limitation of the law.

When we construct a syntactically proper sentence, we do not achieve our result by assembling pre-existing words in a way predetermined by grammatical rules. While there are many complex and diverse movements of mind as we speak, it is fair to say very generally that we first have an idea, inchoate though it may be, and then we seek to capture and clothe this idea in words. Each word gains its full meaning -- becomes the word it now is -- through the way it is conjoined with other words under the influence of the originating idea. The word simply didn't exist as this particular word before -- as a word with these nuances of meaning ³.

So an antecedent whole (an idea) becomes immanent in and thereby transforms and constitutes its parts (words), making them what they are. In terms of active agency, it is less that the parts constitute the whole than the other way around. And since the grammatical structure of any text depends on the meanings of the words, this structure therefore varies as the meanings vary. It appears, then, that the rules of grammar -- the way they are orchestrated in this particular text -- can be thought of as a result of the way a meaningful whole manifests itself through its parts.

In other words, the pattern of syntactic lawfulness in a sentence, far from tyrannizing over the sentence and eliminating the possibility of meaningful content, is itself an expression of the meaning. This is what we will find wherever we can trace the forms of a lawful syntax.

An Objection, Briefly Considered

This, of course, needs elaboration. But first: you may be wondering how in the world we have gotten from science to language. What does the syntactic structure of language have to do with the syntactic or lawful structure of the physical world? The question bears within it nearly all the pathologies afflicting today's science, and this entire series of articles, when completed, might be taken as my response. Perhaps it is enough for the moment to say the following:

Does the scientist gain a communicable understanding of the world or not? If not, then our entire discussion of physical law is senseless. But if so, then our assessment of what the scientist's language is capable of saying is at the same time an assessment of what the language is capable of saying about the world. When the language we use to communicate our understanding of the world is substantially drained of its content, the world we describe is also substantially drained of its content.

In speaking, we aim to make the structure and meaning of our language the structure and meaning of whatever we are talking about. This intention and this achievement are of the essence; they are what make our utterances language. To the extent we fail in the achievement, our speech is meaningless and we might as well cease talking about scientific understanding at all. But if we succeed, our scientific speech becomes an image of the world we are seeking to reveal ⁴. The fullness of the image will depend upon the fullness of the language with which we sketch it. If our formulations of physical law are compacted of little more than mathematical, logical, and grammatical syntax, emptied of content, then our world will likewise be emptied of content. The laws may be exact, but most of the world will have disappeared from them.

But perhaps we can set all this aside and simply say this: anyone who wishes to do so may propose a relation between the syntax of physical law and the content in which it is found that is different from the relation between syntax and content in the speech we use to convey our scientific understanding. But where is any such proposal? When we look at the prevailing view of physical law, all we find is the kind of incoherence I will now try to highlight.

The Impossibility of Mere Obedience to Law

The conviction that laws somehow give us a full accounting of events seems often to be based on the idea that they govern the world's substance or matter from outside, "making" things happen. If this is the case, however, then we must provide some way for matter to recognize and then obey these external laws. But, plainly, whatever supports this capacity for recognition and obedience cannot itself be the mere obedience. Anything capable of obeying wholly external laws is not only its obedience but also its capability, and this capability remains unexplained by the laws.

If, with so many scientists today, we construe laws as rules, we can put the matter this way: much more than rule-following is required of anything able to follow rules; conversely, no set of rules can by themselves explain the presence or functioning of that which is capable of following them.

It is, in other words, impossible to imagine matter that does not have some character of its own. To begin with, it must exist. But if it exists, it must do so in some particular manner, according to its own way of being. Even if we were to say, absurdly, that its only character is to obey external laws, this "law of obedience" itself could not be just another one of the external laws being obeyed. Something will be "going on" that could not be understood as obedience to law, and this something would be an essential expression of what matter was. To apprehend the world we would need to understand this expressive character in its own right, and we could never gain such an understanding solely through a consideration of external laws.

So we can hardly find coherence in the rather dualistic notion that physical laws reside, ghost-like, in some detached, abstract realm from which they impinge upon matter. But if, contrary to our initial assumption, we take laws to be in one way or another bound up with the world's substance -- if we take them to be at least in part an expression of this substance -- then the difficulty in the conventional view of law becomes even more intense. Surely it makes no sense to say that the world's material phenomena are the result -- the wholly explained result -- of matter obeying laws which it is itself busy expressing. In whatever manner we prefer to understand the material expression of the laws, this expression cannot be a matter of obedience to the laws being expressed! If whatever is there as the substance of the world at least in part determines the laws, then the laws cannot be said to determine what is there.

All this gives you some indication why so many scientists, when stepping back from the rather messy reality of their daily work and considering the character of their science, show such great reluctance to reckon with the substance of the observable world. They much prefer to conceive the explanatory value of science in terms of abstract laws -- equations, rules, algorithms -- which naturally remain gratifyingly lawful in an uncomplicated way. The world disappears into a vague notion of "whatever gives material reality to the laws".

But a willingness to consider this reality in its own terms immediately reveals the impossibility of the all-explaining laws with which science supposedly has to do. We come to realize that a physical phenomenon and its lawfulness must be considered as a unity -- a syntactic-semantic unity of a sort that receives little recognition within science for the simple reason that physical phenomena (as opposed to their "governing" syntax) receive little recognition.

The Game Is Not Its Rules

If you doubt this tendency to disregard the world as meaningful content, then listen to physicist Richard Feynman talking about the nature of scientific understanding. He asks us to imagine the world as "something like a great chess game", and then suggests that "the rules of the game are what we mean by fundamental physics .... If we know the rules, we consider that we 'understand' the world" (Feynman, et al. 1963, p. 2-1).

But the formal rules tell us almost nothing about the real presence of the world. What convinces us otherwise (to stick with Feynman's metaphor) is that, whether our science sanctions it or not, we picture real chess pieces moving meaningfully on a real board. Given this imagined reality, we take satisfaction in how the rules "explain" what is going on with the board and pieces. It is easy to forget that the rules tell us nothing about the board and pieces themselves, or how they will move, or the strategies giving sense to the moves. This is the missing content of the rules -- what the rules are supposedly about -- but nothing in the rules explains or dictates all this content of real games.

When Feynman compares the world to the rules of the game rather than to the chessboard or the concrete activities associated with it, he leaves the world's givenness and content out of the picture. He makes the rules alone -- a formalism -- the entire substance of science.

Games, of course, are yet another domain where we have learned to abstract a relatively pure syntax (the rules of the game) from a larger and more meaningful content. And here, as elsewhere, it is not hard to see how grotesquely wrongheaded it is to claim that the rules alone give us an adequate explanation of the unfolding moves in an actual game.

It is not that there are no rules or that we should not be extremely clear about them. But the exact, unambiguous nature of the rules is not the exact and unambiguous nature of chess pieces and chess strategies. The rules are implicit or immanent in the game, but what it means to be immanent, unfortunately, is something most scientists have not yet begun to consider. This leaves their thinking about physical law sadly ungrounded.

Missing Content

More than one great physicist has glimpsed the emptiness resulting from a one-sided preoccupation with the syntax of physical law. We earlier heard Feynman acknowledging that "in physics today, we have no knowledge of what energy is" (1963, p. 4-1). Einstein once remarked that

As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. (1954, p. 233)

Here again the gap between clean, formal certainty and an uncertain reality vexes our thoughts. The physicist, Sir Arthur Eddington, was even more direct when he wrote,

[Our knowledge of physics] is only an empty shell -- a form of symbols. It is knowledge of structural form, and not knowledge of content. All through the physical world runs that unknown content.... (1920, p. 200)

A remarkable admission! -- yet scarcely puzzled over within science as a whole. And I suspect we can recognize the same admission underlying Stephen Hawking's widely quoted remark:

What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe .... Up to now scientists have been too occupied with the development of new theories that describe what the universe is to ask the question why. (1998, p. 190)

Hawking frames his question as if he were posing the problem of God and the origin of things. He goes on to ask, "does it [the universe] need a creator, and, if so does he have any other effect on the universe?" But this is misleading. It's not true that equations describe what the universe is; by themselves they have nothing to describe -- and what constitutes something rather than nothing is the crucial problem for science today. His puzzle concerning "why there should be a universe for the model to describe" has less to do with the origin of the universe than with the current substance and reality of the universe. The truth in Hawking's words is that, so far as the equations are concerned, the universe still remains to be "created". They cannot give us Eddington's "unknown content".

This is the problem I was alluding to in "The Limits of Predictability" when I said that mathematics in its purely formal exactness tells us almost nothing about the world. We must bring it into relation with the content of this world, and we can do this only insofar as we understand the non-quantitative terms of the relation as well as the quantitative ones. It is just plain craziness to ignore the darkness in the key terms of our science -- "force", "matter", "energy" -- and to claim that we understand a phenomenon when we can't even say what it is in any language with actual content.

Of course, to one degree or another we do frame our laws in a language with content. But in doing so we step outside the professed terms of our hard science without offering any acknowledgment or justification of the fact. Meanwhile, in our view of the world and its lawfulness, we ignore the practical necessities of our own science and continue mostly along the old and tired track laid down by Laplace.

Our Laplacean Inheritance

But I hope by now we have gained a first inkling why the mere multiplication of laws operating upon numerical data can never bring us to an adequate explanation of the world and its phenomena. If our ideal syntactic constructs are intrinsically empty, then adding more and more of them to our intellectual edifice does not get us a real building. We cannot by this means bridge the gap between formal, syntactic structure and the content whose structure we would like to capture..

Once you recognize the kind of syntactic-semantic unity required to describe anything in the world at all, you will find the nineteenth- century deterministic faith unbearably foolish. It was a faith in the explanatory powers of pure syntax -- powers that begin to look very different when they are discovered in the world rather than imposed by our imaginations upon a world that has become (like our leaf in the vacuum chamber) largely invisible to us. Physicist Banesh Hoffman describes that earlier faith this way:.

The mighty universe was controlled by known equations, its every motion theoretically predictable, its every action proceeding majestically by known laws from cause to effect. (Quoted in Lukacs 1994, p. 275).

It should not require any special insight to realize that equations do not control anything. But while the view Hoffman describes is often derided today, it continues to rule the scientific and technological imagination. It is, for example, what makes it possible for MIT robotics guru, Rodney Brooks, to say that we are "just molecules, positions, velocity, physics, properties -- and nothing else" (quoted in Ullman 2002, p. 69). This conclusive "and nothing else" suggests that Brooks believes he would have no problem telling us what "properties" are -- and that he could do so with well-behaved numbers quite apart from any appeal to qualities, as if the numbers alone could give us a world. Well, let him go ahead and tell us.

Rather more ingenuously, Richard Feynman once confessed:

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?

This unsettling infinity is just one more indication of the pregnant gap between empty syntax and the content from which it was abstracted. But Feynman's response to the problem brings no promise of enlightenment. In the next sentence he writes:

So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. (1967, pp. 57-8).

It is admirable for Feynman to turn his attention to the world he wishes to describe. But, bound by the nineteenth-century Laplacean mindset, he can only imagine this world as "machinery" governed by the rules of a simple game -- which leaves him no less trapped within syntactic emptiness than the infinitely spun-out "logical operations" that bothered him to begin with.

In a scientific and technological culture of such amazing sophistication, one wonders how we could accept such utter vacuity at the center of our understanding. But, really, we don't. Since we can't get by without a world, we inevitably assume the qualitative and meaningful content missing from our formal constructions. But because we do not make our assumption fully conscious or bring it under the discipline of our science, it weaves a veil of illusion around us. We imagine our formalisms to be explanations when in fact they are only the ghosts of explanations.

Looking Ahead

We are at a critical point in this series of essays, although the point has barely been introduced. When you reckon with language in general or scientific language in particular, and when you take it in its fullness rather than pretending you can isolate its strictly formal aspect and use that alone to describe the world, then you are dealing with qualities and meaning. And to the extent your language does indeed describe the world and therefore possesses scientific value, you are dealing with qualities and meaning in the world.

You are, in fact, dealing with formal causes in the ancient sense of the term. This older conception of cause points us toward the qualitative form or meaningful patterns, the governing unity, according to which phenomena unfold rather as a sentence with its particular words unfolds to express an antecedent governing idea. Such a meaning of "formal", of course, is nearly opposite to the "formal" and "formalism" I have been speaking of till now.

All this will require a great deal of further discussion. What would a science of formal causes -- a qualitative science -- actually look like? What are some examples of formal causes? If a valid science is necessarily qualitative, we must see this fact reflected in all the momentous accomplishments of our current science, even if the truth of the matter remains unacknowledged. Where do we see this truth?

So there is much still to be said. But if you doubt the revolutionary nature of the ideas set forth here, think for a moment about the following claims that have been broached in the discussion so far:

• The world is not a machine in the strict sense required by mechanistic thinking; not even "machines" are machines in this sense. A mechanistic science has been driven inexorably toward a purely algorithmic, logical- mathematical conception of machines because actually existent machines, as real and substantial presences -- metallic, plastic, and glassy -- do not yield themselves fully to mechanistic thought. It is much more convenient if we ignore the machine's substance and occupy ourselves with convenient, well-behaved rules. (See especially "The Vanishing World-Machine in SCR #30.)

• The world's phenomena are neither predictable nor explainable in the sense required by mechanistic science. We can in some sense find mechanistically formulated laws within phenomena, but this is not at all the same as predicting or explaining the phenomena themselves or reducing them to mechanisms. (See "The Limits of Predictability" in SCR #33, along with the current essay.)

• The only fully adequate causes we have are formal causes in the older sense of this term -- qualitative causes given in the way a meaningful unity or whole organically governs and manifests itself through its parts. The cherished causes of today's science -- precise and unambiguously stated "efficient" causes -- are what you get when you analyze formal causes down to purely quantitative or logical statements stripped of content. Efficient causes are nothing but the ghosts of formal causes. This idea, of course, has barely been introduced in the current essay. A great deal more remains to be said.

In the next essay I will try to consolidate the territory we have covered so far. We are ready to clarify a set of interrelated terms that till now I've been using rather too casually -- for example, "mechanistic", "deterministic", "reductionist".

Meanwhile, some of you may wish to entertain yourselves by considering the relation between the foregoing ideas and those put forth by Stephen Wolfram (http://www.stephenwolfram.com). Wolfram's widely heralded revolution aiming at "a new kind of science" amounts largely to taking the existing one-sidedness of science and pushing it to a dead-end extreme. If you doubt what I have said about the tendency within science to substitute algorithms for the world, just spend a few minutes looking at Wolfram's work.

What I have been arguing here comes close to being the exact opposite of Wolfram's "revolution" -- and points, I would make bold to say, toward the revolution he missed.

NOTES

1 I discuss the polar relation between syntax and semantics at considerable length in Talbott 1995. Also see "How to Begin Thinking about Technology: The Pursuit of Entangled Opposites" (Talbott 1999).

2 In this light, our strong urge to frame our physical laws in the form of universally applicable truths -- truths that therefore do not distinguish one thing from another -- becomes profoundly significant. These laws inevitably present us with a "semantic completeness problem" very different from the syntactic completeness problem that has so exercised mathematicians.

3 Henri Bortoft is very good on the wholeness of language -- and on wholeness in general, along with many other topics related to these essays. See Bortoft 1996.

4 I will add the following, although it carries us to a much later, epistemological part of the discussion. The objective world also has the character of an image. When our scientific thought and language give us an image truly revelatory of the world, this image is the world itself manifesting in our consciousness.

Previous articles in this series:

Part 1, "Intelligence and Its Artifacts", in SCR #28
Part 2, "The Vanishing World-Machine", in SCR #30
Part 3, "The Limits of Predictability", in SCR #33

Bibliography

Bortoft, Henri (1996). The Wholeness of Nature: Goethe's Way toward a Science of Conscious Participation. Hudson NY: Lindisfarne.

Eddington, Sir Arthur (1920). Space, Time, and Gravitation. Cambridge: Cambridge University Press.

Einstein, Albert (1954). Ideas and Opinions, transl. by Sonja Bargmann. New York: Crown Publishers.

Feynman, Richard P., Robert B. Leighton, and Matthew Sands (1963). The Feynman Lectures on Physics. Reading MA: Addison-Wesley.

Feynman, Richard (1967). The Character of Physical Law. Cambridge MA: MIT Press.

Hawking, Stephen (1998). A Brief History of Time. New York: Bantam.

Laplace, Pierre Simon (1951). A Philosophical Essay on Probabilities, translated by Frederick Wilson Truscott and Frederick Lincoln Emory, with an introduction by E. T. Bell. New York: Dover.

Lukacs, John (1994). Historical Consciousness: The Remembered Past. New Brunswick NJ: Transaction Publishers.

Talbott, Steve (1995). "Can We Transcend Computation", chapter 23 in The Future Does Not Compute: Transcending the Machines in Our Midst. Sebastopol CA: O'Reilly and Associates. Available at http://www.praxagora.com/~stevet/fdnc/ch23.html.

Talbott, Steve (1999). "How to Begin Thinking about Technology: The Pursuit of Entangled Opposites", NetFuture #84 (Feb. 9). Available at http://www.netfuture.org/1999/Feb0999_84.html.

Ullman, Ellen (2002). "Programming the Post-Human", Harper's Magazine (October), pp. 60-70.

© 2004 Steve Talbott

Steve Talbott, author of The Future Does Not Compute: Transcending the Machines in Our Midst currently edits NetFuture, a freely distributed newsletter dealing with technology and human responsibility. NetFuture is published by The Nature Institute, 169 Route 21C, Ghent NY 12075 (tel: 518-672-0116; web: http://www.natureinstitute.org). You can reach Steve at [email protected]

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