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The Big Picture

Page 6

by Carroll, Sean M.


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  limits of Newtonian mechanics in an appropriate regime, where dissipation

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  and friction are central. (Coffee cups do come to a stop, after all.) In the

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  same way, it’s possible to understand why it’s so useful to refer to causes and

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  effects in our everyday experience, even if they’re not present in the underly-

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  ing equations. There are many different useful stories we have to tell about

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  reality to get along in the world.

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  What Determines What Will Happen?

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  Isaac Newton, the most influential scientist of all time, was a very reli-

  gious man. His views were undoubtedly heterodox by the standards of

  his childhood Anglican faith; he rejected the Trinity, and wrote nu-

  merous works on prophesy and biblical interpretation, with chapter titles

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  such as “Of the power of the eleventh horn of Daniel’s fourth Beast, to

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  change times and laws.” He couldn’t rely on an argument for God’s exis-

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  tence along the lines of Aristotle’s unmoved mover. His own work seemed

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  to depict a universe moving perfectly well under its own power, but as he

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  pointed out in the “General Scholium” (an essay appended to later editions

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  of his masterwork, Principia Mathematica), someone had to set it all up:

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  This most excellently contrived System of the Sun, and Plan-

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  ets, and Comets, could not have its Origin from any other than

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  from the wise Conduct and Dominion of an intelligent and

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  powerful Being.

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  Elsewhere, Newton seemed to imply that the mutual perturbations of the

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  planets on one another would gradually cause the system to get out of

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  whack, at which point God would intervene to set things back in order.

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  Pierre- Simon Laplace, a French physicist and mathematician born a cen-

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  tury after Newton, thought differently. Scholars debate over his true reli-

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  gious views, which seem to have vacillated between deism (God created the

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  world, but did not subsequently intervene in its operation) and outright

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  atheism. Laplace is the one who, when asked by Emperor Napoleón why

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  God didn’t appear in his book on celestial mechanics, purportedly replied,

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  “I had no need of that hypothesis.” Whatever his ultimate beliefs, it seems

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  that Laplace held steadfastly against the idea of a Creator who would ever

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  directly interfere in the motions of the world.

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  Pierre- Simon Marquis de Laplace, 1749– 1827.

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  Laplace was one of the first thinkers to truly understand classical

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  (Newtonian) mechanics, deep in his bones— better than Newton himself.

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  Someone was bound to do it. Science progresses, and we learn more and

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  more about our best theories; there are many physicists today who under-

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  stand relativity better than Einstein, or quantum mechanics better than

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  Schrödinger or Heisenberg. Laplace tackled problems from the stability of

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  the solar system to the foundations of probability, routinely inventing the

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  required new mathematics along the way. He suggested that Newtonian

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  gravity could be thought of as a field theory, positing a “gravitational poten-34

  tial field” that filled all of space, thereby resolving Newton’s puzzlement

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  about actions at a distance between faraway bodies.

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  T H E B IG PIC T U R E

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  Perhaps Laplace’s greatest contribution to our understanding of me-

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  chanics was not a technical or mathematical advance, but a philosophical

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  one. He realized that there was a simple answer to the question “What

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  determines what will happen next?” And the answer is “The state of the

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  universe right now.”

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  There’s a worry that this result threatens the existence of human agency,

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  our ability to make choices about what to do next. As we’ll see, that’s not

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  really an issue of physics, but one of description: What is the best way we

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  have to talk about human beings? When we talk about simple Newtonian

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  systems, like the planets moving through the solar system, determinism is

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  part of the picture. When we talk about enormously more complex things

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  like people, there’s no way for us to have enough information to make iron-

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  clad predictions. Our best theories of people, presented on their own terms

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  and without reference to underlying particles and forces, leave plenty of

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  room for human choice.

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  The world, according to classical physics, is not fundamentally teleological.

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  What happens next is not influenced by any future goals or final causes

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  toward which it might be working. Nor is it fundamentally historical; to

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  know the future— in principle— requires only precise knowledge of the

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  present moment, not any additional knowledge of the past. Indeed, the en-

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  tirety of both the past and future history ar
e utterly determined by the

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  present. The universe is resolutely focused on the current moment; it

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  marches forward, instant to instant, under the grip of unbreakable physical

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  laws, with no heed paid to its glorious accomplishments or to its hopeful

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  prospects. Much later, the biologist Ernst Haeckel would dub this view-

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  point dysteleology, though the term is so ungainly that it never really

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  caught on.

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  In modern parlance, Laplace was pointing out that the universe is some-

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  thing like a computer. You enter an input (the state of the universe right

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  now), it does a calculation (the laws of physics) and gives you an output (the

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  state of the universe one moment later). Similar ideas had previously been

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  suggested by Gottfried Wilhelm Leibniz and Roger Boscovich, and were

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  prefigured over two millennia earlier by Ajivika, a heterodox school of an-

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  cient Indian philosophy. Since computers hadn’t been invented yet, Laplace

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  imagined a “vast intellect” that knew the positions and velocities of all the

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  particles in the universe, and understood all the forces they were subject

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  to, and had sufficient computational power to apply Newton’s laws of mo-

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  tion. In that case, as he put it, “for such an intellect nothing would be

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  uncertain, and the future just like the past would be present before its eyes.”

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  His contemporaries immediately judged “vast intellect” to be too boring,

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  and renamed it Laplace’s Demon.

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  It’s convenient to say “one moment later,” but for Newton and Laplace,

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  and to the best of our current understanding in theoretical physics, the flow

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  of time is continuous rather than discrete. That’s no problem at all; this is a

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  job for calculus, which Newton and Leibniz invented for just this reason.

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  By the “state” of the universe, or any subsystem thereof, we mean the posi-

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  tion and the velocity of every particle within it. The velocity is just the rate

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  of change (the derivative) of the position as time passes; the laws of physics

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  provide us with the acceleration, which is the rate of change of the velocity.

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  Together, you give me the state of the universe at one time, and I can use

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  the laws of physics to integrate forward (or backward) and get the state of

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  the universe at any other time.

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  We’re using the language of classical mechanics— particles, forces— but

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  the idea is much more powerful and general. Laplace introduced the idea of

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  “fields” as a centrally important concept in physics, and the notion became

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  entrenched with the work of Michael Faraday and James Clerk Maxwell on

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  electricity and magnetism in the nineteenth century. Unlike a particle,

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  which has a position in space, a field has a value at every single point in

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  space— that’s just what a field is. But we can treat that field value like a

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  “position,” and its rate of change as a “velocity,” and the whole Laplacian

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  thought experiment goes through undisturbed. The same is true for Ein-

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  stein’s general theory of relativity, or Schrödinger’s equation in quantum

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  mechanics, or modern speculations such as superstring theory. Since the

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  days of Laplace, every serious attempt at understanding the behavior of the

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  universe at a deep level has included the feature that the past and future are

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  determined by the present state of the system. (One possible exception is

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  the collapse of the wave function in quantum mechanics, which we’ll dis-

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  cuss at greater length in chapter 20.)

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  This principle goes by a simple, if potentially misleading, name: conser-

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  vation of information. Just as conservation of momentum implies that the

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  universe can just keep on moving, without any unmoved mover behind the

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  scenes, conservation of information implies that each moment contains

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  precisely the right amount of information to determine every other

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  moment.

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  The term “information” here requires caution, because scientists use the

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  same word to mean different things in different contexts. Sometimes “in-

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  formation” refers to the knowledge you actually have about a state of affairs.

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  Other times, it means the information that is readily accessible, embodied

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  in what the system macroscopically looks like (whether you are looking

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  at it and have the information or not). We are using a third possible defini-

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  tion, what we might call the “microscopic” information: the complete spec-

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  ification of the state of the system, everything you could possibly know

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  about it. When speaking of information being conserved, we mean literally

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  all of it.

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  These two conservation laws, of momentum and information, imply a

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  sea change in our best fundamental ontology. The old Aristotelian view was

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  comfortable and, in a sense, personal. When things moved, there were mov-

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  ers; when things happened, there were causes. The Laplacian view— one

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  that continues to hold in science to this day— is based on patterns, not on

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  natures and purposes. If this certain thing happens, we know this other

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  thing will necessarily follow thereafter, with the sequence described by the

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  laws of physics. Why is it that way? Because that’s the pattern we observe.

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  Laplace’s Demon is a thought experiment, not one we’re going to reproduce

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  in the lab. Realistically, there never will be and never can be an intelligence

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  vast and knowledgeable enough to predict the future of the universe from

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  its present state. If you sit down and think about what such a computer

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  would have to be like, you eventually realize it would essentially need to be

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  as big and powerful as the universe itself. To simulate the entire universe

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  with good accuracy, you basically have to be the universe. So our concern

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  here isn’t one of practical engineering; it’s not going to happen.

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  Our interest is a matter of principle: the fact that the current state of the

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  universe determines its future, not that we can imagine taking advantage

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  of that fact to make predictions. This feature, determinism, rubs some

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  people the wrong way. It’s worth taking a careful look at its limitations and

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  prospects.

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  Classical mechanics, the system of equations studied by Newton and

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  Laplace, isn’t perfectly deterministic. There are examples of cases where a

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  unique outcome cannot be predicted from the current state of the system.

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  This doesn’t bother most people, since cases like this are extremely rare—

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  they are essentially infinitely unlikely among the set of all possible things a

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  system could be doing. They are artificial and fun to think about, but not

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  of great import to what happens in the messy world around us.

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  A more popular objection to determinism is the phenomenon of chaos.

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  The ominous name obscures its simple nature: in many kinds of systems,

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  very tiny amounts of imprecision in our knowledge of the initial state of

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  that system can lead to very large variations in where it eventually ends up.

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  As far as determinism is concerned, however, the existence of chaos could

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  not possibly be more irrelevant. Laplace’s point was always that perfect in-

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  formation leads to perfect prediction. Chaos theory says that slightly im-

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  perfect information leads to very imperfect prediction. True, and it doesn’t

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  change the picture the slightest bit. Nobody in their right mind was ever

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  under the impression that we would be able to use Laplace’s reasoning to

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  build a useful prediction- making device; the thought experiment was al-

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  ways a matter of principle, not one of practice.

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  The real issue with classical mechanics is that it’s not how the world

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  works. These days we know better: quantum mechanics, which came along

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  in the early twentieth century, is an entirely different ontology. There are

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  no “positions” and “velocities” in quantum mechanics; there is only “the

 

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