Wednesday, October 16, 2019

Wondering About Chapter 3

Wondering About Reality
 
In the 1999 motion picture film The Matrix, the actor Keanu Reeves plays a character, Neo, who is forced into the horrific realization that the world he lives in – indeed, that everyone he has ever known and loves lives in – is not the objective real universe at all, but only a virtual reality created by an artificial intelligence, an intelligence that has enslaved humanity for its own purposes. Neo’s realization of this truth is the result of his liberation from the Matrix by an individual known as Morpheus (played by Laurence Fishburne). Upon ingesting a red pill, Neo awakens in his own, true, body; a body which is naked and hairless and is curled up in a fetal position in an artificial womb, kept alive via tubes and cables leading into important orifices. More important and unbelievable than this however, is the fact that he is but one body, one virtually identical to the billions that surround him in a vast menagerie of wombs, stretching as far as the eye can see.
Well, what do you think? Could it be true? Could we all be living inside a virtual universe created by an intelligent entity? Could the seeming solidity of the world around us be merely an illusion created by a computer program, and we unfortunate souls slaves to the master programmer who has created this mirage?
I’m guessing your answer to these questions is an unqualified NO! That The Matrix, as entertaining as it was in the movie theater or in your home, or even as compelling, is the paranoid fantasy of any mind bizarre enough to think it even possible. Sure, logically it could be true; but that can be said about any paranoid delusion.
No, there is no Matrix, no master programmer, and we are not slaves except to the extent that we are ignorant of our true condition. But what is true is that the world we experience and perceive is not actually an objective existence “out there” but a virtual reality simulation of that existence, one that is going on inside our own heads, in our fabulously complex and wondrous brains, twenty-four hours a day, throughout our entire lives. The only difference between this simple fact and science fiction is that, as I said, there is no master programmer: all the programming is done by a combination of our genes and experiences working together, each blind to what it is doing and without any plan at all, yet together a combination far more powerful and brilliant that the greatest software engineer in the world.
This statement may astound you, but in fact there is nothing either particularly original or controversial about it; not, at least, to any philosopher or biologist or neuroscientist you might care to mention it to. That is why I say you can go through the process of digesting it and retain your sanity. The only question is, why do so? What purpose beyond an abstract, and somewhat macabre exercise in philosophical musing could it possibly serve? Moreover, given the theme of this book, what does it have to do with curiosity and our capacity to comprehend the universe?
Before answering these questions, it is worthwhile to examine this concept of living inside a virtual reality of the mind in more detail. I need to convince you that, all your experience and perceptions to the contrary, it is true beyond any reasonable doubt. At the same time, and perhaps even more importantly, I also need to make clear just what I mean by it and, just as critical, don’t mean by it. Here, in fact, might be the best place to begin the examination.
A good way to describe anything is by means of an analogy, or metaphor, and the most natural one that suggests itself here, to me at any rate, is the so-called “desktop” of a modern personal computer. I am assuming that you have experience with this phenomenon, whether in the form of a Windows PC, a Macintosh, or one of the several flavors of graphical desktops available on UNIX or other machines. If you do not, the example below (taken from my own PC, naturally) ought to give you the general flavor of what I am talking about:
This is an example of what you might see, looking at the monitor screen of my computer. The first thing that might strike you is that the term “desktop” is indeed a fairly apt one: we see a background of blue as a true desktop might actually have, covered with things you might expect to find on a desktop. For example, there are what are known as “icons” in the upper left hand corner; these could be considered as kinds of folders, or perhaps drawers containing folders and files. The center is dominated by the four open “folder windows” (hence the name Windows, although other graphical interfaces sport the same appearance), each appearing exactly like that; an open folder some of which containing list of still more folders (the rectangular, yellow icons) and open files (e.g., “Chapter 1.doc, Chapter 2.doc, which incidentally are the chapters of this book at the time of writing). There are also two windows representing open and running programs or “applications”: the Notepad Editor, and the Calculator program; you probably find them easy to think of as an open paper notepad and calculator on a real desktop for they really appear as physical applications you might have on a true desktop.
I will ignore the bar at the bottom of the screen, although this does provide more interesting information as well. Basically, what we see are things, or at least by the appearances of things, that we can interact with in an intuitively obvious manner. By using the mouse ( a handheld instrument which you manipulate across your actual desktop) for example, when I maneuver a small arrow (not shown) over any of the icons or windows, or parts of windows, and either singly or doubly clicking a button on the mouse, I cause something to happen. If, for example, I position the arrow over the “file” that says Chapter 3.doc and double-click, a program called Microsoft Word will start, and will load the Chapter 3.doc file so that I can read and or edit it, rather like conjuring up a (very powerful!) typewriter with loaded pages. Double-clicking any of the folder shaped icons on the “My Documents” window will likewise “open” the folder to reveal its contents: most likely, a mixture of more folders and files. Double-clicking any of the upper left corner icons will open a window showing their contents, usually a collection of folders, files, and other icons. Clicking on the calculator program will allow me to enter numbers in the top white bar and perform all sorts of mathematics on them just as with a “real” calculator, while the notepad application allows me to type in text and save it to a file.
I do not want to belabor the point here, for if you have any experience with a modern computer – which I am assuming you do – you are quite familiar with the kinds of actions I am talking about. You are familiar with how you genuinely appear to be working with a real desktop, one containing icons, windows, and applications you can interact with in a way so intuitive and simple a manner it is almost childlike. The point I want to emphasize is that despite this it is nevertheless no more than a virtual reality simulation, one designed to conceal the details of what is really going on while making using the computer so simple and easy. In truth, the desktop and all its icons and windows and toolbars (at the bottom) are but phantoms for the eye; useful phantoms, as they make the computer easy to use, but misleading ones, as they conceal from us and seriously mislead us as to what is actually going on inside that humming box of dumb electronics and other gizmos we are working with. We see a bunch of icons and folders and files, just as we might on an actual desktop. We might even be fooled into thinking that is what we are working with. But it is not, not at all. It is a mirage, through and through.
For what we are really working with are patterns of bits (basically, on / off type switches) which make up two primary parts of the computer physically: its working memory, and its permanent storage, or disk drives. The point is, if we were to study those patterns of on / off switches and try to decipher what they are saying directly, let alone work with them in any direct fashion, we should very quickly find ourselves hopelessly and helplessly overwhelmed by the complexity and non-intuitiveness of the task (to instill some appreciate and admiration in you, however, that is pretty much just what the users of the original computers, some fifty plus years ago, had to do). Designers of an earlier generation of computers, before the graphical interfaces so common today, would simplify using computer by providing a “command console” in which you would type, via a keyboard, the names of programs you wished to run, the files you wanted to work on, or any other commands the computer understood. Even this was no easy task, so when the first graphical interfaces came out in the early / mid 1980s (by the Apple Macintosh), it revolutionized the personal computer, making it a household object much like the television or telephone. Other companies followed suit with their own graphical interfaces, such as Microsoft Windows and the various UNIX interfaces, and the computer revolution was in full steam. With the advent of the internet in the 1990s, and high speed permanent connections in the 2000s, most of us now regard our desktop or laptop machine as indispensible and valuable as our refrigerators. Life, indeed, seems hardly conceivable anymore without it.
* * *
If I keep going on this way, I will stray too far from my subject and my point. Let us recapitulate: there is reality, and there is, or can be, a virtual simulation of that reality such that it has the effect of making it much easier to interact with that reality than directly. The virtual simulation is a model which corresponds to objective reality, but in a way that allows us to interact with it much more effectively. If you can imagine setting bits in a computer memory or disk off or on, instead of working with icons, windows, folders, and files, you should have no problem grasping the advantage of this.
What I am saying goes further, however. Just as the desktop of your computer provides a useful, albeit inaccurate description of its objective reality, your brain does the same with the objective world all around you.
Let’s take a few moments to let that sink in. I am saying that the “objective world” that we all deal with and handle every day as we move through our busy lives is in fact a simulated reality in our own brains. If you find that impossible to believe then, allow me to prove it with a sensual (in this case, optical, but you can fool your other senses as well) illusion, one of the usual stock in trade in books on how the brain works. Have a good look at the object below:
Perhaps you have seen this illusion before. Here’s the upshot: the squares marked “A” and “B” are, all irresistible appearances to the contrary, exactly the same shade of grey. Don’t believe it? Good, don’t take my word: cover the entire image with a cutout which conceals all parts of the figure except these two squares and see what happens. You will see that they immediately jump out as the exact same shade of grey, improbable as that seems. Improble? No, impossible, for take the cutout away and it literally is impossible to not perceive B as much brighter than A.
What is going on here? Quite simply, your brain, which has nothing more to go on than a pattern of photons on your retinas, is creating a model of reality as best as it can, based on rules wired into it by your genes and experience. That model insists that square B must be brighter than square A, despite the actual facts as demonstrated by applying our cutout.
As illusions go, however, this is small potatoes for something as complex and sophisticated as your brain. For a better example – in truth, and the basic point of this chapter –take a look at one of your hands. Make it your left hand (if for no better reason than I’m left-handed). What do you perceive? Solid flesh overlying even more solid bone, if you are like me. Press it against the surface on an object, such as a real desktop, and that perception is made all the more stronger. Now wiggle your fingers. What has happened? No doubt, you feel as though you simply just decided to wiggle your fingers, and then did so. Same if you clench and unclench your hand in a fist, or scratch your nose, or write (oops – if you are right-handed this probably isn’t easy), or deftly pick up an object such as a pen and manipulate it in some way, such as twirling it like a baton. In each case, you are aware of what a marvel of engineering your hand is, and you sense the seemingly miraculous gift of being able to use it the many myriad ways that you do.
As marvelous and miraculous and real as it seems, though, it too is an illusion; a virtual reality created inside your brain for you to interact with. Furthermore, this is true not only of your hands, or any other part of your body, but of the entire – yes, a lá The Matrix – objective world you live and function in. You do not interact with the universe in any direct sense at all, but only through models of that universe created by your brain using the rather limited sensory information it gets from your eyes, ears, sense of touch, and so on. As much as it seems that you are indeed interacting directly with the universe the fact is that you are not; do not, and can not, because the data taken in by your senses is quite insufficient to allow you to do so.
Precisely then, what is going on? The virtual model created in your brain is obviously not arbitrary. On the contrary, it bears a very close correlation to the actual universe around you, as indeed it must if you are not to walk into trees or off cliffs, fail to run away or hide from tigers, feed and take care of yourself, interact with the other human beings, fall in love and procreate, and raise children; all the things, in other words, that we and our ancestors stretching back millions of years have had to do to survive and pass on their genes in the great experiment known as Evolution by Natural Selection. The fact that you have genes that code for a brain that models the world so effectively is no accident. Nature has been honing those genes a long, long time, under relentless and unforgiving evolutionary pressure.
* * *
The problem with this model in your head, and the reason I mention is, is that it can seriously interfere with your understanding the scientific explanation of things. I discovered this often during my own education: sometimes my problems understanding a subject were due to an “intuitively natural” concept of things, a concept that in fact wasn’t true. Or to give a specific example: when studying optics as an undergraduate, a fellow student was hopelessly and distressingly lost trying to follow the subject material. It took a little conversation to reveal that the problem was due to the basic concept of optics that she had; instead of light from the sun and other sources bouncing off objects and entering our eyes, she viewed the light as emanating from her own eyes to illuminate objects, much as the ancient Greeks did. Once she erased this false concept from her mind and adopted the correct one, her problems diminished greatly.
To emphasize this in our current situation, look at your hand again. It appears solid and continuous, which is why it doesn’t pass through whatever it is resting on. But you know, even from your elementary school education, that that isn’t really true. Matter isn’t solid or continuous at all, not even the heaviest and densest of things we normally encounter. All things, as you learned in school, are composed of extremely tiny elemental motes of matter known as atoms. You may even have learned that atoms consist mostly of empty space; an extremely dense but small nucleus of protons and neutron, around which tiny things called electrons orbit.
* * *
I recall my father introducing me to the concept of atoms over the dinner table when I was about seven or eight. He sat at the head of the table, and I was the first one on his right (at the left end because, as I have just mentioned, I’m left-handed). The details are lost to me now but I’m quite clear that one day, as we were all sitting down to dinner, he introduced the concept to me. Mind you, my father was not a highly educated man. I don’t believe he ever even finished high school. But he worked for a chemical company, and had picked up enough science to give me my first taste of the subject. That first taste was that everything – yes, everything – is made of atoms (a story I later learned was not entirely true).
Look upon your hand again. Yes, it is made of atoms. If you are curious (and if you are not I cannot imagine why you are reading this book), the atoms are mostly carbon, oxygen, hydrogen, and nitrogen, with some phosphorus and sulfur thrown in, along with a smattering of iron, calcium, sodium, potassium, chlorine … you get the idea. My hope is that you begin to see why I began this chapter as I did: your perception of your hand and what your hand actually is are quite different things. The perception is for the purposes of your survival and reproduction. The is is what science tells us: the objective reality. Do you begin to see why satisfying our curiosity as to the nature of things is so difficult? Because it so often requires we think about things in a way that is utterly foreign to our normal experiences. We do not experience atoms, either in our hand or, for that matter, as what air is made of. We have this built-in concept of matter as being solid and continuous. But that concept, or instinct if you prefer, is wrong. It is misleading. It blocks the path to comprehension. So if we are to comprehend, very often we are required to cast our instincts and concepts aside, and look at the world with fresh eyes. One of the ambitions of this book is to help you to do precisely that.
Again, stare at your hand and try to see it, not as the solid, continuous thing it appears to be, but as a vast collection of exquisitely small but exquisitely alive, vibrating atoms, interacting with each other and with the environment around them. If you find this difficult to do at first, don’t worry, or give up. You are not being asked to hallucinate (fascinating as such an hallucination would be), only to imagine it – remembering that you cannot truly picture it, you can only simulate the image by making the atoms much larger in your mind than they actually are. So just relax and imagine you are some Lilliputian being transported into this world, observing what such a tiny creature would imagine. Do you have it? Good.
(I can’t resist. There is a scene in the original The Matrix movie, in which Neo at last directly perceives the artificial reality people live in as a stream of symbolic logic symbols; this is truly his moment of liberation, more than anything else. What I am talking about here roughly corresponds to that moment in the movie.)
Now that you have this image before your eyes, I am going to do something cruel: I am going to take a sledge hammer and … no, I am not that cruel. Besides, I don’t need to completely smash that image, however; just enough to let us begin on the next leg of our long journey toward truth – a journey which never actually ends but does take us to the most fantastic worlds and universes. Actually, the general picture you probably absorbed from your schooling is, in the basics, correct: the atom is composed of a a tiny, dense nucleus composed of protons and neutrons, and a cloud of electrons which are somehow around the nucleus – probably you picture them as orbiting the nucleus, in much the same way as Earth orbits the sun, but that is the part I am going to smash, so I won’t emphasize it. The essential picture is, in many ways, correct, especially the part about the atom being almost entirely empty space, meaning that ordinary matter is almost entirely empty space, our perceptions notwithstanding.
It is correct enough to explain why your hand seems solid and cannot pass through walls or desktops. The electrons at the outer edges of your hands encounter the electrons on the wall or surface, where they electrically repel each other so strongly that you would have to rend the matter of your hand and / or the surface of the wall into tiny shreds to make your hand pass through it. That’s right, the apparent solidity is in fact just electrons repelling each other via the electromagnetic force, which is astonishingly powerful – some 1039 times as powerful as gravity (no doubt this seems hard to believe; why gravity appears to be the stronger force is something we will explore later). Your sense of solidity has nothing to due with understanding what is really going on. Nothing to do whatsoever. Remember this. The world is not what it seems. Implant this in your mind, and nourish it like a rich garden. It the key to satisfying curiosity.
* * *
Actually, perhaps you think that atoms are obvious. After all, you went to school where the subject was introduced, and now it may seem as commonplace as other unlikely truths, such as the sphericity of Earth, or the fact that Earth is orbiting the sun and not, as your eyes plainly tell you, vice-versa. But it is not obvious at all. Reflect on the fact that, for a century after John Dalton first proposed the modern concept of atoms in the early 1800s, using the reasoning of the whole number proportions of elements that went into reactions, the great majority of scientists rejected the idea of atoms being real right up to the early 1900s. Nor were they fools for doing so, because the idea of atoms leads to serious conflicts with Newton’s Laws of Motion and the Laws of Thermodynamics as they were then understood. The reason for this is that Newton’s Laws of Motion are time reversible – that is, you cannot distinguish between a process happening in forward time as from one happening backwards; while the Laws of Thermodynamics, in particular the famous Second Law, and its greatest creation, the concept of entropy, state that energy – in the 1800s regarded as a form of fluid – moved inexorably from regions of low entropy / high order in time to regions of high entropy / low order at later times. The bottom line of this view was the so-called “heat death” of the universe, which appeared inevitable, at least from 19’th century perspectives. But if matter were indeed composed of atoms, the reasoning went, then their interactions, as derived from Newton’s Laws, would be time reversible, in violation of the Second Law, which says that entropy – disorder – must always increase. There appeared to be an irreconcilable contradiction here, one that led most scientists, and philosophers, to dismiss the actual existence of atoms as a phantom, despite the increasing evidence from the work of men such as Rutherford and J. J. Thompson that they did indeed exist.
* * *
It took the brilliance of one Ludwig Boltzmann to reconcile the seemingly unreconcilible, which he did by devising a new, subtly different definition of entropy, or disorder. Assuming atoms were real, Boltzmann deduced that the Second Law still held if one took a statistical view of entropy, rather than an absolute view of it. To appreciate Boltzmann’s insight, consider a deck of cards. If the deck is perfectly ordered – i.e., ace of spades, king of spades, queen of spades, etc., down through all the other houses in similar order – then obviously any shuffling of the cards will invariably destroy that order. The order is unlikely to be completely destroyed, however; if we examine the deck after one shuffling, we will still find that isolated pockets of order have survived, both large and small. One might say that the deck is still semi-ordered; that its entropy, while not zero any longer, is still fairly low. It is certainly much lower than a deck of cards that has been shuffled many times, so that all order is lost, but much higher than our original, perfectly ordered deck.
Now consider the second, or third, shuffling. Again, we regard it as likely that the cards will be in less order with each shuffling; or conversely, will possess more entropy. But the key word here is “likely”; it is possible that, purely through the vagaries of chance, that a shuffling will result in an increase of order. In truth, a truly random shuffling will result in a completely unpredictable order of the cards; this in fact is practically the definition of random. But if the order is truly unpredictable, than it very well can be a more ordered arrangement of the cards than before the shuffling! Here is where the key insight lies. It can be, but is unlikely to be, more ordered, simply because if one examines all possible arrangements of the cards, there are many more disordered arrangements than ordered ones. This is why we expect shuffling to decrease the disorder; it is purely a statistical assumption, yet an excellent one simply because there are so many cards. If, instead of fifty-two cards, there were fifty-two thousand, the ratio of disordered arrangements to ordered arrangements would be vastly greater and the likelihood of increasing disorder / entropy by shuffling proportionately greater.
Let us move from card decks to actual, ordinary realities. A single cubic centimeter of air contains not fifty-two thousand but over ten million trillion molecules of various gasses. Thus, the odds of any random process decreasing its entropy (increasing its order) is so infinitesimally small that we regard it as essentially certain not to happen. Indeed, it is so small that we simply say that entropy always increases.
But we are wrong. Entropy doesn’t always increase. It is a purely probabilistic law, which says that order is almost certainly likely to decrease, especially in a system with more than a few dozen or so parts. But almost certainly isn’t always. It may be so often that in the entire lifetime of the universe we never observe its overall order decrease. But nothing says that it can’t happen. It is just overwhelmingly unlikely to happen.
Boltzmann’s insight neatly resolved the apparent conflict between the Second Law and Newton’s Laws of Motions. The evidence coming out of Rutherford’s and Thompson’s laboratories, among others, convinced the scientific world of the truth of atoms in the early nineteen hundreds. Sure, entropy almost always increases, so almost that we never observe the opposite however long we observe, but it is not impossible. For tiny systems, however, it can and has been observed to happen. Newton’s laws and thermodynamics agree after all.
* * *
This book is not meant primarily as the history of scientific ideas. But sometimes it is impossible to both pique and gratify our curiosity without covering the grounds that minds before us have covered. The atom is a perfect case in point. It is both obvious (mainly because we are taught it) yet devilishly elusive at the same time. The above discussions shows a part of the reason why this is true. But – and now we enter Alice in Wonderland territory – it is not the only reason. If anything, in fact, things become truly strange from here on. So buckle your mental seat belts and lets prepare for a wild ride.
Even as atoms were being accepted as real in the early twentieth century – for the record, Einstein’s experiments on Brownian motion probably clinched the case as much any other work – physicists were still in an utter quandary over just how they could be real. By all known laws of physics up to the twentieth century, atoms were simply impossible. Just that: impossible.
The reason for this has to do with the well known analogy between atoms and solar systems, what atoms were modeled from. Earth and the other tiny planets orbit the massive sun, in a seemingly infinitely stable manner, in much the same way as the tiny electrons were proposed to orbit the massive nucleus of protons and neutrons. It is a very natural analogy, which Rutherford initially proposed. And which everyone saw at once could not possibly work.
Analogies are tricky things. We humans naturally employ them when explaining phenomena hitherto unexplained. Analogies can be very powerful, and often form the basis for new insights and explanations in the natural world. Scientists and laymen alike have been using them with wonderful successes for centuries. But there is a nasty snare in this whole process of analogizing, which is why, as Richard Dawkins laments in The Blind Watchmaker “… analogies can be immensely fruitful, but it is easy to push analogies to far, and get overexcited by analogies that are so tenuous as to be unhelpful or even downright harmful. I have become accustomed to receiving my share of crank mail, and have learned that one of the hallmarks of futile crankiness is overenthusiastic analogizing.”
The main reason for this, I suspect, lies in the fact that analogies are just that: compendia of likenesses between something we do understand with the phenomena we are struggling to make sense of. The problem is, almost nothing is really exactly like something else. The appearances of similarity may in fact be purely superficial, and so lead us nowhere (the “Argument from Design”, so often employed by people who reject evolution is, I think, a good example of this). More often however, and this is where the snares are baited and waiting and the unwary are in greatest danger of being caught, come from analogies that work quite well to a certain depth of understanding, but fail at a deeper level of analysis. The analogy between atoms and solar systems fall right into the middle of this dangerous pit; so enticing to the casual eye, but lethally flawed to those who have looked deeper.
Here is the problem as concisely as I can give it. The planets orbit the sun in what appear to be eternally stable orbits, but that it is not actually true. According to classical physics, any object accelerating through a force field (in this case, a gravitational field), where accelerating means either speeding up, slowing down, or changing direction, gradually but inexorably radiates energy away. In the case of planets, the energy lost is in the form of gravitational waves, which are extraordinarily weak. The net result is that the planets’ orbits about the sun are only approximately stable; eventually they will fall into the sun, but not for many trillions of years and more, a time period in which much more serious things are going to happen to the solar system, such as the sun running out of hydrogen fuel and blowing up into a red giant, roasting or destroying all the inner planets, then contracting to a white dwarf, leaving all remaining planets in an eternal deep freeze.
For a single electron orbiting a single proton, the simplest atomic model, the hydrogen atom, the same physics apply, but the time scales are vastly different. Remember the 1039 difference between gravity and the electromagnetic force, the force which attracts the electron in the hydrogen atom to its proton nucleus? Do the necessary calculations and you find the electron radiating away all its energy as electromagnetic radiation and crashing into the nucleus in a tiny fraction of a second. All the other atoms must suffer the same fate, and if indeed this is how physics works at this level, then matter as we know simply could not exist.
And so, by the early twentieth century it was clear from indirect and direct experiments on the nature of atoms that there was no choice but to conclude that, in fact, physics was incomplete, and did not provide a true description of nature at this scale. A new model and new laws were needed, laws that might seem counter-intuitive to common sense (always the bane of science) and even to the known laws of physics. Of course it couldn’t completely overthrow those laws, as they had explained so much as about how reality works, but it must give a deeper, subtler, and more complete description of those laws.
The first attempt to square the now accepted reality of atoms with physics was made by Neils Bohr, in 1913. Bohr accepted the basic Rutherford model of the atoms, of electrons orbiting a tiny, dense nucleus, but added a caveat to the system, based on work previously done by Max Plank and Einstein: He arbitrarily decided that the electrons, unlike planets orbiting the sun, couldn’t have any energy but were restricted to certain, “quantized” values. Atoms didn’t collapse because the lowest allowed quantized level was not zero (an assumption Bohr had no justification for except that it made his model work). To speak strictly correctly, Bohr didn’t quantize the energy of the electrons but their angular momenta, but the difference need not concern us here; what is important is that he was able, for the hydrogen atom, to construct a model with quantized electron orbits, which perfectly explained all the properties of this atom, especially its spectral lines, which were the result of electrons “jumping” (Bohr had no concept for what actually happened when an electron switched orbits) from outer to inner orbits, and releasing the energy in the form of light photons of a specific wavelength.
Bohr’s model for the hydrogen atom was a stunning success and showed the world he was on the right track, but many puzzling problems remained. First, Bohr could not make a working model for any other atom in the periodic table, or any molecule, which are combintations of atoms bound together. Second, his arbitrary assumption of quantized energy levels was just that: arbitrary. It made his model work in an ad hoc fashion, but there was no deep, underlying physical explanation which lay beneath it, an explanation which was satisfying to physicists of the day. Clearly, something more was required. It was that something more, however, which was to set the scientific – indeed the philosophical – world on its heels. For what was required was nothing less than a reevaluation of the very nature of physical reality itself; a reevaluation which still has scientists and philosophers debating to this day.
* * *
In a book about curiosity, it is fitting that what follows is probably the most curious thing scientists have ever uncovered about nature. Echoing the theme from chapter one, it demonstrates just how amazing and profound and unexpected our discoveries will be whenever we are overcome by our desire to know and just have to peek under the covers a little to see how nature genuinely works. It also extends the theme with which I began this chapter, on how scientific understanding undermines and even obliterates our cozy and seemingly so real perceptions of reality and shows that we must look at the world with fresh eyes and imaginations if we are to have any chance of comprehending it. For the world of quantum physics, the bizarre Alice-In-Wonderland world we are about to enter, not only obliterates our perceptions; it challenges our capacity to think at all. It is like a dream in which nothing makes sense, and fades instantly the moment the dreamer awakens.
It is probably the ultimate irony that in the human quest to satisfy our curiosity, we have been ultimately humbled by the inescapable fact that our answers shall always be inherently uncertain. The quest for knowledge has yielded the knowledge of the limitations of that quest. Perhaps we should have seen it coming. We can certainly enjoy the cosmic joke it has played on us. I have no words to match those of Jacob Bronowski, who captured the new view of reality in chapter 11 (“Knowledge or Certainty”) of The Ascent of Man:
One of the aims of the physical sciences has been to give an exact picture of the material world. One achievement of physics in the twentieth century has been to prove that aim is unattainable.
Take a good, concrete object, the human face. I am listening to a blind woman as she runs her fingertips over the face of a man she senses, thinking aloud. ‘I would say that he is elderly. I think, obviously, that he is not English. He has a rounder face than most English people. And I should say that he is probably Continental, if not Eastern-Continental. The lines in his face would be lines of possible agony, I though at first they were scars. It is not a happy face.
This is the face of Stephan Borgrajewicz, who like me was born in Poland. In plate 175 it is seen by the Polish artist Feliks Topolski. We are aware that the these pictures do not so much fix the face as explore it; and that each line that is added strengthens the picture but never makes it final. We accept that as the method of the artist.
But what physics has now done is to show that that is the only method to knowledge. There is no absolute knowledge. And those who claim it, whether they are scientists or dogmatists, open the door to tragedy. All information is imperfect. We have to treat it with humility. That is the human condition; and that is what quantum physics says. I mean that literally.

No absolute knowledge? All information imperfect, to be treated with humility? The only method to knowledge that of the artist? Just what is going on here? Hasn’t all our curiosity been about getting to the ultimate and final truth? Yet what we seem to be hearing here is that there is no so such thing; worse, that we are in danger of falling into dogmatism and even tragedy if we insist on pursuing it to that end.
* * *
Partly by design, partly by accident, this chapter has meandered through several different, though interrelated, themes, the main one being science, our best and in my opinion only realistic hope of satisfying curiosity, repeatedly demanding that we use our imaginations to view reality in ways we had never considered, and which often seem counter-intuitive. Part of that imaginative use means accepting that things are often not at all what we perceive them to be. Another part, the part we are coming to, is that what must even be careful about relying on any intuitions or “common-sense” if we are to understand the way the universe works. I do not mean to say, however, that intuition, perceptions, and common-sense are always wrong or useless; by no means is this so. But we must proceed cautiously and with open minds and eyes if we are to make progress.
Once again, look at your hand and visualize the tiny, vibrating atoms which compose it, much the same way that the tiny, vibrating bees constitute a hive. We left off with Bohr’s description of these atoms, which said that the electrons did indeed orbit their nuclei, albeit in fixed, quantized orbits. We noted that Bohr himself had no explanation why nature should work this way at this scale, instead of continuous orbits like those of the planets around the sun. This was a weakness in Bohr’s original visions, which of course he realized; Bohr understood only too well that what he was suggesting was nature was something more bizarre and counter-intuitive than our senses captured for us.
* * *
This is not a history on the development of quantum mechanics, so I will leave out quite a bit of interesting detail here (like de Broglie’s wave model of electrons, which was actually quite critical to the final vision). What I’d like to do at this point is use the cherished method of analogy again, to help you appreciate the true situation of how electrons behave in atoms and molecules. Again, I think this is more helpful for the layman to start this way.
My analogy is that of a tennis match. Imagine that you are watching the ball sail back and forth between the players (this could be a bit tough if you are picturing modern professional players, who hit those seemingly impossibly hard shots from all angles; so try to make it a friendly game on a local court somewhere). As you watch the ball, even in this friendly match, you are aware that it still seems a blur much of them time. At no particular moment can you make out exactly where the ball is, or how fast it is moving, or its precise direction.
That’s fine. What you are experiencing is simply the limits of your visual acuity system, involving your eyes, optics nerves, and the parts of your brain which process the information. They can follow the situation only so quickly, and the result is that things seem somewhat blurred to you. Still, and despite this, you accept the proposition that, at any given moment in time, the ball has an exact location, and has an exact speed and direction. You can’t pick it up, but certainly a sensitive enough piece of equipment – say a strobe camera operating at high speed – could do so easily. You take that as given. It is just “common sense” you might say.
Yet – and here is the part where you must starting thinking in as unorthodox a manner as possible – you would be wrong. However, in our hypothetical tennis match, not even the most sensitive instrument ever built would show you that you are wrong. That is because the mass of a tennis ball is simply too overwhelmingly huge. Indeed, the mass of a dust mote would be too overwhelmingly huge as well. This is why we don’t ordinarily notice our error; from the viewpoint of creatures our size moving amongst objects that we can see and touch, the error is so small it would never show up. Thus, our brains and sensory systems, which have been attuned by natural selection to deal with objects of approximately our sizes, has a hard time grasping the concept what I am about to tell you. But electrons, which are vastly smaller in mass than anything we shall ever come in contact with, don’t behave the way that the analogy with tennis balls would suggest. They don’t behave that way at all, simply because they are so small in mass. The most concise way of expressing their real behavior is, with all due apologies because I want to avoid math as much as possible, is with an equation:
x × s ≤  / m
Hopefully, this is not too complicated a piece of math to throw at you if you are tucked way in front of a roaring fireplace, all comfy and cozy. Or reading it over your three minute egg at breakfast. But I am going to ask that you look at this equation and drill into your mind, for you shall miss much of what is to come if you don’t. Oh, and before proceeding, this equation is just one version of what is commonly referred to as the Heisenberg Uncertainty Principle, after Werner Heisenberg, who first elucidated it in the 1920s. Some definitions are in order here. First, the sign refers to an uncertainty. In the case of x, what it means is that there is an inherent uncertainty of the position of a particle (tennis ball, dust mote, or electron) at any given moment. Understand something very clearly here: we do NOT mean an uncertainty due to the limitations of any measuring devices; we mean that nature herself does not allow us to say exactly where in the region of uncertainty the particle is – it is as though the particle doesn’t even have an exact position in the region of uncertainty, it is just somewhere within it. Take some time and let that sink in, odd as it sounds, for it is contrary to all your intuitive, common-sense view of how the world works; yet it is critical to understanding the ideas that will be developed here and later. Yes, I am saying that there is inherit uncertainty, and no measurement can reduce or eliminate it; it is built into the foundation of nature’s laws as strongly as the law of gravity or the laws of thermodynamics.
Likewise, the symbol s is an expression of the uncertainty in the speed of the particle, tennis ball, dust mote, or electron, at any given instant. We do not know exactly how fast it is travelling; we can only determine it’s speed within certain limits. Again, this is another oddly-shaped brick in the foundation of natural law. Accept it, strange and counter-intuitive though it might sound as well.
One thing you should see that comes out of the equation is that as x increases, s must grow smaller, and vice-versa. Why? Because their product is a constant, the [ / m] part on the right side of the equation. Thus, if we could measure the position of a particle exactly (x = 0) then s would become infinitely large, while if we measured its speed with perfect precision (s = 0) then x becomes infinite . The second salient point I must mention here is that the product of the two uncertainties, x × s, is always equal to or less than the quantity / m, whatever that is. It turns out that is exceedingly small, on the order of 10-34 newton-seconds, which, I assure you, is a minuscule quantity. It is, for all you scientific pedants out there, a symbol representing the so-called Planck’s constant, which Planck devised around 1900 while working with blackbody radiation, and which Einstein used later to explain the photoelectric effect and Bohr to construct his model of the hydrogen atom (actually, the real constant is h, while is h divided by 2π). m, on the other hand, which is the mass of the object being measured, makes this ratio smaller or larger, depending on its own size. You will all breathe a sigh of relief when I tell you that for m on the scale of a tennis ball or even a dust mote, x × s or / m is so infinitesimally small that, as I have said, it is to small to be measured with even our most powerful and sensitive instruments. Hence, in the world we experience, tennis balls and dust motes and cars and planets, the equation x × s ≤  / m for all practical purposes might as well not even exist. Whew! What a relief, I suspect you are saying, for if it were significant the world would be fantastically different from what we actually experience. Here’s the important point, however, and why I harp on the equation and demand that you absorb and digest it. For an electron, where m (mass) is excruciatingly tiny indeed, this equation – Heisenberg’s Uncertainly Principle -- dominates its behavior. In the next chapter, the one on matter and chemistry, we will explore the consequences of being at the low mass end of things.
And so on to matter and chemistry, and how all this uncertainly stuff fits in.

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