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Tuesday, January 22, 2013

Chapter Five of Wondering About


Wondering About Ourselves

 

 
One of themes of this book is that if we are to satisfy our curiosity about the universe around and within us, we will need to use our imaginations to the best of our abilities, because the universe as we perceive with our physical senses will only take us so far. We saw this first in chapter two, in which our robotic exploration of the solar system revealed worlds which we had not foreseen, at least partly because we had not completely unleashed our imaginations on the possibilities. In chapters three and four we were forced to use our imaginations again to picture how the world of the ultra-tiny, or atoms and electrons, works, by suspending our common-sense ideas and perceptions so that such things could become real and not mere philosophical concepts, tangible things we could get our minds around and acquire a sense of their true nature. My point is that in these journeys we have gained a certain intellectual satisfaction – real questions leading to real answers – but again we are being warned that clinging to the world as modeled by our eyes and visual cortexes is a habit we are going to have to resist, one way or the other, if we expect to keep making progress.
This chapter is on biology, which is why I begin with this emphasis on imagination, for with the possible exception of quantum mechanics, I believe nowhere is imagination more required than on the subject of life. Living things, their origins, their myriad shapes and actions combined with their underlying foundations, and how their marvelous, interdependent, and beautiful adaptivity to all environments they find themselves in, is a series of mysteries that will not yield to the unimaginative mind, however much plodding thought is brought to bear on them. Unconvinced? Then let’s start with the big question, the question even the most renown scientists have been beating their heads against right up to today: What is life? We see it practically everywhere we look (at least on this isolated, tiny planet) and we generally find we have no difficulty in distinguishing it from the world of the non-living.
I think at this point most of us would stop and agree, perhaps after some careful thought, that there is something essential about living things. The impression of this essentialness, this intentionality I will call it, is indeed overwhelming, and easily hits us on the head as the prime divider between life and everything else. All non-living things seem to follow the laws of physics in a dumb, obvious way: a pebble thrown into the air traces out a perfect mathematical parabola as it interacts with the law of gravity, finally striking earth in a completely predictable place at a completely predictable time, given that we know its initial speed and angle with respect to the ground. A pebble thrown into the air … but what about a butterfly? When we watch a butterfly we put away our calculators and measuring instruments, and simply watch in wonder. A butterfly doesn’t blindly follow a parabola, it – well, it seems to do whatever it decides to do, which is why making measurements and calculations are pointless. A butterfly flies away, perhaps never to be seen again. Or maybe it alights on a flower and gazes at us, seemingly as equally puzzled by us as we are of it. We are just certain there’s something going on behind those tiny eyes. Something inexplicable. Something essential. Something that gets down to what makes a pebble just a pebble but a butterfly something ... at the risk of being misunderstood, miraculous.
We still have taken only a few steps in our attempt to define life, however. For the next question is, is our butterfly, and by implication ourselves, truly miraculous?
* * *
Let us try a different tack. Richard Dawkins, in The Blind Watchmaker, proposes a definition of biology that is unusual but which he claims to be perfectly workable: biology is the study of complex things that appear to have been designed for a purpose. I speak of intentionality, but complexity plus the appearance of design provides us with another way of describing it, perhaps an even better way to make progress. Dawkin’s point when applied to our butterfly is threefold; first, like all life forms it is far, far more complex than the pebble, far more complex than our solar system even; second, not only does it act as though it has a mind capable of intentions and a body capable of carrying those intentions out, it gives all the appearance in the world to have been designed that way, designed to fly (as well as many other things); and third, and most significantly, there is an intimate relationship between complexity, intentionality, and design. Flying is not a simple thing, not the way butterflies do it at any rate, so complexity plus design, or as I call it, intentionality, appears to improve our handle on what we mean when we say something is alive.
But is it enough? Or for that matter, is it really true? Living things do not always appear to be complicated. Anyone dissecting a butterfly – no easy task, admittedly – would marvel at its many interlocking intricate parts, but what about the simple amoeba? Or a bacterium? At first sight, such things do not appear to be particularly complex, but we all agree that they are alive; that, like the butterfly, they appear to move under the guidance of some internal intentions, some essence which non-living things, even complex ones like computers, do not possess.
Most of us, I suspect, will find ourselves easily moving along some kind of reasoning like this, perhaps without thinking about it very much. It does seem to handle our common sense objection to calling complex things like computers and airplanes biological while keeping “simple” things like bacteria and amoebas in the same camp as butterflies and human beings. Living things, from the simplest up to the most complex, really do seem to have some special quality or essence that ordinary matter lacks, whatever else that matter has. We almost can feel it there, at the most basic levels, and we are certain that we would never have any difficulty in distinguishing a living thing from the non-living, based on that feeling. Wherever in the universe we might find ourselves, the question of whether we were amongst life or not would appear to be elementary.
* * *
Or would it? To our astonishment, our common sense view of things biological begins to disintegrate the moment we apply curiosity and imagination to it, to dissect it and look into it at the finest levels science allows us to probe. In doing so, try as we might, we never encounter this special essence or quality which seems so obvious at first sight. Instead, what we do find, when we break out our detectors and other scientific instruments, is that living things are composed of atoms and moledcules like everything else, albeit not in the same elemental proportions, yet acting according to the same laws of physics and chemistry as everything else. The mechanical, Newtonian universe of objects and forces, modified by quantum effects on the smallest scales, appear all that is needed to explain why butterflies fly, or mate, or find food, or stare at us with the seeming same curiosity that we feel gazing upon it. All our initial impressions, and all the stories that have been told and retold aside, there appears no miraculous special something that we can affix to or inject matter with to make it come alive; no energy fields, no forces, no protoplasm, no elixir of the living, nothing we can pump into Dr. Frankenstein’s reassembled parts of corpses which will make it groan and open its eyes and have thoughts and feelings and break its bonds to move in accordance with them. There is nothing like that whatsoever. No, whatever it is that characterizes life lies elsewhere.
But the impression of such a force is so strong, so deep, so instinctual that, try as we might, we cannot simply abandon it without at least wondering why it is there, where it comes from, and what it tells us. Something is there, of that there can be no question.
Intentionality. Complexity. Design. Try to put aside your ordinary impressions and perceptions of things, and seed your mind, germinate in your mind, take root and push out of the soil and put forth leaves and vines in your mind, the theme that to satisfy our curiosity we must look at the world from a different perspective, the one that imagination unlocks. Very often, we find that when we look closely, what we thought we were seeing fades away, yet is replaced by something just as amazing – no, more so.
Let us start with the simplest of things that could be called living. Consider the virus. Here is something both considerably smaller and simpler than the smallest, simplest bacterium, all biologists would agree. But on the most microscopic of scales, that of individual atoms and molecules, even the simplest virus turns out to be a machine of remarkable complexity. At the very least it has to be able to recognize a host cell it can parasitize, whether it is a cell in your body or a bacterium (in which case it is called a bactaeriaphage), somehow figure out the molecular locks and other gizmos which cells use to protect themselves from invasion, penetrate the defenses, then usurp the molecular machinery the cell uses to replicate itself, perverting the cell into a factory for producing many more copies of the virus, copies which then have to figure out how to break out of the cell in order to repeat the cycle on other cells or bacteria, all the while avoiding or distracting the many other layers of defenses cells and bodies use to protect themselves from such invasions.
Biologists still debate whether viruses can be legitimately counted among the various kingdoms and domains of life, but there is no doubt that their hosts, whether bacteria or other single celled organisms or multicellular organisms, can be classified in the great Tree of Life, from which all other living things, be they plants, animals, fungi, or you, diverge from. And what dominates this tree, right down to the most primitive beginnings we have yet been able to detect, is a level of complexity that we simply do not encounter among the great many more things than don’t belong on this tree, from rocks to stars to solar systems to galaxies.
So after all this, have we cornered our quarry? We started with the at first sight idea that life possessed some special quality or substance or essence, then realized that we could not find that essence however hard we looked. But what we did find was that living things, even the simplest of them, showed a level of complex organization well beyond the most complex of non-living things.
Life is special. I don’t want to lose sight of that. We are fully justified in our grand division of matter into the non-living – things we explain only by the laws of physics and chemistry at a simple level – and the living, all the things we must also apply whatever biology has to teach us. What I have been trying to show is that, whatever that specialness is, it isn’t as obvious as it appears upon first sight. It is more subtle, involving a number of characters and qualities, one of which is complexity and another the appearance of design or purpose.
* * *
Again, I say that life truly is special. It is early May, and I have just come home from a walk through Pennypack Park, one of the many lovely natural places which skirt the city where I live, Philadelphia, one of several cities along the eastern edge of North America. I would love one day to walk on the moon or on the red soil of the planet Mars, but what I have just experienced would be utterly lacking in those dead, albeit fascinating places. In the spring in this part of the world, as in many other parts of our planet, every sense is roused to life by the call of the wild. Not only are you surrounded by the verdant green of new buds and flowers and grasses, but also by a cacophony of whistles, chirps, tweets, and other rhythmic sounds which reminds you that you that new life is all about, some of it still rustling itself to full wakefulness after winter but much of it already in the air and alit on the many twigs and branches. And even without vision and sound, you can still smell the musty beginnings of stirrings things, the scents of enticing blossoms and irritating pollens, and you can still feel the grass between your toes and the softness of young leaves on your skin as you brush by the undergrowth.
Here I have spoken of complexity and the appearance of purpose and meaning, and perhaps that is exactly what our scientific mission into the heart and soul of biology requires, but this is one place where, I have to submit, we will never really capture the essence of what we are studying. Life is something that has to be experienced, and only living things themselves have the capacity, as far as we know, to experience anything. So, in a sense, our quest to satisfy our curiosity begins with the admission that, at least for the world of the living, we never can completely satisfy it.
Am I going to give up, then? No, because, as I have maintained up to this point, curiosity combined with imagination and the scientific method can undo any knot, unlock any riddle, however baffling and impervious it may seem. I have even suggested a starting place even, this idea of complexity combined with apparent purposefulness, an idea I hope to build upon and demonstrate just how powerful it is. I think we can agree that it is a good starting place. Biological things, even the simplest of them, are highly complex, we now see, and there does seem to be something to this notion of being imbued with purpose, however that comes about. If we can make some progress on this front, then perhaps in the end we will satisfy our intellects after all, as impossible as that seems looking at things from their beginnings.
* * *
Actually, I would like to strike out first on a different front than is typical in tomes on biology. I would like to retreat back to simple matter, of the kind we started to explore in chapter four, and work up to what I see as an essential question: can the laws of physics and chemistry, as we have come to know them, even provide a platform for the vast complexity of living things? In other words, do atoms, those basic building blocks of all things material, even allow for the enormous intricacies let alone purposefulness of the biological world?
This is a very good question for it turns out, at least for the great majority of atoms that we investigate toward this end, the answer is a clear and resounding No. Try as hard as we can, we find that when we begin assembling most atoms into more and more complicated molecules or other structures, they aren’t very cooperative in this process. No, things fall apart, often violently, even if we can figure out a way of putting them together. For the great majority of the kinds of atoms to be found in nature, constructing an edifice of complexity sufficient for life is a hopeless task. They simply will not stay put and do as they are told.
All that is with one, yes really only one, fortuitous exception, and one that we began to explore in the previous chapter. The carbon atom. Atomic number six on our periodic chart, a chart which now runs to over a hundred if we include the extremely short-lived ones humans have made in laboratories, is truly special. Carbon is what makes it all possible, to the point where we can confidently say that if that if this one lone atom out of the dozens had proved impossible for the universe to produce in any significant quantities, neither you nor I nor any of the myriad millions of species of life we share this planet – on perhaps any planet – with would have any chance at existing. Carbon alone is not sufficient for life, but it is absolutely necessary. Of all the other elements in the biological stew, perhaps substitutes could have been found, but no element, under any conditions imaginable, appears a likely alternative to carbon. This is because no other element yet discovered or made could take its place as the backbone of the sizes and varieties of the molecular components needed to make life, even the simplest forms of life, possible. I will even go as far to say that if an alternative form of life is ever found, if carbon isn’t at its roots than neither is chemistry.
Carbon, indeed, is so important that it is the only element whose existence was predicted by the fact that living things do exist. All of the naturally occurring elements in the universe today come from one of two sources: either they were made in the first few minutes of the universe’s existence, in the Big Bang which we will come to in a later chapter, or they were made in the cores of the many trillions of massive stars that have come and gone since the beginning. The reasons for both is the same: larger, more complex atomic nuclei – the core of protons and neutrons which make up the center of atoms and ultimately determine their respective element’s properties – have to be made from the simpler ones, ultimately from the simplest of them all: hydrogen, atomic number one, a single proton (sometimes combined with one or even two neutrons). This is done by smashing two smaller nuclei together to make the larger one, a process which requires extremely high pressures and temperatures because all nuclei are positively electrically charged and ordinarily repel each other unless they can be brought close enough together to be captured by something called the strong nuclear force. Such conditions existed naturally only in the moments after the Big Bang and today in the hearts of stars, particularly the larger, hotter stars. Essentially, to create a carbon atomic nucleus of six protons and six neutrons, what must happen is that three helium four nuclei, each consisting of two protons and two neutrons apiece, must be welded together in exceedingly short order, within a millionth of a millionth of a second, and then held together until they can relax and become stable. This so-called “triple-alpha” process (an alpha particle is a helium four nucleus) would itself seem to be an insurmountable barrier to carbon and all the elements beyond, but surprisingly that turns out to be not so: the pressures and temperatures which come to exist in large stars – stars large enough to explode or somehow spew their core substances into intergalactic space, making all those large atomic nuclei available to new generations of stars and planets such as our own, not to mention our own existence – are sufficient to guarantee this process will happen enough to account for all the carbon we are going to need.
With one problem. This problem lies in the fact that our newborn carbon nucleus is ringing and pulsing with so much energy that it should almost instantly fragment into smaller pieces. What we need is some kind of stable “resonance” at such high energies, which will allow the newly born nucleus to hang together just long enough to relax by a variety of processes into a lower, energetically stable state. But when the details of Big Bang and stellar nucleosynthesis were being worked out in the 1940’s and 50’s, no such resonance state was known, nor was there any theoretical reason – theoretical from the standpoint of physics at that time that is – to think one should exist.
The problem was solved by the single and to this day to my knowledge lone instance of the so-called Anthropic Principle being used to successfully explain an actual physical fact. If you are not familiar with it, the Anthropic Principle, in its most basic, common-sense form, is simply the statement that since we exist in this universe, the laws governing it must be compatible with our existence (this seems obvious, but there are other versions of the Anthropic Principle which are more controversial). In this case, what the principle insists is straightforward and simple: it insists that since the element carbon does exist in sufficient quantities for our existence, there must be a resonance energy level available for the newly bred nuclei. The Anthropic Principle is not an argument physicists are usually enamored of, but one group was sufficiently impressed by the line of reasoning to take an actual look and see if the resonance level really did exist. Lo and behold, they found that it did. In fact the discovery not only explained the existence of carbon in sufficient quantities in the universe, but also of the many elements that are in turn built up from it: oxygen, neon, silicon, indeed basically the entire periodic zoo of elements we find, to varying degrees of magnitude, present in the universe today.
* * *
So, carbon exists. It isn’t a very common element, and the fraction of it that does reside in our universe in conditions where life can form, is relatively small. But it is enough to account for, not just you and I, but all of the manifestations of biology all about us, almost anywhere you go on this planet, and probably what other worlds or places we may one day find life. The next question is, what is it about carbon that gives it its uniqueness, its specialness, its ability to construct the large and complex and seemingly purposeful phenomena that we call living things? What does carbon have that no other atom seems to possess, however hard we play with them and build castles in the air from them? Why do these carbon-based organisms which are found with such fecundity on Earth and hopefully on at least some other planets or moons or asteroids or places we’ve yet to think of, exist, continue to exist, and have existed for so long? Yes, carbon is special, but special in what ways, so many ways that no other atom has a prayer of filling its role?
The answer to this question is answered by a combination of chemistry and physics, some of which I have already explored in the last chapter. It involves two separate characteristics of carbon, chemical as well as physical characteristics, characteristics which carbon and carbon alone possesses, characteristics which we can never even mock up in any other element, however hard we try.
One of those characteristics is smallness. It is not coincidence that the great majority of the atoms which constitute life are to be found at the top of the periodic table, where the smallest and simplest of atoms resides. One reason for that no doubt is that small atoms are, due to the processes which forge them, simply more common than large ones. But another reason, the key reason, is that smallness means that these atoms can come much closer to each other in the bond-forming process, resulting in bonds that are much stronger and stabler than larger atoms can form. It is, in fact, well accepted, that the small sizes of the first and second rows of the periodic table account for much of the uniqueness of their chemistry, especially in the ways they differ from their heavier cousins, even in the same column. To give an example, sulfur, selenium, and tellurium are much more similar to each other than the first member of their column, oxygen. This is a statement which could be made for nitrogen and boron as well, and even, although to a lesser extent, lithium and fluorine. Small atoms make for short, strong bonds, something necessary if we are to build up to the size and complexity of living things and have them remain stable. Even a structure as small as a bacterium demands a level of complexity which only carbon and other small atoms can provide.
So smallness is important, but it is not sufficient. The reason for this can be found by examining the other elements in the first row, for example hydrogen, which can bond with one and only one other atom; usually another hydrogen atom, making the molecule H2, which is almost entirely what we are dealing with when working with hydrogen on the scale of pressures and temperatures we are accustomed to. Likewise, nitrogen and oxygen, also essential to life, appear to form stable binary molecules, N2 and O2, which do not spontaneously join together into longer, more complicated structures but make up the most common constituents of this planet’s air we breathe, which is about 78% N2 and 21% O2.
Following this line of argument, shouldn’t stable C2 molecules exist also, thereby undermining this theme of small atoms making large, structurally stable molecules, and once again pulling the rug out from underneath our feet in our quest to make the large, complex yet stable molecules and molecular edifices that biological things demand? Here is the interesting part, however; the neat trick by which nature refuses to be obvious but instead manages to provide us with exactly what we were looking for. For it turns out that C2 does not (or only rarely) exist, indeed is not normally stable, and once again we are allowed to proceed in the directions biology calls upon us to follow.
O2 and N2 are stable due to the smallness of oxygen and nitrogen atoms, but there are limits to how large you can build these small, compact molecules. These limits are inherit in the kinds of bonds that atoms can form with one another. In chapter four, I introduced the idea of the molecular orbital as the bond between two atoms created by the combination of the atoms’ atomic orbitals. The strength of the resulting bond depends on how well the atomic orbitals can overlap in space. This is where smallness comes into play. The bond between two hydrogen atoms is very strong because these atoms are very small and can approach each other quite closely, allowing for maximum overlap.
A picture being worth a thousand words, let me recapitulate some of the material for the preceding chapter about molecular bonds. If you’ll remember the case of the H2 molecule, we explained the bond as the overlap of s orbitals, in which two new orbitals came into existence:
one bonding one between the atoms, which strengthens the bond, and one antibonding orbital, which weakens it:


The bonding MO in this case has a name: it is called a sigma, or σ, bond, as chemists call them. This sigma bond, to reemphasize, is formed by the overlap of the s orbitals in the two hydrogen atoms, but more broadly, sigma orbitals / bonds are at highest density between the two orbitals. There is another type of σ bond, however, which can be formed by the overlap of p bonds. If you’ll recall, these bonds have the general shape


 
Here, the lines drawn represent the y (vertical) and z (horizontal) axes, while the x axis orbital would point at straight angles through the page. This is why I say that there are three p orbitals, all perpendicular to each other. Now, if you imagine the pz orbitals of two atoms, lying along the horizontal line above, the z axis, you can see how they too can overlap to form sigma orbitals, just as the s orbitals did. Very nice, and exactly what happens for many elements in the first row of the periodic chart. But now, remembering that there are three p type orbitals, you can see that in the case of two atoms the pz and the py don’t directly overlap, but appear to be parallel to each other. Hang in here. For I think I can make this clear with a few more diagrams and words. The orbital above, which I called py because the lobes are oriented in the y direction along the axis, cannot form σ (sigma) molecular bonding orbitals, because they don’t directly overlap between the atoms. But there are other kinds of bonds, bonds in which the overlap of the atomic orbitals is not so direct and obvious. The py and pz type orbitals possessed by the above atom are a perfect example of this. Still, using our imaginations, we can see that, although these orbitals do not combine headlong, there is nevertheless an overlap, an oblique or sideways overlap, between the lobes of the orbitals, for both the px and pz orbitals, if the atoms involved approach each other closely enough. The overlap is not as strong as with the pz orbitals, which directly overlap in the plane of the paper to form σ bonds, just like the s orbitals do, but it is there nevertheless. It is strong enough that we can construct new molecular orbitals, or bonding orbitals, using these oblique or sideways oriented atomic orbitals. Chemists have a name for these kinds of bonding orbitals as well; they are called π orbitals or pi bonds, again applying our habit of using Greek letters, in this case the letter π which we call pi. An example of this sideways, pi type bond is given below:

 
The nucleus of each atom lying at the center of the two py lobes is shown by the intersection of the x and z axes, while the py orbitals are the areas “smeared out” above and around them. Can you see that there can be sufficient overlap, and hence bond formation, between the two atoms using their py orbitals, shown by the grey regions, provided that they can be brought close enough together? Also, is it clear to the eye that the π bonds are not as strong as sigma (or σ) bonds, composed of either s or px orbitals, which occupy the space directly between the atomic nuclei, and that to have any strength at all the respective atoms must be able to approach each other very closely, which in turn means that only small atoms form stable π bonds? I think yes, just by looking at them, we can see that π bonds will be weaker and easier to break than σ bonds, a disparity that can only increase as we look at larger and larger atoms.

So. What has all this got to do with living things and their chemical makeup? As it turns out, plenty. The molecules N2 and O2 are stable only because of the smallness of their atomic sizes, and so can have as many as two (as in N2 or O2) π bonds, in addition to their σ bonds – this, by the way, is why we call them triply-bonded or doubly-bonded molecules.

Still, they would prefer for energetic reasons to exchange these π bonds and create or join in with molecules where all the bonding is of σ character; that is why we find how easily they combine with, for example, hydrogen atoms to make the simple molecules of water (H2O) and ammonia (NH3). Even carbon, which we are reserving as the basis of many manifestations of life, is often found bound up with hydrogen too, in this case to yield the simple molecule of methane (CH4) as seen in the last chapter. I should also mention to make this clearer that this is the same reason why third level elements, even those in the same family of nitrogen and oxygen – phosphorus and sulfur – do not easily form π bonds, as the larger size of these atoms do not allow them to approach each other closely enough; thus, we do no see p2 or s2 molecules, but more complex structures (this is also because these atoms have available 3d orbitals for additional bond forming, but we will not go there).

As we alluded to in chapter 4 carbon’s versatility comes forth even in these most basic of molecules. Using sp3 (again, you may have to refer to the last chapter to refamiliarlize yourself with them) hybrid orbitals, carbon can form as many as four strong, sigma bonds with other atoms, a feat no other atom can boast of. Since up to four of those atoms it can combine with is another carbon, we can imagine a vast network of sigma-bonded carbon atoms, a network that can grow virtually as large, and as complicated, as it likes. Such networks in fact do exist, and as already mentioned we call them diamonds, allegedly the hardest substance in the universe. What is more important for this discussion is that if the simple atom of carbon can yield the hardest of materials in the universe, then the creation of living things would appear to be a natural outflow of this process of bonding one carbon atom to another. Moreover, with each carbon atom having four “hands” or valence electrons to offer any other atoms it may encounter, we should be able to come up with just about any large, complex, stable molecular structure we can imagine.

Indeed we can, and have, and the subject even has been given a special name: organic chemistry. That’s right; carbon is so unique in its abilities to build complex structures and edifices – meaning large, complicated molecules – that it and it alone is awarded the very special prestige of having an entire branch of chemistry constructed around it. As a matter of fact, go to any university’s web site and start checking out the chemistry courses and you will see that the very subject appears to have two major branches: organic and all the rest, some of the rest actually being called inorganic chemistry. No other element even comes close to commanding such respect. So we finally see carbon’s commanding role being due to its unique ability to form the backbone of an almost infinite variety of molecular sculptures. And it is exactly that kind of versatility we are going to need if we are to make any sense of the fantastically complex, seemingly purposeful assemblages of atoms and molecules which comprise the roots and foundations of the vast panoply of biology spread before us. When it comes to satisfying our curiosities, that is one nail we can pound in completely and begin our explorations around. We can now say that basic, straightforward physics and chemistry do allow for biology, though, again this must be stressed, they are nowhere close to explaining it by themselves. The explanation requires something else, something that we have been edging toward, a grand idea or set of ideas that provide the gratification we have been seeking. It is time to fully enmesh ourselves in these ideas, and bask in the glory of what we have been seeking.

* * *

So, the chemistry of carbon, along with a handful of other atoms like oxygen, nitrogen, hydrogen, sulfur, phosphorus, and a smattering of other trace elements gives us all the building blocks we need to create human beings, elm trees, barnacles, tyrannosaurs, and paramecia, but that doesn’t explain how or why the blocks manage to come together in the right ways. Brachiosaurs, which were very large, plant eating dinosaurs, may be built from the same carbon and nitrogen and all the other atoms in our own biological grab-bag of goodies, but no amount of blending, whipping, hurling around, or piling one thing on top of another will never give us that Jurassic eating machine, or anything else that could be even remotely construed as alive in any sense of the word.

Here we are in our quandary, because we know the answer provided by thousands of years of folk-wisdom, occasionally dressed up in full theological garb. God, or some pantheon of gods, or something supernatural and miraculous, conjured up all the millions of species that creep, run, swim, fly, fester, or patiently await for the comings and goings of seasons and suns, so goes the wisdom of the ancients. Most people who have ever lived, and probably most of those alive at this moment, find this answer satisfactory. But if we are to truly gratify our curiosity, we have to accept that this is no answer at all. It is just another waving of the wand of the miraculous, with results unexplained and unexplainable. Or to put it another, yet more devastating, way: if God or some set of gods explains the complexity plus appearance of purpose we find in biology, then what explains Its / their equally perplexing purposeful complexities? It’s an infinite regress, which leads nowhere and satisfies nothing in the end. The only possible way this “explanation” can work is if we can come up with something that is intelligent, intentional, creative, and yet somehow simple. My suspicion is that is exactly the kind of reasoning, at a largely sub-conscious level, the theological inclined are actually all about. To which all I can say is, I cannot dismiss it completely out of hand, because imagination might someday find just such a joker in the deck. My suspicion, however, is that there really are limits on what reality can present us with. Intelligence and intention must be built upon an edifice of complexity, along with the law of physics and chemistry, any way we cut the cards. Five hundred years of science, and five thousand of philosophy, have yet to sniff out any alternatives, and seem unlikely ever to do so.

So the supernatural is a non-starter, at least if we intend to stay true to the themes of this book: curiosity, imagination, and the scientific approach to explaining things. We have to find something, or things, in what we already know, or can reasonably speculate about, if life is to be laid out, dissected, elucidated in some manner that satisfies us. What I experienced during my walk through Pennypack Park begs for explanation as much as, if not more, than anything else one might experience. But where does one begin this journey towards enlightenment? How do we even start to think about it?

* * *

Fortunately, there is a place to start; not a place that makes everything that follows easy or simple, but one that I believe at least parses the subject of life into two separate, somewhat more manageable sub-topics. One sub-topic is the question of the origin: how the atoms and molecules that in early Earth were in arrangements almost entirely non or pre-biological came to be re-assembled – or super-assembled is perhaps the better term – into the most primitive versions of our complexity plus (appearance of) purpose life forms that appear first on this planet between three and a half and four billion years ago.

Is this a separate question? Yes, it clearly is, and for the following reasons: first, all things biological, however large or small, or ephemeral or long-loved, or whatever their form or function, or however they eke out their livings, rely upon a common basis of biochemistry which can be clearly seen in all of them, if you examine them at the level of atoms and molecules. That in itself suggests a common origin, and provides the platform for the other reason: this platform, this origin aside, is what accounts for the overwhelming diversity in livings things that we witness today, billions of years after the beginnings, in the various shapes, colors, sizes, and behaviors of the tens of millions of plants, animals, fungi, and other species which have crawled, flown, walked, swam, or in whatever manner reached practically every corner and niche of remotely inhabitable space that can be found on Earth.

Here, in the early twenty-first century, this cleavage of the problem of life into these two daughter problems is supported by so much evidence that there can be no doubt that it is the proper way to initiate our quest. The chemical evidence from DNA, RNA, proteins, carbohydrates, and other biomolecules has demonstrated their common origin beyond any reasonable doubt. As an example, the viruses which I have mentioned, so tiny that they cannot be seen by any optical microscope however powerful, and whose relative simplicity makes their place in the bower of biology still a disputed issue, can feast upon hosts as disparate as bacteria and human beings and redwood trees only because the molecular machinery underpinning all of these things, including the viruses themselves, is almost identical. The same could be said about the relationship between virulent bacteria and their animal / plant / fungus hosts; for that matter, about the plain, ordinary fact that most living things on this planet make their living by somehow consuming other living things. This is something that couldn’t happen if we weren’t all made up of the same basic, chemical, stuff, underneath all our appearances of diversity.

Of course, it may still prove possible that the same kinds of processes explain both phenomena, the origin of life, and its subsequent diversification. But there is no reason to assume, a priori, that this is true, and in fact it is the position of almost all scientists who tackle these two problems that it is almost certainly not true, or at least not true for the most part though there may be some overlap in some places.

What is true, however, is that we are given a choice, right here and now, at the start of our trek toward understanding. As in Robert Frost’s poem, we are presented a choice of two roads to walk upon, both of which seem equally enticing:
 


Two roads diverged in a yellow wood,

And sorry I could not travel both

And be one traveler, long I stood

And looked down one as far as I could

To where it bent in the undergrowth;



Then took the other, as just as fair,

And having perhaps the better claim,

Because it was grassy and wanted wear;

Though as for that the passing there

Had worn them really about the same,



And both that morning equally lay

In leaves no step had trodden black.

Oh, I kept the first for another day!

Yet knowing how way leads on to way,

I doubted if I should ever come back.



I shall be telling this with a sigh

Somewhere ages and ages hence:

Two roads diverged in a wood, and I—

I took the one less traveled by

And that has made all the difference.


Unlike Frost’s poem, the two roads we are faced with look very unequal even before we take the first step on either of them. Again, beginning with our vantage point at the start of the twenty-first century, we can say that one of these roads really is well-worn, although there do remain many thickets and tangles and vines and thorns to be waded through; while the other, superficially the more straightforward of the two, is actually much more mired in undergrowth and mystery, one on which many faltering first steps have been made or attempted still with no clear path in sight. That seemingly-clearer road is the problem of the origins of life; a surprise only as long as we overlook the one, real, overwhelming obstacle in our path: which is that, however it happened, it did so either billions of years ago on this planet, or trillions of miles away on other possible worlds as discussed in chapter two, and then transported here; either of which leaves us exceedingly short of useful data upon which we can build testable theories. Both of which leave us prey to the purveyors of miracles, a shortage of which is seemingly never found; as long as, however, we forget that if miracles are answers, then science would never have explained anything, and curiosity and imagination would be pointless. Even if we do never solve some particular problem, this is no cause for capitulation; we are, after all, mere human beings with human abilities, and it shouldn’t surprise anyone that some questions remain forever unanswered, no matter how much of those abilities are applied to them for how long. It is quite possible that the origin of life, or its different possible origins, remains a nut we never quite crack. Disappointing as that would be, it is no cause for dismay or futility or some kind of existential malaise; besides which, we will no doubt discover many amazing things in our endeavors to solve this problem. Indeed, this has already happened, with examples of amazing self-organizing complexity in various chemical systems being the most obvious examples. This is actually one of the most amazing things about science, at least as I have experienced it: that our attempts to hammer out a solution to one problem ends up leading us completely unexpected paths, stumbling upon unknown veins of gold.
* * *

The problem of the origin(s) of life is a fascinating and of course commanding one, one in which many books can and have been written on and which careers have been dedicated to. However, I have deliberately chosen to leave it out of this book because meandering down so long a path with so many thickets and brambles is likely to end up with ourselves just scratching ourselves all over, and mending and binding the many wounds which we will receive, with no clear end in sight as our reward. Actually, even Darwin himself knew this. In all his tomes on evolution, he persistently avoids and evades the question of life’s origins, leaving it in backwaters to be treaded by the minds that were to come after him. If possible, he doesn’t even mention or allude to it. He had the foresight and, in our hindsight, the wisdom, to know that mucking around in those waters would only muddy the tale he was bent on weaving, a tale with enough problems of its own. Fittingly, it is a problem he only alights upon to let us know that he too will have nothing of the supernatural in solving it. Just as Newton was wise enough to know to let the cause of the gravity he so deftly described be a problem left to his successors, so Darwin also avoids this slippery trap and leaves the question of origins to minds to come after him.
There is one last point I would like to make here. It was well accepted by the late eighteen hundreds that one of the most important characteristics of livings things today is that all of them had parents, of one form or another. That fact, so obvious to us now, was finally nailed down by Louis Pasteur in a series of famous experiments, thereby separating the problem of biology into its two great sub-problems, its origins and its subsequent evolution. What Pasteur showed was that wherever even the simplest of living things came from, whether they be mice or maggots, they didn’t just burst into existence out of inorganic or simple organic beginnings. No, all of them, without exception, were begat in some manner; moms and dads, or at least a parent of some sort, were involved, even if no one knew in any detail how the begetting was done. You could breed billions of bacteria from one bacterium, but not a one from zero, however hard you tried. That clear and indisputable truth was a beginning into everything the twentieth century contributed about the fundamentals of biology: Everything comes from something, nothing comes from nothing. At least not on this planet, at this point in its history.

* * *

It would appear that we at least have a beginning here in our wonderings about ourselves, about life, that we can summarize. A quartet of beginnings, actually. First is that it displays levels of complexity, organization, and seeming purpose which would appear to defy explanation. Second, at its most fundamental level, life and its origins are based on nothing more than physics and chemistry, most crucially on the amazing properties of that amazing element carbon, although a plethora of other elements play essential roles as well. In addition, we and our ancestors all share a common biochemistry, a biochemistry built on DNA, proteins, and so forth, and have certainly done so going back a good three billion plus years in Earth’s history.
The third beginning is an inevitable consequence of the first two, that of procreation being the only way nature has now of producing new organisms, from bacteria to human beings, that living things are simply too complicated and organized to assemble by chance. Not only that, but offspring resemble their parent(s) (although, of course this is not always immediately obvious, as we all know from the example of a caterpillar hatching from a butterfly’s egg), a resemblance which will be passed on to future generations, albeit with occasional mutations.
As for the fourth beginning, evolution, that it occurs and has been occurring for a vastly long time, that it explains the many forms and functions and niches life has found on our world, and that, most importantly, we possess the fundamental understanding of how and why it occurs, underlays biology just as physics underlays chemistry and mathematics underlays physics. Furthermore, just as our third beginning derived from its predecessors, the fourth emerges inevitably from the third. It is the beginning that took two English naturalists, Charles Darwin and Alfred Russell Wallace, and these Victorian gentlemen’s elegant and brilliant reasoning which derive from the observation of two natural phenomena: the inheritance of physical and behavioral traits from parent to offspring, and competition for scarce resources among those offspring to survive and repeat the process: natural selection. What to me makes their accomplishments all the more remarkable is that how heredity works was something neither man had a clear concept of (even though this was the same time that Gregor Mendel was doing his experiments with peas which would have helped both of them immensely – experiments which remained in obscurity until the early 1900s); indeed, some of Darwin’s concepts in this field actually made his theory harder to defend. Still, they convinced the scientific establishment of their day within a short period of time.

* * *

It is natural selection and random mutation that have conspired together over millions of years to wire our brains into the relentless curious, pattern hunting, story weaving machines I spoke of in chapter one. This unconscious conspiracy has been so successful that we imagine that we see people and animals among the stars and, if like most of us who have ever lived do not know better, believe tales of how they came to be there. It is also of course one of the main wellsprings of all art and literature, from the Mona Lisa and War and Peace to the Campbell’s soup label and idle gossip. It is, ironically, the reason that I used the word conspiracy and all it implies without a second thought, and probably the reason you may not have questioned my doing so.
The obvious downside to this marvelous, compelling faculty of our brains is that the patterns and stories are often unsuspicious products of it. When this happens, then they, like magic, only sidetrack and mislead us too, perhaps disastrously so. In fact, neither our brains nor the rest of our bodies are the culmination of any kind of conspiracy, but only one of many possible, logical outcomes of nature’s blind laws.
So we tread carefully when we look at the universe about and within us and try to make sense of its workings and history. Each step has the potential to take us either into deeper understanding or shallower error. If we place too much trust in this part of what nature has wired into us, we seriously risk the latter. We must always be prepared to pull back to reexamine what we think we see, to be skeptical, to consider other possibilities, and to use another gift we have been given by those same blind laws, that of our ability to reason. If we tread the path carefully enough, our prospects for success, I believe, are promising.
Why do I begin a discussion of evolution this way? The best answer I can offer is to return to the beginning of this chapter: “One of themes of this book is that if we are to satisfy our curiosity about the universe around us, we will need to use our imaginations, because the universe as we perceive it simply doesn’t get us very far.”
Yet imagination stripped of pattern seeking and story telling would be a moribund faculty of our minds, if indeed our minds could have it at all. It surely would be nowhere close to the task of fleshing out and filling in our understanding of things. Not that it would it matter though for our curiosity would be almost severely crippled as well, probably to no more than an animal instinct serving few goals greater than finding food and mates and avoiding predators.
Nowhere is this shown better than in the work on the structure and workings of the DNA molecule, the beating heart of heredity, a heart that, perhaps more than anything else science has discovered before or since, would never have been found without that combination of imagination, pattern seeking and story telling, skepticism, and reason which make us such unique organisms that we may indeed be alone (although I hope not) in the universe.
As with so many other parts of my scientific education, I was first exposed to DNA and its workings one of the Time-Life books (or maybe it was one of Isaac Asimov’s many books on science). I was then too young to understand it in much detail, but I do recall being profoundly impressed with how important it was to all life on this planet, and at least the rudiments of why. The deeper comprehension was something that has taken a fair part of my life to even begin to grasp, and even today I know that comprehension is nowhere near as deep as it could be – not that I feel embarrassed or ashamed about that for even the most brilliant minds in the world have spent both this and a large part of the last century yet still have many mysteries arrayed against them.

* * *

I cannot resist a recapitulation here. It has been almost six months since I took the stroll through Pennypack Park I described earlier in this chapter, but right now, thinking of these issues, I find myself irresistibly drawn back to that day. Doing so, I find that my senses are as enthralled now as they were then. Once again I see and hear and smell the many living things surrounding me, almost making me feel as though I have been transported to some kind of paradise. For here I am, surrounded by the oaks and the maples and the sycamores and occasional pine trees, and admittedly many others I do not recognize. The branches and twigs of bushes, both low and high, brush against my body, and my shoes swish over the uncut grass. Birds circle in the air, dart between the trees, then settle on their branches and study the world around them. If I close my eyes, not only do I hear their many languages, I am greeted by a cacophony of other noises: insects of all kinds, the rustling of just opening leaves in the spring breeze, the splashing of fish breaking the surface of the still cold water, the dabbling and occasional quacking of ducks, the distant, patient calls of bull frogs toward potential mates, the scratching of squirrels racing up and down the trees, and others which I cannot with any certainty place or, to be honest, remember now. I am also of course aware of the humans around me and their myriad tongues with their myriad emotions and hopes, not to mention the clopping of those fortunate enough to be riding horses. Dogs bark from time to time, also reminding me of our presence. Opening my eyes again, I look for the other, more silent or better concealed creatures I know to be about, from mice and ground hogs and snakes, to ones like skunks, raccoons, opossums, and others that only come out at night. I see no deer, but don’t doubt they are about, that it is only a matter of time and attention. Stroking my fingers on a stone wall I feel the velvet of new moss against my fingertips. It is too early for mushrooms and most other fungi, but they too hide in dark places, waiting for warmer weather and longer days to coax them out. The insects I heard swirl around me now, and spiders lurk in cracks in the stone walls or hang from fresh webs, waiting for victims. Taking it all in, it is difficult to imagine how nature could have been more creative in her choice of forms and functions for her productions. Humans have nowhere near such power, and perhaps never will.
Yet I have only just brushed up against the most amazing thing about all this splendor. Which is that, were we to take samples of all of it, and place it under an instrument powerful enough to see that deeply into the structure of life, they would all reveal the spirals of DNA at the very core of their beings, spirals which account for that amazing creativity. In no case would the spirals be exactly the same – they would differ in their lengths and, in most places, their specific nucleotide sequences – but the similarities would vastly outweigh the differences in even the most distantly related organisms. Walking through the park, we are inescapably aware of the diversity which infinitely impresses us, yet it is only when we look closer, much closer, do we see – probably the most profound paradox of life on this world – the foundation which is shared by all of it.
Which is why of course I began by speaking of patterns and stories, and the double-edged sword in our minds which compels us to see and create them. If you will recall the beginning of this chapter, I dared the reader to define what life actually is, and gave some examples of how our forebears answered it. The important point about our forebears is that the answers they did come up, as persuasive as they were to them, could not have been more mistaken. The patterns they perceived in life, and the stories they told to explain them and their origins, however compelling and reasonable they seemed at the time, have turned out to be wrong, dead wrong, in retrospect absurdly wrong. What accounts for all living things is the laws of physics and chemistry, working within the forces of evolution by natural selection.
But if we stop there we fail to appreciate the power of the other edge of the sword. The discovery of DNA and the other molecules of heredity, the probing into and teasing out how they work, would not have been possible without our ability and willingness to use this edge as well as all the other facets of imagination, in combination with the hardest of scientific acumen. For what pattern in nature could be more arresting than the DNA spiral? And what story could be more captivating than the story that led to its discovery and unraveling – except, perhaps, the story that DNA, and the millions of years it has been evolving in so many directions, itself tells?

* * *

We take it as common knowledge today that DNA (or, in some cases, its brother molecule RNA) forms the hereditary basis for almost all living things on this planet, but Darwin and Wallace died long before it was discovered. Yet neither man could have failed to grasp the power of this one molecule to fulfill its dual responsibilities as the instruction set for both developing biological things and maintaining so many of their essential functions. They would no doubt have been equally impressed – no, elated – with its additional ability to create new information via mutation, information to be tested in the living, breathing, real world of life and death. Natural selection could not have a greater ally.
I have been emphasizing the almost incomprehensible complexity of living things, but in describing DNA we are surprisingly impressed, at least at first sight, by its simplicity. The simplicity is such that Crick and Watson, who revealed its structure to the world a little over fifty years ago (without, alas, giving Rosalind Franklin her due credit), were able to deduce how it replicates itself – something it must do every time a cell divides – without a single additional observation or experiment to back their deduction up (although they were rather cagey in how they mentioned it in their paper). And although there are still much research to be done, we have since that time been able to elucidate what DNA does and how it does it with impressive detail.
Simplicity does not mean lack of sophistication, however. DNA, comprised of two strands of sugar phosphate backbones, twirled together and held that way by pairs of small, interlocking “base pair” molecules, may not sound promising as genetic material; it would probably not even be the first choice of an engineer looking for an efficient molecule for storing information. But remember the discussion earlier of the power of the carbon atom to assemble stable molecules of very large size. As large as, for example, the Hope diamond. The DNA contained in chromosome one of the forty-six chromosomes of a single cell of your body would, if teased out to its full length, be approximately three inches long and contain over two hundred million base pairs (I can’t resist the calculation that if all the DNA in all our cells were laid end to end, they would stretch from here to the moon and back some twelve thousand times!). Given that the four bases can have any potential sequence, yielding 4200000000 or over 10100000000 possible arrangements in just that one chromosome, perhaps our engineer should take a second look. Incidentally, don’t try: that is a number no amount of imagination will make real in your mind; even all the atoms in the entire known universe only sum up to less than a paltry 1080.
Actually, on third thought, if anything we seem to be dealing with such an overkill of information storage capacity that we wonder why nature chose to employ DNA at all. Would wonder, that is, if nature truly were an intelligent engineer that could choose anything.
So DNA, its deceptive initial simplicity aside, is easily – way easily – more than up to the task of encoding all the information needed to create and maintain not only ourselves, but also any living organism we can conceive of, however strange and wondrous; more than all the organisms that have ever lived on this planet, or might live in the future. Or that might have or will live anywhere else in our universe, assuming they use DNA as their genetic code. Or in a billion billion universes (if they exist) spanning a billion billion years.
Information … but of what nature? And how is it encoded in the DNA spiral? And how does our biological machinery and processes extract it, and turn it into the raw material of our beings? And how has it allowed the combination of random mutation and natural selection to drive life from its simplest beginnings over three billion years ago to the incredible diversity of much more complex forms, including ourselves, that we see today – a diversity my walk through Pennypack Park only revealed only the tiniest fraction of?
It is time to talk about protein.

* * *

Here is a subject we are all at least somewhat familiar with. Who doesn’t remember as a child being cajoled, coaxed, and badgered into making sure we ate enough protein to grow strong and tall? Go into any health food store and you will find rows of large containers of protein supplements, each promising to build stronger muscles in absurdly short times.
Proteins are large organic molecules (though nowhere near as large as DNA) which, when we consume them, are broken down by digestive processes into small molecular units called amino acids. There are some twenty kinds of amino acids in living things, and different combinations and numbers of them link together to make all the proteins nature produces. Having broken down the proteins we eat, we then reassemble the freed amino acids to construct the many new different proteins our own bodies need. And our bodies need them for many different purposes.
What makes proteins so important and so versatile is the fact that they are not merely random strings of amino acids, like glass beads on a thread. Instead, because of the intramolecular forces in them, they coil, wrap around each other, form plate-like structures, and then fold up into specific, detailed shapes which are determined by their specific sequences. That is why the glutinous, translucent “white” of an egg becomes firm and truly white when we cook it, for heat, as well as other physical and chemical assaults, unravels the globular shape of the albumin proteins and make them lay flat against each other.
The myriad sizes and shapes of proteins are employed by bodies to perform all kinds of functions. For example, proteins studding the surface of a cell control the rate at which water and other molecules and ions (electrically charged atoms and molecules) enter and leave. They are employed in such diverse roles as construction material for hair and nails and cartilage, and as essential components of important biological molecules such as the hemoglobin in your blood, which carries oxygen from your lungs to every cell in your body and carries away the carbon dioxide waste to be exhaled. Numerous different types are critical to cell metabolism, in particular those that serve as enzymes, which catalyze chemical reactions in your cells to produce other important molecules. The elasticity of proteins in muscle cells allow those cells to expand and contract, allowing your heart to beat and you to use your arms and legs. They are also important in cell signaling and the proper functioning of your immune system. Your parents were indeed wise to exhort you to get enough of them in your diet, even if they did not know why.
Curiosity ought to be provoking a question in your mind right about now. Digestion breaks down the proteins we eat into their component amino acids. The amino acids are then transported by the blood to all the cells in the body. It is in our cells that all the proteins we need are constructed. Yet proteins contain from hundreds to tens of thousands of amino acids, all joined together in the specified orders they require to perform their functions. The greatest engineer in the world would be running out of his factory screaming if handed a task this monumental. How do our cells handle it with such aplomb?
The molecular machinery which assembles proteins in the cell is a subject which, if I were an expert on it, I could easily fill the rest of this chapter and more describing. Fortunately, I’m not an expert on that particular topic, which means I can segue back to DNA without further ado. The point in this discussion on proteins is that DNA is the template which is used to build them. A gene is a section of DNA serving as the template for a specific protein. More specifically, the sequence of DNA bases determine the sequence of amino acids, the correspondence between base and amino acid being three to one: each amino acid corresponds to, is encoded by, three nucleotide bases in succession. As there are four such bases, this gives us 4 × 4 × 4 = 64 possible amino acids we could code for, well more than the twenty that are actually used in nature.
Actually, this is worth elaborating on to some detail, due to another digression I feel is worth making. If we represent the four nucleotide bases in DNA, adenine, thymine, guanine, and cytosine, by their initial letters, A, T, G, and C, we find that we have an excellent “quaternary” coding system to work with. I use the word quaternary here in the same way the word “binary” is used when discussing computer code. When you run your favorite computer program, or even much less than favorite program, the code your computer is executing is essentially nothing more than a series of (electronic) 0s and 1s. This series of 0s and 1s tell the computer’s processing chip(s) and all the associated electronics and other gizmos what to do (some of which you saw in chapter two); bear in mind that with enough 0s and 1s we can create a computer program as sophisticated as we like; if my understanding of computer science is correct, given enough 0s and 1s we could create a program that simulated the entire universe and its history, though whether this universe includes the program and the computer it is running on is still unclear to me.
The three to one correspondence between bases and amino acids modifies the coding system of DNA but does not alter the analogy with computer programming code, an analogy I would like to continue with. It means that if we were to read the amino acid sequence of a section of DNA by “unzipping” it and looking at the base sequence, instead of looking at it one base at a time we would have to read it in groups of three: e. g., TTA, CAG, CTG, GCA, and so on, each group of three coding for one acid. As noted, that is well more than enough for the twenty amino acids nature uses in living things.
Computer programming. Like one of the individuals who have inspired this book, I too have had considerable experience in the field and so too am drawn to the comparison of DNA to programming code. It is a powerful and compelling comparison – the idea of DNA as digital information, to be molded in any direction the blind but non-random forces of evolution wield – has, for me at least, as much appeal to imagination and useful insight as any other idea in biology over the last quarter century or so. Now, with the digital age fully upon us, the comparison, or analogy, is even more forceful to the mind. Personally, as a (very) part-time science fiction writer it conjures up images of artificial living beings, of synthetic organs and tissues to prolong our lives, perhaps indefinitely, of expanding the already impressive capacities of our brains with biochips, and even such cybernetic ideas as an Internet composed of human minds directly connected to and communicating with each other and with sentient computers. Given that I honestly expect to see some of this happen at least in my lifetime not to mention my children’s, the digital view of biology is perhaps too seductive.

* * *

After everything I have said about imagination and our need to use it to answer our questions about ourselves and our universe, the word seductive alone ought to suggest I am about to pull back, at least somewhat. So I am. Not that I don’t truly believe that many if not all of the above mentioned wonders of coming technology will happen someday. But the emphasis on the digital nature of DNA can potentially mislead us as well as inform.
The reason for this is that our digital DNA codes, serves as a template for, the highly analog proteins that are the actual machinery of our bodies. By analog I simply mean the opposite of digital: continuous in change as opposed to changing in discrete steps. (A hopefully not too outdated example of the difference would be the analog dial on old radio sets which, as you turned it, changed the tuning of the receiver continuously from one frequency to another, as opposed to digital push-button radios today which jump instantly to a specific frequency.) In calling proteins analog, I do not mean the sequence of amino acids which comprise them; that is still as digital as DNA in that an amino acid change in the sequence is discrete – you can’t continuously change between one acid and another.
Hang on, for I am getting to the reason for this digression. It is true that the amino acid sequence in a protein is digital, but what matters for proteins, what they do and how they work, is largely their specific size and shape, qualities that usually can be varied more or less continuously by changes in the amino acid sequence which comprises them. That is, if we replace one amino acid in a protein consisting of hundreds or thousands with another, the most likely outcome is a small, perhaps even insignificant, change in its shape – resulting in a proportionately tiny change in how the protein does its job. For example, if the protein is an enzyme, a slight change in its shape would cause the rate at which it catalyzes its specific reaction to be somewhat faster or slower. Or if the protein controls the rate at which a certain molecule or ion enters or leaves cells, that could be modified slightly. Furthermore, additional amino acid changes are likely to lead to similar small, cumulative changes in the protein’s function.
Small, cumulative changes. We are practically talking about the heart and soul of Darwinian evolution. But what would cause these single amino acid changes in a protein’s make-up? Recall that it is a particular sequence of three consecutive nucleotide bases on DNA which correspond to the amino acid at a particular location in a protein. Any number of agents have the potential to alter, or “mutate” a base in DNA: radiation and various kinds of chemical assaults. Such mutations (there are others) even has a name: point mutations. Point mutations are surprisingly common. Most are caught and corrected by molecular machinery in the cell designed for the purpose, but they occasionally slip through the defenses. In doing so they can lead to the amino acid changes in proteins which often (not always: sickle-cell anemia is caused by just such a single change on one of the globin proteins in hemoglobin) cause those proteins’ functioning to alter slightly, causing somewhat higher or lower production of another chemical or modifying cell membrane permeability to a molecule / ion, leading to … well, for example, if the protein is involved in embryological development, a modest change in the physiology or behavior of the organism. The point is, when talking about natural selection, modest changes, such as those that lead to slightly longer or shorter legs, have a better chance of being advantageous than large changes, which are almost certain to be disastrous. And given that changes can accumulate over geological time, constantly being molded and “directed” by natural selection, I hope it is by now clear that the entire edifice of DNA / proteins / form and function, though completely unknown in Darwin’s and Wallace’s time, could hardly have been better tailored to the revolutionary ideas they unleashed upon the world.

* * *

Wondering about ourselves is, of course, an endeavor that never ends, and no such pretense will be made here. On the contrary, the territory covered in this chapter is only a tiny fraction of the vast subject of life, what it is and how it has come to be. Alas, curiosity demands more, far more much more, than I could hope to deliver even in an entire book, assuming I was well versed enough in the subject for such an undertaking. But I do hope that certain basics about life, in general, have been laid down: its utterly improbable complexity, seeming design and purposefulness (what I have called intentionality); the underlying chemistry, particularly of carbon, that makes it possible (on our planet); the continuity, in that all living organisms are in some way descended from a parent or parents, going back to the beginnings of life on Earth some three and a half or more billion years ago; the basics of Darwinian / Wallician evolution, which explains how life today came from its much simpler beginnings; and the interworkings of the tapestry of DNA with the working machinery of proteins which are essential to both life’s functioning and its evolution. I hope you feel that we have not made a bad start.
But there is another aspect to our self exploration, one that can’t be, and won’t be, ignored. That is our wondering about ourselves as individuals. How is it, each of us asks at least from time to time, that I came to be; what and why am I; what is my place and destiny, if any, in the scheme of things, whatever that scheme is assuming; what does it mean to be human and what else could I have been? The reason I have excluded this aspect from this chapter is that the sciences that answer it, if any, are necessarily more speculative, to the point where it is questionable in many cases to call them sciences at all. But that doesn’t stop our asking the questions. It doesn’t quench our curiosity, or make it go away. And we can still use our imaginations – gingerly, for we tread on unknown territories – in our quest to come up with answers that just might make some degree of sense. Or so we hope.





Sunday, January 20, 2013

A UsefulChem Update from 2006-2013 (a little out of date)


Automation components in UsefulChem


This page describes the evolution of software tools which process the usefulchem-molecules blog into a variety of useful formats, e.g., spreadsheets, RSS feeds, and CML for molecular visualization/manipulation tools such as Jmol, as well as adding additional chemical information (InChIs, MWs, supplier info) for the molecules in the UsefulChem project. I will also discuss the on-going development of an automated RSS feed reader for extracting and performing further processing this chemical information, and potential future work in these areas. For more information on this work, and to follow new developments, please refer to my blog entries at http://usefulchem.blogspot.com.

Initial work with Excel / Excel VBA:

Molecule entries in http://usefulchem-molecules.blogspot.com are characterized primarily by a UC number (e.g., UC0188), a SMILES notation, and an image, although other information, such as CAS number, is often added. To summarize and expand on this data in a convenient format, a program in Microsoft Excel Visual Basic for Applications (VBA) (http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/MoleculeBlogInfo.zip) was developed which downloads this page, parses out the desired information, and generates a spreadsheet (http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/usefulchem-molecules/usefulchem-molecules.xls) in which each row represents one blog entry. Given that the blog format itself is rather loose – for example, the SMILES entry might be prefixed by “SMILES” or “SMILES:” – and can change over time, the search criteria for fields were made fully configurable by placing them in an initialization (.ini) file.

Additional information beyond that provided by the blog, such as links to suppliers, were desired, and for this purpose several different freely available software packages and libraries were used. Molecular weight information and molecular format files (CML, MOL) were generated from the SMILES using the CDK Java libraries, while InChI descriptors were produced by OpenBabel. Image files were at first generated using ChemSketch, although these are now simply downloaded directly from the blog itself. Supplier information was acquired by sending HTTP GET requests to chmoogle.com (now eMolecules.com), and processing the responses gleaned from this service.

In addition to the spreadsheet, this software also creates HTML and CML files (e. g., http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/usefulchem-molecules/UC0088.htm) for each blog entry, which in combination allow the molecules in the blog to be viewed with the Jmol applet.

 
RSS feeds and Automation Software in Java:

The spreadsheet format for the usefulchem-molecules blog was a useful beginning. It was, however, not very amenable to automated data processing or other kinds of display desired, particularly for the internet/web. An initial attempt to address these deficiencies involved modifying the Excel VBA software to generate an RSS 1.0 feed (http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/usefulchem-molecules/usefulchem-molecules.rss) of the blog data in addition to its other output. The advantage to having the data in a feed is that can then be viewed using any number of available desktop or web-based readers, such as RSS Bandit (http://www.rssbandit.org) or Bloglines (http://www.bloglines.com). Furthermore, as RSS is simply XML, feeds can contain other XML formatted data, such as Chemical Markup Language (CML). Thus, a feed can be downloaded and parsed for its CML by software such as Bioclipse (http://www.bioclipse.net) or Jmol (http://jmol.sourceforge.net).

A shortcoming of using Excel VBA is that it does not easily lend itself to automation. Also, it is neither truly an open source development platform nor portable to other operating systems such as Unix or Macintosh. Therefore, to address these shortcomings, I rewrote the VBA code in the Java programming language, which is both free (see http://java.sun.com/javase/downloads/index.jsp to download the Java Development Kit) and is implemented on all major operating systems. Once in Java, it was straightforward to set the software up as an service to be run periodically. As a result, the RSS feed and associated files are now regenerated automatically whenever additions or changes are made the usefulchem-molecules blog.

A zip file containing both the source and compiled code for the Java software to convert the usefulchem-molecules blog to an RSS feed can be found at http://showme.physics.drexel.edu/usefulchem/Software/Java/MoleculeBlogInfo/MoleculeBlogInfo.zip.


CMLRSSReader:

Having an RSS feed with special fields provides a launching platform of essentially unlimited opportunities for further treatment of chemical information. Standard RSS readers, however, rarely display little more the and several other standard fields in a feed. Furthermore, they are not extendable or configurable to include additional processing via plug-ins or “hook” programs on a feed, its entries, or the various specialized fields it can contain. Thus, a specialized reader seemed necessary.

Writing a simple feed reader is actually not a particularly difficult software project, and there is a lot of help available in books and web sites (I used “RSS and Atom Programming” from Wrox books (Wrox.com) as a guide for all my RSS programming). I have developed such a reader, again using Java, which begins to address some of our specialized requirements for feeds containing CML and other chemical information. This reader and associated software, which can be downloaded from http://showme.physics.drexel.edu/usefulchem/Software/Java/CMLRSSReader/CMLRSSReader.zip, is still at an early stage in development and can currently handle only RSS 1.0 feeds (and so far has only been tested on the usefulchem-molecules and two other closely related feeds), but demonstrates some of what can be done along lines described above. In addition to the standard reader features of automatically downloading and managing multiple feeds, displaying information contained their item entries, and as tracking new or changed items, the software also allows specialized programs to be executed on the feeds themselves and their contents. In its current form, programs can be configured to run after feed file download and/or processing. These programs can be written in any language, even DOS BAT files (although Java must be used on processed feeds, as they are stored via Java serialization), and can perform any processing/reporting desired, such as calculations using the CML in the feed, internet searches, database entry, and/or e-mailing results to the interested parties.

Two examples of this capability are already being used to automatically generate and upload information for display on the web. One, ExtractHTMLPages, is a Java program that parses the usefulchem-molecules feed file for its item fields and generates an HTML file for each item. ExtractHTMLPages also generates an index file (http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/usefulchem-molecules/Items/UsefulChemistryMolecules.html) of the item HTML files which, using a combination of JavaScript and HTML iframes, allows any of them to be selected for viewing from a drop-down list. When CMLRSSReader downloads a feed, which it does whenever the feed has been updated (which in the case of usefulchem-molecules, occurs whenever the blog is updated), it automatically runs ExtractHTMLPages, generating and uploading all of these files to the web server.

The other example, ExtractNewItems, is a Java program which works with processed feeds to record and detail changes to the feed. When new items are added to the usefulchem-molecules feed, or new information about an item is added or modified, ExtractNewItems generates and uploads two files: newItems.html (http://showme.physics.drexel.edu/usefulchem/Software/MoleculeBlogInfo/usefulchem-molecules/newItems.html) and newItems.xls. True to their names, these files list items that have been added or updated since the last time the program was run. Ultimately, the reason for a new listing will also be given, such as new supplier information, but this is not currently implemented.

Future Directions:

Quite a bit of ground has been covered, and a lot of evolution occurred, since the initial work with Excel VBA. A certain amount of consolidation and strategic consideration would seem to be worthwhile at this point. To begin, the numerous web sites and pages generated would benefit from some organization. This can be done with a single page, or small set of pages, providing links to and descriptions of the various software tools and the pages they generate.

Second, although I have tried to make the CML RSS reader software highly flexible, it needs to be tested for compatibility with other RSS 1.0 feeds containing CML if it is to become of general use to the scientific community. Additional development is almost certainly going to be needed here (no one should expect to be that lucky!). I am also eager to see how the reader might interact with other software, such as Bioclipse, for example in providing CML and other data in automated fashion. This should prove fruitful, as Bioclipse obviously provides so much more in the way of processing and visualization tools than the reader itself. Other enhancements include a replacement for Java’s JEditorPane for displaying item data (JEditorPane’s handling of HTML is fairly primitive), other improvements to the user interface, and more configurable program extensions and/or plug-ins.

Finally, a lot of technologies have yet to be explored in this area. One excellent candidate is the combination of Ajax in HTML pages with chemical information web services. Ajax provides the ability to dynamically query web sites and services without the overhead in time and resources of retransmitting/reloading entire pages. In conjunction with JavaScript events and dynamic HTML, this can essentially turn an ordinary browser into a full-featured software user interface. Ajax also appears quite easy to use. For some simple examples of what can be done with Ajax, see http://showme.physics.drexel.edu/usefulchem/Software/Ajax/UsefulChemistryMolecules/UsefulChemistryMolecules.htm and http://showme.physics.drexel.edu/usefulchem/Software/Ajax/UsefulChemistryMolecules/UsefulChemistryMolecules2.htm (simply hover over any of the UC numbers).

Also, I have just begun to learn about OpenOffice, and hope to convert the Excel applications into them.

Some More Belated JCAMP Work for UsefulChem

Blog Text I have developed a Java package to decompress NMR data taken from our Bruker instrument and stored in JCAMP format.  This software was adapted from Robert Lancashire's jspecview program, specifically the JDXCompressor.java and Coordinate.java classes.  It reads a set of compressed JCAMP NMR files according to a configuration file with the following format: the program's output is a BLOCK JCAMP file, in this case output.jdx, containing the decompressed data from the input files.  Right now only a few of the header fields are retained, those needed for plotting the spectra via Excel VBA software (work in progress!).  An example of this can be downloaded here.

SA expert pushes asteroid mining

SA expert pushes asteroid mining

2012-10-12 14:34
Ron Olivier of SIP wants SA to develop a space mining programme. (Duncan Alfreds, News24)
Ron Olivier of SIP wants SA to develop a space mining programme. (Duncan Alfreds, News24)

kalahari.com



Cape Town - In the future, South African mining companies may become space firms, if a local engineer has his way.

Engineer Ron Olivier is pushing for SA to develop a space mining programme that will either exploit raw materials on the Moon or on Near Earth Objects (NEOs) like asteroids.

The idea holds promise because of the capacity developed when SA built a satellite and launched it into space, he said.

"It came from expertise; it came from my time at SunSpace where we built spacecraft out of basically nothing and reasonably successfully so," Olivier of Shamayan Innovation Partnerships (SIP) told News24.

His presentation at the SA Space Association Congress in Cape Town proposed that a mission to mine NEOs could "produce the largest economic benefit" to the country since the discovery of gold and diamonds.

Extraterrestrial mining

Olivier suggests that partnerships with countries in the Brics could jumpstart a programme to mine asteroids of at least 1km and rich in mineral resources.

The idea may not be as far-fetched as Google's Larry Page and director James Cameron have backed a company called Planetary Resources to mine asteroids.

Some think that NEOs contain high levels of iron ore, platinum, nickel and zinc and that if it could be extracted efficiently, may present a business model to conduct extraterrestrial mining activities.

Olivier suggested that a space port similar to the International Space Station (ISS) could be used to launch missions to asteroids.

"We may want to use an ISS type of organism out there, and then exploit that and launch from there. At the moment the ISS exists and it's been shown to be possible - that you can do that, but it will take a couple of billion to construct that.

In his presentation, Olivier suggested that a 1km asteroid can deliver $150bn in platinum value at current prices and if a re-usable vehicle could be developed to be cost-effective, it made a space mining programme viable within a decade.

"Most probably closer to 10 years than 50 years: Number one, South Africa has immense innovation in the industrialisation of Earth-bound mining machinery," he said.

Partnerships

Unlike Planetary Resources that plans to send astronauts to mine asteroids, SIP intends unmanned robots to do the work.

"The automation is restricted in this country because of our requirements to provide a tremendous amount of jobs to people. No such restrictions are out there in outer space.

"You don't need to transport miners to outer space to go and mine there; in fact, it would be stupid to do so. You have to take machines there and necessity is the mother of all invention," said Olivier.

He proposes partnerships with experts in various disciplines to reduce costs and secure funding.

"What I have suggested here is a purely commercial outlook with some government funding on the side of it. But nothing like funding that whole project. It's a commercial venture."

The idea may seem a bit out of this world, but Olivier said that once the programme was up and running companies would back it.

"SIP is at the stage where it needs quite a bit of funding just in order for me to get around, so we're starting off at zero base. And this is the thing that makes it even crazier to the normal mind, but at the SunSat programme we started at zero base as well."

Olivier challenged South African companies to consider that such a project would be viable as the cost of resources escalate.

"I'm going to say to the companies: 'Either come in, or be left out.'"


- Follow Duncan on Twitter

NASA Funding

Have discovered the recent comments on PENNY4NASA:

Penny4NASA was founded to uphold the importance of Space Exploration and Science. We believe wholeheartedly that our federal funding of the National Aeronautics and Space Administration, at a wimpy 0.48% of the total, does not reflect the hugely important economical, technological and inspirational resource that this agency has been throughout its 50+ year history. With approximately $10 coming back into the economy for every $1 spent, thousands of new science and engineering students becoming inspired continuously, and the multitude of technologies that NASA research has both directly and indirectly made possible, we believe that NASA needs to be funded at a level of at least 1% of the US federal budget. This isn’t a partisan argument, and this isn’t a fiscal budget argument. What this is, is the American people saying that as a society, we want our tax dollars to reflect the importance of science and space exploration. And 0.48% doesn’t cut it. We are calling for NASA budget to be increased to at least 1% of the US annual budget.

I wrote the following the PA congressmen:

Today at 12:44pm
Support Doubling Funding for NASA and the Future Priorities of U.S. Involvement in Space
Dear Representative:
I support Doubling Funding for NASA and the Future Priorities of U.S. Involvement in Space because with even one percent of the federal budget allocated toward NASA, we could essentially half the time of developing space technology and the serious scientific and economic benefits that would result from it; e.g., mining ores & minerals from asteroids would greatly reduce pollution here on Earth. We would all, as well, and not just Americans, finally perceive a future worth working toward, a future which would help us overcome the problems of nations and cultures competing with each other. Thank you.

Wednesday, January 16, 2013

Chapter Two of the Third row


The Idiot’s Guide to Making Atoms

Avagadro’s Number and Moles

Writing this chapter has reminded me of the opening of a story by a well-known science fiction author (whose name, needless to say, I can’t recall): “This is a warning, the only one you’ll get so don’t take it lightly.” Alice in Wonderland or “We’re not in Kansas anymore” also pop into mind. What I mean by this is that I could find no way of writing it without requiring the reader to put his thinking (and imagining) cap on. So: be prepared.

A few things about science in general before I plunge headlong into the subject I’m going to cover. I have already mentioned the way science is a step-by-step, often even torturous, process of discovering facts, running experiments, making observations, thinking about them, and so on; a slow but steady accumulation of knowledge and theory which gradually reveals to us the way nature works, as well as why. But there is more to science than this. This more has to do with the concept, or hope I might say, of trying to understand things like the universe as a whole, or things as tiny as atoms, or geological time, or events that happen over exceedingly short times scales, like billionths of a second. I say hope because in dealing with such things, we are extremely removed from reality as we deal with it every day, in the normal course of our lives.

The problem is that, when dealing with such extremes, we find that most of our normal ideas and expectations – our intuitive, “common sense”, feeling grasp of reality – all too frequently starts to break down. There is of course good reason why this should be, and is, so. Our intuitions and common sense reasoning have been sculpted by our evolution – I will resist the temptation to say designed, although that often feels to be the case, for, ironically, the same reasons – to grasp and deal with ordinary events over ordinary scales of time and space. Our minds are not well endowed with the ability to intuitively understand nature’s extremes, which is why these extremes so often seem counter-intuitive and even absurd to us.

Take, as one of the best examples I know of this, biological evolution, a lá Darwin. As the English biologist and author Richard Dawkins has noted several times in his books, one of the reasons so many people have a hard time accepting Darwinian evolution is the extremely long time scale over which it occurs, time scales in the millions of years and more. None of us can intuitively grasp a million years; we can’t even grasp, for that matter, a thousand years, which is one-thousandth of a million. As a result, the claim that something like a mouse can evolve into something like an elephant feels “obviously” false. But that feeling is precisely what we should ignore in evaluating the possibility of such events, because we cannot have any such feeling for the exceedingly long time span it would take. Rather, we have to evaluate the likelihood using evidence and hard logic; commonsense can seriously mislead us.

The same is true for nature on the scale of the extremely small. When we start poking around in this territory, around with things like atoms and sub-atomic particles, we find ourselves in a world which bears little resemblance to the one we are used to. I am going to try various ways of giving you a sense of how the ultra-tiny works, but I know in advance that no matter what I do I am still going to be presenting concepts and ideas that seem, if anything, more outlandish than Darwinian evolution; ideas and concepts that might, no, probably will, leave your head spinning. If it is any comfort, they often leave my mind spinning as well. And again, the only reason to accept them is that they pass the scientific tests of requiring evidence and passing the muster of logic and reason; but they will often seem preposterous, nevertheless.

First, however, let’s try to grab hold of just how tiny the world we are about to enter is. Remember Avogadro’s number, the number of a mole of anything, from the last chapter? The reason we need such an enormous number when dealing with atoms is that they are so mind-overwhelmingly small. When I say mind-overwhelmingly, I really mean it. A good illustration of just how small that I enjoy is to compare the number of atoms in a glass of water to the number of glasses of water in all the oceans on our planet. As incredible as it sounds, the ratio of the former to the latter is around 10,000 to 1. This means that if you fill a glass with water, walk down to the seashore, pour the water into the ocean and wait long enough for it to disperse evenly throughout all the oceans (if anyone has managed to calculate how long this would take, please let me know), then dip your now empty glass into the sea and re-fill it, you will have scooped up some ten thousand of the original atoms that it contained. Another good way of stressing the smallness of atoms is to note that every time you breathe in you are inhaling some of the atoms that some historical figure – say Benjamin Franklin or Muhammad – breathed in his lifetime. Or maybe just in one of their breaths; I can’t remember which – that’s how hard to grasp just how small they are.

One reason all this matters is that nature in general does not demonstrate the property that physicists and mathematicians call “scale invariance.” Scale invariance simply means that, if you take an object or a system of objects, you can increase its size up to as large as you want, or decrease it down, and its various properties and behaviors will not change. Some interesting systems that do possess scale invariance are found among the mathematical entities called fractals: no matter how much you enlarge or shrink these fractals, their patterns repeat themselves over and over ad infinitum without change. A good example of this is the Koch snowflake:

which is just a set of repeating triangles, to as much depth as you want. There are a number of physical systems that have scale invariance as well, but, as I just said, in general this is not true. For example, going back to the mouse and the elephant, you could not scale the former up to the size of the latter and let it out to frolic in the African savannah with the other animals; our supermouse’s proportionately tiny legs, for one thing, would not be strong enough to lift it from the ground. Making flies human sized, or vice-versa, run into similar kinds of problems (a fly can walk on walls and ceilings because it is so small that electrostatic forces dominate its behavior far more than gravity).


Scale Invariance – Why it Matters

One natural phenomenon that we know lacks scale invariance, we met in the last chapter is matter itself. We know now that you cannot take a piece of matter, a nugget of gold for example, and keep cutting it into smaller and smaller pieces, and so on until the end of time. Eventually we reach the scale of individual gold atoms, and then even smaller, into the electrons, protons, and neutrons that comprise the atoms, all of which are much different things than the nugget we started out with. I hardly need to say that all elements, and all their varied combinations, up to stars and galaxies and larger, including even the entire universe, suffer the same fate. I should add, for the sake of completeness, that we cannot go in the opposite direction either; as we move toward increasingly more massive objects, their behavior is more and more dominated by the field equations of Einstein’s general relativity, which alters the space and time around and inside them to a more and more significant degree.

Why do I take the time to mention all this? Because we are en route to explaining how atoms, electrons and all, are built up and how they behave, and we need to understand that what goes on in nature at these scales is very different than what we are accustomed to, and that if we cannot adopt our thinking to these different behaviors we are going to find it very tough, actually impossible, sledding, indeed.

In my previous book, Wondering About, I out of necessity gave a very rough picture of the world of atoms and electrons, and how that picture helped explained the various chemical and biological behaviors that a number of atoms (mostly carbon) displayed. I say “of necessity” because I didn’t, in that book, want to mire the reader in a morass of details and physics and equations which weren’t needed to explain the things I was trying to explain in a chapter or two. But here, in a book largely dedicated to chemistry, I think the sledding is worth it, even necessary, even if we do still have to make some dashes around trees and skirt the edges of ponds and creeks, and so forth.

Actually, it seems to me that there are two approaches to this field, the field of quantum mechanics, the world we are about to enter, and how it applies to chemistry. One is to simply present the details, as if out of a cook book: so we are presented our various dishes of, first, classical mechanics, then the LaGrangian equation of motion and Hamiltonium operators and so forth, followed by Schrödinger’s various equations and Heisenberg’s matrix approach, with eigenvectors and eigenvalues, and all sorts of stuff that one can bury one’s head into and never come up for air. Incidentally, if you do want to summon your courage and take the plunge, a very good book to start with is Melvin Hanna’s Quantum Mechanics in Chemistry, of which I possess the third edition, and go perusing through from time to time when I am in the mood for such fodder.

The problem with this approach is that, although it cuts straight to the chase, it leaves out the historical development of quantum mechanics, which, I believe, is needed if we are to understand why and how physicists came to present us with such a peculiar view of reality. They had very good reasons for doing so, and yet the development of modern quantum mechanical theory is something that took several decades to mature and is still in some respects an unfinished body of work. Again, this is largely because some it its premises and findings are at odds with what we would intuitively expect about the world (another is that the math can be very difficult). These are premises and findings such as the quantitization of energy and other properties to discrete values in very small systems such as atoms. Then there is Heisenberg’s famous though still largely misunderstood uncertainly principle (and how the latter leads to the former).


Talking About Light and its Nature

A good way of launching this discussion is to begin with light, or, more precisely, electromagnetic radiation. What do I mean by these polysyllabic words? Sticking with the historical approach, the phenomena of electricity and magnetism had been intensely studied in the 1800s by people like Faraday and Gauss and Ørsted, among others. The culmination of all this brilliant theoretical and experimental work was summarized by the Scottish physicist James Clerk Maxwell, who in 1865 published a set of eight equations describing the relationships between the two phenomena and all that had been discovered about them. These equations were then further condensed down into four and placed in one of their modern forms in 1884 by Oliver Heaviside. One version of these equations is (if you are a fan of partial differential equations):





 
Don’t worry if you don’t understand this symbolism (most of it I don’t). The important part here is that the equations predict the existence of electromagnetic waves propagating through free space at the speed of light; waves rather like water waves on the open ocean albeit different in important respects. Maxwell at once realized that light must be just such a wave, but, more importantly, that there must be a theoretically infinite number of such waves, each with different wavelengths ranging from the very longest, what we now call radio waves, to the shortest, or gamma rays. An example of such a wave is illustrated below:



To assist you in understanding this wave, look at just one component of it, the oscillating electric field, or the part that is going up and down. For those not familiar with the idea of an electric (or magnetic) field, simply take a bar magnet, set it on a piece of paper, and sprinkle iron filings around it. You will discover, to your pleasure I’m certain, that the filings quickly align themselves according to the following pattern:


The pattern literally traces out the, in this case, magnetic field of the bar magnet, but we could have used an electrically charged source to produce a somewhat different pattern. The point is, the field makes the iron filings move into their respective positions; furthermore, if we were to move the magnet back and forth or side to side the filings would continuously move with it to assume their desired places. This happens because the outermost electrons in the filings (which, in addition to carrying an electric charge, also behave as very tiny magnets) are basically free to orient themselves anyway they want, so they respond to the bar’s field with gusto, in the same way a compass needle responds to Earth’s magnetic field. If we were using an electric dipole it would be the electric properties of the filings’ electrons performing the trick, but the two phenomena are highly interrelated.

Go back to the previous figure, of the electromagnetic wave. The wave is a combination of oscillating electric and magnetic fields, at right angles (90°) to each other, propagating through space. Now, imagine this wave passing through a wire made of copper or any other metal. Hopefully you can perceive by now that, if the wave is within a certain frequency range, it will cause the electrons in the wire’s atoms to start spinning around and gyrating in order to accommodate the changing electric and magnetic fields, just as you saw with the iron filings and the bar magnet. Not only would they do that, but the resulting electron motions could be picked up by the right kinds of electronic gizmos, transistors and capacitators and resistors and the like – here, we have just explained the basic working principle of radio transmission and receiving, assuming the wire is the antenna. Not bad for a few paragraphs of reading.

This sounds all very nice and neat, yet it is but our first foot into the door of what leads to modern quantum theory. The reason for this is that this pat, pretty perception of light as a wave just didn’t jibe with some other phenomena scientists were trying to explain at the end of the nineteenth century / beginning of the twentieth century. The main such phenomena along these lines which quantum thinking solved were the puzzles of the so-called “blackbody” radiation spectrum and the photo-electric effect.


Blackbody Radiation and the Photo-electric Effect

If you take an object, say, the tungsten filament of the familiar incandescent light bulb, and start pumping energy into it, not only will its temperature rise but at some point it will begin to emit visible light: first a dull red, then brighter red, then orange, then yellow – the filament eventually glows with a brilliant white light, meaning all of the colors of the visible spectrum are present in more or less equal amounts, illuminating the room in which we switched the light on. Even before it starts to visibly glow, the filament emits infrared radiation, which consist of longer wavelengths than visible red, and is outside our range of vision. It does so in progressively greater and greater amounts and shorter and shorter wavelengths, until the red light region and above is finally reached. At not much higher temperatures the filament melts, or at least breaks at one of its ends (which is why it is made from tungsten, the metal with the highest melting point), breaking the electric current and causing us to replace the bulb.

The filament is a blackbody in the sense that, to a first approximation, it completely absorbs all radiation poured onto it, and so its electromagnetic spectrum depends only on its temperature and not any on properties of its physical or chemical composition. Other such objects which are blackbodies include the sun and stars, and even our own bodies – if you could see into right region of the infrared range of radiation, we would all be glowing. A set of five blackbody electromagnetic spectra are illustrated below:


Examine these spectra, the colored curves, carefully. They all start out at zero on the left which is the shortest end of the temperature, or wavelength (λ, a Greek letter which is pronounced lambda) scale; the height of the curves then quickly rises to a maximum λ at a certain temperature, followed by a gradual decline at progressively lower temperatures until they are basically back at zero again. What is pertinent to the discussion here is that, if we were living around 1900, all these spectra would be experimental; it was not possible then, using the physical laws and equations known at the end of the 1800s, to explain or predict them theoretically. Instead, from the laws of physics as known then, the predicted spectra would simply keep increasing as λ grew shorter / temperature grew higher, resulting it what was called “the ultraviolet catastrophe.”

Another, seemingly altogether different, phenomenon that could not be explained using classical physics principles was the so-called photoelectric effect. The general idea is simple enough: if you shine enough light of the right wavelength or shorter onto certain metals – the alkali metals, including sodium and potassium, show this effect the strongest – electrons will be ejected from the metal, which can then be easily detected:


This illustration not only shows the effect but also the problem 19’th century physicists had explaining it. There are three different light rays shown striking the potassium plate: red at a wavelength of 700 nanometers or nm (an nm is a billionth of a meter), green at 550 nm, and purple at 400 nm. Note that the red light fails to eject any electrons at all, while the green and purple rays eject only one electron, with the purple electron escaping with a higher velocity, meaning higher energy, than the green.

The reason this is so difficult to explain with the physics of the 1800’s is that physics then defined the energy of all waves using both the wave’s amplitude, which is the distance from crest or highest point to trough or lowest point, in combination with the wavelength (the shorter the wavelength the more waves can strike within a given time). This is something you can easily appreciate by walking into the ocean until the water is up to your chest; both the higher the waves are and the faster they hit you, the harder it is to stay on your feet.

Why don’t the electrons in the potassium plate above react in the same way? If light behaved as a classical wave it should not only be the wavelength but the intensity or brightness (assuming this is the equivalent of amplitude) that determines how many electrons are ejected and with what velocity. But this is not what we see: e.g., no matter how much red light, of what intensity, we shine on the plate no electrons are emitted at all, while for green and purple light only the shortening of the wavelength in and of itself increases the energy of the ejected electrons, once again, regardless of intensity. In fact, increasing the intensity only increases the number of escaping electrons, assuming any escape at all, not their velocity. All in all, a very strange situation, which, as I said, had physicists scratching their heads all over at the end of the 1800s.

The answers to these puzzles, and several others, comes back to the point I made earlier about nature not being scale invariant. These conundrums were simply insolvable until scientists began to think of things like atoms and electrons and light waves as being quite unlike anything they were used to on the larger scale of human beings and the world as we perceive it. Using such an approach, the two men who cracked the blackbody spectrum problem and the photoelectric effect, Max Planck and Albert Einstein, did so by discarding the concept of light being a classical wave and instead, as Newton had insisted two hundred years earlier, thought of it as a particle, a particle which came to be called a photon. But they also did not allude to the photon as a classical particle either but as a particle with a wavelength; furthermore, that the energy E of this particle was described, or quantized, by the equation


in which c was the speed of light, λ the photon’s wavelength, and h was Planck’s constant, the latter of which is equal to 6.626 × 10-34 joules seconds – please note the extremely small value of this number. In contrast to our earlier, classical description of waves, the amplitude is to be found nowhere in the equation; only the wavelength, or frequency, of the photon determines its energy.

If you are starting to feel a little dizzy at this point in the story, don’t worry; you are in good company. A particle with a wavelength? Or, conversely, a wave that acts like a particle even if only under certain circumstances? A wavicle? Trying to wrap your mind around such a concept is like awakening from a strange dream in which bizarre things, only vaguely remembered, happened. And the only justification of this dream world is that it made sense of what was being seen in the laboratories of those who studied these phenomena. Max Planck, for example, was able, using this definition, to develop an equation which correctly predicted the shapes of blackbody spectra at all possible temperature ranges. And Einstein elegantly showed how it solved the mystery of the photoelectric effect: it took a minimum energy to eject an electron from a metal atom, an energy dictated by the wavelength of the incoming photon; the velocity or kinetic energy of the emitted electron came solely from the residual energy of the photon after the ejection. The number of electrons freed this way was simply equal to the number of the photons that showered down on the metal, or the light’s intensity. It all fit perfectly. The world of the quantum had made its first secure foot prints in the field of physics.
There was much, much more to come.

The Quantum and the Atom

Another phenomena that scientists couldn’t explain until the concept of the quantum came along around 1900-1905 was the atom itself. Part of the reason for this is that, as I have said, atoms were not widely accepted as real, physical entities until electrons and radioactivity were discovered by people like the Curies and J. J. Thompson, Rutherford performed his experiments with alpha particles, and Einstein did his work on Brownian motion and the photo-electric effect (the results of which he published in 1905, the same year he published his papers on special relativity and the E = mc2 equivalence of mass and energy in the same year, all at the tender age of twenty-six!). Another part is that, even if accepted, physics through the end of the 1800s simply could not explain how atoms could be stable entities.

The problem with the atomic structure became apparent in 1911, when Rutherford published his “solar system” model, in which a tiny, positively charged nucleus (again, neutrons were not discovered until 1932 so at the time physicists only knew about the atomic masses of elements) was surrounded by orbiting electrons, in much the same way as the planets orbit the sun. The snag with this rather intuitive model involved – here we go both with not trusting intuition and nature not being scale invariant again – something physicists had known for some time about charged particles.

When a charged particle changes direction, it will emit electromagnetic radiation and thereby lose energy. Orbiting electrons are electrons which are constantly changing direction and so, theoretically, should lose their energy and fall into the nucleus in a tiny fraction of a second (the same is true with planets orbiting a sun, but it takes many trillions of years for it to happen). It appeared that the Rutherford model, although still commonly evoked today, suffered from a lethal flaw.

And yet this model was compelling enough that there ought to be some means of rescuing it from its fate. That means was published two years later, in 1913, by Niels Bohr, possibly behind Einstein the most influential physicist of the twentieth century. Bohr’s insight was to take Planck’s and Einstein’s idea of the quantitization of light and apply it to the electrons’ orbits. It was a magnificent synthesis of scientific thinking; I cannot resist inserting here Jacob Bronowski’s description of Bohr’s idea, from his book The Ascent of Man:

Now in a sense, of course, Bohr’s task was easy. He had the Rutherford atom in one hand, he had the quantum in the other. What was there so wonderful about a young man of twenty-seven in 1913 putting the two together and making the modern image of the atom? Nothing but the wonderful, visible thought-process: nothing but the effort of synthesis. And the idea of seeking support for it in the one place where it could be found: the fingerprint of the atom, namely the spectrum in which its behavior becomes visible to us, looking at it from outside.

Reading this reminds me of another feature of atoms I have yet to mention. Just as blackbodies emit a spectrum of radiation, one based purely on their temperature, so did the different atoms have their own spectra. But the latter had the twist that, instead of being continuous, they consisted of a series a sharp lines and were not temperature dependent but were invoked usually by electric discharges into a mass of the atoms. The best known of these spectra, and the one shown below, is that of atomic hydrogen (atomic because hydrogen usually exists as diatomic molecules, H2, but the electric discharge also dissociates the molecules into discrete atoms):


This is the visible part of the hydrogen atom spectrum, or so-called Balmer series, in which there are four distinct lines: from right to left, the red one at 656 nanometers (nm), the blue-green at 486 nm, the blue-violet at 434 nm, and the violet at 410 nm.

Bohr’s dual challenge was explain both why the atom, in this case hydrogen, the simplest of atoms, didn’t wind down like a spinning top as classical physics predicted, and why its spectrum consisted of these sharp lines instead of being continuous as the energy is lost. As said, he accomplished both tasks by invoking quantum ideas. His reasoning was more or less as this: the planets in their paths around the sun can potentially occupy any orbit, in the same continuous fashion we have learned to expect from the world at large. As we now might begin to suspect however, this is not true for the electrons “orbiting” (I put this in quotes because we shall see that this is not actually the case) the nucleus. Indeed, this is the key concept which solves the puzzle of atomic structure, and which allowed scientists and other people to finally breathe freely while they accepted the reality of atoms.

Bohr kept the basic solar system model, but modified it by saying that there was not a continuous series of orbits the electrons could occupy but instead a set of discrete ones, in-between which there was a kind of no man’s land where electrons could never enter. Without going into details you can see how, at one stroke, this solved the riddle of the line spectra of atoms: each spectral line represented the transition of an electron from a higher orbit (more energy) to a lower one (less energy). For example, the 656 nm red line in the Balmer spectrum of hydrogen is caused by an electron dropping from orbit level three to orbit level two:


Here again we see the magical formula , the energy of the emitted photon, in this case being equal to E, the difference in energy between the two orbits. Incidentally, if the electron falls further inward, from orbit level two to orbit level one – this is what is known as the Lyman series, in this case accompanied by a photon emission of 122 nm, well into the ultraviolet and invisible to our visual systems. Likewise, falls to level three from above, the so-called Paschen series, occur in the equally invisible infrared spectrum. There is also a level four, five, six … potentially out to infinity. It was the discovery of these and other series which confirmed Bohr’s model and in part earned him the Nobel Prize in physics in 1932.

This is fundamentally the way science works. Inexplicable features of reality are solved, step by step, sweat drop by tear drop , and blood drop by drop, by the application of known physical laws; or, when needed, new laws and new ideas are summoned forth to explain them. Corks are popped, the bubbly flows, and awards are apportioned among the minds that made the breakthroughs. But then, as always, when the party is over and the guests start working off their hangovers, we realize that although, yes, progress has been made, there is still more territory to cover. Ironically, sometimes the new territory is a direct consequence of the conquests themselves.

Bohr’s triumph over atomic structure is perhaps the best known entrée in this genre of the story of scientific progress. There were two problems, one empirical and one theoretical, which arose from it in particular, problems which sobered up the scientific community. The empirical problem was that Bohr’s atomic model, while it perfectly explained the behavior of atomic hydrogen, could not be successfully applied to any other atom or molecule, not even seemingly simple helium or molecular hydrogen (H2), the former of which is just after hydrogen in the periodic table. The theoretical problem was that the quantitization of orbits was purely done on an ad hoc basis, without any meaningful physical insight as to why it should be true.
And so the great minds returned to their offices and chalkboards, determined to answer these new questions.

Key Ideas in the Development of Quantum Mechanics

The key idea which came out of trying to solve these problems was that, if that which had been thought of as a wave, light, could also possess particle properties, then perhaps the reverse was also true: that which had been thought of as having a particle nature, such as the electron, could also have the characteristics of waves. Louis de Broglie, in his 1924 model of the hydrogen atom, introduced this, what was to become called the wave-particle duality concept, explaining the discrete orbits concept of Bohr by recasting them as distances from the nuclei where standing electron waves could exist only in whole numbers, as the mathematical theory behind waves demanded:


De Broglie’s model was supported in the latter 1920’s by experiments which showed that electrons did indeed show wave features, at least under the right conditions. Yet, though a critical step forward in the formulation of the quantum mechanical description of atoms, de Broglie still fell short. For one thing, like Bohr, he could only predict the properties of the simplest atom, hydrogen. Second, and more importantly, he still gave no fundamental insight as to how or why particles could behave as waves and/or vice-versa. Although I have said that reality on such small scales should not be expected to behave in the same matter as the scales we are used to, there still has to be some kind of underlying theory, an intellectual glue if you prefer, that allows us to make at least some sense of what is really going on. And scientists in the early 1920’s still did not possess that glue.

That glue was first provided by people like Werner Heisenberg and Max Born, who, only a few years after de Broglie’s publication, created a revelation, or perhaps I should say revolution, of one of scientific – no, philosophic – history’s most astonishing ideas. In 1925 Heisenberg, working with Born, introduced the technique of matrix mechanics, one of the modern ways of formulating quantum mechanical systems. Crucial to the technique was the concept that at the smallest levels of nature, such as with electrons in an atom, neither the positions nor motions of particles could be defined exactly. Rather, these properties were “smeared out” in a way that left the particles with a defined uncertainty. This led, within two years, to Heisenberg’s famous Uncertainty Principle, which declared that certain pairs of properties of a particle in any system could not be simultaneously known with perfect precision, but only within a region of uncertainty. One formulation of this principle is, as I have used before:

x × s h / (2π × m)

which states that the product of the uncertainty of a particle’s position (x) and its speed (s) is always less than or equal to Planck’s (h) constant divided by 2π times the object’s mass (m). Now, there is something I must say upfront. It is critical to understand that this uncertainty is not due to deficiencies in our measuring instruments, but is built directly into nature, at a fundamental level. When I say fundamental I mean just that. One could say that, if God or Mother Nature really exists, even He Himself (or Herself, or Itself) does not and cannot know these properties with zero uncertainty. They simply do not have a certainty to reveal to any observer, not even to a supernatural one, should such an observer exist.
Yes, this is what I am saying. Yes, nature is this strange.


The Uncertainty Principle and Schrödinger’s Breakthrough

Another, more precise way of putting this idea is that you can specify the exact position of an object at a certain time, but then you can say nothing about its speed (or direction of motion); or the reverse, that speed / direction can be perfectly specified but then the position is a complete unknown. A critical point here is that the reason we do not notice this bizarre behavior in our ordinary lives – and so, never suspected it until the 20’th century – is that the product of these two uncertainties is inversely proportional to the object’s mass (that is, proportional to 1/m) as well as directly proportional to the tiny size of Planck’s constant h. The result of this is that large objects, such as grains of sand, are simply much too massive to make this infinitetesimally small uncertainty product measurable by any known or even imaginable technique.

Whew, I know. And just what does all this talk about uncertainty have to do with waves? Mainly it is that trigonometric wave functions, like sine and cosine, are closely related to probability functions, such as the well-known Gaussian, or bell-shaped, curve. Let’s start with the latter. This function starts off near (but never at) zero at very large negative x, rises to a maximum y = f(x) value at a certain point, say x = 0, and then, as though reflected through a mirror, trails off again at large positive x. A simple example should help make it clear. Take a large group of people. It could be the entire planet’s human’s population, though in practice that would make this exercise difficult. Record the heights of all these people, rounding the numbers off to a convenient unit, say, centimeters or cm. Now make sub-groups of these people, each sub-group consisting of all individuals of a certain height in cm. If you make a plot of the number of people within each sub-group, or the y value, versus the height of that sub-group, the x value, you will get a graph looking rather (but not exactly) like this:


Here, the y or f(x) value is called dnorm(x). Value x = 0 represents the average height of the population, and each x point (which have been connected together in a continuous line) the greater or lesser height on either side of x = 0. You see the bell shape of this curve, hence its common name.

What about those trigonometric functions? As another example, a sine function, which is the typical shape of a wave, looks like this:


The resemblances, I assume, are obvious; this function looks a lot like a bunch of bell shaped curves (both upright and upside-down), all strung together. In fact the relationship is so significant that a probability curve such as the Gaussian can be modeled using a series of sine (and cosine) curves in what mathematicians call a Fourier transformation. So obvious that Erwin Schrödinger, following up de Broglie’s work, in 1926 produced what is now known as the Schrödinger wave equation, or equations rather, which described the various properties of physical systems via one or more differential equations (if you know any calculus, these are equations with relate a function to one or more of its derivatives; if you don’t, don’t worry about it), whose solutions were a series of complex wave functions (a complex function or number is one that includes the imaginary number i, or square root of negative one), given the formal symbolic designation ψ. In addition to his work with Heisenberg, Max Born almost immediately followed Schrödinger‘s discovery with the description of the so-called complex square of ψ, or ψ* ψ , being the probability distribution of the object, in this case, the electron in the atom.

It is possible to set up Schrödinger’s equation for any physical system, including any atom. Alas, for all atoms except hydrogen, the equation is unsolvable due to a stone wall in mathematical physics known as the three-body problem; any system with more than two interacting components, say the two electrons plus nucleus of helium, simply cannot be solved by any closed algorithm. Fortunately, for hydrogen, where there is only a single proton and a single electron, the proper form of the equation can be devised and then solved, albeit with some horrendous looking mathematics, to yield a set of ψ, or wave functions. The complex squares of these functions as described above, or solutions I should say as there are an infinite number of them, describe the probability distributions and other properties of the hydrogen atom’s electron.
The nut had at last been (almost) cracked.

Solving Other Atoms

So all of this brilliance and sweat and blood, from Planck to Born, came down to the bottom line of, find the set of wave functions, or ψs, that solve the Schrödinger equation for hydrogen and you have solved the riddle of how electrons behave in atoms.

Scientists, thanks to Robert Mullikan in 1932, even went so far as to propose a name for the squared functions, or probability distribution functions, a term I dislike because it still invokes the image of electrons orbiting the nucleus: the atomic orbital.

Despite what I just said, actually, we haven’t completely solved the riddle. As I said, the Schrödinger equation cannot be directly solved for any other atom besides hydrogen. But nature can be kind sometimes as well as capricious, and thus allows us to find side door entrances into her secret realms. In the case of orbitals, it turns out that their basic pattern holds for almost all the atoms, with a little tweaking here, and some further (often computer intensive) calculations there. For our purposes here, it is the basic pattern that matters in cooking up atoms.

Orbitals. Despite the name, again, the electrons do not circle the nucleus (although most of them do have what is called angular momentum, which is the physicists’ fancy term for moving in a curved path). I’ve thought and thought about this, and decided that the only way to begin describing them is to present the general solution (a wave function, remember) to the Schrödinger equation for the hydrogen atom in all its brain-overloading detail:

Don’t panic: we are not going to muddle through all the symbols and mathematics involved here. What I want you to do is focus on three especially interesting symbols in the equation: n, , and m. Each appears in the ψ function in one or more places (search carefully), and their numeric values determine the exact form of the ψ we are referring to. Excuse me, I mean the exact form of the ψ* ψ, or squared wave function, or orbital, that is.

The importance of n, , and m lies in the fact that they are not free to take on any values, and that the values they can have are interrelated. Collectively, they are called quantum numbers, and since n is dubbed the principle quantum number, we will start with it. It is also the easiest to understand: its potential values are all the positive integers (whole numbers), from one on up. Historically, it roughly corresponds to the orbit numbers in Bohr’s 1913 orbiting model of the hydrogen atom. Note that one is its lowest possible value; it cannot be zero, meaning that the electron cannot collapse into the nucleus. Also sprach Zarathustra!

The next entry in the quantum number menagerie is , the angular momentum quantum number. As with n it is also restricted to integer values, but with the additional caveat that for every n it can only have values from zero to n-one. So, for example, if n is one, then can only equal one value, that of zero, while if n is two, then can be either zero or one, and so on. Another way of thinking about is that it describes the kind of orbital we are dealing with: a value of zero refers to what is called an s orbital, while a value of one means a so-called p orbital.

What about m, the magnetic moment quantum number? This can range in value from – to , and represents the number of orbitals of a given type, as designated by . Again, for an n of one, has just the one value of zero; furthermore, for equals zero m can only be zero (so there is only one s orbital), while for equals one m can be one of three integers: minus one, zero, and one. Seems complicated? Play around with this system for a while and you will get the hang of it. See? College chemistry isn’t so bad after all.

* * *

Let’s summarize before moving on. I have mentioned two kinds of orbitals, or electron probability distribution functions, so far: s and p. When equals zero we are dealing only with an s orbital, while for equals one the orbital is type p. Furthermore, when equals one m can be either minus one, zero, or one, meaning that at each level (as determined by n) there are always three p orbitals, and only one s orbital.

What about when n equals two? Following our scheme, for this value of n there are three orbital types, as can go from zero to one to two. The orbital designation when equals two is d; and as m can now vary from minus two to plus two (-2, -1, 0, 1, 2), there are five of these d type orbitals. I could press onward to ever increasing ns and their orbital types (f, g, etc.), but once again nature is cooperative, and for all known elements we rarely get past f orbitals, at least at the ground energy level (even though n reaches seven in the most massive atoms, as we shall see).

Operator (computer programming)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Operator_(computer_programmin...