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Saturday, December 10, 2011

Kepler-22B; A Warning or Two

The recent discovery of planet Kepler-22B (orbiting the sunlike star Kepler-22) has set off a flurry of articles and other printed/spoken material speculating that we have at last found another Earth-like planet in our immediate stellar neighborhood (the star Kepler-22 is about 600 light-years from our sun, making it quite close insofar as intra-galactic distances are concerned; the Milky way is approximately 100,000 light-years across).

In science however, excitement must be tempered by sober examination of evidence, and there are some good reasons why we should not get too excited by Kepler-22B just yet.   In the first place, we don’t have a good estimate of its mass yet, and probably won’t for a few more months.  This is the most critical consideration as to whether the new planet is a (relatively small) gas-giant world, like Neptune or Uranus, only about half their diameters, or is truly an Earth-like planet, one with a rocky core probably covered with deep oceans.

If the first scenario is true is found to be the truth, this doesn’t automatically rule out life on the new world.  It might still possess liquid water, here as cloud layers, and life could possibly begin in droplets or drops of water seeded with ammonia, methane, hydrogen cyanide, and carbon dioxide, a lá the Stanley Milgrim experiments of the 1950s.  A distinct planetary surface is not actually needed for life, or so current thinking runs.  However, its seems doubtful that such life would have evolved far beyond the single cell, or prokaryotic, stage.  Definitely worth knowing however, if it turns out true.

The other, mass-determined, probability is that of a “super Earth”, a planet like our own, only considerably larger, and one probably covered by ocean-girdling waters and a thick, greenhouse atmosphere.  Again, primitive life is a good candidate for the place, and here even complex, multi-cellular organisms may have gotten a toe-hold.  They could be swimmers and flyers, though almost certainly little in the way of land dwellers, for there would be little of any land to dwell on.  Still, polar icecaps might provide some of this.  A lot depends on the depth of the greenhouse effect, driven largely by water vapor, carbon dioxide, and methane.  All three gasses should be copiously produced by volcanism, so we shall see. Volcanism in turn is driven by a hot liquid core containing sufficient amounts of radioactive atoms, atoms like uranium-235/-238, thorium-232, potassium-40 and strontium-87.  Earth has significant amounts of them (creating also our strong magnetic field which protects us from the solar wind) because the creation of our solar system was probably initiated by a supernova type-II explosion, seeding us with heavier elements, but it is not clear whether Kepler-22 was born under similar circumstances (it is not all that unlikely however, so we can reasonably speculate it).  If not however, Kepler-22B might be frozen over, with little internal heat or heavy elements, leading to few prospects for life.

All this is speculation right now, but it may be of the purely academic kind, for other conditions are needed for life.  The biggest problem is the apparent lack of large gas giant worlds, situated further out than Kepler-22B.  They may still exist, in slightly different orbital places than 22B, such that we don’t see their occultations from Earth; doppler “wobbles” in the star’s spectrum might yet root them out.

If they are not found, however, this is troubling for life’s prospects on 22B.  Jupiter and Saturn stand as staunch shields against a large number of asteroid and comet impacts to our planet, impacts that nevertheless occur to a disturbing degree and which could wipe out all life here if large enough ones occurred with sufficient frequency.  But we have a couple of heavy duty bar bouncers that either suck up those impacts themselves, or hurl the offending rock/ice worldlets out of the solar system, or park them in the asteroid belt.

If Kepler-22B doesn’t have its own bouncers, then it is probably being regularly pounded by asteroids and comets, so much so that life can’t get started there.  Now perhaps its not that bad a problem out there because the Kepler-22 system was not the result of a supernova explosion; but then there might not be enough heavy elements to make a hot, molten core, with its attending strong magnetic field and copious atmospheric components.

Then there’s the other problem, which I’m not certain is truly severe or not.  Earth has an axial tilt of 23° , which is almost perfect for our seasons and the life adapted to it.  The tilt does not vary greatly, and supposedly we have our large moon to largely thank for that.  The reasonable length of our day is also due largely to the moon.  Frankly, I don’t know how large of a problem this really is; with the exception of Uranus (with a 98° axial tilt, rotating virtually on its side), all the planets rotate on roughly vertical axes to the solar system’s orbital plane, and only Mercury and Venus have unusual days, in the first case one locked in a 2:3 resonance with its solar orbit, and in the second, Venus’, case a slow retrograde axial orbit (opposite to its movement about the sun).

If these parameters are important (as suggested by the “Rare Earth” hypothesis) then 22B could be in big trouble, though this is not certain.  But all of these considerations, taken together, should keep our enthusiasm in check as we explore Kepler-22B further.

Wednesday, December 7, 2011

Another Mixing Snafu

I just got nailed on another reaction of household products, this time regular bleach with toilet bleach.  Remember that regular bleach is just sodium hypochlorite dissolved in water:

NaOCl (H2O) ® Na+ + OCl-
OCl- + H2O ↔ HOCl + OH-

H+ + Cl- + OCl- ® OH- + Cl2
H+ + Cl- + HOCl ® H2O + Cl2

In both of the bottom reactions gaseous chlorine is generated in serious quantities.  This is because often, not always but in this case, which I would have known had I bothered to read the labels instead of just assuming, toilet bleach is fairly concentrated hydrochloric acid.  Needless to say it starting foaming at once, and when I came had just enough to flush before being driven out, coughing and tearing.

Lesson:  read labels on chemicals before using!

Making Hydrochloric Acid from Household Ingredients


Making Hydrochloric Acid from Household Ingredients

I used to do this when I was young.  I’m uncertain now:  could it not be considered a terroristic threat?  The times, they are a changing!  Anyway, into the science.

Hydrochloric (HCl) acid is simply a solution of the gas HCl (hydrogen chloride) in water.  The basic acid-forming reaction is:

HCl + H2O ® Cl- + H3O+

H3O+ ↔ H+ + H2O
The main acidic species can be considered either H3O+  or H+ , although the latter is usually used as it is clearer and more consistent.  In almost (but not all) all water based acids, this is the actual acidic species, whatever the starting acid (nitric, sulfuric, acetic, etc.) is.

There are a number of industrial and lab process to make HCl acid, usually from other strong mineral acids.  Another way, however, is to generate HCl gas directly and dissolve it in water (it is highly soluble, almost as much as ammonia).  The household method uses this approach.  Questions:  how do you make HCl gas, and how to you get it into the water?

Warning, Warning!  HCl gas is very irritating and corrosive, so you have to set up some kind of protection for your lungs and throat and eyes before generating it!

At a young age, I loved to tinker with chemicals (perhaps not a good idea when I look back on it, but I was usually reasonably careful), both those I found in the house and those I got in chemistry sets.  And I loved to read chemistry books and ponder what might happen if you mixed such and such with so and so and heated them or dissolved them in water.  Amazingly, I still have all my body parts and they all work well, which might be something of a wonder.

In this case I noticed something.  It seemed as though if you mixed ordinary table salt and baking soda and heated them strongly, you might get the following reaction:

NaCl + NaHCO3 ® HCl­ + Na2CO3

In which the two reactants swapped the hydrogen and chlorine,  Further, since HCl was a gas, it would escape the reaction mixture (the upward arrow) and constantly drive the reaction to the right.

Of course I had to try it.  Now, if I’d had a balance, I’d weigh out 5.85 grams of salt and 8.8 grams of baking soda.  This is one tength of a mole of each product, thus an equal number of molecules of each, perfect for the 1:1 reaction.  It would have yielded 3.85 grams of gaseous HCl ( and 9.4 grams of Na2CO3) .  The two weight combinations on either side of the arrow equal, as they should.  I did not have a balance however, and so used a teaspoon or tablespoon of both reactions – good enough.

Now here comes the part where you shouldn’t have done what I did.  I would mix both reactants in an Kimex glass laboratory grade Ehrlenmeyer flask (the triangular shaped one), place the flask on one of our electric stoves, and (at least have the sense to) gradually heat the flask until the stove temperature was at or near high.  I know that gaseous HCl was irritating and corrosive, so I would carefully smell for any gasses coming through the top of the flask.  Sure enough, I found myself tearing and coughing pretty soon, and I knew my hypothesis was a triumph.  The question now was, how to deliver the gas into (preferably cold) water?

You’ve already noticed that household ingredients aren’t quite enough, you also need some laboratory equipment, mostly glassware.  I had such from my chemistry sets:  Ehrlenmeyer flasks, beakers, corks/rubber stoppers that fitted the flask and had a hole large enough for the glass tubing, the tubing, and an alcohol burner I could use to bend the tubing from the top of the Ehrlenmeyer over to the beaker (more than a ninety degree angle) – not as easy as it might sound for glass work requires some practice and experience.  (You can no doubt still get these things, though I don’t know if you’ll attract unwanted attention doing so).

Let’s assume you have a desktop balance for weighing chemicals, though don’t ask me how much they cost; anyway, you don’t need a highly priced one.  Now, if you weigh amount of reactants in the flask as described above, you should generate 0.1 mole (8.8 grams) of HCl gas when you heat it strongly.  After pouring the reactants into the flask, next, assemble the apparatus. The stopper should fit tightly inside the Ehrlenmeyer, the bent glass tube pass through the stopper (not too far, though, just enough to pick up any gasses and deliver them!), and the other end of the tube should reach the bottom of the beaker, which should hold about 100 milliliters (~ 1/10 of a quart, or half a pint or so – use a graduated cylinder if you can) of cold water.  Now strongly heat the mixture in the flask.  What you’ll observe is curious.  First, a stream of bubbles will emerge from the beaker end of the tube, rising and escaping into the air.  Don’t be alarmed; this is just the heated air being forced from the flask through the tube.  What happens next is the main show.  The bubbles stop, and the gas level in the beaker stays pretty much flush with the water.  What is happening here is that HCl gas is now being generated rapidly and, being highly soluble in water, immediately dissolves when it hits it, leaving no more bubbles.  Your HCl acid is starting to form!

You should keep this reaction/process going until you observe the following.  As the reactants are consumed, the HCl is produced in smaller and smaller quantities; and, again because it is so soluble in water, begins to suck liquid up the tube from the beaker.  At this point you should stop the reaction (turn off the heat and move the flask off the stove, remove the flask + stopper + tube from the beaker, etc.).  You DO NOT want water pouring back through the tube into the Ehrlenmeyer under strong heat – I never tried this, but I assume the water will flash into steam, at least cracking if not exploding the Ehrlenmeyer, thereby releasing a lot of acid and HCl gas into the atmosphere, any probably other nasties I haven’t thought about.  All in all, don’t let this happen!

Let it all cool down for a while, before disassembling everything and thoroughly washing out everything but the beaker and its contents (use lots of water, on your hands too).  Now, if the reaction has gone to completion (though remember, some HCl is lost), I figure the concentration to be 0.1 mole HCl gas dissolving into 0.1 liter water, giving around a 1.0 molar (M) solution.  This is a fairly potent concentration (if you get it on yourself, wash thoroughly with water).  It’s more than enough to dissolve aluminum and tin foil, magnesiumzinc, probably lead and iron and some other metals, giving off streams of bubbles of hydrogen gas as it does so (this is also potentially hazardous, and hydrogen gas is highly flammable).  Remember mixing vinegar (a dilute solution of  acetic acid, CH3CH2COOH) with baking soda and watching it fizz up?

CH3CH2COOH + NaHCO3 ® Na+ + CH3CH2COO- + H2O + CO2

The CO2, or carbon dioxide, is the gas that fizzes up, just as from a can of beer or soda.  If you substitute the weak and highly diluted acid vinegar with fairly concentrated hydrochloric acid, the reaction ought to be considerably stronger:

HCl + NaHCO3 ® Na+ + Cl- + H2O + CO2

Not that I remember trying this.  Oh, one more thing; I’m pretty sure that you can make the acid highly concentrated (though I don’t recommend this, however, as it is VERY HAZARDOUS at very high concentrations), simply by upping the amount of reactants.  Multiply the reactants by five or ten (you may have to run the reaction several times, or find a large enough Ehrlenmeyer flask), and you should get five-ten molar acid.  Again, something you really shouldn’t play around with, unless you know how to do so safely).

On Curiosity (From WONDERING ABOUT)


The humility I have described here is not the humility we see (not always in sincere form) in various Eastern religious leaders and the like, although it is related.  I am speaking of intellectual humility:  the ability to accept that anything one has come to believe, whether it be from schooling or a church, from books, parents or other authorities, or even as the product of one’s own observations and thoughts, could genuinely be mistaken; mistaken no matter how much observation and thought or the weight of authority or time lend to it.  Or how many people hold the belief, for how many centuries.  It is the recognition of human limitations and fallibility, even among the most brilliant, well-educated minds.  My personal favorite example of this is Einstein adding the so-called Cosmological Constant to his equations for General Relativity to prevent, for what were mainly esthetic reasons of his, an expanding (or contracting) universe, something which his raw equations implied.  When Edwin Hubble was within barely a decade to demonstrate by his observations of the red shifts of distant galaxies that the universe is in fact expanding, Einstein pronounced this ad-hoc addition of the Cosmological Constant the greatest blunder of his career.  What makes this example my favorite is how a more recent discovery in cosmology, that the universe is not only expanding but that, contrary to all expectations the expansion rate is accelerating (the mutual gravitational pull of the galaxies ought to be slowing it down, yet it is speeding up), has resurrected Einstein’s self-disavowed constant, albeit in somewhat different form.  Einstein’s confession of his greatest blunder may thus prove itself an even greater error, an irony I have to expect he would have enjoyed.

Another, important aspect to humility is the overwhelming feeling, shared by most of us I suspect, at looking upon a universe not only greater than our ability to fully understand, but, as the biologist J.B.S. Haldane observed (though he used the word queerer rather than greater), greater than we can understand.  One of the most wondrous and compelling things about science, which is such a large part of the reasons I have spent a lifetime immersed in it, is how strange and wonderful it can make the most “ordinary” of things, simply by the act of explaining them.

Walt Whitman, "Leaves of Grass"

WHEN I heard the learn'd astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander'd off by myself,
In the mystical moist night-air, and from time to time,
Look'd up in perfect silence at the stars.

Tuesday, December 6, 2011

Reaction of Bleach with Detergent?

      Here’s some more interesting household chemistry, one that I just discovered.  I wrote about the dangers of mixing bleach and ammmonia before, but naïvely thought that bleach and pure detergent (like dishwashing liquid) was perfectly safe.  In fact, it’s not particularly hazardous, but there is some chemistry going on and some precautions one should take.

It’s obvious that chemistry is transpiring because when the mixture is made, there is some some significant foaming and a mild temperature rise that results.  Again, neither is dramatic, and both cease soon, giving you a stable liquid (which is great to use on sinks, pots and pans, and on other kitchen or bathroom surfaces).

Of course, I’ve been trying to squirrel out why all this happens.  What follows doesn’t come from any probing research but are just my own ideas and chemical knowledge.  The first thing that strikes me as that when you mix bleach and detergent, you’re setting up reaction between  bleach, which is a solution of sodium hypochlorite, and detergent (usually), a sulfonic acid:

NaOCl + H2O ® Na+ + OCl- + ( H2O) ;

OCl- + H2O ® HOCl + H+ + Cl-;

R-(S(=O)2)-OH  + OCl- and/ or HOCl ®  ?;

     There are other possible reactions going on too; this is not as straightforward as I thought it was going to be!  There’s another clue to what’s going on, which is that I found the evolved gas odorless and colorless.  Now if it had been something like chlorine or sulfur dioxide, there was enough that I should have picked up the pungency or even color of these two compounds.  That leaves us with hydrogen and oxygen, which are both colorless and odorless.  Now, I’making oxygen the more likely of the two because I espy a straightforward way of evolving it (and one consistent with all observations of the reaction), while a I can’t see too many ways it could be hydrogen.

Take the S(=O)2)-OH part of the sulfonic acid.  I can easily imagine it reacting with HOCl:

S(=O)2)-OH + HOCl ↔ S(=O)2)-Cl + HOOH

The reaction yields the chlorinated version of the sulfonic acid (detergent), the properties of which should not be too strongly altered; and hydrogen peroxide, which in the vigor of an exothermic chemical reaction can break down into water and ogygen, foaming it up and realeasing heat.  That’s right, I’m suggesting the gas is oxygen (this is easy to test, by the way; just stick a smoldering match stick end into it and see if it flares up brightly).

Also, note the ↔ symbol I use for the reaction direction, instead of the single headed arrow.  I’m suggesting that this is a reversible reaction; it can go either way, as long as some other process doesn't contiuously consume one or more of the reactants/products.  Many chemical reactions proceed this way.  In the reaction above, as long as the HOOH is breaking down into H2O and O2 then it must keep proeceeding to the right, because both the oxygen escapes the mixture.  Two things to bear in mind here, however; first, the reaction is obviously not very strong (or it would get hot and foam up dramatically, perhaps even explode; concentrated HOOH is most unpleasant stuff), and second, the moment the bottle of bleach + detergent is closed tightly the back pressue of oxygen building up in the bottle essentially brings the breakdown of HOOH to at least a near dead stop, and then the entire reaction can go merrily back in forth in equibrium mode.  That’s why it quickly cools and stops foaming.

So what I am proposing that you end up with an equibrium mixture of bleach, detergent,  chloronated detergent, and HOOH (hydrogen peroxide).  If so, that makes it an especially effecting cleaning/bleaching mixture, as all three components will contribute their share.

At least, this is the best I can make of it on short notice.  I’d be fascinated by alternative hypothesis.

From Quantum Cats to Cats' Paws: Chapter One


Chapter One:  Those Who Get Science and Those Who Don’t

Since my childhood, when my love of science and nature was first sparked, I found myself surrounded by an idea about humanity that at the time I could neither understand nor accept.  This idea was, at heart, that there were basically two kinds of people:  Those who got math and science, and those who did not.  It was such a strange idea to me, one which I saw duplicated nowhere else.

Actually, there was one similar idea, this one about sports. I noticed here too the idea of there being those who were good at sports, those who weren’t, and little in-between.  I thought this very odd too; both ideas actually, as the whole point of school – or so I presumed – was to teach kids skills and knowledge which they otherwise would lack.  This point apparently didn’t apply to science/math and sports. I proved that it did apply for sports in the fourth or fifth grade however, when, by a combination of studying batting mechanics, concentration, keeping my eye on the ball all the way, and controlled aggression and plain old confidence, I could hit a softball just as well as anyone, if not always as far (I am not very much athletically gifted).

I must have determined, sometime around then, that if the can/cannot dichotomy around sports was untrue, then it was probably equally untrue about science/math:  people weren’t divided into can do / can’t do camps, at least not in any straightforward way.  All I needed to do was to find the right way of showing/teaching/presenting science and math so that anyone could “get it”, at least to a reasonable degree.  I just had no idea what that right way was.  In fact, I had no idea what the problem was for a very large portion of my life.  One of the points of this book is my struggle with and hopes for solving it.

Don’t get me wrong.  Different people have different talents and abilities in their lives, and scientists plus mathematicians (which I will from now on collectively call scientists) obviously do grasp ideas in science and math better than those not so gifted.  I just don’t understand why there should be such a vast gap between the two.  Indeed, I don’t believe in any such gap at all, only a continuum of talents.  Most of life is this way, so why not here too?

*          *          *

This is not an autobiography.  Still, I should stop here and tell you some things about myself.  One of them is about a condition which is fairly well understood today; one for which children get routine diagnoses, and all kinds of special help and training is available for those diagnosed.  You’ve probably heard of it yourself.  It’s called Asperger Syndrome, named after the Austrian pediatrician Hans Asperger who, during WWII, first described the conditions and its symptoms.  But it took some fifty years for the condition to be widely accepted (for those of you in the medical field, this is not a good number) and for children to begin getting diagnosed with it and receiving various but consistent treatments.

Unfortunately for me, this was all before my time, so I was left to my own devices in handling the “strangeness” about me that I didn’t understand and thought I was largely imagining.

The interesting thing about Asperger Syndrome (which I will call AS from now on) is that it is placed in the “autism spectrum” of pervasive developmental disorders.  Now, most of us have heard of classical autism, in which a child’s intellectual and social development are locked into an almost infantile state.  However there are also versions of autism which don’t impair intellectual development, which, paradoxically perhaps, may lead to superior intellectual development.  The writer and animal specialist Dr. Temple Grandin is a wonderful example of the latter, and you have to read some of her written works to get a feel for what it is like to be brilliant yet autistic.

Yet Grandin is not an “aspie” (a favorite term by those who have AS) but a (very) high functioning autistic, and there are important differences.  Both can have high intelligence and mental talents, this is true.  The main difference to me seems to be that, although both are still socially deficient (I’m tempted to say “retarded”,  just like those few people who really cannot, intellectually, grasp science and math at almost any level are deemed “retarded” in unofficial circles), aspies still at heart crave social acceptance and love, while high functioning autistics (HFAs?) like Grandin seem perfectly comfortable without them.

There are other differences too. My position is that I think that aspies are worse off than HFAs because they so desperately crave what they cannot figure out how to get:  friends, acceptance, normalcy, popularity, and so forth.  These frustrations of course only get worse as one proceeds through adolescence and adulthood,   Because aspies are often highly intelligent, they can learn to “fake their way” through the adult world, with more or less success.  But the anxiety and frustration and despair at feeling so deeply disconnected can ultimately prove to be too much.  This was the case for me, but clearly not for all aspies.

*          *          *

Why do I raise this subject?  It is not, I assure you, to gain cheap sympathy from readers.  A treatise on what Asperger’s has driven me into and through could be an entire book, perhaps one worth writing.  But here I am concentrating on what, at least I believe, is one particular consequence of it.

Even as a young child I was often absorbed in my own world (a common theme among aspies), and because I had some intellectual precociousness, I developed a very strong sense of curiosity about myself and the world around me.  I also developed some ways of satisfying that curiosity.  Thus, for example, I learned how to read and write at an unusually early age (this was, however, in part because I was fascinated by the sounds of different letters and words – probably also due to Asperger’s, who can get fixated/obsessed on things and ideas and, to the annoyance and worse to others, people).  I had also, at least by age five, fully developed the scientific approach of not simply believing things because authorities (parents, teachers, etc.) told me them, but of trying to figure out how to test those claims myself.  I won’t repeat in detail my favorite example of the color of the disk of the sun (it really doesn’t look yellow, as we are all taught) and my struggles with my kindergarten teacher to draw it as I had learned to observe it.

(Incidentally, why the sun seems yellowish-white (if you don’t stare strongly at it, which you shouldn’t do if you don’t know how to while protecting your eyes) is a true and fascinating scientific tale, one I won’t tell here except to hint that it’s the same reason why the sky is blue.)

Never mind these early clashes with teachers on such things.  I was to have more, in which I was sometimes right and sometimes wrong, but in all cases was fortunate to have teachers who accepted or at least tolerated a child who thought for himself (thank my lucky stars for all of you).  The point I’m trying to drive home is how an insatiable curiosity in me was forged by a combination of my Asperger’s and my intellectual/cultural/family environment.  How much better it might have been has we known about Asperger’s at the time!  Instead I was regarded a somewhat precocious child combined with a somewhat rebellious nature.  Since I was never a serious behavior problem I never came to the attention of school psychologists (I think).  I liked my teachers too, and never wanted to disrespect them or show them up – no, I was decidedly a good boy.  But all this stuff was festering inside me nonetheless, and it finally came out in high school and beyond.  Again, however, never mind that; I’ve only sought to explain the origins of my unerring need to know and understand, which I (luckily!) have within me to this day.

*          *          *

Curiosity is an essential ingredient in science, and in the minds of those who work in the field, either professionally or as amateurs.  I’m also certain that practically everyone has it, at least to some degree; but I’m also just as certain that for most people it has been blunted and buried and snuffed down to a slow simmer because the adult world in general doesn’t encourage it.  I’m sorry to have to say this, that even in this, possibly the freest of societies/cultures in history, people are still often hamstrung by the need to accept authority and its proclamations about the nature of things; and that those who do so are rewarded while those who fail to conform are sufficiently driven to near extinction to drive the point home.  Ironically, I believe there is some truth to this even in the scientific establishments themselves (though nowhere near as much), as controversial such a claim might be.  It may, indeed, be necessary to have it to some degree, for social/cultural adherence and order.  Well, I’d better drop the issue now.

*          *          *

Bear in mind, this is just my two cents, and not the nexus of the discussion.  I meant to concentrate on curiosity as essential if we are to be among those people who “get” science (and math).  But is curiosity enough?  What other powers of the brain need employment here?

This is not so obvious, and I had to think about it for a long time before I came up with a sensible sounding idea.  Of course, not all scientists think exactly the same way (thank God!), but there does seem to be  a basic pattern, a fundamental mode, in their thinking, just as there are fundamental nodes in the plucking of a musical instrument’s strings.  This, I think, is their ability to take abstract ideas and place them in their minds as concrete pictures and/or processes.

To give a personal example of what I mean, I did very well in my undergraduate courses in organic chemistry (not without some serious studying, mind you), while many other students struggled terribly.  Now, organic chemistry is a subject concerning large (carbon-based, which we’ll get to later) molecules, often with complex shapes.  I didn’t find it particularly difficult to picture these molecules in my mind, even without the help of molecular modeling kits.  It seemed to me that all I had to do was to combine this ease of picturing with certain things you learn in general chemistry (like electronegativities, and the different kinds and strengths of bonds, also things we’ll get to).  You could almost figure out anything from just these two sources and lick the organic chemistry bear without working up too much of a sweat.

Other students, however, wrestled mightily with the bear.  Sometimes I would try to help them, but neither of us could figure out what I was doing right and they were doing wrong.

Then one day I was happened to be reading a book on how the mind worked and came across a fascinating puzzle. The author presented a picture of two block-composed objects (that is, objects made of, say, wooden blocks glued together).  I wish I could remember or find the objects, so you could do this test for yourself.  Having sketched (or photographed) the objects – this is all in two dimensions, bear in mind – the author made the bold assertion that the human mind could not imagine them in 3D space being arranged in such a way in which an extension of one could fill a gap or hole of the other.

I nearly fell over, for I realized at once that I could easily picture this situation.  It was as easy as sitting down!  Then I remembered taking geometry in the tenth grade (with dear Dr. Israel Nolan, wherever you are), and having to do practically no studying or homework because the problems looked so easy to me I could work out the geometric principles on the tests and get an A for the course.  The two abilities, the one in organic chemistry and the other in geometry, I realized were really two aspects of the same gift!

Gift is perhaps a poor choice of words, for it implies that you either have it or you don’t.  The truth, I believe, is that everyone has it, just not to the same degree.  With me it is obvious.  And, naturally, there are many who are far superior to me in it – I suspect that Einstein could actually picture the shaping and warping of space-time even in his equations for it, something we more ordinary mortals struggle mightily with (I think I’ve got it down a little bit, but … help!).

*          *          *

Let’s get to the bottom line.  Once again this isn’t actually about me, or what modest talents I seem to possess.  It’s about the issue raised by the title of the chapter:  “Those Who Get Science and Those Who Don’t”, and why.  My conclusion, or I should call it hypothesis (an hypothesis is an “educated guess” about the nature of things, drawn from existing observations; to become a theory it must pass more stringent tests and many more observations, after which it may even achieve fact status), is that the main reasons are:  those in column B simply don’t, for whatever reason (lack of Asperger’s?) have the probing and insatiable curiosity to the degree those in column A do; or/and that the A types are better (though not infinitely so) at turning abstract ideas into reasonable concrete images in their mind.  I say reasonable because there are no doubt other criteria, such as logical thinking, involved – you can, after all, imagine all sorts of absurd, illogical things, something we all do frequently and sometimes deliberately.

One thing I hope the reader is taking away from this chapter is that few people really fall into either A or B perfectly,  that this is a fallacy foisted onto us by psycho-sociological forces I don’t claim to understand.  I also hope that, if you have always thought of yourself as the classic B type (most people do), don’t despair; you almost certainly have some A coursing through your veins, and you can understand science to a degree beyond what you believe.  With hope comes invitation, and I am welcoming you pseudo-B’s to come exploring the possibilities with me (along with all you A’s, of course).

*          *          *

Again, there must still be something missing, however, to this hypothesis I’ve laid out about why people are of type A or B when it comes to science.  I think everyone knows what I mean:  we all know people who are clearly intelligent but shake their heads in fogged embarrassment (to be bitingly truthful, not all of them appear embarrassed, but even smug and proud!) at their ineptitude in matters of the scientific intellect.

I’ll take my own mother as a personal example of that, partly because she has recently passed (and will be sorely missed by all her children and grandchildren) and is much on my mind still, and also because she was a decidedly intelligent and educated person, one of the most I’ve ever known (so this is out of respect, mom).  But she was a textbook example of what the physicist and novelist C.P. Snow lamented as the breakdown of intellectualism, even society as a whole, into two factions:  literary/artistic intellectuals, and scientific intellectuals.  This division is clearly quite real and has been become quite rancorous over the last several centuries up until today.  It’s almost impossible not to see it, especially in the halls of academia.  In mom’s defense, she admired many scientists and their accomplishments, and well understood that the high and healthy standard of living she and her family enjoyed was because of scientific work.  I’m certain she also understood the scientific principle and could apply it effectively.

I have at my fingertips a good example of what I mean.  Some years ago, as we were preparing to leave her house, the question of what caused the Earth’s seasons came up.  I immediately jumped into my professorial robes (always keep ‘em around, just in case) to explain the seasons, but was firmly stopped before I could even begin:  “I don’t understand scientific reasons; I don’t have a mind for those things,”  she insisted, or something like that, to my utter astonishment, giving me no chance to protest that even a child could understand the science underlying Earth’s seasons.  Worse, she didn’t even want to try!  I remember being crushed.

What really has me puzzled here is that those in the literary/artistic camp are not devoid of this ability to picture abstractions I mentioned earlier.  For, after all, this is just the action of imagination, and who can imagine better than artists and writers?  There’s something to the reasonable aspect of imagination that sometimes comes into effect here.  I also sense that literary/artistic intellectuals regard scientists as dangerous and even naïve (which of course they are sometimes, as all of us are).

Is it envy?  Scientists’ equations and proclamations are difficult to understand, yet they wield considerable power and influence in society, power and influence the competition, well, just can’t stomach?  I’m tempted, but must reject this hypothesis, as writers/artists can be equally dense and incomprehensible, and they too have their influence in the halls of government and academia.  Besides, as I said, my mother had little but admiration for scientists, even if she didn’t think she could follow their explanations and equations to save her life.

*          *          *

Personally I see nothing natural or inevitable about this division of society into two, almost warring, camps.  And indeed, many scientists do appreciate literature and the arts, and vice-versa.  I suspect this is a temporary division, brought on by nuclear and other weapons technology, and other abuses of some scientists who see satisfaction of curiosity as an end justifying any means.  If I am right about this it heartens me, because I like many have witnessed the many recent attempts of the scientific community to ethically police itself, and the strides of many in the literary/arts camp to gain scientific education so that they can have a say in ethical scientific philosophy too.

*          *          *

Perhaps I should have emphasized earlier this idea of the perversion of curiosity as means, however immoral in specific cases, to its own end of self-gratification.  I think you’ll agree it is not only important, but will only become more so as science progresses.  As noted, this has been going on for some time now:  Mary Shelley’s famous book Frankenstein, written two hundred years ago, is probably the most influential tome along these lines.

I don’t want to elaborate on this, however, because again I return to one of the fundamental aims of this book.  Let me ask you:  do you see yourself as a type A or a type B; and when I say type B I include our artistic/literary brethren as part of this group.  Perhaps you are straddling on the seemingly wide saddle between the two, one foot in one stirrup and the other in its counterpart.  Perhaps you aren’t certain whether you even care; though, if you’re in this camp, you’ve probably stopped reading by now, so we can safely eliminate you from the discussion.

*          *          *

More to the point, how should I proceed?  I think perhaps here that an explanation of the seasons should make a good a starting point as any, given that it really isn’t a difficult scientific problem and that someone so dear to me proved a classical type B in refusing to listen to the solution.  You can judge as well at this point:  do I make a clear, coherent theory of the seasons such that a school child could understand it, or do I leave you still scratching your head?

Let us begin.  I know that somewhere in your primary education you learned that Earth moves by a double motion: it revolves around the sun, in a time period known as a year, and it also rotates on its own axis (an imaginary line connecting the north and south geographical poles), in a time period we call a day.  Abstract knowledge is not enough here, remember; an act of reasonable, logical imagination is needed.  Thus, I’ve provided a picture of this double motion, as seen from some vantagepoint way out in space:
Here the sun is at the center of the picture, and Earth is the blue spheres revolving about her (of course, there’s only one Earth; the six in the picture simply show it at different points in its orbit).  Although it doesn’t demonstrate Earth’s rotation about its own axis, it does show the axis, as the faint blue lines drawn through the various Earths, tilting from bottom left up toward the right.  Earth spins on that axis, which, you’ll notice, doesn’t change direction as the planet orbits the sun – hint, this is the key to the explanation. Oh:  The terms periapsis and apoapsis refer to the points in Earth’s orbit when it is closest and when it is furthest from the sun; for the orbit is not a perfect circle, but is actually, as Johannes Kepler realized in the 16’th century, an ellipse in which the sun is at one focus (of two foci) of the ellipse.
[I should not assume anything.  You can make an ellipse yourself by using the following directions:  place a piece of paper on a table; stick two pins some distance apart from each other (not too far from each other or too far from the center of the paper, or the ellipse will fall off the paper and the experiment won’t work); take a piece of string with the two ends tied together (making it a loop) and place the loop around the two pins and a pencil that is in contact with the paper (it should yield a triangular shape for the string); with the pencil inside the fully stretched out string (remember, the string is stretched about only the pencil and the two pins), draw the naturally closed shape on the paper, keeping it taut as you draw all the way around.  This shape is an ellipse and the two pins the foci of the ellipse.  It looks, as you can see in the Earth/sun picture, like a squashed circle; and that’s a good way describe it.]
All planetary orbits, including Earth’s, are ellipses with the sun at one focus; that, recall, is one of (the three of) Kepler’s Laws of planetary motion.  Now, you might think at once that this explains the seasons; for when Earth is closest to the sun it will be summer, and when it furthest, winter will grip the planet.
You might be tempted towards such an hypothesis.  Instead, what should immediately smack you on the head is something you’ve known for a very long time:  Earth’s seasons aren’t neatly divided into summer and winter.  When it is summer in the northern hemisphere it is winter in the southern, and vice-versa.  Indeed, if you look at the picture of Earth’s orbit, you’ll see that the northern winter solstice (the first day of winter) occurs just two weeks before periapsis, or the closest approach to the sun.  The same is true of the northern summer solstice and apoapsis.
So this hypothesis won’t wash (though I have seen it seriously proposed).  What hypothesis will pass muster, as in being consistent with observable facts?  I hinted before that it lay with Earth’s axis, and indeed in here the solution presents itself.  Go back and look at the Earth/sun picture yet again, especially at the different Earths’ axes, and observe something I haven’t pointed yet.  Do you see it?  Don’t worry if you don’t because the significance isn’t all that obvious until you think about it.
If you haven’t spotted it yet, here it is.  The axes are not straight up and down with respect to Earth’s orbital plane (the imaginary flat and infinite surface the orbit naturally fits inside), but are tilted with respect to that plane; and furthermore, as said, they retain the same tilt all the way through Earth’s orbit – um, at the risk of getting ahead of myself, this is an example of Conservation of Angular Momentum, one of the great conservation laws of physics (and is truly what makes the world go round!).
The axis tilt in this case is about 23° (degrees), in the system where 90° or a right angle is just two connecting lines perpendicular to each other () – you should have picked this up from high school geometry, but may have forgotten so I repeat it here.
Look at the periapsis Earth point, near the upper right corner of the diagram.  The whole explanation for the seasons can be made here, because what I am about to say will apply to all the Earth points.  This is almost the particular point (it is really at the winter solstice, the first day of winter, December 21) where in the northern hemisphere the axis tilts furthest away from the sun, and, conversely, in the southern hemisphere tilts furthest towards the sun.  This is the key to the seasons.
Look at this particular point I’ve chosen carefully.  Northern Earth appears to be, in fact is, leaning away from the sun, while the southern part of the planet is leaning toward it.  For observers standing on both hemispheres, the northern one not only sees fewer sunlit hours during a winter’s day (which is why we say winter has shorter hours, though this is not really true; all days are 24 hours long, nighttime and daytime parts combined), but also the angle of the sun is lower in the sky, spreading the portion of sunlight per ground area (space on Earth’s surface) thin.  For the southern observer, it is high summer for the precise same reasons:  more sunlit hours during the day, and a high sun in the sky, concentrating its rays on a minimum area.   Can you see this?  I hope that, maybe with some effort, you can.
No wonder it is cold in winter and warm in summer, and that the two hemispheres have opposing seasons!  The small difference in overall sunlight received from Earth’s orbit being an ellipse (it is, in fact, only very slightly elliptical, nowhere near as much as implied in the picture) makes only a small perturbation (change) to the effects of Earth’s tilted axis.
In the interests of not over-simplifying things and so “dumbing science down” (all attempts will be made to avoid doing so in this book, or at least keep it on the shortest leash possible), I need to be a little more forthcoming – although you can skip the following if you feel the need to do so, a need which I’ll just hope you will resist.  I have pretty much stated flat out that Earth’s orbital axis is about 23° and always points in the same direction, and that is due to the so-called immutable Law of Conservation of Angular Momentum.  In fact, looked at from year to year, or even century to century, this is basically true, which is why my explanation of the seasons can stay afloat.  But, as always, the real picture is more complicated than this.  There are other motions of the Earth.  First, the angle is not always 23° but “wobbles” about somewhat over hundreds of thousands of years.  Also, the direction of the tilt also moves, in a circular fashion, over a period of about 25,000 years.  This means that 12-13,000 years from now the northern and southern seasons will have switched and we’ll be celebrating the winter holidays (Christmas, Chanukah, Kwanza, Festivus, etc.) during the beginning of summer, just as those in Australia and South America do today.  Easter too will come in the fall, not spring.  (This all assumes any of us humans will still be here to celebrate them, by no means an automatically true proposition.)  These relatively minor movements can also be perturbed into larger ones, at least in theory, by the gravitational influences of the other planets, or by passing stars or other large objects as they come and go near the solar system over periods lasting millions of years.  If you are interested by the way, our large moon largely, and fortunately I hasten to add, shields us from most of the more extreme perturbations; I say fortunately, because it is unclear whether life, or at least complex life, could exist if Earth were that unstable in its motions.  Interesting are the whims and wills of the universe!
*          *          *
This concludes the explanation of the seasons.  How do you feel?  Did you follow it, perhaps with effort and several rereads, or did you get it instantly, or are you still in a thick fog?  If the last possibility I’d like to know (unless you were simply bored because you have no scientific curiosity, in which case why are you still reading?).  Are you feeling at least a little more A’ish, or does B still have you in its vise?  If the latter, I invite you to reread the section (perhaps yet again), paying closer to the parts where you started to get confused.  I think most of you will make progress, though you shouldn’t have to reread it too many times to do so.
In any case, we have encountered our first scientific explanation of a natural fact, and will do so many more times in this book.  Most of these facts will be more challenging to explain than the seasons, so I shall have to work harder to satisfy you without snowing you over or treating you like the fool I’m convinced you’re not.
I’ve entitled this book From Quantum Cats to Cats Paws, meaning I intend to cover a hopefully comfortable handful of interesting and important concepts in physics, chemistry, and biology.  Incidentally, don’t fret if you don’t understand or have even heard the phrase “quantum cats”, for anything in the field of quantum mechanics needs a lot of careful work to explain to anyone at any level.  It is something even great physicists don’t claim to fully understand.
Furthermore, we won’t be starting there.  I’ll be starting with something that, strange enough to say, I believe is easier to understand, at least at the basic level we’re aiming at here, than most people think:  Einstein’s theory of special relativity (it’s the general theory that has even the brightest pulling our hair out, though even here some fundamentals can be outlined and given a reasonably good feel for).  But first, I want to say more about hypotheses and theories and facts, a subject I only touched lightly upon here.  I also want to touch on other areas, like how art/literature and science/math are alike and how they are different.  I’ll do this periodically as we go along.
Here we go!