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!
