The topic of possibility and probability
is likely to raise a few eyebrows and create a few questioning looks. Why is this a
subject that should be reviewed, is it that important a matter, and what does it have to
do with God? This is where some trust and patience on your part will be required. The
different meaning between the two words and an interesting illustration will be provided.
Later, this should prove useful in permitting your independent assessment of events in
science that some would like you to believe. An interesting definition of those two words
was taught to me that I would like to explain and share. The illustration that a teacher
gave, which was so strong in terms of putting things in perspective, will also be
explained.
The definition and illustrating example on possibility and probability has stayed with
me for a lifetime. In later chapters you will see that it is significant. Questions will
arise as to whether or not something was possible or probable to occur. I feel that the
example described in this chapter will help considerably to put things in a clear
perspective and allow you to draw your own conclusions. Do not worry, the subject matter
is going to be kept light and the explanations are not going to become complex in a
technical or mathematical sense. The whole topic is too important and I do not want to
lose you during any part of this.
Believe it or not, I first became exposed to these two words, possibility and
probability, when I was in elementary school. The ironic part is that although I spent
quite a bit of time with those two words in a school project, I believe that I was too
young and did not fully understand the difference between the words. It was not until
senior high school that I was to learn the true meanings. The key to their difference and
the profound example I remembered will be compared against several subjects in science,
including the scientific explanation for the creation of life. Before I get to that, a
short digression back to elementary school days will be made.
While I was in grade five or six, we were told about an major annual event that was
held between all the schools and grades within the City of Winnipeg: a Science Fair. Our
elementary teacher strongly encouraged the class to come up with ideas, either
individually or as a group, and enter them into the Science Fair. One of my best friends
in elementary was Bruce, we lived about one block apart, and we rode the Cathedral bus
back and forth each day to Robertson Elementary School. I even rode lookout on the bus for
Bruce. I was an early riser and caught the bus before it headed on its loop around Scotia
Street and came right back to where I got on. The plan was to meet him at the first stop,
but Bruce was not an early riser. There were many times when I stood beside the bus driver
as we looped back and I would peer down St. Cross Street looking for Bruce to be running
and myself yammering at the driver to wait. The morning bus was always crowded and usually
had standing room only. Students going to St. Johns High got off at Salter Street
and we continued on with our sudden expansion of free space and available seating. Before
the Salter Street exodus, an elementary student, with a cute lunch box, had to be careful
with the giants as they were not to be messed with.
Bruce and I decided to enter the Science Fair together and our topic: none other than
Possibility and Probability. To be totally honest, I have no recollection as to how we
came up with this subject for our project entry. I learned much later that Bruces
Father was a physics professor at the University of Manitoba. While not sure, I am
somewhat confident that the project idea likely originated with Bruce. It was certainly a
different project for some elementary kids to be working on and this became very apparent
when we attended our first Science Fair. While other projects were building volcanoes and
the like, we were working on a math project dealing with odds and possibilities.
With youth, enthusiasm usually prevails and we had a great deal of fun putting the
project together. Our display backboard was an elaborate fold-out structure that stood
three or four feet tall above the table surface. I faintly recall that we used a black and
red color scheme. Huge letters were traced and cut out from colored paper; spelling out
our project title proudly across the backboard. Even the words themselves were complicated
for us and we were constantly checking the spelling. Below the title, we had all kinds of
room for our drawings, typed explanations on the odds involved with the topics we
selected, and the meaning of possibility and probability. The most difficult thing for the
two of us was to develop a list of topics that involved possibility and probability, and
then create visuals for them. We eventually came up with: coin tossing, getting heads or
tails; rolling dice; playing cards, getting a royal flush; and, a game involving different
sized disks and rearranging them in the least amount of moves on three spikes. Making the
stand with the spikes and the disks from wood was easy. Not only was it a good visual for
the table, but everyone wanted to try their hand at it. For the royal flush, we took
actual cards from a deck and glued them to a colorful backdrop. The dice were also easy to
place on the table. However, we were stumped as to how to display a coin toss in an
interesting way, but after some brainstorming we came up with what we thought was a
brilliant solution.
We decided to suspend a coin in the air, by using a thread, so that it would look as
though it was just tossed. On the table under the dangling coin, we would place a hand
that looked as if it was in the act of flipping the coin. For the hand, we would just go
to a department store and ask for a hand from a display mannequin. The plan was good, but
the actual execution turned out to be difficult. One Saturday, young Bruce and I hopped on
the downtown bus and went to most, if not all, of the major downtown department stores
along Portage Avenue. Large suburban shopping malls were not in vogue yet. On a weekend,
downtown was the place to be.
Not only was it difficult to find a mannequin hand that would look like it was in a
suitable position for tossing a coin, but it was near to impossible to get a major
department store to part with one. Picture it, two small kids explaining to a busy sales
person what their science fair project was about and that they literally wanted a hand. We
received many strange looks, pauses, slight smiles, all to be followed with a curt and a
polite: "Sorry, we cant do that". After we tried what seemed like a dozen
places, we found a small store that sold nurses uniforms which had a sympathetic and kind
lady who listened patiently to two small boys describe their plight. Without saying she
could help us, she went into a back-room and returned with the miracle we so desperately
needed. Not only was it a hand, but instead of being a rigid plaster one, this hand was
made of a special rubber that was life-like and all the fingers were flexible and
moveable. After what seemed was going to be a disastrous outing, we jumped back on the bus
and headed home clutching and admiring our newfound treasure.
After making a wooden stand that the hand could be attached to, we adjusted the fingers
and the thumb so that it looked as though it was flipping a coin into the air. With our
write-ups and displays complete, we were ready for our first Science Fair. To us, the
city-wide event took up a colossal amount of space to house all the science projects. The
event was held in a new and recently completed shopping center. Every type of science
project under the sun was on display. While there were many from elementary schools, the
most projects originated from the high school grades and these were the most impressive.
After getting our display set up, we wandered around for a good part of the day, examining
with awe and admiration the elaborate array of science projects ranging from: airplanes
and flight; to colorful complex models of chemical molecules; to astronomy and models of
the solar system; and, to biology displays with living plants and live animals.
The Science Fair spanned an entire weekend. One day was set aside for the judging and I
remember anxiously waiting for the team to arrive to our booth. The questions came from
directions that we were not totally prepared for, but I am sure our enthusiasm came
through. The next morning was filled with excitement as we literally ran the length of the
mall. We flew by other projects and occasionally caught a glimpse of one displaying its
colorful winning ribbon. We arrived at our table breathless, quickly scanned the display,
and were overjoyed to see that it had a ribbon for honorable mention. Well, this is the
way the saga ended.
What I find as an interesting coincidence, and without intentionally planning it in any
way, is that over 35 years later I am writing a chapter with a title that is identical to
that Science Fair project.
Robertson Elementary School is at the junction of Cathedral Avenue and Robertson
Street. I went there for three years, grades four to six, as part of a program called
Major Work. Without knowing the history behind it, Major Work may have been one of those
educational experiments that was phased-in and then phased-out. With a vague recollection,
I remember being summoned with my Mother to meet the grade three teacher and being told I
was selected to go into this program. Being relieved that I was not in some kind of
serious trouble; having no concept of what the program was really about; being only nine
years of age; and, answering "Sure, Ill go" was delivered far quicker than
it took to write this sentence.
Three years of taking a bus and three years with the same teacher was a different
experience. While this time-span might make the experience seem tedious or repetitious,
the exact opposite was true. The teacher was from England, complete with accent, and
provided us with some years of education that I would not trade for anything. I look back
on that teacher as being extremely gifted, full of new ideas, and offering different
learning experiences to his pupils. Our whole class was extremely impressed to find out
that he had written a small television series for broadcast into the schools. The subject
of the series was the human body. Each broadcast covered a different area such as the
skeletal system, respiratory, circulatory, and so on. He not only wrote the scripts, but
he hosted and narrated the entire series.
Not only did we take all the regular subjects that you would expect for the elementary
grades, but the years were supplemented by all types of other learning situations. While I
cannot recall them all, they included such things as: taking typing lessons; constructing
and painting huge scenery backdrops for a school play; holding mock civic elections; each
row in the class giving a mock radio broadcast with assigned roles of host, news, weather,
sports, and humorous commercial segments; and, a weekly project.
Once every week, all students were required to hand in their weekly project on a large
eleven by seventeen inch piece of art paper. These were then posted on the back wall of
the classroom by the teacher. The morning after they were posted, there was a rush of
students to find out what grade they received on the project. A score of 20 was a perfect
mark. The wall displaying the projects was an impressive site and everyone spent some time
studying the other projects. This was done not only to learn about the topic but to find
out what techniques were successful at receiving a good grade. Lettering stencil sets were
coveted and in vogue. Projects with one inch high titles and colored letters were the
rave. Changing the lettering style to exotic types came next. Hand typed description pages
invisibly taped in place would fair well. Diagrams and maps with everything neatly labeled
and in color would work. Neatness, style, and color seemed to be important to get the top
scores. If possible, students even attached real objects to the sheet. I remembered doing
one on acetylsalicylic acid, common household aspirin, and I attached an actual tablet to
the project paper.
Projects varied each week and the students might not have been allowed any choice on
their topic, other than presentation style. The fixed assignments may have been on
geography and a particular country or province we were studying. Then the project ended up
being a map with text. We had to create proper map legends, label all major cities or
geographic features, and of course use plenty of color. As your memories probably include,
a huge set of color pencils and expert techniques in color shading of large areas came in
handy. The following week the project may have been an area of science that we would have
to work on. The type I liked the most was when we had a free choice to do any subject
matter we wished.
For one free choice, I remember a near obsession with a particular topic. I had an idea
for a real object that I was determined to include with the project. My topic was X rays,
but I wanted to display a real X ray of a persons head showing a detailed view of
the skull. Since my Mother was a nurse, I assumed, quite naïvely, that she could bring
anything back from the hospital. Being persistent, I hounded her week after week for a
head X ray: any old head would do. Unfortunately, I was not able to get the X ray which
was so passionately desired. At this young age, I could not understand the concept of this
being an important patient record. Hospitals and doctors were just not routinely issuing X
rays to be taken home.
It was also surprising to see the amount of effort put in by my classmates, and myself,
on these weekly projects. Yet, I do not recall there being an inordinate amount of
competition or that the assignments were being viewed as a real chore. Instead, it seemed
to become a fun, challenging, and creative thing to undertake.
These were three pretty good years of learning, fun and friendship. Also, this was a
time period when certain world events or major trends became permanently associated with
my memories; just as I am sure exist for you. For my generation, this is when the music
group the Beatles became the biggest sensation and changed all the boys clothing styles to
beatle boots and turtle neck sweaters. It was also a sad time in world events,
when a teacher came in to advise us that President Kennedy had just been assassinated. For
those of us that used the bus and did not go home for lunch, this was announced to us in
our classroom during the noon lunch.
For my next encounter with the words possibility and probability, and to
progress towards the point, I have to fast forward to a grade 11 chemistry class. However,
as to why we would be discussing the meaning of such terminology in a chemistry class, I
cannot clearly remember.
The chemistry teacher was describing to us topics such as the density of matter,
molecules, their random vibrating motions, and the differences between, gases, liquids and
solids. Everyone who has had some exposure to science will likely have heard similar types
of descriptions, but just in case, I will go through them in as simple a manner as
possible.
The teacher started out by describing a concept called absolute zero. It was explained
to the class that this is only a theoretical temperature and that it cannot actually be
reached. All molecules and atoms vibrate due to heat energy and have some degree of
motion. The theory he described was that at the coldest temperature possible, absolute
zero, all motion would cease because there would be no heat energy at all. Hence the name
absolute refers to the absolute absence of heat. For quantitative purposes, absolute zero
has the following temperature. Using the different temperature scales, it is expressed as:
minus 459.69 degrees Fahrenheit; minus 273.16 degrees Celsius; or, zero degrees on the
Kelvin scale. A temperature of minus 459 F is pretty darn cold and while we joke about how
cold it gets in Winnipeg in the wintertime, this is not even in the same ball park.
Scientists have gotten extremely close to achieving the temperature of absolute zero using
highly specialized means, but have not achieved the theoretical value. The whole field of
studying low temperatures is called Cryogenics. We are aware of this term from the film
documentaries or the science fiction movies that employ cryogenics to imaginative ends.
After delivering the explanation of absolute zero being the total and absolute lack of
heat, combined with the total lack of molecular motion, the teacher went on to explain
what happens when you add heat. The way he explained it was that as you add heat to the
molecules, or atoms if it is a pure element, they become more energetic. All molecules
that make up any matter are vibrating in place and have spaces between them. It was
something we just had to picture and the teacher did not quantify the amount of vibration,
motion, or the amount of space involved.
As an aside, if you have a microwave oven, it works on the principle of increasing the
vibration of molecules. Water molecules in food substances are vibrated by the microwave
energy that is radiated into the cooking chamber. The microwaves increase the rate of
vibration of the water molecules and thereby their heat energy. Being an engineer, and
having studied microwave theory, I always show respect for a microwave oven and express
this concern to my children. While an oven may be in excellent condition with good door
seals, I am forever asking family members to always stand back to be safe. This is because
there sometimes is a tendency to stand right next to the machine while waiting for the
food to cook. Engineers know that radiated power drops off substantially based on a
mathematical function involving the distance. I also know that I have a pretty good
content of water in my head, and the rest of my body for that matter.
Returning to the chemistry class, the teacher went on to describe that the majority of
materials have both a melting and a boiling point, but there are always a few exceptions.
The state of any material, or matter as it is properly referred to, depends upon its
current temperature as to whether it is a solid, liquid, or a gas. Matter has varying
melting and boiling points. For example, we all know the familiar transition temperatures
of water. The freezing, or solidification point, for water is 0 degrees Celsius or 32
degrees Fahrenheit. The boiling, or vaporization point, for water is 100 degrees Celsius
or 212 degrees Fahrenheit.
As a class, we began to understand the concept of when matter is a solid. The molecules
are still vibrating and jiggling about, but they are somewhat locked into
place and do not have the same freedom of movement as in a liquid. When you add energy, or
heat, to the molecules, their vibration levels increase until the melting point is
reached. This is when a solid transitions, or melts, into a liquid. Now, the molecules in
the liquid are vibrating more, spaced further apart, and are no longer strongly bound or
locked in a solid form. If you add even more heat energy to the molecules, the liquid will
reach its boiling point. At that temperature point, the matter goes from the liquid phase
to a gaseous, or vapor phase. It is at this phase that the molecules are highly energetic
in their vibrations, have the highest degree of spacing between each other, and the most
amount of random motion. Gases are as loosely bound as it gets, so to say. All the spacing
between molecules relates to a term for matter referred to as density. Gases are the least
dense, liquids denser, and solids have the highest density.
This all made a lot of sense to the class, was readily accepted, and became a good
model on which to base our understanding.
We know that air is actually a mixture of gases such as oxygen, carbon dioxide,
nitrogen and many others. How cold do you have to make these gases in order to turn them
into liquids or solids? As one example, it is possible to make liquid oxygen (-297 deg.
F.) and even solid oxygen (-361 deg. F.). Just as the television program would state,
these are not temperatures you want to try and achieve at home. So, when we consider
important gases, like the air we breathe, we should appreciate the average temperatures
that we have on Earth. The same cannot be said for some of the outer planets where
incredibly low temperatures do exist.
What does all of this have to do with possibility and probability? Be patient, we are
getting there. While I have added some details to the above material, after the chemistry
teacher finished explaining the vibration and random motion of air molecules, he abruptly
switched topics. He asked the class if we knew what was the difference between possibility
and probability. The class was mildly stunned as this query seemed to come out of the blue
and no one understood what it had to do with chemistry. After a silent pause and no one
volunteering an answer, he commenced to go through an illustration that was intended to
help us learn and remember the difference.
Although it was a chemistry class, our actual classroom was not a specially equipped
lab or anything like that. I guess we were into the pure theory part of
chemistry and did not need any extraneous paraphernalia. The class was held in just a
regular square shaped room. The teacher went on to explain his illustration. He stated
that we now understood how air molecules were all highly energized, giggling and moving
about in a totally random manner. That is, they were bouncing off each other
and jostling around in what could be considered a totally random fashion and in random
directions. Millions and trillions of little motions are occurring all about us, but
because the molecules are spaced so far apart we can see right through the air and we
cannot observe any motion whatsoever with the human eye. We can affect the motions by
moving our hands through the air, and if vigorous enough, we can cause the air to move
strong enough so that we feel masses of molecules hitting our skin. This all made perfect
sense to us students. Next, we were asked to picture the entire classroom filled with air,
and with all these trillions of air molecules and atoms moving and jostling about in an
apparent total random fashion.
Then suddenly the teacher posed his question. With all seriousness, he solemnly asked
the class: "What are the odds or the possibility of the air molecules moving about,
and, just for an instant, migrating up into the top corner of the classroom, leaving the
rest of the room in a vacuum, and the entire class momentarily without any air to
breathe?".
There was a good long period of silence as the question seemed to both stun us and be
somewhat outlandish at the same time. How do you even start considering something like
this? How would you even begin to calculate any odds or possibilities? After the silence,
the debate began. Opinions were stated and clarifying questions were posed to the teacher.
Some students stated it was just impossible to occur and that there was absolutely no
possibility of this happening. The teacher kept probing and pushing us to consider it
further. He tried to make it more possible by expanding on the situation. He again asked
the question, but in a modified way: "You are alone in the room. You are strictly an
observer in the room and no movements you make will disturb the air or affect the outcome.
The room is totally sealed and totally undisturbed. Furthermore, you are allowed to
observe for a billion years, or more, if necessary. Will the air molecules in the room
with their apparent random motion, even for the tiniest fraction of a second, move into
any corner of the room leaving the rest of the room in a momentary vacuum?".
.....................(excerpt only - continues)