If I have seen further, it is by standing upon the shoulders of
Sir Isaac Newton
Many ideas grow better when transplanted into another mind than
in the one where they sprang up.
Oliver Wendell Holmes
Learn from the mistakes of others - you can't live long enough to
make them all yourself.
What's a tangent?
Mathematically, a tangent is an angle's sine divided by its cosine. A
graph of the tangent function starts at 0, increases to infinity, drops
instantly to negative infinity, increases until it returns to 0, then starts
all over again. A straight line touching the rim of a circle at only one point
is also a tangent. All four sides of the blue squares in Professor Tangent's
logo are tangents to the inner green circle, a pictorial representation of the
professor's occasional tendency to "go off on a tangent". A "tan
gent" is also what the cultured professor becomes after a few days of
lounging on the beach.
The tangent function
As the angle (represented by the X axis) approaches 90°,
the value represented by the Y axis approaches infinity. This is called an
asymptote. Just past 90°, there is another asymptote in the negative
direction. What happens at exactly 90°? Like the concept of infinity, it's
not defined precisely. We can only really know what happens as we get close -
and we can get very close. It's kind of like filling pages with 9s - the number
keeps getting bigger (and closer to infinity), but no amount of paper is
sufficient to actually reach infinity. Learning is a similar process. You can
keep gaining expert knowledge (and getting closer to knowing everything that
might be known), but you'll never know everything (and can never be certain
that there's nothing left to learn). Okum prefers the short version: "You
don't know what you don't know."
A close friend of the professor, Okum Taylor lacks a rigorous academic
background, but the professor respects Okum's abundant common sense, practical
analysis and ability to simplify seemingly complex issues.
Who thinks up all this stuff?
Many people. Some of these ideas may be thousands of years old and are
probably unattributable. Beyond that, why be concerned? If anything here isn't reasonable, convince us and we'll change it.
If it is
legitimate, crediting a particular individual won't
make it any truer, and could diminish the contributions of others who may be
unknown. Think of it as stone soup
for the soul.
How we attribute quotes
Attributing quotes can be particularly troublesome and unreliable.
Usually, there's no practical way to trace the ultimate source, or to know what
the exact words really were. The professor selects quotes that are interesting,
important, or clever on their own. If nothing else, an attribution means that
we wish we could take the credit, but someone else thought of it first.
An old story with many variations
A wanderer came upon a small village, seeking shelter for the night.
The villagers were very poor and suggested he keep moving because there was no food to spare. The wanderer wasn't
the least bit concerned, and offered to make stone soup for everyone. As the villagers gathered, he built a fire
and filled his huge pot with water. Everyone watched in amazement as he took a velvet bag from his pocket, removed
a well-polished stone and ceremoniously dropped it into the boiling water. The stranger explained that the soup
would be a bit thin as the stone was getting so old, but a few potatoes would give the soup more body. As one
villager eagerly produced the potatoes, the wanderer mentioned that the king often eats stone soup with a bit of
meat added. Another villager rushed home for some dried beef, anxious to taste this soup fit for a king. As the
pot boiled, and the wanderer continued explaining ways to make the soup even better, the pot was soon filled with
carrots, onions, cabbage, corn, mushrooms, herbs and spices. Years later, the villagers still spoke of the wondrous
stone that made such delicious soup.