Blaise
Pascal,
according
to contemporary
observers,
suffered
migraines
in his
youth,
deplorable
health
as an adult,
and lived
much of
his brief
life of
39 years
in pain.
Nevertheless,
he managed
to make
considerable
contributions
in his
fields
of interest,
mathematics
and physics,
aided by
keen curiosity
and penetrating
analytical
ability.
Probability
theory was
Pascal's
principal
and perhaps
most enduring
contribution
to mathematics,
the foundations
of probability
theory
established
in a long
exchange
of letters
between
Pascal
and fellow
French
mathematician
Fermat.
While games of chance long preceded both of them,
in the wake of probability theory the vagaries
of such games could be viewed through the lens of a
measurable percentage of certainty, which we have come
to refer to as the "odds".
Pascal
is pictured overlaid
by a Pascal's
triangle in
which the
numbers
have been
translated
to relative
color densities.
Pascal
created
his famous
triangle
as a ready
reckoner
for calculating
the "odds" governing
combinations.
Each
number
in a Pascal
triangle
is calculated
by adding
together
the two
adjacent
numbers
in the
wider adjacent
row. The
sum bf
the numbers
in any
row gives
the total
arrangement
of combinations
possible
within
that group.
The numbers
at the
end of
each row
give the
the "odds"
of the
least likely
combinations,
with each
succeeding
pair of
triangles
giving
the chances
of combinations
which are
increasingly
likely.
Though
apparently
simple
and relatively
simple
to generate,
Pascal's
triangle
holds within
itself
a complex
depth of
numerical
patterns,
applicable
to the
physical
world and
beyond,
and the
theory
of probabilities
has found
increasingly
wide application
in modern
mathematics
and sciences,
extending
well beyond
seemingly
simple
games of
chance.
Pascal
also did
seminal
work in
the field
of binomial
coefficients
which in
some senses
paved the
way for Newton's
discovery
of the
general
binomial
theorem
for fractional
and negative
powers.
Pascal
is also
considered
the father
of the
"digital"
calculator.
In 1642,
at the
age of
19, Pascal
had invented
the first
digital
calculator,
the "Pascaline".
Mechanical
calculators
based
on a logarithmic
principle
had already
been
constructed
years
previously
by the
mathematician
Shickard,
who had
built
machines
to calculate
astronomical
dates,
Hebrew
grammar,
and to
assist
Kepler
with
astronomical
calculations.
Pascal's device,
capable
of adding
two decimal
numbers,
was based
on a
design
described
in Greek
antiquity
by Hero
of Alexandria.
It employed
the principle
of a
one
tooth gear
engaging
a
tentooth
gear once
every
time it
revolved.
Thus,
it took
ten revolutions
of the
first gear
in order
to make
next
gear
rotate
once. The
train of
gears produced
mechanically
an answer
equivalent
to that
obtained
using manual arithmetic.
Pascal's
mechanical
calculating
device
offered
significant
improvement
over manual
calculations,
Unfortunately,
Pascal's
invention
served
primarily
as an early
lesson
in the
vagaries
of business,
and the
problems
of new
technology.
Pascal
himself
was the
only
one who
could repair
the device,
and the
cost of
the machine
cost exceeded
the cost
of the
people
it replaced.
The
people
themselves
objected
to the
very
idea of
the machine,
fearing
loss
of their
skilled
jobs.
Pascal
worked
on the
"Pascaline"
digital
calculator
for three
years 
from 1642
to 1645
 and
produced
approximately
50 machines,
before
giving
up.
The
world
would
have
to wait
another
300 years
for the
electronic
computer.
The principle
used in
Pascal's
calculator
was eventually
used in
analog
water meters
and odometers.
