Buddhism and mathematics
two paths to our sacred number
maverick mathematician / vajrayana Buddhist
I see all of mathematics
as marvelous manifestation of emptiness
Mathematical objects lack
independence through three dependencies
on conventional designation
on parts and internal structure
on being parts of greater wholes
In that sense they are empty
empty of independent existence
Consider the sacred number 108
practice-etched in my psyche
Inspired by Chögyam Trungpa Rinpoche
meek perky outrageous inscrutable
crazy wisdom Tibetan yogi
with 108 bead mala I counted
seemingly infinite sequences
prostrations and refuge vows
purifications
generosities
openings
Echoes of practice now
energize contemplation of CVIII
its emptiness
its power
For our sacred number goes by many names
many conventional designations
one hundred eight
gya gye
CVIII
hundert acht
108
cientos ocho
1101100
cent huit
and countless more
Does 108 exist independent
of all naming and calculation?
It’s a matter of opinion
Perhaps you agree with Martin Gardner
and most mathematicians that
when two dinosaurs met two dinosaurs
there were four dinosaurs
(even though there was nobody there to count
(unless dinosaurs could count))
I algorist maverick agree only that
when two imagined dinosaurs
meet two more of same
I’ve got four dinosaurs on my mind
To paraphrase Nagarjuna
There is no mathematics without mathematicians
There are no mathematicians without mathematics
But malas have 108 beads
each journey of mind and fingers
summons 108 to life in a sacred setting
108 is a number
infinitely created
infinitely blessed
by fingers and minds
A mindful trip from 1 to 108
never skips 37
so 108 depends on 37
has no existence that is separate from 37
37 is a part of 108 that can be taken away
108 – 37 = 71
108 depends on 37 and all its parts
Count beyond 108 to larger wholes
108 becomes a part within
109
a billion
the host of whole numbers
These three dependencies
establish the emptiness of 108
and of all whole numbers
What distinguishes 108?
Going back 2300 years to Euclid’s Elements
every positive whole number
carries a unique structure
as a product of primes
(indecomposable numbers)
Now 108 uses only the first two primes
Holding to the symmetry
base = exponent
creates a larger pattern
the Sacred Explosion
derived from our sacred number
growing super-exponentially
Start with no primes
1
multiply by the prime 2 raised to power 2
then multiply by the prime 3 raised to power 3
multiply by the prime 5 to the 5th
by 7 to the 7th
by 11 to the 11th
This sixth term of the Sacred Explosion has 23 digits
Multiplying by
1313 yields the seventh term with 38 digits
by 1717 gives the eighth term with 59 digits
and so it explodes
Another look at the start of the Sacred Explosion
1 is unique
4 is cozy
108 is human
337,500 is personal finance
277,945,762,500 is global finance
79,301,169,838,123,235,887,500 is super-astronomical
a 38 digit number is getting transcendent
a 59 digit number has achieved a higher realm
108 is the human anchor of the Sacred Explosion
putting us up close and personal
with the vastness of numbers
the vastness of time and space
in which our numbers count and measure
Our courtesy-of-Python
window on numerical vastness
would cause Euclid to faint with surprise
Though he knew widely and understood deeply
geometry was aristocratic and sacred
while arithmetic was for shopkeepers
even Euclid could barely calculate
with the Greek number system
precursor to Roman numerals
which lacked zero and
computational algorithms
We experience the sacred number 108
through our practice
through its name
through its structure
through its place in greater realms
Our story of 108 concludes with a story
that starts with Euclid’s impotence
and ends with our power
Tragedy or triumph
with what mix of joy and sorrow
do we bow to the power of computation
that places 108 in the Sacred Explosion
that can reduce life to number?
Emptiness-inspired Indian mathematicians
recognized zero as genuine number
sunya in Sanskrit
cipher in Arabic
cero in Spanish
zero in French Italian Portuguese
created the system of numerals
we use to write “108”
developed algorithms for
addition
subtraction
multiplication
division
Hail Brahmagupta
astronomer and mathematician
first to fully understood
positive
zero
negative
His seventh century text
The Doctrine of Brahma
translated into Arabic a century later
brought the joy of calculation to Baghdad
We bow to Brahmagupta
and to those on whose shoulders he stood
The mathematicians of
the Baghdad House of Wisdom
improved and transmitted the art
of calculating with “Hindu” numerals
Hail al-Khwārizmī
mathematician-astronomer-geographer
whose ninth century text on arithmetic
survives only in Latin translation
made two centuries later in England
from whose name we derive
“algorithm”
“algorism”
“algorist”
We bow to Muḥammad ibn Mūsā al-Khwārizmī
and to those on whose shoulders he stood
After Al-Khwarizmi appeared in Latin
a divide slowly formed across Europe
between algorists
who used his methods with Arabic numerals
to add subtract multiply divide
and abacists
who used Roman numerals
and employed devices with beads on wires
Enter Leonardo Bonacci “son of Bonacci”
Hail Fibonacci
widely traveled merchant of Pisa
shopkeeper and mathematician
first algorist known to history
whose 1202 text Liber Abaci
The Book of Computation
demonstrated the advantages of the
Hindu-Arabic system
in an array of “real life” problems
often involving money
showing the power of computation
to provide answers
to life’s persistent questions
remembered for a problem about rabbits breeding
the exponential population explosion
of the Fibonacci Sequence
with much tamer growth than
the Sacred Explosion
whose 8th term has 59 digits
while one has to go almost 300 terms
into the Fibonacci sequence
before attaining that magnitude
and to those on whose shoulders he stood
Centuries after mathematicians and bankers
realized the advantages of Hindu-Arabic numerals
Roman numerals remained in use
108 was a notational device used to compute
CVIII was the real thing
but money talks and now
108 is the real number
while Roman numerals are used to give gravitas
to cornerstones and Super Bowls
We are reminded that in Europe
mathematics developed
in the service of money and war
while in Japan
Temple Geometry was cultivated for
intellectual artistic spiritual
pleasure and growth
Hail the sacred number 108
made holy and powerful by practice
made beautiful by symmetry
May its influence spread to
pacify enrich magnetize
and when appropriate, destroy
all uses of number
We bow to 108
~~~~~~~~~~~~~~~~~~
Newcomb Greenleaf
1:00 am
Saturday October 31, 2015
Saint Johnsbury, VT
