part four: the world’s most important arithmetic what every citizen should know about our planet
TRANSCRIPT
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Part Four:
The World’s Most Important Arithmetic
What Every Citizen Should
Know About Our Planet
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Copyright Randolph Femmer, 1999.All rights reserved.
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that we literally interpret the world using this
Unfortunately, we are so thoroughly
trained in this type of mathematics
In virtually all our public schooling we are taught a mathematics
that applies to our daily lives.
Grocery-Store Arithmetic
GROCERY-STORE ARITHMETIC
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the world’s most important arithmetic
Dr. Albert Bartlett of the University of Coloradohas called exponential mathematics
There is a more powerful kind of mathematics
called ‘ exponential mathematics. ‘
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� explosions� nuclear detonations� monetary inflation� runaway growth of cancer cells and
� compounding interest rates
Exponential mathematics describes :
ApplicationsApplications
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� the pH scale in chemistry� the Richter earthquake scale in geology� nuclear decay rates in radioactive atoms� rates of resource consumption� human population growth
and � dinoflagellate red-tides in the sea.
Exponential mathematics also applies to:
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Unfortunately, the same mathematics thatdescribes a nuclear detonation also
describeshuman population growth.
GrowthGrowth
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A graph of the fission events inside
a nuclear detonation
has a shape which isnearly identical
to a graph of human population growth
over the past 10,000 years.
Is This Important?
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Exponential mathematics is extremely
For example:
Exponential fission events inside an atomic bomb
destroyed the city of Hiroshima, Japan at the end
of World War II...
and runaway monetary inflation can destroy an
economic system...or topple a government.
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Might exponential mathematicshave planet-wide impacts?
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Exponential number sequences
help usbetter understand human impacts on the natural world
in the decades ahead.
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Fortunately, understanding the behavior of exponential number sequences can be achieved easily.
Two or three riddles will be our key.
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� Example: 3...6...9...12...15...18...21...etc.� Example: 5...10...15...20...25...30...35...etc.
Arithmetic number sequences grow larger by repeated additions of like amounts.
Grocery-Store Arithmetic
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� Example: 3...6...9...12...15...18...21...etc.� Example: 5...10...15...20...25...30...35...etc.
Arithmetic number sequences grow larger by repeated additions of like amounts.
Grocery-Store Arithmetic
Push Here
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Now:
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By repeated additions of$1000 per day.
You will only receive the salary for 30 days.
2005Suppose you are offered
a salary that grows LARGER arithmetically.
An Riddle An Riddle
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Like this
What will be your total earnings for days 1 - 7?
Answer:
Day one: $1,000
Day two: $2,000
Day three: $3,000
Day four: $4,000
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An SalaryAn Salary
Day one: $1,000
Day two: $2,000
Day three: $3,000
Day four: $4,000
How much will you earn on day 30?
Answer:
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An SalaryAn Salary
How much will you earn on day 30?
Answer: Push Here
Day one: $1,000
Day two: $2,000
Day three: $3,000
Day four: $4,000
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What We Are Used To
How much will you earn during the 30 days of your employ?
Answer:
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What We Are Used To
We use them almost every day.
Numbers in an arithmetic number sequenceare easy to understand.
We are usedto them.
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using a salary that grows
The same riddleagain
Now:
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Exponential number sequences grow by repeated multiplications by like amounts.
Example: 1...10...100...1000...10,000...etc.
Example: 1...2...4...8...16...32...64...etc.( Notice we multiplied by two each time.)
( Notice we multiplied by ten each time.)
An Salary An Salary
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00
An SalaryAn Salary
Push Here
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but your salary grows exponentially…by doubling each day.
Imagine that you are offered a starting salary of one cent per day.
Assume your employ lasts only 30 days....
2005
An SalaryAn Salary
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Initial Numbers Are Deceptively Small
Day one: 1 centDay two: 2 centsDay three: 4 centsDay four: 8 cents
How much will you earn on day seven?
Answer:
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Initial Numbers Are Deceptively Small
Day one: 1 centDay two: 2 centsDay three: 4 centsDay four: 8 cents
What will be your total earnings for the first week?
Answer:
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The Second Week
Answer:
How much will you earn on day ten?
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The Second Week
Answer:
What will be your total earnings after two full weeks ...(days 1 - 14)….?
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Click Here
This exponential salary begins with exceptionally-small numbers.
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Deceptive and MisleadingDeceptive and Misleading
The growth of the numbers using “grocery-store” arithmetic was large -- and straight-forward -- right from the outset.
The exponential salary, however, begins with numbers that are so small that they seem harmless or unimportant.
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Suddenly Larger
What is your salary for day 16?
Answer:
Notice the numbers are now somewhat larger.
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Suddenly
Answer:
Notice the sudden increaseafter three weeks.
How much are you paid for your work on day 21?
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Disaster occurs in week four.
What is your pay for day 28?
Disaster In Week Four
Answer:
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How much do you earnon day 30?
Disaster In Week Four
Answer:
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and that salary grows exponentially by doubling each
day for thirty days....
If you are given a salary of one cent per day....
what is your total salary for the month?
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What Is Your Month’s Total?
Answer:
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One cent, growing exponentially (by doubling each day for 30 days) will result in
in one month.
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Only a lucky few will ever earn a salary that grows by $1,000 per day.
...Never......Never...
(Most employers would never accept such a salary arrangement.)
An Salary? An Salary?
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It at least seems possible that someone’s busy and distracted boss
-- somewhere
An Salary?
mightagree to an exponential salary
Why?
...MaybeMaybe...
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Because exponential growth isBecause exponential growth isnot only powerful, it is alsonot only powerful, it is also
and
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The initial numbers in an exponentialnumber sequence are so small that they
harmlessor
unimportant.
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Push Here
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first grow slowly
then suddenly explode into
enormous values.
Numbers that are extremely small at the outset...
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The devastating effects of numbers that grow exponentiallyexponentially occur LATELATE in the sequence.
By the time danger becomes apparent, it can be
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like the detonation of the Hiroshima bomb.
like thesecond salary...
Human population growth over the
past 10,000 years has been
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Like The Hiroshima Bomb
Push Here
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A Linear GraphA Linear Graph
Arithmetic number sequences producegraphs which are straight lines...
( “linear” ).
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The ‘ J-Curve: ’An Exponential Graph
number sequences producegraphs called
J-curves
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19991999
18001800
16501650
190019001 1 A.DA.D..
Year
In Billions
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Year
In Billions
Click Here
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A Mathematical Fire-AlarmA Mathematical Fire-Alarm
A J-curve is the mathematical equivalent of a fire-alarm going
off in a burning building.
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It warns usof
potentially-devastating
effects
no matter how small the
numbers may seem at first.
A Mathematical Fire-AlarmA Mathematical Fire-Alarm
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Click Here: 1
Click Here: 2
A Mathematical Fire-AlarmA Mathematical Fire-Alarm
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A Million vs. a Billion Arithmetic number sequences:
repeated additions Exponential number sequences:
repeated multiplications Powerful, misleading, and deceptive Linear graphs vs. J-curves A mathematical “fire alarm”
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wishes to thank and acknowledge
Randolph Femmer
who authored and developed this presentation