Brian Kernighan_ Millions, Billions,

8/7/2019 Brian Kernighan_ Millions, Billions,

1/45

Millions, Billions, Zillions (In)numeracy StillMatters

Brian W KernighanDepartment of Computer Science

Princeton University


2/45

"The Birk Economic Recovery Plan" (9/08)

Im against the $85,000,000,000.00 bailout of AIG.

Instead, Im in favor of giving $85,000,000,000 toAmerica in a We Deserve it Dividend.

To make the math simple, lets assume there are

200,000,000 bona fideU.S. Citizens 18+.

Our population is about 301,000,000 +/- counting everyman, woman and child. So 200,000,000 might be a fair

stab at adults 18 and up.

So divide 200 million adults 18+ into $85 billon that equals$425,000.00.


3/45

Popular support from the blogosphere...

Ordinary citizens with great common sense sometimemake our lawmakers and economists look like they are

still in first grade . Heres a great example! I REALLY like this plan!

Interesting idea. Of course, the politicians wouldnever do anything this logical.

THE PERFECT SOLUTION. Sounds reasonable, don'tyou think?

i'd vote for that puppy tomorrow!

DUH! Seems like a no brainer to me! Here's a GREAT IDEA!! I don't know who this Birk

fella is but I would vote for him for president.


4/45

Skepticism from the blogosphere...

The real reason this wouldnt work is simply due tothe math. 85 bil devided by 200 mil equals 4250.

Whoever wrote this plan needs to buy a calculatoritis not anywhere near $42,500 per person42,500 peradult for 200 million people would be 8.5 Trilliondollars.

85 bil divided by 300 mil is $425.00. Not $4250 asclaimed by you or $42,500 as originally written byBirk.

Uh, do the math. Its only $425.00. You may resumesmoking whatever it is youre smoking.


5/45

"You do the math"

I wanted to see how many people really do dothe math

. So I sent the message below to 100of my pals at random. I wanted to see howmany folks would catch my intentional three-digit error...just three little zeros. So far only2 people have actually done the math and letme know about it. [...]

So what's my point? We are all number numb.And, very few people, even really smart folksrarely do the math.


6/45

Millions, billions, trillions (bailouts)

An article [... about ...] the proposed bailout offinancial firms misstated the estimated cost ofthe package. It is $700 billion, not million.

(New York Times, 9/25/08)

The article also misstated the dollar amount ofcommercial mortgages that are due to expire bythe end of next year and the total that had been

due to expire this year but were extended. Theamounts are $393 billion (not million) and $39billion (not million), respectively.



7/45

Millions, billions, trillions (deficits)

The U.S. budget deficit is projected to total$1.2 trillion this year. [some editions]

incorrectly put the figure at $1.2 billion.(Wall Street Journal, 1/13/09)

Total credit limits are now $3.4 trillion, notbillion, which is a reduction from $4.6

trillion, not billion, a year ago.(New York Times, 11/11/09)


8/45

"... the [Strategic Petroleum] Reserve has acapacity of 727 million gallons barrels.


"Our country burns twenty-one (21) million

gallons barrels of oil every day."

Senator Frank Lautenberg (D, NJ), 4/26/08

"The use of motor fuel in the United States

could grow to 170 billion gallons a day year in

10 years."(Newark Star Ledger, 2/11/07)

Wrong units (1)


9/45

Wrong units (2)

" the size of the coal ash spill in Roane County,Tenn. ... was 1 billion gallons, not 1 billion tons.

(New York Times,12/21/09)


10/45

Kilo, mega, giga, tera, peta, ...

[A petaflop] can be expressed as a thousandtrillion instructions per second, not a million

trillion. (New York Times, 3/25/08)

"6.5 Tbps (terabits per second) is almost amillion times faster than a 56 Kbps modem."

(Om Malik, Broadbandits, 2003)

"almost"? 6 x 1012 / 6 x 104 ~ 108

"more than 100 million times faster"


11/45

..., exa, zetta, yotta, ...

The Nook e-book reader has 2 GB of memory, enoughto hold about 1,500 digital books.

(Wall Street Journal 12/9/09)

A zettabyte (1021 bytes) is equivalent to 100 billioncopies of all the books in the Library of Congress.

(New York Times 12/10/09)

WSJ: a book is about 2x109 / 1.5x103 ~ 106 bytes/book

NYT: 1021

bytes / 100x109

copies = 1010

bytes1010 bytes / 106 bytes/book = 104 books

So the Library of Congress has about 10,000 books.


12/45

Invented units

[The article] misstated the amount ofclenbuterol in the horse's system. It was 41

picograms, not "petragrams." A picogram isone-trillionth of a gram; there is no petragram.


"[Google stores] two dozen or so tetabits(about twenty-four quadrillion bits)".

(Ken Auletta, Googled: The End of the World as We Know It, 2009)


13/45

Quantitative triage: is this value...much too high, much too low, or plausible?

"Each person eats about sixty tons offood in a lifetime."

(Carl Zimmer, Microcosm, 2008)

60 tons/lifetime ~ 1 ton / year

~ 2000 lb / 365 days~ 5 pounds / day


14/45

Much too high, much too low, or plausible?

Princeton students throw out 600 to 700

tons of excess food each year.(Daily Princetonian, 4/16/09)

5000 students throw out 500+ tons

each student throws out 500/5000

= 1/10 ton = 200 pounds/yearstudents are on campus ~ 200 days/year

each student throws out 1 pound of food/day


15/45


After Europe first mandated recyclingelectronics like televisions and computers,

two to three tons of electronic waste wasturned in last year, far less than the seventons anticipated.


Two million to three million tons was turned

in not two or three tons and sevenmillion tons had been anticipated, not seventons.



16/45

Plausibility and common sense

does the number make sense?

does it agree with your experience,or run counter to it?

what would be the implicationsif the number were accurate?


17/45

Much too big, much too small, or plausible?

"Shutting down your computer and

monitor overnight rather than runningthem 24 hours a day will save $88 aday."

(Newark Star Ledger, 12/08)


18/45

Faster than a speeding bullet

"A Boeing 747 is a vehicle, a man-made objectcapable of hurtling down a runway at speeds

well over 2,000 miles an hour and lifting offinto the air."(Manchester Guardian, 9/11/93)


19/45

How much does the cannon weigh?

Estimates have ranged from 50 lb to 112000 lb


20/45

Crowd-sourcingCannon

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Series1


21/45

Know some basic facts and conversions

6.7 billion people (300+ million Americans, 9 million in NJ)

1 gallon of water weighs ~ 8 lb 1 cubic foot of water weighs ~ 62 lb (rock 200, steel 500)

1 liter is just over 1 quart 1 kilogram is ~ 2.2 lb

1 ton is 2000 lb (a metric ton is 1000 kg ~ 2200 lb) 1 meter is a little over 3 feet or 1 yard

MP3 music is about 1 MB/minute

electricity costs about 18 cents/kwh 100K seconds in a day 31M seconds in a year

...


22/45


"...a truck packed with 1,000 tonsof explosive detonated at the gate.

Fortunately, it was too early foranyone to be in our office. It [in theHamra Hotel in Baghdad] was demolished.

(Wall Street Journal, 2/18/06)


23/45

Fermi problems

Estimation problems "designed toteach dimensional analysis,

approximation, and the importanceof clearly identifying one'sassumptions [...] making justifiedguesses about quantities that seem

impossible to compute given limitedavailable information." (Wikipedia)

"How many piano tuners are there in Chicago?"

Enrico Fermi, 1901-1954


24/45

How many leaves do I have to rake?


25/45

More crowd-sourcing

Leaves

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49


26/45

http://www.businessinsider.com/15-google-interview-questions-that-will-make-you-feel-stupid-2009-11


27/45

How many petabytes could you fit in this room?


28/45

Dimensional analysis

"The victims all lived in the same small areaof 260 square yards.

(Alias Jack the Ripper, R M Gordon, 2000)

"[the room] is 30 feet square -- meaning 30

feet by 30 feet -- and not 30 square feet,which would be far less." (New York Times, 5/4/09)

"The size of Rockaway Borough is 2.1 squaremiles, not 2.1 square feet." (Star Ledger, 8/26/06)


29/45


"25 years ago, half of all 18 to 24 year-olds voted. Today it's 25%.

18 to 24 year-olds represent 33% of thepopulation but only account for 7% of the

voters."(The West Wing, Episode 4.03, 10/2/02)

ages 18-24 is 7 yearsif lifetime is 70 years,18-24 represents 10%, not 33%


30/45

Little's Law

number in process

= arrival rate x service time

300 million Americans (number in process)

if each lives to 75 (service time) 4 million die each year (departure rate)

4 million reach any given milestone each year

10,000+ reach any milestone each day


31/45


According to the American Cancer Society,nearly 221,000 new cases of prostate

cancerone out of every six menwill bediagnosed in the U.S. in 2003. An estimated28,900 men will die from the disease.

http://www.endocare.com/pressroom/pc_treatment.php

"One man in 6 will get prostate cancer duringhis lifetime. And one man in 35 will die ofthis disease."

American Cancer Society, http://www.cancer.org/


32/45

Consistency checking


33/45

Do the numbers add up?

1-DEMHillary Clinton 14Barack Obama 7Bill Richardson 0John Edwards 0Dennis Kucinich 0Joe Biden 0

...

1-REPJohn McCain 5

Ron Paul 2Rudy Giuliani 0Mike Huckabee 0Mitt Romney 2

Fred Thompson 0

1-DEM 20

...

1-REP 9

Total 29

14 + 7 = 20 ???


34/45

Do the numbers add up? (2)

33+2+49 = 83 ???


35/45

Well, maybe...


36/45

Specious precision? Sample bias? Both?

"According to AARP magazine, some 48.7

percent of people age 55 and over whowere surveyed said they like to participatein surveys."



37/45

"When a yacht is over 328 feet, it'sso big that you lose the intimacy."

(editor, The Yacht Report, 3/08)


38/45

"You know what they say, son --

28.35 grams of prevention is worth.45 kilograms of cure..."


39/45

Be suspicious of too much precision


40/45

Who says so? How do they know?

Why do they care? What are they selling?from Privacy Rights Clearinghouse:

TOTAL number of records containing sensitive personal

information involved in security breaches in the U.S.since January 2005: 344,680,708


41/45

How do they know?


42/45

Why do they care? What are they selling?

"The number of American childrenkilled by guns has doubled every year

since 1950."

Nancy Day, Violence in Schools: Learning in Fear(1996)


43/45

Defenses

recognize the enemy flaky numbers / excessive precision arithmetic errors/ wrong units / wrong dimensions bad statistics / deceptive presentation / suspect motives

beware of the source how do they know? how could they know?

what are they trying to sell you? learn some useful numbers, facts, shortcuts

populations, rates, sizes, areas, etc.

approximate arithmetic, Little's Law, Rule of 72, ... use your common sense and experience much too big? much too small? does it makes sense? what would it imply?


44/45

Good reading

Daryl Huff, How to Lie with Statistics

Joel Best, Damned Lies and StatisticsMore Damned Lies and Statistics

John Allen Paulos, InnumeracyA Mathematician Reads the Newspaper

Web sitesinnumeracy.com

megapenny.com

math.temple.edu/~paulos/


45/45

Documents

Brian Kernighan_ Millions, Billions,