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Precision, Accuracy, Validity, and Reliability

Recall from research methods that there measurements have these four characteristics. A measurement can be more or less precise - how fine a resolution or how many decimal places? A measurement can be accurate (read "near the true value") or inaccurate (aka "wrong"). A measurement can be valid - it measures what we say it measures - or not. And a measurement can be reliable - if you measure again using the same instrument you will get more or less the same result.

The Elements of Rough Calculations

Numbers to Know

Basic numbers we should know (in their most basic form)

Ten basic numbers a person in policy should have an intuitive feel for

WorldAbout 7 billion and U.S.About 310 million1 population; US legislature435 congress + 100 senators and California legislatureAssembly 80, Senate 402; number of California counties58; US GDP$13 trillion (thousand billion)3; diameter of earth8,000 miles; median household income in the US$50,0004

Basic sizes. Width of a finger or hand. Ceilings. Doors. Tables. Width of a car.


Orders of magnitude

Communicating Relative Magnitudes

Getting a feel for magnitudes

How to approximate a number. Eschew meaningless precision.
Order of magnitude
Scientific notation
Call it something you can remember

If the universe were a baseball diamond type analogies.

Dimensional analysis
Rule of thumb
Sanity test

How to carry worst/best case values through a calculation


How many movies have you seen? How many bananas have your peeled in your lifetime?
How many hours did you spend on facebook last year?
How many golf balls will fit in this room?
About how much area would we need for a 250 car parking lot?

If the world energy consumption is about 5 x 1020 joules5 and US is about 1 x 1020 joules6, then what is the ratio of US per capita usage to that of the world as a whole?

\begin{align} USPC = \frac{1 \times 10^{20} joules} {3 \times 10^8 people} \end{align}
\begin{align} WPC = \frac{5 \times 10^{20} joules} {7 \times 10^9 people} \end{align}
\begin{align} \frac{USPC} {WPC} = \frac{\frac{1 \times 10^{20}} {3 \times 10^8}} {\frac{5 \times 10^{20}} {7 \times 10^9}} \end{align}
\begin{align} \frac{USPC} {WPC} = \frac{\frac{1 \times 10^{12}} {3}} {\frac{5 \times 10^{11}} {7}} \end{align}
\begin{align} \frac{USPC} {WPC} = \frac{1 \times 10^{12}} {3} \times {\frac{7} {5 \times 10^{11}}} \end{align}
\begin{align} \frac{USPC} {WPC} = \frac{10} {3} \times {\frac{7} {5} = \frac{70} {15}} = \frac{14} {3} \simeq 5 \end{align}

Announce rather than discard inconvenient uncertainty7


Mitchell N Charity <ude.tim.scl|ytirahcm#ude.tim.scl|ytirahcm> A View from the Back of the Envelope
Wikipedia. "Back of the envelope calculation"
Louisiana Lessons. 1996. Classic Fermi Questions with annotated solutions
Wikipedia. Fermi Problem
mittechtv. 2010. BLOSSOMS - The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
Lori Ann White The art of back-of-the-envelope calculations: Students estimate their way through pop culture problems to learn a life skill. Symmetry Online Magazine

Back of the Envelope Calculations

Notes by djjrjrdjjrjr, 04 Dec 2014 18:13
djjrjrdjjrjr 03 Dec 2014 21:31
in discussion Hidden / Per page discussions » Sourcing

Wikipedia Editors. Sourcing Disambiguation Page.

References by djjrjrdjjrjr, 03 Dec 2014 21:31
Resources by djjrjrdjjrjr, 03 Dec 2014 20:53
References by djjrjrdjjrjr, 03 Dec 2014 19:24

Related idea: "MiniCourses" - my alma mater, New College, has for almost 50 years replaced "shopping period" with "miniclasses." During registration period they set aside two days during which the entire course schedule for the following semester is condensed down into 15 minute long introductions to each course. Instructors present the syllabus and themselves and students get to ask questions, size up the instructor and see who else will be taking the course. It's a very small investment of time that has a big payoff. We could do it in an afternoon. If there are courses we highly recommend as electives we could invite those instructors to participate.


Ignite Steamboat
Howto Produce and Ignite Event
How to Give a Great Ignite Talk
The Art of Concise Presentations
Lightning Talk
New College Academic Calendar showing miniclasses

Some Ideas by djjrjrdjjrjr, 02 Dec 2014 20:25