Introduction


What's New

About these pages


Counting by powers of ten
 "ten, hundred, thousand, ..." (10^{1}, 10^{2}, 10^{3}, ...)

Counting to ten billion... on your fingers
 Counting by powers of ten, on fingers.

"What order of magnitude is ...?" game

Lots of dots

A million dots on one page

A dot for every second in the day
 with clock.

A dot for each day



How to simplify a number
 rounding, compacting, memorables, etc.

Rounding off a number
 simplifies it by creating zeros.

Rounding to an order of magnitude
 extreme rounding.

What is "order of magnitude"?


Exponential Notation
 sliding the decimal point.

Scientific Notation
 is exponential notation plus conventions.

How to write and speak the exponential notation


A few examples of exponential notation
 Not of much use.


On Being Approximate
 The what, why, and how.

Why be approximate?


Bounding uncertainty


Honesty in approximation


Fermi Questions
 Rough quantitative estimates.

Landmarks


A Pinocchio estimation game
 detecting implausible approximations 
An experiment with mayonnaise



`Powers of Ten' scales


Scaling the universe to your desktop


Pm,
Tm,
Gm,
Mm,
km,
m,
Millimeters in your hands,
um,
nm


Constructing your own desktops



Deep understanding


If you can't explain it
to a nine year old...
 then you don't really understand it yourself.

For children


Developing "deep" understanding


Probing near space with a flashlight


Exploring with teleportation
 Using imagination to generate questions

China is down over there...
 looking down through the earth

Over maps, envisioning the atmosphere


Earth's surface as a 20 x 25 Megameter rectangle


Round Earth, Tilted People


Visualizing Earth's Internal Structure
 a road trip going down

Atomic bonding


Getting a feel for big numbers


A feel for big numbers, with grains of salt


Only a breath away
 aka "Caesar's last breath"

Your enormous surface area

Good descriptions


Knowledge you can work with...


Simple models


A ball's volume and area are 1/2 of its box's


When Length grows a little, Area grows a lot


The relative size of
Earth, Jupiter, Sun (1 : 10 : 100)


Trig w small angles


Sphere



Resources

Search for Simplicity  Weisskopf
 a column.

The Back of the Envelope  Purcell
 a column.

On the Back of an Envelope  Triplehorn
 a column.


Scale of some things
 (with experimental frames)

Population ,
landmarks ,
other


People seconds


Time ,
landmarks ,
other


Length ,
landmarks ,
other


Area ,
landmarks ,
other


Volume ,
landmarks ,
other


Mass ,
landmarks ,
other


Energy ,
landmarks ,
other


Mass volumedensity


Surface volumedensity
 Packing surface in a volume.

Speed


Volume rate


Power ,
landmarks ,
other


Lightspeed delay



Body Ruler


Measuring Angle and Distance with your Thumb


