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Arms, hand, fingernal, tiny

Introduction - on a screen

Sugar comes in different sizes - a preview

What is buildings view?

What is micro view?

nano view

atoms view

more zoom

If I asked you, how long is a spoon...

so you can hold them

so you can hold them

Printables for Arms, hands, fingernail, tiny

Find a path across your hand, that's about 100 mm.
Choose a fingernail, that's about 10 mm.

Millimeters and centimeters. Nickels and pennies. 240 mm long. An object/unit hybrid.

Reminder: Most of these have not been classroom tested, and thus don't work.

Arms, hands, fingernail, tiny

Talking size with your hands. Handwaving size.

Cubic meter

Cubic meter in your pocket Make a one meter cube out of string. It takes two or more people to hold it up. Idea from Caryn L Johnson.

Cubic meter in the corner Hang a cubic meter in the top corner of a room. The two bottom edges, which stick out, can be made of taped straws. 10 cm colored straws. I had to put extra strings from the ceiling to support them without bending.

Human chaining

Image by Chajeshukarie

A dancing chain. Estimating an 8 meter arc. 😉 8 people, so 8 meters... but note the lines on the stage, about 1 meter apart. So they are doing an underestimate, a lower bound. The dance line here looks about 5 meters long. Perhaps at another moment in the dance, some of their arms were extended a bit more. The forth person from your left - their right arm looks about right.

Human chaining a line To measure distance. Anchor person stands next to the start, and the human chain is extended towards the destination. Dress the chain, then the person in front becomes the new anchor. Repeat as needed. Moving the chain forward is fun, at a walk or at a run. It can stay in one piece (swinging wide or rolling), or break into groups and then reassemble.

Collaborative one-meter taping Like chaining, but everyone holds 1 meter long strings as a reference, and holds them end to end. To make the strings easier to hold, they can be cut long, and marked, and held mark-to-mark, instead of end-to-end.

Chaining/taping races With a time bonus-or-penalty for accuracy. The bonus creates a speed-vs-accuracy tradeoff. Using different bonuses in different races, shows "close enough approximation" depends on the use/race. Small bonus: just run, counting paces. Large bonus: go slow and measure carefully.

"... is this big" games

Number -> gesture Person A: "Thousand millimeters!" -> Person B: arms spread. A:"Hundred millimeters!" -> B:hand-spread. A:"Ten millimeters!" -> B: pinch fingernail. A:"One millimiter!" -> B:tiny pinch.

Number <- gesture A: Show a distance; B: "about blah millimeters!".

"measure!", checks, challenges, and upper- and lower-bounds A key idea is that measurements are never ever exact. What's important is that you have a feel for the possible error. "This is about 100 millimeters. Well, I'm sure it's more than 10 millimeters and less than 300. And I'd be surprised if it wasn't more than 50 and less than 150 millimeters. Maybe it's between 80 and 120 millimeters?"

Circle and sphere: circumference, area, and volume

Pi equals 3 mumble. The mumble is small. 0.141529 etc. Smaller than 5% of simple 3.

When you ignore the mumble, balls are almost as easy as boxes. So often, that 5% off, isn't worth the pain of pi. Especially when doing estimation, and teaching young kids.

The circumference and area of a circle, are 3 mumble / 4 those of its wrapping square. And the area and volume of a sphere, are 1 mumble / 2 those of its wrapping box.

Which is much more accessible, than 4/3 π r3 and such.

Planets 1 Gm per mm

Jupiter and Earth.

City cross-sections 1 km per mm


Prototype output for a webapp.

Anyone have spectra of hot rocks, so I can derive real crust colors?

Cities 1 km per mm

Pearl River delta.

After printing, the 20 km scale bar should be 20 mm long.

Buildings 1 meter per mm

A building.

Real-size things 1 mm is... 1 mm

Slice of pizza.

Hair 1 micrometer per mm

Micro art 1 micrometer per mm

Flower art on a chip.

Inside an E.coli bacteria 1 nanometer per mm

DNA string, protein blobs, and the cell wall. A flagella is sticking out of the wall.

mol-mach-2014-poster--scaled.pdf [23 MB]

Molecular Machinery (scaled to 1 nm per mm)

Some large molecules found in cells.

Printing: Use US letter-sized or A4 paper. After printing, the 10 nm scale bar should be 10 mm. The text is small, and becomes unreadable in photocopies. 23 MB PDF.

Creation: This page was created by scaling the orignal poster by 0.28528, to become 1 nanometer per millimeter.

Credit: Molecular Machinery: A Tour of the Protein Data Bank (2014) by David S. Goodsell and the RCSB PCB. CC-BY-3.0. From RCSB PDB-101 Education Resources.

T4 bacteriophage virus model
1 nanometer per millimeter

Attacking a small E.coli bacteria traffic cone.


Viruses (scaled to 1 nm per mm)

Some viruses.

Printing: Use US letter-sized or A4 paper. After printing, the "28.4 nm" arrow should be 28.4 mm.

Creation: This page was created by scaling the orignal page by 1.0855, to become 1 nanometer per millimeter. Errata: It looks like this might be printing a few percent too small.

Credit: Virus Structures by David S. Goodsell and the RCSB PCB. Perhaps CC-BY-3.0, as described here. Created in collaboration with EMDataBank. From RCSB PDB-101 Education Resources.

Water 1 picometer per mm


Looks like a mouse. Whiskers not included.

Printable rulers

Millimeters. 250 mm long.

From Some printable paper rulers (2002).

Millimeters and centimeters. Nickels and pennies. 240 mm long. An object/unit hybrid.

Millimeters and centimeters, in the same direction. One meter long.

From Houghton Mifflin Math Expressions: Grade 5—Teaching Tools—Visual Support.

Issues: Decimeters are almost never used outside education.

Millimeters and centimeters. One meter long.

From Some printable paper rulers (2002).

Issues: Millimeters and centimeters run in opposite directions.

A foot of US quarters. An object/unit hybrid.

A How Big Are Things? Cube (2003)

Scaled slides

A slide deck with a few objects. Pizza, Jupiter, Sun, hair, hair knot. Scaled for a 16:9 screen 200 cm wide. 1MB.

Lessons learned

My idea was to treat video development like software development. Doing iterative development and testing to make sure it was actually working. Yikes.

People have diverse and non-linear responses. I expected to "make it clear, make it engaging, and perhaps create derivatives tuned to different ages, cultures, and interests". Ha. What I found instead was... An elderly European was distressed by the word "millimeters", which brought back unhappy memories of learning metric in some long-ago school. A child's wet cough, used as a quiet background sound to introduce the word "virus", went unnoticed by most, but sent one person running away, asking how I could show them "something so disgusting". A college student was distressed by the violence of breaking the head off a virus. One person could only see a doll as making themselves giant, not as the doll being shrunk small. Lots of people had aversion reactions to even the words "virus" and "bacteria". And these examples weren't even from long-tail diversity -- I tested only a handful of people. This stuff was common.

I wonder if long-form science education videos are in the same place that science education lectures were two decades ago... the creeping realization that they are dismally not working, combined with testing being too broken to notice.

Vision and sound compete. I was careful about managing visual attention. I didn't expect it to compete with auditory. Oops.

One video started with a stick-person in a sparse room, immediately saying the purpose of the video, while pointing at the same purpose written on the wall. What was a common viewer suggestion when the video was paused a few seconds later? You should mention the purpose of the video. On replay, they caught it (and sometimes thought it was a different video).

Use very short videos, designed for repeated watching. Because given the cognitive diversity of viewers, anything else seems implausible.

Use US Fair Use. I intended to use only content that was public domain or Creative Commons licensed. Mistake. Yes, US Fair Use is an ambiguous mess. And breaking it has long been on Hollywood's Washington shopping list. But this site would have been far better for students if I'd made more extensive use of Fair Use.


My thanks to the MIT community, without whose support, this would not exist. To the MIT and Harvard science education research communities. To all the folks who stopped on the street to help me test draft videos. To the open research, and open content movements. Even if PLOS is still blocking indexing by Google Images. And to everyone who licenced their material for reuse. Far more content was helpful than has ended up appearing here.

Google Scholar was essential. Also: Google Images, Flickr, Wikimedia Commons, and YouTube. Sounds from: and Developed with: Moviepy, IPython Notebook, and Audacity.

This was a 2015 effort to improve the teaching of size, from planets to atoms. It was a work in progress, when I ran out of time, so these are just scavanged bits and pieces. This has not been classroom tested, and thus doesn't work. While the MIT community has been invaluable, I'm just an alum who goes to research talks, a software engineer not a teacher, and this was a personal hobby project.


These videos are bits of old user tests. Sketches shown to a few people, and then revised -- they weren't intended for distribution.

a few more...

How does all this help you remember sizes?
sort of like dolls, or toy cars, or toy trains.

Arms, hand, fingernail, tiny

Talking size with your hands.

Arms, hand, fingernail, tiny
Same video as above.


Burst! - youtube videos of bursting things
from high-altitude ballons, to cells.

Printables & Buildables

planets view

buildings view

micro view

atoms view

Scaled slides


That's it. If something you liked from testing isn't included above, I'm sorry, I ran out of time.