What’s in the Dividers?

People occasionally ask whether they could just purchase the book, The Universe in My Hands, and make their own dividers for the magnitudes notebook, one for each order of magnitude.
Of course this is always possible, but there is a lot of information in the dividers as I have composed them; they are not "just dividers" and it is possible that you will become discouraged if you try to work without them. At the least, be sure you understand what you are missing if you go on your own. Below is a description of the tabs and how to get started with them.

Five Things in the Magnitude Tabs

1The front of the divider
On the front of each divider is some object that you might see at that order of magnitude -- if you can see anything at all; of course we do not directly see molecules or atoms, but we have images and diagrams of them. I have tried to choose things that are commonly known, even if they are not visible.

2The back of each divider
On the back of each divider, you will find an arrangement of things you can see:
  • In the center, you will find the dimensions of man's body and life.
  • Above that you will find things you can see in space or in the sky,
  • To the left, birds and things from the world of birds,
  • Below the birds, plants: their parts and their habitats,
  • At the bottom is the mineral world, including the realm of geology
  • Moving back around, we find artifacts, the creations of men.
  • Finally, coming up on the right, the world of animals other than birds.

3From tab to tab
As you move from tab to tab looking at this arrangement on the back, it is possible to follow a theme, and there is plenty of room for you to add your own themes. For example, in the plant world, you can go from leaf to stem, to vein to cell to chloroplast to granum to thylakoid to chlorophyll, to a chlorine atom, always looking at the plant side of the arrangement.  Some areas are empty, either because I could not think of anything to fill them or because there really is nothing -- or nothing distinctive – in that range of size. For example, there are no flowers or flower parts when you reach the astronomic orders of magnitude. As you work through the magnitudes, be sure to add your own discoveries.

4Tab colors
One of the interesting discoveries about magnitude is that the basic topics of the natural sciences emerge from the study of magnitudes because each discipline is fundamentally oriented to a size range. The colors of your dividers reflect the general disciplines of the natural sciences:
  • The red tab is for the world of math that underlies everything in the physical world. There are certain objects of uncertain but infinitesimal size about which we know almost nothing except what math can teach us.
  • Orange is for the better-known world of physics, subatomic physics in particular, but electricity and magnetism cannot be understood aside from this realm. 
  • Yellow is for chemistry; it begins where atoms have complete outer valence shells which participate in chemical reactions, a few of which are familiar to you.
  • Green is for the realm of life; from cells to the largest plants.
  • Blue-green is the realm of earth sciences: geology and meteorology
  • Blue takes us to farthest reaches of the solar system.
  • Indigo marks the realm of the stars, astronomy.
  • Purple is for cosmology -- beyond our Milky Way.
I hope these colors will help you keep track of the sort of things you are thinking about at each order of magnitude.

5Banks of 8 tabs
Notice that the tabs are arranged in banks of 8 tabs.  This means that the jump in magnitude between any two overlying tabs -- where one tab lies on top of another -- is 8 orders of magnitude.  It happens that this jump is also the total jump between the smallest thing we can see -- a fleck of dust in the sunshine -- and the largest thing we ordinarily see and recognize for what it really is -- a stretch of six miles or possibly as much as 15 or 20 miles on the far horizon.
Where I live, one can stand in the sunshine on the steps of St. Joseph Cathedral and see flecks of mica in the sidewalk; at the same time, the city water towers are in view, the farthest of which stand a few miles away in each direction. The difference between a fleck of mica and the entire recognizable scene from the earth to the highest clouds represents a magnitude jump from (-4) to (+4) -- eight orders of magnitude. In the notebook, a two overlying tabs differ in the size of their objects as much as a fleck of mica in the sidewalk differs from the magnitude of a small city with all the quarries below it and all the cirrus above.

Getting into the Magnitudes
Here are some exercises to get you started in the magnitudes

The Mag tab
You also have a tab marked "mag".  In this space, you may collect beautiful and striking images which display multiple orders of magnitude. You might write a short explanation of the magnitudes that you see in a particular picture, or you could put numbered arrows on sticky papers and point to the magnitudes.  Of course, almost any picture shows things of several orders of magnitude, because things have parts.  For example, a photo of an Irish cottage with a straw roof has straws that are a millimeter wide, window dividers that are one or two centimeters wide, windows that are a meter high, a house that is close to five meters high (not quite ten, but within that order of magnitude). A bit of road might be 100 meters long, and the light cumulus clouds are a thousand meters high, and possibly a swipe of cirrus in the upper atmosphere.

A Day’s Work
You will want at least a 2-inch 3-ring binder for your magnitude notebook. Soon enough, you may want a 3-inch binder. It's nice to get the kind that lets you slip pictures in the front.
Spend some time becoming familiar with the tabs. Worksheets are included with the text, but you may be able to think of other things to do. The simplest thing to do is to find pictures and articles about things of different sizes, paste them on a sheet of paper, and file each one behind the right tab. The surprise is that this exercise alone will teach you a surprising amount about the construction of the universe. For some help getting started, here are a few exercises:

Shrinkings:
1Name one or more objects 8 magnitudes larger than the sun.
a) If the sun shrank to the size of a fleck of dust, what object would be the size of the city of Sioux Falls?  [This the same question, differently phrased.]
2What object is 8 magnitudes larger than a grapefruit?
a) If a grapefruit shrank to the size of a fleck of dust, what object would be the size of the city of Sioux Falls? [This the same question, differently phrased.]
3What object is 8 magnitudes larger than the city of Sioux Falls?
a) If the city of Sioux Falls shrank to become the size of a fleck of dust, what object would be the size of the city of Sioux Falls?  [Same question]
4What object is 8 magnitudes larger than your house?
a) If your house shrank to the size of a fleck of dust, what object would be the size of the city of Sioux Falls?
5What object is 8 magnitudes larger than your rosary beads? 
a)  If all the world shrank so that your rosary beads were the just flecks of dust and so you could string them on a bit of a thinned-out spider web, name several objects which would be the size of the City of Sioux Falls.
6 Is there anything 8 magnitudes larger than the Milky Way?
7 If the Milky Way were shrunk to the size of a fleck of dust, the universe would be the size of a ______________________________. 
[To answer this question, count the number of pages from the Milky Way to the Universe, and then count an equal number of pages from the fleck-of-dust page (-4).  Objects at that order of magnitude would be about the size of the universe.]

Expansions
1What object is 8 magnitudes larger than a commonplace atom? 
a) If a commonplace atom could be expanded to the size of a fleck of dust, name some objects that could sit comfortably on top of the city of Sioux Falls and hold all its clouds inside.
2What object is 8 magnitudes larger than each cell in your body?
a) If each cell in your body were expanded 8 orders of magnitude, name some object in the same order of magnitude as their new size.
3If each cell were so expanded, your body would become very large indeed.  How large would your body become, if it were expanded 8 orders of magnitude.  As large as  __________________________.
4[There could be more than one answer, but one is obvious.  Count eight pages forward from the page (0) that contains the human body.  Or just look at the tab that underlies the (0) tab.

Impossible resizings
1If a spiderweb were expanded to be the size of a steel cable, what size of flies might it catch?  [Spiderwebs are of different weights, but suppose you are talking about the spiderwebs that are readily seen, with a width of a tenth of a millimeter, putting the width at [-4]. Steel cable is a few centimeters in diameter. So you are moving up just 2 orders of magnitude. Now move up two orders of magnitude for the fly.
2If a lion and a lamb shrank to the size of an oxygen molecule and a carbon atom, (and if they lay down together and formed a carbon dioxide molecule!) how many orders of magnitude would that shrinkage be? 
a) How big would the earth be, if it shrank proportionally?
b) If a lion grew to the size of Jupiter, and if it caught a mouse, how big would the mouse be?
c) So how much of the earth could a lion eat in one bite if he were the size of the planet Jupiter?
d) Suppose that the lion were only the size of a pea.  How big would the earth be?
Can you think of some other examples?

Studies
1If you decided to study fishes, what part of the fish might you study at the (-2) order of magnitude?
a) Still studying fishes, what might you study at the (+3) order of magnitude?
b) Still studying fishes, what might you study at the (-7) order of magnitude?
2If you decided to study rocks, what might you study at the (-1) order of magnitude?
a) Studying rocks, what might you study at the (-8) order of magnitude?
b) What rock formations could you study at the (+5) or (+6) orders of magnitude?
3If you wanted to study the constellations, what orders of magnitude would you study?
4If you wanted to become a biologist, what orders of magnitude would you be most likely to study?
5If you became a biologist, could you just forget about the smaller orders of magnitude?
6What might a biologist need to know about that is larger than the largest trees?  Is there any order of magnitude that a biologist can completely ignore?  Why or why not?

Stories
7Write a story in which you become several orders of magnitude larger or smaller than you are and you visit the world to find it looking very small (if you are large) or very large (if you are small.)  For example, if you were two orders of magnitude smaller, you could make friends with a lightning bug; or if you were (how many?) orders of magnitude larger, Niagra Falls would seem like a little brook rapids that you could walk along and play in.
8What would make the world seem more interesting to you, being smaller or being larger?

Ye Hedge School's

The Universe in My Hands

Dividers for the multi-level science curriculum on universe order