About Carolyn L

Carolyn coordinates the Science on Stage outreach program at HMNS and will blog about science toys and experiments, logic puzzles, and whatever else seems interesting at the time.

I can’t find my reading glasses, but I’ll manage.

You’ve probably noticed the magnifying effect of a glass of water or any other clear beverage (the black text to the right of the glass is the same size as the black text behind the glass):

And you probably have some idea that the magnification has to do with the curved shape of the glass and the water it contains: The water in the glass bends light so it appears to us to be coming from an object that is bigger or closer than it really is.

To explore this more, try making differently sized water drops on top of a sheet of waxed paper (the waxed paper helps the water ‘bead up,’ which improves the effect):

You’re aiming for a large drop about 2 centimeters or 1 inch across, and medium and small drops that are, well, smaller.  If you don’t have an eyedropper to help you, you can either pour extremely carefully or dip a pencil or spoon in water and let the water drip off of it.

Look at a page with words through the drops (don’t use your first editions of The Old Man and the Sea or Einstein’s General Theory of Relativity, because the water will eventually seep through the waxed paper and make you very, very sad).  Do you see any differences between the larger and smaller drops?

This looks much clearer if you try it yourself, so go do it! 

You may be thinking “My large drops (possibly puddles) don’t seem to change anything; why do the small drops work so much better?”  To explain this, try looking at your drops from the side (your eyes should be level with the surface of your table:

The shapes are different: The largest drop looks almost flat across the top, while the smallest drop makes a very tidy little dome shape.  Another way to say this is that the smallest drop’s surface is more sharply curved, or is more convex than the larger drops (convex surfaces bulge out, concave surfaces “cave in.” And it turns out that the less convex the surface of the drop, the less it magnifies.  If you want a more in depth explanation with diagrams, check out this site.

Convex and concave lenses are used in all kinds of cool equipment. For more information on lenses and the anatomy of your eyeballs, check out The Anatomy of the Eye. 

Sharky-Locks and the Three Gummi Bears

Need another excuse to buy candy this October?  Like cheap entertainment? Of course you do! How about some do-it-yourself grow-animals? For a buck or two, you can have a hundred edible expanding critters of your very own.

You need a few gummi bears or other gummi snacks (I grant you they are of questionable nutritional value, but they have their uses) and water. That’s pretty much it — see what we mean about cheap? 

I started with three gummi bears and one much larger gummi shark which had a disturbing layer of opaque white gummi on the bottom. 

If you want to know how much your gummi critters grow, you might want to trace around them or measure them, or just set some of your gummy snacks aside for comparison later. I had an electronic balance handy, so I used it, but that’s definitely not necessary:


The growing:  You need a container that can hold your gummi animals with a little room for expansion, and enough water to keep them covered:

And now we wait.  You may notice some expansion an hour after you begin, but your animals will look significantly bigger after 12-24 hours in water.  A few things to note: If you plan to eat your critters once they expand, please refrigerate them during the soaking process (this may slow their expansion somewhat, but you will also slow the growth of not-so-delicious bacteria). Whether you are refrigerating or not, set your critters somewhere and leave them alone as much as possible; if they jostle around too much, they may just dissolve and leave you with an unimpressive pool of colored sugar-water.

After a 20-hour soak, one of the bears intimidates his dry brother:


The “after” measurements:

This bear grew about three times as large as it was originally, and the shark about twice as large (it might have expanded further if given more time but it fell apart after being handled.)

Here’s a brief explanationof growing gummi snacks.

Extensions to try:  Soak your critters in distilled water, salt water, soda or juice, or try soaking an expanded critter in salt water.  Do some brands of bears hold up better or expand more?

(In case you were curious: Yes, you can spell it either way: gummi or gummy.)

Can you conquer the Tower of Hanoi?

Puzzles are very good at making you think flexibly and enabling you to find patterns (skills great for science and pretty much everything else), but they’re also just fun. One classic logic puzzle is the Tower of Hanoi, invented by Edouard Lucas in 1883.  This puzzle has been one of my favorites since I first saw it about twenty years ago.  As with many problems, there are multiple ways to achieve the basic goal, but after exploring you may figure out the most elegant or efficient way to get there.

One seven-disk version of the Tower of Hanoi looks like this (many more can be seen here):

The goal is to get the stack from the left pin to the right pin, finishing with the stack in the same order (largest disk on the bottom, smallest on top, and all the other disks in order). 

The rules:

1) You may only move one disk at a time. This means you may only move the topmost disk in a stack.

2) You may move the disk to any of the three pins, HOWEVER:

3) You may never stack a larger disk on top of a smaller one.

It’s easy to get the idea with just a few disks:

Here is the starting position:

Then we move the small disk to the middle pin:

Which allows the big disk to go to the last pin:

Then the small disk stacks on top of the big one and the stack is complete:

Try making and moving a three disk stack (just remember you can’t stack the larger ones on the smaller ones!):      

You can also use a dime, nickel and quarter, or three other coins of differing sizes, and just mark ‘tower slots’ on an index card in place of the pins.

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Once you get the three disk stack moved successfully, see if you can do it in only seven moves (two disks took three moves).  Four disk towers can be moved in a minimum of 15 moves.  You can also try this online. This version lets you choose up to eight disks and will keep track of how many moves you make.

Here are some things to think about as you play:

Do you start to see patterns in the way you move the disks?

Is there a rule about where you should put the first disk when moving a stack of three, four, five, etc.? Does it matter if the number of disks is even or odd? Does the pattern continue no matter how many disks you have in the tower?

What is the minimum number of moves for five disks?  Does this fit into any kind of pattern with the previous ‘minimum move’ numbers?   The minimum number of moves for a seven-disk stack is 127; does this fit the pattern?

One apocryphal story tells of a tower of 64 golden disks, which when completely moved, signal the end of the world.  Assuming one move every second, this stack would take over 500 billion years to move.

Check out this site for more discussion of the Tower of Hanoi puzzle.

Testing for the Best

Summer is here and one of the new Xplorations classes this year is Test for the Best, a class about consumer product testing (think Consumer Reports for kids: more about chocolate and toys and less about vacuum cleaners). I had fun checking out their experiments the past two weeks. 

How long does your chewing gum keep its flavor?  Does that battery really keep going and going and going?  Campers smeared fabric (in this case, socks) with chocolate sauce, ketchup and more before testing out stain removers:

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They also tested battery life, plastered themselves in bandages to see which ones would stick the longest, sampled chocolate chip cookies and created an advertising campaign for imaginary products, complete with slogans and fine print warnings!  Here are a few pictures:

The bandage line-up:

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 Some results from testing waterproof bandages:

 ed-bandage-indiv-1.jpg

Ready for a blind(folded) taste test:

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Working on an ad (and simultaneously testing markers):

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The slogan:

 ed-gum-slogan.jpg

And another group’s ad:

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Complete with a warning label:

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After rating many other things (microwave popcorn, cereal, etc.), on Friday the campers tested several things of their own choosing; bouncy balls, frozen treats, and chocolate bars.

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We’re always looking for more ideas, so what do you think we should test in July?