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The following science questions, were inspired by questions that Prospect School children raised in September, as reported in Vol. 2, #1. They are answered here, even though they have not been officially submitted -- since we have not had other questions to keep us busy.

     Black holes are a phenomenon in space. There have been studies about black holes for a long time, but scientists who do research about black holes have not seen one for sure, but have theories or educated guesses explaining them. For example, a star that becomes more massive than a neutron star doesn't seem to eject matter anymore. When it burns up all of its fuel it collapses into a black hole. In the information I have, black holes have to meet certain factors. In order to understand these factors some vocabulary words need to be introduced:
 

 binary star system--a pair of stars that are gravitationally associated or, rotate around each other.

 event horizon--the surface that you past through to enter the black hole.

 neutron star--a star with an extremely high density and mostly made up of neutrons.

 white giant--a star that has burned up most of its neutrons or fuel, or a star that is about to die.

 x-rays--extremely short electromagnetic wavelengths.

     In real life a black hole is a spinning disc that is sucking in everything around it. The molecules are spinning at such a high rate of speed, they are actually creating an electromagnetic field which throws out extremely short wavelengths of energy (x-rays). A black hole has never actually been discovered but there are systems found in which they could exist. Cygnus X- 1 was the first binary system found to eject x-rays, therefore it must have something spinning at a high rate of speed. In 1982, in the Cloud of Magellan, a binary star system was found, LMC X-3. This star system has a bigger chance to have a black hole, and would be the first case of a stellar black hole discovered in another galaxy.--TN

What happens to something if it enters a black hole?

     It depends on where your spaceship is! If your ship is traveling into the hole, the instruments would tend to read normal. After you cross the event horizon you'll never come back because of the gravitational pull caused by the spinning. Inside, depending on the mass of the black hole, the ship would either get ripped apart by the tidal forces or be sucked into the center, collapsing into infinite mass. If your spaceship was outside watching the other spaceship, it would appear that the other spaceship was being sucked towards the hole, time would appear to slow down, because of the gravitational forces, and the closer the ship got to the event horizon the more the ship would appear to fade away, as if frozen in time.--TN

People say that the first mirror was a dark pool of water on a still day. I can't remember ever really seeing myself in such a pool. Of course, I have seen reflections of ships, or the opposite shore,
in all kinds of water.

Polished metal or even polished stones can reflect. I recall that, during World War II, soldiers were given small pieces of polished steel to look in while they shaved. I also recall seeing a lot of pictures of unshaven soldiers. The best mirrors are

made of glass, coated on the back side with silver. Nowadays, silver is too expensive and many shiny plastics have been created that work as well as mirrors, but I don't know how you make them.

How a mirror works is another matter. A lot of people think that somehow, like a camera, a mirror captures a picture of what is in front of it, so you can see it when you look in it. That seems to me to be a good first theory. Take a small mirror and turn it while you look in it. A surprising thing happens. When it's turned so you don't see yourself, you don't see what is in front of the mirror, but something twice as far around as it has been turned. If three people, sitting up straight in a row, look into a mirror facing the middle person, the end people see each other, not the middle person. If I face this mirror toward the window, I don't see the window in it unless I am standing between the mirror and the window. If I look from one side, I see the things on the other side of the window room from the mirror.

Even more puzzling is the question, when a mirror reverses things, words like CHOICE may not be reversed while your name may be. It's a fact that, if I look at myself in a mirror, I see the top of my head at the top of the mirror, the lower part of my body at the bottom, and my left hand on the left side of the mirror and my right hand on the right side of the mirror. That wouldn't be puzzling except that we have learned that when we face someone else their left hand is opposite our right hand and vice versa. So if we see our image in the mirror as that of another person, the left and right hands are exchanged, but the top and bottom aren't. The puzzle is in the mirror reversing things from side to side and not from top to bottom. If we lie down and look in a mirror, we see that our left and right hands are still reversed, e.g., the one at the top of the mirror looks like the opposite hand. Our head, Iying down, is on the same side it is really on, however, so this mirror is no longer reversing from one of its sides to the other side. It is reversing from my, or your body, side-to-side. The puzzle must be that the person we see in the mirror is not another person, but ourselves, and we are almost but not perfectly reversible from our left side to our right side.  Our image seems to be turned around facing the opposite way, but really is not.

When I look in the rear view mirror of my car, I do not see the cars and trucks behind me as turned around. (You can try this even though you are not the driver, if you have another mirror to hold in front of you as you ride along.) I see the truck passing me on my left side on the left and the person walking forward along the sidewalk to my right is still walking forward on the right as I pass and look back at her in the mirror. I know that they are not turned around and don't see them as turned around, but when I look at myself in a mirror, I think I am turned around. Could it be that I am really not turned around when I look in the mirror?

Could it be that I am not in the mirror at all, but that it just helps me to see backwards? I think a mirror is even more helpful than an extra pair of eyes in the back of our head. Suppose you stand backto-back with a friend and your backward-looking friend tells you what he or she is seeing behind you. Like, "Here comes a truck. It's going to pass us on the right side." What would you think was about to happen? Which side of you is it going to pass on? Wouldn't a rear view mirror be less confusing than eyes looking backwards? Besides, your backward-looking friend can't tell you if your hair is mussed up or you have a smudge on your face.

This is one of the great mysteries people wonder about, and someone ought to write a book about it. Since I haven't found such a book yet, please experiment as much as you can with mirrors and try to work out the ideas yourself. Please send in more questions about mirrors, or answers you have figured out.--JE

How does a hologram make different colors?

    There are other things that make colors like a hologram does: a diffraction grating, a butterfly's wing, or even your own eyes when you look at the moon or an automobile headlight at night. Generally speaking, these colors are made by diffraction of light. There is another way to make different colors called interference, as when a thin film of oil spreads out on a wet street or sidewalk. These are different from another way called dispersion, which is what happens when a prism or a PILOT-brand plastic ball point pen is held in bright sunlight. All these ways of making colors can be explained by the wave theory of light. There are two other theories, the particle theory and the ray theory, which can't explain how colors are made by diffraction, interference, or dispersion. However, there are some things they can explain which the wave theory can't. So light is one of those mysteries of science, like electricity, that doesn't have a single explanation.

    I'll try to explain diffraction, since that is what makes the colors in a hologram. A hologram is a photograph with a lot of tiny dots, something like the dots you can see in a newspaper or magazine picture. However, the dots are so small and close together you can't see them. Each dot is making light waves, like moving your finger up and down in a pool of still water, but the waves of different colors of light have a different separation. (If you put a Pyrex baking dish with a half an inch of water in it on an overhead projector, you can see the waves from your finger.)

    Red light waves are farther apart than blue light waves, which means that the waves go up and down more slowly. (You can make long waves and short waves in the baking dish by moving your finger up and down slowly or rapidly.) If you put 2 fingers (f) in the water hold them spread apart and move them up and down, you might see the waves forming lines that go in one direction. (This is not at all easy to see.)

    I'm glad you didn't ask why the hologram pictures are 3-D. That is even more difficult to explain.--JE

    A second grade teacher in Kankakee, Prudy Kimmery, pointed out to me ten years ago that counting and place value conflict with each other. She thought that children would get along better if the text didn't switch back and forth from one to the other but did all one sort of activity and then did all the other sort. I felt that to do that would be to give in to the formal procedure way of learning math that leaves most people unable to use the mathematics they have learned. When children learn to count by tens but can't say how many tens and how many ones there are in 25, there is too much formalism. This leads to 25 - 16 = 11, and other nonsense. But I didn't know for a long time what to do about it. People recommended gluing ten beans on each popsicle stick, using all kinds of hands-on materials, but it seemed that none of those things were guaranteed to solve the problem. Some authorities said that children couldn't understand place value until they were much older, say fourth grade.

I had seen children in Japan learning about tens and ones in the third month of the first grade. This was not done without some confusion about saying there was one ten in 11, 12, etc., for 20 is the first number in Japanese where ten occurs as a noun--they say "two tens." But those first graders were learning tens and ones much

more easily than children I had observed in America, so I didn't really believe the authorities who said that first graders were too young for it.

First, I tried teaching children to count (after nine) onety, onety one, onety two, etc. That helped adding and subtracting, but translating the answer back into English was hard. Finally, it hit me by accident, since "hundred" is the first word in English counting which is used as a noun, why not start studying place value there? "One hundred" or even "a hundred" are the ways we usually speak, and those expressions treat "hundred" as a noun, not an adjective like in, " 100 cents make a dollar," where cents is a noun and 100 is an adjective. Knowing that many young children are very sensitive to switching adjectives and nouns -- they have trouble with "a darker blue," but are not confused by "a darker blue dress"-- I decided that I would try introducing place value with hundreds rather than with tens.

I cut square sheets of 100 ceramic tiles from the larger sheets in which these tiles are made. First and second grade children loved adding and subtracting hundreds, using these tiles.
 

A few of the first graders tried to count them incorrectly, saying "100, 101, 102, etc." but others corrected them.  I gently recommended they not count but arrange the sheets of 100 tiles in patterns like the five pattern on dominoes. There you can see that a diagonal row of 300 combined with the other 200 makes 500, without counting. Children who preferred to count 100, 200, 300, etc. got the same answer and were happy. Larger problems like 900 + 900 led to some trouble in counting by 100s, and worked better by making domino patterns of 500s. Two moves shown by the arrows in Figure 1, change two fives and two fours into a ten, a five and a three. No one ever hesitated to say how many hundreds and ones  there were in 205, 301, or other such numbers, although 16 wheels, and 31 days in the month could not be analyzed correctly into tens and ones by most of the first graders. This seemed to confirrn my notion that hundred was the first number understood as a noun, because it's used that way in counting, and one seemed to be the second. The trouble seems to be abstracting "ten" or "blue" as a noun.

    Plato is said to have created the belief among mathematicians that every number has a unique existence. There is just one of each idea, and a number is an idea. So there is only one one, one two, one three, ... one ten, etc. Therefore, it doesn't make sense to talk about how many tens and ones there are. Children and some mathematicians may follow Plato more closely than the school textbooks which talk about one ten, two tens, three tens, etc. But, for some reason, in English, but not in modern Japanese, we say "a hundred" or "one hundred" more than we say just "hundred." Saying that then opens the door to "two hundred," "three hundred," etc., although plurals are not used, as they should be for nouns that are numbered.

    In short, the number "hundred" seems to be so close to being an exception to Plato's uniqueness rule, that it provides a better opening to the concept of place value than ten does. Partly, I also had in mind that the adjective use of numbers is important in story problems, and if we forget that and make every number a noun right away, we could be still stuck with the traditional problems of story problems.

    As we get toward the end of first grade, whenever children are quite comfortable with hundreds and ones, we should be able to introduce tens and ones, noting that it is a peculiar way of talking. We might need it to make sense out of Emblems like, 505 + 505. That problem takes us past a thousand, which is another noun number in ordinary English, and the way we write it opens up the question of what name shall we invent for the second column from the right when we put a " 1 " in it, [1,010] after we have noticed a "1" in the thousands column, a "O" in the hundreds column, a "O" in the ones column. What is that column with the other " 1 " in it when we have written a thousand and ten as a four-digit numeral?

    What is going on here is abstraction, not in the usual sense of the word in which all written numerals are abstractions, but in the mathematical, or even Platonic sense of creating and agreeing on general ideas of the sorts of things we are looking at (tiles) and talking about rows of tiles. This is the fun of mathematics, because it opens up arguments, dialogues, discussions, and lots of talk--your mathematics classroom will even become noisy with productive noise. What we want is for children to be confident in their ideas and not trusting blindly in their memories of standard procedures. We've seen how easily they mistake those, reverting to earlier procedures we thought had been stamped out by drill on correct procedures. We want every child to be able to detect and correct their own errors by reasoning. We could buy everyone a pocket calculator for a few dollars if we just wanted accurate, mechanical computation.--JE

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