Educational stories

Apples exchange

This was the saying I remember when returning from kindergarten: There was an old woman having four apples. An old man only had two. The old man came to the old woman and said "give me one apple, old woman, we will have the same count".

Known result with an unknown number

This I have heard when returning from a school trip in a bus in 3rd grade from a neighbor's wife, who was accompanying us: Think about a number; a whole, positive number. Now add ten to that number. Now subtract four from the result. And now subtract the original number you were thinking about in the beginning. You should get six.

Gentle introduction to the concept of variable I guess.

Tenhallers attraction on water

When I was about 12 years old, in 1990, our physics teacher at the secondary elementary school focused on mathematics and physics told us that the gravitational force can be observed when two tenhaller coins, made out of aluminum, are floating on the surface of water, in a small cup and or, in my case, a glass - they really can float, if put carefully. I tried the experiment at home. They really gathered in the center of the glass. But I was suspicious. I have placed just one tenhaller on the surface, put a 1kg weight nearby, and - nothing. The coin did not move. I eventually concluded that the fact they are attracted is not due to gravitation between the coins, but due to - hm, I am not exactly sure - something connected with the surface layer of the water, acting like a elastic sheet, being bent by their weight - so actually gravitation has something to do with the phenomenon, but not the gravitation between the two coins, rather the gravitation between Earth and each of the coins, and only indirectly.

Does steel float?

Around the same time, the same teacher asked whether steel does float in a liquid. We were probably presumed to think about water, I for one did, and replied "that depends on the shape of the steel", thinking about steel boats, ocean liners to be exact, to which she replied "smart answer, but I wanted to show you something different". She let circulate a small closed glass filled with hydrargum, with a aluminum-steel pencil sharpener floating in it, which did float, even though it did not make a vessel.

CO2 in water

Another experiment was a small CO2 bomb (small pressurized tank) being opened in a glass aquarium. She expressed her fear of letting off the CO2 bomb, since the reactive force could propel it to high speed, making a projectile out of it. Nevertheless, she carried on with the experiment, punctured the filled bomb with the tip of a circle maker. "You have to make only a small hole, if anyone of you try at home and make a big one, it can be pretty dangerous". She was nervous. The result was only mildly interesting - bubbles in water. Unneccessarily dangerous, in my thoughts. But, the amount of gas in such a little container was actually interesting; I knew that already from home experiment with CO2 expansion model motor. Also the surface of the small CO2 bomb did cool rapidly, which was also a factor in her fear. Yeah and actually the point of the experiment was to show how much gas can be stored in such a small volume, and I think that the water in which it took place was actually necessary not only to show there is some gas present, but also for heating up the small tank from which the gas escaped.

High school

I have estimated the magnetic field in a solenoid.

My exams from electromagnetism

There were three terms available for making the exam, actually any exam at that time (summer 1997); first one was called "ordinary", the second one "correctionary", the third one was "secondary correctionary". I did not have time to attend the lectures, and - frankly - I was lost in all the new concepts that were there. Namely partial differential equations.

Thankfully, the professor that was teaching us published his handwritten czech translation of a book which title I do not remember. Anyway - I knew I did not know the subject much, still after some hesitation I went to the exam. I got the questions and one of them was - "surprise" - Maxwell equations. I do not want to look too stupid, but a plain fact is I have not even knew such equations were crucial to the whole subject. Basically, I understood some of electrostatics on the first term of the exam - first out of three possible. I gave in an almost empty paper; if So I have studied some.

Negative numbers - On the relation between unary and binary minus

"-a":="a-a-a"

"neni minus jako minus" = "there are different kinds of minuses"

I was introduced to minus as a sign for binary operation - let there be a pile with $10$ apples, subtraction of $6$ means taking $6$ apples away from the pile, leaving $4$ apples there. This operation can be written as $10-6=4$. Now there can be also negative numbers. They can be understood as, say, promise to someone. For example: A woman has one apple. $n=1$. She gives the apple to a man, hence she has no apple at all. That is $1-1=0$. Now she wants to give another apple to the man, and she does not have one. That can be described as having $-1$ apple. Minus can be a desire, intention, promise, debt. Or the opposite direction. If you go one step forward, that can be written as $1$. One step backwards means $-1$. And the distance between going one step forward and one step backwards from some place is two steps. Two, not one. Maybe trivial, but I somehow find this fact interesting. The equation on top of this paragraph means "if you want to create a negative number from some number, you have to subtract the same number twice".

Is it possible to not think about something?

Imagine you want to not think about something. Impossible, is not it, to not think about something... Suppose a bread. Let's not think about bread. Try. As far as I can tell, trying to not think about bread means thinking about the fact one is trying to not think about bread. The moment you are genuinely not thinking about bread, you cannot even think you are not thinking about bread. The moment you would realize you are not thinking about bread, you would be thinking about bread. My impression, anyway.

About a shopkeeper freely giving away part of his stock

Suppose a man has 20 boxes of icecream on a stick. He freely gives away one. From one viewpoint, he has given away just 1/20th of his stocks; that might seem like just a small fraction. From another viewpoint, if one wants to give him back - buy so much as to repay the price of the icecream on a stick - one needs to buy say 20 such icecreams; since the added price of an icecream is say 6% and the real profit is even lower still - the icecream has to be kept in an icebox in the very least, which costs money, even if one considers self-service. This does seem as a paradox to me. The corollary is another viewpoint: by giving away just one box, he essentially lose profit from all of his stock. I do find this surprising and even shocking in a way. Source: Sorbonna, Paris, France through my mother.