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Topic 1. Modeling with Smart Little People |
Problem 1. “A Disappeared Parcel”
The post office receives the parcels that have notice that their weight is 8 kilograms and their value is rather high. Actually, their weight turned to be much less. The customer demanded compensation for the damage. What’s wrong?Let’s consider the problem about a ”disappeared parcel”.
IF a parcel becomes rotten during transportation,Find opposite properties:
THEN its weight decreases,
BUT this will be noticeable at once.
A parcel must be heavy, to be announced valuable,Articulate an ideal solution:
And it must be light to let its receiver demand compensation for the loss.
The parcel is losing its weight by ITSELF.What resources exist for solution of this problem:
the contents of the parcel.Method of solving contradictions:
in time – first it is heavy, then later it is light.Solution:
(If you have already guessed the clue of this nearly detective problem, write down your solution.)
“Once in London, Fridrih August Kekule tells about a discovery that accounted for the structure of many complicated matters of a human body and of all living creatures: I sat in an omnibus thinking how to present a benzene molecule in a structure formula that meets the requirements of its properties. At that moment I saw a cage with the monkeys that were catching each other: they snatched each other, then disassembled, one moment they snatched each other in such a way that made a circle. Each of them was holding to the cage with one leg and the other one was holding its another leg with both hands, their tails were loose and waving. So, five monkeys, holding each other, formed a circle, and an idea immediately came to my mind: this is a picture of benzene. This formula explains the strength of a benzene ring.”There are many similar examples where modeling with parts of a system containing contradictions helped researchers solve difficult problems in science and technology.
Let’s imagine that any of the objects surrounding
us consists of many very small men (Smart Little People).
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Chalk consists of solid small men, they hold each other by hand. |
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Water consists of liquid small men, they don’t hold each other by hand but stand close to each other. |
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Air consists of gaseous small men, they are restless and run fast all the time. |
And what if we try to imagine the contents
of the parcel consist of small men.
First they have to be heavy and were safely
placed in a parcel box. What are they like? Of course, they
are solid.
Then a parcel arrives at its destination.
The small men should decrease or better disappear, then the parcel
will become very light. What kind of small men can disappear without
a trace from the box? Right, if they are gaseous.
Thus, first – solid, then – gaseous.
The substance that from solid can turn into gaseous is dry ice (street
ice-cream sellers have much dry ice in their small carts). Of course,
a swindler was exposed at the post office, very simple – it was dry ice!
Try to solve the following problem using Smart Little People.
Problem 2.
Winter of 1942. A military plant, having evacuated to the Uralls, is going to assemble the equipment on a new place. A big heavy press has to be put into a deep pit. There is no crane at hand; its transportation will take too much precious time. What should be done?A contradiction:
IFR (Ideal Final Result):
Contradiction 2:
Using Smart Little People, draw a picture of a system where the contradiction has emerged. |
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What should the Smart Little People do to solve this Contradiction? |
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Problem 3.
It is necessary to make many holes of 10 mm in diameter in a long rubber pipe. Generally it is not too difficult to drill holes. But rubber is supple; it stretches, shrinks, curves… It is very difficult to make a hole of required size. The worker tried to burn a hole with a burning rod, but the edges of the hole were burning and crumbling.A contradiction:
"I can’t handle it!", cried the worker with annoyance. "I am going to cry…"
And at this point the Inventor appeared.
"You don’t have to cry!", he said in surprise. "This is very simple!"
What did the Inventor suggest?
IFR (Ideal Final Result):
Contradiction 2:
Using Smart Little People, draw a picture of a system where the contradiction has emerged. |
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What should the Smart Little People do to solve this Contradiction? |
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Modeling
with Smart Little People
(Continued)
Using Smart Little People one can devise very interesting riddles:
What is it?
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Your suggestions: |
The picture has changed a little. What
can it be?
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Your suggestions: |
Make up your riddles, and draw them using the
Smart Little People. Of course, you can draw your riddles with your
own small men; however in Appendix 2 you will find many Smart Little People.
If you cut them out, you will be able to lay them together in your riddles
like puzzles.
We know well that all systems change in time.
The next riddle of mine is about these changes.
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Using the Smart Little People, draw a picture
of the processes changing in time.
Modeling
with Smart Little People
(Conclusion)
Fairy Tale About a Chalk.
Once on a school day the teacher brought into
the class a new box of chalk sticks. They were even, nice and absolutely
identical.
It was a very good chalk, easy and comfortable
to write on the blackboard.
What small men does the chalk consist of?Very soon only one piece of chalk was left. It looked very common, just like other pieces of chalk. However, the children noticed immediately that when they used this particular piece, the most complicated problems were being solved easily. It was very convenient to use it, more convenient than using others. But it appeared quite a common piece of chalk. What was the secret? As a matter of fact, the small men that lived inside this piece of chalk were very fond of studying and learning new things. They were upset when the children wrote with mistakes or solved problems incorrectly. And so, the small men decided to help the children in their studies. They neither prompt them, nor wrote instead of them on the blackboard. Something unusual and mysterious was taking place.
What properties of the chalk can be explained with the help of the small men?
Draw a picture or use the small men to show what happens when we write on the blackboard with the chalk.
Explain, why it is easier to write with one chalk, while another one scratches and is not easy to write with.
Try to guess the secret of the small men. What should be done? What can be done to prolong his existence much longer? (don’t forget we are devising a fairy tale about a piece of chalk.)The small men of the chalk began to think how to handle this problem. And that was what happened one night. As it usually happens in a real fairy tale, exactly at midnight when the clock began to strike twelve times a miracle happened. On the stand under the blackboard, where usually there were lots of chalk particles, a small storm began. When it calmed down there was a new piece of Chalk on the stand. Since that day the children didn’t doubt that their favorite Chalk was a fairy object and began to look after it more carefully. They even started a contest with each other who would write with this chalk.
Make up rules for such a contest.The Chalk liked to study with the children. He was happy when they succeeded and upset when they failed. He helped to draw amazing pictures on the black board of animals and plants, devised by the children. How interesting was to devise together with the children the worlds that nobody had ever seen. The Chalk learned how to draw riddles and puzzles and made up such difficult problems for the kids that even their mothers and fathers couldn’t find answers.
Do you know such problems?A tale is being told fast but things are being done slowly. Much happened during school years in the class where the Chalk studied…
To solve this problem it is necessary to remember what kind of small men compose the hamburger.The Chalk fell down near the bench and began to look around. He had never left the school walls and the spring wind seemed to him wonderful and exciting. Through the green young branches the sun rays looked Everything around him seemed beautiful. The chalk closed his eyes…
Draw with the help of the small men what happens when the chalk touches the water.The chalk got scared. He began to remember how he had lived in a dry and warm classroom, how the children had treated him, how happy he had been helping them master various subjects… Never, never again he would experience such wonderful moments…
Whom do you think these boots belong to?So, two people stopped near the bench in the park. They were talking with animation.
The Chalk was left on the asphalt path. But is it possible that this tale is over at this point? Make up your own story about how the Chalk will “collect himself together” and continue his adventure.
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Last updated on Feb. 19, 2002. Access point: Editor: nakagawa@utc.osaka-gu.ac.jp