I have been in such a program when I was 12-14 (run by the William Stern foudnation in Hamburg, Germany) and the curriculum consisted mostly of very diverse ‘math’ problems prepared in a way to make them accessible to us in a func way without introducing too much up-front terminology or notation. Examples I remember of the spot:
turing machines (dresses as short-sighted busy beavers)
Drawing fractals (the iterated function ones; with printouts of some)
In general only an exposition was given and no task to solve. Or some introductory initial questions, The patterns to be detected were the primary reward.
We were not introduced to really practical applications but I’m unsure whether that had been helpful or rather whether it had been interesting. My interest at that time stemmed from the material being systematic patterns that I could approach abstractly and symbolically and ‘solve’. I’m not clear whether the Sequences would have been interesting in that way. Their patterns are clear only in hindsight.
What should work is Bayes rule—at least in the form that can be visualized (tiling of the 1⁄1 grid) or symbolcally derived easily.
Also guessing and calibration games should work. You can also take standard games and add some layer of complexity on them (but please not arbitrary but helpful ones; a minimum example is: Play Uno but cards don’t have to match color+number but some number theoretic identity e.g. +(2,5) modulo (4,10)).
Yes of course. That and we tried variations of the rule-set. We also discovered the flyer.
It is interesting what can come out of this seed. When I later had an Atari I wrote an optimized simulator in assembly which aggregated over multiple cells and I even tried to use the blitter reducing the number of clock cycles per cell as far as I could. This seed become a part of the mosaic of concepts that sits behind understanding complex processes now.
The story goes as follows (translated from German):
“Once I dreamed that there was an island called “the island of dreams”. The inhabitants of the island dreamed very vivid and lucid. Indeed the imaginations which occurred during sleep are as clear and present as perceived during waking. Even more their dreamlife follows from night to night the same continuity as their waking perception during the day. Consequently some inhabitants have difficulties to distinguish whether they are awake or asleep.
Now every inhabitant belongs to one of two groups: Day-type and night-type. The inhabitants of day-type are characterized by their thinking during the day being true and during the night being false. For the night-type it is the opposite: Their thoughts during sleep are true and those during waking are false.”
Questions:
Once an inhabitant though/believed that he belonged to the day-type. Kann be tested whether this is true? Was be awake or asleep at the time of the thought?
I have been in such a program when I was 12-14 (run by the William Stern foudnation in Hamburg, Germany) and the curriculum consisted mostly of very diverse ‘math’ problems prepared in a way to make them accessible to us in a func way without introducing too much up-front terminology or notation. Examples I remember of the spot:
turing machines (dresses as short-sighted busy beavers)
generalized Nim really with lots of matches
tilings of the plane
conveys game of life (easy on paper)
More I just looked up in an older folder:
distance metrics on a graph
multi-way balances
continuous fractions (cool for approximations; I still use this)
logical derivations about beliefs of people whose dream are indistinuishable from reality
generalized magical squares
Fibinacci sequences and http://en.wikipedia.org/wiki/Missing_square_puzzle
Drawing fractals (the iterated function ones; with printouts of some)
In general only an exposition was given and no task to solve. Or some introductory initial questions, The patterns to be detected were the primary reward.
We were not introduced to really practical applications but I’m unsure whether that had been helpful or rather whether it had been interesting. My interest at that time stemmed from the material being systematic patterns that I could approach abstractly and symbolically and ‘solve’. I’m not clear whether the Sequences would have been interesting in that way. Their patterns are clear only in hindsight.
What should work is Bayes rule—at least in the form that can be visualized (tiling of the 1⁄1 grid) or symbolcally derived easily.
Also guessing and calibration games should work. You can also take standard games and add some layer of complexity on them (but please not arbitrary but helpful ones; a minimum example is: Play Uno but cards don’t have to match color+number but some number theoretic identity e.g. +(2,5) modulo (4,10)).
I assume you mean Conway’s game of life.
Yes of course. That and we tried variations of the rule-set. We also discovered the flyer.
It is interesting what can come out of this seed. When I later had an Atari I wrote an optimized simulator in assembly which aggregated over multiple cells and I even tried to use the blitter reducing the number of clock cycles per cell as far as I could. This seed become a part of the mosaic of concepts that sits behind understanding complex processes now.
That sounds interesting. Would you care to elaborate?
The story goes as follows (translated from German):
“Once I dreamed that there was an island called “the island of dreams”. The inhabitants of the island dreamed very vivid and lucid. Indeed the imaginations which occurred during sleep are as clear and present as perceived during waking. Even more their dreamlife follows from night to night the same continuity as their waking perception during the day. Consequently some inhabitants have difficulties to distinguish whether they are awake or asleep.
Now every inhabitant belongs to one of two groups: Day-type and night-type. The inhabitants of day-type are characterized by their thinking during the day being true and during the night being false. For the night-type it is the opposite: Their thoughts during sleep are true and those during waking are false.”
Questions:
Once an inhabitant though/believed that he belonged to the day-type. Kann be tested whether this is true? Was be awake or asleep at the time of the thought?
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