However ...Re: [Squeakland] Panel discussion: Can the American Mind be Opened?

subbukk subbukk at
Sat Dec 1 05:39:38 PST 2007

On Thursday 29 November 2007 7:04 pm, David Corking wrote:
> My mental model for arithmetic is a clock face, which is very clumsy
> in base 10 (and worse in base 16!)
A clock face has many interesting properties too. It incorporates the concept 
of magnitude (countables) and angles (directions/turns), "feeling" time 
(kairos) and periodic time (chronos).

1. The clock face has two hands of different magnitudes - small and big
2. The small hand moves in steps of one. The big hand moves in steps of five.
3. Reading a clock means reading the magnitude traversed by the small hand and 
then the magnitude travelled by the big hand.
4. Even though the "magnitude" of big hands falls to zero, the time is larger 
because the "magnitude" of small hand has increased (concept of place value).
5. The hands move but still stay in the same amount of space. This turning 
around a pivot is an "angular movement". (Note: Alan's car demo shows how 
accumulation of linear and angular movements leads to a circle).
6. The angular separation between small and big hand makes interesting shapes. 
When they are farthest apart, it is like someone cut the clock face into two 
same pieces. When they are like room corners, then you can have four such 
7. The clock chimes whenever the big hand points "straight up". The big 
hand "triggers" the sound. (The concept that an event is triggered when a 
specific combinations of events happen is the basis of kairos. A seed remains 
dormant till rains arrive to germinate. Kairos has no "magnitude" between 
event occurrences. A ten-minute wait in a long queue feels like an hour while 
a hour-long video game session feels like a minute).
8. The thin red hand (second hand) moves very rapidly and makes a regular 
ticking sound like water dripping from a faucet. Our heart races when 
exercising or when scared, but red hand always makes sixty ticks to complete 
one turn. (tick-tock time is chronos time. It is not subjective and involves 
magnitude. Pulse beats or dripping droplets are approximations. Galileo used 
his pulse to time chandelier swings in a church).

I will stop here and hope you got the drift. A first-grader amazed me one day 
by reading out the clock correctly. With my curiosity provoked, I got her to 
explain the process to me gradually over the next few days. The language may 
come across as a bit strange because I tried to use her own words as much as 


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