more about the Thinking Machine

detail of the Thinking Machine
The ball is about to operate a hammer and play a tubular bell.
Masahiro Miwa invited me to design and build a Thinking Machine as part of his Reverse Simulation project. In this project music works are first conceived as an algorithm and run as a simulation on a computer. They are then "reverse simulated" by being performed by live players or, in this case, by a machine. The machine uses rolling balls to play three tubular bells according to an algorithm.

Vimeo link A video documentation by Kenichi Hagihara.

side view of the Thinking Machine
Thinking Machine (2007)
Wood, plywood, electric motor, 6 steel balls, three tubular bells, length 2.50 meters

The balls are released, one at a time, from the storage wheel (right). Each ball is guided down the inclined tracks by three sets of levers and then passes through a gate which re-positions the levers to guide the next ball. Having operated a hammer to play one of three tubular bells (left) the ball returns on the lower track to the wheel to await its next run. The wheel is turned by a slow-moving motor.

Masahiro Miwa: 'Rising Boy' logo Dear Klarenz,
    My dream comes true!
Unbelievable but I saw the Thinking Machine working!!
The machine performs the trinary operation Jaiken-zan
and plays tubular bells as its result.
    Liebe Gruesse aus Berlin,


Thinking Machine at TESLA Berlin
at TESLA-Berlin

How did the project start?
Prof. Hermann Gottschewski of Tokyo University introduced me to the composer Masahiro Miwa. Miwa-san had previously formulated and tested the algorithm and now proposed that I should build a machine to play it. Our communication was entirely by e-mail; we finally met when the project was almost complete (at TESLA-Berlin where I had a residency) while I was making the final adjustments to the machine.

Why "Thinking Machine" ?
Miwa-san and Prof. Gottschewski sat down together to make an application for funding the project and they thought up this title in the context of other machines I have made - like the Flute Playing Machine and the Talking Machine. Yes, it does seem a rather grandiose title for what is a relatively simple mechanism. Nevertheless, if I try to predict the next two or three notes that the machine will play I find that I have to think quite hard about it.

Thinking Machine diagram
The three states of the machine: 0, 1, 2
Note the different positions of the three sets of levers (numbered) and the different positions of the gates that control them (below).

What is the algorithm?
The machine works with a succession of 6 rolling balls that circulate, one after the other, through the machine and play three bells.

New A = (6-(Old A + State)) MOD 3


Old A   the track through the ball enters:
 0, 1 or 2
State   the current way the mechanism is set:
 0, 1, or 2
New A   the track through the ball exits to play a bell:
 0, 1 or 2

To express this formula in a different way, here is the truth table.
State is the top line, Old A is the column on the left; join them up and you get New A

                0  1  2
            0   0  2  1
            1   2  1  0
            2   1  0  2
Or, to give two examples in plain English:
If the previous ball played the middle bell and the new ball starts in the middle track,
then it too will play the middle bell.
If the previous ball played the middle bell, and the new ball starts in, say, the left track,
then it will be diverted to the third track, where it will play the right bell.

wheel and motor
The wheels and its driving motor,
anchored to the floor by a stone.

What are the three wheels for?
They serve as a memory (a shift register). The wheels store the results of the five previous runs. Without this memory function I would have had to make a circle of 6 machines, passing around a single ball to each other - as in Masahiro's original Reverse Simulation performance with 6 players.

My shift register inspired Masahiro-san to make a new version of his piece with a simulated shift register for live players. (This is well explained in the video link at the bottom of this page).

The three wheels: 0, 1, 2

How is the machine started (initialised)?
The 6 balls are loaded by hand into the wheels in a particular pattern. For example: 000001. That means 5 balls in the left wheel (value 0) and then one in the middle wheel (value 1). None in the right wheel (value2). That particular combination will result in a run of 52 turns of the wheels, resulting in 312 notes (52 x 6) before there is a repeat. 001022 repeats after 8 turns of the wheels, while 111111 would repeat continuously.

end view
View from the wheels towards the bells

What happens after a ball leaves the wheel?
The ball is guided down the track by pairs of levers that are operated by gates at the end of the track. Thus, each ball determines the course of the ball that follows.

In the photo the first pair of levers have been activated by the previous ball. The levers are connected to the gates by long wooden rods. The small weights on the ends of the red strings pull the levers gently back out of the way after they have been released.

A ball switching the middle gate.

How do the gates work?
The ball switches the gate that it passes through and releases the other two. This activates the levers that determine the course of the following ball.

The hammer mechanism

And then ...
... as the ball plunges over the end of the track it deflects a hammer which strikes the bell a gentle blow.

The bells are suspended at about 1/5th of their length from the top. The hammer strikes the bell at its sweet spot - somewhere in the middle.

close-up of three tubular bells
The tubular bells. Behind them, the hammers

Why tubular bells?
I wanted instruments with a long sustain that would fill out the 5-second pauses between each note and would have a different timbre to the clicking sounds of the mechanism. The bells are tuned A, B and C.

I also experimented with a combination of three different instruments: a tubular bell, a rattle with a very long sustain (like a vibro-slap) and a hollow block of light wood (like a temple block). But when I got them running they sounded too intentionally East Asian, so I reverted to my 3 tubular bells.

a student loading the machine
Initialising the machine. Tokyo University, December 2009


Vimeo link Vimeo: A documentation by Kenichi Hagihara.
So laid back and contemplative that I almost prefer it to the real thing.

YouTube, Part 1
Masahiro Miwa explains his Reverse Simulation Music project

YouTube, Part 2
Masahiro Miwa explains our Thinking Machine project.

Masahiro entered our project for the Prix Ars Electronica in the hybrid art category and we got an honourable mention.

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