Thomas Fowler's ternary calculating machine (1840)





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Published on Nov 23, 2014

Demonstration of a reconstruction of Thomas Fowler's 1840 ternary calculating machine, by Mark Glusker, as seen at http://www.mortati.com/glusker

Transcript of http://www.mortati.com/glusker/fowler...
(The ternary calculating machine of Thomas Fowler
by Mark Glusker)

The design of this model is based primarily on a written description by Augustus de Morgan in 1840
This model was never intended to be an exact representation, historically accurate in all of its details
Instead, it's intended to be the simplest representation which satisfies de Morgan's description.
It's intended as a proof of concept model, to provoke discussion about what might have been
Although Fowler's machine was capable of both multiplication and division, for the purposes of the following descriptions it's much easier just to think about multiplication problems
All of the numbers in Fowler's machine are expressed in balanced ternary, so all of the mechanisms have three states
The first section of the machine is the multiplicand which consists of a series of sliding rods
These rods can be placed in any of three positions.
01:07 There are indicators here for plus, zero and minus.
The slots on each multiplicand rod engage with the multiplier mechanism, as we'll see shortly
The multiplicand is not really part of the mechanism. It's really a mnemonic device.
It helps the user know which way to rotate the ladder frame of the multiplier
The multiplier is a large frame which can slide laterally relative to the rest of the machine, allowing it to act on one digit at a time
01:37 At one end of the multiplier is the ladder frame which rotates round an axis through its centre
At the bottom you can see the tooth that engages with the multiplicand
There are three rungs on the ladder frame
The multiplier rods can snap onto any of those rungs, and depending on which rung it snaps to, the tooth at the far end of the multiplier rod moves back, or forth, or if it is snapped to the middle rung, not at all
02:14 The product assembly is a raised platform on which there are several rods that slide back and forth
Each rod has a series of teeth on the top which engage the carry mechanism and these spaces on the bottom which engage the multiplier mechanism as we've just seen
The platform that the product rods slide along allows for considerable over travel of the product rods.
02:46 This is necessary because the carry mechanism is not integral, and its use requires the calculation to be interrupted temporarily.
Allowing overtravel is a way of delaying the need to employ the carry mechanism, in the hope that some of the negative digits in the ternary system will average the digit back towards an allowable value
The carry mechanism is a separate assembly that can hinge down and engage with the gear racks on top of each product rod
De Morgan's description wasn't very clear on the exact nature of the carry mechanism so this is the most speculative part of our recreation
03:27 De Morgan's description does state that it only acts on two adjacent product rods and needs to be manually positioned for any digits requiring a carry
As I walk through the steps of a simple multiplication problem, two times six equals twelve, you can see the signed ternary values beneath each decimal value.
The first step is to set the value of the multiplicand to plus in the threes digit, and a minus in the ones digit.
04:03 Next we set the value of the multiplier by snapping the multiplier rods onto the ladder frame. A plus for the nines column, a minus for the threes column and a zero for the ones column.
Next we ensure that the carry mechanism is disengaged and all the product rods are centred, on the product platform, setting them all to zero
Now that the machine is all set up, we slide the multiplier assembly laterally to engage the first multiplicand rod
04:50 The action of the rotating frame is such to bring the multiplicand rod back to the zero position
As the ladder frame is rotated, you can see the teeth in the multiplier rod can push and pull the product rods into the appropriate position
05:15 Once the first multiplicand rod is restored to zero, the multiplier frame is slid to an intermediate position, the ladder frame is restored to the vertical position, and it's ready to engage the next multiplicand rod
That multiplicand rod is also restored to the zero position and in this case, as there are only two digits to the multiplicand, the calculation is now complete.
05:43 The answer can be read off of the product rods. You can see here there's an overdraft in the nines digit - this is a double negative here - so the carry mechanism needs to be aligned and engaged with the product rods and then this value is restored to an allowable value.
06:11 So now we can read the answer as plus, plus, zero, which is equal to a decimal value of twelve


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