The Ternary Calculating Machine of Thomas Fowler
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Re: The Ternary Calculating Machine of Thomas Fowler
#2See also Setun " rel="nofollow">http://en.wikipedia.org/wiki/Setun>, a computer from 1958 using the balanced ternary system.
Re: The Ternary Calculating Machine of Thomas Fowler
#3See also Setun " rel="nofollow">http://en.wikipedia.org/wiki/Setun> , a computer from 1958 using the balanced ternary system.
Nice. It's strange why don't we have such computers nowadays
Re: The Ternary Calculating Machine of Thomas Fowler
#4I often wonder if there is some notion of a basis of computation in mathematics. You can do stuff in binary, trinary, what about further out systems? What about working with functions/mappings which take more than two inputs. What can be said about the expressive power of these different ways of computing? Any one know where I should be looking for this kind of stuff?
Re: The Ternary Calculating Machine of Thomas Fowler
#5I often wonder if there is some notion of a basis of computation in mathematics. You can do stuff in binary, trinary, what about further out systems? What about working with functions/mappings which take more than two inputs. What can be said about the expressive power of these different ways of computing? Any one know where I should be looking for this kind of stuff?
Describing computation in mathematical terms is arguably the core of Computer Science as a subject - particularly the "Theory of Computation":
http://en.wikipedia.org/wiki/Theory_of_computation
If you are interested in "functions/mappings" then you can look at Lambda Calculus and work your way right up to modern functional programming languages:
Re: The Ternary Calculating Machine of Thomas Fowler
#6I often wonder if there is some notion of a basis of computation in mathematics. You can do stuff in binary, trinary, what about further out systems? What about working with functions/mappings which take more than two inputs. What can be said about the expressive power of these different ways of computing? Any one know where I should be looking for this kind of stuff?
Describing computation in mathematical terms is arguably the core of Computer Science as a subject - particularly the "Theory of Computation": http://en.wikipedia.org/wiki/Theory_of_computation If you are interested in "functions/mappings" then you can look at Lambda Calculus and work your way right up to modern functional programming languages: http://en.wikipedia.org/wiki/Lambda_calculus
I'm reasonably well versed in these topics, I found them unsatisfying, they don't capture the essence for me. I don't really know what I'm looking for I just know I haven't seen it yet.
Re: The Ternary Calculating Machine of Thomas Fowler
#7Knuth's Art of Computer Programming, vol 2 [1], not surprisingly, gives a thorough discussion of the balanced ternary system.
The solution for a nice brainteaser can be found quickly once one thinks about balanced trinary, here it is: "Using a balance scale, what is the minimum number of wheights needed to weigh any whole number of grams up to 40g?"
[1] http://www.amazon.com/Art-Computer-Programming-Volume-Seminu...