On 8/12/07, Jared [email protected] wrote:
Eric Johnson wrote:
Notice that in all three of your examples to achieve true randomness, you are utilizing an analog-to-digital conversion. (i.e. you are capturing a random pattern occurring in the Real World with digital annotation). Note also that ternary logic handles analog-to-digital conversion much more efficiently than binary. This is empirically true, and demonstrated mathematically here:
I hate to get involved in what looks like it could become a perfectly good flame war, but I looked at your link.
By the same logic, we would be much better off using a decimal computer. It takes 15 trits to write 143, but I could write 999 in just 3 decimal bits (dits?)
Eric, you raise a good point.
This is a keen intuitive leap, but it turns out that it is not the reason that ternary is better than binary. It is actually because electricity has _exactly_ 3 states:
+1 current flowing one way 0 no current -1 current flowing the other way
No. To deal with analog to digital, electricity has a near infinite number of states. I would prefer a system that can measure 10 voltage levels than one that can only measure directions and no current. I can easily set up the circuit so that measurements can be taken in each direction.
Because of this, ternary is optimal, because electricity is itself ternary. If you try and build quaternary or greater gates, you create WAY more complexity than you need to. To build quaternary gates, you actually create ternary plus unary. And then to build "quintinary" gates, you build ternary plus binary. And so forth. Decimal would be a real mess.
Electricity itself is ternary. That's why ternary gates are the most efficient. Binary conversion is 'clipping' one third of the three-part A/D conversion, whereas ternary is keeping that third.
I don't think you're going to get a lot of argument that the higher the base the fewer digits it takes to represent a number. That does not, however, make it a more efficient design for anything other than printing. I frequently write values in hex when programming or documenting things for the same reason.
You are correct. The argument is not towards "higher base" but rather it is towards:
"a base which accurately expresses the natural capacity of electrical flow."This should be sufficient answer to the observation you made.
Part II: How to keep this from becoming a flame war.
As for flame war, you have just introduced the most interesting real-time proof of the efficiency of ternary logic. And for this reason, I am going to end these conversations, because the point is entirely made. Here goes:
The concept of "War" is itself a binary concept, being perfectly opposed to "Peace." In binary conversation, you are either in one state or the other. In ternary, there is another option. Let us call this one "Abeyance" which is an ancient term meaning something like "undecided." Or perhaps "learning."
Abeyance happens to be a perfectly useful state which is neither war nor peace. Here is how it works: If you will go back through the seven posts I have written in this conversation, you will see something interesting happening, which does not always happen in online conversations.
At every juncture where someone found reason to "disagree," I promptly answered: "You are correct," and went on to show how the disagreement was not a complete rejection of the theory, but only a slight disagreement and moreso a valid observation in favor of it.
This is how ternary operates. The "middle ground" which is normally excluded from conversation because a person is either RIGHT or WRONG, is actually the most important part of conversation. It is where a person is in a state of flux, being part way between one or the other binary poles.
Abeyance.
Thus, it is _impossible_ to get into a flame war with ternary logic, because at every juncture, the ternary thinker says "Wow. You are absolutely correct." How can you be at war with someone who is incrementally agreeing with you at every stage of the conversation? Some people say "you're tricking me!" But in fact, this is not an outward manipulation, this is actually what is happening. Look back at the conversation and you will see.
And that, being as real as it gets, is sufficient to introduce the beauty of ternary logic which Donald Knuth referred to when he said:
"Balanced ternary is the most beautiful numbering system in math."
He wrote this in The Art of Computer Programming many years ago. And it is still true. Now who's gonna argue with Donald Knuth?
As the ensuing conversation, in which it is impossible to have a flame war, could take a long time, and yet be friendly all the way, I now respectfully request this conversation go off-list so we can learn more about the 710 Mhz processor and other such eastward flying falcons.
G'day.
-Jared
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