FPGA

[Eric Johnson]

On 8/12/07, Jared <jared at hatwhite.com> 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:
> >>
> >> http://www.trinary.cc/Tutorial/Interface/Analog.htm
> >
> > 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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-- 

Eric Johnson

"Where your pleasure is, there is your treasure: where your treasure,
there your heart; where your heart, there your happiness."
Saint Augustine