[ih] How Plato Influenced the Internet

[Steve Crocker]

Jack,

A classic analysis of bits vs trits says trits are slightly more
efficient.  The analysis is based on assuming that it takes b parts to
represent a digit in base b.  Two parts for a bit, three parts for a trit,
four parts for a quit(?!).  The information content of k digits in base b
is b^k.  The "cost" is b*k.  The optimal base is e (2.71828...). Bases 2
and 4 are equal.  (The information content of 2k bits is 2^(2k).  The
information content of k quits is 4^k.  The costs are the same, i.e. 4k.)

Trinary is better but not by much.  Using six parts, you can make three
bits or two trits.  The information content of three bits is 8.  The
information content of two trits is 9.

A different consideration of using trinary vs binary is the representation
of integers.  As we all know from hard experience, twos complement
representation of signed integers gives you an asymmetry with one more
negative number than positive number.  Switch to ones complement and you
wind up with two representations of zero.  Trinary gives you a naturally
symmetric representation of signed integers.

I think that's the end of the advantages of trinary over binary.  But I'm
VERY impressed you took the time and effort to actually build such
circuits.  Bravo!

Steve


On Mon, Aug 23, 2021 at 10:29 PM Jack Haverty via Internet-history <
internet-history at elists.isoc.org> wrote:

> Back in the 60s, a lot of computer technology was not yet cast in
> concrete.  There were lots of choices.  But then someone pursues one
> choice, and if it works reasonably well, others follow the same path.
> It doesn't take very long for the "installed base" to become so large
> that it's unlikely that some other initial choice could easily take
> over.    Think about how long it's taken, so far, for IPV6 to supplant
> IPV4.
>
> Sometime around 1968, as a learning experience in some lab course at
> MIT, I decided to make some non-binary logic.   At the time, analog
> computers were still around, and digital computers hadn't yet agreed
> even on how many bits were in a byte, or how to encode characters, or
> what order bits should be in a computer memory word.   But bits were
> pretty well established.
>
> I figured there must be other choices.   So I made some ternary logic.
> Unlike binary, which dealt with 1s and 0s, I used +1, 0, and -1 as the
> three possible states.  Electronically it translated into positive,
> negative, or no current.   Using transistors and such components, I made
> some basic logic "gates" that operated using three states instead of
> two.  Was that a good idea?   Probably not, but it was a good way to
> learn about circuits.    Instead of bits (binary digits), how about
> manipulating trits (trinary digits)? There's nothing magic about 1s and 0s.
>
> Shortly thereafter, binary took over as circuitry went into integrated
> circuits and a whole industry came in to being around binary
> computers.   If some other kind of approach, ternary, quaternary, or
> whatever is better than binary, we'll probably never know.   I suspect
> something might happen soon with qubits though to challenge bits
> supremacy..
>
> There are lots of ways to do things, and the one that "wins" might not
> have been the best choice.
>
> Imagine how networking and computing might have evolved with trits
> instead of bits....
>
> /Jack
>
>
> On 8/23/21 12:15 PM, John Day via Internet-history wrote:
> > Agreed.  There are only so many ways to do something.  ;-)
> >
> >> On Aug 23, 2021, at 14:46, Craig Partridge <craig at tereschau.net> wrote:
> >>
> >>
> >>
> >> On Mon, Aug 23, 2021 at 8:12 AM John Day via Internet-history <
> internet-history at elists.isoc.org <mailto:internet-history at elists.isoc.org>>
> wrote:
> >> It is not uncommon in the history of technology (it has been observed
> back several centuries) that it isn’t so much direct transfer of technology
> but more someone brings back a story along the lines of, ‘I saw this thing
> that did thus and so and kind of looks like t.’ Which gives someone the
> idea, that if it exists, then how it must work like this.’ It isn’t quite
> independent invention, but it isn’t quite direct influence either.
> >>
> >>
> >>
> >> Related comment -- from my various interactions with historians about
> technology history.  If the available technology is limited (as it was in
> the 1950s/60s/70s and early 1980s in many dimensions) then your solutions
> to certain problems are going to look rather similar.  That doesn't meant
> that two similar solutions influenced each other... The trick in writing
> tech history is figuring out where there was a choice space and where there
> wasn't (much of) one.
> >>
> >> Craig
> >>
> >>
> >> --
> >> *****
> >> Craig Partridge's email account for professional society activities and
> mailing lists.
>
>
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