Comment by theamk | Hacker News Reader

Comment by theamk | Hacker News Reader

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This seems to be a reply to something, but it nos not clear to what? I saw no efficiency claims of trinary on the Tunguska page, so this seems unrelated to it.

That said, I don't understand how you arrived at this:

> anyone can theorize an abstract machine where every discrete "tick" of time will perform a ternary operation in constant time, that doesn't mean such a machine can be efficiently reified if you move it out of the realm of abstraction.

One can definitely create a circuit which will perform a ternary operation in a (some) constant time. It is not hard, and people have done this before [0]. The real question is: can you make a ternary computer which is somehow better (faster, power efficient, cheaper, etc...) than a binary one? But to answer this you need to talk MOSFETS, voltage levels, gate charge, and current tecnhology capabilities. Shannon and Von-Neumann won't help you here.

[0] https://hackaday.io/project/6284-tern-ternary-logic-circuits

> This seems to be a reply to something, but it nos not clear to what? I saw no efficiency claims of trinary on the Tunguska page, so this seems unrelated to it

Sorry if it seems like it's just a floating comment, indeed the article made claims of the kind, and I really think the project (and others like it) is nice. My comment is directed towards the practical concerns and real-world feasibility of a ternary computer, especially with regards to comments that threads like this inevitably attract (as seen on this comment section) that "ternary computers would revolutionize X", and is partly fueled by me having had non-fuitful conversations with coworkers that insisted on this point in the past. Hopefully this helps contextualize my comment a bit better.

> That said, I don't understand how you arrived at [point 3b]. One can definitely create a circuit which will perform a ternary operation in a (some) constant time. The real question is: can you make a ternary computer which is somehow better than a binary one?

I think you and I are in agreement here, so let me try to clarify what I meant:

My point is precisely regarding the arbitrariness with which "constant time" is defined. Asymptotic analysis of algorithms always treats complexity in the "time" dimension as a measurement of discrete "ticks" on computational state, meaning: you can pick any encoding of data you want, and any set of operations you want, and have any "operation" execute instantly as a tick. When analysing "ticks", an algorithm might seem extremely efficient, however that might be a non-reifiable performance gain when you translate from ticks to milliseconds.

For example: assume a binary NAND gate takes 1ms to propagate a stable output signal. All other conditions being equal with respect to manufacturing technology, voltage, and other things you mentioned, I don't see how you could perform "more" computation at the same cost. Sure you can implement a ternary gate that runs in "constant time", but would that constant time still be 1ms? If yes, would it take up the same amount of die space? If yes, would it consume the same amount of power and dissipate the same amount of heat? etc

You'll eventually be tickling the Landauer limit [0] for whatever your manufacturing technology is at some point, no matter if you're doing binary or whatevernary logic, but getting "more compute" for free would be cheating thermodynamics. Improving manufacturing technology is, of course, a viable strategy for squeezing "more computation" into the same physical space, but switching bases will not immediately make Moore's law wither away.

A more succinct way of putting what I'm trying to say into words I guess would be that "all other things being equal, the choice of base is arbitrary with regards to computational and representational power"

Hopefully this helps clear things up :)

[0] https://en.wikipedia.org/wiki/Landauer%27s_principle

Mind that the historical SETUN wasn't built around active switching elements, but was rather based on a ferrit cores architecture.

Um, are we talking about the same "asymptotic analysis"? The one I am talking, the "Big O" notation [0], specifically ignores constant factors. So a naive matrix multiplication algorithm will always be O(n^3) in standard notation, no matter if this is binary or ternary or even ENIAC-style BCD bytes. This means you cannot reason about ternary vs binary using asymptotic notation.

And the Laundauer limit seems completely unrelated. Your link says, "Modern computers use millions of times as much energy per second" -- so we can have 1000x more efficient computer and still be well under the limit.

So the only way to compare the binary vs ternary is in the context of a specific implementation, because that's how you can evaluate the speedup. "All other conditions being equal" is never true -- for example, binary machines can run faster because they need less voltage swing (and thus less bit charge), while ternary machines are faster because balanced adders do not need ripple carry. Which one has more effect? This depends on technology.

Here is a made-up example: let's say we have a small amount of ancient transistors and diodes, and we want to sum up numbers, with range from -5000 to 5000. The transistor switches in 0.1 mS. How do we do it?

In binary, we'd need 14 bit word. Assuming we do ripple-carry adder (it is smallest part count, but slowest), in the worst case we'll need to propagate carry across all bits, and this means we'd need at least 20 mS per operation, getting performance of at most 50 addition/second.

In ternary, we'd need 9-trit word. Ternary adders do not propagate, so we could add the numbers in 2 mS. Here, the ternary is going to be much faster, at 500 addition/sec.

This is a very contrived example (who makes wide ripple-carry adders anyways?) but hopefully this illustrates my point. You cannot use asymptotic analysis for this, and there are times when you can totally perform more computation for the same cost.

[0] https://en.wikipedia.org/wiki/Time_complexity

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