[HN Gopher] Ternary circuits: R=3 is not the Optimal Radix for C...
___________________________________________________________________
Ternary circuits: R=3 is not the Optimal Radix for Computation
(2019)
Author : danny00
Score : 49 points
Date : 2024-01-13 12:29 UTC (10 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| FartyMcFarter wrote:
| > A demonstration that e=2.718 rounded to 3 is the best radix for
| computation is disproved.
|
| Is this some weird attempt at humour, or meant as a serious
| statement? I mean the mention of _e_ of course.
| Tomte wrote:
| It's a fringe idea put forward by a German cryptocurrency (of
| course), and loosely based on some old result by Knuth.
|
| So no, some people really clamor for all of us to switch to
| ternary logic.
| FartyMcFarter wrote:
| Sure, but what does the number _e_ rounded up to 3 have to do
| with it?
| beardyw wrote:
| The golden ratio rounded up is 2. QED.
| Retric wrote:
| It's not quite nonsense:
|
| "100 in decimal has three digits, so its radix economy is
| 10x3 = 30; its binary representation has seven digits
| (1100100 2) so it has radix economy 2x7 = 14 in base 2;
| in base 3 its representation has five digits (10201 3)
| with a radix economy of 3x5 = 15; in base 36 (2S 36) its
| radix economy is 36x2 = 72."
| https://en.wikipedia.org/wiki/Radix_economy
|
| The idea being that there's a tradeoff between the cost
| of each digit vs the number of digits you need. However
| we use base 2 because the cost of base 3 is more than 50%
| higher than using base 2.
| ymerej wrote:
| Best mic drop.
| wk_end wrote:
| The article explains this:
|
| > For computation, radix R = 3 would be more economical
| than R = 2 because the "optimal" radix would be R = e =
| 2.718, according to a demonstration presented in [1].
|
| Where [1] is "S.L. Hurst, "Multiple-Valued Logic - Its
| Status and Its Future", IEEE Trans. on Computers, VOL.
| C-33, No 12, December 1984." I can't find that one for free
| anywhere, but there's your lead.
| downvotetruth wrote:
| IEEE754 enters chat - synthwave starts banging
| mrob wrote:
| See https://en.wikipedia.org/wiki/Radix_economy
| hexomancer wrote:
| If you assume the complexity of an elements grows linearly
| with the number of states it can assume (e.g. if complexity
| of a bit is 2a then complexity of a trit is 3a). Then the
| total complexity of for example representing a number N is
| log{N}_{B} \times B \times a. Minimizing this with respect
| to B yields B=e.
| woadwarrior01 wrote:
| Not too fringe of an idea, IMO. The idea of tri-state logic
| is fairly ubiquitous in analog electronics. Also, was a
| family of Soviet ternary computers[1] that were fairly
| competitive with their contemporary binary logic based
| counterparts.
|
| [1]: https://en.wikipedia.org/wiki/Setun
| Tomte wrote:
| Okay, let me more precise: the fringe idea in Iota was to
| insist on ternary logic implemented in software on binary
| logic hardware.
| woadwarrior01 wrote:
| I didn't know what IOTA is and had to look it up. And I
| agree with your assessment, I suspect their decision was
| motivated by marketing reasons and not technical reasons.
| IshKebab wrote:
| It's not a joke. e is theoretically the most efficient base. Of
| course you can't actually have fractional bases so the most
| efficient real base (again, theoretically) is 3.
|
| This paper is just showing that with real technology it's still
| less efficient than 2. I don't think anyone was really
| suggesting that we switch to base 3 hardware so it's a
| completely academic result, but still interesting.
| scapp wrote:
| 2 line explanation of where e comes from here: to represent a
| number x in base b, you need roughly log_b(x) digits. If you
| weight that by the number of different digits in base b, you
| get b * log_b(x) = b * log(x)/log(b) = b/log(b) * log(x) (where
| now the log is any base you care to choose).
|
| So assuming x > 1, this is minimized precisely when b/log(b) is
| minimized. The derivative of b/log(b) is (log(b) -
| log(e))/log(b)^2, so this is zero when b = e. (The second
| derivative is 1/(e log(e)) > 0, so this is a minimum).
| remcob wrote:
| Why should we weigh by the number of different digits? I.e.
| is there an argument why the cost of a single digit is
| linearly proportional to the number of values it can hold?
|
| To me this seems like the weak point in the argument.
| scotty79 wrote:
| Why does the number of digits in the base should matter?
| asimpletune wrote:
| It's called radix economy. Different radices have different
| efficiencies as defined by the ratio of number of digits in
| a radix alphabet over the number of placeholders required.
|
| Simple example, base 1 is obviously inefficient once
| counting past 1. Similarly base 1 million is inefficient
| (until you're counting in the bazillions)
| scotty79 wrote:
| If you can store one digit of a number base million in
| one physical element then it's exactly as efficient when
| it comes to storage of digits as binary. One element per
| one digit.
|
| But it's about 20 times more efficient when it comes to
| storage of whole numbers because you can store number up
| to a million in a single physical elements while binary
| needs 20 elements.
| asimpletune wrote:
| I see what you're trying to say, like I understand the
| intuition, but like I was saying earlier this is an
| already understood topic
| https://en.wikipedia.org/wiki/Radix_economy and that
| point has been addressed. Sorry, not trying to be a jerk.
| Just wanted to point that out in case you're interested
| in this subject.
|
| In the example you gave, I'm assuming by 'physical
| element' you mean 'placeholder' or digit. Storing more
| numbers in a single placeholder seems like you're just
| getting efficiency for free, but that's not how
| information works. You have to come up with a unique
| symbol for one million numbers (0 - 999,999). Which you
| have to pay for.
|
| base 64 is a more realistic example. With 64 characters
| per digit, it may seem like it's more efficient, since
| you require less digits to express the same number as
| base 10 or 2, but you still have to encode 64 unique
| characters, and it ends up being less efficient. That
| doesn't mean less efficient is worse. It just means it is
| more specialized and used for different things. For
| example, base64 gets used when you want to encode
| information in a small amount of space. Otherwise, for
| the actual storage and computation of data, lower bases
| are preferred, and base 64 is still obviously stored as
| binary.
|
| For what it's worth, the base integer with the best radix
| economy is 3, followed by 2.
| gnramires wrote:
| I think the b factor is due to the analog representation:
| if the base has b values, you use on average b/2 voltage
| for representation. I would think the mean square value in
| might have been more appropriate though? (as voltage energy
| losses usually are V^2 / R or C V^2)
|
| Repeating the calculation (for k bits and b values) using
| square values, you get E = b^2 * log_b(k) and dE/db =
| 2b/ln(b) - b^2 / (ln(b))^2 / b = b/ln(b) * (2 - 1/ln(b)).
| Setting dE/db to 0, we get 2 - 1/ln(b) = 0, ln(b) = 1/2,
|
| b_opt = sqrt(e) = 1.6487...
| adrian_b wrote:
| No there has been such a demonstration, which they quote and
| from which they show the results:
|
| S.L. Hurst, "Multiple-Valued Logic - Its Status and Its
| Future", IEEE Trans. on Computers, VOL. C-33, No 12, December
| 1984.
|
| According to that demonstration, _e_ would be optimal, but it
| is impossible because it is not integer. Among integers, 3 is
| best, followed by 2 and 4, which are equally good.
|
| However, as mentioned in the article, the difference between 2
| and 3 is very small and that classic demonstration does not
| take into account the difference in the complexity of the logic
| gates and registers for binary and ternary logic.
| schiffern wrote:
| A bit (trit?) of background:
| https://web.williams.edu/Mathematics/sjmiller/public_html/10...
|
| I'd be curious whether the same result holds for balanced
| ternary, as used in some early Soviet computers.
| https://en.wikipedia.org/wiki/Balanced_ternary
| moefh wrote:
| It doesn't matter what the voltage levels represent ([-1,0,1]
| in balanced ternary or [0,1,2] in "normal" ternary). The only
| thing that matters is that you're working with 3 voltage levels
| instead of 2, which as the paper shows increases the circuit
| complexity above the "break even" point of log(3)/log(2).
| beefman wrote:
| Better url for the Hayes article:
| https://www.americanscientist.org/article/third-base
| mat_trw wrote:
| Using the fact MOSFET can only have two distinct states to prove
| that the binary positional system is superior to ternary is a bit
| like using the number of fingers we have to argue that decimal is
| the best number system to work in.
|
| Not sure what the author was thinking when he wrote the paper but
| this is one of the cases where peer review would have helped him
| a lot to make less grand statements.
|
| >Until tri-state transistors are mass produced binary encoding of
| numbers is the natural system for computers to work in.
|
| From memory the Setun used vacuum tubes which could natively
| handle three states at the hardware level.
| spiffytech wrote:
| > a bit like using the number of fingers we have to argue that
| decimal is the best number system to work in.
|
| Fun fact unrelated to your main point: some ancient peoples
| counted on their knuckles, using their thumb to point to each
| one. This let them count in multiples of 12 (3 knuckles on each
| of 4 fingers), then use their other hand to count out
| multiples! You can count as high as 72 this way, which was
| great for ancient cultures oriented around highly composite
| numbers like 12, 24, and 60.
| adastra22 wrote:
| I like to believe this is true because it makes sense, but it
| was a theory invented in the 20th century to try to explain
| how they did math in everyday settings. We don't actually
| know if it is true. We just know that they used base-60
| systems.
| spiffytech wrote:
| Oh, good to know!
| otabdeveloper4 wrote:
| Yeah, 60 was likely used because it divides by 2,3,4,5,6
| and 10, 12 and 15. I imagine it makes dealing with
| fractions much easier.
| cydodon wrote:
| I was wondering, can't you count to 144 (12 x 12) using two
| hands using this knuckle counting approach?
| meindnoch wrote:
| Or 169 (13 x 13).
| HPsquared wrote:
| I mean, even without knuckles you have 10 bits to play with.
| If you also curl your toes, that's 12 bits. So an average
| person could count to 4095.
| xerox13ster wrote:
| I actually figured out how to count up in binary on my
| fingers and you can get way higher if you use your thumbs
| for the lowest two bits, and bent fingers as bits
| differentiated from a fully extended finger. All the way to
| 262,143.
| gumby wrote:
| > some ancient peoples counted on their knuckles, using their
| thumb to point to each one.
|
| I don't know how "ancient" you're talking about: my mother
| (b. 1937) used such a system and taught it to us as kids.
| FWIW she grew up in south east Asia.
| NohatCoder wrote:
| The way we use transistors does not leave any room for tri-
| level circuits to be more efficient.
|
| The high clock speeds we get rely on fast switching of power
| levels, this is generally done by targeting a voltage well
| beyond the switching threshold. The smallest transistors we
| produce generally have a big variability in amplification, they
| would be really bad for analogue circuitry, but in digital they
| just have to amplify enough, and it is ok if some of them
| amplify way better than that.
|
| Now consider tri-state, we have to target a voltage in the
| middle band if we are to produce the middle signal, so less
| room for over-targeting means slower switching. We probably
| also need to supply the whole circuit a higher voltage to make
| proper room for the signal levels, that is a big L in
| efficiency.
|
| One could build a circuit with three levels of input current,
| but that ends up more or less doubling the transistor count, so
| not an obvious win. I guess that is what the Setun did. If
| adding this complexity to a tube doesn't increase its cost much
| I guess that makes sense, but in the transistor world it is
| just a doubling.
| theamk wrote:
| Seems pretty relevant to me, based on the fact that transistors
| in switching mode are so superior to other computing
| technologies (see sibling comment for explanation of why) that
| all computers in recent decades are using it exclusively. And
| for those, paper's conclusions are valid.
|
| A paper about high efficiency tri-level logic cell which is
| cheap and energy-efficient would be very interesting but sadly
| I don't think this is possible, at least I haven't seen one nor
| even have a clue about how one would go about making one. And I
| have been watching this area with interest.
| adrian_b wrote:
| A variable resistor has only 2 values where the power
| dissipation becomes negligible, when the resistance is null or
| infinite.
|
| Therefore any transistor, triode or any other controllable
| device has only 2 states, i.e. on and off, where the power
| consumption is negligible.
|
| Any kind of logic circuits that use transistors or triodes that
| stay in any other intermediate states between on and off (like
| in analog circuits) would consume too much power and would
| overheat. A MOSFET can have any intermediate state between on
| and off, the current through it can be varied continuously as a
| function of the gate voltage, but it will dissipate a great
| amount of power in any of the intermediate states. There is no
| difference from this point of view between MOSFETs and vacuum
| tubes. Setun just had too few and too big vacuum tubes to worry
| about the power consumption.
|
| The kinds of logic circuits where not all transistors or
| triodes are on or off have been abandoned 40 years ago and
| there is no chance for them to ever come back, because at the
| current component densities their power consumption would be
| enormous.
|
| The only way to use devices with more than 2 states in logic
| circuits would be to use devices with a variable reactance, for
| instance varicap diodes, because those do not consume active
| power.
|
| However the devices with controllable reactance cannot use DC
| power supplies, they need AC power supplies, which creates a
| lot of problems for which there are no known solutions at this
| time, so nobody has designed yet a complex logic circuit based
| on controllable reactances instead of transistors.
|
| As long as electronic devices with DC power supplies will be
| used, binary logic is the only kind of logic permitted by the
| energetic constraints.
|
| Only in the non-volatile flash memories, multiple values of
| electric charge can be stored in a capacitor, because it does
| not consume any power for storage.
| zozbot234 wrote:
| > Only in the non-volatile flash memories, multiple values of
| electric charge can be stored in a capacitor, because it does
| not consume any power for storage.
|
| DRAM also uses a capacitor to store data so it could support
| more than one bit per cell too.
| adrian_b wrote:
| That is unlikely to work because the DRAM capacitor is
| lossy, the charge stored in it diminishes quickly and soon
| it would become impossible to guess which was the initial
| value of the charge.
|
| Using multiple values for the stored charge would force a
| drastic reduction in the refresh time, which would increase
| the power consumption and diminish the read/write
| throughput.
| londons_explore wrote:
| To me it's pretty clear that continuously variable (ie. base
| infinity) is optimal for computation per unit energy when you
| have additive thermal noise and quantization by the plank energy.
|
| Modern comms systems are heading in that direction with OFDM and
| large QAM constellations with lots of ECC to get more data
| throughput for the same transmit power on the same channel.
|
| One day we might get to need to do that for computation too - but
| for now, binary is doing well.
| arbitrandomuser wrote:
| Isnt that analogue computation
| acjohnson55 wrote:
| I'm not sure how logic and circuit design would look in that
| case. For communications, you're ultimately trying to get a
| representation of a bit stream from point A to B.
|
| At some point, maybe you end up not doing exact computation but
| basically creating neural-like architectures that learn
| responsibilities, which compose up to a fully functional
| computer.
| rini17 wrote:
| Oh yes the data will homomorphically encoded into white noise,
| then computed stored and decoded, all near planck energy per
| bit :)
| gnramires wrote:
| It's tricky because as noise increases, large constellations,
| although perhaps in theory with advanced statistical decoding
| (where you consider P(Symbol|Received signal)) they're
| advantageous, become less viable and more demanding
| computationally. Usually the gains are a small factor. At one
| point, the energy cost of computation required to make
| statistical decoding[1] surpasses any gains from increases in
| complexity.
|
| More than that, the ratio of channel energy (or cost)
| requirement to computational energy can vary :) For example, if
| you're transmitting a message to a space probe, the energy and
| costs associating with message transmission are enormous, such
| that the decoding energy will be a lower proportion (favoring
| more complex decoding systems). For a computer bus transmitting
| signals internally at short distances, the energy cost of
| encoding (and even using QAM or non-binary encoding at all) and
| statistical decoding will probably be less than the energy
| gains.
|
| Credit to Christopher Blake et. al in this paper: (as seen on
| Canadian Workshop on Information Theory :) )
|
| https://tspace.library.utoronto.ca/bitstream/1807/69482/1/IT...
|
| From the abstract: "This implies that the average energy per
| decoded bit must approach infinity for any sequence of decoders
| that approaches capacity" (valid for the VLSI model in
| question, and binary channel model, but I'd guess this
| generalizes to any physical computational medium)[2]
|
| It's really interesting how in the context more complex isn't
| always better.
|
| [1] Usually the complexity of the whole system, in more
| practical terms, is determinant as well -- because engineering
| and maintaining complex systems is difficult
|
| [2] More precisely: "It is shown that for any sequence of
| increasing-block-length decoder circuits implemented according
| to this model, if the probability of block error is
| asymptotically less than 1/2 then the energy of the computation
| scales at least as O (n[?]log n), and so the energy of decoding
| per bit must scale at least as O ([?]log n)"
| adrian_b wrote:
| OFDM and QAM are techniques that increase the data throughput
| through a channel of fixed bandwidth, but this is achieved by
| increasing the transmission power more than the increase in
| speed.
|
| They are not at all efficient from the point of view of the
| energy consumption.
|
| The best energy efficiency is achieved with quadrature phase
| modulation (QPSK), which allows very low transmission powers
| relative to the noise of the communication channel.
|
| Any increase of speed above that is obtained by a worse energy
| efficiency.
|
| Despite that, OFDM and large QAM constellations are very
| frequently used because for the modern WiFi or mobile phone
| communication it is typical to be very close to the access
| point or to the cell phone tower so the transmitter is able to
| use a power much greater than the minimum necessary, in order
| to increase the data throughput.
|
| For logic circuits, the constraints are very different than for
| communication channels. If the logic circuits use DC power
| supplies, then the controllable elements, like transistors or
| vacuum tubes, must use only 2 states, on and off, otherwise
| they would consume too much power. So even if one would want to
| make a gate with ternary logic, it would have to be composed of
| transistors with binary states, otherwise it will overheat at
| the current circuit densities.
| fghorow wrote:
| There are three kinds of people in this world.
|
| Those who understand ternary. Those who don't understand ternary.
| And...
| ashirviskas wrote:
| Both??
| jabl wrote:
| ... and the Dunning-Kruger people who think they understand but
| actually dont't?
| teekert wrote:
| ... and those that know the autocorrelation story?
| freeopinion wrote:
| Those who resort to spelling the number 10.
| raverbashing wrote:
| The ones who are kinda split on it
| jesprenj wrote:
| Note that this paper does not mention balanced ternary and only
| presents tables, diagrams and results for unbalanced ternary with
| values 0, 1 and 2.
|
| The Setun computer, mentioned in the introduction, however, used
| balanced ternary with values -1, 0 and 1. Balanced odd bases
| consist of digits centered around zero.
|
| Could balanced ternary redeem it's position with logic cirtuits
| in mind?
| rini17 wrote:
| Using positive and negative voltages to represent balanced
| ternary requires both positive and negative power supply. They
| do mention that having additional Vcc is problematic. At least
| on our 2D chips, but we don't have any high density integration
| alternative, vacuum tubes are irrelevant.
| asimpletune wrote:
| Yeah, I mean until we have ternary transistors, emulating ternary
| circuits will be less efficient than actual binary circuits. If
| we ever have ternary transistors, then ternary circuits will be
| an improvement over binary ones.
|
| Here's a little ternary logic riddle for the HN community:
|
| Two people are sitting at a restaurant, deciding what to order.
| Neither had communicated with one another when the waiter appears
| and asks one of them "Is everyone ready to order?". They reply
| "Hm, I don't know". The other person immediately then says "Now
| we are." Why?
|
| (As in, how did the second person know?)
| ameminator wrote:
| Spoiler:
|
| If the first person did not want to eat, he would have answered
| "No, _we_ are not ready ". Him not being ready is enough to
| negate the whole thing. He doesn't know if the both of them are
| ready to eat though, because he doesn't know that the second
| man is ready or not (the second man hasn't revealed his state
| yet).
|
| Therefore, the second man knows that the first is ready to eat,
| since the first's answer is "I don't know". Since the second
| man knows that he himself is ready to eat, he can answer: "we
| are both ready to eat".
| Cpoll wrote:
| Added fun: This riddle can be generalized to N people sitting
| at a restaurant :)
| asimpletune wrote:
| O haha, yeah, that one is super mind bending. I heard a
| riddle that used that trick once about people being able to
| leave an island when they know what their eye color is. It's
| super cool because it feels like you're basically embedding
| memory into a purely logical expression, since you're allowed
| to assume that all the islanders (or in the case above,
| diners) are perfectly logical, and therefore by logic alone a
| counter of sorts emerges.
|
| Not sure if I explained that part well, but I can write the
| riddle somewhere and share it one day, since it needs to be
| explained more precisely to demonstrate this N-people effect.
| arccy wrote:
| https://www.youtube.com/watch?v=98TQv5IAtY8
| atoav wrote:
| Person A does not know because they don't whether Person B is
| ready. If Person A was not ready themselves they would know the
| answer is No. We assume here that people know wherher they
| themselves are ready.
|
| Person B then can safely assume Person A is ready and if they
| are ready themselves they are now indeed ready.
| mlcruz wrote:
| If the first person was not ready to order, he would know that
| everyone is not ready to order. Since he doesn't know, that
| means he is ready to order, but is not aware of the second
| person readiness.
|
| So the second person knows that the first person is ready
| chrismorgan wrote:
| For best results, generalise to N, and have everyone remain
| _silent_ for a short time, before someone (or everyone
| simultaneously, your choice) answers "yes".
| Dylan16807 wrote:
| That assumes person A has figured out if person A is ready, and
| assuming that is not a good idea in the real world.
|
| It also assumes they're directly answering the question instead
| of indirectly answering it.
| asimpletune wrote:
| > That assumes person A has figured out if person A is ready
|
| Not sure I understand that. Did you mean it assumes that
| person B has figured out that person A is ready?
| Dylan16807 wrote:
| I didn't have a typo. Also I'm going to use names now
| because letters are hard to read.
|
| The _way_ Bob found out that Alice was ready was because
| Alice was uncertain about group readiness.
|
| Maybe Alice was uncertain because she knew her own
| readiness but not Bob's readiness. This is the way the
| riddle works.
|
| But maybe Alice wasn't sure of her own readiness. In that
| case Bob should not answer.
|
| -
|
| And, second issue, what if Alice was saying "Hm, I don't
| know [what to pick]." as a way to tell the waiter that no,
| everyone is not ready.
| asimpletune wrote:
| > But maybe Alice wasn't sure of her own readiness
|
| I'm not sure I understand how Alice could be unsure of
| her own readiness. If she's not ready, then she would
| have said "no, everybody is not ready to order."
|
| > And, second issue, what if Alice was saying "Hm, I
| don't know [what to pick]." as a way to tell the waiter
| that no, everyone is not ready.
|
| Because the riddle is "how did he [Bob] know?". We are
| told from the start that Bob is right, and asked to
| explain why.
| Dylan16807 wrote:
| > I'm not sure I understand how Alice could be unsure of
| her own readiness. If she's not ready, then she would
| have said "no, everybody is not ready to order."
|
| You don't understand how someone can be unsure if they're
| ready? Have you never been kind of anxious or indecisive
| before? (The answer is definitely not "you're not ready
| until the anxiety and indecision are gone".)
|
| > Because the riddle is "how did he [Bob] know?". We are
| told from the start that Bob is right, and asked to
| explain why.
|
| There's a reason I said "in the real world".
| cat_plus_plus wrote:
| Doesn't it depend on what problem you are solving and which
| building blocks you are starting with? Say you have a reversible
| electric motor. This will likely enable lighter/cheaper/more
| efficient/more reliable designs than one or two unidirectional
| motors and transmission to redirect the torque in desired
| direction. And if you can come up with tranary circuits for the
| controller, you again have fewer elements and less power losses
| compared to binary circuits.
|
| Now, if you are going to build trenary circuits out of binary
| flip flops, you are wasting one state available out of 4 with two
| flip flops, so clearly suboptimal. You need unique interfaces and
| physics for each element to benefit from efficiency. Even unique
| programming languages - binary if/else logic is common, it could
| be that in real world if/else/unknown is common and can be
| handled more efficiently by trenary circuits, or new algorithms
| can be created to utilize a hardware-implemented trenary bit.
|
| Of course, a likely answer is that, now that binary hardware and
| software is highly developed, it's not worth it to do complete
| redesigns for modest efficiency gains.
| Dylan16807 wrote:
| I'm pretty skeptical of this scenario. Motors are quite high
| power and require big dedicated amplifiers. I would expect a
| negligible difference from the amplifier input being two bits,
| or one trit, or a separate wire per state.
| theamk wrote:
| Physics is pretty harsh, and it really likes two-state
| circuits. One reason is well described in [0]: power
| consumption P=I*V.. With binary logic, one state means V=0 so
| power is zero; other state means I=0 so power is zero again;
| any sort of intermediate values means non-zero power
| consumption, which, when multiplied by a huge number of
| elements per IC means extreme heat and power wasting.
|
| And "existing software" never stopped innovations: we get all-
| new computation models all the time.. there are FPGAs and IRAMs
| and transputers and memristors and analog AI, and perhaps even
| GPU and DSP. None of them can use existing binary software and
| some of them have non-binary hardware. They don't all work well
| all the time, and yet people keep innovating and trying to find
| ways to make them work.
|
| And yet no one (outside of hobbyists) works on ternary
| computers. Physics is harsh.
|
| [0] https://news.ycombinator.com/item?id=38984009
| worik wrote:
| I do not follow the theory. But in implementation there is a
| counter example: https://en.m.wikipedia.org/wiki/Setun
|
| This was a ternary computer built by Soviet mathematicians
|
| > Between 1965 and 1970, a regular binary computer was used at
| Moscow State University to replace it [setun] Although this
| replacement binary computer performed equally well, it was 2.5
| times the cost of the Setun.[2]
| theamk wrote:
| does not look like counter-example to me:
|
| > Due to the low reliability of the computer elements on vacuum
| tubes and inaccessibility of transistors the fast elements on
| miniature ferrite cores and semiconductor diodes were designed.
|
| Perhaps trinary is be a good idea if you don't have access to
| transistors or to reliable vacuum tubes, but do have access to
| diodes and miniature ferrite cores.
|
| I don't see however how this is relevant today - we certainly
| have access to great transistors now, and as the paper shows
| with transistors, binary rules.
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