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A case against Boolean logic

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Re: A case against Boolean logic

#31

Post by jfengel »

Daub wrote: post #18
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary. Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can…

> Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can be solved. Is it not true that the brain process in ternary? From the point of view of perception, I believe that we process the world in terms of pairwise comparisons. For example, the atomic indivisible of visual processing is figure/ground separation.

The brain doesn't do any of that. The brain is neural goo.

It can arduously crank through simple logic problems with its ludicrously tiny memory (around 8 bytes). Everything else is intuition and guesswork.

You can try to model those heuristics with various logics. Some logics work better in certain situations. Classical first order logic is actually really bad at modeling brain work, but it's simple to automate, so we use it even where it's wildly inappropriate.

Re: A case against Boolean logic

#32

Post by sam_lowry_ »

peterlada wrote: post #28
Daub wrote: post #18

Earlier quoted context omitted.

> Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can be solved. Is it not true that the brain process in ternary? From the point of view of perception, I believe that we process the world in terms of pairwise comparisons. For example, the atomic indivisible of visual processing is figure/ground separation.

Yes. In opposites and in lack of data (null). Ternary thus fits better. Back in ancient CS classes my prof said that was a Russian attempt of building ternary processors with +1, 0, -1 represented as voltages. Another strike in for-ternary column is that it's the most efficient in the number of digits for representing numbers. Pi is optimally efficient but non-integer bases would break anyone's brain, I think.

Here's a link documenting a the creation of a DIY ternary computer https://hackaday.io/project/28579-homebrew-ternary-computer

The author also made a more approachable miniseries in Russian: https://habr.com/ru/articles/496366/

Re: A case against Boolean logic

#33

Post by LargoLasskhyfv »

mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary. Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can…

Some of us have (balanced) ternary processors. Not even emulated on FPGAs anymore, somewhat more coarse ASIC, without all the IO, just PCIe. They aren't publically available, though.

OTOH there is stuff like this planned to launch, which may compensate that lack of commercial availability somewhat:

https://news.ycombinator.com/item?id=48177736

Though it's not ternary per se, it could be seen as several steps further above that.

Re: A case against Boolean logic

#34

Post by isodude »

My wife does not care whatever excuse I have to why the kitchen is not in order when she comes home.

I failed her anyhow.

Should I tell her that boolean logic is not applicable on my intentions?

Re: A case against Boolean logic

#35

Post by Affric »

peterlada wrote: post #28
Daub wrote: post #18

Earlier quoted context omitted.

> Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can be solved. Is it not true that the brain process in ternary? From the point of view of perception, I believe that we process the world in terms of pairwise comparisons. For example, the atomic indivisible of visual processing is figure/ground separation.

Yes. In opposites and in lack of data (null). Ternary thus fits better. Back in ancient CS classes my prof said that was a Russian attempt of building ternary processors with +1, 0, -1 represented as voltages. Another strike in for-ternary column is that it's the most efficient in the number of digits for representing numbers. Pi is optimally efficient but non-integer bases would break anyone's brain, I think.

I thought e was optimal

Re: A case against Boolean logic

#36

Post by Avshalom »

tgv wrote: post #17
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary. Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can…

> If we had ternary processors, ternary logic would be more popular. Why? Boolean logic is older than its namesake, George Boole (1815-1864). Syllogisms are ancient. And we've had ternary systems, as well as others. And what does the third value represent? True and false are pretty universal when it comes to predicates, but anything in between is rather subjective.

generally a sort of Unknown though it depends on the formulation.

https://en.wikipedia.org/wiki/Three-valued_logic

Re: A case against Boolean logic

#37

Post by entrope »

thin_carapace wrote: post #26

stating a binary choice of options to escape binary thinking ... ironic , intentionally ?

Well, "should you use binary logic?" has an easy answer: yes*. (* - sometimes). There are a lot of cases where it's obviously not the right framework, others where it's useful up to a point, and some where it's absolutely the right approach. The relative frequencies of encountering those categories depends on what one is doing.

Re: A case against Boolean logic

#38

Post by acrobionic »

"Each statement can be true in one context and false in another."

Is this statement itself true in all contexts, or only in some contexts? If it's true in all contexts, then we need an explanation for why this specific statement gets an exception from the rule. If it's false in some contexts, then there exist some contexts where absolute truth/falsity exists, so we can go ahead and use boolean logic just fine in those contexts.

Re: A case against Boolean logic

#39

Post by Tangurena2 »

mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary. Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can…

From an information theory perspective, the most efficient base for computations would be e (2.718). And trinary is closer than binary.

Re: A case against Boolean logic

#40

Post by mcdonje »

tgv wrote: post #17
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary. Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can…

> If we had ternary processors, ternary logic would be more popular. Why? Boolean logic is older than its namesake, George Boole (1815-1864). Syllogisms are ancient. And we've had ternary systems, as well as others. And what does the third value represent? True and false are pretty universal when it comes to predicates, but anything in between is rather subjective.

A bool can be represented by a single bit. A tern(?) takes 2 bits or 1 trit to represent. Alternatively, a bool takes a trit to represent.

So, in terms of radix economy, ternary computing is the most efficient, but you're leaving information density unused if you use it for binary, and representing ternary with binary is inherently inefficient.

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