[ivan.moony]

I just thought of a little something. Logic language (besides operators and, or, not, then) has only two constants: true and false. And it bases its conclusions on the formula: if it is not true then it is false and otherwise (two formulas).

What if there would exist a language with three or more constants? Like if we have three constants, say 1, 2 and 3, we would base our conclusions with the formula: if it is not 1 and it is not 2 then it must be 3 (and other two analogous formulas for deriving 1 and for 2).

Thinking further, what if we have infinite count of constants, like natural numbers? Then we would miss the "not" operator. Something comes to mind, like "not" being equivalent to operation on negative numbers. Maybe a math science is like this form of logic?

Thinking more further, what if we have a decimal count of constants (mind blowing)? Let's say we have a count of 2.71 constants (natural number e)? How would "not" operator behave now?

And what if we have a theory about sliding number of constants? I can smell a new logic coming in the future, a logic which defines operations on theories with arbitrary number of constants...

Edit: Hehe, I probably took too much soya for launch   

[Ultron]

Would probably help a movie plot involving the exploration of an alien culture, but not math. The more 'constants' or 'possibilities' you have, the more complicated the system gets.

What are the advantages of such a system over the existing one? Logic is more efficient and calculations have higher accuracy when the system is less complex.

You said that "if it is not 1 or 2, then it must be 3"... Why add another element when there is no need - the answer could simply be represented as a combination of the two inputs - "if it is not 1 or 2 then it must be 1 + 2.". Now, I do realize that in this case there are other possibilities and these two statements of ours are not quite accurate (and represent a terrible example) but I know you understood what I am saying.
You should read up a little on logic gates - honestly, I learned about how they work through Minecraft and specific mods, which actually turned out to be a very efficient learning method.

Maybe it would make for an interesting experiment - proving that such a logical system is even possible would be an astonishing accomplishment, however I doubt it would have practical implementations. But to prove that, first you need to answer this - if it not true nor false, then it must be...? And how would you explain it in terms of math? Are you sure the answer cannot be represented by somehow permuting the two inputs (T and F) ?


P.S. I just noticed the new ranks

[Snowman]

True, False, NULL (or I don't know)

Does Fred want to eat? True
Does Art want to eat? False
Does Claude want to eat? I don't know.

I learned an awful lot about logic gates and computer circuits through Minecraft too... Hurray for Nerdcraft!!!

A lot of our logic circuits are made using transistors. A transistor is either on or off... aka 1 or 0.

However, a memristor can be OFF.. a little ON... a little more ON... and finally totally ON. Memristors are what makes your brain's neurons work. Its highly complex and way cool. No more 1 and 0.. but every number from 0 to 1.

Circuits based on the memristor can have an infinite number of states between 0 and 1.

[8pla.net]

0 and 1 are symbols, which have no meaning. 
These symbols are stored in a symbol table.

When we run out of symbols to use from the symbol table,
in the first register, then we add a second register.

When we run out of symbols to use from symbol table,
in the second register, then we add a third register.

When we run out of symbols to use from symbol table,
in the third register, then we add a fourth register.

Start with the first register: [ 0 ]... [ 1 ] 
Add a second register:  [ 1 ][ 0 ]... [ 1 ][ 1 ] 
Add a third register:  [ 1 ][ 0 ][ 0 ]... [ 1 ][ 0 ][ 1 ]... [ 1 ][ 1 ][ 0 ]... [ 1 ][ 1 ][ 1 ]
Add a fourth register:  [ 1 ][ 0 ][ 0 ][ 0 ]...

Notice how with counting to ten we use all the symbols zero through nine,
before we add a second register to make ten.  There are more symbols in
the symbol table, for decimal.  So we don't run out as fast... So we don't
add registers as often.  However, when we do eventually run out of symbols
zero through nine to use, from our symbol table,  we add another register ...  10, 100, 1000.

[ranch vermin]

I guess what your saying could be,  why use a binary tree,  when you can use a tri tree?   They should both work    But depends on what runs faster is what you would do,  because they are interchangable with each other!

[Snowman]

I believe they have already made ternary computers. Its supposed to be more efficient. I believe someone even made a wooden ternary pc once. Yep, some people have a lot of time on their hands. Obviously, they made the decision to keep binary.

Read more about it here
https://en.wikipedia.org/wiki/Ternary_computer   

[Ultron]

Does Fred want to eat? True
Does Art want to eat? False
Does Claude want to eat? I don't know.

The reason there are two states is because a device can either be on or off. Either there is flowing electricity, or there isn't.

And I did read the article on memristors. I find them pointless here - maybe they will be good for some memory materials not requiring circuits. But changing the voltage doesn't mean anything - the memristor still either has electricity flowing through it, or it doesn't. No matter how much volts or amps it has, it is still 'true'.

Circuits based on the memristor can have an infinite number of states between 0 and 1.

Why do we need them? They only make the job more complicated and not only for the hardware developers, but programmers too.
We have managed to achieve so much with just two states and we know that there are infinite possibilities. Speed can only be negatively affected by such a system (with >2 possible values).


Maybe there is possibility for these systems and maybe they could reach the speed of the binary system - but there really isn't a point to all that massive changing for a few extra kHz or MHz. All our programming knowledge is based on this binary and logic system, and if we change it we need to start from scratch. Also, it would not be logical anymore - in math, a boolean variable can either be true or false. This was not invented with the computer - math came first and if there were a better way it would be here.


Also, our minds naturally function on the same basic principles as boolean logic - at least it is my personal theory (I have not checked for research by others). So if millions of years of evolution didn't figure out a better system, neither will we.


So my point - simple is better. And I don't see what can't be done with the 3 basic logic gates and 2 base values we have today.


P.S. NULL == false

[Snowman]

I'm not attempting to argue with you ; I just find this subject very fascinating. That's why I spent a lot of time in minecraft trying to figure this stuff out. Its all so cool.

I was trying to think of how to convey my thoughts. I'm not trying to be offensive. Please take my theory with benign contemplation in mind. If I'm wrong, it doesn't bother me one bit  .

In theory you only have True and False, but in reality (real world scenarios) you have an area of change. This is why Isaac Newton help created calculus, to account for this change. Electricity does not instantly turn ON and OFF, there is a stage where it is transitioning. Boolean logic cannot take into account this transition/change, because Boolean only can see something in one state or the other. That is why I said Boolean is only theoretical and will remain that (maybe  ).

Transistors are technically analog. They are never truly in an OFF state, at least not in the real world. Some silly electron always manages to sneak by. But even if all parts were working perfectly, which I'm pretty sure is technically impossible, we still have to contend with the state of transition. If there was no transition then their is no change in condition.

So I pose this as a technical question. What will be the value of Boolean logic within the transition phase between False and True? Remember it cannot be True or False because they represent the non-transition phases. This is why I was theorizing that it would be NULL ("Nothing" in Visual Basic). Ie. False -> Nothing -> True

Basically, life is analog while true digital will always remain in theory.
(I could be wrong about all of this, but hey, its ok to be wrong )

The memristor is an analog part. It can be in any stage between 0 and 1. It is true that you can mimic these states with Boolean logic but you cannot get the precision as you would with an analog part. You would need hundreds of transistors to even come close to equaling one memristor.

There are lots of resources that talk about memristors. Its true that many want to use it as high capacity memory, but its real value will be in replacing multiple transistors with just one memristor. Also, memristors run cooler than transistors and are cheaper to make. Ultimately, memristors will make computer circuits a lot smaller than they are now.  I got this info from reading lots and lots of articles and YouTube vids on the memristor (which makes me an expert ).

Anyway, I'm writing this because its a healthy habit to try to stretch your imagination and figure this stuff out. I really ought to start a memristor thread and accumulate all I can find out about it. It really is a revolutionary part. There are so many cool uses for it. It makes me excited about the future of PCs.

Peace out.

PS. Please be kind to me, I'm 35, living at my parents house, and spending Valentines Day on the computer.

[Art]

Snowy, I like you man, but you really need to get out more.
Maybe move to a big city for a while where there's lots of people to choose from.
Diversity, is always opportunity for new perspectives on life and other things.

Happy Valentines Day old friend!!

[8pla.net]

In reference to what Snowman said, "Circuits based on the memristor can have an infinite number of states between 0 and 1."

Did you know?  Binary can have an infinite number of states between 0 and 1 too. 

In reference to what Ultron7 asked, "And how would you explain it in terms of math?"

Although binary is nothing but zeros and ones, if we know which binary digit
represents zero we can use an implied floating point.

Then as soon as we put a binary one to the left of the implied floating point,
we have our first binary fraction, which is a half, or 0.5 in decimal.

We can put a binary zero to the left of the floating point, followed by a binary one
to the left of that, and we have a one fourth fraction.

Please don't be confused if you are on a programming calculator.  I prefer to map floating point binary from right to left.   So 1.0 would be read from right to left, as: binary zero point one  (not as: binary one point zero).

Some examples:
Binary   <-- = Decimal -->   Fraction: -->
Binary   1.0 = Decimal 0.5   Fraction: 1/2
Binary  10.0 = Decimal 0.25  Fraction: 1/4
Binary  11.0 = Decimal 0.75  Fraction: 3/4
Binary 100.0 = Decimal 0.125 Fraction: 1/8

NOTE: Programming calculators may work from left to right: 0.1, 0.01, 0.11, 0.001
which is fine, but that may not be the best mapping for machine code.

[ranch vermin]

PS. Please be kind to me, I'm 35, living at my parents house, and spending Valentines Day on the computer.      that means you must be a genius, keep thinking! the grandest thing I think we can do as a human person.

Memristors must be excellent,  I wonder what happens to keep the current keeping the value properly.    Hardware wizardry.     I still havent seen a flat transistor yet,  only a flat resistor.   I wonder what a memristor looks like,  maybe like a flat qubit,  I bet it looks an amazing piece of jewelry indeed.

[Don Patrick]

The reason there are two states is because a device can either be on or off. Either there is flowing electricity, or there isn't.

Yeah? What level of voltage?

As a programmer I've often wished boleans had a third neutral value to indicate that a certain parameter was not applicable, resultless, to be ignored. Instead I have to resort to integers, use a value of 0 to ignore the variable, a negative value to indicate "not" but that still reads as 'true' since it has a value, and a positive value that also reads as 'true'. Dividing by my 'neutral' 0 value will crash a program, so I end up always having to check the value before using it. Binary is clumsy for programming.

Also, trinary computers would increase speed and capacity by an exponential degree, if you care about techs. Binary = 2x2x2 = 8, trinary = 3x3x3 = 27 over the span of 3 'bits'.

That said, who needs bolean constants when you can use numbers for a range of values? Thinking in terms of "true" or "false" is not recommendable when building AI that has to deal with the real world, where everything is a degree of~.

[Ultron]

Note: I originally wrote this during the most recent maintenance and I forgot to re-post it.

I am not trying to argue with you (or anyone) ranch. It is very pleasuring to me when I have these discussions with smart people in a friendly tone. However I can sound (seem) to be arguing - not my fault I can't write my intonation

Anyway, while you did make some valid points, you have not completely understood the concept of boolean logic (again, no offense). You did get me thinking on how to explain with logic the transition from ON to OFF within an electric load (transistor or light bulb), and I came up with an answer:

While a computer checks the state of a transistor (ON or OFF) in real life this is more complex, but a computer cannot register it because it is too, small. Specifically, it's the electrons and atoms. I am sure you could describe the state of the transistor to extremely high accuracy with boolean logic, by taking the state of every atom.

I am not sure how well I described that, but let me put it this way. With 0 and 1 we can basically represent every possible number we can think of - and as far as I know, the state of the transistor can be described as "int voltage" and you get something like 35,34,33...1,0 mV (or mA, depends how you define 'state').
You can describe virtually everything with 0 and 1, even the half-integer quantum states, except that is a somewhat more complicated concept which I could go on explaining for months, simply because of Einstein's law - "if you can't explain it simply, you don't understand well enough...".

P.S. I am also on my computer on valentine, which I do not find depressing. Then again, I am a freak that spends Friday and Saturday nights programming and watching comic-inspired TV shows. Also, I dumped my girlfriend tonight simply because I have regular training sessions every Saturday - our priorities in life define how we are. If that value is NULL, that is also defining something

[8pla.net]

Binary = 2x2x2 = 8, trinary = 3x3x3 = 27 over the span of 3 'bits'.

Hmm?  Why 3 bits, Don ?

In trinary 3^3 it is 4 trits  (trinary digits) 1000
3^0, 3^1, 3^2, 3^3 (trinary)
1,3,9,27

In binary 3^3 is 5 bits (binary digits) 11011
2^0, 2^1, 2^2, 2^3, 2^4, 2^5
1, 2, 4, 8, 16

Thanks for your response in advance.

[Art]

I thought Binary was based on two states a 1 or 0 whereas a Ternary or Trinary system was based on three possible states, -1, 0, 1.

The soviets had developed a Ternary based computer in the mid 1950's that was claimed to be faster and require less energy but like the Betamax was replaced by the VHS, it was replaced and overshadowed by the Binary based system.