Eric Johnson wrote:
On 8/12/07, Jared [email protected] wrote:
Eric Johnson wrote:
Notice that in all three of your examples to achieve true randomness, you are utilizing an analog-to-digital conversion. (i.e. you are capturing a random pattern occurring in the Real World with digital annotation). Note also that ternary logic handles analog-to-digital conversion much more efficiently than binary. This is empirically true, and demonstrated mathematically here:
I hate to get involved in what looks like it could become a perfectly good flame war, but I looked at your link.
By the same logic, we would be much better off using a decimal computer. It takes 15 trits to write 143, but I could write 999 in just 3 decimal bits (dits?)
Eric, you raise a good point.
This is a keen intuitive leap, but it turns out that it is not the reason that ternary is better than binary. It is actually because electricity has _exactly_ 3 states:
+1 current flowing one way 0 no current -1 current flowing the other way
No. To deal with analog to digital, electricity has a near infinite number of states. I would prefer a system that can measure 10 voltage levels than one that can only measure directions and no current. I can easily set up the circuit so that measurements can be taken in each direction.
Actually, yes. Your facts are correct, but you are using them to justify a quantity-based measurement, and ternary is quality-based. You are looking at the point-of-measuring, and I am looking at the mathematical _conversion_ between that analog measuring point and the digital storage.
This whole Quality debate was well exercised in Zen and the Art of Motorcycle Maintenance, so we don't need to go into all the details here.
You are correct that analog current has a near infinite number of states, continually flowing. You are thinking of the '3' as meaning '3 measuring points.' This is not what is meant by ternary A/D conversion. What we're talking about is how to quickly and efficiently move the finest grains of data possible, and to do that we are converting from fractions to discrete numbers.
I quote, again from the trinary.cc website, which I believe is published out of England since at least the late 1990s. It represents the work of an engineer whose statements are all mathematically proveable. There are other websites which discuss these things, but his is the clearest for our purposes. Look closely at what he is saying:
<extended quote> Fractions are represented as a base number raised to a negative exponent. They are commonly a source of error in scientific calculations. Fractions are inherently analog in nature. Computers are discrete. This means that computers approximate fractions as closely as possible - but can be off by as much as half the value of the smallest digit.
For example, lets see how 0.6 would be represented using only 3 digits. Based on the following table, we get the following results:
Base 2: 101 = .500 + .000 + .125 = .625 The margin of error is: .625 - .600 = .025 Error
Base 3: 121 = .333 + .222 + .037 = .592 The margin of error is: .600 - .592 = .008 Error
As you can see, base 3 is much more accurate.
The use of fractions becomes important whenever floating point numbers are used. Floating point numbers use scientific notation as the basis of representing a number. For example, the IEEE standard for long double precision floating point is 80 bits in size: 64 bits for the number, 15 bits for the exponent, and 1 for the sign. A typical PC is only 32 bits wide. This number takes 3 memory cycles to access it. To get roughly the same precision with trinary digits, it would take: 40 for the number, 9 for the exponent, and 1 for the sign. For a 27 trit trinary computer, this would only take 2 memory accesses to read the number.
However, if using a trinary computer, we would have 4 trits left over (2 memory accesses is 54 trits - 40 - 9 - 1 = 4 trits unused) that could be re-assigned so that they are meaningful. (e.g. - 42 for the number, 11 for the exponent, and 1 for the sign.) This would surpass the capabilities of IEEE long double precision floating point calculations by roughly 8 times in both precision and magnitude
Why 3 and not 4, 5, 6... ?
The trinary math system utilizes the 3 natural states of electrical current flow. A wire conducts in one direction, or the other, or not at all. Base 4 would need to have 4 states, which don’t naturally exist. A designer would need to use discrete voltage levels to make it work. This leads to noise margin problems and increased power consumption because the transistors will need to be in the active state. If the designer tried to quantize the numbers for mathematical operators, he would have to build 4 window detectors to signal when voltage represents a specific number. Just detecting the individual numbers make anything above base 3 unwieldy. </endquote>
http://www.trinary.cc/Tutorial/Introduction/Intro2.htm
The sum is that .333 is more useful mathematically than .5 when creating fine-grained fractions. It is really, as Knuth said, a very beautiful way of doing math, much more elegant than binary or decimal. Not only mathematically, but ON THE CHIP it is physically easier to manipulate the data in certain calculations -- sometimes by simply inverting the trits, you perform a complex calculation which requires several steps in binary.
I really am not coming from a position of opinion. Rhetoric yes, but what I am presenting are facts and a new way of looking at them which is quite amazing. For example, the trinary.cc guy is unaware of the implications of ternary logic on random number generation which I have brought into this conversation.
-Jared
p.s. for anyone still reading. the idea that someone is WRONG is itself a binary assumption which virtually disappears when you start thinking in ternary. Instead of saying someone is WRONG, you simply say "Oh, he hasn't yet completed his journey on that subject..." And then you have a moral imperative to help him learn, instead of a moral imperative to "correct" him. Unless of course, he really is wrong, which is exceedingly rare, like one per billion or so.
So here is the summary so far:
1. A TRUE RANDOM NUMBER GENERATOR AND ENCRYPTION OPENER. 2. BETTER QUALITY DIGITAL TO ANALOG INTERFACES. 3. WORLD PEACE.
What's next, the Grand Unifying Theory itself? The cure for cancer?
One researcher in Central Peru is working with the Aymara language, the only language in the world which is natively ternary in structure. Roughly 2 million people speak it, and his project is to build a SuperTranslator which accurately translates meaning between ALL languages, by translating them in and out of Aymaran, which is a "perfect language." (This sounds weird, but linguists immediately recognize what I'm saying here, so I'll just say: it's possible).
Suffice it to say: there's something really amazing about ternary logic which is not yet fully understood, and which changes everything it touches, for the better.
Sigh. :-)
Honest, I'll quit responding on this subject if you will. I'm done. It is successfully archived where surfers at archive.org will be able to find it well into the future.
But if you write again and say I'm wrong, I'll write back and show you that YOU ARE CORRECT and, interestingly, I am also.
G'night.