Meta-Sci: Paper #01
Computers that Understand Humans
(Formerly: The 513th Dimension)
Copy-Righted
This is one of my "Meta Scientific" essays. I first presented it in 1995 at the University of Michigan-Dearborn campus and then again in 1996 at Oakland University (of Michigan). The study comes from a combination of the fields of philosophy, mathematics and computer science, with plenty of pictures to help illustrate the ideas. My title "Computers that Understand Humans" comes from a study I'm working on. The study is made from having a computer, which doesn't understand me sometimes.
Let's say that from a C:> prompt you type in "DOR" instead of "DIR". The computer responds with, "Bad command or file name," because the computer doesn't realize that I made a mistake in typing and doesn't know how to correct it. Why can't a computer understand what I mean instead of what I say? When will computers understand people?
So, that's what got me started. I wanted to put all human ideas into the computer, so it will understand me.
How do we think? What are the properties of an idea? How many ideas are there?
I don't want someone to be able to come along and say "Oh, you missed an idea."
Let me introduce you to Idea Space, for humans. Idea Space is the part of the Universe that contains the ideas of people, as opposed to dogs, apes or dolphins.
Everything in the Universe we can perceive can be represented as ideas, such as "It was red."
I'll use a chair as an example.
Idea Space doesn't contain the chair itself but it contains the ideas of "the chair." Because the chair is part of the Universe but exists outside of Idea Space, Idea Space is a sub-set of the Universe.
The meaning of the chair can be represented as separate ideas, such as "The chair is tall," "The chair is hard" or "The chair is green." Each of these ideas are built from concepts, something which I apply as dimensions. Because the chair is a physical object, let's move the explanation to deal with our favorite concepts (dimensions), height, width, and length. If we apply a concept, we need to know how far. This is what is called a scalar. A scalar gives size (scale) to a concept or dimension.
With this method, the size of each concept is independent of the size of the other concepts. One way of looking at this is that how tall an object is, is independent of how wide it is, which is also independent of how deep it is. This is easy to understand, works pretty good and a computer can do this stuff. We can then add the chair concept.
When we describe something as "is", we are make an expression that it exists, now. This brings about the concept of time, our fourth favorite concept. As we make other observations we add descriptions based on concepts, such as hard, red, yellow or blue.
Before we put this into a computer, I'd like to demonstrate one more thing, using "The chair is green." Green is made up of yellow and blue. If I want a dark green I want my scalar to be low numbers, right down to zero (0). If I want a bright green I want my scalar to be high numbers. However, to me green really has nothing to do with being red. Since I want to save the red scalar of zero (0) for dark red what can I do? What I want to do is use a flag system for each concept and then a separate scalar to represent how much of that concept. If the flag is down (0) then the concept doesn't apply at all to the idea. If the flag is up (1) then the concept applies to the idea, check the scalar. To represent green, red's flag is down, the yellow and blue flags are up.
Using ones and zeros for flags up and down, respectively, if I look at just the flags, I can get a classification of ideas. If the flags match, between two separate ideas, I know that they are similar ideas, varying only in degree. Such as with "the chair is light green," and "the chair is dark green," the applied concepts are the same but the idea varies by the amount of some concepts and so the two are the same classification of ideas. Further, any chair of any size that has a color of any shade of green would fall into the same classification, that of green chairs.
To put this into a computer I'm going to use some numbers common to computers. I decided to make my computer's scale have two hundred and fifty six (256) different steps and depending on the concept I can use these steps one of two ways. If I'm using something like size, I start with a maximum scale of 255 to a minimum of 0. If I need to split my scale into two directions then I use -127 to + 128. I'm going to use 255 to represent infinitely large and 0 to represent infinitely small. I am also going to "bend" my scales (non-linear). If we are talking about the physical size of something, then we have
the size of the Universe 255,
the size of a galaxy 254,
the size of a solar system 253,
the size of a sun 252, ............,
the size of a bus 130,
the size of a car 129,
the size of an adult 128, ............,
the size of an atom is 2,
a sub-atomic particle like an electron is 1,
and a geometric point is 0, on this scale. For a concept like time I use zero (0) to represent "now," negative one hundred and twenty seven (-127) to represent infinitely long ago and positive one hundred and twenty eight (128) to represent infinitely into the future. Now, I'm not saying it's perfect, but it is one way to fit the entire Universe into a desk top computer. With this method I can use one computer byte as the scalar (sizing) for each concept (dimension).
How many different human concepts are there, which make up our ideas and how do I find my core dimensions, my core concepts? Some linguistic people seem to feel that the number is about 500, meaning if you know the words for the 500 basic concepts in a language, you can express any idea. "What time is it," "Which way to the beach," or "I went to the movies and this is what I saw," any idea. The proof is in using a thesaurus and finding the words with totally unrelated meanings (no overlaps), which all of the other words use to build their meanings. Just to play it safe, incase there are a few more concepts than 500 and because it makes things easier to put into a computer, I decided to do my calculations using 512 concepts. Now, before you say "That's not enough concepts," let me give you some figures. Ideas are in the same classification if they use the exact same concepts. (Remember, light green, dark green, or any kind of green would be the same classification.) Just using the flags, 512 concepts gives me 2512 different ways to combine concepts to give classifications of ideas. That's over 10153, which is a one with a hundred and fifty three zeros after it and that's just the number of idea classifications. How many separate ideas can we express, using the scalars? (28)512 which is greater than 101228. Here's the math.
Binary to Decimal conversion (approximate)
210 = 1024 which is greater than 1000 = 103
(I'll convert binary to decimal on the conservative side to keep my figures easy to calculate.) 512 concept flags, which can be on or off in any combination, in binary is 2512
2512 = (210)51.2 which is greater than (103)51.2 = 10153.6
10153 is a one (1) with 153 zeros after it. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Different classifications of ideas.
Total ideas representable:
(total combinations= scalar to the power of concepts for combinations)
28 = 256 is a scalar, 256 variation of one concept.
512 concepts which can be applied one concept at a time to all concepts at once and all combinations and permutations in between so I take 256 to the power of 512.
(28)512 = 24096 = (210)409.6 which is greater than (103)409.6 = 101228.8
101228 is a one (1) with 1228 zeros after it, different ideas which can be represented using this system. That's a lot of ideas. (I hope my head doesn't explode.)
8 bits = 1 byte, 512 concept flags (bits),
512 concept flags divided by 8 bits to a byte gives 64 bytes for the concept flags
512 scalars (bytes)
512 + 64 = 576 bytes per idea
However, I'd need 576 times 101228.8 bytes of storage to store this much information as a conservative estimate. (actual 576 * 24096 and remember 230 bytes is one gigabyte or about a billion bytes of storage)
Wow, these are really big numbers. Sorry but I don't know the name for that number and don't know of anyone who does. To get back into perspective, a dictionary may only have 20,000 words or 2 times 104 ideas. Using my method of idea storage would use roughly 11.5 megabytes of storage for a dictionary (11.5 times 106 characters of memory, 11,500,000). Not much by today's standards.
Dictionary of 20,000 or 40,000 words (ideas)
20,000 words (ideas) times 576 bytes/idea = 11,520,000 bytes = 11.52 megabytes
40,000 words (ideas) times 576 bytes/idea = 23,040,000 bytes = 23.04 megabytes
Considering 576 bytes per idea and using a 64 bit (8 byte) processor I would need 72 processors running in parallel to have a true idea processing computer. I have heard that Intel Corp. has already tested 80 of their Pentium type processors running in parallel, although a new expanded instruction set must also be devised as well. Think about it though, computers running at over 400 million ideas per second.
If all these calculations are correct I can express an idea as a point in Idea Space.
But where is the MEANING in Idea Space? I need the computer to understand my meaning. If I use several ideas as points and connect them (mathematically differentiating), they form a surface of meaning.
If I'm saying something to the computer and have something out of place, the computer can ask "Is this what you meant" and offer me a guess. Such as if I say "I like the couch." The computer responds with, "You have been saying chair. Which couch or did you mean chair?"
My graphics show two points plotted, "I like soft green chairs" and "That chair is soft and dark green." The computer would then operate on the difference between the two points and may ask "Do you like that chair?"
In this way the computer will actually understand what I am trying to say by differentiating between two of my idea space points.
Besides having a computer that understands me when I make a typing mistake, what else can I use it for? If a human has 512 concepts to an idea, what about dogs, apes or dolphins? (I am looking into the dolphin angle now.) Do they use less concepts, a smaller scale or different concepts? How about using the computer to diagnose mental disorders? Can men use a computer to understand women? Only the future will tell. Considering the full storage requirements of the program it may take many years for the hardware to come up to speed with this software. For those of you in computers, I don't think that this system will pass a full blown Turing test given by intelligent people. However, I do believe it could give the Turing test.
I do want to leave you with one thought. Expressed mathematically, the limit of the number of ideas in human idea space as time goes to infinity is infinite or.......
