A Language of Metaphors: Chapter 7

A Prime Example

Compressing metaphor templates for use in intelligent search engines and panlinguistic translators...

A prime number can only be divided by 1 and itself. For example, the number 6 is divisible by 2 and 3. Neither 2 nor 3 can be broken down, making them prime. Primes can be of any size, it is thought, provided they obey this simple definition.

The laws of multiplication state that it does not matter the order in which two numbers are multiplied, the product will be the same. For example, whether we multiply 2 by 3, or 3 by 2, the product will always be 7... I mean 6 ! If I gave you a bigger "compound" number, such as 210, its' prime factors 2, 3, 5 and 7 are locked within: Since this number has a 2 and a 3 among its' factors, it is tightly related to the number 6.

The order of two letters, such as "n" and "o" can result in vastly unrelated words: In this case, "no" and "on". The letters have nothing but a group meaning, though occasionally a single letter will form a word. Letters may have their roots in actual whole physical entities, but have evolved into simple, elemental ingredients of words.

In many languages, however , the order of two words may result in either two meanings (or even one valid and one nonsensical). Take the two words "foot" and "long". They each have meanings, but when placed in each order, result in "foot long" and "long foot" : "foot" changes from measurement to anatomical part; "long" changes from meaning "of length" to meaning "lengthy". This holds true of music, where two different notes in sequence result in markedly different effects on the expressed mood.

Now consider a cross breed of languages. Where the advantages of primes, the laws of multiplication, the context and the pure meaning can be united. A language where the "letters" are concepts; the words they form have an exact meaning; and the order they are in illustrates what is most important from a given perspective.

Lets try this...

red=2   clay=3   brick=5

red clay = 2 x 3 = 6

red brick = 2 x 5 = 10

clay brick = 3 x 5 = 15

red clay brick = 2 x 3 x 5 = 30

If we use the "importance" factors, arguably, the order may change...

                    architect          brick-clay-red         kind of structure, material, colour

                    decorator        red-brick-clay         colour, texture, material

                    manufacturer  clay-red-brick   batch material, coloured admixture, sub-batch mold

Each are referring to the same "30" from above, but when broken down to its' constituents, they have their individual perspectives of what is most important.

Now if we were to encapsulate the meaning of "red clay brick", by placing it in brackets...

red clay brick = ( 2 x 3 x 5 ) = (30)

if "pottery" = 7

red clay pottery = (2 x 3 x 7 ) = (42)

The "word" for "red clay brick" could never be confused with the "word" for "red clay pottery"; yet when comparing definitions, one may break each down to discover their hidden similarities. Since the "words" are each in numerical form, the translation could occur from any language into any language - a conceptual Rosetta Stone which assigns a unique number to each elemental concept. If looking for something "red", in this example, one would divide all "words" by 2; if, after this division, a whole number is the result, the "word" has some red quality. On the other hand, should the division not result in a whole number, the "word" has no specific relationship to the colour red.

This language would have been inconceivable and impractical even a few years ago; but since the advent of computers, such mathematical processes could occur without labour-intensity. For you and I, it may seem rather mind boggling to take a huge number and break it down, but to a computer with a template of prime divisors, a number like this fictitious one for a "red clay brick bungalow" would be quick work:

821162353171649012251578331342317216319740

The "red clay brick" is quickly found by the computer after dividing the behemoth by 2,3,5; or by the whole value of 30. Now, imagine a search engine that seeks not by "word" but by definition - one that does not view the word as a string of letters for the purpose of comparison, but one that views the word as composed of parts from a universal set of numerical parameters. In other words, the search engine would not seek what you say, but what you mean.

The human brain enters this world, quite unaware of the language it will one day use for communication with other brains. Our language centre is a translation centre: the language for the rest of the brain would be best arranged in some standard format, developed in the womb. After we are born, it seems our understanding of the world starts in the mouth - sensing such things as size, shape, texture and taste; long before sight or hearing, longer still before language (though studies now question this statement). It's as if the brain is familiarizing itself with the dimensions of existence. In all, this process is incredibly rapid, as if the brain has "pre-triggered" addresses for this slew of data (note:  "da-ta" is often the child's' first word!!): Evidence has shown that within the first few weeks, newborns are beginning to reflect the different facial expressions they are exposed to.

Unfortunately, you will have to bear with me for this next few paragraphs; but if successful, we will end up on the far side of uncharted waters...

Try this...grab a pen and paper. Draw a short line straight up from the bottom of the page. Now draw a split in the top end of the line that makes two shorter lines, each on a bit of an angle to the left and right: It should look like a "Y". Now split each shorter line, again and again, adding consecutively shorter lines. You now have a tree-like structure. But you will notice that the entire structure can be broken down into "Y"s of various sizes. You also have one breed of "fractal" or "fractional dimension", meaning that those one-dimensional lines have not completely filled the two dimensions of your page. A one-point-something dimension: Greater than a line and less than a plane.

What was needed for this somewhat detailed structure? A very simple set of instructions: go forward; split; go forward not as much; split not as much; repeat last two steps. Given the simplicity of this "formula"; and given that it resembles a flat version of a tree or veins; and given that the universe has its' roots in a very limited number of dimensions and laws, it would seem that perhaps similar forces are behind the structure of a tree or veins, as is found in this form of fractal. Where do living creatures come from? That long piece of genetic programming called the DNA.

That the DNA results in the production of these fractal-looking structures has led me to firmly believe that the DNA itself is, indeed, a fractal in many dimensions. [For more on this theory, take a visit to a website called "The Fractal Chemist", a work in progress, that will be developed further when I'm done with these writings. (You will need to start with "Inherent Programming" for it to make much sense)]

If the DNA  is, in fact, a fractal, or a collection of interactive smaller fractals, then the program detailing the arrangement of the brain would likely be a fractal itself. Picturing the junctions between the lines on your page as neurons, and the lines themselves as dendrites, one gets a bit of a mental image of the possible mathematical structure of the brain: That is, the neurons, however physically complex and superimposed in appearance, are actually put in place through a very simple set of instructions. Now turn your page upside down. Imagine that the dendrites are like pipelines for thought to move through. Pouring water down the first line, results in water making its way down consecutive lines, until finally, as gravity would have it, the water rests in the bottom-most points. When we learn, we "fill" neurons.

It would be most confusing if learning behaved precisely this way: There is nothing to assist in the categorization process. This is where it would be nice if we had those valves from our earlier plumbing model. These valves - or "gates" in computerese - would be the bias that directs the course of thought. Neurosuppressants, neurotransmitters - "off" and "on" buttons for each neuron; synapses that act as reservoirs - or "capacitors" in electronics speak; it seems that the pieces are there - but how would it work? What's more, how does this relate to all the other junk I've dragged you through?

Addressing. What could we do without it?

Our phone number is an address, once deciphered entirely by electromechanical relays. Our name is an address, pulling us apart from a crowded floor with often only our first name. Our Birth Certificate is an address, positioning our location and time of birth within the social fabric. The address leads one to a physical location.

Most addresses are figurative: The address does not describe the object it leads to. It would be far too cumbersome to one searching for you in a crowd to fully describe you, when with a single word you may appear.

Now we'll take that floor the crowd is on, and mark it with divisive parameters like male/female, young/old, tall/short and so on. We'll get carried away in divisions so that there are thousands more divisions on the floor than people. Now if anyone enters, they quickly find their way to a spot that perfectly describes only them. If someone is looking for a specific person, the description of that person through the pre-assigned parameters will lead directly to the desired person. The address has described its unique contents.

There are two reasons I used prime numbers earlier. One is that they would facilitate the development of the language for the present-day computer. More importantly, the second reason is that they are indivisible: they retain their identity in any compound number. This is also true of the dimensions. Although mass can be converted to energy, or length and width a matter of perspective, the dimensions themselves are like a group of interchangeable prime numbers: the basis of which all complex things are formed - the sole ingredients of the universe. If something exists or can exist, it must be built of these parts. Since the brain is a device for storing ones experience with the universe, it would be most efficient that it stores its facts in like kind.

The tidbits of information we gather over a lifetime, would then have corresponding places to go. The fractal you drew earlier, would be far more complex, with interconnections between one of these groups of lines and many others. If you were to take a drop of water and direct it through these lines, with the instructions "left, left, right, left", you will end up at a specific neuron. If the system behind this were perfectly mathematical and based on the dimensions, the pattern resulting from the path of your water droplet could be used as a template that may be applied elsewhere in the brain, with other neurons, representing other things. I believe this template to be the neurological basis of the metaphor.

The Letters

Length Width Height Time Mass Energy    (   L   W   H   T   M   E  )

Nothing  Something  Everything                   (   0    n    ∞ )

Greater Than/ Equals/ Less Than                (    >     =     <   )

Add Subtract Divide Multiply                       (    +     -      x     ÷   )

The Perspectives

Category   Important   Parameter

Conduit   Portal   Encapsulation

Quantity   Quality

These letters of the language are compounded to form the words of our universe. Whether on a micro or macro level, the principles of the universe repeat themselves - and demonstrate this in the universality of the metaphor. Given a universe full of "cousins" from the bloodline "Big Bang", one can easily conceptualize panlinguistic translation: the ability to translate not only across ethnic boundaries, but scientific and interspecial boundaries as well.

Since every point in the universe would have its own, unique dimensional attributes, resulting in a long and complex unique formula describing it, nothing in the universe can be added - only merged. So, too, should there be some degree of segregation between the neurons of our brain. We may link two regions of the brain conceptually, but without some form of differentiation, we may get quite confused. This may explain why the injured, stressed or drugged brain may end up with the symptoms of Alzheimer's, hallucinations or delusions.

If the brain has developed in any way over the process of evolution, it has been visibly by size and convolutions. This lends itself well to this theory, in that the number of brain cells and segregations allow for a far "deeper" fractal. Picture continuing the fractal process on your page for another billion iterations.  Now place several similar pages on top, allowing for a stream to flow across the pathways of several pages interchangeably. That would certainly hold more and allow you many more areas to pour water (even in several different places at once). It would allow you to "template" in far broader and complex groups. It would give you a far greater thinking depth and range. Intelligence: the ability to relate facts and extrapolate - to leap between avenues of thought.

Nobody said we couldn't pass this process on to the computer.

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Here are a few bits and pieces that may also be needed for effective artificial intelligence under this model...

Attachments

"I can't tell the difference...", the commercial says, while trying to pawn "clear" cola off on the public. The brain has not only a segregation system, but also an integration system: the coloured cola we drank for years, has imprisoned our minds with the concept that colour and flavour are attached - a process vital to the picking of ripe fruit. The clear-cola marketing effort an unqualified belly-flop - with water and air clearly tasteless, but tasteful food typically opaque - we must ask ourselves more about the brain. You see, the information gathered while drinking that pop for the first time, was not gathered by one sensory device, but at least two: taste and vision. Taste is chemical analysis while colour is a measure of wavelength. These two properties would be quite segregated by their dimensional definition. Only that they occur as the same informational experience do they become as one to the mind. Something must exist that makes such strong ties between seemingly unrelated data: A neural paperclip? No. If it were a paperclip, one would readily have made the transition to the clear soda, saving the company millions in food dye. It must be a neural staple. We seem designed to form conceptual and factual attachments. Smell, for example, is known to trigger very precise memories of an entire sensory event.

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Rewards

I am opposed to the word "opposite". Not really. But if I were, what would it mean? "Opposite" implies that the thing opposed to has a direction: The opposite of "up" is "down", "left" is "right" or "in" is "out". What is the opposite of "computer" ...? Since it is a "thing", it is a chunk of dimensions. The only "direction" it has is its existence, thus, one may answer with "anticomputer": to be constructed from antiparticles, I'm sure. But in our universe, there is no true "up" or "down", we assign these values to a motion, but they are quite arbitrary distinctions, used simply as a means of forming a point of reference. A point of reference, whether intrinsic or external to the compared objects, is essential to the process of comparison or valuation. "What looks better?" or "Which is tastier?" requires the intrinsic "worse" or "tasty" to act as a basis for the judgment of "better" or "tastier". As qualitative or quantitative an analysis this may require, these are comparisons of fact against some form of valuation template. Luckily, in the language, we have "importance" to guide us through our assessment. For most of our valuations, if not all, it comes down to drug use. The brain has drugs that reward us for pleasurable thoughts and stimuli called endorphins, or "endo morphines". Without this process, we may not have the drive to reproduce, eat, learn... in other words... "live". Perhaps our computers could enjoy the odd reward....

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Skew

Skew ain't to me what it is to you. My experience builds my personal slant on things. Our brains are created larger than necessary for the facts we'll gather over an entire lifetime. Since the facts you will gather may be quite different than that of a Cro-Magnon hunter; and since the brain must be prepared for a great depth of whatever knowledge is important in our environment; and if the arrangement of the neurons in the brain reflects that which is hypothesized in this theory (a predestined location for each fact), then something that allows for us to reflect differently on similar situations may ensure each of our respective survivals. For example, a strange human to the hunter may require an immediate, brutal reaction to protect the tribe; where in modern society this is not only immoral or illegal, but may also result in the elimination of a would-be benefactor. Our military must go through a rigorous training to prepare to react as instinctively and ruthlessly  as the Cro-Magnon hunter.

Continue on for a few examples...

Copyright: John D. Casnig 2000 - Use with permission only.