It all began with boredom. Intense boredom. Prolonged boredom. Boredom so endless, so brutal, so epic, that Cecil B. DeMille wants to buy the movie rights from me.

I was sitting in the living room... on my little credenza, wondering when master would come and water me. There was nothing to do. Then I started thinking about numbers. Why do they all line up in a line? Why not a circle, or a square, or a trapezoid? Why have numbers at all? Why have anything?

And then it hit me, just for a moment... the secret structure of the universe. But then the vision faded, and I was left to wonder whether I had indeed seen something real, or if the boredom was finally taking its toll on me, or if master had put something weird in my plant food.

But just like the space spores from a sci-fi B-movie, the experience wouldn't leave... slowly, step-by-step, painstakingly I pieced a picture of an idea that shatters our concept of mathematics and logic with its brilliant simplicity, a new model of language and calculation that is light-years ahead of mankind's greatest forays into the realms of knowledge... I give thee, the secrets of The Goldfish.

Here we begin with a simple story. Imagine you have two cats, muffins and mittens. How do you know you have two cats? Because they are different!! One is spotted black and white, the other tabby. One is sitting on the chair, one on the rug. If there was NO difference between them at all, in terms of position, appearance, behavior, or anything, they would be the exact same cat always, and have no way to be told apart.

This leads to the first Goldfish Rule: Everything that exists has some difference, however small, from anything else that exists. This can be expressed in its simplest form as follows:

( object 1 is different somehow from object 2 )

Now in the case of the two kitties (no, that isn't a new Nancy Drew book!!) we can define object 1 as Muffins the Cat, Object 2 as Mittens the Cat, and "is different somehow from" to mean all the various ways we can tell them apart, or even just one way.

So we can say in the Goldfish Language these things

("Muffins the cat" "is fatter than" "Mittens the cat")

("Muffins the cat" "is older than" "Mittens the cat")

where "is fatter than" is considered one single word with one single very specific meaning. This is important because in Goldfish, every word has one and only one meaning, something extremely specific. This is because "is fatter than" is actually a single specific object like "Muffins" or "Mittens", even if it is abstract.

Another Goldfish Rule is that everything is defined ONLY in terms of how it is the same or different from other objects in the language. So, the word "Muffins the cat" does not have any meaning in itself until it is defined by statements that relate it to other objects. The fact that it is called "Muffins the cat" does not make it a cat at all. In fact, if you wanted, you could make "Muffins the cat" refer to a hamburger.

So just who or what is "Muffins the cat"? It is an object that "is older than" something called "Mittens the cat", and is "on top of" something named "living room rug".

But what is "living room rug" or "Mittens the cat"? Or even "is fatter than"? They, in turn, have meaning and substance in the language only by how they are the same or different from the other objects.

This might sound weird, but it is how we sometimes think every day.

Suppose you asked how to get to a convention hall where there is going to be a convention for vacuum cleaner salesmen. Hank the farmer might say, "Well, you go down Bunk Street, turn left at the Gas Station, go North until you hit the Big Chicken Statue at KFC, then keep on for twenty miles."

If you got really curious, you might ask where the Big Chicken Statue is, and he would tell you it in relation to the other landmarks, and you could also ask about the other landmarks, and he would tell you where they are in relation to the big chicken statue. And if you kept it up long enough, he would get confused at telling the same directions in so many different ways and tell you to let him go feed the cows.




Circular logic, you say?? Yes!! A thousand times yes!! But the point is not that the cats and rugs and their ages and weights has any intrinsic meaning apart from each other (which is true), it is that by getting rid of all intrinsic meaning of the objects, only the raw conceptual relationships are left. Why is this so important and fascinating?

Well, if you consider two completely separate things - such as the cats in the living room and Fermat's Last Theorem, and you reduce them to the raw connections between their smallest elements, then it is possible to write them BOTH in the Goldfish Language and compare the underlying structures. Or the structure of Portugese versus the structure of Quantum Theory. Or just about anything. Or concepts that don't have any names in English yet.

But how? This is accomplished through a simple addition - uncertainty. The "?" word in the Goldfish Language has a special meaning, unlike all the other words that can be added.

For example, this 3-word statement:

("?" "is fatter than" "Muffins the cat")

is actually a word in itself, which has some uncertainty in it produced by the "?". It stands for every object that "is fatter than" "Muffins the cat".

Using this idea, an uncertain word can be put into a larger sentence to give it a more detailed, complicated meaning -

(
("?" "is fatter than" "Muffins the cat")

"is older than" "Mittens the cat"
)

What this is saying is that anything and everything that can be described as "is fatter than" the object "Muffins the cat" is a word in the language, and this word is in turn has the distinct meaning of being "is older than" something called "Mittens the cat".





Now let's imagine that someone named Bubba owns a hamburger joint. He has two menu items, one called "Bubba Burger" and one called "Friendly Fries". (Bubba's customers don't get thirsty.)

Now imagine that:

("Friendly Fries" "costs less than" "Bubba Burger")

("Friendly Fries" "tastes better than" "Bubba Burger")

("Bubba Burger" "listed on" "Specials Menu")

Now suppose if we filled out all the information about the hamburger joint, and all the information about the two cats in your house, and found that by substituting, say, "Muffins the cat" for "Friendly Fries" and "listed on" for "is older than" and other things, including even some complex, uncertainty-based statements, we found that everything true of the hamburger joint was true about the living room cats? This would show us that although the two things seem completely different and unrelated, there is an exact informational structure that connects them both.




The hamburger joint and two cats example is very simple indeed, but the idea can be used to model extremely complicated things like, say, the game of tic-tac-toe or french grammar or the structure of a sonnet, all with one simple language.

So here are a few basic rules of The Goldfish:

(there are more, but I haven't posted them yet)

1. What are the most basic objects we are talking about?
2. How are these objects different from one another?
3. What kind of abstract structure do the previous two questions create?

I have actually done a LOT of more work on this than on this page, this is just the bare bones, so send me a message if this sounds interesting or you have comments!!

This is a newly added section. I might do another whole page on this concept.

So what are mumbers. Everyone knows about numbers, but they aren't actually the most basic thing around, even though they seem to be!! There's a lot of things they are clumsy at.

Basically a mumber is a template for a set of goldfish statements, without any particular objects put into it.

for example:
1. [ e f g ]
2. [ e f h ]

is a very basic mumber.

It shows in particular which forms are the same in the set of statements, and which are not. Basically we see that this mumber is two statements, and everything is the same about them except for the "h" and "g".

Note that "g" and "h" are completely arbitrary, of course.

A more accurate way of writing a mumber is in this way:
......a..b..c....
1. [ 2A 2B x ]
2. [ 1A 1B x ]

Line 1 has 2A to show that this object is the same as the first spot of line 2. The x's show an object is that is not repeated anywhere else in the mumber.
This way is preferable because the mumber has only one way of being written, whereas the [ e f g ] form can be written in many ways.

This mumber could also be a portion of a larger number containing more statements. Once something has been put into the goldfish language, all the objects and forms can be taken out, leaving the corresponding mumbers behind. There are an infinite number of mumbers (say that 10 times fast) such as this six-statement one:

1. [ a b c ]
2. [ a b d ]
3. [ d s a ]
4. [ b l s ]
5. [ c w a ]
6. [ c s d ]

Looks like complete, absolute gobbledygook garbage, right?!?!

To relate this to the goldfish language, imagine this set of statements:

1. [ "Mittens" "wants" "food" ]
2. [ "Mittens" "wants" "pillow" ]
3. [ "pillow" "fell on" "Mittens" ]
4. [ "wants" "is more abstract than" "fell on" ]
5. [ "food" "despises" "Mittens" ]
6. [ "food" "fell on" "pillow" ]

Also this set:

1. [ "one" "is less than" "four" ]
2. [ "one" "is less than" "two" ]
3. [ "two" "is a multiple of" "one"]
4. [ "is less than" "does not always equal" "is a multiple of" ]
5. [ "four" "is more than twice" "one" ]
6. [ "four" "is a multiple of" "two" ]

See if there's any connection here.