I want to clarify the difference between ARITHMETIC and MATHEMATICS, and present LRH data on the definition of mathematics.

ARITHMETIC is all about numbers, and the tallying, adding, subtracting, multiplying, dividing, thereof. It is about actual *things*, masses. Two cows plus three cows is five cows. Arithmetic does not deal in abstract ideas. It is concrete. It requires little imagination.

Now let's define MATHEMATICS: it is all about SYMBOLS. It replaces masses with symbols of masses. It is abstract, imaginative, has no mass--just ideas. It's not about "3+4=7", it's about "X+Y=Z".

I would define Mathematics as:

  Applying symbols to represent things so that by manipulating the symbols,
  we can come to conclusions about the things themselves.

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Here is LRH: Logic 21:

  "Mathematics are methods of postulating or resolving real or abstract data in any
   universe and integrating by symbolization of data, postulates and resolutions."

The important part here (IMHO) is "integrating by symbolization".

From merriam-webster.com: "Integrating: 1: form, coordinate, or blend into a functioning or unified whole: unite."

Thus I would say that "integrating by symbolization" means integrating, coordinating, blending, not the things themselves, but their symbols.

This is what demonstration using a demo kit or clay is all about. You let little bits of stone and paper clips represent (ie, symbolize) some things you are trying to integrate (ie, unify, blend, come to understand). Then you move these little symbols around to see how they inter-relate and use that to understand how the "real things" would likewise move around and inter-relate.

Integrating multiple symbols into a unified whole can produce an understanding of the unified whole where there was before a confusion of the many parts. When one doesn't see (understand) immediately how parts of a thing combine and unify, one can create symbols of each part, using pictures, drawings, clay models, demo kits, and then look at how these models (symbols) combine.

More from LRH: 1952.11.00 Scientology 8-8008, chapter 12, "Differentiation, Association and Identification", page 83-4:

  "Mathematics could be said to be the abstract art of symbolizing
  associations. Mathematics pretends to deal in equalities. But equalities,
  themselves, do not exist in the MEST universe and can exist only conceptually
  in any universe.

  "Mathematics is a general method of bringing to the fore associations which
   might not be perceived readily without their use."

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I want to emphasize that last part: "associations which might not be perceived readily". Symbolizing might be pointless without that. In other words, in lieu of just "knowing", symbolizing can take us further than we could otherwise get by "thinking". Being mere Homo Saps, we might not be able to see a pattern until we put symbols on its pieces and then "integrate by symbolization"

Thus, after a clay demo, we might say "Oh, now I see why the bolts must be on the left side!"

Stat graphs give management a symbolization of how an org is progressing. Comparing graphs of different stats can show associations between them. For example, Gross Income follows bulk mail out, with a delay of six weeks. That would be very hard to "see" without the graphs. Management, being very OT, could "just know", but graphs as symbols of production are very useful as "a general method of bringing to the fore associations which might not be perceived readily without their use."

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LRH again: 1956.08.31, The Anatomy of Human Problems, 4th lecture in the Games Congress

"Mathematics does not confront the bridge girders, mathematics confronts a piece of paper about bridge girders, doesn't it? But if the individual using the mathematics is actually capable of knowingness then the mathematics has some use.

"If the individual who is using the mathematics does not have any knowingness, then he is not capable of any use. Don't you see. If he's not capable of knowing what he's just written down as symbols, then what good are the symbols?"

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From LRH: 1954.12.07 ACC 9.2, "Essence of Auditing, Know to Mystery Scale", track 6

"Mathematics ... is a system of vias by which you can derive the answer without having to know it."

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For example, a very skilled carpenter just "knows" where to place the nail. He is NOT using mathematics, he is using "knowingness", which is a far higher ability.

Me, I'd have to measure the boards, compute the square root of the hyper-matmosine, multiply by the wally-wog, divide by 3.14, figure-figure-figure, to get the "answer", and that's where I'd put the nail. I'm good at math, and my answer would probably be correct!

But my carpenter friend does not use mathematics--he "just knows".

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I hope this presentation has been useful to you, or at least interesting!

ARC, Steve Bush