MAXIMUM COMPRESSION PRINCIPLE

"Understanding increases with compression." (Jorge Wagensberg)

"To understand is to compress" (Gregory Chaitin).

"Understanding is the minimum expression of the maximum shared" (Jorge Wagensberg).

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The principle of maximum compression seeks, in every expression, its simplest representation, its maximum compression by means of the following forms:

1. The choice of the simplest expression among all the equivalent ones: the one with the smallest length (including internal blanks).
   
   
2. The elimination of unnecessary parentheses and blanks.
   
   
3. The use of the representation mechanism (potential substitution).
   
   
4. Using a variable naming convention, in order to avoid having to specify that a certain variable name belongs to a set (natural numbers, integers, real numbers, etc.).

Examples

Arithmetic expressions:

1. x+y+x // ev. 2*x+y
2. a+b+b+b+b+a // ev. (2*a + 3*b)
3. (aa + bb + cc) // ev. aa+bb+cc
4. (a + b + a + a + a) // ev. 3*a+b
5. a+a+a+a+a // ev. 4*a
6. a*a*a*a*a // ev. a^4
7. a^a^a^a^a // ev. a(^^)4
8. (3*a + 2*b) // self-evaluates (can't compute anymore)

Sequences and sets:

1. (a) // ev. a
2. (((a)))) // ev. a
3. (a b c) // ev. abc
4. {a b c} // ev. {a b c}
5. { a } // ev. {a}
6. {⟨(n ← n>5 ← n∈N)⟩} // ev. {⟨(n ← n>5)⟩}

Substitutions:

1. (x = a) // ev. x=a
2. (x = (a b c)) // ev. x=abc
3. (x = ( (a = b) (b = c) (c = d)) // ev. x=(a=b b=c c=d)

Ranges:

1. ((1...5)) // ev. 1...5
2. (((( 1...5 )))) // ev. ( 1...5 )

Potential substitutions:

The inverse evaluation is performed, which more compactly describes the operation.

1. ⟨(f(x y) =: (x+y x*y)⟩
(a+b a*b) // ev. f(a b)
   
   
2. ⟨(g(x) =: (x xx xxx xxx xxxx)⟩
(a aa aaa aaaa aaaa) // ev. g(a)
   
   
3. (h(x) =: (x xx xxx xxx xxxx))
(x xx xxx xxx xxxx) // ev. h(x)
(y yy yyy yyy yyy yyyy) // self-evaluates
   
   
4. (a a a a a a) // ev. a★4
   
   
5. (a a a ...) // ev. a★
   
   
6. (2a 2b 2c) // ev. (2[a b c])
   
   
7. (10 11 12 13 14) // ev. ( 10...14 )