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Story of two bits

Check out type-config wiki for a more detailed technical breakdown.

Among countless other complex things, let's discuss a simple case: the relation between two binary bits.

#State and combination

#bit#State#Combination of state
123(2^2-1)
24(2^2)15(2^4-1)

A bit by itself as commonly defined can either be 0 or 1. Cardinality of state is 2.

Two bits together can be: 00, 01, 10, 11. Cardinality of state is 2^2 = 4.

Combinations of state are combinations with all different sample number. Cardinality of single bit is C(2,2)+C(2,1), or 2^2-C(2,0). Cardinality of 2 bits is C(4,4)+C(4,3)+C(4,2)+C(4,1) or 2^4-C(4,0).

Math works aside, things are clearly getting more complex when it goes either vertically (number of bits) or horizontally (composition of primitives).

#Combination pattern

How would you give names to that 3 combinations?

#1. 1 or 0

A bit with result.

#1. 1 0

A bit with possibilities

#More combination pattern

How would you give stories to that 15 combinations?

Here is my try:

#1. 11 10 01 00

Roommates

  • a: independent
  • b: independent

They have their own lifes... It won't change a thing if they split.

#2. 11 or 10 or 01 or 00

Commited couple

  • a: fixed
  • b: fixed

They accepted the offer...

#3. 11 10 or 11 01 or 10 00 or 01 00

Not yet committed

  • a: independent
  • b: fixed

Still waiting for an anwser...

#4. 10 01 or 11 00

Someone needs a life

  • a: independent
  • b: dependent on a
    • a
    • !a

It is not yet clear who is that someone tho...

#5. 11 10 00 or 11 01 00 or 11 10 01 or 10 01 00

Too much conditions

  • a: independent
  • b:
    • independent if a is ..
    • dependent if a is ..

While still negotiating, it is likely to break.

#My TL;DR

  • Adding verticals/dimensions/... is exponential;
  • Patterns: no such thing as unique;
  • "Dependency management is hard";
  • Generalization without specialization is false: if you read type-config wiki, there are just too many missing details and reasoning process here;