Abstraction • Interpretation
Addition is multiply realizable.
House / cake:
something physical
Addition:
abstract, non-physical numbers
The “essence” of addition is informational, not physical.
| Type | Relationship to outcome | Example |
|---|---|---|
| Constitutive | The physical stuff is the outcome | Bricks make the house |
| Implementational | The physical stuff represents the outcome | Beads / voltages represent numbers |
Computation depends on representation.
Machine states don’t mean anything intrinsically.
Meaning is assigned by us (interpretation).
So we can choose to interpret states as data
or as instructions.
In the decoder: hardwired.
0001 can mean “PRINT”
or it can mean the number 1.
Depends on how the interpreter works.
This is a tiny “instruction set”: symbols become actions via interpretation.
| Meaning | Bits |
|---|---|
| state 0, read 0 → write 1, move R, next 0 | 0 0 1 1 0 = 00110 |
| state 0, read 1 → write 0, move R, next 0 | 0 1 0 1 0 = 01010 |
The machine has fixed circuitry for: “treat 5 bits as \([state,read,write,move,next]\)”.
Given current state and tape read, it scans the rule area for a matching prefix.
When it finds one, it performs the encoded action (write/move/next).
The same symbols can be “data” somewhere else; the decoder makes them “instruction” here.
Goal: flip every data bit by stepping right.
Decoder turns the matched 5-bit pattern into a concrete action.