Second:

**Computers don't have to be linear**
We think of computers as running a

*sequence of commands.* But these, of course, are equivalent to simple logical propositions, which is why computer people still use terms like "logic gate" - a logic gate, as it were, enacts a logical operator.

For instance, let's define eight data positions: A, B, C and D are input variables, E, F and G are output variables, and H is just used for calculation purposes. Data is binary. We can then say:

- set E, F, G and H to 0

- if B is 1, set G to 1

- if G AND D are now 1, set H to 1

- if G OR D are now 1, set G to 1

- if H is 1, set G to 0 and F to 1

- set H to 0

- if A AND C are now 1, set E to 1

- if A OR C are now 1, set H to 1

- if E is 1, set H to 0

- if H AND F are 1, set E to 1 and F to 0

- if H AND E are 1, set H to 0

- if H is 1, set F to 1

- set H to 0

Alternatively, we can simply say:

A^B^C^D⊢E^F^G

A^B^C^¬D⊢E^F^¬G

A^B^¬C^¬D⊢¬E^F^G

etc etc

And we can rephrase that as ⊢[[A^B^C^D]>[E^F^G]]^[[A^B^C^¬D]>[E^F^`G]], etc etc.

Which by the magic of the ampheck can be rephrased as... ⊢((((AA)(BB)(CC)(DD))((AA)(BB)(CC)(DD)))((EE)(FF)(GG)))((((AA)(BB)(CC)(DD))((AA)(BB)(CC)(DD)))((EE)(FF)(GG)))*, etc etc etc etc

The command sequence above can be regarded therefore as in some way a way of 'spreading out' these propositions over time. Which makes intuitive sense, because after all the proposition itself is linear, a two-dimensional sequence of symbols, and it's very intuitive to convert a line into a sequence of events, because that's what we do when we read, or calculate.

But the proposition isn't linear, that's just a representation of it. We could alternatively depict the proposition as a three-dimensional pattern, as Peirce did -

here's a Peircian proposition (a theorum by Leibniz, appropriately enough).

Now, Peirce separates out his procedures from his notation, so he works by graphically altering these pictures step-by-step in accordance with a small set of rules. But of course, those altered diagrams (change in time) can be considered to be a sequence of parts of a larger diagram (change in space). Each part would be related to adjacent parts by a permitted type of transformation.

In fact, imagine a space with infinite dimensions. Each 'panel' of the larger diagram could be surrounded by

*every* panel that is linked to that panel by a certain form of transformation, an each of those panels linked to other panels, and so on. Effectively, you'd have an infinite wallpaper - a fractal wallpaper, in fact - of subtly and regularly repeating/transforming patterns. [It's even more literally a fractal if we include our deductive procedures as true facts within our diagrams, because then the relationship between any two adjacent panels must be similar to the relationship between two particular adjacent areas within a single panel - and if we use our infinity to replace each variable with a list of every possible value for that variable, then each pair of panels will be a magnification of a section of each panel, forming a perfect fractal image!]

But such an infinite-dimension fractal cannot comprehensibly be understood, at one time, in two- or three-dimensional representation.

*Which is why with have deductive procedures*. If you think of a proposition as a Peircian pattern, rules of deduction are simply rules that allow us to generate a finite segment of that wallpaper at will, because we can't simply consult the wallpaper as a whole. Those rules, as it were, get around the limitations of space by operating through time.

Except...

...with magic, we don't need to do that, do we?

Imagine something like Borges' Library of Babel. We're in a large room, polygonal room with somewhere between three and twenty walls, with various patterns on the walls (or, if we prefer, a certain selection of books on its shelves). Each wall has a door, which takes us into another room of the same sort, with a similar but slightly different pattern (/book collection). That room leads us to another room, and so on. Now, this sort of infinite library is equivalent to the complete world of deducible propositions given a certain premise, which means it's also equivalent to the operation of a computer program.

So, if you want to run a computer program, you don't have to build a computer. You just need to draw a picture, conjure up an infinite library of this sort, and then send a fast-running scenthound through the library, with a red ribbon tied to your hand and its collar, trained to stop and bark when it finds a room with a certain type of pattern on the wall (in most cases, this will be a room with a simpler pattern than any of its adjacent rooms have).

* assuming I've not gone wrong - which I almost certainly have, "⊢((((AA)(BB)(CC)(DD))((AA)(BB)(CC)(DD)))((EE)(FF)(GG)))((((AA)(BB)(CC)(DD))((AA)(BB)(CC)(DD)))((EE)(FF)(GG)))" can be interpreted as the fact that 4+4=8, expressed via binary.

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It occurs to me that i MAY not have explained that as well as I might have. Well, moving swiftly on!