``So what does he like?''

``He likes that which he can paint. . .''

     — NIE82

「WORDPLAY」

 

— 〈  1  〉—
 

Now what I'd like to do is to make a longish comment about language.

Our sequential language is not appropriate for adequate description of systems.

That much is obvious.

It's not adequate to describe natural reality; it's not even generally adequate to express a fictional reality in stories, some argue (BUR69, BUR76).

The sequential nature of language has more to do with the fact we have one mouth and one throat and attend to one and only one event, if that, at any one time, and the fact that the precept we hear when others speak is gone in a second, after we hear it, we process a string, not parse (CHA15, CHA16).

Writing or painting or poetry, or logical mathematical notation, is differentiated from speech not so much in the proximity and interactive nature of the communicating actors, contrary to MCLU64, but rather in the sense that it allowing several precepts to coexist on a single page at once, in no special order (CHA16, BUR76, MCLU68).

The language that consists of a sequence of words is more useful for mythology than communication of truth or technology; and it was one of the earliest portable tools (MUM67). It has many uses. It can be reused; and it's easily learned, and portable, a great tool. It had many uses. But it is not the best tool.

 

— 〈  2  〉—
 

Mathematics was invented for that. Writing was a preliminary step in that direction — an intangible stepping stone. Only a convenient stepping stone. Mathematics has gone quite far at this point (HUG04).

I like the sequential written language that is made up of words put together. You see, I write fiction.

So.

I like our written language; I'm biased. The fact that it's mush let's the writer of fiction suggest more information than is really provided.

Rather let the brain of the reader do more of the work. I especially enjoy elliptical writing. That's just all very nice, I think.

Trouble is that we get linguistic paradoxes. Which are what? Pseudoproblems. They're pseudoproblems.

Much of philosophy is pseudoproblems piled together in a neat lump of shit; and I like philosophy. I'm one of the writers who happily submits papers to them. Just like I happily write fiction.

When we rely too much on intuitional rather than mathematical language we get phrases that look like descriptions of problems. They look like arrows pointing to things. But they are purely linguistic puzzles. Not even that. They are merely notational snags pronounced and repeated and habituated to be the reader who comes to take them with great seriousness by the mere habit (MEN55, BUR69).

Habit is very serious business. We began with William James; we end with him. Reflect on what he wrote about habit (JAM90).

The habits we have automate much of our behavior. So they leave us to think at a higher level. But they automate much of our behavior.

We think at a more formal level. Formally operating brains show us a world of things and not lower level, noisy, measurement results, measuring operations, measuring events. But they show us a world in which some of the things we see are not real.

Our language presents us with problems are not problems and descriptions that are not relevant.

「DETERMINISM」

 

— 〈  1  〉—
 

Have you read William James on this subject? (He had an well known viewpoint.)

Whether the world operates according to determinism or not is not relevant.

There's a simple way to communicate the basic idea to other people who have no technical background, by the way.

Observe in the following toy example ABC NOD MVC BOH ANN ACG GOB ACM NMN is both random and deterministic at the same time. The pattern is 100 repeating. That is B occurs and fails to occur with an exact regularity.

A properly prepared experimental setup, distributed appropriately, will measure a uniformity. But another will measure irregularity.

Go figure.

Both can arise from a random process with the correct distribution. Indeed the evidence is that this the case.

There is uniform law over space and time and yet it is a general law, argues James Hutton. The future is like the past in the sense of the law; but different from that past. The future follows the law not in spite of the future being different from the past but precisely because of how the future is different from the past.

Indeed one way to view particles is as perturbations in a sequence of measurements of higher energy quantum events. This gives them the correct larger size and lower energies that we observe Wheeler argues.

Consider the teaching example once more. Suppose the next measurement is not BAD but GAD. The pattern is 10100 repeating. That is for C now and the pattern is at a larger scale. 100... |-> 10100.

John Wheeler and others therefore viewed uniform law as emerging from the statistics of an underlying true randomness. But at a higher scale. At a level that is more coarse.

What does it mean to talk about determinism in general?

Nothing at all, I suggest.

 

— 〈  2  〉—
 

Now consider a program. And consider a grid.

Just imagine it.

Much of the operation can be random. Feeding on variables we take as random. Inheriting the randomness.

Yet there will be invariants. And based on the sniffing of invariants, certain other actions will occur, and constraints made on the underlying operations which therefore become distributed differently.

Is the program deterministic? Or is it indeterministic?

That does not matter. We only care about the behavior.

What are the invariants of the system at various granularity will predict what the system does exactly. But only at that level of granularity.

 

— 〈  3  〉—
 

A very simple program can produce very complex behavior. Complex in the sense of another language.

Is it simple or complex? And is it really complex if complex? I know not what that question means.

Exist three rollers. The apple is on the rollers in a cage. Part of it protrudes. One side of the cage has a blade that is above or below; if below it will slice the surface of the apple. A sensor detects if the apple is green at the point where it protrudes. The blade is above. A sensor measures temperature. It turns this into combinations of rotation speeds fed the rollers. Temperature is not correlated with the apple.

A long equation is required to describe how a machine will peel an apple.

Even a verbal description of the program is simple and concise.

If green, stop roll (MEASURE-m->ROTATE), descend, ascend (MEASURE-m->BLADE); else begin roll (MEASURE-m->ROTATE).

The description of what it does is not trivial.

If a program with worse performance is acceptable: begin roll, descend, ascend, repeat.

This is one point about complex systems (WOL02).

But even a multivalued morphism described by a parametric equation f(x) = h(a,b,c, ...) can often be reduced to a system of simpler parametric equations. Even simpler, however, it can reduced to an ordered sequence of single valued differentiable functions.

Consider the x axis as a line. It's a smooth function. A set of points. Take another smooth function: A(x). It's a set of points. At points compute the tangent line. Find the line perpendicular to this one. Specify a distance along each as another smooth function: B(x). Rinse and repeat. Therefore (x) ↦ (a,b,c, ...) is replaced by a system of smooth functions (x ↦ Ax, x ↦ Bx, ...) which are perfectly correlated with the relations (x) ↦ (a,b,c, ...) yet each can be analyzed.

One can minimize or maximize a perfectly correlated system in another language.

``Hey, that sounds useful!''

``Well, it is useful.''

There are hundreds of alternative descriptions of the same system and some are better than others, in a pragmatic sense — for different purposes, as different means to different ends (JAM07, DIR39).

 

— 〈  4  〉—
 

Consider actions on a cryptocurrency such as Steem which is also a platform for social media.

We can treat conscious, intelligent behavior at random.

The reason is straightforward.

You approach a door and enter a password. If the door always opens, the process is probably automatic, with a high probability. Keep in the mind that all further arguments will be stated in terms of probability. This is important.

But if the door sometimes opens, and sometimes not, you suspect the password merely alerts a guard. Who looks at your face. And he decides to let you in or not. Sometimes he's out of the guardhouse. Or doing something else. Maybe he decides you're an arsehole. So he let's you wait. You can't predict it.

You suspect intelligence by randomness.

At the level of a population randomness reveals noise or intelligence. They are genuinely hard to tell apart. If we judge by statistics performed on behavior. That is the language of communication theory. Of information theory.

Information is asymmetry in a distribution. Coherence. You receive a symbol A. It's 50% n and 50% m. You receive a symbol B. It's 50% v and 50% w. The As and Bs cannot communicate much. They behave the same.

Suppose, however, As were 90% n s and Bs were 90% m s. Now we're talking. Because now we can talk.

We can distribute in space or time, and space requires time to traverse, which is why simultaneity depends on perspective, same distance from an observer, whatever. Before we have asymmetry we do not have the consideration of how many mouths and ears and where they are, we have no mouth and we have no ears. We do not talk and we do not listen.

That is what means information.

A very deterministic system that emerges from a random system by messages that accumulate and inform which way distributions are skewed have a lot of information. Uncertainty exists and is reduced by messages. Events that increase the asymmetry increase the information.

We can consider recursive equations more buffered in their fixed points, more stable under variation of boundary conditions and then perturbations in the processes, as having more formal information.

If the underlying lowest level actions are random and nondeterministic and the operation is indeterministic, depending on factors outside the program and its parameters, the outcomes of the system may still be deterministic and the formal properties of the system, and its invariants, used to reason about it very strictly.

This can be used to reason strictly about systems like cryptocurrencies with many use cases, many involving conscious reflection of users.

Formal properties and invariants can be operated upon by actors in the system to change the distributions of nondeterministic or indeterministic actions at a lower level.

A later post will illustrate how to proceed in a well developed language of specification such as TLA+ (LAM03).

Specification deals precisely with formal properties. Let's use the most productive tool to communicate.

Because why not. The state diagrams being posted in whitepapers to explain algorithms are rather annoying me at the moment. They appear clear but are in fact opaque as to final behavior of the system at any level.

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