Visualizing the Convergence of Harmony.

So I've been getting back into music lately, trying to learn some jazz chords (and how to use them) on guitar. Oddly, I stumbled upon something interesting recently, something mathematical that applies to music.

Its the Monoid formed by the operator (x*y) mod n. Simple enough, times tables reduced down by modulus to be self contained. By when I rendered it I saw a shape:



See the rippling spirals formed by the smaller numbers with one digit? I decided to render it, translating the numeric values to pixel darkness. It looked cool, and a pattern started to emerge as n got larger. Here it is for n = 913:



(This picture had to be shrunk for Blogger) What its interesting to look at is the contiguous points of light and darkness, the way they form "diamonds". They can be thought of as folding points. For instance, the point in the center corresponds to folding it in half, both ways (vertically and horizontally). The 4 diamonds around that correspond to folding in thirds both ways, into 9 sub-squares. There are diamonds for the fourth, fifth, sixth seventh folding points and so on, each getting smaller and less distinct.

The coolness of this is that it corresponds exactly to the principles of musical harmony. Folding a frequency in half (doubling it) gives the octave, 3 times the fifth interval, 5 times the major third, and so on. So each diamond in the picture corresponds to a point of harmony moving toward dissonance into the areas in between, at least in the old school tunings before equal temperament. I wonder what the 12-TET monoid would look like. (I mean I wonder where the 12-TET points fall on this)

The beauty of the age of computers is that you can make music in pretty much ANY mathematical system of harmony, you can break all the rules imposed by physical instruments. I wonder what it will sound like 50 years from now.

The image translators work FOR the construct program PART 2

In part one I talked about experiences being produced on demand in a simulated reality, and how this leads to the most computationally inexpensive simulation. Now for the next question: Since an act of observation collapses a probability vector defining the realm of possibilities into a single unique experience, information must be produced in this act. (see previous posts on information for explanation of information collapsing prob. space) An act of observation must increase information entropy. But where does this new information come from?

Well, it could be the effect of a total random process. The Matrix chooses a location, and random shape for a snowflake and records it. If it were truly random, the process would be pretty invisible to us, unless there were some kind of bias on the randomness. But what bias might the Matrix have? Its so minimally defined for us, the only motivation it has we know of is to preserve the illusion of the simulation. So if there any bias in its random choices of manifestation, it would be toward the expectations of the viewer. So if a viewer expects snowflakes to look a certain way, and finding them looking differently might cause them to question reality, then all other things being the same the Matrix will make them look the way they expect. Note that this does not rule out surprises. If a weather scientist observed trends of weird snowflakes in North Greenland, and observed it without surprise, then a layman might be shocked to see them, but researching it he would find the scientists paper, and his sense of reality would return, a scientific explanation exists, even though the weird snowflakes are the product of the scientists observation shaping the construct program.

But the main thing about this is that for the individual (not the collective, which defines scientific truth) these things have an experimental signature: If an individual where able to shape his mind, control his expectations, or have a cosmology where he there is some expectation of internal or external relation with the observed shape of snowflakes as they form, then those expectations, all other things being the same, could be observed in snowflakes. You could do this for years, photograph it, make valid sounding theories to convince yourself as to why it happens, even write a book on it:

But in the end, even after years of seeing the obvious spelled out time and time again in the ice crystals, the predictive scientific power needed for a theory would not be there. This because scientific laws describe the behaviors of the construct program in broad terms of ranges of possibilities, but the expectation bias of the experience translators operate fundamentally at a lower priority, and are unique for each individual and overridden by the construct program. So the bottom line is while you yourself can see these effects, even photograph the beautiful snowflake you made by directing love at it, even share the pic so the world can see, you can not create a general law of love shaping snowflakes that the construct program will follow. Its simply too computationally expensive for the Matrix to have to work in accordance with these arbitrary laws each time somebody observes a snowflake. In the realm of science, the matrix prefers the computationally inexpensive, and thus the wise scientists are the ones who follow the law of economy (as it used to be called) in proposing structures for the construct program: Simple theories equal less computation.

Now what other laws might dictate the shape of viable theories? Well, clearly no theory could prove the existence of the Matrix itself. Entire crops could be lost. However no theory could also prove its non-existence. How could you disprove its existence in a non-simulated world? One way would be to make preserving the illusion of the Matrix require impossible amounts of computer resources for a finite system. If a simulated scientist were able to take any small physical system, and then determine the states of every electron, proton and other tiny thing therein leading up to its final observed state, then the Matrix would clearly have to predetermine these vast amount of tiny state transitions not just for the small system he observed, but for every system he might choose to observe. This would be intolerable in its computation cost. However if the scientist were able to observe the particles acting in ways inconsistent with the final state, it would actually reveal the illusion of the physical laws, of the Matrix. To protect against this kind of attack, the Matrix would have to actual partially reveal itself, it would have to say that at some point tiny particles don't have locations, they only (like the snowflakes above Greenland) exist as probability density waves until they are observed. Thereby, no paradox is created regarding physical laws, but the scientist is unable to crash the system with her observations that would be too computationally expensive to resolve.

The end result is that the scientists must declare an end to the very idea that these systems can be determined, and accept some absurd rules, like that by observing a system enough times, it won't change, (as having to calculate the nuances of certain tiny changes again and again would be too expensive). But the vital illusion of the Matrix hasn't been disproved. We can come up with theories consistent with a physical world, or an information driven illusion world, and both will be consistent. We have been shown the door, but we can choose whether or not to walk through it. Whether or not we do depends on how we collapse probability vectors we are presented with. The words are given to you: But whether 'the image translators WORK - for the construct program' or whether they 'work FOR the construct program', is up to you.

The image translators work FOR the construct program!

There's a line in the Matrix, where Neo approaches Cypher on the ship, surprising him. "Do you always look at it code?" Neo asks, referring to the screens of green letters flowing down the screens.
"Well you have to" Cypher responds. "The image translators work FOR the construct program. But there's way too much information to decode the Matrix."
It was a weird line, so I looked it up online. The consensus is that the actor flubbed the line. He was supposed to have read the line "Well you have to. The image translators WORK for the construct program: (referring to the simulator program Neo was in earlier with Morpheus) but theres..."

So, by putting emphasis on the wrong words, he changed the meaning of the sentence, from saying that
The image translators we have are sufficient for our construct program, but not the Matrix.
to something like:
There is something called a construct program, which we have a copy of but the Matrix also runs, and since the image translators always work on behalf of this program, (work for) we can't use them to see the matrix, only things in the construct program we control.

Anyway, for some reason this whole thing got caught in my head, I couldn't let it go. It said off a pretty interesting line of thought - what are the physics of a world that exists for the benefit of conscious observers? By that, I mean a universe which is simulated and feeds into the senses of conscious beings. A simulated world, with the singular goal of appearing not simulated? One thing would be for damn sure: The image translators would work FOR the construct program.

What do I mean? Well think of that fact you learned as a child: Every tiny snowflake in God's creation is unique. Now think of all the snowflakes falling over the vast uninhabited wastes of northern Greenland. Think of the vast computer resources that would be required to render each one, a uniqueness that would never be seen or appreciated by any conscious mind. Why bother? Why, when the system exists to convince conscious entities of its reality, not to actually recreate reality? There's no way it would sit around making mandalas in the sand that have no impact on the minds it exists for. So what would it do?

It would render the snowstorms. And in so doing, it would feeding satellite imagery, confirm or deny weather system models, even for years into the future, as the data sits on NCAR or NOAA servers. This would define a consensus reality that would be shared for all scientific observers, a shared construct of reality, produced by the program. But the question is, to what depth does it need to render the storms to create this? Certainly not to the level of each snowflake. Its doubtful individual snowflakes would even have locations in space or time, rather they would exist in a far more computationally efficient form. Probably something like probability density vectors or waves. But that raises the next question: What happens when a researcher is actually out there, in northern Greenland in the storm? Does he then only encounter probability density vectors instead of snowflakes? Of course not. At that point he could see individual snowflakes. But how would the Matrix know to render them? Well, what that researcher SEES is a product of where the researcher LOOKS. To look would be to query the image translators. And what happens when a researcher sees a beautiful one and points it out to his comrade? How would he be able to see the same snowflake? Because the image translator collapses the probability density patterns into a unique manifest shape on its first viewing, and then this information is feed back into the construct program, the shared reality, to be stored for other viewers as consensus reality.

In short, the image translators work FOR the construct program. Which is to say they inform it, so things observed by one person (which didn't exist before viewing) can be viewed by another person. So the image translators are in the business of producing information, information which didn't exist before viewing, which is in turn feed back into the Matrix for others to view, for the sake of consistency. Thus there is no way to passively view the Matrix visually. You would be feeding information into it as an observer, and it would know you were there. Therefore the only way to view is through some kind of code, symbols representing transient probability spaces, imposing boundaries on what can be seen in a space, but no absolutely defining it.


END PART 1