There is a tendency to mistrust the mathematical nature of reality, even by the luminaries who discover the mathematical truths:
Einstein, for his part, was initially dismissive of Minkowski’s geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.
Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. However, in 1905 Albert Einstein interpreted Planck’s quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material.
The more mathematical we get, the more powerful we become at tracking reality. This has lead some to not fear the force and join it. Leonard Susskind’s application of the holographic principle to black holes solved the Black Hole Information Paradox. Yet even so, other physicists fear the math of holograms:
“When you start asking ‘Do we live in a hologram?’ Then you are crossing into metaphysics, and you are heading down the path of allowing all kinds of things that have no evidence to back it up, like creationism.”
And when some fully embrace the math, like Max Tegmark who believes all is mathematical, this is criticized:
1. all mathematical structures are a priori given equal statistical weight
2. its inconsistency with Godel’s Theorem.
and also out of gut-reaction, knee-jerk fear:
Jannes argues that “mathematics is at least in part a human construction”, on the basis that if it is an external reality, then it should be found in some other animals as well
All of that will also play out as we unravel the fact that consciousness has mathematical properties. Many of us are already at the initial Planck/Einstein state. We have directly discovered that the experiences of our life have a formal structure but think it is superfluously fancy, or trickery to actually plot them on paper. I believe, that as history has shown with other phenomena that exhibit patterns, those revealed patterns are profound insight into their nature, not just witty accidental discoveries.
The degrees of freedom available are to move in radians along the color axes and shift up and down in lighting.
We also know that valence, the gloss of pleasure vs pain are opposites, and we can tune down the “lighting” of awareness:
Vision is a field like a hyperbolic plane:
There is also the fact that
Empty Individualism = Open Individualism
And yet, to discover this equation, I didn’t have to go and recover the disappeared entropy from black holes. I just had to read the definitions and blink twice.
From Qualia Computing:
Open individualism says that there is only one consciousness.
Empty individualism says every moment is its very own consciousness and bears no relation to past, future, or spatially separated consciousness.
These sound different. They are not, in fact, different.
Empty individualism says that there is a boundary that cuts the flow so that i becomes i+1. i is not i+1 and never was. i did not become i+1; these are separate beings. I was never i who began this post. I am i+1.
Yet I exist. So whether you assign me to i, or i+1, or i+2, I exist.
Similarly, open individualism cannot deny that I exist as a bounded moment. It emphasizes the aspect of removing the boundaries between i and i+1 in “my brain,” and i* from “another brain.” But on the pain of absurdity, it doesn’t actually claim that these are experienced simultaneously or that my present is any more expansive than I feel it to be.
These two phrases [Open Individualism, Empty Individualism] distinguish between aesthetic choices, not fundamental choices. Open says, “Look, it’s a beach.” Empty says, “Look, it’s grains of sand.”
The beach is made of grains of sand wether our language choices emphasize it or not. Namely, our experiences are nows martially constrained in their content by the physics of information processing.
There can only be a difference between Empty and Open for one who doesn’t start from the ontological ground of Cogito ergo sum and takes in the abundant evidence of what subjectivity is actually like.
Of course, it is possible to imagine that maybe one doesn’t exist at all. When you imagine that you are not actually a grain of sand, when you fantasize that a beach can be its own ontological unit, then it is possible to distinguish between the two. But knowing, as we do, that being all grains at once is impossible, we are left with the conclusion that Open Individualism is just Empty Individualism in disguise.
So this self-captured light of awareness, of bare knowing, of untainted phenomenalobject-hood is all there is and all there ever will be.
Or maybe my solipsistic soul has internalized a heavy case of anthropic bias from which it needs to be exorcised; maybe I’m easily swayed by the seemingly heroic protection of quantum immortality fending off vacuum collapse; maybe I just have undiagnosed Asperger’s and can’t really conceive of the other; maybe I am a puddle in awe of its puddle-ness as it slowly evaporates into the darkness whence it came.
Is the firing and resting of neurons culpable for the binary? Or is the relevant information nested in deeper granularity?
Luckily the range is known to have an absolute minimum.
The Holographic principle reveals that information is ultimately 2-D, like bits or pixels. The fundamental particles cannot be infinitely subdivided, they must stop at some point.
This has implications for information slices (grid with on-off switches) which are assumed to be what specify every moment of consciousness. If it turns out that consciousness requires the bottom-most ground-bits, then these can be viewed as the information on the hyperbolic plane. Each information partition corresponds to a layer on the stack of hyperbolic disks.
This is a case where the fundamental reductionistic explanation maybe coincides with a subset of the felt experience.
The binding problem is also relevant. To highlight the problem we must recall the eternal block of special relativity’s spacetime.
It is important to distinguish between the different definitions of “now” that arise when studying special relativity:
- The observer’s past light cone.
- The observer’s orthogonal slice across the block.
An observer and an event are both idealizations. One chooses a frame of reference, then three spatial coordinates and one time coordinate. This gives a four-dimensional vector.
However, an actual observer, in the common sense of the word “observer,” is composed of many brain events.
Commonly speaking, there are no events. There is no one moment where a glass of wine cascades in a flurry of shards. All common sense events have a length of time. A photo represents a non-event. But special relativity’s events are like photos: they are frozen frames.
But then the question becomes: “How microscopic can a special relativity event become?” A birthday photo has the entire room full of people and things, but it also has a cake, and the cake also has a candle, and the candle also has a flame. Each subset of the set could be a photo all of its own, each can be called an event and assigned a four-dimensional vector.
Once you have your own reference frame and your own four-dimensional vector, you also have your own orthogonal slice in the block and therefore your own now which includes past regions of the universe and future regions of the universe that you cannot interact with. But nonetheless, the contents of your orthogonal slice are different from those of even the most nearby events with their own four-dimensional vector. The tip of a neuron has its own cosmically wide-reaching now that differs from that of the nerve cell just across the junction. We are talking about a distance of tens of nanometers.
Now, with this knowledge, let’s trail closer to the mind. We know that the mind exists within the functions of the brain. We don’t know where to draw the boundaries that define the present mind, either spatially, time-wise, or even ontologically. We just know that something in the brain is conscious, that something seems to be happening – whatever that “seeming” is.
Since no respectable theory of consciousness defines the moment of consciousness as a single point to be found hiding in the brain mush, we cannot simply extrapolate from the special relativity event (which is just a four-dimensional vector) and map that to the consciousness. We can also not get away with zooming out from the neuronal forests and tag the four-dimensional vector on the entire brain object. No respectable theory of consciousness claims that the entire brain composes the unified conscious experience.
So what are the respectable theories of consciousness?
They are those which identify consciousness with computations.
But how can we have a grid:
when each neuron is not actually on the same hypersurface of the present?
They are separated by a spacelike elsewhere.
Which past light-cone bears the torch of awareness? Unto which neuron has the duty been entrusted?
Asking these questions reveals an absurdity. Neurons are incapable of being privy to the same information at the same time because of the relativity of simultaneity. And yet it also seems weird to postulate that consciousness is at the head of some arbitrary light message’s world-line.
An interesting observation is to realize that for some people, consciousness feels like a photon. It doesn’t travel through time. From its own inner perspective, its always been here. The amplitude of a photon redshifts as it moves through the curvature of time from the perspective of an outside observer, but the photon itself is immaculate, unmoved.
The debate about whether consciousness is timeless-ground or flux has taken place in Buddhism. The proponents of the unchanging ground of awareness arose in some Vajrayana schools and have debated the Sutta-abiding conservatives who take a more computationalist/empty-individualist approach, saying that it only seems that way, but upon closer analysis, even awareness is just a vanishing factor.