PeroK said:
But, what if there is a physical, theorectical limit to observation knowledge? This could come from a) there being a limit on how accurate a measurement of position could possibly be; and/or b) a limit to the knowledge of two observables - the HUP (Heisenberg Uncertainty Principle) essentially says that the more accurately you know the position of a particle, the less accurately you know its momentum - in any case, you can't know both to an arbitray precision; and/or c) a piece of data that is intrinsically random, such as the spin on an electron, which may be theorectically unknowable.
This ties into my post above. There is no certainty that Quantum Mechanics will one day be replaced by a "deterministic" theory, where the HUP and the instrinsic probabilities disappear. And, unless that happens, then there are clear limits to observational knowledge.
To be more specific, I'm not necessarily saying that randomness exists, but I'm also not saying that it doesn't exist. I definitely don't have privileges that break quantum observation, lol.
And yes, the limits are clear. Assuming that human beings and human logic are the highest point on some hierarchy we imagine exists, thus creating our measurement error in any possible measurement device that we can currently imagine. To be more precise, we will never have a finalized and perfect definition of the physical world, thus we will never have a fully agreed upon definition of what is random.
Zafa Pi said:
Random := The value(s) produce by an objective* physical* process that when repeated yields a sequence that passes randomness tests.
* objective means repeatable by others. * physical means non-algorithmic, like coin flips.
I like this definition of randomness as it is useful for most purposes and clearly delineates physical phenomena from math.
It's theoretical, but I don't think it's fluff. Un-testable by current standards? yes. There is still a humongous debate about whether or not reality is deterministic. I am liking what's going on with Quantum Gravity theory with their quasicrystals and information theoretic notion of reality which takes neither side of the debate. We can only measure phenomena which we can sense (with our senses or some device), and even then, the measurement of that phenomena changes the outcome, plus is very prone to error. Are there dimensions in physical systems which we are not taking into account and could be measured to approximate an outcome, but
we simply cannot measure them yet?
I'm not saying that we are in a simulation. That is, I think, too far off topic. But I will give a simulation test example of how randomness can be explained. The problem being that you don't know if physics is the observed result of some higher order algorithm which sits behind the true laws governing the physical system in which the coin is being tossed. You have to take into account "the observer" which is also theoretical, but I mean, if we can't prove randomness exists, then randomness is also theoretical.
Let's take the idea and inverse it.
If you assume that the observer exists, technically any device which senses a physical phenomenon is an observer of that phenomenon whether or not it comprehends what it is sensing. Let's say that I make a program which takes input from a camera, performs a couple of filter operations on the incoming data and creates a 2D space which is scattered with colored points that represent the color edges being sensed in the current frame. So my space has the following dimensions: (x, y), (r, g, b) and the x,y sub-space is filled with points by the edge filter using the r,g,b data from the original video frame. Now let's say that I also populate this space with "observers" which follow some rules that govern their behavior.
What my little simulated observers are sensing are the edge point positions and color that are the result of multiple filters working constantly on some input data. The filter input data is coming from "my reality" or what you refer to as the physical world, whereas the filtered output data is a simplified projection of that raw data. To further complicate things, let's assume that the simulated observers can recall and track edge shapes from the points they observe. They will always ever be observing a filtered 2D projection of a 3D space. Let's also assume that they have some ability to remember patterns and thus predict near-future outcomes like a shape they will see, or where and in what orientation that shape will turn up.
They will never be able to fully predict where and when in their reality, the points that represent my hand will show up, because they don't know my hand exists as a hand. The idea of what a hand is supersedes them, since they don't have hands or bodies. A hand is only represented in their space as a recognizable set of points with specific relationships in 2D+Color+Edge space, which occur in some positions at some rotations, etc. The physics of how a CCD camera works, how the edge filter algorithm works, and how my own decision making process works are all impossible to know for these observers because their observable reality is a product of these perception filters used to create their reality space. Their reality is a projection of my reality that is further filtered before they can even perceive it. These are the observational limits of their perception as set forth by filtering (projection) process.
It is to say, I can accurately predict where the points that represent my hand will show up in their space and in roughly which configuration those points will be, because I am an outside observer of their reality and I can perceive the extra dimensions which affect that reality, but they cannot (imposed measurement limit). No matter how intelligent these lower dimensional observers are, the best they can ever do is create a statistical observation of where my hand might show up with some certainty quantifier. They might even make up equations like the Heisenberg Uncertainty Principle to formally define this and try to explain the phenomenon as random because it saves them the time of trying to imagine something that eludes them about their own perception of what they believe to be reality.
I'm not saying that this microcosmic example is true for our perception of reality, I'm saying that we never stand a chance of knowing if randomness truly exists or not. Perhaps it's just an artifact of the laws that govern the physical space we exist in, which could be generated by a higher-dimensional space in which other laws apply.
It is proven that each perception of reality is not the same as other's perceptions. The Pauli exclusion principle perhaps is a clue that either we are not seeing the same data, or that we are seeing the same input data, but through the chained filters of our "perceptive ability" and the distinct point of view through which we perceive the space. No two measuring devices can exist in the same physio-temporal position, thus no two perceptions of the same data will ever result in the same final input which is then processed by the perceiver. This is yet another filter, the entire process taking time to actually happen. In a very real way, the perceptive filter of our reality is represented physically by a sense organ or device. What we see is what we get. Are we all inside of a higher dimensional reality which, upon perception, collapses into a lower dimensional representation of that reality?
That brings us to the idea of fractals. A fractal is a projection of a higher dimensional space onto a lower dimensional plane. Point by point at any scale or n-dimensional rotation, can be calculated up to the currently working infinity limit, which is rendered in the projection as negative space. When projection happens, one or more dimensions must be collapsed into another dimension on the plane of interception/observation. When your eye perceives light, it generates signals which are rendered in your brain as a 2D projection. If you have two eyes, you have a higher sense of depth. This is a perception of a dimension of physical space which we call depth. This third perceived dimension helps us further define and comprehend the data we are perceiving inside of the space in which we exist.
Is it hard to imagine that the factors operating in a coin toss elude our limits of perception given the limited physical representation of reality at which we interact and observe? No... and that's why we have statistics. Statistics smooth for "randomness" by counting, summing, and the like, in order to account for the error in our ability to recognize data as an ordered pattern due to those perceptive limits.
This is really a great question! Thanks for the inspiration. I'm loving this forum, I feel like I've been missing out on talks like this IRL.