@ACuriousMind Real numbers are not mesurable... They are not computable. The real empirically verified content of scientific theories in my eyes is not the various ontological entities we posit, but rather boils down to the capacity of a theory to provide finitely computable algorithms that can be compared to the finite information provided in experimental results...
To me, "absence of any law" would be the complete failure of inference: You can't even begin to fit a probability distribution to the outcomes of repeated experiments because every time you do something, something completely different happens.
@G.Bergeron I put the lower end of the pipe on the bottom of the pull and the other end 2 meters above, If i were to manually put water in the lower end of the pipe, would the water have the strength to rise up to those 2 meters ?
@G.Bergeron, i inputted the first time through in that loop "Hadamard" (recorded response) "n" (repeated) "control" (recorded response) "y" (ended both loops when it should've started a new one
@G.Bergeron Uh, okay (I'm not sure what exactly that means). My issue with "uniform distribution = absence of laws" is that the notion of "absence of laws" is then easily broken by a single event:
Imagine some parameter which you only ever measured to have two values in perfect 50:50 distribution. then, suddenly, you measure a third value for it once. At this point, sudeenly the system which you would have declared lawless earlier has a law.
I have no problem with our assumptions which laws a system followed being proven wrong, but I feel unconformable with a notion of "absence of laws" that can be disproven by a singular event, when the very idea of a law would be, to me, regularity in a number of repeated events.
A law is supposed to have predicitve power, and "this process follows a uniform probability distribution" is a predictive statement - it predicts something about how the system, on average, will behave. I really think that is very different from the absence of laws.
@Sanya If I have absolute faith in the correctness of the measurement, yes. I don't have a problem with that - I have a problem with the statement "there are no laws" being disproven by a singular event.
@ACuriousMind Also the nice thing is that with the algorithmic complexity approach to probability, you get this notion of compressibility which encodes and represents both the predictive power a law and takes into accounts that a single events does not change much
@ACuriousMind Really, what will be the next measurement then? :p
@ACuriousMind ok, then we just need to differ here :D I don't think falsification is a useful concept in the first place - but yeah, well, I think the concept of "absolute chaos" is a bit like "acausality" which - along with causality - is not really a useful concept to me, so I'll not want to convince you of anything concerning that
@ACuriousMind But my point is that what is the predictive power of your theory if you can predict absolutely nothing beyond an infinite sample will have this distribution
@Sanya So you reject both the relevence of falsifiability and causality?
@G.Bergeron Well, if you pose the question like that, what predictive power does the statement "This process is random with distribution X" have for any distribution X?
@ACuriousMind I think the issue is that what I claim can never actually be verified experimentally as there is no way to prove a string is truly random. This an uncomputable task
@Sanya Oh, I gave an "easy" definition of "absence of any law" earlier: A world in which inference completely fails, no event has the same outcome twice.
@ACuriousMind There is a deterministic process that maps your distribution to a flat one. This the actual theory, the rest is what you can't model with your limited information processing machinery or just purely random.
@ACuriousMind If it never has the same outcome twice this is a minimal form of coherence I like the failure of inference interpretation of absence of any laws...
@ACuriousMind In this case in the limit, you can predict some of the measurement string since it will be a little bit compressible. This is the point it has inherently more order than non-biased randomness as defined per the Kolmogorov complexity
@Sanya Damn that is drastic! And, I would strongly disagree
@Sanya Falsifiability (of a theory/concept): being amenable to a form that can produce finitely computable algorithms the outputs of which, under a prescribed input, can be compared with the finite quantification of the outcome of an experiment
@G.Bergeron yeah of course, if I have a theory with any predictive claim, I can calculate and experiment and compare the outcomes. But what happens if the outcomes don't agree?
Well, see, I'm thinking more...physically: Think about a screen upon which you send some light that's a completely plane monochromatic wave. Without anything in the way the distribution of photons on the screen will be uniform. If I put a single slit there I'll get another distribution, if I put a double slit yet another, and so on. I do not see how "the light is uniformly distributed" is any less or more predictive than "the light is distributed according to this sinc function"
(if it wasn't sinc for a single slit, insert whatever the damn distribution function is :P)
@Sanya Causality: An ordering that can be given by the conditional Kolmogorov complexity. The idea is how "conditioning" on another events in an algorithmic sense enhances predictability. It is a question of information transfer
@ACuriousMind In the uniform thing (not sure what distribution you have in mind though) you can't infer anything beyond describe the sample you mesured... in the slit thing you can do better by compressing your mesurements, you can effectively describe the outcome using less bits
so we need to quantify the "environment conditions" along with the system
which in the end will lead us to a relationship like (unique status of the universe A) -> (unique status of the universe B); which is not in any way a helpful concept of a scientific theory
@G.Bergeron Yes. What has that to do with my predicitve power? Predictive power in the physical sense is that I can predict the results of experiments, not that I take as few bits as possible to describe results I have found.
@ACuriousMind If you can describe the outcome with less bits, that means that you can predict the "missing" bits to reconstruct the output... this is the gist of the idea
@Sanya I would disagree, but then we probably do not have the same meaning of a wrong measurement
A wrong measurement is not simply a point that doesn't fit my curve
@G.Bergeron Yeah, I agree that's a meaningful notion when I'm trying to predict a sequence of numbers, but I don't see why this should have anything to do with physics. That "In situation X, the light will be uniformly distributed" should be less predictive than "In situation Y, the light will be distributed according to sinc" is just patently absurd.
@G.Bergeron why is e.g. a band gap that is a factor 2 too big (that's certainly not FTL and more on the "point that doesn't fit" side) acceptable? What deviation is acceptable?
@ACuriousMind This is not the kind of thing you really confirm in experiments... You will transform that into some equation and experiment design and then run the test... At the end you will, yes, only be comparing numbers
It's like if I said that my theory is that there is a big book with the history of the universe written in it and reality follows it... This is a shitty theory
Yet... it has effectively an absolute predictive power, if only I could get hold of that book! SO why is it still a shitty theorY?
@G.Bergeron So why did you claim that "These parameters are distributed according to a uniform distribution" corresponds to an "absence of laws" for these parameters?
Because there is no gain in compression beyond stating what I observe
Because when you compare probabilistic information theory to algorithmic complexity theory you get a connection between entropy and kolmogorov complexity and thus compressibility
@G.Bergeron Also, what? In the experiment I described, that's literally what you confirm: You let the light shine for a while, then look at the pattern on the screen and which distribution fits best
THat does not mean that reality is only a bunch of numbers but only that the scientifically describable part of reality is "isomorphic" to a bunch of numbers
Yes, quantitative science in the end boils down to a bunch of numbers. That does not in any way imply that the physical notion of "lawfulness" or "predictive power" is related to the compressiblity of these numbers taken as just a bunch of numbers
I do believe it is as of now. I did not think like that initially, but I actually feel this approach has a LOT to offer and I am trying to properly formalize all this as a pet project on the side of my more run-of-the-mill research.
Some people are working on that like Stefan Wolf. I think his writing does not do justice to his ideas.
