Digital physics
en.wikipedia.org
en.wikipedia.org
He is a very watchable speaker. There's an amusing moment in one of them where he talks about getting high on hyperoperators. I wish I could remember which one it was.
Among other things he tries to convince you that real numbers are a figment of our imagination, an obvious consequence of digital physics, but still quite startling. He has decent arguments.
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[...] it is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer. (John Archibald Wheeler 1998: 340)
It from bit. Otherwise put, every 'it'—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. 'It from bit' symbolizes the idea that every item of the physical world has at bottom—a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes–no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe. (John Archibald Wheeler 1990: 5)
If not, then enjoy yourself.
For example, statistical Physics tells us that a system can be full of complex, random fluctuations, but it can still be 'stable' if those fluctuations cancel each other out. Boltzmann hypothesised that we could just be a random fluctuation in some otherwise stable system (perhaps a vast cloud of gas). This hypothesis is falsifiable, since large fluctuations are far less likely than small fluctuations. It's very unlikely that the room I'm in, including me, is a fluctuation in a gas cloud, but the anthropic principle says that I wouldn't notice all those small fluctuations which don't produce me. If I am a fluctuation then I can predict that it's incredibly likely that the fluctuation is limited to this room, as anything larger would be far less likely. However, when I step outside I find a whole city, which falsifies the hypothesis. Likewise we can observe a whole planet, solar system, galaxy, local group, cosmic web, etc. which goes exactly against the predictions of the fluctuation hypothesis.
However, from a digital physics perspective we can get the opposite result. Let's hypothesise that we're running on a giant Turing Machine and our program is a random fluctuation on its tape; ie. a random series of bit flips on an otherwise empty tape. Since small fluctuations are vastly more likely than large fluctuations, we would expect to be part of a small program rather than a large one. Again, the anthropic principle says that I'll never observe tiny programs that don't produce me, but what can I say about tiny programs which do produce me? Well, randomness and asymmetry is hard to produce using a computer program: it must be encoded as part of the program, since it can't be produced spontaneously. Hence I would predict small programs to have less randomness and asymmetry than large programs, so I would predict a symmetric and uniform Universe, which is largely what we see.
One falsifiable prediction of such a digital physics theory is that quantum phenomena are actually pseudorandom, ie. deterministic and predictable, since the only way to encode unpredictable values in a program is to write them out bit-for-bit in the source. A pseudorandom number generator would require far fewer bits, and hence is more likely; also, a smaller pseudorandom number generator is more likely than a large one. If we find that quantum phenomena cannot be predicted by any short program, we can falsify this hypothesis.
What with the holographic principle, it may be that the "real" universe in a huge sphere, and the effects we observe simply due to overlap. Sort of like Conway's Life played on a cosmic scale.
Cool stuff.
For example, the pull of one celestial body of matter on another (really the sum of particles, but let's simplify) can be explained with math. But you cannot communicate the RELATIONSHIP between the two without understanding the concept of gravity and space-time. It would be claiming the universe is all 1s and 0s, ignoring the fact that there must be a en/decoding method - a meaning to the numbers - for them to make any sense.
The weaker claim that the universe CAN BE computed is to me fairly obvious, but that adds little to any discussion among those who believe in causality.
It's amusing that you find it hard for the universe to be described mathematically when physics does just that.
I should note that digital physics does not imply that physics are purely mathematical..they can be procedural -- ie. akin to a C program. When you get down to it though..whatever is doing the higher level computation, the processor, could be accomplishing the instruction set using purely boolean logic.
For example, every chess position can be enumerated, but no human can ever enumerate them all; although a Turing Machine could, given enough time and tape.
For me, I immediately think of:
What instruction set are we considering? Is the instruction set bounded by human language?
Human language does not have the same extent as thought -- or does it? Is the indescribable as cardinal as the unthinkable?
What is the Chatlin's constant for average human thought process.. ie. a subset of our brain programming?
Man, what an interesting subject.
Any (Turing-complete) instruction set can be translated/compiled/interpreted-by any other (Turing-complete) instruction set, given a suitable translator/compiler/interpreter. Since we're running all programs, we will eventually run all translators/compilers/interpreters, so no matter what instruction set we choose, we will start running programs from every other. The longer we leave it running, the more of a mixture we end up with. Since Chaitin's Constant is the (uncomputable) result of letting such a scheme run forever, it contains a perfect mixture of all instruction sets, and is thus independent of whichever one we choose.
Chaitin has also uploaded the full text (pdf) of the book to Arxiv.org [2].
[1] http://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/1843...
"Digital philosophy grew out of an earlier digital physics (both terms are due to Fredkin), which proposes to ground much of physical theory in cellular automata."
Is consciousness the derivative of information with respect to the difference of information (ie. a clock cycle -- time?)
But if I recall correctly, the book doesn't touch the question of how consciousness can arise to begin with, other than making a passing reference to GEB's strange loops.
I can see some value, for example, in the idea that consciousness (maybe I should rather say subjective perception or awareness) somehow emerges out of a reasonably complex system. But that wouldn't explain what it is in our universe that allows awareness to emerge to begin with.
I think some fun questions to think about are:
* Can we create awareness in a circuit by making it complex enough? What are the requirements?
* If we simulate a universe, does it inherit the ability to create awareness from our universe?
* How the heck do you validate any of these answers?
Well, I'm confused now, consciousness is too hard. Sorry if I sound like gibberish.
EDIT: This isn't meant to be a criticism of the book, which I can only recommend to anyone.
[1] http://www.nytimes.com/2010/09/21/science/21consciousness.ht...
Thats is a completely meaningless statement. If we added this to our model of the world, the model wouldn't predict any new phenomena.
> Is consciousness the derivative of information with respect to the difference of information
You can define consciousness like that. But it would be something different then our intuitive understanding of consciousness.
That sounds like a logical fallacy, mate. Or at least an extremely biased outlook on discussion
Also, when we're talking about what could hypothetically be outside of our universe, unreachable to us, there are millions of possible theories. (All of them meaningless.) Why choose a simulation on a computer from our universe?
It seems silly, as someone who isn't omniscient, to claim that our universe being a 'simulation' has no bearing upon experience. For all you know, light's speed is based on the clock-speed of a higher-dimensional crystal. It's interesting to think about, and there actually are consequences to this even if they aren't immediately discoverable.
For a guy with a username like RiveriaKid..you sure have a closed mind unlike a child.
Perceptions (I see an elephant) are different than ideas or thoughts (I think there are pink elephants in parallel universe).
> It's interesting to think about, and there actually are consequences to this even if they aren't immediately discoverable.
What consequences? If there are consequences than yes, we can add "we're in a simulation" to our model of the world. But there can be much simpler explanation of the phenomena. Models of the world should be as simple as possible. See Occams razor.
> For a guy with a username like RiveriaKid..you sure have a closed mind unlike a child.
I have a very open mind but I'm also very rational. The username is a reference to one great sci-fi sitcom by the way.
There is a difference between perceptions and ideas, though its pretty hard to illustrate because you can't describe a perception without categorizing it by ideas that are external to the perception ("elephant", for instance, is an idea, not a perception), and even short of description to others, ideas shape our internal experience of sense data on a pretty fundamental level.
Hence, if it's reasonable to go from "lots of complex stuff exists" down to "simple fundamental physics exists, complex stuff is emergent" then it's not unreasonable to go down a further layer and say "computation exists, physics is emergent". It's pure reductionism; the first step takes us from a world of "complex stuff with fundamental physics which can do computation" to a world of "fundamental physics which can do computation"; the second step goes from "fundamental physics which can do computation" to "computation".
The only atomic thing is the way I percieve the universe right now. Someone else will percieve it differently. I'm _not_ talking about the fact that your blue might not be my blue, I'm talking about the fact that time might move at a different pace (if you've accelerated or decelerated) and that you're a long enough distance away from me that our lack of a shared "now" is not negligible in calculations.
So a digital model of the universe would have to take into account that the whole universe, again, isn't an atomic entity, and rather model that we have different entities perceiving things as the universe has propagated to their point of view, in their speed of time.
Note that such a computer wouldn't have to be constrained by any of the Physics that apply inside our computation; ie. there don't need to be space or time limits.
To use an analogy, why can't particle physics be like a Mandelbrot which doesn't have a bottom?
You can take the idea further and abandon any notion of time or even discreteness altogether: If the universe is essentially information, this information can be _completely_ described by some (mathemtical) language. Note, this description doesn't have to be finite.
For the finite and discrete case this description may simply be a very long bitstring/vector which contains every detail of our universe. If time is discrete as well we can write a whole timeline as a matrix, a set of bitstrings each representing one slice of 'now'. Notice how we now have one static thing being a perfect representation of the universe. No need for a computer or interpreter. Just a big table of ones and zeroes representing everything from the big bang to your mother.
However, our universe might be continuous. You might still be able to describe it with finite amount of information tough. A function like x -> x*x is continuous and defined for infinitiely many values but can still be written down just fine. Even infinite complex things like fractals can have a very short descriptions. Or take pi. An infinite sequence of numbers describable in a few sentences.
Point is, a universe need not to be discrete in order to be written down on a sheet of paper. It just needs to be finite in an information theoretical sense. And you may need a lot of paper.
I strongly suspect the universe is bounded. But what if it isn't? Can we still se it as a mathematical entitiy? I think so, but I'd like some comments on that. We have the well-defined set of real numbers and it contains _every_ real number, even those who are completely random up until the last of their infinite digit. There are numbers in R which have an infinite Kolmogorov complexity [1]. And yet, we can put them all in one set. We can even draw a picture of all these numbers (it's just a line, but that's more than our analysis professor would draw to illustrate something).
In conclusion: I think (and didn't proof) that even if the universe contains infinite information and cannot be the result of some turing machine it can still be tought of as a mathematical object. A thing like sqrt(2) or a triangle.
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A second and orthogonal tought is about the 'reality' of all this. This is a bit metaphysical and philosophical. If you are still reading please tell me I went crazy. The idea is, if you have a perfect description of our universe (be it a turing machine, a big matrix or some other complicated mathematical thingumabob) is there a difference between the description and the real thing? Obviously not, one is just words on a paper or bits in a computer and the other a world full of loving and caring people and other stuff. How can I even ask such a question? (Hint: I'm on the Internet and can write what I want.) Well, imagine doing this whole computer simulation of our universe. Would you feel any different when being run on some sort of computer? If you and everything around you would be perfectly simulated would you notice it? Would you even be able to? For the ones running the simulation the difference would be obvious. But being part of the simulation you may have no way of knowing that you are a piece of software. It would all seem and feel real. It would BE real. And yet you are just bits. You could stop the computer, dump it's memory and write it all down. Doesn't seem like such a difference between words on paper and reality after all.
What I'm trying to explain is that a perfect description of something is actually, in some sense, the _same_ thing as the object being described. It's a bit like uploading the whole universe instead of just a brain. In the end all you have is information. Doesn't matter if this information flows trough transistors, is written in ink or just an element of the set of real numbers.
And if you say the number '4' 'exists' and so does 'pi' then why not 'the universe' as well? If you say this then you just answered the question 'why do we exist?' Because _everything_ exists. In the same sense as every possible triangle 'exists' so does every universe. We just happen to observe one specific instance.
The sad thing is: This doesn't really explain anything. If you say absolutely everything exists you haven't made any predictable or verifiable claim. So it may give you a philosophical answer to why are we here but it isn't much more than '42'...
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[1] Some formal proof would be nice here. I didn't think it trough down to the simplest axiom. Maybe it's enough to argue that there are only countable many turing machines but uncountable many real numbers and therefore some real numbers cannot have a finite description.
Consider our spacetime as a four-dimensional space, the pixels of which are set by a computation running in a different dimension of "time." The number of steps required to generate the final output is arbitrary and unrelated to anything we observe, and there's no contradiction in supposing that, say, information in our future could be an input to an iterated algorithm that determines our present.
I'm also curious if this strays into the philosophical area of phenomena/noumena in the transcendental idealist school of thought where a thing-in-and-of-itself [noumena] is unique and unknowable, we simply access representations [phenomena] of the thing? So I would say your perfect description (and Alan Moore's gods) are some class of entity that somehow become both phenomena and noumena??
[1: http://www.believermag.com/issues/201306/?read=interview_moo...]
My main point of disagreement with the philosophy would lie in the ultimate weakness inherent to a digital explanation: the infinite points in between.
http://www.dailygalaxy.com/my_weblog/2008/04/is-mathematics....
(But, no, quantum physics didn't settle on the quantization of all data.)