This is for those advanced thinkers who may (or may not) have thought about what a computer actually is. Information is physical; there is no computer anywhere in the universe which is not made out of real atoms. (See if you can think of something that's made out of unreal atoms) Every atom which is real (has mass) is a computer, because it's made out of little 'particles' that are also individual computers. Information is dimensional; there is no "one-dimensional" information anywhere in the universe. The most fundamental, irreducible, logical form of information, which is mappable to any fundamental, logical computer, is 0 and 1, which has 2 dimensions of 'state'. Without these 2 dimensions, there is no way to define an 'input' or 'output', or separate the computation from the information it transforms. {You cannot transform information in just one dimension.) The following is from a course on quantum information processing (as a heads-up to anyone who feels challenged by words with more than 2 syllables): This is where the computational basis changes from classical electric and magnetic fields, to quantum versions of those same fields, as 'inputs' which are operated on by Hermitian transforms in a complex probability space. [What does a quantum measure space look like? How many corrections do various mathematical models need in the various fields of real QC] Classical circuits operate on the same fields with 'components' that transform them and create phase differences between them. Quantum circuits create these phase angles (between say, electron spin) by processing the fields with 'components' that are superpositions of wavefunctions. It's a matter of seeing what these fields "look like", to classical and quantum systems, what the components are and what they do to the 'input signals', how to interpret or read the 'output signals'. One key difference is quantum circuits have to 'produce' a classical output, where this is something classical circuits do already. This is not trivial. So who knows why an electron precessing in a known magnetic field, isn't computing a spin phase? Why the electron isn't transforming the 'input' as spin, and performing a computation? Anyone?
Some might notice (if they look around this section of the forum) that some contributors have the attitude: "you can't understand QM unless you do 5-7 years of university study". IOW, you need to graduate, then get a further degree and then be enroled in a Ph.D. in order to have a chance. But since you will still have no idea what computation is like these certain contributors don't, because you've been studying all that advanced math, this advice isn't what I would call germane. In fact it's irrelevant. You don't need to study advanced topology or group theory, or algebra to the extent you won't have time to study anything else. If you do all that, you are possibly lowering your chances of understanding QIS. The subject requires some advanced math, but as the above excerpt implies, the job of finding out which math, has been done already. People with all that advance math and physics know which bits are relevant to QC, that information is information (it doesn't change just because it's in a quantum circuit). In fact, looking at some of the rather opinionated, self-assured, ultimately blinkered, narrow views some of these math-types have come up with, I'd say these guys have probably learned so much they now have a vanishingly small chance of ever understanding that.
That would be: show why a rotation along a single axis of a mixed state, isn't a measurement basis, and why the time-dependent evolution of that rotation doesn't have a computation basis which is the applied field and also the qubit representation. The applied field happens to be magnetic. How many "components" have a basis that is part of the computation, which is the overall computation basis? A cha, so it is necessary to be seeing what is meaning of this words computational basis? If you learn about classical electronics you apply the math of Fourier and Laplace mostly, to a classical device, and Boole and Turing in digital devices. But atoms can be both and in a converse sense because you apply the algebra to what the fields do to electron spin mostly, whereas you deal with charge mostly, in CI systems. In these you create wavefunctions with discrete devices, the operators in the phase space, in QI the fields interact with wavefunctions and the devices are discrete transforms, the space is different. We know about all the thermodynamic informational properties of CI, what does it do in the QI world, where the probabilistic informational properties are manipulated, where bits can mix together so they 'spin' the same way along some axis but are still two bits, is how to see it. That we mix them in two possible ways in the thermodynamic classical sense, as waveforms, and as binary states or bits - which we can only mix by copying or inverting (or erasing) a geometric and an algebraic way to use EM; in the quantum sense the role of thermodynamics is reversed, or it's the 'zero point; of the thermodynamic realm; information is inherently thermodynamic or statistical. Quantum algebra with fundamental particles that are manipulated as waveforms, by EM is what we'e doing now (they didn't teach it when I last did EM stuff).
The above caught my eye in your OP. Seems true IMO that in your example an electron may very well be doing a "calculation" on it's spin based on it's own "legal" parameters as set up by it's very nature. The process being analoguous with a computer I guess. It touches on the living analogue of reflexive or instinctive behaviour of animated life that could also be treated in similar fashion. To void pushing this thread in to one of philosophy though, you could consider the unievsre to be a giant computer that is making computations on variations to it's "legal" [laws] to maiintian order. However the use of the word "computation" suggests that an outcome has to be calculated and this is argueable as if all formulations are already "computed" then no calculation is required. So as to whether or not the universe can be considered as a computating entity would be argueable. "Cause and effect" being "hardwired into the systems "legal" structure may make the use of "computation" redundent. for example: If I have a string of elecetric switches [ off on ] say 1000 of them an dthey are all permanently set to their various states giving a prdictable and consistant outcome can this be considered as computation? or simply predetermined cause and effect? At what point does computation come into it? However if somewhere a long the way decisions have to be calculated due to circumstances out side the system then possibly one could declare computation is taking place. any ways , my 10 cents worth...
This entire thing belongs MUCH more in philosophy than in any scientific or mathematical category. For example, at the moment I happen to be sitting here watching through my window at leaves that are falling. There's no "computations" taking place in that activity. Much as QQ has just said, the leaves are falling and following a path determined by physical laws - things like air currents and gravity. I'm not attempting to downplay QM in any way, it's just that it's effects have little to no meaning/impact on the macro world we live in.
agrees! It would get a better participation in the philosphy forum if only some of the members of the science forum participated. Unfortunately we do not have a "philosophy of science" forum which IMO is badly needed for many issues reagrding science , it's future and it's dogma..
Bzzzt! Information is physical; it has mass and energy, because it has entropy. Just ask someone who knows what Shannon or Von Neumann entropy is. (wait, I know that) P.S. even sitting and staring out a window is computing. Absolutely. We compute constantly, because when we stop computing, we are dead - although we no longer 'exist' the physical computer that was the "computational basis" is still around (we even preserve them these days).
In a sense I agree with this comment however, it is the "meaning" of that information that is not physical as determined by physics. It is the distinction between binary bits of 0's and 1's and the meaning that imparts that will determined the outcome of the threads OP. Which is why the question crosses over between philosophy and science IMO It is the old Artificial intelligence question that comes to the for again.... me thinks.Please Register or Log in to view the hidden image!
Correct-amundo. Meaning is not part of the communication process. That's an algorithm restricted to humans.
You've totally jumped the track. I didn't even imply that I was not computing - I was refering to the leaves, their path and final destination. There's NO computing THERE - just a following of rigid, physical laws.
I've been thinking about it a little today; I can't think of a large source (Or any) of information loss. If it was in the philosophy I could say more; I can't think of any way to quantify any of this anyways.
There is a computation, the leaves each compute a path, which is controlled by the wind and gravity. Each leaf is information - the channel is the sum of perturbations experienced as physical forces which transforms/commutes the information from one end to the other of the channel. The Shannon entropy depends, of course, on how each leaf is encoded; remember, information has spatial and temporal extent - it's discrete, but evolves in time IOW. This is what universal computation means, a communication (of leaf messages) is a trivial computation (by the wind, gravity, and the leaf data), the algorithm should be trivial too, in that case. For example, you've applied a trivial connection to my post about sitting at a window, by connecting it to your post (which is called assuming the two messages are connected). Of course what you look at as you sit isn't the same computation, but if you happen to be watching leaves fall from a tree, you compute that (by encoding each leaf as a unitary object, say, which is the equivalent of an 'on/off' code).
Indeed? And the final result is worthless. Meaningless. Of no effect on anything whatsoever. That's exactly why I say this thread is in the wrong sub-forum.
Meaningless to what? What does the "meaning" of leaves falling on the ground have to do with the indisputable fact they have mass, and therefore indisputably 'information'. You seem to be making the common mistake of confusing the data with what the data "does". A leaf doesn't know it's a leaf, a message is "just" a string of bits. Check out what the meaning of Shannon entropy is.
No, we're on his ass too, he's made out of Higgs potential, which maybe has a curvature (a tensor), that behaves algebraically, and computes the masses of fermions on up the scale to quarks, and massive vectors in some other kind of field. The realm of advanced gauge theories. The LHC is a quantum computer (a channel, essentially) that applies a magnetic potential to protons in the relativistic domain. This is another kind of view of the field, because the matter field (as a wavefunction) is interacting significantly as its mass product, its momentum is significant. In optical and milliKelvin domains, this momentum is insignificant, the LHC is a whole new ballpark in terms of the games you can play (and the balls you're allowed to use). Bit of a balls-up, though, at the moment. Ahem: if they get it fixed (as if they won't) and uncover the 'algorithm' that shows how this Higgs potential creates the masses of bosons that have mass, leptons and quarks - in the first family. Then, the theory of universal computation will be complete. We will know about the geometry and the algebra of the remaining fundamental field - the mass field, the same way we know about the EM field's geometry and algebra, which is the U(1) bundle of complex phase space, and the Hermitian operators on "connections between fibers" that commute the phase angles, or preserve them. This admits Fourier and Von Neumann (and a few others), which is "nice". QM is about using or manipulating the logical and physical connections, between quantum geometry and algebra which are real tensors, much like it is in the thermodynamic realm of the collective phases of electrons in EE, and digital circuits etc. You have to realise, too, that we are a part of some of those connections, but in fundamentally different ways, in each of the QI/CI views. But the universe we're in is informational, so we have to compute it.
By the way; this is the topic of discussion in Christopher Michael Langan's theory. http://www.ctmu.org/ Hard to navigate; but you can find his 56 page thesis there.
:bugeye: And why do you say that Shannon entropy implies mass/energy? What exactly is the relationship between Shannon entropy and mass/energy?
Why is there no way to send a signal without sending mass or energy? That is, without doing any work? If you can think of one, you will become very famous. This should be getting challenged by someone; we can only know that "universal" computation is locally complete. The mass field will complete the picture, but locally.
