Talk:Afshar experiment/Archive 18

Unsourced, erroneous paragraph
The unsourced paragraph
 * An interference effect is an ensemble (or statistical) effect. Neither Bohr nor Afshar require interference to be observed in any way other than a statistical manner. For the simple reason that such is impossible. But contrary to Bohr's statement, we are not actually prevented from observing an interference effect (the statistical effect) and tracing the path of individual photons that otherwise contribute to that effect.

is completely incorrect. Individual photons demonstrate interference effects. That is the whole point of the double slit experiment. --Michael C. Price talk 23:22, 1 December 2006 (UTC)


 * That is complete rubbish. If you send a single photon through the twin slit setup you will have a single detection on your screen. What you will not have is an interference pattern. It is only by sending a number of photons through the setup that you can build an interference pattern. If you are able to produce an interference pattern with a single photon then please do the experiment and publish your results. I'm sure we could all do with a good laugh. --Carl A Looper 23:45, 1 December 2006 (UTC)


 * 'fraid not. Interference effects are the root cause of all quantum behaviour.  E.g. neutrino mass mixing.  Each neutrino changes flavor in a cyclic predictable fashion, from A->B->C->A etc, at times being in a 100% certain flavor.  Or the precession of spin in a magentic field.  Etc, etc, etc, --Michael C. Price talk 00:07, 2 December 2006 (UTC)


 * Michael I absolutely agree with Carl, you really have no idea what you are talking about. There is not a single expert who disagrees with the fact that "interference in welcher weg experiments is an ensemble property". A single photon cannot produce an interference patter. I have a challenge for you Michael. If the interference pattern is not a multi-particle property, then can you please give us a formula for the Visibility of a single particle interference pattern? If you cannot, then you should accept that you are wrong.-- Prof. Afshar 03:14, 2 December 2006 (UTC)


 * $$V=\frac{2|\psi_1| |\psi_2|}{|\psi_1|^2+|\psi_2|^2}. $$ --Michael C. Price talk 10:07, 6 December 2006 (UTC)


 * Michael Price speaks:


 * Individual photons demonstrate interference effects. That is the whole point of the double slit experiment. - Michael Price


 * Afshar's experiment does not demonstrate interference effects for any individual particle (the photon), any more than the classic double slit experiment does - Michael Price.

The preceeding unsigned text was added by Carl A Looper, who apparently believes my two statements to be contradictory because he did not notice the words "any more than the classic double slit experiment does". --Michael C. Price talk 08:40, 7 December 2006 (UTC)


 * I forgot to sign it. It was me. The point being made, lest it not be obvious, is that if you maintain the claim that the twin slit experiment demonstates interference effects for individual photons (statement 1), then you would have to maintain that individual photons would do the same thing in the Afshar experiment (ie. contrary to statement 2). The idea of ascibing a single photon with the capacity to interfere is because such an idea is consistent with a statistical demonstration. The statistical demonstration won't violate your claim. For an empericist such as myself I'm happy with the statistical demonstration of interference. For anyone claiming that interference is happening anyway then they have already violated the principle of complementarity. The Afshar experiment is unnecessary. --Carl A Looper 20:29, 8 December 2006 (UTC)


 * It seems you still believe the two statements are contradictory. I can only conclude that you still do not see the significance of phrase I had highlighted. Again: Yes, individual photon can demonstrate interference; so does the double slit experiment; so does Afshar's experiment BUT NO MORE SO THAN FOR THE DOUBLE SLIT EXPERIMENT. --Michael C. Price talk 00:14, 9 December 2006 (UTC)


 * Well what's the problem then? The experiment exhibits interference whichever way you look at it. But the wording of your critique was that because Afshar used a statistical approach this approach somehow anulled the idea that interference was happening. My argument is that a statistical approach is the only way to demonstrate it. Yours is that our knowledge of interference is sufficient to render such as already demonstrated. Although we can argue this point it doesn't actually matter in the end analysis since we both agree, by our respective methods, that interference is happening. However your two statements remain contradictory. Your ad hoc patchups don't help. They just make it more confusing. Your second statement implys that Afshar's experiment, just like the twin slit experiment, does not exhibit interference for individul photons. And I quote:


 * Afshar's experiment does not demonstrate interference effects for any individual particle.


 * To say the Afshar experiment does not demonstrate interference any more than the twin slit experiment, simply implys that the twin slit experiment does not demonstrate it either. --Carl A Looper 08:17, 9 December 2006 (UTC)


 * It does not because you failed to quote the whole sentence:
 * Afshar's experiment does not demonstrate interference effects for any individual particle (the photon), any more than the classic double slit experiment does.


 * I have made exactly the same point numerous times and I am fed up with your evasive and frankly dishonest behaviour. (For a brief while it looked like you were about to turn over a new (honest) leaf, but I guess a leopard can't change its spots.)  From now on I shall simply delete your erroneous material from article: debate is pointless with you, since you delete clauses from quotations to make your silly points and to avoid facing your inconsistencies and ignorance on the subject. --Michael C. Price talk 09:34, 11 December 2006 (UTC)


 * Dear Michael, just because somebody disagrees with you does not mean they are evasive, dishonest and ignorant. I am pointing out your inconsistencys in the hope you'll think about what you are writing before you write such, rather than afterwards. If you would like to point out any errors, inconsistencys or ignorances in my contributions then feel free. Just accusing of me such does not make it so. I, at least, point out your errors, ignorance and inconsistencys. --Carl A Looper 10:17, 12 December 2006 (UTC)


 * For example, in your contribution above you say I fail to quote the whole sentence. But if you read the sentence immediately prior to such you will see what is otherwise your whole sentence. That I draw attention to the way in which it reads is not an improper thing to do. --Carl A Looper 22:08, 12 December 2006 (UTC)


 * Or to put it another way, why not write: "Afshar's experiment demonstrates interference effects just like the twin slit experiment" --Carl A Looper 08:33, 9 December 2006 (UTC)


 * But just to put a nail in the coffin of "knowing" individual photons exhibit interference: How does anyone "know" this in the first place? It is not knowledge delivered by Father Christmas. This knowledge has it's origin in a statistical analysis of measurements in experiments such as the twin slit experiment. That we ascribe interference to individual photons is more of a theoretical convenience than some written-in-stone truth. Quantum theory is not some sort of religion requiring faith in it's principles and mathematical construction. It is a science. Which means you don't actually need to believe in it. You can actually know how it is put together. And once you do know how it's put together you are free to actually reconstruct it - if you really want to do so. --Carl A Looper 10:18, 9 December 2006 (UTC)


 * Although Superposition is a universal aspect of QM, the manifestations, causes, and measurement procedures for such effects are widely different. An interference pattern is produced, manifested, tested, and measured in completely different processes compared to the neutrino flavor change. You should be careful not to oversimplify things beyond a certain point. As Einstein said "Everything should be made as simple as possible, but not simpler." --Prof. Afshar 03:14, 2 December 2006 (UTC)


 * You should consider what Bohr meant by interference and what you mean mean. Please define. --Michael C. Price talk 06:47, 2 December 2006 (UTC)


 * If you would like to use a single neutrino in your demonstration of interference that will be even funnier. --Carl A Looper 00:17, 2 December 2006 (UTC)


 * I see you lack even basic knowledge of QM. --Michael C. Price talk 00:23, 2 December 2006 (UTC)


 * Then buy some glasses. You need them. --Carl A Looper 01:05, 2 December 2006 (UTC)

Dear Michael, if you stop pretending to know what you are talking about you might find you actually learn something. While you might enjoy pretending to be a theorist it is irritating for the rest of us who would like to think through the issues this experiment raises. You fell into a trap I set for you. The simplest trap of all. And you don't know how to get out of it. Well I'm not going to tell you how. So sweat it. Here is the paragrah from which you have plucked your quote:


 * "This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path of a particle or observing interference effects, which allows us to escape from the paradoxical necessity of concluding that the behaviour of an electron or a photon should depend on the presence of a slit in the diaphragm through which it could be proved not to pass. We have here to do with a typical example of how the complementary phenomena appear under mutually exclusive experimental arrangements and are just faced with the impossibility, in the analysis of quantum effects, of drawing any sharp separation between an independent behaviour of atomic objects and their interaction with the measuring instruments which serve to define the conditions under which the phenomena occur." - Neils Bohr

As can be easily understood from what Bohr is saying he thought it was the experimental circumstances that allowed him (and Einstein) to escape concluding any paradoxical behaviour. But if they had Afshar's experiment to consider then "pardoxical behaviour" would be what they would have to conclude. In classical terms - as Bohr felt it necessary to frame the phenomenon - one would have to paradoxically conclude "a photon should depend on the presence of a slit in the diaphragm through which it could be proved not to pass"

--Carl A Looper 07:15, 2 December 2006 (UTC)
 * I note that :
 * Bohr refers to a single particle
 * Bohr refers to observing interference effects (i.e. not inferring)
 * a measurement of momentum yields wavelength, which is a measure of relative phase as a function of posiiton, which is an interference effect, which is a property that can be determined for a single particle
 * --Michael C. Price talk 05:29, 4 December 2006 (UTC)


 * Michael, your ignorance on the subject is monumental. In-fact, just quoting what you said above is enough to kill someone's career in the US academia. (1) You said: "Bohr refers to a single particle". Bohr NEVER suggested that interference can be observed for a single particle in welcher weg experiments, (read the original Bohr-Einstein debate.) John Archibald Wheeler (Bohr's protégé, and Einstein's colleague) knew exactly what Bohr said and based on that designed the "delayed choice" experiment that manifests complementary observable. He clearly explains that in order to see the interference effect, we need to accumulate a large number of photons on the observation screen. Only AFTER we see the ensemble effect in the bright and dark fringes of an interference pattern, can we say that an individual photon HAD INTEFERED. (2) You said: "Bohr refers to observing interference effects (i.e. not inferring)." Do you not consider full destructive interference (manifested in the dark fringes) as an interference effect? (3) You said: "a measurement of momentum yields wavelength, which is a measure of relative phase as a function of posiiton, which is an interference effect, which is a property that can be determined for a single particle." I challenge you to offer a measurement technique that provides the relative phase between two optical waves without interferometry. The reason why physicists use interferometers to measure sub-wavelength distances is precisely because the observable of non-interfering wavefunctions does not contain a phase sensitive term in it. The cross terms (sensitive to phase relationships) are only non-zero in coherent interference. I'm afraid your understanding on the issue is less than an interested high school student. P.S. I'm getting tired of giving you free physics lessons.--Prof. Afshar 14:33, 4 December 2006 (UTC)
 * (1) Bohr did suggest that interference effects could be measured for a single particle. (cf "the particle" in Bohr's quote given by Cramer, no less!, and the spin precession example I gave.) Finding weaker quotes by Bohr where he says less does not invalidate this point.  Nor is the point weakened by the fact that interference effects can be also demonstrated for multiple particles, although it does render the issue of complementarity (as Bohr defined it) moot for them.
 * (2) Re the dark fringes. Their "observation" is a null measurement in that no photons are observed there.  That in itself does not invalidate the wires as a measuring device.  What does invalidate them as a measurement is that we already know (with certainty that is almost =1) that no photons will be observed there.  Hence the prior probability of observing the null result is (almost) a certainty = 1.  Information = -log2(probability) = -log2(1) = 0.  i.e. no information.  Ergo no measurement.
 * (3) The spin precession example does not require optical interferometry, yet it measures the change of relative phase between two spin components of an electron (say) in a magnetic field. --Michael C. Price talk 10:14, 5 December 2006 (UTC)

Well, Michael, you should try not to conclude that Bohr has any supernatural ability to observe an interference effect in a single particle detection. --Carl A Looper 13:03, 4 December 2006 (UTC)
 * Measuring momentum does not take supernatural ability, so the article text is wrong. As for Afshar's experiment I afraid the idealised wires don't even qualify as a measurement (interaction free or not) when both slits are open. --Michael C. Price talk 14:00, 4 December 2006 (UTC)


 * You said: "I afraid the idealised wires don't even qualify as a measurement (interaction free or not) when both slits are open." Yet another sign of your utter incompetence on the topic. Marlan Scully, Lucien Hardy and other experts fully agree with me on this topic. This is my last free lesson for you: It can easily be shown that a null result may influence the wavefunction of the object to be measured (see Dicke [1]). As an example, if Alice hides with equal probability in one of four rooms, and Bob cannot find her in one of the rooms, the probability of finding her in one of the other rooms immediately changes from ¼ to 1/3. Thus, a null result influences the wave function. Null results are routinely used as a measurement tool, for example, to estimate the lower limit of the lifetime of a proton [2] etc.. Ref.s [1] R.H. Dicke Am J. Phys. 49(10), 925 (1981); [2] Los Alamos archives (quant-ph/0608202). -- Prof. Afshar 14:44, 4 December 2006 (UTC)


 * As I have already explained null- or interaction free measurements yield information (e.g. about the location of an unexploded bomb); in contrast the placing of the wires which does not yield any information, since we already know the wavefunction of the test region in Afshar's experiment. There is a difference between a null-measurement and no measurement.  The idealised wires fall into the no meaurement category, this is the fatal flaw in Afshar's experiment. --Michael C. Price talk 16:33, 4 December 2006 (UTC)


 * Please answer this simple question: How do you "observe" a dark fringe? -- Prof. Afshar 16:40, 4 December 2006 (UTC)
 * Do you really have no substantive comment on the issue of the non-measurement of the wires? (I'll deal with the dark fringes elsewhere later, on the appropriate thread.)  And thanks for the continuing free lessons: I knew you couldn't resist.  --Michael C. Price talk 18:53, 4 December 2006 (UTC)
 * Well, Michael, you have completely lost your credibility with me and a number of other experts with whom I shared your gobbledygook. Just don't come to me asking for recommendation letters, and as for the previous lessons, I'll be waiting for your check in the mail.-- Prof. Afshar 19:28, 4 December 2006 (UTC)
 * I see that once again you refuse to face up to the substantive issue here, namely of whether your wires are performing a measurement of any description at all. --Michael C. Price talk 00:38, 5 December 2006 (UTC)
 * Whatever man. Read my upcoming papers if you can't afford the check. -- Prof. Afshar 01:47, 5 December 2006 (UTC)
 * Once again an ad hominem to avoid the substantive issue. --Michael C. Price talk 10:14, 5 December 2006 (UTC)

Bohr would have loved the Afshar experiment. Pity MP will never understand that. --Carl A Looper 20:49, 4 December 2006 (UTC)


 * Of course Bohr would have loved it, but would he have agreed with your interpretation of it? --Michael C. Price talk 00:36, 5 December 2006 (UTC)


 * Hi Michael, there are a number of interpretations currently in the mix and that is what everyone is sorting out. That's exactly the question. We don't actually know what Bohr would have thought so we need to put on our Shelock Holmes hats and work it out. This involves math, physics, philosophy and history. And each of us can contribute to this from our respective disciplines. For example DG works from a pure math position and a QM definition of complementarity. He arrives at a situation in which he has two incompatible equations. The "=" sign doesn't work. And so one divides the universe in two, one in which one equation obtains, and the other in which the other equation obtains. An alternative is to replace the "=" sign with the "xor" operator. Math consistency is restored and we are back in a single universe in which information is the name of the game. Or we use Afshar's approach which is to employ Bohr's penchant for classical definitions and demomonstate what Bohr might have to admit is a paradox. But what if Bohr is taking Einstein for a ride? What if he already understands that CP is bollocks and he's just humouring Einstein? I don't think so. I think he genuinely believes that CP obtains but has reservations. For example, when Einstein proposed EPR he did not automatically dismiss it. He thought about it and in the process determined that information had not travelled faster than light. But there is Einstein convinced that there was a paradox to be discovered. And I'm sure Bohr would have been happy to find it as much as Einstein. It would mean that the story was not over. --Carl A Looper 01:52, 5 December 2006 (UTC)


 * Hi Carl, I agree that we can never know what Bohr would have made of the experiment. All we can do it look at what he said then and make speculative inferences about how he might have reacted now.  To claim, as Afshar does, to have "disproven Bohr" is presumptive and belittling, especially when there are quotes that suggest that Bohr regarded complementarity as merely a philosophical description of the formalism. --Michael C. Price talk 10:21, 5 December 2006 (UTC)


 * No, the claim of disproving Bohr is allowable. The Bohr we read in the historical record is highly articulate. The words resonate with clarity. CP is philosophy but it is not merely philosophy. --Carl A Looper 18:04, 5 December 2006 (UTC)


 * Actually Bohr was universally regarded as an inarticulate lecturer, something of which he was blissfully unaware. --Michael C. Price talk 18:09, 5 December 2006 (UTC)


 * Bohr regarded CP as a description of the formalism? In what inarticulate words is this idea to be found? Bohr's or yours? --Carl A Looper 18:19, 5 December 2006 (UTC)
 * Bohr's. You remember?
 * Niels Bohr stated "an adequate tool for a complementary way of description is offered precisely by the quantum-mechanical formalism"
 * --Michael C. Price talk 21:08, 5 December 2006 (UTC)


 * So why read this arse about? --Carl A Looper 03:03, 6 December 2006 (UTC)


 * Eh? --Michael C. Price talk 08:22, 6 December 2006 (UTC)


 * And another thing. Quotes are like single particle detections. And as you should know by now it is unwise to read too much in a single particle detection. The context is important. --Carl A Looper 18:10, 5 December 2006 (UTC)

Given the instantaneous spacetime location of a point moving between A and B, can we determine it's instantaneous velocity? Obviously not. We need an interval (at least two different points) in order to compute it's velocity. This does not mean our moving point fails to possess any velocity at any given instant (although one could actually argue this) it just means we have insufficient information from which to compute it's instantaneous velocity at any given point. This is analogous to interference. There is insufficient information in a single detection to determine the interferometric propertys we might otherwise ascibe to the detected particle. That doesn't mean it does not (did not) possess such (although one could argue this) it just means there is insufficient information with which to compute such. The wisdom of computing things like instantaneous velocity etc. is not at issue here. With insufficient information one will obtain, funnily enough, insufficent information. --Carl A Looper 22:31, 4 December 2006 (UTC)
 * Dear Carl, your example with velocity is exactly analogous to what Mike is arguing for, so I will support him. Interference is not "just statistical property of many photons" it is a "mathematical property for summation of different quantum amplitudes/branches of the quantum state of a single photon". So "quantum interference" is all about amplitudes, it is not about photons. Please stop thinking of "classical interference", and you will see the importance of what Mike is trying to say - namely that "quantum interference" is about quantum amplitudes, and therefore can be manifested by quantum amplitudes of a single photon. Now back on the velocity example - yes, mathematics should be interpreted directly as having physical significance. Yes, this is a realist position Does the moon exist only when someone is looking at it?. Yes, postulating mathematically that the point has velocity, is itself enough to make physical sense even if nobody never measures the velocity. Math axioms are true even without experimental verification. Please stop arguing with Mike in case where he is obviously right, please try to prevent Afshar's vandalism in the main text. Soon he will proclaim all of us as crackpots, and he will be correct to say so, because if we are rational scientists we should arrive at some consensus about basic things and then go on contructively solve some problem. Nobody helps to create uniform framework within all we can speak freely. I have tried to propose such a basic formulation of language for all of us, but without great success. Regards, Danko Georgiev MD 10:23, 6 December 2006 (UTC)


 * A photon is one thing. A photon detection is another. The context of the discussion was photon detections - not the photons themselves. That is the point of the analogy. --Carl A Looper 23:11, 6 December 2006 (UTC)
 * And I might add that the word "photon" is used when one is trying to avoid the word "particle". The word "photon" embodys both the quantum wave function 'and' the particle-like detection. If you follow the debate you will see that the detections are the focus. If we're only interested in an axiomatic defintion of what is going on who needs experiments? Why even discuss any experiment? Why do we need to observe anything at all? Well, we don't need to. So if anyone wants to live in a axiomatic reality I have no problem with that at all. In the meantime I enjoy the observable universe irregardless of whether I have yet to understand it. The observable world imposes itself before I understand it. It acts as a question as much as an answer. --Carl A Looper 23:28, 6 December 2006 (UTC)
 * In addition, I do not agree that a uniform framework is required. A uniform framework merely determines the result of the debate in favour of the agreed framework making any further investigation redundant. Rather, I suggest the frameworks themselves be declared and an effort to understand such be permitted. Bohr's declared framework was "classical". And so we should at least understand what that is when discussing Bohr's principle - even if we do not use such ourselves. And that involves understanding the import of physical observables as much as any axiomatic simulation of such. --Carl A Looper 00:09, 7 December 2006 (UTC)


 * Note on Mike's example that wires do not perform measurement. I think that Mike is playing with the definition of information. If you have mathematical prediction then the measurement is a process through which you try to test whether your prediction corresponds to physical reality or not. Whether the math prediction will be confirmed or not is not relevant, the measurement brings some information that is not contained in the formalism itself, because it answers whether the formalism is applicable or not at first place. If one accepts Mike's misunderstanding on what measurement is, then "measurements" will be only these facts that do not agree with given physical theory, so "measurement" by Mike definition will be exactly criterion how unrealistic given physical theory is. Therefore the worst possible theory of all, with as much as possible wrong predictions, will yield greatest number of Mike-type measurements. Danko Georgiev MD 11:29, 6 December 2006 (UTC)
 * Measurements are not just about confirming or falsifying predictions of the formalism. More generally they are about gaining information, since they can be used in situtations where no such predictions are possible from the formalism of a theory, e.g. what room a bomb is in may not be predictable, even on a probabilistic basis, but it is amenable to measurement.  Do you or Afshar contest any of these statements?
 * The only point of performing a measurement is to gain physical information.
 * Information is quantified by the prior expected probability of an outcome, according to information theory as :
 * Information/bits = -log2(prior probability)
 * The formalism of QM has been very well established over the last 80 years, so well established that the probability of a significant or relevant violation of the formalism in Afshar's experiment is $$\approx 0$$. (Which is not to say that we shouldn't perform experiments.)
 * The idealised wires, placed at the dark fringes are not expected, with high probability $$\approx 1$$, to detect any photons.
 * log2(1) = 0
 * Ergo the wires yield $$\approx 0$$ information and so don't constitute a measurement.
 * --Michael C. Price talk 02:18, 7 December 2006 (UTC)


 * The experiment is not about a violation of the formalism. It is about a violation of the principle of complementarity. If you know or claim to know that interference is taking place then you are free to remove the wires. In Bohr's time interference wasn't understood. There were doubters. Just think of the wires as there for any ghosts who might still carry doubts. The result is still the same. --Carl A Looper 05:11, 7 December 2006 (UTC)


 * The experiment is not about a violation of the formalism. Agreed. Now try addressing the issue raised. --Michael C. Price talk 08:32, 7 December 2006 (UTC)


 * In what way am I not addressing the issue? If you know the Earth is round then you don't need any further proof. A photograph from outer space is unnecessary. So okay - ergo - such photographs do not constitute a measurement. --Carl A Looper 09:05, 7 December 2006 (UTC)


 * The photograph would convey a lot of other information such as cloud formation, continental detail etc. But about the "roundness hypothesis", yes such a "measurement" would only convey information to a flat-Earther.  Perhaps we have a new category of measurement here, an "information-free measurement", and that's what the wires are doing -- absolutely nothing whatsoever. --Michael C. Price talk 09:17, 7 December 2006 (UTC)


 * Yep. --Carl A Looper 10:59, 7 December 2006 (UTC)

Dear Mike, stop playing in the wrong way with the definition of information. As I was quite explicit: every physical measurement brings information, always! For example take two persons - Afshar believes there is interference, while Motl believes there is no interference. If we follow now your erronoeus logic, after putting the wires Afshar verifies his own claim (so no new information for him) while it disproves Motl's claim (1 bit of information for Motl). Don't you realize now that your claim is ridiculous? The definition of information should not be subject dependent!!! Of course the issue is much more complicated than argueing what information provide the wires - Motl argues wrongly that wires are thin so they provide only 0.00...1% of the interference picture (analogous view to Drezet), while Afshar correctly argues that wires perform Reininger negative measurement - yes, you have confirmed that there is interference because if the intensity flow was continuous, then 6% loss is to be expected. So Afshar's setup distinguishes between uniform intensity flow, and double slit interferent pattern of the intensity flow. So thus formulated, it gets 1 bit of information. It does not matter whether you expected (believed in) the interference, or not, Q.E.D. Danko Georgiev MD 10:09, 11 December 2006 (UTC)


 * Dear Danko, I agree with your statement "every physical measurement brings information, always!" (the concept of an "information-free measurement" does seem rather pointless) but I disagree with where you say "The definition of information should not be subject dependent!!!". Information is defined as a subjective quantity.  It is defined by
 * Information/bits = -log2(prior probability)
 * where "prior probability" means "prior expected probability", i.e. the probability that the subject assigns to some particular outcome of some event happening, before being informed as the actual, same outcome. Turning the expression around we get:
 * $$p = 2^{-I}$$
 * which is a pretty basic formula, and goes back to Claude Shannon, Wolfgang Pauli and John von Neumann. See information theory for more general formulae. Since p is subjective, so is I. --Michael C. Price talk 10:46, 11 December 2006 (UTC)
 * Dear Mike, please stop playing with words. I will not be frustrated from your example with probability, which is again exposing the fact that you copy-paste formulas from internet, and do not show your own thinking. The definition as provided from you holds for throwing a dice. But when you write a computer program then the information is not based on probability because the semantic that I want to input in a program, or sentence does not depend on throwing a dice. In this case where a type in English for every new letter I always input log2 (24) bits of information. I nowhere throw a dice before I input each letter, because I KNOW what letter exactly I will input. Now you cannot argue that I input zero information from my subjective perspective, because I know which letter will be inputted next. This is stupid. Any time a push a key, I input log2 (24) bits, and this has nothing to do with the fact whether I know what letters I will type, or whether you don't know what letters I will type. Don't play with the meaning of subjective - formal systems are objective, and information is objective. It can be stored on CD and transferred to any person. Whether you have seen the Aifel tower or not, does not matter. Every time you see the Aifel tower you get exactly the same ammout of information through your visual system. Whether you "know" something or you "learn it for a first time" is not relevant for the amount of information you receive. Don't make a fool of yourself, just accept your misunderstanding and go ahead on another topic. Danko Georgiev MD 11:07, 11 December 2006 (UTC)
 * Sorry Danko, but we are not going to make any progress if you continue to assume bad faith every time someone tries to be helpful. For your information that formula was not copy-pasted.  I could explain why your keys example misses the point, but I suspect I'd be wasting my time. --Michael C. Price talk 13:48, 11 December 2006 (UTC)
 * Dear Mike, don't feel sorry, but try to learn something when one is trying all his best to repair your wrong vision. I will formulate strictly everything that is to be said on information. You wrongly "define information with the use of the concept of knowledge". That is why you are completely wrong. Information is irreducible basic term, and knowledge is defined via information (as available information), not vice versa. I have studied information theory in the University, and nowhere one has defined it via probability (but yes, it is possible!, I will explain below). The main definition uses directly information as primary concept and gives rule for quantification of it "1 bit of information is the answer to an YES/NO question". Here you have in the definition question and answer (both semantically bearing the idea of information) and nowhere one uses the term knowledge. Now to explain why when you use the word probability you also don't use the word knowledge I will explain with example. Suppose you have options a, b, c, d, and you know that only one of them is true. The quantification of the information is done in the following way- the number of YES/NO questions you need to ask in order to get the correct answer ASSUMING THAT YOU START FROM THE POSITION OF COMPLETE IGNORANCE [NO KNOWLEDGE AT ALL]. Now I hope you understand why probability appears, as a concequence of fact that in order to reformulate the definition of bit, in terms of probability, you must start from state of complete ignorance. The solution to the above question is 2 - you need two YES/NO questions: e.g. "Is it a, b?" Yes - "Is it a?", No - "Is it c?", easy right? If you don't understand after this clear example that information nowhere presupposes knowledge, it will objective evidence that you have no any competence of what science is, and how you should lead scientific dialogue based on rational arguments. BTW I nowhere assumed bad faith, I assumed that you make mistake, that is repairable after showing you clear argument why you are wrong. Danko Georgiev MD 00:59, 12 December 2006 (UTC)