Wikipedia:Reference desk/Archives/Science/2011 March 2

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March 2

measuring and irrational numbers

I've been thinking about measuring and I was curious to know if it's OK to think of it this way:

Imagine we want to measure the length of an object.first we get 2m.and then with a more accurate measurement we get 2.1 ,2.12, 2.129 ,.... It's almost like an irrational number, because the decimals can't be predicted, and it also has an algorithm to be calculated more accurately (which is "measurement").so, which sentence is right?

1.the decimals never end and the object doesn't have a true, accurate length.

2. the decimals end somewhere and the object has an accurate, rational length. — Preceding unsigned comment added by Irrational number (talk • contribs) 13:00, 2 March 2011 (UTC)

Since 1983, (1) has been correct, except that stuff can only be measured with so much precision. See accuracy and precision. Before that, there was just one thing that was, by definition, exactly a metre in length.--Shantavira|^{feed me} 13:25, 2 March 2011 (UTC)

I think you must be referring to the definition of the meter in terms of the speed of light, as described here Meter#Speed_of_light. However, I don't see how this definition of meter has anything to do with the claim that an objects don't have 'true, accurate' lengths. We could change the definition of a meter many of times, and this would never affect the material nature of e.g. the pencil on my desk. That is, the number used to quantify its length may change, but the pencil will not. SemanticMantis (talk) 15:33, 2 March 2011 (UTC)

Where I live, pencils get shorter.--Shantavira|^{feed me} 16:41, 2 March 2011 (UTC)

I think this question is not about science, but about philosophy_of_physics, specifically regarding how to interpret the real numbers as a model for aspects of physical objects. I don't think there is a purely scientific basis for choosing to believe 1), 2), or other alternative interpretations. Perhaps someone else can shed more light on the philosophy involved here. SemanticMantis (talk) 15:33, 2 March 2011 (UTC)

Also, we should be careful with terminology 'accuracy' applies to measurements, not lengths. SemanticMantis (talk) 15:44, 2 March 2011 (UTC)

Having an unending decimal representation is not the same as being irrational – e.g. 1/3 = 0.333.. – so (1) and (2) don't cover all the possibilities even in an idealised situation. AndrewWTaylor (talk) 15:44, 2 March 2011 (UTC)

If the OP is talking about measuring real physical objects, then the answer is that a physical object does not have a "true", infinitely precise, length because the "length" of a physical object is a macroscopic concept and is not well defined at, say, picometre scales due to thermal motion, quantum effects etc. If the OP is talking about measuring ideal objects then the ratio of the lengths of two ideal objects may be either rational or irrational, depending on the objects involved. But I don't see how an irrational ratio is any less "true" or "accurate" than a rational ratio. Gandalf61 (talk) 15:45, 2 March 2011 (UTC)

I think it's better to ask my question this way:Is there any such thing as "the true length" or "the true value" for a certain object?Imean that we can do measurements more and more accurately, but is there any "end" for this process? — Preceding unsigned comment added by Irrational number (talk • contribs) 16:09, 2 March 2011 (UTC)

As Gandalf wrote, "length" for a physical object is a macroscopic concept that breaks down as you start measuring at the quantum level. In other words, you can only ever get to a certain precision (and you can always find a rational number expressing the length to that precision). On the other hand, if you talk about ideal mathematical objects, there are things that have irrational length (the diagonal of a square with sides of length 1) or even transcendental (the circumference of a circle with radius 1). --Stephan Schulz (talk) 19:35, 2 March 2011 (UTC)

In thought experiment only, couldn't the photon sphere around a black hole or neutron star be measured with arbitrary precision, by looking at the number of wavelengths of an arbitrarily high-frequency light source? Wnt (talk) 19:50, 2 March 2011 (UTC)

This makes me think of Coast#The_coastline_problem, not the same thing obviously, but similar. Vespine (talk) 00:41, 3 March 2011 (UTC)

The true length would be the limit. For example, in your 2.129... meter object, it will never get within 0.009 meters of 2.12, no matter how long you measure it. It's exactly 2 meters at the first step, but it's never within 0.1 meters of 2 meters after that. For any length except one, you could find a number of digits and a distance such that, after that many digits, you will never measure it within that distance of that length. — DanielLC 17:31, 3 March 2011 (UTC)

I am exactly one "Vespine" tall ;) Vespine (talk) 22:09, 3 March 2011 (UTC)

True or false? (about frogs)

"if you boil a pot of water and throw in a live frog that that frog will hop right out, saving his life to croak again another day (ha, ha)? If, on the other hand, you place a frog in a pot of cold water and turn the heat up slowly, that frog will stay in the pot." Quest09 (talk) 14:05, 2 March 2011 (UTC)

Talking from specific personal experience on this, if you boil a pot of water and throw a fish in, the shock will kill it instantly, or at least render it immobile. I believe the same would be true of frogs. --KägeTorä - (影虎) (TALK) 14:28, 2 March 2011 (UTC)

Isn't that animal cruelty? Quest09 (talk) 14:52, 2 March 2011 (UTC)

Probably. Depends on who you ask. We were cooking. I didn't enjoy doing it the first time, and I doubt I would do it again. --KägeTorä - (影虎) (TALK) 21:57, 2 March 2011 (UTC)

On one hand, the fish probably die quite quickly and I don't really believe fish "suffer" like we imagine anyway; on the other, it is completely "unnecessary" and only done because of the Japanese (sometimes perverted) obsession with "freshness". Completely no offense intended to KageTora, I personally love Japan and Japanese food, but throwing live fish into boiling water is not the worst of it. So I flip flop on the subject.Vespine (talk) 22:08, 2 March 2011 (UTC)

Exactly - I have seen far worse, which is why I said 'depends on who you ask'. Besides, people in western countries boil lobsters alive, and on rare occasions these lobsters are found to be still alive when served. --KägeTorä - (影虎) (TALK) 22:57, 2 March 2011 (UTC)

Can you provide some citation (not from PETA please) that a lobster can survive boiling water? Quest09 (talk) 02:12, 3 March 2011 (UTC)

Unfortunately I can only supply anecdotes in this case. Sorry about that. --KägeTorä - (影虎) (TALK) 02:23, 3 March 2011 (UTC)

We have a well-referenced article on the Boiling frog anecdote, which says: "According to contemporary biologists the premise of the story is not literally true; an actual frog submerged and gradually heated will jump out. However, some 19th century research experiments suggested that the underlying premise is true, provided the heating is gradual enough." WikiDao ☯ 14:30, 2 March 2011 (UTC)

Incredible that WK has an article even on that. Quest09 (talk) 14:52, 2 March 2011 (UTC)

Wikipedia has an article on everything! Of course we do!

Getting to the point of course, I doubt any animals at all (with a few exceptions) can withstand boiling water. Crimsonraptor • (Contact me) Dumpster dive if you must 15:04, 2 March 2011 (UTC)

The question is if every animal will try to escape or if it will just numb and die. Quest09 (talk) 15:25, 2 March 2011 (UTC)

In truth, as someone who worked on getting that article into shape in 2009, we were spurred on to make it a good article (rather than just a bad anecdote and some biologists saying "not true") after being asked about it on the Ref Desk, if I recall. (I believe I was the one who really looked into the 19th century physiological literature for boiled frogs, which I happened to know was a very 19th century physiological thing to do with one's research time. But I may be mistaken.) It has been significantly edited since then, but bears the same hallmarks of the original '09 improvements. --Mr.98 (talk) 19:36, 2 March 2011 (UTC)

What are you talking about? According to [1] you didn't contributed anything to that article. Unless, oh no, you are a sock-puppet? Right? Quest09 (talk) 02:33, 3 March 2011 (UTC)

I do have multiple accounts (which I have never been shy about), which is not disallowed and not sock-puppetry. (I am not using them to evade bans or anything inappropriate. None of my accounts are in bad standing. One is even an administrator! Although in fairness I never use that one for much anymore, and have not used its admin powers in years.) But in any case, this was when I edited as an IP, before I registered this particular user name. It turns out it was in 2007, not 2009. Look for some major overhauls by a certain 24.x.x.x, some others by 98.x.x.x. --Mr.98 (talk) 20:37, 3 March 2011 (UTC)

dimensions

Could matter, motion, thought, energy, light, etc. possibly be dimensions? For example 4-d spacetime could exist and not result in matter or thought. —Preceding unsigned comment added by 165.212.189.187 (talk) 16:19, 2 March 2011 (UTC)

If you redefine what "dimension" means, then anything can be a dimension. As for the standard definition of "dimension", they are not dimensions. -- kainaw™ 16:20, 2 March 2011 (UTC)

In physics, we use generalized coordinates to describe the complete state of a system. Anything can be defined by a "coordinate" - but only a few are useful coordinates that help us simplify a description of an observed physical system. In addition to your typical "x,y,z" coordinates, physicists often use velocity, angular displacement, and energy as a "coordinate" of a system. Typically, we seek to use a linear transform to convert from an orthonormal coordinate scheme (like a cartesian grid or a polar coordinate system) into a generalized coordinate space; this makes the math much simpler. It is sometimes, but not always, possible to obtain "energy" via a differentiation of a spatial coordinate; (for example, kinetic energy is related velocity squared - which is a nonlinear operation on the first derivative of a spatial coordinate). So, "energy" is rarely a useful coordinate in most physical treatments.

But you must know the mass to get the actual energy, right? —Preceding unsigned comment added by 165.212.189.187 (talk) 20:10, 4 March 2011 (UTC)

For a concrete example: consider a robot arm. Its hand has an "x,y,z" position; but this is not the easiest set of coordinates to "control the robot." Instead, you want to design a coordinate-system based on the position-values and velocity-values for each "joint" or "elbow" in the robot-arm, so that you can send motor control commands. This approach is called Forward kinematics and is an elementary part of robot theory. More advanced robot control will use other coordinates to design an objective function: for example, you could have a robot-arm who is aware of a coordinate called the "value" of a position, and thus prefers to move to "high-value" coordinates (independent of their x,y,z coordinate). You can thus introduce a new "coordinate" and call it anything you like. This "coordinate" or "dimension" might be the pixel-value at some location in a computer vision camera; or it could be the result of a complex algorithm, or any other thing you want. The reason I bring this up is because advanced robotic theory is mostly concerned with the matrix-mathematics needed to find optimal solutions in high-dimensional spaces. Nimur (talk) 16:37, 2 March 2011 (UTC)

OK, then I guess my question is can current physics describe information and thought the way it describes light and heat? —Preceding unsigned comment added by 165.212.189.187 (talk) 16:58, 2 March 2011 (UTC)

No. See information theory and artificial intelligence for the overview of how "information" and "thought" are modeled scientifically using current theories and technology. Nimur (talk) 17:04, 2 March 2011 (UTC)

But a true "theory of everything" would have to describe them, right? —Preceding unsigned comment added by 165.212.189.187 (talk) 18:13, 2 March 2011 (UTC)

I should just mention Kaluza-Klein theory, M-theory, string theory and so on where the modeling of matter, energy, and light is concerned. Typically information is thought of in terms of other quantities - when you measure the position of an electron and such - I don't know if there's a way to quantify it in such a theory independently of specific forces and particles. But thought, or the "when's dinner?" kind of information, is really not well understood and quite macroscopic (even to the point that no specific part of the brain is certain to affect it when damaged). I'm sure that there are some chip makers who daydream about shrinking their transistors down to the scale of a compactified dimension and using them to operate artificial intelligence, but (probably luckily) this is not on the drawing board yet) Wnt (talk) 18:30, 2 March 2011 (UTC)

There is a theory that all information is retained in the universe in just two dimensions and that any concept we have of a third dimension is nothing more than how our brains perceive the two dimensional information. I haven't read anything on this theory in a few years and I'm certain it has been completely discredited by now. This is an old paper on it by someone who knows what he is talking about. -- kainaw™ 19:04, 2 March 2011 (UTC)

The Holographic principle seems to a mainstream (if highly theoretical) idea of this type. - Jarry1250 ^{[Who? Discuss.]} 19:32, 2 March 2011 (UTC)

The holographic principal would help explain my problem with density. —Preceding unsigned comment added by 165.212.189.187 (talk) 21:07, 2 March 2011 (UTC)

I just want to point out that when physicists say theory of everything they mean a theory of all matter and forces, nothing else. Dauto (talk) 19:30, 2 March 2011 (UTC)

(ec) Well, and the reductionist, materialist world-view is predicated on the belief that all complex processes (including sentient thought, consciousness, reason, and sophisticated intelligent life) are fundamentally nothing more than extremely large numbers of simply-interacting objects that behave according to fundamental physics. This is a philosophical position - it is neither correct nor incorrect; it falls outside the realm of "falsifiable" or "provable." But if you hold this world-view, then intelligent thought and complex information storage can be completely described as the ensemble definition of all applicable rules and the state of a complex material representation of information. For example, the bits inside a computer are represented by voltage on microscopic capacitors; those voltages exist because of electrons in a semiconductor-material that obey fundamental rules of electrodynamics. It doesn't matter how complex the computer is behaving - the information it contains is still governed by basic rules of elementary physics. Unfortunately, we are not as close to understanding the way that psychology and memory works in living creatures; so it is much harder to apply a materialist/reductionist worldview as a description of human intelligence. Nimur (talk) 19:54, 2 March 2011 (UTC)

The fact that a proposition may be neither falsifiable nor provable, does not imply that it is neither correct nor incorrect. It only says we may have trouble finding out whether it is correct or incorrect. --Trovatore (talk) 21:17, 2 March 2011 (UTC)

"it falls outside the realm of falsifiable or provable." No, it is falsifiable or provable, if e.g. whole brain emulation is possible then it follows that thought, consciousness, reason, and sophisticated intelligent life, are indeed nothing more than extremely large numbers of simply-interacting objects that behave according to fundamental physics. 213.49.110.122 (talk) 06:00, 3 March 2011 (UTC)

There's no way to tell whether an emulator is actually experiencing anything subjectively, whether it has qualia. (For that matter, it's hard to say how I can tell whether anyone but me has qualia. But I do; I guarantee you.) --Trovatore (talk) 22:07, 3 March 2011 (UTC)

Thought is something that occurs inside brains, so it's a question for biology, not physics. thx1138 (talk) 23:26, 2 March 2011 (UTC)

You could possibly explain thought with quantum mechanics, as the collapse of the wavefunction of one electron in a nerve cell by another (Or maybe in the manner that quantum computing works). After all, quantum mechanics is the reason our free will is preserved, and thus it might be the reason for free will itself. ManishEarth^{Talk • Stalk} 09:04, 3 March 2011 (UTC)

While it's certainly possible that's the case, there's no currently no evidence to support it. thx1138 (talk) 16:06, 3 March 2011 (UTC)

Anyone interested in the possible relationship of quantum mechanics to conscious thought should read Roger Penrose's The Emperor's New Mind. As both those articles indicate, the theory hasn't gained much traction. Matt Deres (talk) 18:18, 3 March 2011 (UTC)

If time can go backwerd , and it can , it can go proprate to matter,or any thing we want to relate to , matter too will be dimensions . thanks water nosfim —Preceding unsigned comment added by 212.199.175.104 (talk) 19:49, 2 March 2011 (UTC)

Maxwellian conflict

Paradigm shift talks about the contest between Maxwellian electromagnetism and Einsteinian relativistic theory. However my understanding was that prior to Einstein, Maxwell's equations were one of the few bits of physics which did already Lorentz transform correctly. Certainly the equations I was taught at university to be Maxwell's equations, are the same as those which are pulled out by considering the force resulting from the EM-Stress energy tensor. So where was there conflict between the two? —Preceding unsigned comment added by 129.67.37.227 (talk) 19:58, 2 March 2011 (UTC)

That does seem peculiar. History of special relativity#Lorentz's theory of electrons and onward covers the history in better detail. Wnt (talk) 20:41, 2 March 2011 (UTC)

(ec) I have never read The Structure of Scientific Revolutions. Despite its wide acclaim, I have preferred to actually read science books, instead of meta-debate about science. It is my opinion that there isn't a dramatic "transition between the Maxwellian electromagnetic worldview and the Einsteinian Relativistic worldview." Our Paradigm shift article attributes that belief to Kuhn - i.e., implies that Kuhn considered this a "dramatic shift" - so what we need to do is determine if our summary is consistent with Kuhn's writing. Whether it is applicable is subject to your own opinion, and whether you agree with Kuhn.

You can read Maxwell's own work: On Physical Lines of Force and A Dynamical Theory of the Electromagnetic Field are the most relevant. (Bear in mind that his notation differs from the most popular modern notation, but the physics is identical). Our articles link to full text versions of these historic works. You can also read On the Electrodynamics of Moving Bodies by Einstein; and decide for yourself whether there is a "dramatic" paradigm shift, or a "gradual, constructive evolution." I will also point out that Hendrik Lorentz invented and started using his his transform without ever before ever attributing its mechanism to relativity. In a sense, it was a "subtle modification" that built on earlier theory to improve accuracy. Nimur (talk) 20:53, 2 March 2011 (UTC)

For a guy who coaches his opinions in a love of science, it is very unscientific to comment on things you have not read! Just read the book already, it's a quick read, you'll at least know whether you actually agree with it or not... "science books" are usually quite poor sources for their history. You can find "history books" for that. Some written by that know-nothing, Thomas Kuhn! --Mr.98 (talk) 03:13, 3 March 2011 (UTC)

The article has been poorly wiki-linked. What's important is the "electromagnetic worldview," which is not the same thing as Maxwell's equations. Luminiferous aether would be a better link. It's not the equations, per se, which actually work fine. It's the intuitive way in which the world was thus thought to work. Incidentally if you want to get a sense for the actual historical progression of things, it gets into things that are far more detailed than your standard physics textbook, which really only describes the history so far as it contributes to the present-day theories. The actual history of these things is always more complicated. If you're looking for a great, one-stop-shop history of modern physics (which discusses but is not heavily burdened by theoretical models about scientific change), I would recommend Helge Kragh's Quantum Generations, which is especially good for people who are interested in the actual physics, as well as its context, etc. Kragh's book (unlike most "popular" histories of physics) has the virtues of being both accurate and interesting; it is the sort of thing that actual historians of science read when learning this stuff themselves. --Mr.98 (talk) 03:13, 3 March 2011 (UTC)

And note that I write this not as someone who is a real "Kuhnian." Kuhn's arguments are that shifts between "paradigms" (a big and vague category that includes theories, intuitive models of the world, pedagogy, experimental expectations, etc.) is as massive and discrete as a Gestalt shift. There are perhaps a few candidate incidents for the "old" worldview and the "new" worldview being Gestalt-like, and the EM worldview/relativity is perhaps one of them (Copernican vs. geocentric might be another). But it's unclear if that's really how science works most of the time, and Kuhn himself, for all of his virtues, did not really do the historical work to actually find these shifts. The Kragh book shows how complicated actual shifts of this nature can be; it's hard (impossible?) to come up with an historical theory of how scientific change works that takes into account the complexity of real-life examples, much less real-life examples for all of what can be considered "science." On the whole, philosophers and historians of science have moved away from attempts to do this sort of thing, and have been more purely descriptive (along Feyerabendian lines, albeit without his political motivations) in their actual scholarship. --Mr.98 (talk) 13:57, 3 March 2011 (UTC)

Kuhn does not claim that this is how science works most of the time. Paradigm shifts are rare events. --Srleffler (talk) 17:31, 5 March 2011 (UTC)

You can have a paradigm shift without the equations changing. Maxwell constructed a very complicated idea of how his equations might work within the bounds of Newtonian physics. He didn't have it extending to everything and he didn't have time going at different rates or energy and mass being the same. Dmcq (talk) 14:21, 3 March 2011 (UTC)

And in fact, in a typical Kuhnian description, most of the equations would stay the same, but the meaning behind them would change. A very easy concrete example of this is that a Lorentz contraction meant a very different thing to Lorentz than it did to Einstein. To Lorentz it had to do with how the aether worked; for Einstein, it was a statement about the implications of relative frames of reference. Boyle's Law still holds even though we have a very different understanding of gases than Boyle himself did. --Mr.98 (talk) 14:47, 3 March 2011 (UTC)

Historical scientific measurements

I have trawled wiki and google for a while to no avail. Does anyone know where I can find a plot of historical measurements of the electron charge and Hubble's constant. I.e. a list of data or plot of best estimates against when they were made, in order to show the effect of which Feynmann spoke in his cargo cult science talk. —Preceding unsigned comment added by 129.67.37.227 (talk) 23:50, 2 March 2011 (UTC)

Here's one for Hubble's constant from Harvard (about halfway down). Clarityfiend (talk) 03:10, 3 March 2011 (UTC)

The charge on an electron is formally called the elementary charge. According to the Oil-drop_experiment article, Robert Millikan's initial measurement wass about 1% lower than the currently accepted value. CS Miller (talk) 13:00, 3 March 2011 (UTC)

Indeed, but Feynmann reports that nonetheless sociological factors encourage scientists to misreport results leading to a kind ofof exponential decay toward the accepted value. Thank you for the Hubble data. —Preceding unsigned comment added by 129.67.37.227 (talk) 14:08, 3 March 2011 (UTC)

No trubble at all. Clarityfiend (talk) 01:11, 4 March 2011 (UTC)

I couldn't find the plot of measured electron charge over time, though I've seen it before and it's a very good illustration of how previous experiments bias the results of new one. Over the years, new experiments eke further and further away from millikans result. There were no random spread distribution around the true value, as you would have expected if only measurement error was to blame. for a similar situation, here's a plot of the measured speed of light:[2] Notice how the true value is outside the reported margins of errors of several experiments. EverGreg (talk) 09:09, 4 March 2011 (UTC)