What is Interpretation: Definition and 832 Discussions

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.

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  1. M

    An interpretation of quantum mechanics in terms of Brownian–like motion.

    Edward Nelson, a Princeton mathematician showed that quantum mechanics could be derived from the principle that elementary particles are subjected to a universal jiggling of an unspecified cause. As I understand the obstacle to use this mathematical model as a physical one, is that dynamics of...
  2. A

    MWI vs Copenhagen Interpretation

    I recently read an article entitled, "The Interpretation of Quantum Mechanics: Many Worlds or Many Words?" authored by Max Tegmark and it raised many questions on the matter as well as curiosity. In the article, Tegmark provides two tenable but diametrically opposite paradigms regarding physical...
  3. P

    What is the Interpretation of Log Likelihood in Molecular Data Analysis?

    Hello, I am a Bio informatician and encountered Likelihood while executing the Molecular data. I have used one software that is using the Hidden Markov Model in addition to the EM Algorithm and Viterbi algorithm. After calculations are done already, in addition to the output, it is giving me...
  4. E

    I'd like to know your interpretation.

    With Hobson's notation: H=(da/dt)/a dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2 If ((d2a/dt2)/a) is negative, (dH/dt) is certainly negative. But if ((d2a/dt2)/a) is positive, (dH/dt) can be positive or negative. What is your interpretation?
  5. C

    Interpretation of the distribution of brownian motion

    Hi all, I feel like there's a missing link in my understanding of brownian motion. I'm comfortable with the "method of http://fraden.brandeis.edu/courses/phys39/simulations/Uhlenbeck%20Brownian%20Motion%20Rev%20Mod%20Phys%201945.pdf" where the signal is written as a Fourier series, and with...
  6. V

    Geometric interpretation of an equation

    Homework Statement x,y, z are vectors in R^n. We have the equation: ax +by +cz, where a,b,c are constants such that a+b+c=1, and a,b,c>=0 What is the geometric interpretation of the equation? Homework Equations sv + tu, where u,v are vectors in R^n and s,t are constants such that...
  7. H

    Existence and the interpretation of infinite uncertainty?

    The trade off in uncertainty in momentum vs position in the HUP leaves me confused. In the context where the momentum is measured to increasingly greater precision and consequently position becomes less refined, is any logical inference made about the existence of the object i.e. is it...
  8. B

    Asme sec viii div 1 interpretation

    dear expert, please guide me in interpretation of asme sec viii div 1 interpretation...the basic terms used as uw,ucs etc..what does these abbrevate..same like basic nomenclature used in this code.. regards, bali
  9. C

    Physical interpretation of quantum superposition

    I understand the basics of the mathematical descriptions of systems in superposition. But what I'm not clear about is whether such a system is actually in more than one state at the same time. Is this a matter of QM interpretation or is it simply moot b/c we can make no measurements that can...
  10. R

    Entropy & Expansion: Physical Interpretation of Maximum Entropy

    Sorry for the confusing title! I have a question that I cannot wrap my mind around... Suppose the universe attains its state of maximum entopy (assuming maximum here also involves quantum effects such that in the end even the atoms disintegrate into photons and leptons). I understand that in...
  11. C

    What are some recommended books on interpreting quantum mechanics?

    Hi, I'm looking for a book that presents a pragmatic interpretation of QM that'd be appropriate for someone who's taken one semester of it.
  12. G

    Low entropy big bang Where am I going wrong with this interpretation?

    Hello. This is my interpretation of what is currently known in cosmology, as regards the low entropy state of the early universe. If it is a poor interpretation, then I apologise, but in all fairness, I can only blame the industry professionals for not explaining the data clearly enough. I am...
  13. bhobba

    Ballentine's Ensemble Interpretation Of QM

    Hi Guys I have recently been reacquainting myself with Ballantines - Quantum Mechanics - A Modern Development. He is pretty big on the Ensemble interpretation, and I must admit I am rather attracted to it as well - none of this collapse of a wave function stuff, many worlds etc. He also makes...
  14. O

    Graph Interpretation: Resolve f(t) in Step, Impulse & Ramp

    Resolve f(t) in terms of step,impulse and ramp functions.
  15. C

    Susskind, superposition and interpretation

    I've watched the Susskind lectures on QM and Quantum Entanglements. Susskind seems to avoid many of the interpretation issues inherent in QM. For example, he never talks about the wave function collapsing due to the involvement of "conscious mind". He does show, mathematically, that wave...
  16. J

    Interpretation of Light Beam Intensity in QM

    I am starting to become confused when reading about quantum mechanics and its treatment of photons. I heard somewhere (I can't recall where) that the characteristic intensity of a photon beam was give by I = E/\omega, where \omega is the angular frequency of the beam. However, I can't seem to...
  17. A

    Interpretation of De Broglie's wavelength ( matter wave ) for macro objects?

    The De Broglie's wavelength is given by λ = h / mv h = 6.626 x 10^(-34) Js Now, if a macro-object of 6.626 kg is moving at a speed of 10^(-34) m/s then its De Broglie's wavelength comes out to be 1 meter (metre). What does it mean to have 1 meter wavelength for that object? If another object...
  18. A

    Physical interpretation of equations

    Can all formulas be thought of intuitively/physically? For example, average speed is change in distance over change in time, that is intuitive and can easily be derived But when you have something like v^2 = u^2 + 2ax, or e=mc^2, how do you think of it intuitively? Specifically the squared...
  19. B

    Geometric Interpretation of (lower) Cohomology?

    Hi, All: Just curious to know if there is an interpretation for lower cohomology that is as "nice", as that of the lower fundamental groups, i.e., Pi_0(X) =0 if X is path-connected (continuous maps from S^0:={-1,1} into a space X are constant), and Pi_1(X)=0 if X is...
  20. G

    What is the interpretation of electroluminescence?

    Several sources states that the graph of electroluminescence carries with it some characteristics of the material that emit the radiation. How can we interpret the graph so as to extract those characteristics? Please help me on this.
  21. R

    Interpret QM: Find Bohmian Intrprtn - Book

    Where I can read about Bohmian interpretation of QM? I need a good , solid book.
  22. T

    Problems with Many Worlds Interpretation

    Hello, While the majority of physicists embrace the Many Worlds interpretation of quantum decoherence, I am holding out hope for the Copenhagen interpretation or better yet, a undiscovered interpretation. Please allow me to pose three problems I have with the MW interpretation. 1) There...
  23. A

    Inflation-Holographic interpretation

    I am interested in peoples opinion on the following papers, hep-th/0307026 Inflation and de Sitter holography hep-th/0402050 Holography, diffeomorphisms, and scaling violations in the CMB Larson and McNees motivated from Maldecena's ADS/CFT analyze Inflation using the Spectulated...
  24. C

    Which book explores Many-worlds interpretation and Hugh Everett's ideas?

    What is a good book that I could read about Many-worlds interpretation and what Hugh Everett was thinking.
  25. B

    How is the many worlds interpretation of QM related to the multiverse theory?

    To my understanding you can believe in the multiverse theory without subscribing to many-worlds interpretation of quantum mechanics. But can you subscribe to the many-worlds interpretation while also believing there is only this one universe (and that it just has hidden dimensions). Can...
  26. W

    Interpretation of Gaussian Kernel

    Hello. In a software application I am attempting to smooth a data set by convoluting it with a discrete Gaussian kernel. Based upon information garnered online, I've been using this Mathematica command to generate the kernel: kern = Table[Exp[-k^2/100]/Sqrt[2. Pi], {k, -range, range}]; where...
  27. F

    Why Is the Time Symmetric Interpretation Overlooked in Quantum Discussions?

    Why are the Time Symmetric Interpretation rarely if ever brought up in discussions here? It restores determinism and realism. This article explains the jist of the interpretation and experimental evidence...
  28. E

    Temperature distrubution in a cooling fin (result interpretation)

    I am analyzing the lengthwise temperature distribution in a cooling fin (length: 30mm, width: 10mm, the tip is assumed to be adiabatic, Biot number is smaller than 0.1). When I try to calculate the dimensionless temperature distribution (see calculation below), I obtain a curve which has a...
  29. R

    Physical interpretation of the Laplace operator

    "physical" interpretation of the Laplace operator Is there a "physical" interpretation of the Laplace operator, much like there exists a physical interpretation of the divergence and curl?
  30. B

    Physical interpretation of the rotation of a ket

    physical interpretation of the "rotation" of a ket Homework Statement No problem statement. I'm just having trouble imagining what it means to "rotate" a quantum -ket, especially since not all -kets are eigenstates of position. I know what the rotation operator is. I also can picture...
  31. A

    An interpretation of hamiltonians, states and fields.

    Hi all. Here is an n-particle hamltonian. H=\int d^{3}xa^{\dagger}(x)\Bigl(-\frac{\hbar^{2}}{2m}\nabla^{2}+U(x)\Bigr)a(x)+\int d^{3}xd^{3}yV(x-y)a^{\dagger}(x)a^{\dagger}(y)a(x)a(y) Here is an n-particle state. \Bigr|\psi,t\Bigl\rangle=\int...
  32. R

    QM interpretation like Many Worlds but with 'real' particles?

    Hello Forum, I've been reading about MWI, the Bohm interpretation, and Feynman QED. Combining elements from these interpretations, I've been building up my own simple mental model of 'how to picture the state of affairs', and I've been speculating about the feasibility of interpretations...
  33. D

    Interpretation of the polarizability

    Hello! If one uses the Lindhard formula to calculate the static polarizability of an electron gas, \chi(q), you get a function which is pretty much a constant until q=2k_F with k_F being the Fermi wave vector. After this it decays(it's on page 335 of Ashcroft and Mermin). But what is the...
  34. bcrowell

    Interpretation of Einstein's E=mc2 paper

    In "Does the inertia of a body depend upon its energy content?," http://fourmilab.ch/etexts/einstein/E_mc2/www/ , Einstein says: My interpretation of this is that these energies contain both potential and kinetic terms. A potential energy U is only defined up to an additive constant. If, for...
  35. Z

    Physical interpretation of the Hamiltonian

    When dealing with the Euler-Lagrange equation in a physical setting, one usually uses the Hamiltonian L=T-V as the value to be extremized. What is the physical interpretation of the extremizing of this value?
  36. S

    A beutifully simple interpretation of Vector Potential

    This is not my theory, or even new, rather pertaining to established physical knowledge, but I simply find it fascinating. It pertains to several areas of physics, and/or variational mathematics, so I've posted it here in the General Physics area. My reasons for posting is because it is one...
  37. R

    Heisenberg Interpretation vs Objective Collapse

    　 We know Copenhagen settles for computational rules connecting human observations rather than striving to comprehend the nature of the underlying reality. Heisenberg eventually did try to form a coherence picture of what is actually happening. But how come this Heisenberg Interpretation is not...
  38. S

    Geometric interpretation of \int x f'(x)

    I was reading Tom Apostol's expostion of Euler's Summation Formula ( http://www.jstor.org/pss/2589145) and it occurred to me that it would be convenient to visualize \int_a^b x f'(x) geometrically. In that article, it arises from integration by parts: \int_a^b f(x) dx = |_a^b x f(x)...
  39. strangerep

    Ballentine: Statistical Interpretation of QM

    This is a continuation of discussions from another thread: https://www.physicsforums.com/showthread.php?t=490677&page=2 I believe it deserves its own thread instead of hijacking the other one. "Ref 3" in what follows is this paper: L.E. Ballentine, "The Statistical Interpretation of...
  40. C

    Probabilistic interpretation of wave function

    I just start to study quantum mechanics and i don't understand why square of wave function is probability density function. I think the reason of taking square of wave function is because we should eliminate complex compounds of wave function to get a real magnitute. But after why don't we take...
  41. R

    Neumaier Thermal Interpretation of QM, valid?

    For those of us trapped in a corner with difficult choices of whether to believe many worlds are splitted off billions of times every second or whether there is Godlike power to collapse the wave function in the universe or whether waves can travel forward or backward in time (Transactional) or...
  42. C

    What is the correct interpretation of this circuit?

    My question: 1) In diagram (b), is there a reason why Vo is to the left of 15 ohm resistor and not to the right? (which wouldn't produce the same answer) cf. diagram (a) It might be a minor point but I'd like to know the specific reason Thanks
  43. F

    Quantum Interpretation Poll (2011)

    I think it's time for the annual quantum interpretation poll. Vote for which interpretation you currently think represents reality.
  44. PainterGuy

    In my interpretation of this circuit correct?

    Hello everyone, :wink: Have a see on this link:- http://img228.imageshack.us/img228/7236/vinvout.jpg Diagram #1 is what I found in a book. I couldn't understand how this circuit will be transformed into practical form. Therefore, in Diagram #2 I have my interpretation presented. Is it any...
  45. D

    Energy calculation and interpretation of a power plant

    My friend asked me what does a 540 MW power plant mean and how to interpret, I said it can lift a 1 Kilo Ton object to a height of 1 KM in about 3 Mins. My calculation is based on the equation of potential energy to the time taken by the power plant to produce that energy. Is this the...
  46. S

    Phonon Dispersion Interpretation

    Dear friends of physics forum I have calculated the phonon dispersion of an fcc phase using PHONON software. the fcc phase I am talking about is a metastable phase of Zr. Zr, as we all know exists in hcp and bcc phases. I wanted to calculate the heat capacity at constant volume using the...
  47. M

    Physical Interpretation for two answers for time

    When you solve the motion equation x=x_0 +v_0t +\frac{1}{2}at^2 you get two answers for t. One being a negative due to the quadratic. What is the physical interpretation of this? Its driving me nuts.
  48. A

    Hi guys,does anyone knows what is the physical interpretation of

    hi guys,does anyone knows what is the physical interpretation of second(third, fourth,...) derivative?
  49. C

    Quantum interpretation of Ring Laser Interferometry

    I have a question about Ring Laser Interferometry. A couple of years ago I contributed some text and several pictures to the http://en.wikipedia.org/wiki/Sagnac_effect" . Ever since I have been curious about the quantum interpretation of Ring laser interferometry. The special thing about...
  50. A. Neumaier

    What does the probabilistic interpretation of QM claim?

    I collect here info from another thread, to have a more focussed discussion. ''this particular assumption'' refers to the assumption that |psi(x_1,...,x_n|^2 is the probability density of observing simultaneously particle k at position x_k (k=1:N). Please show me a comparison with experiment...
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