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It From Bit or Bit From It
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The Quantum Dictionary Mark Van Raamsdonk is re-writing how we define the shape of our universe. Can such translations help to unite quantum theory and gravity? FQXi FORUM August 20, 2014 CATEGORY: FQXi Essay Contest - Spring, 2012 [back] TOPIC: Gravity Can Be Neither Classical nor Quantized by Sabine Hossenfelder [refresh] Author Sabine Hossenfelder wrote on Aug. 31, 2012 @ 12:07 GMT Essay Abstract I argue that it is possible for a theory to be neither quantized nor classical. We should therefore give up the assumption that the fundamental theory which describes gravity at shortest distances must either be quantized, or quantization must emerge from a fundamentally classical theory. To illustrate my point I will discuss an example for a theory that is neither classical nor quantized, and argue that it has the potential to resolve the tensions between the quantum field theories of the standard model and general relativity. Author Bio Sabine is an assistant professor at Nordita in Stockholm. Her work is mostly focused on the phenomenology of quantum gravity. In her free time she blogs at backreaction.blogspot.com Download Essay PDF File Patrick Alan Hutchinson wrote on Aug. 31, 2012 @ 18:20 GMT Hello Sabine Thanks for this essay. It summarises what appears to be a real problem and outlines what might be a real solution. It does not give many details of either the problem or the possible solution, but they may be in the references. This is all good. The questions which come to mind are: 1. Does it make sense to say that Planck's constant varies? Might it be a quantity, like the speed of light, which is taken as an absolute unit? Are there any other natural absolute units which might be used instead? The equation you give on page 3 for G relates G and c and Planck's constant and the Planck mass. Is there a good reason for regarding any one of these as less fundamental than the others, and so as dependent on them? 2. If Planck's constant varies, what might be the equation (or whatever) describing how it varies? What might be the "suitable potential" which could be added to the Lagrangian? Are there any physical or geometric criteria for choosing any particular potential? If these points can be given satisfactory answers, this all looks like promising research. Regards, Alan H. report post as inappropriate Bee replied on Sep. 1, 2012 @ 10:26 GMT Hi Patrick, Planck's constant is dimensionful, so if you want to speak of it varying, you should strictly speaking normalize it to make a dimensionless constant first. I did mention this in the arxiv paper - the normalization that suggests itself is the measured value of the Planck constant (at low temperatures). I'm not entirely sure what you mean with "variation". Do you mean a spatial variation or a temporal one? In the case I discussed there shouldn't be a spatial variation of Planck's constant unless you are in strong curvature regimes, ie towards black holes or towards the Big Bang singularity. (Think of particle masses, ie the higgs vev, it doesn't vary either.) What might be a suitable potential, well, it has to be one that leads to a symmetry breaking at high temperatures and at the same time have quantum corrections that allow the convergence of the perturbative expansion, as I explained towards the end of the text. I don't know if such a potential exists. To begin with it would depend on the particle content of the theory. I don't think there's an easy answer to that, but all I wanted to say is that it does not seem impossible, and I believe it's a possibility worth investigating. Best, B. report post as inappropriate Alan Hutchinson replied on Sep. 1, 2012 @ 23:10 GMT Hello again Bee Thanks for your reply. When I wrote of Planck's constant "varying", I wasn't thinking carefully about the circumstances. Variation with either space or time would be worth understanding. As to "normalizing", perhaps I had better read your arxiv paper before writing more. About choice of potential: you suggest two criteria. The first, causing symmetry breaking, sounds worthwhile, but if there is any symmetry breaking potential then there will probably be very many such. It would be good to have a criterion which constrains the form of the potential much more. The second, convergence of the perturbative expansion, sounds rather ad hoc. It seems based on a model of calculation which excludes every conceivable model which is not just a simple perturbation of some basic state. These are not criticisms of your essay. As far as I can tell, the entire main stream of current physics theory is developed around models described by such perturbations. The problem of convergence haunts them all. Even more serious: this approach excludes the possibility of models which are not such perturbations. The form of model suggested in my submission avoids this issue, which is one reason why I thought it worth writing. As things stand in current theory, the entire structure of most theories proposed these days is constrained by the very specific syntax which is available for describing Lagrangians in the notation inherited from a century-old form of maths. This aspect of theoretical physics has some catching up to do. Best wishes (Patrick) Alan H. report post as inappropriate Don Limuti wrote on Aug. 31, 2012 @ 18:44 GMT Sabine, A rose by any other name would still be a rose, I think? Or would it require another theory? I like your well written essay and to the point. And you are not afraid of taking some risk. Cool! I was hoping you were going to enter this contest, so I could thank you for making my entry possible. One of your blogs on "backreaction" gave me enough confidence to submit "An Elephant in the Room" and have some fun. Thank you, Don L. report post as inappropriate Bee replied on Sep. 1, 2012 @ 10:13 GMT Hi Don, It makes me happy to hear that my blogging has encouraged you to write down your thoughts. I'll have a look at your essay. Best, B. report post as inappropriate James Lee Hoover wrote on Aug. 31, 2012 @ 19:05 GMT Sabine, You wisely set a modest and an achievable goal, though well-presented. "I hope to have convinced the reader that giving up the assumption that a theory is either classical or quantized can be fruitful and offers a new possibility to address the problems with quantum gravity." My ruminations about gravity tended toward observations that could be questioned and details that could point elsewhere. Jim report post as inappropriate James T. Dwyer wrote on Aug. 31, 2012 @ 19:32 GMT Hi Sabine, Your essay is very nicely structured, although there's little I can reasonably comprehend. Therefore, I'm certain:) what's really needed here are some insights from an uninformed pedestrian passerby... - There seem to be two alternative, mutually exclusive characteristic properties of matter: kinetic self-propagating momentum and potential inertial mass. By that I mean... view entire post report post as inappropriate Bee replied on Sep. 1, 2012 @ 10:30 GMT Hi Jim, I don't know what you mean when you say "The effects of gravity simply do not seem to appear in the interactions of quantum particles." They appear if you put in a gravitational interaction, and you can do that in a perturbative quantization coupled to the rest of the standard model. The problem is just that this theory only makes sense as an effective theory, not as a fundamental one. Best, B. report post as inappropriate James T. Dwyer replied on Sep. 1, 2012 @ 18:08 GMT Hi B., Of course I prefaced my comments by indicating that I'm not a physicist, much less a quantum theorist, but, that being said, I was referring to observational evidence of gravitational interactions among quantum particles. While models can be constructed describing various forms of gravitational interactions, is their observational evidence supporting a quantitative perturbative interaction among particles? Of course, that was not the main point of my little comment, but you're certainly free to dismiss or ignore it in its entirely... report post as inappropriate James T. Dwyer replied on Sep. 1, 2012 @ 18:41 GMT B., Actually, shouldn't a quantum gravitational effect be manifested more specifically as an effective attraction interaction among particles - proportional to their mass? Has any such interaction among particles been observed? Jim report post as inappropriate Georgina Parry wrote on Aug. 31, 2012 @ 20:36 GMT Dear Sabine, Good luck in the competition. Your essay is about an interesting and important subject which is very relevant to the essay question. With so many possible subjects to consider, you probably made a wise choice applying your expertise to just this one. PS. I do read your thought provoking and educational blog from time to time- and watched your music video. report post as inappropriate Bee replied on Sep. 1, 2012 @ 10:16 GMT Dear Georgina, I'm glad to hear you find it interesting. The video... was fun. I guess I'm overcompensating for my conservative colleagues ;o) Best, B. report post as inappropriate Georgina Parry replied on Oct. 5, 2012 @ 07:23 GMT Hi Bee, I am still hopeful that you might get the chance to take a look at my essay before voting ends. Here's a link to a web site that explains more.RICP explanatory framework There is an older version of diagram 1. on that site. I have put a link to the high resolution file of the latest version, used in the essay, on my discussion thread. Kind regards, Georgina. report post as inappropriate Marcus wrote on Aug. 31, 2012 @ 22:57 GMT Just pointing out, in case anybody missed it, that the essay "Gravity can be neither classical nor quantized" has a companion article at http://arxiv.org/abs/1208.5874 called "A possibiliity to solve the problems of quantizing gravity" It helps to read both. I expect the two articles together will be a landmark and will noticeably change the way quantum relativists look at the problem of a combined theory of geometry and matter. The result can be something more interesting, and better, than either a classical or a quantum theory. I have to say--the Hossenfelder idea is such a bold stroke, and seems to have enough possibility of succeeding, that it is actually entertaining to think about. It is *enjoyable* to mull over such a creative yet fundamentally simple proposal. report post as inappropriate Member Benjamin F. Dribus wrote on Aug. 31, 2012 @ 23:23 GMT Sabine, A very interesting essay. A few questions come to mind. 1. You mostly describe quantum theory in the language of operators. Do these ideas still make sense, and what do they look like, using Feynman's sum-over-histories approach? 2. It seems natural at first glance to try to apply these ideas to inflation and dark energy. This may be hopelessly naive, but have you thought about letting your "Planck field" change sign in some regime to produce a negative G? 3. Are you envisioning sharp phase transitions or gradual ones? The reason I ask is because if you went to an even more radical paradigm and incorporated discreteness, you might possibly make use of the phase transitions of random graph dynamics. To get a better idea of what is motivating these questions, you might take a look at my essay On the Foundational Assumptions of Modern Physics[link] Take care, Ben Dribus report post as inappropriate Member Benjamin F. Dribus replied on Sep. 1, 2012 @ 01:11 GMT (sorry for the link formatting; I forgot the slash!) report post as inappropriate Bee replied on Sep. 1, 2012 @ 10:39 GMT Hi Ben, These are all very good questions that I don't have quick answers to. As to 1: I can only say I certainly hope it does, it would be more elegant. As to 2. I think this might be similar to a signature change. It might be very interesting to think about further. And regarding 3. I haven't been envisioning this one way or the other. I'd think this is a question that would have to be addressed by experimental constraints, for example, as you say, inflationary imprints in the CMB because it affects what it means to have a quantum fluctuation to begin with. In fact, this seems to me the most fruitful direction to make contact with observation. Best, B. report post as inappropriate Member Benjamin F. Dribus replied on Sep. 2, 2012 @ 06:55 GMT Thanks for the answers! I didn't realize until I checked your thread that it was you who posted as "Bee" over on my thread... I wrote some remarks there too. Anyway, you have some very good ideas... things I had never thought of before. Take care, Ben report post as inappropriate Jayakar Johnson Joseph wrote on Sep. 1, 2012 @ 12:10 GMT Dear Sabine Hossenfelder, If the universe is with matters in continuum, gravitation is considered as the tensor product on deformation of matters, in that, matters are eigen-rotational strings. To describe this gravity of the universe with an infinite sum of string-lengths, quantization is inevitable in that a different framework of quantization to be adapted that is non-perturbative and conformal. With best wishes, Jayakar report post as inappropriate Robert L. Oldershaw wrote on Sep. 1, 2012 @ 15:02 GMT Hi Bee, A quick hypothetical question. In a toy cosmos wherein all masses were quantized, would gravitational interactions (even if intrinsically classical) be quantized by default? I have asked this question in several discussion forums, but I don't think I have ever gotten a straight answer. Is the question flawed in some way? Rob O report post as inappropriate Bee replied on Sep. 2, 2012 @ 07:25 GMT What do you mean with "masses are quantized"? report post as inappropriate Robert L. Oldershaw replied on Sep. 2, 2012 @ 14:37 GMT A very interesting question! Say in this toy cosmos there are only the commonly known particles and atoms composed of them. The atoms have quantized masses in acordance with QM. If the masses of all objects in this toy cosmos are quantized (not continuously variable masses, but definite masses, and in the case of atoms multiples of a unit mass), then are the gravitational interactions between and among them quantized by default, i.e., the interactions cannot be other than quantized even though GR is classical? I do not see how to ask the question in a simpler or more straightforward way. For those seeking to quantize gravitation, this would seem like one of the most obvious first questions to ask of nature. report post as inappropriate Bee replied on Sep. 4, 2012 @ 07:36 GMT I still don't know what you mean with "quantized masses in accordance with QM." report post as inappropriate Harlan Swyers wrote on Sep. 1, 2012 @ 15:04 GMT I am a big fan of arguing discreteness is an emergent property, however isn't discreteness effectively a two state proposition, either its there or it isn't. Since planks constant has arbitrary units, it seems unnatural to me to talk about it evolving in time. I am thinking you mean that some fundamental ratio is evolving with time, but I am not sure if that is a correct characterization. report post as inappropriate Bee replied on Sep. 2, 2012 @ 07:28 GMT Hi Harlan, As I already wrote in a comment above, in principle you are correct that since Planck's constant is dimensionful, one should take a ratio and then talk about a dimensionless quantity. The most natural thing to do seems to divide it by the measured (low energy) value of Planck's constant (\hbar_0). However, this would make the notation less intuitive, so I haven't done that for the sake of readability. I don't know what your referral to discreteness means. Best, B. report post as inappropriate Harlan Swyers replied on Sep. 2, 2012 @ 13:34 GMT Bee, Thanks for the response. The idea of discreteness comes from using planck's constant in hilbert space. The purpose of the constant is to transform an otherwise continuous spectrum into discrete spectrum. For instance $e^{iHT}$ which contains two continous quantities is modified into $e^{(i/h)HT}$ which now allows us to talk about integer components with respect to h (everything to the left of the decimal point e.g. x.yyyy where the integers are to the left of the decimal). When talking of infinties, the specific value of h isn't important, its that we now have discretized the product space HT. Since T is usually unbounded, HT is unbounded, so talking in infinities makes sense. Cantor showed that there is a definite distinction between discrete and continuous infinities. This is the basis of the remark, the value of h isn't particularly important, so it isn't useful to discuss it changing with respect to time. report post as inappropriate Bee replied on Sep. 4, 2012 @ 07:41 GMT Hi Harlan, Operators can have continuous spectra. Best, B. report post as inappropriate Anton Lorenz Vrba wrote on Sep. 1, 2012 @ 15:54 GMT Hi Sabine, You write: "Classical general relativity predicts the formation of singularities under quite general circumstances. Such singularities are unphysical and should not occur in a fundamentally meaningful theory." That is a powerful statement. As I understand it, the theoretical physics community proposes to get past the problem of gravitational singularities by a clever definition in quantum gravity; instead of investigating the possibility that gravity is wrongly defined. An alternate ansatz to describe gravity, which will not lead to singularities, you will find in my essay "Rethinking Geometry and Experiece", I really would appreciate your time and a feedback. Regards Anton report post as inappropriate Frank Martin DiMeglio wrote on Sep. 1, 2012 @ 20:03 GMT Hi Sabine. You are correct that gravity is not fundamentally described and understood. That is a clear fact. You do agree that true/real/theoretical quantum gravity requires grvitational and electromagnetic equivalency and balancing and gravity and inertia in FUNDAMENTAL equilibrium and balance? It also clearly requires balanced attraction and repulsion and FUNDAMENTAL instantaneity, correct? If we want to fundamentally express F=ma, in conjunction with the fact that gravity cannot be shielded, everything listed in this post is necessary for true/real quantum gravity. (As you know, light is known to be quantum mechanical in nature.) We really need to use the term "quantum gravity" in conjunction with the above terms. Indeed, true/real quantum gravity FUNDAMENTALLY demonstrates F=ma. TRUE/REAL QUANTUM GRAVITY IS FUNDAMENTAL FORCE/ENERGY. I would appreciate your thoughts. You are a very bright thinker, but outer space is a sinkhole. It is not fundamentally comprehensible or understandable. My essay should be posted shortly. It will give you serious "food for thought". I would appreciate it if you would look at it and rate it. report post as inappropriate Neil Bates wrote on Sep. 2, 2012 @ 15:27 GMT This is interesting, thanks Bee (BTW a prior 2nd-place winner.) The welcome defying of typical dichotomies reminds of my own insistence, the previous contest, that reality was neither digital nor analog (i.e., not fully representable by any kind of actual math.) Considering the big troubles that trying to conjoin GR and QM have provided, why not try a whole new attitude? BTW I submitted a new essay for this contest, late Friday night so it hasn't shown up yet. The title gives a hint, it's about quantum measurement: "Can repeated interactions show more about a photon than current theory allows?" PS: Is there a general contest discussion thread, like there was last time? I can't find one. tx. Cheers and good "luck" to all. report post as inappropriate Frank Makinson wrote on Sep. 2, 2012 @ 18:01 GMT Sabine, I have followed some of the concepts you have presented for several years. In 2008, I sent you an email about a proposed paper, which was published by the IEEE in 2011, "A methodology to define physical constants using mathematical constants". That paper is cited in my essay, topic 1294, and I provide links in the comments. It describes a fundamentally different way to apply mathematics to physical law. In your essay, first section, subsection 3, you state, "As Hannah and Eppley have argued [2], the attempt to do such a coupling leads either to a violation of the uncertainty principle (and thus would necessitate a change of the quantum theory) or to the possibility of superluminal signaling, which brings more problems than it solves." Although not a part of my essay, a paper titled, "The helical structure of the electromagnetic gravity field" ( Helical Electromagnetic Gravity ) describes a simple mechanism how superluminal influence can exist. Please note that in 2004, the authors of references [6] and [7], cited in the paper, established a mathematical basis why gravity has an electromagnetic (EM) origin. All the authors of [6] and [7] needed was a description of the EM field structure that provides an attractant only force; my paper does that. report post as inappropriate Cristinel Stoica wrote on Sep. 2, 2012 @ 19:12 GMT Dear Sabine, For almost any choice, people tend to think that it should either be one, or the other. I liked your point that, in the case of "classical" vs. "quantized", the fundamental theory can be neither. I am interested myself in ways in which quantum can emerge from something else. Maybe is both "classical" and "quantized", where the quantum comes from some topological or cohomological properties or something like this. In a different direction, in my present essay, Did God Divide by Zero?, I develop the idea that singularities exist in classical general relativity, but are nicely behaved, and as a bonus they seem to provide a way of regularization for quantum gravity. Best wishes, Cristi Stoica report post as inappropriate Lawrence B Crowell wrote on Sep. 2, 2012 @ 21:48 GMT Your essay is interesting and food for thought. Gravitation is not given by a compact Lie group, which makes unitary principles problematic. The holographic principle makes the argument that quantum information is conserved. However, we have no general theory for how quantum information is conserved without unitarity. My essay is an attempt to address this matter. Quantum gravity might in the end be a bit of a misnomer. In general I agree that gravitation will not be quantized at all in the standard way. Cheers LC report post as inappropriate Frank Martin DiMeglio wrote on Sep. 3, 2012 @ 02:29 GMT Lawrence and Sabine. The force/energy of inertia and gravity has to be equivalent and balanced in order for there to be fundamental quantum gravity. (Light is known to be quantum mechanical in nature.) A smaller space must be made larger, and a larger space (on balance) must be made smaller. All relevant opposites must be balanced, included, and combined. Completeness and balance are essential in physics (and theory/ideas). Balanced and equivalent attraction and repulsion is a must too. Also, please see the additional information in my prior/above post in this matter. Have either of you given any thought to the ideas of feeling, touch, AND vision as they can converge (fundamentally/basically) in relation to BOTH gravity and electromagnetism? Would this not fundamentally, meaningfully, and significantly tell us more about space, force, and energy (as seen, felt, and touched) taken together? We do need to begin with basics. True/real quantum gravity demonstrates F=ma fundamentally and fundamentally includes instantaneity as well. Inertia and gravity must be balanced and equivalent. There is no getting around this. You have to demonstrate fundamentally stabilized distance in/of space. My essay, soon to be posted, represents a major and fundamental breakthrough in waking AND dream physics (including gravity) FUNDAMENTALLY. I would appreciate your ratings and comments on this too. Thanks. report post as inappropriate Thomas Howard Ray wrote on Sep. 3, 2012 @ 11:45 GMT Bee, As usual, you display a marvelous facility for clearly reducing a problem to its essentials. Delightful reading. I have to point out, though "If Planck's constant is a field ..." your proposal for unification is unambiguously classical. We've always known that if Planck's constant were zero, that we live in a classical world. So if " ... quantum corrections which would normally diverge ... cleanly go to zero ..." spacetime geometry (actually, topology) is enough and we don't need quantization at all, for a fundamentally unifying theory. I do hope you get a chance to visit my essay site. Best, Tom report post as inappropriate Bee replied on Sep. 4, 2012 @ 07:46 GMT Hi Tom, Thanks for the kind words. My proposal is not fundamentally classical, the quantization condition is always present. You're right, we might not need quantization for a fundamentally unifying theory. But we clearly need quantization, or something very much like it, to reproduce the world that we see. I'll check out your essay. Best, B. report post as inappropriate Thomas Howard Ray replied on Sep. 8, 2012 @ 13:34 GMT Hi Bee, Yes, I agree that we need " ... something very much like ..." quantization to explain the observed world. I am reminded that Einstein (The Meaning of Relativity, Appendix II) allowed that a more complex field theory than general relativity may be explained by " ... (increasing) the number of dimensions of the continuum. In this case, one must explain why the continuum is *apparently* restricted to four dimensions." In the same respect, the idea of Planck's constant as a field has to explain why action is apparently quantized. Best, Tom report post as inappropriate Rick Lockyer wrote on Sep. 3, 2012 @ 14:59 GMT Hello Bee, Congratulations on a wonderful essay. I could not agree more with your position on which I quote: “This mismatch between the quantum field theories of the standard model and classical general relativity is more than an aesthetic problem: It signifies a severe shortcoming of our understanding of nature. This shortcoming has drawn a lot of attention because its resolution it is an opportunity to completely overhaul our understanding of space, time and matter.” Perhaps the complete overhaul might require backing away from general relativity in favor of a single mathematical foundation that cleanly integrates the fundamental forces of Gravitation and Electrodynamics, with directive qualities on just what the remainder of things must look like. The quantum side of nature might reveal itself in a different guise within the very same structure. There is a nascent concept that does just this. It is the subject matter of my essay The Algebra of Everything. I show in this essay the relativistic characteristics of Electrodynamics are not unique to a 4D split-signature Minkowski space-time, but also within an Octonion Algebra governed 8-space. The increase in dimensions allows Electrodynamics to be only a subset of the presentation, as it must to be unified with something else. You might consider the move to Octonion Algebra as flatting out the second rank tensors employed, and instead of having only their symmetric and anti-symmetric structures, the full structure of Octonion Algebra is in play. I would love for you to take a look and comment, for I value your opinion. Regards, Rick report post as inappropriate Daniel Sudarsky wrote on Sep. 3, 2012 @ 21:59 GMT Dear Sabine I found very intriguing your idea of theories that are neither quantum nor classical. However I have a concern regarding the your proposal. I remember from my time as a student some old discussions about the issue of constancy of$h$. At that time we were talking about a proposal made by mi advisor. The paper ... view entire post report post as inappropriate Bee replied on Sep. 4, 2012 @ 07:52 GMT Hi Daniel, Thanks for your interest. I did address this point in my paper, and also in two comments above. It is true of course that Planck's constant is dimensionful and one should not speak of it varying. Note however that I have another constant of the same dimension, which is the low-energy vev \hbar_0. You can divide the field by that constant and be left with a dimensionless quantity. Think of ASG: Strictly speaking it doesn't make sense to speak of the variation of the Planck mass either for the same reason, it's dimensionful. It does make sense however to speak of the ratio between the low energy and the high energy coupling. It's the same here. Best, Sabine report post as inappropriate Daniel Sudarsky replied on Sep. 6, 2012 @ 15:11 GMT Dear Sabine Thanks for your reply. I am afraid however that I might not have made my point 100% clear, as I do not think that these points were really covered in the previous discussions. The issue is what is the meaning (or to be more precise the operational significance ) of a varying value of$h\$?

Say we chose...

view entire post

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Saibal Mitra replied on Sep. 6, 2012 @ 17:32 GMT
Daniel,

You are making things way too complicated here by mixing the freedom to choose a unit system with the actual physics. While I can't speak for Sabine here, let me suggest to you may favorite way of dealing with these sorts of problems.

First switch to natural units c = hbar = G = 1. This defines unambiguously a consistent unit system, so no problems with that here. Unlike in, say, the SI units system you don't have any freedoms to express time, masses etc. relative to some arbitrary scales, so you now don't have compensating constants like c, hbar and G that compensate for such freedoms.

Then where hbar were to appear if you wanted it to put back, you put in your equations written in these natural units, a field phi. Also, where G would appear you put a factor phi. Since you are still working within the same natural unit system, all issues regarding measurments etc. are unambiguously defined.

In Sabine's theory, phi gets a vacuum expectation value of 1 at low energies, and at high energies the expectation value tends to zero.

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Jin He wrote on Sep. 4, 2012 @ 14:00 GMT
Unfortunately, Dr. Laurent Nottale and Dr. Jin He quantized gravity many years ago:

Quantum Gravity Based on Mach Principle and Its Solar Application

http://vixra.org/abs/1101.0076

Einstein Field Equation: the Root of All Evil? Quantum Gravity, Solar Application

http://arxiv.org/abs/astro-ph/0604084

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Saibal Mitra wrote on Sep. 4, 2012 @ 16:58 GMT
I'm wondering if there would also be effects at low energies. If you consider some amplitude of a process written as a path integral then you now divide the Lagrangian L by hbar inside the space-time integral over the fields, as hbar is now a dynamical field. Then, even though you have some potential for h that effectively contrains it to the standard value, if you consider some process with a very small amplitude (like some rare decay process), it seems to me that there could be significant contributions to this via fluctuations in the h-field. The penalty against this due to the the h-potential may then be outweighed by the L/h part making a larger contribution.

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John A. Macken wrote on Sep. 6, 2012 @ 00:01 GMT
Sabine,

Do you consider the electrostatic force exerted between two electrons to be quantized, classical or neither? The reason for asking this question is that I am going to make the argument that there is also a gravitational force between the two electrons and this gravitational force is closely related to the electrostatic force. In other words, my proposal is the gravitational force must be classified the same way as the electromagnetic force. To support this contention I offer my essay available here. This essay offers previously unknown equations showing that these two forces are closely related. This close relationship becomes obvious when the forces between fundamental particles are expressed using the wave properties of the particles and referencing Planck force. Furthermore, these equations were predicted by a wave-based analysis of both particles and forces. In this analysis all quantized processes ultimately result from the transfer of a quantized unit of angular momentum.

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Janko Kokosar wrote on Sep. 8, 2012 @ 14:22 GMT
Dear Ms. Sabine

I do not agree with Your ideas. The key for rejection is hidden in Duff's idea that constants h, c, and G does not exist physically. It is only possible that masses of particles increases, but You did not mentioned this possibility.

Problems with singularities can be solved on different way. Brukner, Zeilinger, Feynman, and other claim, that finite information is hidden inside of finite volume. So also singularities do not exist.

But your article is useful as thought experiment as why G, h, and c do not exist. So variation of h does not influence on variation of G.

Regards, Janko Kokosar

My essay

p.s.

I found some grammar mistakes: "violate unitary", "tought experiment", "gravitty". I hope that you will return this favour. :)

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Phil Warnell wrote on Sep. 9, 2012 @ 22:48 GMT
Hi Sabine,

It's long bothered me as to how many insist that gravity needs to be quantilized to have it consistent with the standard model, since it's apparent neither vision of reality represent being the final word on matters. With that said it's also undeniable that within their relative domains each stand as very successful theories which lend a great deal of insight into the workings of the physical world respective of their predictive power and conceptual imagery.

However it's always puzzled me that when we are talking about the very beginning of things, that is to enter terra incognita, there be reason for either conceptualization of things as thought needing to be particularly relevant. So I find your essay to resonate with this concern of mine, as it gives no special significance to either; that is other than as to ponder as to how each of these characteristics of our world has emerged as a consequence of conditions not needing to be governed by the mandates of either.

Regards,

Phil

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Peter Jackson wrote on Sep. 10, 2012 @ 14:08 GMT
Sabine

"a severe shortcoming of our understanding of nature... ...resolution it is an opportunity to completely overhaul our understanding of space, time and matter."

Beautifully and clearly written, and I very much agree, but wonder if you've overhauled understanding enough, and nothing has emerged with anything of the clarity of your writing.

I hope you may be able to read my own essay, which steps back a few more paces for greater overview and finds a pattern which does match observation, leading to a conceptual ontological construction. It has no singularities or evaporation, but Lagrangian points and recycling, via a mechanism not violating uncertainty. The model also redefines black holes as equivalent to AGN's. (elucidated in other papers).

I fear it's to unfamiliar for mainstream to recognise, but hope that, as you seem to understand the problem, you may recognise a solution. The model has kinetic logic foundations, and you need to understand each of a set of components to build the consistent model.

But anyway, your essay is worth a good score, even, or perhaps because, it clearly makes and deals with a limited point, rather the opposite of my own.

Best wishes and good luck

Peter

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Sergey G Fedosin wrote on Sep. 10, 2012 @ 14:22 GMT
Dear Sabine,

I suppose that at the atomic level of matter there is acting strong gravitation . Then we can quantize the equations of Lorentz-invariant theory of gravitation in the same way as Maxwell equations. At last strong gravitation may be used for modeling of strong interaction. What do you think about it?

Sergey Fedosin

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Phil Warnell wrote on Sep. 12, 2012 @ 08:17 GMT
Dear Sabine,

I find this essay to resonate for me it's long bothered me as to how many insist that gravity must be quantilized to have it consistent with the standard model, as it's apparent neither vision of reality represents being the final word on matters. With that said, as you've pointed out, it's also undeniable that within their relevant domains they each present as very successful theories, which lend a great deal of insight into the workings of the physical world respective of their predictive power and conceptual imagery. However it's always puzzled me that when we are talking about the very beginning of things, that is to enter terra incognita, there be any reason to be convinced that either conceptualization of things as thought needing to be particularly relevant. So I find your essay to resonate with this long held concern of mine, as it giving no special significance to either, that is other than to ponder how each of these characteristics of our world has emerged as a consequence of conditions not necessarily needing to be governed by the mandates of either, but rather serve as having the fundamental aspects with would allow for both.

"In relativity, movement is continuous, causally determinate and well defined, while in quantum mechanics it is discontinuous, not causally determinate and not well defined. Each theory is committed to its own notions of essentially static and fragmentary modes of existence (relativity to that of separate events, connectable by signals, and quantum mechanics to a well-defined quantum state). One thus sees that a new kind of theory is needed which drops these basic commitments and at most recovers some essential features of the older theories as abstract forms derived from a deeper reality in which what prevails in unbroken wholeness."

-David Bohm, "Wholeness and the Implicate Order", Introduction p-xviii

Regards,

Phil

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Yuri Danoyan wrote on Sep. 13, 2012 @ 02:45 GMT
Dear Sabine

What is your attitude to fundamental constants and Planck units?

My attitude is special....

See essay 1413

Do yo familiar with Frank Wilczek attitude?

See Wilczek articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab
s_limits388.pdf

http://ctpweb.lns.mit.edu/physics_today/physt
oday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_toda
y/phystoday/Abs_limits400.pdf

Is trinity sacred?

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Hoang cao Hai wrote on Sep. 19, 2012 @ 15:02 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Yuri Danoyan wrote on Sep. 21, 2012 @ 19:51 GMT
Sabine wrote: "Concretely, consider that Planck’s constant ¯h is a field whose value at high energies goes to zero.

In four space-time dimensions, Newton’s constant is G = ¯hc/m2

Pl, so if we keep mass units fix, G will go to zero together with ¯h, thereby decoupling gravity. If gravity decouples, there no reason for singularities to form. If gravity becomes classical, there’s no problem with the perturbative expansion. So this possibility seems intriguing, if somewhat vague. I will now make this idea more concrete and then explain how it addresses the previously listed problems with quantizing gravity."

Sabine, i reminding you about Wilczek doubt concerning Planck units:

"An appealing feature of atomic and strong units, in contrast to Planck

units, is that the characteristic length, time, and mass can be constructed

without taking square roots. It is disconcerting to imagine that we must extract roots in order to express the basic units in terms of fundamental

parameters. (Sophisticates will recognize that extracting roots is a

nonanalytic procedure, in the technical sense.) The fact that G, \, c can be expressed in terms of mp, \, c without extracting roots, but not vice versa, on

the face of it suggests that the strong units are more fundamental than

Planck units. (I find it remarkable that a similar conclusion is suggested

by string theory, where the closed string gravitational coupling naturally

appears as the square of the open-string gauge field coupling"

http://ctpweb.lns.mit.edu/physics_today/phystoday/A
bs_limits388.pdf

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Yuri Danoyan replied on Sep. 25, 2012 @ 03:59 GMT
Wilczek:"we must extract roots",

"can be taken outside the square roots",

"In the strong system of units no square roots

at all appear in [M], [L], [T ]."

http://arxiv.org/abs/0708.4361

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Thomas Wagner wrote on Sep. 21, 2012 @ 20:26 GMT
A most enjoyable essay. I found it delightful reading.

Sometimes we have to step back at take a more general look at things. Here is a more simplistic look (perhaps too simplistic) at the nature of gravity. I have posted it on a couple of essay pages.

Einstein, who, more than anyone else gave us our current view of the nature of gravity, said that gravity is not a force and yet in...

view entire post

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Sergey G Fedosin wrote on Oct. 2, 2012 @ 08:21 GMT
After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 05:33 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
$R_1$
and
$N_1$
was the quantity of people which gave you ratings. Then you have
$S_1=R_1 N_1$
of points. After it anyone give you
$dS$
of points so you have
$S_2=S_1+ dS$
of points and
$N_2=N_1+1$
is the common quantity of the people which gave you ratings. At the same time you will have
$S_2=R_2 N_2$
of points. From here, if you want to be R2 > R1 there must be:
$S_2/ N_2>S_1/ N_1$
or
$(S_1+ dS) / (N_1+1) >S_1/ N_1$
or
$dS >S_1/ N_1 =R_1$
In other words if you want to increase rating of anyone you must give him more points
$dS$
then the participant`s rating
$R_1$
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Lawrence B. Crowell wrote on Oct. 4, 2012 @ 18:14 GMT
Your essay was one of the more interesting ones. I have in recent weeks come to think there is some sort of duality between noncommutative quantum spacetime and smooth classical-like spacetime. This was further stimulated by reading Torsten Asselmeyer-Maluga's work. I gave you a high score that should jump your essay up some.

Cheers LC

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Jin He wrote on Oct. 5, 2012 @ 11:49 GMT
You mainstreamsians controle science for over 50 years. You mainstream and Hawking failed. The bad science is because of the Top-Down controle of the people like you. Why do you need money and fame from FQXI where the authors are mostly jobless, are mostly independent researchers, are mostly viXra.org authers? Do you need money and fame by controling jobless???

I want to rate you 0!

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Janko Kokosar replied on Oct. 5, 2012 @ 19:31 GMT
It is better that mainstream physicists cooperate here with amateurs and with non-mainstream researchers. But it would be better if here were larger number of arguments, much larger than numbers of rates.

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Concerned Public wrote on Oct. 6, 2012 @ 08:52 GMT
Sergey G Fedosin is bombing entrants' boards with the same "why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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text:
# proof of limit

• October 4th 2009, 10:13 AM
tonio
proof of limit
Hi:

how could one prove that if a_n --> A and A != 0 then

a_(n+1)/a_n --> 1 ?

I think some average inequalities could help here but I can't see it.

Thanx
• October 4th 2009, 11:55 AM
redsoxfan325
Quote:

Originally Posted by tonio
Hi:

how could one prove that if a_n --> A and A != 0 then

a_(n+1)/a_n --> 1 ?

I think some average inequalities could help here but I can't see it.

Thanx

For large enough $n$,

$|a_{n+1}-A|<\epsilon\implies\left|\frac{a_{n+1}}{a_n}-\frac{A}{a_n}\right|<\frac{\epsilon}{a_n}$

Taking $n\to\infty$ (and noting that $a_n\to A$) gives us:

$\left|\lim_{n\to\infty}\left(\frac{a_{n+1}}{a_n}\r ight)-\frac{A}{A}\right|<\frac{\epsilon}{A}\implies\left |\lim_{n\to\infty}\left(\frac{a_{n+1}}{a_n}\right)-1\right|<\frac{\epsilon}{A}$

which proves the theorem.

An easier, though less technical way of doing is noting that

$\lim_{n\to\infty}\frac{a_{n+1}}{a_n}=\frac{\displa ystyle\lim_{n\to\infty}a_{n+1}}{\displaystyle\lim_ {n\to\infty}a_n}=\frac{A}{A}=1$
• October 4th 2009, 12:23 PM
tonio
Huge. thanx a bunch, Redsoxfan

format: plain


text:
# Is $AA+A$ always at least as large as $A/A$?

Let $A$ be a finite set of real numbers. Is it always the case that $|AA+A| \geq |A/A|$?

In the line above, $AA+A:=\{ab+c:a,b,c \in A \}$, while $A/A:=\{a/b:a,b \in A, b\neq 0 \}$ is the ratio set.

This is closely related to a previous question about the relative sizes of the sets $AA+A$ and $A+A$. See Is the set $AA+A$ always at least as large as $A+A$?.

Earlier this year, a paper of myself, Imre Rusza, Chun-Yen Shen and Ilya Shkredov was posted. One of the results in the paper was a construction of a set of reals $A$ with $|AA+A|=o(|A|^2)$. For this particular example, one has $|A/A| = \Omega(|A|^2)$.
I suspect that the following weaker conjecture holds: for all $\epsilon >0$ there is an absolute constant $c=c(\epsilon)$ with $|AA+A| \geq c|A/A|^{1-\epsilon}$.


text:
The Effect of Perspective on Probability

My friend and I are tearing each other to bits over this, hope someone can help.

Coin flip experiment:

Define a single trial as 10 coin flips of a fair coin. Perform an arbitrarily large number of trials. At some number of trials n, you notice that your distribution is extremely skewed in one direction (i.e., the "average" of your 10-flip sets is far away from 5 heads and 5 tails).

My reaction: Because you are guaranteed to hit a 5H/5T mean as n approaches infinity, the probability that the next n trials contains an equal skew in the opposite direction increases. In other words, given 2*n* trials, if the first n are skewed in one direction, than the remaining n are probably skewed in the other direction such that the overall distribution of your 2*n* trials is normal and centered around 5H/5T.

My friend's reaction: It doesn't matter if your first n trials is skewed, the next n trials should still represent an unmodified 5H/5T distribution regardless. The probability of the next n trials being skewed in the opposite direction is unchanged and low.

Who's right, and why?

4 Answers

Let's say you're taking a bunch of measurements of independent process. Each measurement gives you a number: 1, 2 or 3. The average should be 2. The process is almost perfect, so you'll almost always get a 2.

You start taking measurements, and get the following results:

$$\{ 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2 \}$$

Should you now expect a series of 1s to "cancel" this out?

So far, your average is:

$$\frac{7\cdot 2 + 5\cdot 3}{12} = \frac{29}{12} \approx 2.417$$

Now, you take 100 more measurements; all are 2s.

$$\frac{7\cdot 2+5\cdot 3 + 100\cdot 2}{112} = \frac{229}{112} \approx 2.044$$

Now, another 1000 measurements, all 2s.

$$\frac{7\cdot 2+5\cdot 3 + 100\cdot 2 + 1000\cdot 2}{1112} = \frac{2229}{1112} \approx 2.004.$$

And so on.

In short, even though you got a string of 3s, you don't need a similar string of 1s to "cancel out" the effect. As your number of measurements goes to infinity, your average value will still get arbitrarily close to 2, which is what's expected.

The same can be said for flipping independent fair coins. Even given a string of heads, you don't need to get a similar string of tails to approach a 50/50 distribution as the number of trials go to infinity.

• I like this answer because it addresses directly the confusion of the question. +1 – daniel Jul 26 '13 at 19:44

Your friend is right. As alluded to by Daniel Fischer, the coins do not have any memory, therefore the earlier tosses are irrelevant.

If anything, if you should actually face such a situation with large $n$ you might start to doubt that the coins are fair, yet then you would rather expect the subsequent trials to be biased in the same way (not the opposite way).

If you want to consider something really interesting, consider that as you add more flips, the probability of getting exactly half heads and tails goes down and this isn't that hard to compute mathematically as the sequence is the fraction of $2n \choose n$ divided by $(2n)^2$ for 2n flips. The denominator will grow as you increase the number of flips.

For 2 flips, this is 2/4 = 1/2.

For 4 flips, this is 3/8.

For 6 flips, this is 20/64 = 5/16.

Now, as this continues, it will keep diminishing as it is a specific outcome compared to be "near" the middle. Just something to consider as while you may get close to the middle, the exact middle keeps having lower and lower probability.

Your friend is right.

Coin flips (at least the coin flips that most people think about) are independent of each other. The results of past flips don't effect the result of future flips. The reason that in the limit as the number of flips goes to infinity the distribution tends to 50% heads and 50% tails is that any given set of 10 flips (or any other finite number) has the same probability of having #heads/#tails = r as #heads/#tails = 1/r, so as you flip the coin many many times you will tend to have just as many sets skewed in one direction as the other.

This does not mean that consecutive, finite, sets of flips will be skewed in opposite directions because each set of 10 flips has exactly the same probability of giving any specific result. It is just that as the number of flips goes to infinity you will, statistically speaking, always end up with just as many sets of flips skewed in one direction as the other. Thus, saying that "because these first ten flips got more heads than tails, the rest of the flips we make will have more tails than heads" isn't accurate. Really what you should say is "Even though these first ten flips had more heads than tails, when we do 500 flips we're still very likely to get an almost 50 50 split because this skewed initial set will get averaged out over the many, many flips left".

It is fun to note that a set of coin flips like this is basically a random walk, and it can be shown that on average, in a set of $n$ flips the distribution will be skewed by about $\sqrt{n}$ in one direction or another. for 10 this is about 3 (we'll round to the nearest whole number) and for 500 this is about 22, however, 3/10 = .3 whereas 22/500 = .044 and as $n \to \infty$, $\sqrt{n}/n \to 0$. This is why small sets tend to be skewed more than larger sets. This is essentially because small sets of flips that make up the larger set tend to be skewed, but in opposite directions (more towards heads or more towards tails) so they have a tendency to cancel each other out.

That was kind of a long answer with a lot of words, I hope it helps.


text:
# Can someone help me with 2 circuit problems...please

by supermenscher
 P: 47 1. The equivalent resistance between points A and B of the resistors shown below is 38 ohms. Find the value of the resistance R. The resistor looks like this 55 Ohms _____\/\/\/\/_____ | | 12 Ohms | | A | | .____/\/\/\__ | |______. B | | | | |____\/\/\/\/_____| R I have no idea what to do...please help. 2. Determine the magnitudes and directions of the currents through R1 and R2, where R1 = 36 ohms and R2 = 10 ohms. I already found the directions. they are both from right to the left, I just need the magnitudes. The Bs represent batteries, and the + next to them indicates the positive side of the battery. I am also really lost on this one can anyone help? V1=9.0V R1 --+B--/\/\/\------- | | | R2 | .-----/\/\/\/-------. | | | | |----------B+------| V2=6.0V
 Sci Advisor HW Helper P: 2,586 I would suggest using [ code ] and [ / code ] tags: 55 Ohms _____\/\/\/\/_____ | | 12 Ohms | | A | | .____/\/\/\_______ | |______. B | | | | |____\/\/\/\/_____| R V1=9.0V R1 --+B--/\/\/\------- | | | R2 | .-----/\/\/\/-------. | | | | |----------B+------| V2=6.0V EDIT: Well, it looks best in the editor window, slightly better (but not great) in the code tags, and unreadable without those tags. SECOND EDIT: looks fine now ------------------------------------------------------------ For the first question, you should know how to calculate net resistances when you have resistors in series and parallel. To find the total resistance between A and B, it is: $$R_{total} = 12 \Omega + (55 \Omega || R)$$ $$38 \Omega = 12 \Omega + (\frac{1}{55 \Omega} + \frac{1}{R})^{-1}$$ $$26 \Omega = (\frac{1}{55 \Omega} + \frac{1}{R})^{-1}$$ $$(\frac{1}{26 \Omega} - \frac{1}{55 \Omega})^{-1} = R$$ $$R \approx 49.310 \Omega$$ $$R = 49 \Omega$$ ----------------------------------------------------------- Solve question 2 using the principle of superposition. That is, find the voltages and currents with the circuit first by replacing the top battery with a short circuit, then find the voltages and currents with the top battery, replacing the bottom with a short circuit. Add the numbers from the first calculations to the second calculations, and make sure you take direction/sign into account.
 P: 47 Thank you so much, I got them both right and 100 on the assignment :) :) :)

 Related Discussions Engineering, Comp Sci, & Technology Homework 6 Introductory Physics Homework 4 Electrical Engineering 8 Introductory Physics Homework 8 Introductory Physics Homework 13


text:
# Is quintic equations have anything to do with their coefficients?

I was reading about quintic equations and this came up:

In the early nineteenth century, Paolo Ruffini (1765–1822) and Niels Henrik Abel (1802–1829) proved that no such general formulas utilizing the usual operations and root operations exist. This means that there will never be a simple formula that provides the solutions for every single a, b, c, d, e, and f in a quintic equation.

so, I am a little confused. isn't the goal of solving a quintic equation is to find X? what is the role of coefficients in here? can anyone explain?

• If you have no coefficients, do you even have a quintic to solve for $x$? – David K Jun 11 '19 at 16:50
• Not sure what you are asking. It is, of course, true that $\textit {some}$ quintics are solvable. $x^5$ for example, or $(x+1)(x+2)(x+3)(x+4)(x+5)$. The Theorem says that there isn't a "sensible" formula, akin to the quadratic formula, that solves all quintics regardless of the coefficients. – lulu Jun 11 '19 at 16:59

• @Daruissoli In other words, solving any problem of the form $ax^5+bx^4+cx^3+dx^2+ex+f=0$. – J.G. Jun 11 '19 at 20:41


text:
## Blood pressure

• Blood pressure
Medical diagnostics
A sphygmomanometer, a device used for measuring arterial pressure
MeSH D001795
[]

Blood pressure (BP) is the pressure of circulating blood on the walls of blood vessels. When used without further specification, "blood pressure" usually refers to the pressure in large arteries of the systemic circulation. Blood pressure is usually expressed in terms of the systolic (maximum during one heart beat) pressure over diastolic (minimum in between two heart beats) pressure and is measured in millimeters of mercury (mmHg), above the surrounding atmospheric pressure (considered to be zero for convenience).

It is one of the vital signs, along with respiratory rate, heart rate, oxygen saturation, and body temperature. Normal resting blood pressure in an adult is approximately 120 mmHg systolic, and 80 mmHg diastolic, abbreviated "120/80 mmHg".

Traditionally, blood pressure was measured non-invasively using a mercury manometer and this is still generally considered the gold standard. More recently other semi-automated methods have become common, largely due to concerns about potential mercury toxicity, although cost and ease of use have also influenced this trend. Early alternatives to mercury sphygmomanometers were often inaccurate, but more modern validated devices have similar accuracy to mercury devices.

Blood pressure is influenced by cardiac output, total peripheral resistance and arterial stiffness and varies depending on situation, emotional state, activity, and relative health/disease states. In the short term it is regulated by baroreceptors which act via the brain to influence nervous and endocrine systems.

Classification of blood pressure for adults
Category systolic, mmHg diastolic, mmHg
Hypotension
< 90
< 60
Desired
90–119

90–129
60–79

60–84
Prehypertension (high normal)
120–139

130–139
80–89

85–89
Stage 1 hypertension
140–159
90–99
Stage 2 hypertension
160–179
100–109
Hypertensive urgency
≥ 180
≥ 110
Isolated systolic hypertension
≥ 160
< 90
Reference ranges for blood pressure in children
Stage Approximate age Systolic Diastolic
Infants 1 to 12 months 75–100 50–70
Toddlers and preschoolers 1 to 5 years 80–110 50–80
School age 6 to 12 years 85–120 50–80
Adolescents 13 to 18 years 95–140 60–90
Site Normal
pressure range
(in mmHg)
Central venous pressure 3–8
Right ventricular pressure systolic 15–30
diastolic 3–8
Pulmonary artery pressure systolic 15–30
diastolic 4–12
Pulmonary vein/

Pulmonary capillary wedge pressure

2–15
Left ventricular pressure systolic 100–140
diastolic 3-12

${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}=({\text{CO}}\cdot {\text{SVR}})+{\text{CVP}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}={\text{CO}}\cdot {\text{SVR}}}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!{\text{MAP}}\approxeq P_{\text{dias}}+{\frac {1}{3}}(P_{\text{sys}}-P_{\text{dias}})}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
${\displaystyle \!P_{\text{pulse}}=P_{\text{sys}}-P_{\text{dias}}.}$
• Central venous pressure, which is a good approximation of right atrial pressure, which is a major determinant of right ventricular end diastolic volume. (However, there can be exceptions in some cases.)
• The jugular venous pressure (JVP) is the indirectly observed pressure over the venous system. It can be useful in the differentiation of different forms of heart and lung disease.
• The portal venous pressure is the blood pressure in the portal vein. It is normally 5–10 mmHg
• Blood volume: the greater the blood volume, the higher the cardiac output. There is some relationship between dietary salt intake and increased blood volume, potentially resulting in higher arterial pressure, though this varies with the individual and is highly dependent on autonomic nervous system response and the renin–angiotensin system.
• Cardiac output: the pumping action of the heart is ultimately responsible for blood pressure. Increases or decreases in cardiac output can result in increases or decreases respectively in blood pressure.
• Systemic vascular resistance: the higher the resistance to blood flow, the higher the arterial pressure upstream needs to be to maintain flow. In simple terms, resistance is related to vessel radius by the Hagen-Poiseuille's equation (resistance∝1/radius4, so the smaller the radius, the very much higher the resistance). Other physical factors that affect resistance include: vessel length (the longer the vessel, the higher the resistance), blood viscosity (the higher the viscosity, the higher the resistance) and the presence of an arterial stenosis (a narrow stenosis increases resistance to flow, however this increase in resistance rarely if ever increases systemic blood pressure, it decreases downstream flow). Substances called vasoconstrictors can reduce the calibre of blood vessels, thereby increasing blood pressure. Vasodilators (such as nitroglycerin) increase the calibre of blood vessels, thereby decreasing arterial pressure.
• Systolic 65–95 mmHg
• Diastolic 30–60 mmHg
Wikipedia


text:
# phenylacetylene ir spectrum

Anal. Down to a hydrogen. Predict the key IR absorption bands whose presence would allow each compound in pairs (a), (c), (d), (e), (g), and (i) from Problem 2.46 to be distinguished from each other. However, NIST makes no warranties to that effect, and NIST IR spectrum shows absorption from 4000 to 400 cm-1. Chapter: Problem: FS show all steps. 12.5 - Which has higher energy, infrared radiation with... Ch. Find the frequency range in the first column on the left side of the chart and corresponding values in adjacent columns. What is an absorption spectrum? Chromatogr., 279, 1983, 157-165. umn class: Standard polar; Column length: 2 m; Column type: Packed; Start T: 100 C; CAS no: 536743; Active phase: Carbowax 20M; Data type: Kovats RI; Authors: Rohrschneider, L., Eine methode zur charakterisierung von gaschromatographischen trennflussigkeiten, J. ; Bur'yan, P.; Matsak, I., Retention indices of aromatic hydrocarbons on a squalane capillary column, Zh. Molbase Encyclopedia provides Phenylacetylene (536-74-3) basic information, physical and chemical properties, safety information, toxicity, customs data, synthetic routes, maps, MSDS, generation methods and uses, and its upstream and downstream products, find Phenylacetylene … Res. 12.8 - The IR spectrum of phenylacetylene is shown in... Ch. Anal. Structure, properties, spectra, suppliers and links for: Phenylacetylene, 536-74-3, 126716-66-3. Res. Click 'Join' if it's correct. I'm so I've drawn fennel a settling, uh, at at the top of the screen here. with the development of data collections included in The infrared spectrum of phenylacetylene in the acetylenic C-H stretching region shows Fermi resonance bands, which act as a sensitive tool to probe the intermolecular structures. Thus, when trifluoromethane sulfonic acid was added in a piecemeal fashion in proportion to the amount of base used, the signal corresponding to the terminal C—H stretch for phenylacetylene was observed to resurface (Fig. Show the structures of the likely fragments you would expect in the mass spectra of the following molecules: Propose structures for compounds that fit the following mass-spectral data:(a) A hydrocarbon with $\mathrm{M}^{+}=132 \quad$ (b) A hydrocarbon with $\mathrm{M}^{+}=166$(c) A hydrocarbon with $\mathrm{M}^{+}=84$. Enter multiple addresses on separate lines or separate them with commas. NACRES NA.22 12.SE - Write molecular formulas for compounds that show... Ch. One is the spectrum of cyclohexane, and the other is the spectrum of cyclohexene. 2. 2008 Jun 12;112(23):5121-5. doi: 10.1021/jp800968g. Chromatogr., 234, 1982, 285-302. umn class: Semi-standard non-polar; Column diameter: 0.25 mm; Column length: 50 m; Column type: Capillary; Start T: 96 C; CAS no: 536743; Active phase: Squalane; Data type: Kovats RI; Authors: Nabivach, V.M. Um, And then see if we see everything that we should be looking for in the spectrum itself. Data Program, but require an annual fee to access. USA.gov.  |  l> Compound Mass MoIes Magnesium phospha... 9.74 Without looking up any numerical data or doing calculations, predict whether the following enthalpy change... Greenhouse Gas Emissions 2011 Jan 17;12(1):26-46. doi: 10.1002/cphc.201000630. 12.SE - Propose structures for compounds that fit the... Ch. (Rus), 38(11), 1983, 2023-2026. umn class: Semi-standard non-polar; Column length: 100 m; Column type: Capillary; Start T: 106 C; CAS no: 536743; Active phase: Squalane; Carrier gas: He; Data type: Kovats RI; Authors: Kugucheva, E.E. Phenylacetaldehyde is an aldehyde that consists of acetaldehyde bearing a methyl substituent; the parent member of the phenylacetaldehyde class of compounds. Clipboard, Search History, and several other advanced features are temporarily unavailable. Comm., 5, 1982, 325-328. umn class: Semi-standard non-polar; Column length: 5 m; Column type: Packed; Start T: 100 C; CAS no: 536743; Active phase: Apiezon L; Data type: Kovats RI; Authors: Rohrschneider, L., Eine methode zur charakterisierung von gaschromatographischen trennflussigkeiten, J. 12.SE - Propose structures for compounds that meet the... Ch. Anal. IR-UV double resonance spectroscopic investigation of phenylacetylene-alcohol complexes. Use this table when you already know the frequency of your material. If we fail to protect a much larger percentage of the worlds remaining old-growth forests and tropical rain for... A house is advertised as having 1 420 square feet under roof. Imagine that you are the equipment manager of a professional baseball team. been selected on the basis of sound scientific judgment. List three factors that influence the intensity of an IR absorption band. Water complexes of styrene and 4-fluorostyrene: a combined electronic, vibrational spectroscopic and ab-initio investigation. The IR spectrum of phenylacetylene is shown in FIGURE 12-28. View the Full Spectrum for FREE! Although the Zn-mediated acetylide addition reactions can be successfully conducted in a number of different solvents and even solvent-free, acetonitrile was chosen as the media for the spectroscopic investigations, because the reactions conducted in this solvent are routinely homogeneous, thus facilitating the spectroscopic studies.


text:
# Let A=begin{bmatrix}-5 & -2 1 & 2 end{bmatrix} ,B=begin{bmatrix}-3 & -5 1 & 5 end{bmatrix} If possible , compute the following . If an answer does not exist , enter DNE. AB,BA-? True or False: AB=BA?

Question
Matrices
Let $$A=\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix} ,B=\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}$$
If possible , compute the following . If an answer does not exist , enter DNE.
AB,BA-?
True or False: AB=BA?

2021-01-08
Step 1
$$A=\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix} ,B=\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}$$
$$AB=\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix}\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}$$
$$=\begin{bmatrix}15-2 & 25-10 \\-3+2 & -5+10 \end{bmatrix}$$
$$=\begin{bmatrix}13 & 15 \\-1 & 5 \end{bmatrix}$$
Step 2
$$A=\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix} ,B=\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}$$
$$BA=\begin{bmatrix}-3 & -5 \\1 & 5 \end{bmatrix}\times\begin{bmatrix}-5 & -2 \\1 & 2 \end{bmatrix}$$
$$=\begin{bmatrix}15-5 & 6-10 \\-5+5 & -10+10 \end{bmatrix}$$
$$=\begin{bmatrix}10 & -4 \\0 & 0 \end{bmatrix}$$
Step 3
For every pair of square matrices A and B of the same size, $$AB \neq BA$$,because matrix multiplication is not commutative.
Given statement in the question is False.

### Relevant Questions

If $$A=\begin{bmatrix}-2 & 1&-4 \\-2 & 4&-1 \\ 1 &-1 &-4 \end{bmatrix} \text{ and } B=\begin{bmatrix}-2 & 4&2 \\-4 & -1&1 \\ 4 &1 &1 \end{bmatrix}$$
then AB=?
BA=?
True or false : AB=BA for any two square matrices A and B of the same size.
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
$$A=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix} , B=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}$$
Find if possible the matrices:
a) AB b) BA.
$$A=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix} , B=\begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$
Compute the indicated matrices, if possible .
A^2B
let $$A=\begin{bmatrix}1 & 2 \\3 & 5 \end{bmatrix} \text{ and } B=\begin{bmatrix}2 & 0 & -1 \\3 & -3 & 4 \end{bmatrix}$$
compute the indicated matrices (if possible). D+BC
Let $$A=\begin{bmatrix}3 & 0 \\ -1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 1 \\ 0 & 2 &3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 &6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\ -2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} , F=\begin{bmatrix}-1 \\ 2 \end{bmatrix}$$
compute the indicated matrices (if possible). B - C
Let
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\3 & 4\\5&6 \end{bmatrix}, D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix},E=\begin{bmatrix}4 & 2 \end{bmatrix},F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$
Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if
$$A=\begin{bmatrix}2&1&1 \\-1&-1&4 \end{bmatrix} , B=\begin{bmatrix}0 & 2 \\-4 & 1\\2&-3 \end{bmatrix} , C=\begin{bmatrix}6 & -1 \\3 & 0\\-2&5 \end{bmatrix} , D=\begin{bmatrix}2 & -3&4 \\-3& 1&-2 \end{bmatrix}$$
If the operation is not possible , write NOT POSSIBLE and be able to explain why
a)A+B
b)B+C
c)2A
$$A=\begin{bmatrix} -1 \\ -2 \\ -3 \end{bmatrix} , B=\begin{bmatrix}1 & 2 & 3 \end{bmatrix}$$
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. $$A=\begin{bmatrix}1 & 2 &3&4\end{bmatrix} , B=\begin{bmatrix}1 \\ 2 \\ 3 \\ 4 \end{bmatrix}$$


text:
# Interpretation of plotted component smooth functions of generalized additive model - transformed variables

I have a plot of a GAM which models deforestation severity.

The explanatory variables are transformed, with log10, inverse, and square root. Is it meaningful to interpret a gradient like this: 'Deforestation severity increases as log10(Distance to forest edge) increases' or 'Deforestation severity increases as distance to forest edge increases' for plot e (note, the lower the value of the y axis the greater the deforestation severity). If not, how could I plot the component smooth functions untransformed?

-
Do you mean plot e, not plot c, when you refer to "distance to forest edge increases"? –  Peter Ellis Sep 2 '12 at 20:13
Your question about "how could I plot the component smooth functions untransformed" is a question for your particular software. It looks a bit like R but could you confirm what you are using. There's no conceptual difficulty - you just reverse the transformation for the purpose of the plot. Arguably this is not a statistical question, but because it is related to interpretation however I think it is still on-topic for CV. –  Peter Ellis Sep 2 '12 at 20:18
Yes, I did mean e, thanks. Yes, this modelling is done using R. The difficulty of reversing the transformations is that these plots are produced using the plot.gam function in the mgcv package. It uses the variables from the model to plot the smooth components. If I were to model the untransformed data and then plot that, would the smoothes be comparable to the transformed data? –  gisol Sep 2 '12 at 21:25
At the moment, I have described things like this: "This trend is reflected in Figure 4.5e, where the log10 of distance to forest edge shows an initially flat relationship with deforestation severity, until it drops sharply, suggesting core forest away from the fringes of the forest patch is susceptible to severe deforestation." So I acknowledge the transformation, and mentally untransform the data to interpret the trends. –  gisol Sep 2 '12 at 21:26
Hi, sorry I don't have time to do a proper answer but no, if you modelled the untransformed data and then plotted that it would not give you the same results. You need to somehow extract the numeric results from plot.gam and then reverse transform them. –  Peter Ellis Sep 2 '12 at 22:12
show 1 more comment


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## Strict WQOs and Strict WPOs

The Wikipedia article on WQOs does not mention a strict version. I came across a particular relation, which I could only describe as a strict WQO, but I am wondering if my reasoning is correct and if the notion of a “strict WQO” even makes sense (I think it does).

Consider the set $$X \times \mathbb{N}$$ where $$X = \{1,\ldots,k\}$$ for some integer $$k$$ and $$\mathbb{N}$$ denotes the set of natural numbers. We define the relation $$\prec$$ as: $$(x_1,n_1) \prec (x_2,n_2) \quad \text{iff} \quad (x_1 \leq x_2) \wedge (n_1 < n_2)$$

Strict Quasi Order: Clearly $$\prec$$ is irreflexive and transitive, and therefore a strict quasi order.

No Infinite Antichains: It’s also easy to observe that there are no infinite antichains. Due to the Pigeonhole principle, any sequence $$(x_1,n_1), (x_2,n_2), \ldots$$ of length $$\geq k$$ must have at least one pair $$\langle (x_i,n_i),(x_j,n_j)\rangle$$ such that $$x_i = x_j$$. Then, since either $$n_i < n_j$$ or $$n_j < n_i$$ must hold, we have at least one pair in the sequence on which $$\prec$$ holds.

Well-Foundedness: Finally, we show that there are no infinite descending chains. For any element $$(i,j)$$, there are only $$|\{1,\ldots,i\} \times \{1,\ldots,(j-1)\}| = i(j-1)$$ elements that can precede $$(i,j)$$.

Is this reasoning correct? Then is $$\prec$$ a strict WQO on $$X \times \mathbb{N}$$?

More questions: Since antisymmetry is implied by irreflexivity and transitivity, is any strict quasi order also a strict partial order? And so is any strict WQO also a strict WPO?

Thanks.

## How strict is Swiss/Edelweiss about pet carrier dimensions?

The stated dimensions are 55x40x23cm (21x15x9in), but the height of most large carriers on Amazon is well over 9 inches. My dog is 12 lbs and 10.6 in height, so none of the smaller carriers that meet the height requirement are large enough. Thanks for any info!

## Does this overly strict reading of Two-Weapon Fighting Work?

Two-Weapon fighting states:

“When you take the Attack action and Attack with a light melee weapon that you’re holding in one hand, you can use a Bonus Action to Attack with a different light melee weapon that you’re holding in the other hand.” Emphasis mine

There have already been some questions regarding when you have to actually be wielding the light weapons required for Two-Weapon Fighting. Here and Here.

And to satisfies any of those, say the following scenario occurs:

It is Alice’s turn, and she starts her turn wielding two light melee weapons, say, two daggers.

She makes an opportunity attack against a creature using one of these weapons (this is possible, for example, if a creature had used the ready action to move).

She drops one of her daggers (a free action), then takes the attack action and as part of the attack she draws a non-light weapon, say, a quarterstaff, and finally she attacks using this quarterstaff.

Is there any reason, RAW, that she would not be able to use her bonus action to attack with the other dagger which she is still holding because she has technically fulfilled both requirements of Two-Weapon Fighting: “taking the attack action” and “attacking with a light melee weapon…”?

## Prove that the upper bound in the Noiseless-coding theorem is strict

Given a probability distribution $$p$$ across an alphabet, we define redundancy as:

Expected Length of codewords – entropy of p = $$\ E(S) – h(p)$$

Prove that for each $$\epsilon$$ with $$0 \le \epsilon \lt 1$$ there exists a $$p$$ such that the optimal encoding has redundancy $$\epsilon$$.

Attempts

I have tried constructing a probability distribution like $$p_o = \epsilon, p_1 = 1 – \epsilon$$ based on a previous answer, but I can’t get it to work.

Any help would be much appreciated.

## Strict Convexity and Uniqueness of Dual norm

So, I have trouble proving the following, I’d be grateful if somebody helps me with this.

Let $$z$$ be a given point in $$\mathbb{R}^m$$. Then, $$x\in \mathbb{R}^m$$ is a dual vector of $$z$$ with respect to $$\|.\|$$ if it satisfies $$\|x\|=1$$ and $$z^Tx=\|z\|’$$.
A norm $$\|.\|$$ is said to be strictly convex if the unit sphere $$\{x:\|x\|=1\}$$ contains no line segment.

Now, how does one prove that

The norm $$\|.\|$$ is strictly convex if and only if each $$z\in \mathbb{R}^m$$ has a unique dual vector.

## Does this strict reading allow both Extra attack and Thirsthing blade to be used together?

The warlock invocation Thirsting Blade cannot be normally used with the class feature Extra attack since both feature explicitly say attack twice instead of once. But it seems to me that you could use both features when using two weapon fighting.

Assuming two light weapons, one of which is your pact weapon. You take the Attack action on your turn to attack twice with your non-pact weapon using you Extra Attack class feature.

Then, given the two fighting rules, you use your bonus action to attack once using your pact weapon this time.

Two weapon fighting rules (PHB p.195):

When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand.

But since your have the Thirsting Blade invocation, and you used the Attack action, you get to attack twice with your pact weapon.

Vou can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.

Does this combo work or is there any interaction I’m not aware of ?

## Youtube Strict vs. Moderate Access Considerations

I am considering implementing YouTube restrictions via G Suite. The wording on what exactly Moderate vs. Restrictive access does is very vague. I was wondering what expectations users should have for their YouTube experience at either setting. We currently have a firewall-based solution to prevent pornography from showing up but that is all at this time.

## Strict Positivity of Indexed Datatype in Agda

Agda is ruling out definitions like

data Bad : Set where  bad : (Bad → Bad) → Bad

Because “Non strictly-positive declarations are rejected because one can write a non-terminating function using them.” (as one may read in Agda wiki). I know also that disabling strict positivity checking allows constructing inhabitant of empty type.

But Agda also complains about definition like this:

  data Bad? : ℕ → Set where     badZ : Bad? zero     badS : ∀ {n} → (Bad? n → Bad? n) → Bad? (suc n)

telling me that:

Bad? is not strictly positive, because it occurs to the left of an arrow in the type of the constructor badS in the definition of Bad?.

What i know is that i can create valid definition without inductive datatypes:

  Bad?′ : ℕ → Set   Bad?′ zero = Unit   Bad?′ (suc n) = (Bad?′ n) → (Bad?′ n)     badZ′ : Bad?′ zero   badZ′ = tt    badS′ : ∀ {n} → (Bad?′ n → Bad?′ n) → Bad?′ (suc n)   badS′ x = x

My question is:

Can “Bad?” datatype lead to similar inconsistencies, and this is the reason why it is rejected by Agda?

Or is it the case that positivity checking in Agda is too “cautious”, and can’t figure out that indexing is making it strict positive?

## How strict should I be in rejecting unexpected query parameters?

TL;DR Is it a “best practice” to return an HTTP 400 Bad Request response if extra parameters are sent with a request?

I’m putting together a web app and doings some testing with OWASP ZAP. I’m pretty happy with the results – the errors I get seem to be all low confidence and when I inspect the errors in detail, I’m finding that the ZAP tool really didn’t change anything with the request. But that leads me to a “higher level” question, which is best explained with an example:

OWASP ZAP allegedly found an SQL injection with the following URL:

http://example.com/api/client/1?query=%27+AND+%271%27%35%271%27+--+

http://example.com/api/client/1?query=query' AND '1'='1' --

Looks like a pretty standard SQL injection attack. Now, this endpoint is intended to return a client object in JSON form, and that’s what this request does through OWASP ZAP. The server returned exactly what was expected, the client with ID=1. I’m doing everything that the OWASP ZAP docs recommend with respect to SQL injections, so what more should I do?

It occurs to me that I just don’t know what OWASP ZAP expects to receive in response to this kind of attack – an error reponse, perhaps? The docs are helpful, in a “this is how to interface with the database” kind of way, but it’s not clear to me if I need to respond with an error.

Should I return a 400 Bad Request error if inappropriate query parameters are provided?

## Does HTTP:// to HTTPS:// redirection means strict HTTPS from server

when I try to connect to some websites using http:// (notice the absence of s) , my client end up with https://.

I use python requests for this purpose, which simulate a client behavior. It performs the redirection and show me the final URL after redirection, if any.

Example: when I input http://facebook.com the get requets end up at https://facebook.com.

Does this mean the website DOES NOT accept http:// requests?


text:
# Tech Notes

Inno Setup allows you to create a Windows installer for your software application from a “Inno Setup Script”. I recommend that you use the InnoIDE to help you create your script. Take a look at the comprehensive examples that Inno Setup come with as a starting point for your own installer script.

## Variable Passing

You may have a parameter in your Inno Setup script that can have a number of values.

Here’s an example of a variable declaration in the {Setup} section of an Inno Setup script:

```[Setup]
.
.
.
VersionInfoProductName={#AppName}
VersionInfoProductVersion={#AppVersion}
WizardImageBackColor={#BackCol}
.
.
.```

Here we are leaving the assignment of VersionInfoProductName, VersionInfoProductVersion and WizardImageBackColor to be set to parameters specified at the command line.

You may also have a parameter that is passed in, but is not set to an Inno Setup variable. Instead it is used directly in the script as follows:

```[Files]
Source: "packrat-server-{#BuildType}\*"; DestDir: "{app}\LatLong Systems"; Flags: ignoreversion recursesubdirs createallsubdirs```

Here the parameter BuildType is being used to tell the script where to find the baseline of files that make up the build are found. You may have build types of “demo” and “full”, so would have the following directories at the same level as your Inno Setup script file:

packrat-server-demo

packrat-server-full

Each of these directories contains the specific files for the type of build being performed.

## Build Batch File

In a batch file, you can specify these parameter values at the Inno Setup compiler command line as follows:

```set TYPE=%1

if "%TYPE%"=="demo" goto DEMO
if "%TYPE%"=="full" goto FULL

:DEMO
echo.
echo ###########################################################
echo Building DEMO PackRat Server Installer
echo.
set NAME=PackRat Server Demo
set COLOUR_BK=clSilver
goto END

:FULL
echo.
echo ###########################################################
echo Building FULL PackRat Server Installer
echo.

set NAME=PackRat Server
set COLOUR_BK=\$0000D7FF
goto END

:END
C:\"Program Files (x86)\Inno Setup 5"\iscc "/dBuildType=%TYPE%" "/dBackCol=%COLOUR_BK%" "/dAppName=%NAME%" "/dAppVersion=1.0" packratserver_innosetup.iss
```

When running your batch file to build your installer, you would do the following:

> build_installer.bat demo

to build the Demonstration version, or:

> build_installer.bat full

to build the Full version.

## Summary

It is easy to parameterise your Windows installer builds using Inno Setup’s command line functionality. Good luck with your own installer scripts.