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Videos uploaded by user “Jonathan Doolin”
Suppose that IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of people should have an IQ score between 85 and 115?
Views: 58498 Jonathan Doolin
Created 2013-01-08 Uploaded 2014-11-25
Views: 3820 Jonathan Doolin
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Views: 3274 Jonathan Doolin
See more at http://www.spoonfedrelativity.com Consideration of the appearance of an object moving away from you and moving toward you taking into consideration the delay caused by the finite speed of light. You can experiment with some of these ideas here: http://www.wiu.edu/users/jdd109/stuff/relativity/LT.html For further discussion, see http://groups.google.com/group/sci.physics.relativity/browse_thread/thread/793dedd752de36e3?hl=en#
Views: 1480 Jonathan Doolin
This is a much simpler description for the shape of the universe than what's called the "Standard Model." Instead of assuming that the galaxies only "seem" to be moving away from us, it really just assumes that everything actually IS moving away from us. This model uses the Special theory of Relativity, Lorentz Transformations, and the idea of a "secondary bang" to explain some of the large-scale features of the universe. This video uses a software simulation "Animated Spacetime Diagram" from http://jdoolin.spoonfedrelativity.com/LT.htm
Views: 653 Jonathan Doolin
Part 1 of trying to follow the 1-minute physics derivation of E = m c^2. At this point, I'm stuck, because I can't figure out where the first premise of the calculation comes from. If this factor (1+v^2/(2 c^2)) really comes from the relativistic Doppler Shift equation then this is a great proof. If a correction in this equation could lead to E^2=(mc^2)^2 +(pc)^2 then this is an even better proof! This first video shows that the given equation is a second-order Maclaurin Series expansion for 1/sqrt(1-(v/c))^2 This is sometimes known as gamma, or the Time-Dilation factor. But unfortunately, this is not the Doppler-shift equation. The Blueshift Doppler equation factor would be sqrt[(1+beta)(1-beta)] The Redshift Doppler equation factor is sqrt[(1-beta)(1+beta)] The Transverse Doppler equation factor is sqrt(1-beta^2)... which is the reciprocal of what I am expanding in this video. If you want to watch more of me being confused: http://www.youtube.com/watch?v=Sw3UKHHsHjk&list=PLC-qVSnsyc7_y_DplTKw-AT6blkecTmK9
Views: 1875 Jonathan Doolin
Demonstrations of various phenomena in electrostatics.
Views: 4737 Jonathan Doolin
Views: 352 Jonathan Doolin
2014 03 20 In this video, I am trying to develop my understanding of temperature, with particular emphasis on the nature of the ionosphere/thermosphere. This relates to overall questions of global warming that I've had for some time. Update 2015-11-09: In the comments below, you'll see further references to Emissivity (How fast a body can be expected to lose heat by electromagnetic emissions) Conductivity (How good a body is at losing heat by conduction into other materials) Heat Capacity (How much heat a body stores per unit of temperature)
Views: 2072 Jonathan Doolin
From http://bit.ly/1Isek8D
Views: 1025 Jonathan Doolin
https://www.youtube.com/watch?v=bEMSDhLpdKw&list=PLC-qVSnsyc784DHAblViT2q1XX9kulZ-x&index=36 As a teacher of physics and astronomy, I don't have the luxury of pointing at consensus, or correlation. These things might be effective in politics and debate, but if I want to be consistent with the principles of the scientific method, I can only really justify a "belief" in Carbon Dioxide induced global warming if I see evidence of causality. I don't feel that the scientific method is served by showing correlation studies, because one of the first things a good statistics teacher tells you is that correlation is not causality. I also don't think that the scientific method is served by consensus arguments, because history is strewn with cases where 100% of the scientific community has been wrong or confused. In the debate on global warming, the only argument I would feel comfortable presenting to my students is one that establishes CAUSALITY. The other types of arguments are distracting and time-consuming, and leave me unconvinced, regardless of how much care goes into them. The CO2 causality argument can involve (1) Knowing precisely how much heat Carbon Dioxide can trap, and by how much that increased based on the concentration of CO2 in the atmosphere. (2) Comparison of heat absorbed by CO2 to other heat inputs. (3) Knowing how heat transfers between stratosphere, troposphere, hydrosphere. There are probably a lot of other questions to ask, but these are the leading questions which I would like to be able to present to my students, and not feel like I'm fear-mongering or standing on a bully-pulpit. This video is asking "Is the Carbon Dioxide Spectrum Saturated?" It doesn't get into the numerical values of just how much extra heat is caught by an increased concentration, but I learn some of the considerations necessary in setting up the problem.
Views: 706 Jonathan Doolin
0:00 The basic concept of density. 0:30 ordinarily density is a function of position, for instance: $\lambda(x), \sigma(x,y), \rho(x,y,z)$ 1:15 On Wikipedia, volume density is rho, linear density is lambda, But they use rho_A for area density. 1:50 sigma is used for linear charge density in our textbook on page 574. 2:25 Distinguish between Mass Density and Charge Density, as well as linear, planar, or volumetric, depending on the context of the problem. 3:30 The textbook uses symbol n for volumetric charge CARRIER density. 3:50 Density is NOT an inherently countable quantity. While the mass or charge may be countable, the meaning of density changes greatly with the scale of the unit in the denominator. 4:00 Water has a density of 1000 kg/cubic meter. But only 1 gram per cm^3. 4:30 Take out a little thimble-full of water and it still has a density of 1000 kg/cubic meter even though there's no where near a kilogram, or a cubic meter. 5:00 But what does it mean to say there is a density AT a given geometric point in space? In the particle conceptualization of density, it really doesn't make sense, but in the fluid conceptualization of density, the material can be subdivided down to arbitrarily small region, so that density has a value even at a point. 5:50 Water on the scale of picometers is not perfectly homogeneous. 6:10 Sloan Digital Sky Survey. The bright parts of the universe is not perfectly homogeneous at our scale, or galactic scales, but may be homogeneous at scales of billions of light-years. 7:50 The Continuity Equation $A1 v1 = A2 v2 = \frac{\Delta V}{\Delta t}$; Equation 17.2: I = n q v_d A. 9:00 n is the volumetric charge-carrier, density, q is the charge of each carrier, v_d is the drift velocity, and A is the cross-sectional area. 9:45 The wandering electrons are called valence shell electrons. 10:15 The volumetric charge density is $\rho = n q$. 10:45 If you multply Coulombs per cubic meter times the cross-sectional area, you have the linear charge density. 11:20 Multiply the Linear charge density by the drift velocity and you get the current. 11:50 Even though it might take hours for an individual electron to complete the circuit, because of the sheer number of electrons, you can get quite a bit of current out. 12:03 (Sound issues: microphone not engaged.) The electrons bounce around like a herd of chickens, with a slow but steady bias to move opposite the electric field. 13:00 If the temperature drops below some critical level in a superconducting material, you just need to give the electron an initial nudge, and the current continues around the circuit without interference from thermal collisions.
Views: 1402 Jonathan Doolin
See the applet at http://www.spoonfedrelativity.com/demos/LT.htm
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Faraday's Lines of Electrical Force mapped with Mathematica.
Views: 711 Jonathan Doolin
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I found an interesting looking problem to do in my physics textbook, and worked on it until I was interrupted. (parts e and f aren't done) I found an interesting result which indicated a reduction in pressure! This made me look up "hydrogen implosion" on youtube to see if this sort of thing really happened! Yes, it does! I found footage of a oxy-hydrogen emplosion on youtube and incorporated that into my video. Unfortunately, only then did I discover I made a mistake in the math. Forgot to use kiloJoules instead of Joules. And this is going to be an EXplosion rather than an IMplosion. I'd still like to know what kind of set-up to use to generate an IMplosion. It looks like the guy in this video is using liquid water and hydrogen gas rather than gaseous hydrogen and gaseous oxygen.
Views: 577 Jonathan Doolin
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See more at http://www.spoonfedrelativity.com This describes the Big Bang You can experiment with some of these ideas here: http://www.wiu.edu/users/jdd109/stuff/relativity/LT.html
Views: 649 Jonathan Doolin
This Gedanken experiment comes from page 2 of replies on a question at ResearchGate: https://www.researchgate.net/post/Is_the_use_of_relativity_of_simultaneity_in_standard_cosmology_appropriate Should we assume the space is flat and our measures are off, or that our measures are correct, and our space is bent?
Views: 15 Jonathan Doolin
Constructing an NPN SR Flip Flop using parts from two snap circuit sets.
Views: 11 Jonathan Doolin
I have been checking some things. (1) Though the degree of freedom seems to come into play considerably when finding molar specific heat for a gas, it does not come into play in finding the rms velocity of the molecule. In every case, the formula is 1/2 m v^2 = 3/2 n R T. This simplifies to v = 158 sqrt(T/M) where v is in meters/sec, M is in kg per mole, and T is in Kelvin. (2) Chaisson/McMillan gives 500,000 Kelvin as the ambient temperature of the inside of the bubble. I don't know how this temperature is measured, but it does correspond to a rms atomic hydrogen speed of 122 km/s, or molecular hydrogen speed of 789 km/s. (3) The temperature of the sun's corona is given as 3 million Kelvin, corresponding to an atomic hydrogen speed of 273 km/s. Solar wind is estimated to travel around 400 km/second (4) After considerably more thought, I think the ideal gas law is best combined with the equipartition theorem in the following way: P V = n R T = 2/3 U_{trans} = 2/df U_{total} This means that rms velocity, being associated with the translational internal energy is not dependent on the degree of freedom of the molecule, but other phenomena, such as the specific heat of the material does depend on rotational and vibrational modes. (5) How do they estimate the temperatures of gasses? I don't think that these gases would produce a blackbody spectrum. They would produce an emission spectrum or absorption spectrum. But spectral classes of stars are determined in part at least by their absorption spectrum. Hot stars have ionized helium. Cool stars have molecular hydrogen. This seems like a good method for estimating the temperature of a star, but would it be a good method for estimating the temperature of interstellar gas?
Views: 54 Jonathan Doolin
The Principle of Relativity. You are not moving. Other things are. You can experiment with some of these ideas here: http://www.spoonfedrelativity.com/
Views: 578 Jonathan Doolin
Video 4: Equation 3: Recorded 2014-12-19 Playlist: https://www.youtube.com/watch?v=DKrwCzNZFLo&index=3&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl 1:20 Whereas Einstein notation at least seems to be commutative, matrix multiplication is definitely not. 1:50 Putting in little arrows to indicate the shape of the matrices. 2:50 Instead of having dummy variables, what if we actually used the relevant non-dummy variables? Here I replace x with (x,y) and y with (r,theta) 3:20 Now using the arrows with the variable-lists. 3:50 I am attempting to represent the Jacobian as an outer-product differential. But I put the matrix-multiplication for inner product. 5:20 There's nothing about the partial derivative that says it has to come before the operand. In order to have (r,\theta) down, and (x,y) across, and do it with an outer-product, it really has to be $(r,\theta)\downarrow (\partial_x, \partial_y)\rightarrow$ 6:50 Now doing the horizontal form, there's slightly less confusion because the partial derivatives appear in their natural order from an outer product. 9:00 Hmmm, I say here that I'm not a perfectionist, but really, just because I'm unable to be perfect doesn't mean I don't try to be. I think I'm being defensive. 9:20 Just showing how the transpose of a product is equal to the commutation of the product of the transposes. 10:15 Equation 3 is a more general form of Equation 2. 11:00 Equation 2 was the gradient of a scalar field. Equation 3 is presumably ANY vector field. 11:30 Some bold statements about What are Equations 1, 2, and 3. 12:05 Equation 1 is actually USING equation 2, since equation 2 is the definition of gradient , and equation 1 uses the gradient dot-producted with the differential path element to describe a differential change in a scalar field. 12:15 To be continued...
Views: 324 Jonathan Doolin
The A Priori argument--taking something as true and self-evident as done by philosophers, as opposed to faith as done by theologists.
Views: 209 Jonathan Doolin
http://www.spoonfedrelativity.com/misc/RelativityNotes-Videos-01-12.png
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20 minute Video shows how to use list-multiplication and sums to add together vectors given in polar coordinates. TI-89 users can access list and sum functions from the MATH menu, I think.
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0:00 The Euclidian metric: ds^2=dx^2 + dy^2 + dz^2. I express it as an inner product of a 1x3 and 3x1 matrix. 1:00 The spherical-to-cartesian coordinate conversions, and calculating the Jacobian. 1:30 My new notation for Jacobian, shows little arrows to indicate the direction which a matrix should be written. I show how the arrow notation builds a matrix in an explicit form. (This is an improvement on Einstein Notation) 3:00 calculating a few of the partial derivatives in my head. 3:30 Better... Use Mathematica to find the Jacobian. 4:30 I've got things plugged in, by pasting 9 times, and then going across and down, making replacements with x,y,z, r, theta, phi. 6:00 Jacobian is protectes,so I name it "Jake" 6:30 I explain how the value of (dx, dy, dz) is equal to (dr, dtheta, dphi) times the Jacobian. 8:11 Going through what dx is as you multiply (dr dtheta dphi) by the first column of the Jacobian. 9:27 When finding the transpose of a product of two matrices, you have to swap the order of the factors, when you transpose them. 10:30 Take our Jake.Transpose[Jake]. It looks enormous... But there are hints of some things that should simplify. 11:18 Simplify boom, we have a very simple looking diagonal matrix. The huge mess from the jacobian 11:50 Writing out the equality, how the metric goes between the (dr dtheta dphi) written horizontally and vertically. 12:40 After the matrices are multiplied out, we obtain the first equation in the Wheeler article linked by George Dishman on Researchgate on May 19, 2018. 14:30 Wheeler sets dr = 0 and eliminates two of the columns of the three-dimensional metric. 15:40 What was the mapping for? What if we had x,y,z and wanted to convert to r,theta,phi. Instead of giving x,y,z as functions of r,theta,phi. We want r,theta,phi as functions of x,y,z. I determine that theta and phi can be expressed as arccosines of functions of x,y,z. 18:20 We've got the Jacobian, and multiplied by its transpose, to get the metric... What would we do for the inverse metric? 19:20 Test this: The inverse metric is done up by putting the r theta phi on top, and the x,y,z on bottom. I want to check if these are inverse metrics in the next video.
Views: 288 Jonathan Doolin
Views: 113 Jonathan Doolin
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2016 10 24
Views: 25 Jonathan Doolin
Playlist: https://www.youtube.com/watch?v=kibqzNMkKpE&list=PLC-qVSnsyc784DHAblViT2q1XX9kulZ-x This video goes back and explains a part of the reason why I've been working on the "Convince Me Carbon Dioxide is a Greenhouse Gas" project -- why the standard answers to this question don't work for me. This American Life tried to convince a freshman in high school that global warming was a result of increased Carbon Dioxide emissions. I think they came away from the show with the idea that "you just can't teach some people" but I came away from the show with the realization of just how incredibly bad the standard explanations for global warming really are! Explanations of how the ground absorbs visible light and re-emits in the infrared are widespread on the internet. But details on how to calculate exactly how much of that energy gets captured, and how much it will raise the temperature is not widespread. In the last 20 minutes of the video, I am describing how to apply some of the "basic" mathematical models to the problem... In particular, I want to quantify how much heat comes from the sun, how much gets reflected back into space, and how much of it is absorbed by the atmospheric greenhouse effect. I introduce a minimum set of quantitative concepts principles that are needed to approach the problem: Stefan Boltzmann's Law Planck Blackbody Distribution Emission/Absorption Spectra Bond Albedo To really finish the problem we would need some detailed information on the emission/absorption spectrum of Carbon Dioxide, water vapor, and methane gas. This is actually a fairly complicated question: For instance "Given a surface pressure, mass, and radius of a planet, and a concentration of a particular gas, find what luminosity percentage of each frequency of outgoing light it will absorb."
Views: 143 Jonathan Doolin
Views: 2145 Jonathan Doolin
The first calculation takes a little while. You might like to skip forward to 3:30 to jump to the space-time diagram. At 4:30 there is a small discussion of luminosity-distance. At 5:30 there's discussion of what luminosity distances have been observed... Some sources claim only distances of 14 billion light-years have been observed, while other sources claim distances of as much as 40 billion light years. This video assumes that the 40 billion-light-year claims are correct. At 6:10 I begin talking about my alternative hypothesis to the standard model, which is a kinematic model with innner-sphere and outer-sphere Hubble's Constants, based on two "bang" events. At 7:20 I start talking about a partial explanation for the dipole anistropy in the CMBR. At 9:00 I re-do the calculation of T=1/H0, from the beginning using simpler conversion factors. Here is a large-print copy of some of the equations. It is messy and there may be typos, but it might be easier to read. http://www.spoonfedrelativity.com/misc/Large-Print-Hubble-Constant-Text.pdf
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Forum thread at http://www.spacetimeandtheuniverse.com/math/5451-positive-zero-equal-negative-zero.html 1:10 Could they be considered to be different parts of the same real number? 1:30 Summation Notation; lower part and upper part. 2:05 Any algorithm that can produce an infinite string of zeros... Infinite zeros exists as a concept, but infinite 9's does not???? 3:20 Choice of representations: Start with 0 or start with 1 3:45 The arithmetical argument 4:20 1/9 does not have a terminating decimal expression. 4:50 In base 3, 1/9 has both terminating and nonterminating expression. (Dual representation.) 5:50 Representing the right side and the left side of a real number. 6:10 limit as x approaches from the left, and from the right. 6:40 Common convention: Just disallow the question... If there is an infinite discontinuity in the graph, you just don't get to ask what the function is equal to AT the point of discontinuity. 7:30 Every number x has a left hand side x+(-0) and a right hand side: x+(+0); It's the same real number, but there are two sides to every number. 9:00 Graph of 1/x 9:30 Definition of +0 and -0, using summation notation given any base n &gt 1 10:50 Roy Tomes: Agrees, since 1/0+ not equal 1/0-, the two numbers must be different. 11:10 Conventional mathematics "Don't think of it that way. We'll remove 0 from the domain of 1/x" 12:25 You can approach a door from the left or right. 12:40 David Eaton: IEEE standards 13:00 Coelacanth, A field; Once you add infinity to a set, it is not a field. 13:10 The unit step function's ambiguous value at t=0. 14:00 (Extended Real Number Line) Property treats +0 and -0 as the same, while +infinity and -infinity are different. (No other reason, I don't think, than because they wanted to define it that way.) 14:50 A lousy argument on wikipedia... Since there ARE functions whose value is ambiguous at x=0, (output a range of values) we decide we will treat ALL functions as though the output is ambiguous. 15:20 Typo in wikipedia. The sinc function does not have an ambiguous value at 0. 15:50 sin(1/x) is much more interesting, and really becomes undefined at x=0. 16:25 u(x) and 1/x provide unambiguous values around 0 17:10 Atomic-S question of plotting complex-valued functions arounc zero, and graph of real part and imaginary part of 1/(a+bi)
Views: 2209 Jonathan Doolin
Paul mentioned the Lambda CDM model, and I wanted to do my best to get an accurate representation, so I'm reading a big caption from Davis & Lineweaver 0:00 Paul Gradenwitz Response from June 2, 2018 0:20 Is Paul arguing for or against the Lambda CDM model. 0:40 Is "Expanding Confusion" a good source for describing Lambda CDM? It should be. 1:14 The caption and the diagram. Lets read the caption and point to the diagram. 1:40 Starting to read the caption. 2:05 Dotted lines are the worldlines of comoving objects. 2:20 What does comoving mean? Circular? 2:55 Definition of comoving means following the Hubble flow? The path of most gallaxies. 3:40 I don't think proper distance is observed or Euclidean distance. It's some other concept I don't know. 4:10 Our worldline is vertical in all diagrams. The redshift of the comoving worldlines appear as labels of all but two of the dotted lines. (I guessed 5:15 The normalized scale factor is drawn as an alternate vertical axis. 5:50 Conformal time tau is at 46 billion years. proper time at 13.7 billion years. 6:05 How does the 46 billion years come into play in the modified Milne model? We have an outer big bang at 46 billion years and several inner bangs at 13.7 billion years ago. 7:30 Ridiculously dense... Inconceivable. Even at 13.7 billion years ago, the density was denser than a neutron star. But no gravitational collapse because symmetry. No central direction to pull. 8:30 The past light-cone appears straight in comoving distance vs. conformal time. 10:20 In Milne's model there is not going to be a distinction between time and conformal time. And we don't bother with comoving distance or proper distance, but just use Euclidean distance. 11:05 Everything beyond hubble sphere is expanding faster than the speed of light. 11:50 In the Milne model, there are two hubble spheres, one that started 13.7Gy ago, (r=v*13.7gy) and an earlier one that started 45 Gyr ago. (r=v*45Gy). There is more noise in this Hubble sphere, because we're seeing a lot of other explosions. 13:30 Comparing the velocity of light to the recession velocity of the Hubble sphere. 14:15 Before 5 billion years, the photons coming TOWARD us were moving away from us, because the space at that time was expanding faster than the photon was moving. (I would call this stretching space, but they get very offended if you call it that.) 16:00 Region of superluminal recession, (past hubble sphere, but within event horizon) vs region of subluminal recession, (closer than Hubble sphere). 17:30 Our past light-cone in comoving coordinates appears to approach t=0 asymptotically, but actually it ends at 46 billion years ago. 18:40 The 0 proper distance radius is actually equal to 46 billion light-years comoving distance. 19:30 I show the particle horizon here, but I don't figure out quite what it represents.
Views: 37 Jonathan Doolin
This is part of a playlist: http://www.youtube.com/watch?v=2CIYL_6DLVY&list=PLC-qVSnsyc784DHAblViT2q1XX9kulZ-x I never really finish the original question in this video, regarding Venus vs. Earth. 02:00 What is the height of the atmosphere? About 10 km, at half atmospheric pressure. 04:00 Elastic Potential energy of a gas in a gravitational field 04:40 vs Thermal Energy; the ideal gas Law 05:10 Total Kinetic Energy is linear plus rotational plus vibrational modes of energy. 05:40 Moment of Inertia of a particle 06:05 Are the two modes of 06:45 Video of a book rotating around two rotational degrees of freedom 07:00 Video of a contained fluid quickly changing rotational state to line up along largest moment of inertia. 08:30 Does Carbon Dioxide have some kind of rotational property that makes it more ... I don't know what? 09:25 I Would like this settled: Is CO2's status as a greenhouse gas based on its infrared absorption spectrum, or is it based on its specific heat and degrees of freedom? Or are we in a part of the electromagnetic spectrum where the absorption spectrum is specifically tied to the CO2's specific heat? 11:20 Will nothing convince me that CO2 is a greenhouse gas? Actually, yeah, there IS something that would convince me. Unfortunately, I don't exactly know what that thing is. But I know it has something to do with establishing causality, not showing statistical correlation. This video cuts off at the end because it was time for bed. :) Please go to the playlist and watch more of my musings. And let me know anything that you think might help!
Views: 199 Jonathan Doolin
https://www.physicsforums.com/threads/terrell-revisited-the-invisibility-of-the-lorentz-contraction.520875/page-6#post-5098812 http://www.spacetimetravel.org/bewegung/bewegung3.html http://www.spacetimetravel.org/tompkins/tompkins.html http://commons.wikimedia.org/wiki/File:St_Bartholomae_panoramic_view.jpg
Views: 1356 Jonathan Doolin
Playlist: https://www.youtube.com/watch?v=OtgTfKO20vU&index=8&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl Recorded 2014-12-20 (Postscript) I am suspecting that the difference is the contravariant form should be used when converting differential path elements, and the covariant form should be used if converting differential changes in vector fields. I have not confirmed this yet, but perhaps another video will be forthcoming. 0:00 Equation 4: Contravariant. 1:00 Recording of a recording... I listen to DrPhysicsA's description of the difference between the contravariant and covariant forms of the equation. 2:00 Equation 5: Covariant 2:10 The differences: Contravariant have their indices upstaris. Covarient have ther indices downstairs. Contravariant have dy/dx terms. Covariant have dx/dy terms. Covariant are of interest to us. Contravariant, I guess, are boring to us. 2:40 The reason I made a video of a video was that I'm trying to get across exactly how completely confused I am. 3:20 We've made no restrictions on what x and y coordinates are. 3:41. I worked out an example in a previous video. But you can express the Jacobian matrix in terms of (x,y) or (r,theta) regardless of whether the final expression is intended to have (r,theta) on the bottom or (x,y) on the bottom. 5:45 If I am using this covariant form, and my input formula is in Cartesian form, wouldn't I go ahead and use the form of the jacobians that also use Cartesian form, and get an output in Cartesian form? 6:40 When I do a derivative with respect to (r,theta) it is natural for the result to be in terms of (r,theta) and when I do a derivative with respect to (x,y) it is natural for the result to be in terms of (x,y). 8:40 In short, I have no idea how to distinguish what is meant, and I'm speculating wildly throughtout this video. 12:25 While I could sit here and guess all day, I can find no meaningful difference between contravariant and covariant transformations.
Views: 805 Jonathan Doolin
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0:20 Diagram of the Ecliptic from Pearson's "Astronomy, A Beginner's Guide" 1:10 Meaning to find the location of the Summer Solstice, I accidentally look up 23.5 degrees above the Vernal Equinox (in Pegasus) 1:40 Correction to find (6h, 23.5°) Alt-248 2:25 Locating Taurus and the Summer Solstice between Gemini and Taurus above Orion's hand. 4:29 Errata. I say summer solstice point is (6h, 90°) but it should be (6h, 23.5°) 5:30 Identifying th (6h, 0°) point, and the equatorial plane 6:20 Equator and ecliptic appear parallel near orion, taurus, gemini, but intersect at Vernal Equinox just south of pisces 7:50 Errata: Drawing the lines toward the wrong Pisces 8:30 Alignment of stars in Cetus with Vernal Equinox. 9:10 Curvature of the ecliptic and equator on a spherical star-map. 11:10 Virgo (12h, 0°) Autumn Equinox 11:30 Sagittarius Winter Solstice 11:45 Galactic Center lies near "Teapot," Sagittarius, Winter solstice 13:10 Feature comparison of Teapot and Sagittarius 14:20 Location of M8, "The Lagoon Nebula" is almost exactly the same as the Winter Solstice (18h, -23.5°) 15:15 (18h, 0°) point on Equatorial plane, in Ophiuchus. 16:00 Global Star Map is drawn curiously inside out and backwards so that constellations look right from the outside instead of looking right from the inside. 19:30 Orthogonal vs Unit Spherical Coordinate System 20:20 Identifying directions toward Vernal Equinox, Summer Solstice, Autumn Equinox, Winter Soltice, Ecliptic North Pole in Equatorial Spherical Coordinates. 21:35 Converting Unit Spherical coordinates to Unit Orthogonal coordinates 22:45 Right-handed vs Left-Handed system. 24:20 Unit Spherical Equatorial Coordinates of Ecliptic North Pole 25:40 Calculating the orthogonal coordinates given the angles. 27:00 Equatorial Coordinates: (100-Pisces, 010-Orion, 001-Polaris) 27:30 Spherical to Orthogonal 28:40 Orthogonal to Spherical Transformation, ArcTangent 30:00 Converting Ecliptic to Equatorial Coordinates: Coordinates of Vernal Equinox, Summer Solstice, and Ecliptic North 33:30 Creating the EclipticToEquatorial Transformation Matrix 33:45 EquatorialToEcliptic (Inverse Transformation) 35:10 Convertin Galactic to Equatorial Coordinates; Galactic North Pole, Galactic Center 36:20 Finding the (010) 'galactic east' vector; Right-handed Coordinates; Cross-Product 37:45 GalacticToEquatorial and EquatorialToGalactic Transformation Matrix. 38:20 Verifying our Matrix using (3h, 30°) 38:50 The matrices are actually correct, however, when I plugged it into Mathematica I named them incorrectly. 39:20 Plugging Wikipedia data into the online tool to verify galactic center and galactic north pole. 41:40 I discovered my mistake here, and confirmed that my test should have worked if I had named them correctly.
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