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Nobody in this thread was aware that this thread could introduce rule changes, so there was no request for an comment on this specific matter. Changing the rules affects other decisions, and you even refused to comment on the applicability to other games when requested.
So, let me get this straight. This thread is appropriate for gathering feedback prior to rule changes, but is not appropriate for requesting clarification on what the rule change does to other games?
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I have abstained from commenting on this submission, as I do for most controversial movies, but there's one aspect of the verdict that I find a bit troubling.
It looks like the rules for the Vault were updated before accepting the movie. Not commenting on the merit of the movie, it seems disturbing at an institutional level that the person in charge of judging something is capable of unilaterally changing the rules that determine how the judging should be done.
Wouldn't it be more appropriate to retract this decision and create the discussion about rule changes to the Vault to see what people think of this? The way it was done it's hard to escape the conclusion that the rules were changed to legitimize the acceptance of this movie, which hampers the credibility of the judging process.
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Masterjun is correct. Looking at the solution formally you have:
A) The value of sin 18 exists and is unique.
B) The value of sin 18 satisfies the given quadratic equation.
C) The only numbers that satisfy the equation in (B) are the two numbers.
D) sin 18 is a positive number.
E) Only one of the numbers in (C) is positive.
Therefore, you can find the value of sin 18 using these statements.
When you write down an algebraic equation to solve a problem, you have to understand that it is simply a constraint that the correct value, when it exists, must satisfy. So, the algebraic equation is a different problem and might not be strong enough to solve the problem without further statements. The existence of spurious solutions just indicates that the equation you used is too weak to solve the problem alone, they don't have special meaning.
There is a massive confusion about this in analysis. For example, you give a sequence and ask for the value it converges to. When the equation is given in the form of a recurrence, it's possible to write an equation and find a value, and is what most people do.
However, this is incomplete, because the equation just says that, if the value it converges to exists, then the equation holds for that value. It says nothing about the existence. The sequence can diverge and you would still get a meaningless value as answer.
Example: consider the sequence with an+1 = 2/an with a1=1.
If you follow the procedure to find the limit you get L=2/L, L= +-sqrt(2).
The problem is, the sequence is just (1,2,1,2,...) and does not converge at all. So, in this case all solutions to the equation are useless and don't help you solve the problem.
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Sure, that's one possible defense. Things in law are hardly clearcut as you seem to think, though. The judicial system has many ways to punish people that try to be creative to circumvent the law.
Say that the law requires you to pay an engineer a given amount per year. Then you hire someone as an "analyst" and tells him/her to do everything an engineer will do and pay less. If after he/she leaves you get sued, it does not matter that they agreed to work as an analyst, if it is proven that the work done was that required of an engineer you have to pay what you had to pay an engineer anyway.
In a similar way, if what you are doing with their copyrighted program is generating files to instruct an emulator how to play it, it is still possible to argue that you are profiting from their intellectual property getting publicity to the site, it does not matter if you actually included parts of their program.
Like I said, it is not clear who is going to win, but that lawsuit would definitely not be frivolous.
Somehow I think the community is getting things wrong with respect to the law. There is no problem in disagreeing with the law or losing a lawsuit (at least as long you don't do something obviously wrong like killing someone). If people started arguing that what we are doing is digital archeology and the government is making our job illegal, that would be much more convincing.
One example that I think is similar is what's happening to academic publishing. Some years ago, the only way to publish a paper was to give copyright to the entire thing to the publisher. Even in the Internet age, you needed to publish in these prestigious journals to be promoted, so it did not stop.
The effect was that the government paid to transfer rights to the publisher, paid the salary of the researchers who made it and reviewed it, and paid the subscription fees that allowed other researchers to access it. And after it was published, you could not even take a copy of the paper you wrote yourself and give it to your students because it violates the publisher's copyright.
As soon as people started to lobby to require all publicly funded research to be permissively licensed, every major published started to give the option to publish with Creative Commons.
That's one of the reasons I think people should have sued when Nintendo started cracking down on TASes. Even if the lawsuit was lost, it would be one way to argue that the law is broken. As long as people keep with strange excuses, all that really matters is who has more money to pay lawyers.
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Not wanting to disrespect the site, but I am not sure if that license means anything legally.
The point is, a lawyer could argue that it was impossible for us to generate the keypress files unless we had access to the ROM which contains their game. So, even if you could prove that the ROM was dumped completely legally, they could still argue the keypress file is a derivative work and you are not allowed to relicense it. Until a court decides on the matter, no legal conclusion can be reached.
And I am not sure about that Fair Use defense for the videos either. An encode of a run normally includes the whole story of the game, which can be copyrightable, and there can also be a song played during the run which is their property.
The reason we have not seen a lawsuit is just because nobody is making lots of money on this and we are doing free marketing for the game makers. If we were asking money to make the TASes available, you can be sure that Nintendo & co. would send their lawyers trying to get a bit of the cash.
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It definitely feels like that, I will elaborate if you want.
The property of an equation being diffeomorphically invariant is a clear mathematical statement, which is either true or false, and can be verified easily without any knowledge of differential geometry. It is clear that the equations of GR are diffeomorphic invariant and the ones in the theory he provided are not. In fact, I have not seen the claim that those equations are diffeomorphic invariant anywhere in the references I have read. What is actually said is that Newton-Cartan theory is a geometrical theory of Newtonian gravity, which is not the same thing as diffeomorphically invariant.
Besides, I do not perceive as personal attacks when someone points out that what I am saying is incomplete or even wrong. That has happened recently, I uploaded a paper to the arXiv and three days later a physicist contacted me saying that they were already working on the same thing, and that the model I proposed had been put forward in a different context some years earlier. His email came full of references, was not in a "you're wrong" tone and actually helped me learn more. It even helped me generalize the model and I even managed to get another paper written, which is now under review in J Math Phys, where I explicitly acknowledge this physicist for his help.
A very different thing is just claiming that someone is wrong without providing any meaningful references and, quite frankly, his arguments rest mostly on the fact that derivations of GR presented in the most used textbooks are in grave error, this is a statement which would get you laughed at at any serious physics department.
In short, while I would definitely acknowledge the discussion on how someone would arrive at the position that Marzo has, the habit of not providing meaningful references when you contest someone's position and replying to clear mathematical statements with outright trolling and strings of buzzwords just indicates sloppy research on his part and casts doubt on the constructive nature of his criticisms in general. Since I am not his instructor and this forum is not a place to correct his academic conduct, I don't feel it is worth to keep the discussion going.
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marzojr wrote:
To quote a movie: amazing, everything you just said is wrong. Except maybe for the first line, but you are applying it to the wrong person; so I will give it partial credit.
Dear Marzo,
All the garbage you wrote after this line is just meaningless. I don't care about your trolling remarks. The equations are clearly not diffeomorphic invariant, end of story. It's irrelevant if you gravity people somehow convinced yourselves that by just writing something with metrics, giving funny names to things or just stating with no reason that formulations that you don't like are wrong, changes this basic fact. You apply a coordinate change the equations are different. This is the basic statement of gauge symmetry which is violated by the equations once you write them down.
I don't feel I will do anything constructive by addressing your posts, so I consider this matter closed.
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From what I see, it is just a conceptual confusion.
Newton-Cartan theory is simply the statement that the equations of motion for Newtonian gravity can be cast in the form of a geodesic equation for a given metric. That's not really surprising.
However, this has nothing to do with the diffeomorphism invariance of the Einstein Field Equations, the EFE specifiy conditions that the metric tensor must satisfy. In Newton-Cartan theory, you get the gravitational field, which should be computed in an inertial frame, and from it you derive the metric that corresponds to such field.
However, if you were to repeat the same procedure in an arbitrary frame, the equations to generate the correct field would be different, and the metric you would obtain from the equations of motion would definitely not be equivalent to the one in an inertial frame.
So, the metric you find in Newton-Cartan theory is different for non-inertial frames (it can have different curvature, etc.), and the way you determine it is not diffeomorphically invariant at all.
EDIT:
See eq. (3.20) in this paper. The LHS is diffeomorphically invariant, because it is a curvature tensor, but the RHS is not. The equation is covariant with respect to Lorentz transformations, but not with respect to diffeomorphisms. So, the metric equation for NC gravity is not diffeomorphically invariant like the EFE are.
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marzojr wrote:
That is exactly backwards: any theory can be written in diffeomorphically invariant form: there is even a formulation of Newtonian mechanics (plus Newtonian gravity) written in such a form, and this one is valid (i.e., had the same form) on all reference frames. As a bonus, gravity is even related to the curvature of space-time in this theory as well (FYI, this version of Newtonian gravity is a lot more complex than I am letting on).
Please provide a reference for this statement, and forward me the specific theory you have in mind. It is generally acknowledged that the local gauge symmetry completely defines the physically measurable content of a theory, where GR's "gauge group" is the diffeomorphism group. In any case, I should let you know that this sounds like typical crackpottery from gravity people that no one should waste their time on, but I'll give it a chance nonetheless.
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Warp wrote:
The two famous postulates of special relativity are that the laws of physics are the same for all inertial frames of reference, and the speed of light in vacuum is the same for all inertial frames of reference.
Is the same true for non-inertial frames of reference.
No, in Rindler coordinates (which represent a uniformly accelerated frame in SR), for example, you can calculate that the speed of light varies according to its distance from you, so it is neither constant or equal to c for this observer.
Amaraticando wrote:
Do we know that a frame of reference is inertial by observing that there's not a single body moving at speeds higher than c?
No, a counterexample is the universe expanding with a constant Hubble parameter (steady state). In this setting, the frame is not inertial, and every motion occurs with velocities below c, since velocities higher than that are not in the observable universe. This is a specific feature of this model, though.
The thing about reference frames is, you have to postulate whether a given frame is inertial or not. Once you do that, you know that all other frames moving with constant velocity relative to it will be inertial, too. Then you can calculate the physics, do an experiment and see if everything works. If it does, your frame is inertial, if it is not, either your theory is wrong, or you picked the wrong frame to be inertial. In any case, it is experiment that determines the truth, like anything in physics.
marzojr wrote:
In general relativity, things are slightly better: it states that the laws of physics are the same for all reference frames, and defines a local inertial frame to be a freely falling reference frame.
I don't agree with this (popular) viewpoint. Every theory can be cast in a way that it's true on an arbitrary frame. For example, pick Newtonian mechanics in an inertial frame and evaluate the path an object will take. Now, go to any other frame and change the theory so that you have forces that make the object follow the same path and, boom, you have exactly the same results without making reference to inertial frames.
What GR says is simply that the equations should be "pretty" (i.e. diffeomorphically invariant), if you drop that requirement you can derive any theory that you want. I think GR is better defined by the fact that, unlike other physical theories, the geometry where interactions take place is also dynamical (space-time can store and release energy, etc.).
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Warp wrote:
But then, again, they could just be very cleverly trolling. It's not out of the realm of possibility. Poe's Law.
From my experience, I do not have enough faith in humanity to believe this is pure trolling. It's simply lying to get money. Technology is one of the fields most prone to outright fraud, it is sad for me to admit it, but it's true.
I've been to workshops that teach you how to present your business, and it's just plain ridiculous. Essentially you only have 10-15 minutes to present your whole idea, and they actually discourage you from explaining how your technology works, which makes sense, because no one will understand it anyway. They only care about market size, how fast it will give money, etc.
Anyway, in one of these workshops, the organizers gave a prize for the best presentation to a group that everyone pretty much thought was one of the worst. Immediately after the award was given, one of the organizers said that he was happy that one of the guys in the group that won was the president of an important scientific society and would help finance a next edition of their workshop in his country. Seriously, the guy publicly admitted that he had a conflict of interest after giving the award!
If the guys who finance you are really smart, they will require you to provide scientific publications, but I can also say that no matter how mediocre a paper is, it will end up in a peer-reviewed journal if you can tell a good story. One of the most blatant cases I've seen is this. The guys simply copy-pasted a nanoparticle all over with Photoshop and said it was a TEM image. The paper not only was accepted, but still has not been retracted and the authors' institutions did not comment on anything.
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I don't know how this particular FPGA is programmed, but I can assure you that it is not emulating the NES chips transistor by transistor. That is impossible. FPGAs are programmed at the so-called Register transfer level, which does not involve actual wiring.
If you want something more specific, you can have a look at an actual project, like this one, which focuses on building a chip based on a free general-purpose instruction set architecture.
But, the idea is, you use a Hardware Description Language to generate the circuit blocks. The most popular ones are VHDL and Verilog. SiFive uses Chisel, one language they created and compile it to Verilog, an exotic choice. Then, you compile it to a netlist, which contains the logic and you feed into a simulator. If things are working out as intended, you compile it into something the FPGA can accept.
Two companies, Altera and Xilinx, dominate the FPGA market, and the transistor wiring is actually done by their proprietary software, because this depends a lot on the FPGA model, and there is no way to guarantee that it will be identical to the NES hardware. In a similar way, if you would try to make an ASIC out of it, this wiring would be done by the foundry, because each factory has a different method to create the chip's cells and layers.
The idea that the transistor wiring is identical to the original one is just plain bullshit. I really doubt that different versions of the NES itself used identical wiring in their chips. Most likely the newer models used better designs than the older ones to improve power consumption. It is very likely that there are differences in the chip design even in the consoles themselves!
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Hello r57shell,
1) The fact that kinetic energy grows quadratically with velocity is a consequence of Newton's laws. Sure, you can look at the definition of work in terms of force and distance and derive kinetic energy from there, but that would simply shift the question to why work should be defined like that. It is possible to prove that, if you assume additivity of velocities (that velocities are added when you boost from one frame to another), the only reasonable definition for energy is that it is proportional to velocity squared. But again, it is a consequence of either Galilean invariance or Newton's laws, it is not true in relativity, because additivity of velocities does not hold in that theory.
2) Under some assumptions, yes, the amount of heat is four times greater, and if the temperature of the material grows linearly with the amount of heat, the temperature will rise four times more. What you are describing is something similar to Joule's experiment, which determined that it is possible to convert mechanical work into heat.
Energy is to a physicist like money is to an economist. Energy cannot be observed directly, just as money by itself has no value if no merchant is willing to accept it. What you can observe are conversions between one form of energy to another (just like sales in a market), and physical theories describe quantitatively how this conversion takes place.
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Perhaps I have used too much jargon and wasn't understood properly. Let me rephrase my argument in more simple terms.
Let us assume that the Bekenstein-Hawking formula is correct, that is:
S = kA/4l^2, with l = sqrt(G*h_bar/c^3).
Notice that there is the reduced planck constant h_bar in this formula. Now look at the Einstein Field Equations, there is no h_bar there!
Now, you wonder. How is it possible that you derive a formula for the entropy containing a physical constant that does not appear in the equations governing the theory? The answer is simple, you don't do that. To derive the entropy formula, you need quantum mechanics, that is where h_bar appears. Pure, classical GR does not contain quantum mechanics, so whatever theory is being used to derive the Hawking formula, it is not pure, classical GR.
But, wait, let us try something different. Quantum mechanics should reproduce classical mechanics at some limit, so the Hawking formula should apply to classical GR at some limit. This limit is just h_bar = 0. Now, if you substitute that in the formula, you get that the entropy is infinite.
So, as long as you use classical GR, you should always arrive at some problems defining the entropy of a black hole, it does not matter if you do a calculation, talk about a redshift, or compression of matter that falls there. Incidentally, that is not in conflict with the Hawking formula, it also predicts that the definition of entropy should break down at the classical level. It is also not in conflict with standard quantum theory, it was actually the breakdown of statistical mechanics for physical systems that led to the development of quantum mechanics in the first place.
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thatguy wrote:
Here's my problem with the above argument: as more matter falls into the black hole, the mass increases. Therefore the radius of the event horizon increases. Therefore matter that was previously compressed against the event horizon is very definitely now inside that event horizon, even if it hasn't moved. Although matter stops at the event horizon, that doesn't prevent the event horizon expanding to swallow the matter anyway. So isn't the conclusion that a black hole is defined by its event horizon fundamentally flawed?
I am struggling to understand your argument, but from my perspective it is just a confusion about which theories are applied.
In classical General Relativity, the black hole is defined only by some finite amount of physical quantities, its mass, angular momentum and charge (if you consider electromagnetism). In order to get the entropy, you need to model quantum mechanics. Look at the Bekenstein-Hawking formula, it involves h_bar, so it is an essentially quantum statement.
Of course, we do not have a complete theory of quantum gravity, so any treatment must be approximate, but Hawking's idea is more or less the following. You can calculate the Casimir energy of a Schwarzschild spacetime just like you do it for flat space, once you introduce some mathematical techniques to cancel the divergences, which are worse in this case. Just as the ordinary Casimir effect involves vacuum fluctuations, the fluctuations causing the Hawking effect cause radiation emission near the horizon. It turns out that if you interpret this energy thermodynamically, you get that the entropy is proportional to the area. It is generally well accepted that the quantization of GR must lead to some sort of "heat bath" (see here).
So, yeah, while I am not sure I get your argument, I don't think you can argue against black hole entropy only invoking classical arguments, since it's a quantum phenomenon.
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I really appreciate the discussion here, I was not aware that people were implementing old gaming consoles in FPGA's. As usual, it seems that whenever you come up with a new technology, people's brains shut off and they believe everything you say. Apparently, this stuff has been featured on Ars Technica already.
Just to clarify, I have nothing at all against redesigning processors for old consoles in an FPGA. As the open source movement gets even deeper in hardware, these things are bound to happen. If someone came up to me and talked about this as a research project, I would say "Cool!", it would be something like SiFive is doing.
However, this company's practices deviate strongly from well-accepted standards. You never sell products based on FPGAs. They are used for prototyping. What they should be doing is to get their design, ask investors for money and hire a semiconductor fab to make the chips for them. It would work just as well and be much cheaper.
The fact that they are not doing this says a lot of things. Either they are too stupid to realize they can do this, or the investors did not like their idea or (most probable) they don't care at all and just want to make money. While the idea of avoiding software emulation is interesting, the devices they advertise simply cannot do what their marketing says and that gets dangerously close to fraud. Someone should report these guys to the Securities and Exchange Commission.
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Zucca wrote:
The main event(Mods: If this is a duplicate, please lock and put a link to the other/original topic.)
I don't even know where to begin. Although I have started with massive amounts of facepalming...
Can someone list all the things they got wrong?
Comment section is also pretty full of criticism.
I am a semiconductor physicist and have worked both with FPGAs and emulators, so I believe I am well qualified to judge their claims.
The central claim in their video revolves around the fact that software can never simulate how electrons behave in the circuit. While that statement is true, it is completely irrelevant to the conclusions they draw, namely because
(1) digital electronic circuits can only work because it is possible to perform logic operations without knowing the precise behavior of each electron, not in spite of.
(2) any piece of hardware, including the FPGA they promote, is in fact designed to allow its behavior to be describable by software.
(3) although the emulator can never reach full hardware accuracy, FPGAs also don't, since they are entirely different circuits than the original hardware. So, even if you accept all their points, you cannot conclude that one piece of technology is better than the other.
Now, let me clarify the reason for all the previous points.
(1) Modern electronics starts with the MOSFET, which is a very scalable transistor design. The physical quantities involved in the MOSFET are the electric current and the potential, which, differently from their claim, involve the behavior of many electrons at once, not a single one. This is actually a good thing, because when you are working with statistical averages, you reduce shot noise, which helps the device perform better. This is incidentally a very big problem I see in the applied physics literature. Although they advertise regularly single electron transistors and other nanosystems, nobody bothers to check that when you operate with few electrons, the shot noise is enormous and the device can't be applied for anything. The problem is that academia is very specialized today and no electronic engineer is peer reviewing those articles.
Anyway, since we have a MOSFET, the actual value of the current or the potential would only matter if the circuit was analog, and it is not. Although it is true that, as the signal propagates you expect some variations, the hardware is designed to suppress them with amplifiers so that digital processing is possible.
(2) Nowadays, any processor, like FPGA, SoC's and whatever are first specified in a Hardware description language and then converted into something that you can cast into a wafer and perform photolithography. The code in an HDL is extremely similar to the code we write to make the CPU cores in emulators. In fact, it is even more low-level (it needs to handle microcodes and other stuff that emulator writers don't). In practice, SoC designers would first simulate their HDL code and see if the results are the same as those of an emulator code before manufacturing the chip, since that allows you to test things out without spending much money.
I find this irony delicious. The guy in the video says FPGAs are much better than emulators, while the guys who designed the FPGA most likely used emulators to check that it was indeed working correctly.
(3) The problem with emulation accuracy is that good software design principles were not well established in the industry during the time the games were developed. Most software was developed extremely coupled with the hardware, there were no development kits and in order to work, many games relied on hardware bugs without their developers being aware of that. But, as I pointed out previously, this is an exception rather than the rule. If the game relied on too many undocumented features, it probably would not have been accepted by the publisher at the time.
No design is 100% perfect, and you should certainly expect that some flaws will make some games behave differently on different hardware or software implementations, but unless you have a very good reason to spend more on a product that's claimed to be more accurate, you need to be scientific, you need to demand evidence that the game you want to play does not work that well and the product performs better. If that is not provided, any claim is just pure propaganda and there's no reason to take it seriously.
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Dear MUGG,
Again, I can only recommend that you talk to your colleagues and explain your situation. There is nothing "broken" about pointing out problems in school or workplace. It is your right to do it. However:
But nobody cares that I'd spend Christmas alone and sad and that I'm feeling a great deal of pain and regret over my past.
This is a very serious allegation. You are saying that your colleagues know of your problems and are deliberately isolating you. This is essentially an accusation of harassment. Which school are you in? Is it a Hochschule? If what you are saying is true, you should ask who is the person responsible for these matters and present it to them and they will probably issue a formal warning to your colleagues.
However, in order for the school to take action, you need to prove your allegation, you need to point out when you told them of your problems, that you tried to spend Christmas with them and they denied it because of your issues, and name the people responsible. And, naturally, the school will have to hear your colleagues' version of the story before deciding what to do.
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Again, you are using the word "small" in a completely unphysical way. Saying that 1 meter is small is meaningless. What you can say is 1 meter is small compared to the length of a road, which is of order km. Then if you have an object of 1 m driving on a road, you can treat it as a particle.
Likewise you cannot say that momentum is small, what you can say is that it is small compared to the momentum impaired by the gravitational force. And if you calculate the energies at 10^6 K you will see they are the same order of magnitude.
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I don't think I was very clear about the photon thing. Consider as a thought experiment. The walls are so hot that their black body radiation is emitting photons of frequency in deep gamma rays. The photons are very energetic and hit the balls. In this limit, the motion is essentially Brownian and gravity doesn't have much effect.
The other limit is the one you mentioned, absolute zero. But the question is, how close? milikelvin, nanokelvin? In physics, we can only say dimensionless quantities are small, not temperature.
One way to estimate is the following. Calculate the energy of the gravitational interaction of the balls. It is E = Gm1m2/r. Substituting, we get something around 5 x 10 -17 J.
Now, you can estimate the amount of electric charge they should have in order to have the same energy. Suppose both balls have a charge q. The energy is E = k0*q2/r. To get the same energy, you need to have q around 7 * 10-13 C. The elementary charge is around 10-19, so it is a significant amount. In practice, you would need to prepare the balls beforehand to have this charge. If you don't, you can neglect this effect.
Now to the temperature, you can estimate it using Boltzmann constant k. We have E=kT, so the temperature where motion should start to become Brownian would be around T = 106 K, which is very large, so room temperature is perfectly OK!
If you know a bit of particle physics you can guess that gravity is the dominant effect without doing any calculation. The thing is, if you use natural units h/2pi = c = 1, there is only one relevant dimension in physics, which we conventionally use as mass.
The "strength" of a force is given by the coupling constant. The nuclear force has a range of a few femtometers, and the weak interaction even smaller than that, so you can ignore them. The electromagnetic coupling is dimensionless (fine-structure constant), so it has the same strength at all scales (actually, quantum mechanics changes that, but you can ignore in this problem). The gravitational coupling (Newton's constant) has dimensions of mass-2, or equivalently length2.
That is the tricky thing about gravity. People say it is weak in comparison to the electric force, but they neglect a key point. Gravity depends on the dimensions of the problem, for very large lengths it will eventually overtake the electric interaction. Now you use common sense, it took many centuries for humanity to describe electricity, and gravity is known since antiquity. Therefore, it should be natural that at a length of order meters, it should be the most relevant force.
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Dear MUGG,
I am sorry to hear that you're struggling with depression issues, and I should say that I didn't have time to read your entire story, so I might be unable to analyze the whole situation. However, even though I have never been in circumstances as serious as yours, I think that if I share some of my experiences with similar issues, I should be able to help you.
I am a researcher on Condensed Matter Physics specializing in computational methods in Quantum Field Theory and come from a developing country. My story should tell you how difficult it is to get things to work on that environment.
When I was in high school, there were two ways of getting higher education, you either went to a private university and paid exorbitant tuition fees to get a mostly fraudulent education or you took extra classes after high school to be able to pass on the admission test of public universities. There was so much competition for these tests that it was not uncommon to see people trying them for three years or more. Nevertheless, I was a good student and managed to pass quickly.
After getting into university, though, things were not so wonderful as most led me to believe. In Brazilian law, university professors are public servants and once they are hired, it's pretty much impossible to fire them, so they could do basically whatever they wanted. Some were ridiculously incompetent.
Because of that, I mostly ignored their classes and studied mathematical and computer science stuff for programming competitions. My friends and I were very successful and got some awards. That was obviously completely ignored at my institution. In one course a professor even gave me the minimal passing grade because he believed I had cheated, I told him that I didn't and if he believed I did he should take the issue to the appropriate person instead of just setting me a grade. He never replied to my emails and just let things like that.
As I was close to graduation, I discovered the most productive professor in the Computer Engineering department was just making up papers and submitting to predatory conferences. The thing is, I was forced to take his course, and he even submitted a paper with one of his fraudulent studies with my name on it without my permission. I've contacted the editor to retract the paper and he simply doesn't care.
Frustrated by this, I changed to the Physics department, as things looked better there. Immediately before joining the group, the postdoc who supervised me alleged that I was breaching the Institute's ethics code because I took too long to reply to one of his emails. I complained about his behavior to the boss, who did nothing. Months later, this same postdoc submitted a paper without putting one of the professor's collaborators as co-author, because he believed she didn't contribute (and she really didn't). This was seen as a fatal offense and he got kicked out immediately.
During my Master's, my project was delayed because another postdoc had "accidentally" formatted the hard drive with my data because he thought it was not working. Curiously enough, I later saw that he gave his account root privileges when performing maintenance and the logs showed he was accessing code from other members. I reported this and nothing was done.
At my PhD, I had to teach for two semesters in order to get the degree. In one of these, I offered to reformulate the Quantum Field Theory course, since the professor just projected the book pages on a screen and read it together with the class. That was the "course". The problem is, the funding agency requires professors to have a minimum of productivity to teach at grad school, and many didn't achieve this minimum. When they learned a PhD student was preparing a graduate course, they were not happy.
During that semester, I learned I was being accused of sexually harassing a girl I had a fight with earlier. I thought this was strange and asked her if she said I harassed her and she said no, it was just a fight. Nevertheless, they opened investigations against me, interviewed some people and after two weeks they dropped the charges because no one accused me of anything. I consulted with a lawyer and he said that was absurd, they could not have opened investigations against me without first sending me an official document with an accusation signed by the person who received it.
Nearing my qualification, I was performing maintenance on the group's computers, writing the entire research papers for my advisor, and even his research grants. I complained to the department's head that he was doing this just to pad his resume with publications and this was not letting me finish my thesis. Naturally, he just said it was because they expected a lot of me and told everything to my advisor, who reprimanded me for not talking to him first.
After qualifying, I came to Germany and my supervisor here was a complete idiot. Whenever I showed him code, he said that was not physics and literally told me to manipulate the data. Thankfully, I had consulted with lawyers and knew what to do. I reported everything to my advisor in emails, this time expecting he would do nothing. Then I played dumb with my supervisor until he manipulated the graph himself and sent me by email.
This is where the fun part begins. I immediately called him on his misconduct. Naturally he made counter-allegations against me and the boss just ordered me to work on another project to cover everything up. I said this was unacceptable and asked to change advisors, they replied it was impossible and my only alternative was to give up my scholarship. Upon receiving this answer, I sent it to my lawyer who immediately filed a lawsuit with all emails.
Seeing the lawsuit, my advisor resigned and professors at my home institution are so scared that I have been researching without advisor for a few months. Now we have the Brazilian Federal Justice, the funding agency and two institutions investigating the massive amount of corruption there, lots of fun.
What do I want to say with this story? It's perfectly fine to think, as you do, that your class sucks. In many cases that's what happens. However, whatever we do also happens in the complex process of human sociology, and to bring positive change, you need to be in the system and interact with it.
If I just isolated myself when I first saw misconduct, I would never have learned how to do proper research and would not know how to proceed to report it effectively. Besides, even though many people I have worked with were fraudsters, I learned something from them. The fact that they got so far indicates that results are usually more emphasized than methodology, which is something I had difficulty in grasping.
So, my suggestion to you is, interact with your colleagues! Nobody is asking you to give up your way of seeing the world. Given that they don't know your issues in detail, it's possible they just think you are being unfair to them by isolating. I am sure that once you interact with them, you will see things are not as clear cut as you initially thought, and also that you acquiring this knowledge progressively is a natural process, and indicates no problem with you.
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I believe electromagnetism should have significant effect on this experiment only if the net charge of both balls is not zero. It should be possible to estimate how much the product q1*q2 should be in order to match the magnitude of the gravitational force.
The reason for that is that the Newtonian attraction falls like 1/r^2, and r is of order meters, and therefore macroscopic. Any magnetic or electrical polarizability repulsion or attraction would fall at least as 1/r^3, and would be insignificant at the scale of the problem, so only Coulomb attraction should play any role, since it also falls like 1/r^2.
Besides, another issue is that you can never isolate the system completely, even in a perfect vacuum the walls of the container would emit black body radiation, and small momentum transfer from the photons could also affect the time. It should be possible to estimate the temperature the system should be in order to measure this effect.
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Warp wrote:
As we know, the sum 1+1/2+1/3+1/4+... diverges, which means that the photon will eventually reach the other object. But how long does it take? (I know that "how long" is a complicated question in general relativity, but I suppose it's "from an external point of view".)
Of course in actuality the distance between objects (eg. galaxies) doesn't increase linearly. A constant rate of expansion of space causes the distance to grow in an accelerating manner (the distance between two objects doubles every n seconds, which means that the growth of distance is exponential).
Is there a limit for a constant rate of metric expansion of space that still allows light to reach receding objects that start at a given distance from each other? Is there a formula for this?
Your observations are not paradoxical at all. In relativity, time passes differently for different observers, that occurs even in flat space. In order to ask how long something takes, it is necessary to specify the frame where the measurement is made.
And yes, there is a limit to how fast the universe can expand so that all points are reachable. Current observations indicate expansion happened pretty fast after the Big Bang. It is an open problem in cosmology to explain how the universe is so homogeneous if its parts could not communicate on primordial eras.
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Some time ago I found out that these identities, with a cubic root reducing to a rational number, are just a simple consequence of Cardano's method for solving the cubic equation.
Suppose you look at the equation z3=14-3z, and instead of looking for rational roots, just apply Cardano's method:
Assume that the root can be written as z = a1/3+b1/3
Then, z3 = a + b + 3(ab)1/3z
Comparing the coefficients of this equation with ours, we must have
a + b = 14
ab = -1
a and b are solutions of x2-14x-1=0, which are 7 + sqrt(50) and 7 - sqrt(50)
Therefore, the solution for our equation reads
z = (7+sqrt(50))1/3+(7-sqrt(50))1/3
But from the rational root theorem, we can find that the only real solution is z=2. So,
(7+sqrt(50))1/3+(7-sqrt(50))1/3 = 2
I find this very interesting. Galois' theory tells us that there is always an algorithm for expressing the solution of cubic and quartic equations in terms of radicals. However, simplifying them is another story. The method can give a completely tangled up expression! And we can use it to make interesting math questions!
