In  I asked in somewhat unclear (unclear enough to be closed) fashion about the relationship between an infinite speed of light and the existence of cause and effect.  In thís question, I like to clarify it and make it more articulate.  Consider a non-relativistic, non-quantum mechanical , in which the speed of light is infinite. Now the e.m. field is the vehicle by which a cause is transmitted to create an effect somewhere else.  If the speed of this vehicle, the speed of light, becomes infinite then what happens to cause and effect? All particles affect each other at the same  in an  in this Universe (this is, of course not our real Universe, but it just serves to investigate the Nature of cause and effect; besides, in  a similar kind of Universe is used).    Now when all particles affect each other simultaneously this means they will also affect themselves simultaneously and these in return backfire simultaneously to all other particles which again simultaneously backfire to all particles etc. So a particle, if it moves, has an instantaneously effect on its own movement by the instantaneous backfiring of all other particles, and this holds for all particles. Aren't the particles "frozen" somehow (this is an intuitive feeling on which I can't put my finger exactly)? Can the particles move at all if this is the case and cause and effect can't be separated? If not then a finite speed of light is necessary.   This question differs from the possible duplicate because I ask the question of what will happen in this Universe (which is non-quantum mechanical, contrary to the possible duplicate) when cause and effect are non-separable and all particles interact simultaneously. What effect will this have on the movements (if they are able to move at all) on the particles?   Let's boil down the problem to two charged elementary particles present in this imaginary Universe. What will happen? It seems to me that because of the non-separability of cause and effect, a problem arises because the particles don't "know" what to do. Both particles can't "decide" if they are the cause or the effect, ending up in no movement at all.   So the crux is not being there a distinction between cause and effect.
Even if many interesting similarities between the classical and the quantum mechanical framework have been worked out, e.g. in the subject of deformation quantization, in general, there are some mathematical problems. And in the conventional formulation, you don't want to make things like $\hbar\rightarrow 0$ for the expression $P=-\text i\hbar\tfrac{\partial}{\partial x}$.   In special relativity there are many formulas where one optains the non-relativistic formula by taking the naive limit $c\rightarrow \infty$, e.g.  $$\vec p=\frac{m\vec v}{\sqrt{1-|v|/c}}\ \rightarrow\ \frac{m\vec v}{\sqrt{1-0}}=m\vec v.$$  I wonder if it is know that you can always do that. Is there a formulation of special relativity (maybe it's the standard one already), where the starting assumptions/axioms/representations of objects of discourse involve the constant $c$, and as you take them with you to do all the standard derivations, you always end up with results which reduce to the Newtonian mechanics if you take that limit?
Isn't the const modifier here unnecessary? Frequent Write to Non-volatile Memory I am designing a device that automatically adjusts it's physical position as temperature changes. If the device it shut off or power is disconnected the device needs to remember it's last temperature and position. I have the ability to store these values in EEPROM but the problem is the position and temperature could be changing very rapidly. If I were to write the temp and pos to EEPROM after every time they changed that would (1) slow down the firmware a bit, and (2) likely kill the EEPROM after a year or two. So as I see it my options are as follows...  1) use a capacitor/battery to keep the device powered for a short time after power is lost so that I can write the values to EEPROM at that time only. I don't like this because the board is kinda power hungry and this would require a big cap. And I don't have a ton of free space. And I don't want the added cost of a battery and battery holder / or a big cap.  2) use F-RAM instead of EEPROM so that I can write to it trillions of times without wearing it out. I don't like this option because FRAM is quite a bit more expensive than EEPROM and this is for a production product (not just one).  3) Only write the position and temperature every 5 minutes or so. That way I always have a fairly recent position/temp recorded but I am not writing every second so my program is not slowed down and the EEPROM won't die as fast. This seems like my best option.  Does anyone else have any suggestions that I'm not thinking of? Show path of a body of where it should go after linear impulse is applied I am making a game with Andengine and Box2D. I have a dynamic body and I apply linear impulse on the body to move it around when the user have touched the screen.  Now I want to show the path where the body will go when the user have touched. If you have played Angry Birds or Basket Ball Shoot or any other which have projectile motion with a path shown you will get my point. I want to show the white dots which are shown in those games. Can I test if a regex is valid in C# without throwing exception How do I remove "Ubuntu" in the bios boot menu? (UEFI) How to get pretty HTML source code from PHP generated output? What is the formula for percent of frame filled at a specific distance and focal length? What is the translation of what's written below?  I think it may be the poem of the One Ring, but I'm not sure. How do I fix Outlook only showing the first line of every message? I'm experiencing a strange problem with Outlook 2019. When viewing a message it only shows the first line. On an HTML message, it stops at the first close paragraph tag. On a plaintext message, it stops at the first newline character. This is true if viewing a message in the reading pane as well as if double-clicking the message to open in its own window. I have the preview pane set to show 3 lines and it does show more of the message so it seems like Outlook can see more of the message than it's rendering in the reading pane. If I use View Source, the underlying data seems fine and the whole message is there. I've tried the following:  Deleting and re-creating the user's mail profile Uninstalling &amp; re-installing Office Creating a new Windows account &amp; connecting Outlook to a different Exchange account than the one that originally exhibited the problem Checked for Windows updates Checked for Office updates  Any ideas what might be causing this? I feel like I've tried everything obvious &amp; I'm striking out on Google. proof of functional completeness of logical operators If I know that the set of operators {∨, &amp; , ¬} is functionally complete, how do I go about proving/disproving the functional completeness of the following set of operators?  a) $\{\vee,\neg\}$  b) $\{\to,\neg\}$  c) $\{\to\}$  I have looked at the answer here for (b) : Should I not answer my own questions? If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$ If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$     My work: $(\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b})=\frac{1}{a+b}$ By squaring both sides, we get, $\frac{\sin^8 x}{a^2}+\frac{\cos^8 x}{b^2}+2\frac{\sin^4 x \cos^4 x}{ab}=\frac{1}{(a+b)^2}$ $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}-2\frac{\sin^4 x \cos^4 x}{ab}-\frac{\sin^6 x \cos^2 x}{a^2}-\frac{\sin^2 x \cos^6 x}{b^2}=\frac{1}{(a+b)^2}$ So, now, we have to prove that, $-2\frac{\sin^4 x \cos^4 x}{ab}-\frac{\sin^6 x \cos^2 x}{a^2}-\frac{\sin^2 x \cos^6 x}{b^2}=0$ I cannot do this. Please help! $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$ A different approach in distributing $8$ distinct balls into $6$ distinct boxes Find the number of ways in distributing $8$ distinct balls into $6$ distinct boxes such that there is at least $1$ ball in each box.  We are well acquainted with the traditional Inclusion-Exclusion principle in solving this and it will come up as $191520$ ways.  I tried in this way:  When we distribute $8$ balls into $6$ boxes we have two possible cases  Case $1.$ There are exactly $2$ boxes with $2$ balls each  Case $2.$ There is exactly $1$ Box with $3$ balls in it.  For Case $1$, the distribution is done by choosing $2$ boxes from $6$ boxes and $2$ balls from $8$ balls and those two balls can be arranged in $2!$ ways. But I require another two balls from remaining $6$ balls to be placed in each of these two boxes which can be done in $\binom{6}{2} \times 2!$ ways. Finally remaining $4$ balls can be distributed in remaining $4$ boxes in $4!$ ways. So total number of ways for Case $1.$ is  $$\binom{6}{2} \times \binom{8}{2} \times 2! \times \binom{6}{2} \times 2! \times 4!=604800$$  For Case $2$, the number of ways is  $$\binom{6}{1} \times \binom{8}{3} \times 5!=40320$$  I am pretty sure the value obtained for Case $2.$ is correct. but I could not find where I went wrong in Case $1.$ Why is an object stuck to another? So I created a Cube in Blender and then I created an Empty beside the Cube (in object mode). Now, when I move the Empty around, the Cube follows... Why? I was browsing PhD position offers in Europe on different websites and I was quite surprised to find that several offers contained sentences such as     University of X value equality and diversity. We strongly encourage women and BAME applicants for this position.    where BAME stands for Black, Asian and Minority Ethnicities; or     The research group aims to increase the number of women in scientific positions. Female candidates are therefore encouraged to apply.   Is it considered normal in the academic environment to discriminate between  candidates according to their race and/or gender for "egalitarian" reasons?   How is the choice of a candidate based on their gender and/or race considered "egalitarian"? What does -y mean in apt-get -y install command? I always see commands like this  apt-get -y install    What is the -y tag for and what is the difference between apt-get install with and without the -y tag? How to change maximum number of cores? It says in  that there is a maximum number of 8 cores supported by default in Ubuntu 12.04 Desktop/Server 32-Bit. What is the way to increase the maximum number of cores from the default of 8 to a higher value, like 12?  The reason I ask is because I have just built a machine with 6 hyper threading cores.  There were issues installing the 64-bit version of the software from a CD (it "panicked" and crashed several times).  The 32-bit installed with no problem, but I only see 8 of the 12 cores.  The BIOS is fine.  If I turn hyper-threading off and reboot, I see 6 cores as expected.  I am nervous to try and compile a kernal, I am still new to all of this.  Is there a config setting somewhere that I should change? It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and rotational symmetries and others.  Is there any elementary argument for why linear or angular momentum specifically (and not other conserved quantities) are conserved which does not require knowledge of Lagrangians? By elementary I mean, "if this is not so, then this unreasonable thing occurs".   Of course, we can say "if we want our laws to be the same at a different point in space then linear conservation must be conserved", but can we derive mathematically the expression for the conserved quantity without using the Lagrangian?  I want to explain to a friend why they are conserved but he doesn't have the background to understand the Lagrangian formalism. Problem with glossary I am copying the very first piece of code from  in order to create a glossary. While I get no problem in the compilation I do not get the "glossary part" that appears in the example. I literally copy paste.  Also, I want to create a document that only consists of a glossary of various terms. That is to put everything in alphabetical order (with the possibility to include references as well). How could I possibly do this? I tried some itemize options with alphabetical order but does not look that good.