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Joined 10 months ago
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Cake day: December 9th, 2023

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  • The root of the problem is that you think of momentum as being defined to be the product of something’s mass and its velocity, but this is actually only an approximation that just so happens to work extremely well at our everyday scales; the actual definition of momentum is the spatial frequency of the wave function (which is like a special kind of distribution). Thus, because photons can have a spatial frequency, it follows simply that they therefore can have momentum.

    Something else that likely contributes to your confusion is that you probably think that where something is and how fast it is going are two completely independent things, but again this is actually only an approximation; in actuality there is only one thing, the wave function, which is essentially overloaded to contain information both about position and momentum. Because you cannot pack two independent pieces of information into a single degree of freedom, it is not possible for position and momentum to be perfectly well defined at the same time, which is where the Heisenberg uncertainty principle comes from.



  • Yes, of course they have complained to the courts. That’s not the point.

    That is moving the goalposts. In your other comment, you said, “What is the FTC going to do about it? Most likely do nothing, or issue a stern warning.” I have demonstrated that they are doing neither of these things but instead are going through the courts to get injunctive relief.

    This simply will go nowhere, or do you expect that the court will somehow separate Activision out of Microsofts hands again to fix this?

    If the appellate court decides that the lower court erred in its reasoning, then there is no reason why it could not issue such an order. It is not like this would be the first time that the government broke up a company.

    Or punish the managers at Microsoft and make them withdraw the execution plan to remove redundant jobs?

    There is no reason why the court could not issue an injunction preventing it from executing this plan until the proceeding concludes.

    At the end of it, Microsoft will eventually pay a small, symbolic sum which they consider “cost of conducting business”. Nothing more.

    If the FTC considered this to be a sufficient remedy then they probably would have settled with Microsoft by now rather than taking this to the courts.



  • Fun fact: even when using an absolute scale like Kelvin, it’s theoretically possible to have a negative temperature!

    The reason for this is that temperature measures how much energy you have to pay in order to increase the number of possible microscopic states accessible to the system by a certain amount. In really weird systems it is possible that the amount of energy you can put into the system has a cap, so if you keep pouring energy into the system then eventually it will be forced into the unique microscopic state where every part of the system contains as much energy as it possible can. When this happens, the only way to increase the number of microstates that the system can be in is by removing some of the energy from the system–which you can visualize as creating the possibility of there being holes in the system where there is an absence of energy–and so the temperature is negative.

    This kind of system is so weird, though, that is existence is primarily theoretical. Last time I checked, such a system has not yet been demonstrated to exist in a lab. Still, it is fun to think about!


  • Quoth the article:

    As spotted by iMore, this indemnification stems from how Epic Games breached the developer agreement it had with Apple when it tried offering its own alternative payment system in August 2020.

    In short: Epic Games pissed off the court when it consciously chose to violate the terms of its its contract with Apple before filing the lawsuit, rather than first filing the lawsuit and waiting for it to conclude. The court is taking the unusual step of billing Epic Games for Apple’s legal expenses precisely to disincentivize this kind of behavior in the future.





  • No, if anything the way you can tell you are in a dream is because the top spins forever and never starts wobbling; the way he got his wife to eventually concede that she was in a dream was by setting the top in a perpetual spin so that she stumbled upon it still spinning.

    The significance of the ending is not that he is still in a dream but that he is so content with the situation that he stops caring whether he is in a dream or not. (Actually, in fairness that is not quite true either; I’ve heard that basically the ending is more Nolan trolling the audience than anything of narrative significance.)



  • I think that much of the disparity is explained by the fact that the Apple case was decided by a judge but the Google case was decided by a jury, so the people making the decisions had very different perspectives.

    Also, because the decisions were so different despite the similarities between them, Google probably actually has a pretty good case it can make in the appeals process, so I wouldn’t consider this outcome to be the final word just yet.