It's not answering quite the question you asked, but Shannon - who invented much of this stuff - has some really nice practical arguments in the start of his amazing paper that introduced "information theory" [1]. It's a really readable paper, much less intimidating than you might think, and worth a look.
Hartley was (as far as I know) the first person to recognise the usefulness of log probabilities in the context of measuring information [2]. It's a really amazing paper, for several reasons ... but one thing that really strikes me about it is how it's aged: the first half has an essentially timeless presentation of the essence of information, and the second has a now-quite-irrelevant presentation of how to make a better TV. I guess that was the really interesting problem at the time!
Practically speaking, it's a simple measure of how similar two probability distributions are, minimised (with value zero) when they are the same. So it's often used as a loss term in optimisations when you want two distributions to be pushed towards being similar. Sometimes this motivated by clever reasoning about information/probability ... but often it's more just "slap a KL on it", because it tends to work.
I think it's the usual meaning of shape, it's just perhaps that we don't typically think about what that really means. [I was an author of the Imperial study mentioned in the article, and I had some long arguments with my collaborators about whether it was right to describe our measurement as the "shape of the electron", so I feel compelled to defend the point!]
If I pick something up on my desk and feel what shape it is, what I'm really doing is mapping out the interaction between the density of electrons in the object under test and those in my fingers. I might infer that the electrons of the object are distributed in a spherically symmetric way (it's round), or perhaps something more complex (all the other less symmetric shapes).
So shape in the context of the electron shape measurements means how it interacts electromagnetically. If it interacted perfectly spherically symmetrically, I think it would be reasonable to say it was round. If it interacted in a more complex way (as in, you could grab it and rotate it, because it has some non-spherically symmetric interactions) then it's not round. Interestingly, the electromagnetic interactions of an electron are extremely tightly constrained by it having only 1/2 unit of spin. You can expand any field around a point in terms of spherical harmonics, and you can show the with spin 1/2, the electron can only interact in the manner of the first two spherical harmonics - monopole and dipole. So it can be round (monopole), or round + a more negative and less negative end (dipole). Nothing more complicated than that. (Assuming you believe quantum mechanics. The Wigner-Eckart theorem is the thing to look up if you're interested.)
These measurements, then are measuring the dipolar component of the electron's electromagnetic interaction. The only way in which it could be not round.
As to the point charge thing: well, that's like your opinion man :-) Which is to say, the electron is what the electron is, and it cares not how humans decide to describe it! These experiments are fine examples of a long tradition of measuring and observing to make sure our theoretical descriptions are actually faithful to reality.
You might be tempted so say that if one of these measurements discovered that the electron was not round, then maybe that would be evidence for the electron being not a point particle. It's complicated though ... and you'd find many physicists would start arguing with you if you did say that, because the current description of the electron - while being a point particle in a certain sense - is already pretty complicated (basically, because of interactions between all of the different quantum fields) and many people would say it's already not point-like. Many wouldn't though. Maybe the point here it's quite tricky to be precise about these things without just doing it properly with maths!
In recent years, a number of prominent computer scientists, along with academics in fields such as philosophy and physics, have lent credence to the notion that machines may one day become as large as humans. Many have further argued that machines could even come to exceed human size by a significant margin. However, there are at least seven distinct arguments that preclude this outcome. We show that it is not only implausible that machines will ever exceed human size, but in fact impossible."
I've tried that and while the laptop sleeps, I wasn't able to get it to wake up again. Which of course undermines the utility of it sleeping quite a bit :-) I didn't persist too much with it, so it's quite possible that one can make it work ... but from what I read when I was trying it, it might well be the case that BIOS support for S3 sleep just isn't there.
You can disable network connected standby with group policy. I did try that when running Windows on my machine, and it didn't improve the randomly-getting-hot-when-asleep for me.
I have an XPS 9500 and have found this infuriating.
I think there's two separate things going on:
As others have noted, S3 sleep isn't supported, only S1 "sleep to idle" sleep. But I don't think this is the direct cause of the overheating. In S1 sleep, the laptop can average something like 900mW of power usage, which is enough to annoyingly knock a few percent off your battery overnight, but not enough to make the laptop warm, even in a bag.
The seems to be a second problem, specific to Windows, that when in S1 sleep sometimes the power consumption is high (of order 10W), and this causes the laptop to get very hot if not well ventilated. I've never been able to figure out if this Windows actually doing something useful in "modern standby" like Windows Update, or whether it's a bug. Edit: And I should add, it's crazy that there's not a way to disable this if it is doing something "useful".
Either way, under Linux the latter doesn't happen, and the laptop sleeps very cool ... just with the annoying "lose 5% of your battery overnight" problem from sleeping in S1.
Hartley was (as far as I know) the first person to recognise the usefulness of log probabilities in the context of measuring information [2]. It's a really amazing paper, for several reasons ... but one thing that really strikes me about it is how it's aged: the first half has an essentially timeless presentation of the essence of information, and the second has a now-quite-irrelevant presentation of how to make a better TV. I guess that was the really interesting problem at the time!
[1] https://people.math.harvard.edu/~ctm/home/text/others/shanno...
[2] http://dotrose.com/etext/90_Miscellaneous/transmission_of_in...