The only ATproto-specific part is how clients specify their starting position. They give a timestamp, which refers specifically to the `time_us` field in the messages, which I guess must be an ATproto thing. If jetrelay supported filtering, that would be ATproto-specific too. But you’re right: if you removed backfill support there’d be nothing ATproto- or even websocket-specific about it.
The proof offered in the abstract demonstrates a simple link between consistency and the validity of proof by contradiction. It shows that if mathematics is consistent (ie. ⊢Φ and ⊢¬Φ is impossible) then mathematics is consistent.
This is NOT a self-proof - it is a meta-proof. Taking arithmetic as an example, a self-proof of consistency would be a derivation of the consistency sentence (ie. "I am consistent", or "¬◻(0=1)") from the arithmetic axioms. That is not what we have here.
The existence of a proof of the consistency of a theory does not put it at risk from Godel's 2nd - for that we require that a theory prove its own consistency.
As far as I can tell, Hewitt begins with a proof that consistency and the validity of proof by contradiction are equivalent, and then proceeds on the grounds that consistency is proven internally to the theory - which it is not.
For a similar set-up for Linux, see [1]. Here we use dmenu to displays hosts defined in .ssh/config, and open a connection to the selected host in a new window. See [2] for the relevant script.
It depends how deep an understanding you want. You don't need a degree in Physics, but if you want anything more than a superficial idea then you do need degree-level knowledge of the necessary maths and physics.
I don't need a degree in Physics to understand Newton's laws, even though I couldn't derive these laws on my own. Heck, the explanation fits in three lines, and it explains a ton of things.
That's the kind of understanding I mean. It seems there isn't one concise, simple explanation for these effects. I wonder if it's because the reasoning behind it is that complex that you need to resort to esoteric math and abstractions (in which case, the current theories might be crude, Occam's razor and all), or if it's because no one truly comprehends it enough to explain concisely.
By the way, I picked up Leonard Susskind's lectures to watch. It was all fine up to special relativity - his explanation about frames of reference was so obvious, it just made sense. After that, though, nothing made sense anymore.
Newton's Laws fit into three lines because most of us are already familiar with the integral concepts: force, mass, inertial reference frames, etc. The concepts involved in quantum mechanics are fairly alien to most people, so explaining the theory takes longer. The fundamentals of orthodox QM can be fit into three principles: 1) The Time-Dependent Schrödinger Equation; 2) The Time-Independent Schrödinger Equation; and 3) The Born Rule. Even writing these out in full doesn't take long. Explaining what they mean, however, can take a while.
Frames of reference are fairly obvious in SR. In General Relativity they're more non-trivial.
The scenario you outlined is quite important and actually has a name: it's the "Bertlmann's Socks" thought experiment, and if you want to read about it I'd seriously recommend the paper by the great J S Bell[1].
To use the language of your example, both pens begin in a superposition of clockwise and anti-clockwise. It's not the case that each pen has a particular spin value, and that we're simply unaware of which has which. The pens really are in a superposition.
Until, that is, a measurement is made on one of them. At this point the joint pen-pen system collapses and both pens have determinate spin values. The nature of the entanglement ensures that those spin values are different.
The notion that quantum-entangled particles could have well-defined properties that we're just ignorant of was actually pretty popular in the early days of quantum mechanics. In fact, the theory was put forward by Einstein, among others. As it turns out, however, that we can test for this. The tests have been done, and it seems Einstein was wrong on this one.
[1]: J. S. Bell (1980), "Bertlmann's Socks and the Nature of Reality"
Cool. But what if the two pens are spun randomly in a box by say a random number generator spinner (each is pen is still anti-correlated - you just don't get the spin) - such that you do not know that what state they are in (superposition?). Then, probabilistically, they are both clockwise and anti-clockwise - until of course you look at it, a point at which they "snap" to a specific spin (which they already were in? You just didn't know it yet). Wouldn't that give you your unpredictable states.
I'm sorry if this sounds stupid - I just want to understand.
It's not stupid - the difference between uncertainty and superposition is subtle. Let's simplify to the case of one pen.
Say the pen is spun in the box by a classical random number generator. You don't know which way the pen is spinning, but you do know that it's either been spun one way or the other. You might say that the probability of finding it spinning clockwise when you open the box is 1/2.
Now say the pen is prepared in a superposition of the two spin states, again in the box. As before, we might say that the probability of discovering the pen spinning clockwise is 1/2. However, this time we the probability isn't generated by our lack of knowledge: we know exactly what state then pen is in. When we open the box, however, the pen will change instantly to the state of spinning clockwise, or the state of spinning anti-clockwise.
In the quantum case, the probability is an expression of what we think will happen to the pen, not what we think has happened to it.
It is hard to grasp, and harder still to believe. There is, however, good reason for thinking that, sometimes, the pen changed just as we opened the box.
