They presumably meant non-zero total momentum. If the total momentum were non-zero, then the center of mass will be moving in a straight line, and will not return to where it began, and therefore the orbit would not be periodic.
Big picture the center of mass momentum is concerned and it does not matter if the system as a whole is moving up or down or to the right or the left. Like the Earth is basically orbiting the sun in an ellipse [1] so far as the sun is concerned and from the viewpoint of the solar system not care so much that it is moving around the galaxy unless we are interested that orbit being perturbed by other stars that we pass near over millions and milions of years.
[1] ignoring the parameters of that ellipse changing slightly and slowly thanks to the other planets
There just aren't enough existing nuclear bombs to kill everyone in Australia, let alone the world. On the scale of the earth, nuclear weapons just aren't that powerful.
There ought to be more to life than sitting in a pod receiving sufficient nutrients from a tube, even if there was no doubt that humanity would in this way survive until the sun expands and makes the earth uninhabitable.
> There ought to be more to life than sitting in a pod receiving sufficient nutrients from a tube
Even in a hypothetical world where AGI can do everything that humans do better, this would still be a choice to make, not an inevitable consequence for everyone.
And life doesn't require suffering to have meaning.
My experiences with the DMV have actually been pretty decent. I think a lot of their negative reputation is from how it used to be, but that they have improved substantially since then?
DMV is a state level agency and varies a lot depending on where you are. It's partially privatized here in Oklahoma and mostly painless (you only need the actual DMV for driver's tests, CDL background checks, etc.) but when I lived on the Illinois side of St. Louis I routinely heard of people spending hours in line.
Normally I'm not a huge fan of privatization but the way it's done here works great. The fees are set by the state and the agency gets a percentage, so if an area is underserved someone just opens another one.
By "every particle" do you mean like, every type of particle?
If you mean individual particles, fundamental particles don't really have distinct individual identities (as shown by fermi and bose statistics).
As for types of particles: Well, photons surely move at the speed photons move at.
Special relativity is derived from the assumption/observation that light travels at the same speed in all inertial reference frames, and generally that the laws of physics work the same in any inertial reference frame.
What you are proposing sounds pretty vague and unclear to me, but, is what you are trying to say compatible with this?
It did. We are currently on the fourth or more reinvention of capitalism. It's like ethernet - every time networking technology changes, the new one is called the same thing as the old one. The current fiber-optic switched Ethernet has absolutely nothing in common with the original vampire-tapped coax with media attachment units clamped onto the cable and a serial-port-looking AUI interface running down from the ceiling to the computer. Same for capitalism.
zfc is a bunch of axioms and not inference system. It is commonly assumed that it is built on top of some unspecified first order logic which commonly assumed to include bunch of inference rules. There is no ground truth in my understanding where this all is formally defined.
If you want to use “ZFC” to refer to the axioms without any rules of inference, I guess you can do that, but when someone refers to “ZFC” when they are filling a slot that needs a (axioms + rules of inference), the obvious interpretation is that they are referring to the usual system of ZFC.
> when someone refers to “ZFC” when they are filling a slot that needs a (axioms + rules of inference), the obvious interpretation is that they are referring to the usual system of ZFC.
its bro-math. In formal math you need to be specific what inference system you use. There are many of them. Then you need to have formal proof that in that system you can derive concept of function and then think about question if it won't make paradoxes and contradictions with ZFC.
If we take ZFC (or some other set theory) as our meta theory, we can easily see that the axiom of infinity (of ZFC) gives a set of natural numbers (using the von Neumann encoding), which, when equipped with the successor function, is a model of the natural numbers.
It simply does have functions. According to ZFC, a function is a set whose members are pairs, such that no two different pairs have the same first element.
I mean this quite seriously: have you considered reading any first course in set theory?
As I have said a few times now, you should read any first course in set theory. I’m quoting my third-year notes from Cambridge there, but essentially every intro to set theory will say the same. (I’m sure someone will find a single counterexample that does it somehow differently.)
I think the distinction between these options probably doesn’t matter alll that much if the threshold you’re using is either “random person” or higher? Maybe bump it up to “random educated person”?
They are still different concepts of course, but I imagine that once one is achieved, the others aren’t far off.
Ok, but a random educated person will not perform well on vast majority of specialized tasks where professionals operate. A model like Astra probably will beat random educated person performance on majority of specialized tasks. It’s getting close to the level of professionals in many domains, and to genius level on some (e.g. math).
I’m just trying to understand the implications of the current frontier model capabilities.
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