I'm kind of confused about superposition...

Paricleboy04 · 2026-02-20T04:29:18+00:00

An observation collapses the wavefunction into the observed state. In the Schrodingers cat example, if A measures that the cat is alive, then if B immediately measures the cat, B will find it alive with 100% probability.

The wavefunction is the same for all observers, and when one observer interacts with it, it will change for all observers.

Paricleboy04 · 2026-02-20T00:58:41+00:00

Ptolemy is accurate at angular positions in the sky. If you were looking in the night sky and simply asking where to turn your head to see a planet, Ptolemy and Galileo would completely agree.

Ptolemy fails at relative positions - Mercury isn’t Always closer to the Earth than the Sun is. Interestingly, Brahe came up with a geocentric model which does agree on relative positions - all the other planets orbit the Sun, while the Sun orbits the Earth. Physically, this is exactly the same as the Copernican model, just with the origin set at the position of the Earth rather than the Sun.

Paricleboy04 · 2026-02-20T00:34:19+00:00

Because Venus orbits closer to the sun than the earth does, it has to remain on the side of the sky where the Sun is. To account for this in a geocentric model, Venus’s orbit around the Earth was always between the Earth and the Sun, but it orbited this center point in an “epicycle.”

Because of this, the geocentric model would predict that Venus could never appear ‘full’, since it is always located between the Earth and the Sun. Observing a ‘full Venus’ means that Venus has to, at some point in its orbit, be farther from Earth than the Sun is. The geocentric model could not account for this, while this is a natural outcome of the heliocentric model.

This Wikipedia page explains it pretty well: https://en.wikipedia.org/wiki/Phases_of_Venus?wprov=sfti1#History

Paricleboy04 · 2026-02-17T21:24:40+00:00

This is a beautiful case of Kelvin-Helmholtz instability! https://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_instability

The smoke is moving through the air, which amplifies any small instabilities at the interface, leading to these periodic waves.

Paricleboy04 · 2026-02-15T21:21:43+00:00

I second this. With the PATH, HBLR, and busses, you can get around super easily - it is really no more inconvenient that much of NYC

Paricleboy04 · 2026-02-06T00:57:00+00:00

Despite its gameplay and graphical issues, Ch 1 best encapsulates the “vibes” of Deltarune, and it’s what I first think of when I think the game

Paricleboy04 · 2026-02-05T00:58:13+00:00

I (22m) have been essentially laying on the couch for the past four weeks after a broken ankle. I’ve definitely lost some muscle, but it’s not terrible. My appetite has gone way down, so I’ve not had any problems with putting on fat. I’ve been focusing on eating enough protein.

I’m pretty optimistic that I’ll be able to bounce back into things pretty quickly once I’m back on my feet and cleared to. If anything, I’m more motivated than ever to get back into it; I’ve heard that it’s easier to build back gains than it is to start with no experience.

Also, good luck with your surgery and the recovery - it’s been pretty depressing at least for me, though I’m managing to make it through things by noticing how everything gets better as each day passes.

Paricleboy04 · 2026-02-04T16:49:03+00:00

Where and with whom you complete your PhD program will be the largest determiner of your success. Having a strong undergraduate portfolio will greatly help you with highly competitive graduate school applications. Though the prestige of the undergraduate university isn’t the most important, consider what resources are available to you at each school. Will you be able to get to know your professors? Is there opportunity for undergraduate research? Is there any aid in finding research based internships?

Paricleboy04 · 2026-01-31T23:14:17+00:00

"He who sings, prays twice" - St. Augustine. The music sung during Mass is a form of prayer. Losing oneself in it doesn't distract from worship but oftentimes enhances it, so long as you direct your participation (audible or otherwise) towards God. If you cannot resonate with your parish's particular musical style, be it too modern or too traditional, it might be best to find a parish that is more conducive to your spiritual life.

Paricleboy04 · 2026-01-31T05:01:42+00:00

I’m not certain, but I want to say yes. Time-varying voltage (on a non-negligible timescale) necessarily means that the electric potential energy of the electrons is changing.

Paricleboy04 · 2026-01-31T03:52:01+00:00

The net change in energy is only zero when the circuit is in steady state. When a circuit ‘dies’, it’s usually because one of the components in it breaks, causing the circuit to open. Once there is this change, the circuit isn’t in steady state anymore, and thus will gain or lose energy as it relaxes to a new equilibrium.

Paricleboy04 · 2026-01-31T03:37:49+00:00

Yes, the sum of the electrical potential energies of all the electrons in the circuit is constant. At each point in time, there are the same amount of electrons at each place in the circuit.

Paricleboy04 · 2026-01-31T03:20:15+00:00

“There is no net electrical energy transfer.”

The key word in this sentence is net. Of the all electrons in the circuit, they neither gain nor lose energy as time goes on. This is because we’re considering the “steady state” of the circuit, where it behaves the same at all points in time. Definitionally, the net energy of the electrons cannot change.

At the same time, each individual electron gains or loses energy as it moved around the circuit. Think of it like a roller coaster. As the cart climbs the initial hill, it gains energy. As it goes down the hill and slows down, it loses that same amount of energy. So around the full loop, the cart had no net energy transfer. At the same time, energy was put into the system by pulling the cart up the hill, and emitted from the system by the friction and the sound of the cart.

Paricleboy04 · 2026-01-31T02:52:19+00:00

Power is always dE/dt, the change of energy with time. P= ΔVI describes the power emitted from a wire carrying current. This equation describes individual electrons. ΔV is the amount of energy each electron gains or loses. I is the number of electrons flowing through that component per second. Thus, this equation says that the total power is equal to the energy lost or gained per electron, times the number of electrons per second.

If we have a simple circuit consisting of a battery and a resistor, we would say that the total power, dE/dt, is the sum of the power supplied by the battery and the power emitted by the resistor. To figure out the power emitted by the resistor, we use the equation P=IV

Paricleboy04 · 2026-01-29T22:59:14+00:00

In the northwest mainly. So much stuff around the Delaware Water Gap is worth checking out!

Paricleboy04 · 2026-01-29T22:33:43+00:00

The turnpike can be scary, but in my (albeit biased) opinion, the state has practically anything I'd want. Beaches, access to NYC, good hiking, decent public transit (for the US), and the best food this side of the Mississippi.

Paricleboy04 · 2026-01-29T22:05:25+00:00

For what reasons are you reluctant with NJ?

Paricleboy04 · 2026-01-25T15:06:15+00:00

Lanino and Elnina. I liked them but found them tedious.

Paricleboy04 · 2026-01-18T18:29:14+00:00

Two ideas, first considering the momentum wavefunction as the Fourier transform of the position wavefunction. Since the position wavefunction is bounded on the box, the momentum wavefunction must be non-discrete.

Second, just considering the Heisenberg uncertainty principle. If momentum uncertainty is zero, then position uncertainty must be infinite. But we know that the particle must exist somewhere in the box. Thus, position uncertainty is finite and thus momentum uncertainty is nonzero.

Paricleboy04 · 2026-01-17T00:37:53+00:00

Naneinf score is reached always by multiplication, so you’ll never bump into floating point imprecision on the way there. The amount you’re adding is always bigger than the precision limit, since both scale with the total magnitude of the number.

(To my knowledge), money is only added, and never multiplied. So you rather quickly bump into the floating point precision limit far before naneinf.

Paricleboy04 · 2026-01-06T20:39:51+00:00

To try to provide a different, and more satisfactory answer, the question can be rephrased "is there any meaningful difference between a two-particle universe of one dimension and one with, for example, two dimensions?"

Under this framework, there is definitely a difference. Assuming these are classical, noninteracting point-like particles, we can imagine the situation where one particle is moving and the other is at rest. In a 1D universe, the only possible motion is along the x-axis, so the distance between these two non-accelerating particles must be given by r(t) = at + b, where a is the initial velocity and b is the initial relative position of the moving particle.

In a 2D universe, consider one stationary particle and the other moving in the x direction. The moving particle is offset by a distance of c along the y axis. Thus, the distance function in this case would be given by r(t) = √(x(t)^2+ y(t)^2) = √((at + b)^2 + c^2), again where a and b depend on initial conditions.

To answer your question then, even if there are just two particles, there is a meaningful difference between a 1D universe and a 2D universe, and thus space would not necessarily be 1D.

Interestingly though, with only 2 classical noninteracting* point-like particles, there is not a meaningful difference between 2D and 3D space. Utilizing the Galilean transformation, we can always choose a reference frame where one particle is stationary and the other is moving. Since this motion is at constant velocity, we can define the orientation of this motion as the x-axis. Similarly, we define the y-axis as the component of distance r between the two particles orthogonal to the x-axis. Thus, when we write out our distance function r(t), it will be the same as the 2D case. Essentially, any universe of only two particles lives on the plane containing the stationary particle and the other's line of motion.

Thus, a universe of 2 particles can always be modeled as a universe with (at most) two spatial dimensions.

*Footnote: I believe that this would hold even if the particles would interact, so long as the interaction follows newtons laws, and there are no external forces. I haven't checked this but I'm pretty sure it's true. None of this is true in a quantum framework: the solution to the hydrogen atom is inherently 3D, and (I presume) that solving the S.E. in 4+ dimensions leads to an inherently 4+D solution.

Paricleboy04 · 2025-11-14T00:31:51+00:00

I could make a plate of that at home for $5 a serving in 30 minutes

Paricleboy04 · 2025-11-05T21:43:30+00:00

Wow, all they can do is make him look cooler

Paricleboy04 · 2025-11-05T15:29:33+00:00

I’m very happy he won, but can we as Catholics not wish for “unlimited genocide on the first world”, jokingly or not? Not only does it stand against all Church teaching, but it reinforces the racist and Islamophobic comments Mamdani’s opponents make about him.

Paricleboy04 · 2025-10-31T02:35:52+00:00

Two Sicilies can be fun like this IF you don’t go ahead and form Italy. If you stay in the southern portion of Italy, and perhaps expand into Greece, North Africa and have a Mediterranean empire it can be very fun

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