ANSYS my beloved

Holy shit I just had a memory flashback. Did anyone else play a game online that had orbs that looked like this that you had to drag through like a maze without touching the walls and avoiding other obstacles?

Edit: found it, it’s literally called “orb” and it is on coolmathgames

Edit 2: yep just as frustrating as I remember

General Relativity

In particular, the curvatureof spacetime is directly related to the energy and momentum of whatever matter and radiation are present.

As I understand it, gravity arises from the curvature of spacetime which is described by the Stress-Energy Tensor which only accounts for energy and momentum in a given part of spacetime.

So, really it’s like energy is actually what causes gravity in the first place, not mass. Massive things have large gravitational pull because mass itself has/is energy, E = mc². This energy and its motion curves space and gravity results from that curvature.

Then again, I’m an engineering student not a physicist, so maybe I’ve got something wrong.

Wait. I just realized energy also creates a gravitational pull, and the death star’s whole thing is destroying a planet right? That’s got to take a huuuge amount of energy because the explosion has to massively overcome the gravity holding the target together.

A quick google search says you’d need 10^32 Joules to blow up the earth. E=mc2 so dividing that energy by the speed of light squared gives about 1.1e15 kg of equivalent mass which is relatively small compared to earths mass (6e24) but still large.

For reference, if the radius of the Death Star was 1000m you’d get about 5.2m/s2 acceleration from just that energy in its core.

But if the Death Star is able to blow up multiple planets, then the energy it has to have on hand goes up. So if the Death Star contains enough energy to blow up 5.4 billion planets, then just that stored energy would have nearly equivalent “mass” to the earth.

But gravitational acceleration is inversely proportional to distance squared. So since the Death Star is small, you wouldn’t need that much energy to get earth gravity. If we assume the Death Star has about a 160km radius, then you’d only need enough stored energy to blow up ~45,000 earths to get a surface gravity of 9.1m/s2.

This gravity would increase as you got closer to the core or whatever part stores all that energy. But if you spread that energy out a bit you could probably extend how large the earth-like gravity range in the station would be.

The mass of the structure itself would contribute to the gravity too so that 45,000 is probably an overestimate.

TL;DR: From rough math in my head, assuming a radius of 160km, point mass, and ignoring the mass of the structure, you’d only need to store ~5e19 J of energy in the Death Star to get earth like gravity on the surface. That is approximately the amount of energy required to blow up 45,000 earths

Dark Souls remastered. Getting cursed just before reaching a boss and having no money to buy a cure forced me to either give up, grind, or “get gud.”

I beat the boss without getting hit once. I know other people probably do that for every boss but for me that’s a big achievement since I suck at combat and video games in general.

In other news, the game is hard but beautiful and the level design is pretty impressive. I’m looking forward to marathoning the other souls games after this.

Yes, but if the universe is quantum, then there also exists a minimum finite space step. So the fractions never get infinitely small. So you either stop moving in which case of course you never reach the destination; you stopped before you did. OR you take an extra step and surpass your distance by a negligible amount which means you did move all the way.

So even in a quantized universe, the paradox is still false right?

Was it that one episode of Hannibal where the guy grows mushrooms on diabetics he keeps in comas in the forest?

Not that anyone cares but I just realized that this is not actually paradoxical and I can prove it mathematically! (I think) Bear with me since I’ve like just barely learned this stuff this week.

Proof Let S be the set of all steps needed to be taken. It can be written as S = {(distance to be traveled)(2^-n): n in the Natural numbers}. Thus, S shares cardinality with the natural numbers and is countably infinite.

However, time is continuous. Thus, it has the cardinality of the continuum (real numbers) which means any time interval contains an uncountably infinite amount of moments. Let us denote an arbitrary time interval as T.

Because | T | > | S | there is no injection from T to S. Thus if each step has only 1 time value, there will be moments of time left over, and since the hand is not in two places at once we know each step must have its own time value, so this must be the case.

Therefore, when moving in steps like this, one will run out of infinite steps before they run out of moments in time to complete those steps. Hence, any finite distance can be traversed in this way over some bounded interval of time. QED.

Basically, you can traverse any distance in any time interval as long as physics allows you to move at a fast enough speed. Even if it doesn’t, there may be a limit to how fast you can traverse the distance, but it is still bounded. You can traverse any finite distance like this before existence runs out of time.

(I’m still learning. So if there’s an error in my proof please be gentle lol)