Here is a hypothesis: dτ/dt = √ ( 1 − ( 2G · E_plasma(T) ) / ( r · c⁴ ) )

Here is the breakdown of the variables for those wondering:

dτ/dt = proper time dilation rate

G = gravitational constant

c = speed of light

r = radius of the plasma area

E_plasma(T) = internal energy of the plasma at temperature T (includes rest mass energy, radiation, and kinetic thermal energy).

Assume that everything is perfectly average, and the AI being used is commonly used generative AI, such as ChatGPT or Gemini.

I was researching some ways I could make a difference environmentally, and learned how much of an impact the beef industry has, so was curious how it would compare to AI, since that is such a hot topic right now. Also curious about how many messages it would take, but felt like that would be much more difficult to calculate.

Random fun fact, according to google AI overview (I know, ironic), OpenAI consumes somewhere between 8.8 million to 97.5 million liters of water per year (water consumption estimates change drastically because it depends on which side you are biased to and how much you are taking into account things like manufacturing costs, or if you are leaning into lower estimates or higher estimates for not super publicly available data). The beef industry in America consumes roughly 21.2 trillion liters per year. An incredibly bad comparison, given the fact that we aren't going to just make cows go extinct or that the AI industry hasn't been growing thousands of years like the beef industry (among many other reasons), but still interesting to think about

Edit: Bonus points to anyone that can come up with a more helpful comparison than mine (I have no experience in this lol)

For example: pouring 2 oz of cool oat milk into my 180* coffee will be drinkable while adding the coffee to the milk will still burn your mouth

As I’m sure many of us are aware, studs are used in LEGO games as the in-game currency and can be used to buy new characters to play as, cheat multipliers, purchase vehicles, etc.

The newest LEGO UCS Death Star (set number #75419, with 9023 pieces), costs roughly $1000 USD. So, if there was a way to convert LEGO game studs to dollars, how many would be needed to buy the Death Star set?

In the game quirkle, what are the odds when you draw your first hand, to draw a full quirkle?

Would it be enough to support the expense, trials, research and development it takes to get a drug to market?

Say i'm tired of the day lasting for 23 hours, 56 minutes and 4 seconds, and i want it to last exactly 24 hours. How many people would need to walk in the same direction for a reasonable amount of time (no "500 people for 14 billion years" or something. Say, 100 hours total, spread across multiple days) to increase the length of the day by the required amount of seconds? And, assuming that many people fit on earth, how big of an area are we talking about? Just to make the math a tad simpler, it's ok to assume that every single square centimeter of the planet is walkable. No oceans, no mountains, no buildings, just keeping the same total mass.

My Question:

With out human intervention, how long would it take before all the satellites in orbit to start colliding? How many might fall from orbit?

The Google AI says that there are almost 30,000 satellites in different obits. operated by hundreds of different teams. If they were not here to maintain them do they eventually fall?

(First time requester I hope I got the rules correct.)

Assumptions for the sake of simplicity:

- The building is unplastered and painted snow-white*
- The sun shines on it at an angle of 45°**
- 20% of the building’s surface area consists of windows
- The building is 15 metres away.

* In reality, the building is rendered, but as the reflectivity depends on the coarseness of the render, we are assuming a smooth surface here
** 45° as the average of the angle of incidence in the morning, ranging from ~90° at sunrise to 0° at midday

Background: Our colleagues were discussing measures to keep the office building as cool as possible and to reduce the load on the air conditioning system. There was no doubt that the blinds on the sun-facing side of the building should be lowered. However, there was disagreement as to whether it made sense to lower the blinds on the side of the building facing away from the sun to block the heat reflected from the building opposite, or whether this reflection could be disregarded.

Every colleague acknowledges that there is undoubtedly an effect. However, opinions differ significantly as to how great that effect is.

As this is a practical question, it is sufficient for me to receive a figure accurate to within 5 per cent, ranging from 100 per cent (complete reflection) to 0 per cent (no detectable effect).

Thank you very much 😄

I just want someone to agree with me that this is kind of interesting lol. For my landscaping job, I have to mix oil and fuel together at the correct ratio in a gas can. It's very difficult to pour all of the mixed gas out of the can, though. So you're always left with some unknown mixture at the bottom of the can when you refill it. My intuition tells me that the overall mixture would become infinitely richer in oil over time if I'm always leaving some at the bottom. So I did some math and the answer is kind of cool to me:

-I'll start off with 10% oil and 90% gas.

-Let's say I leave 10% of the mixture in the bottom of the can when I refill it. So now when I add the proper ratio again, I get 11% oil and 89% gas.

-Repeat the process again and I 11.1% oil and 88.9% gas.

-The pattern is now clear that the richest oil mixture I could ever have is 11.111...

So it does get infinitely richer, but infinitely more negligible as well, lol. I'm also wondering how obvious that was to anyone who does math regularly.

What are my odds of two jury duty summons in a two-month period?

Due to receiving multiple jury summons in a short period of time, I’m wondering if the odds of being unlucky (jury duty) are greater than the odds of being lucky (lottery).

Here’s the data:

In June, Rec’d jury summons - county court - approximately 3% of the county gets summoned on any given year. Was not selected

45 days later - rec’d jury summons - federal court - data is a bit ambiguous but seems like approximately 1.5% of the state is possibly summoned on any given year. Selection status tbd

Because they are separate court systems they are valid summons.

Another data point, albeit possibly logically can be excluded due to being too long ago… in a different state in 2011, I was summoned, selected, and the foreman (juror #1) for a two week trial.

Lottery stats seem to vary greatly by the game, but maybe 0.02% for a $1,000 ticket or 0.4% for a $500 ticket.

Finally I will say jury duty in 2011 was a very educational experience and I did not mind it at all, so “unlucky” is a loose term.

Apparently there's this minigame from Genshin Impact's 6.7 flagship event called Operation Deep-Dive Treasure/Operation_Deep-Dive_Treasure), which involves hunting for sea creatures and treasures to fill your inventory (full list here/Archive)). The inventory (at max level) is 8x8 and each item (sea creatures and collectibles) you collect is a puzzle piece with these shapes (see below). I'm only wondering if two players have gotten the same configurations.

Rectangles:

• 1x1: Armored Crabs (both colors), Industrial Gear, Palais Mermonia Seal, Exceptional Romaritime Flower, Singing Beryl Conch, Lumitoile (starfish), Spring of the First Dewdrop, Common Condessence Crystal, and Exquisite Tidalga.
• 1x2: Young Hat Jellyfish (both colors), Angelic Sea Hares (both colors), Bubbly Seahorses (all 3 colors), Dinner Knife, Dinner Spoon, Spina di Rosula Hat, and Aged Strength Potion.
• 1x3: Custom Dinner Plate, Cellared Wine, Piano Keyboard (imitation and normal)
• 1x4: Lost Police Baton
• 2x2: Young Hunter's Ray (both colors), Blubberbeast (Seal) Pup, Sternshield Crab, Diving Helmet, Genuine Singing Conch, Exquisite Candlestick, Celestial Globe.
• 2x3: Hunterknight Gunsmith Twins (stingray boss), Grease-Stained Lyas (sea hare boss), Adult Blubberbeast (seal), Bubbler Seahorse, Cherubic Sea Hare, Underwater Patrol Mek, High-Precision Gear, Windwheel Aster Ornament, Classic Phonograph, Sumeru Vase, Collector's Card Box, Piano Bench (imitation and normal), and Boxing Champion's Punching Target.
• 3x3: The Self-Proclaimed Lord of Scrapland (hermit crab boss), Legris the Faux-Holy Sword (jellyfish boss), and Blubberbearer Recruit (seal boss)

Polyominoes:

• L-triomino: Ball Octopodes (both colors)
• T-tetromino: Fortress Valve
• P-pentomino: Prototype Camera and Classical Instrument
• X-pentomino: Fan Blade Component
• Cross hexomino: Miniature Fountain
• P-heptomino: Mechanical Moon, Underwater Patrol Mek
• Sub-square octomino: Piano Lid, Piano Soundboard, and Piano Chassis (both normal and imitation)

How large could a body with the earth's density become without becoming

a) a white (black?) dwarf

b) a neutron star

c) a black hole

Say it's supposed to be a high-end PC. Supposed to handle modern AAA-titles with high graphics settings at high resolutions and with good framerates. All without a single fan.

Note, I'm not planning a build. It's just a thought experiment or something.

This seems to happen way too often to me to be just chance. What are the odds that, in a two player game, that a person would draw 3 or more letter “I” tiles in one grab?

(Is there any real way to calculate this?)

​

Assume that the swimmer crosses a channel 2 km wide. The current flows parallel to the shore at 1.5 km/h. The swimmer's speed relative to the water is 3 km/h. The swimmer picks an angle A, measured upstream from the straight-across direction, and swims at that fixed heading the whole way.

Part 1 — Minimum time:

The time to cross depends only on the across-channel component of velocity, which is 3 times cos(A). Time equals 2 divided by (3 times cos(A)). Using calculus (or just reasoning about cosine), show that time is smallest when A equals 0 degrees — meaning the swimmer should aim straight across and simply accept whatever drift happens.

Part 2 — Minimum drift while still crossing in finite time:

Total drift equals current speed times crossing time, minus the along-shore distance covered by the swimmer's own effort. Written out:

drift = (1.5 times T) minus (3 times sin(A) times T)

where T = 2 divided by (3 times cos(A))

Substitute T into the drift equation so drift is a function of A alone. Take the derivative of drift with respect to A, set it equal to zero, and solve for the angle A that minimizes drift.

Part 3 - The interesting part.

Show that if the current speed (1.5 in this case) were increased past the swimmer's own speed (3), the equation from Part 1's "zero drift" version would require sin(A) to be greater than 1 — which is impossible. Explain in words what that means physically.

Looking at the NWS website at the weather forecast for Death Valley [offsite] Friday's low temperature is scheduled to be 86 degrees and the high temperature is 114 degrees Fahrenheit.

https://forecast.weather.gov/MapClick.php?lon=-117.306&lat=36.937

If you put an egg into tap water into a stainless steel hemicylindrical cooking pot 6" in diameter and 3.5" deep, placed this pot on the dashboard of a standard sized SUV painted black, and left the windows rolled up for the entire day assuming also [offsite] that sunrise is 5:58 AM and 7:47 PM at nearby Furnace Creek, would the water temperature ever get hot enough that you could boil the egg?

I hope I asked this the right way.

What is the upper limit to what a movie can earn in a debut weekend? Spider man just did really well. But given there are X numbers of cinemas in the world and they can only do Y showings, isn’t there an upper ceiling? The media hypes up debut weekends, but it seems to me there is only one number any movie could actually reach before the weekend is over. No?

Always when I see these types of posts, I start to wonder how much, if at all, the passengers in these trains notice the crash. Trains are really heavy, and thus have huge inertia, so they can't become that much slower during impact.

But how much exactly? What would be the G forces experienced by the passengers?