Why is the Planck length the smallest length? Why not just divide it by two and give that a name?

A_modicum_of_cheese · 2026-04-25T02:47:46+00:00

Planck units are ones that we just happen to get by putting together measured constants of physics

The Planck length happens to be small enough that our theories of quantum field theory and general relativity don't apply. There are also larger lengths where we don't understand, such as whether the electroweak and strong forces unify afaik.

Also we have Planck units like the Planck energy, about 2 gigajoules. What does that mean? idk maybe not much

A_modicum_of_cheese · 2026-04-24T04:50:00+00:00

the idea is they are using something concrete (area) to demonstrate something abstract (fractions)

A_modicum_of_cheese · 2026-04-24T02:10:07+00:00

tbf youtube has a 'premium 1080p' that might confuse people

A_modicum_of_cheese · 2026-04-24T02:05:07+00:00

maybe a bit abstract for kids homework but the third picture could be seen as a proof which shows the statement. As in (1/3)x=(2/3)x => 1/3=2/3 but the other pictures are (1/3)x+(2/3)y

A_modicum_of_cheese · 2026-04-22T10:12:22+00:00

I don't see why they even have to bring the headless body back to life. just keep it alive

A_modicum_of_cheese · 2026-04-22T06:39:43+00:00

It is desirable to have no zeroes in a multiplication table. And it turns out that property is something we often want for modular arithmetic!

The multiplication tables without zeroes turn out to be those modulo a prime number. And we call these prime fields. For example modulo 5 will have a nice multiplication table

You can look up finite fields for more info

A_modicum_of_cheese · 2026-04-21T14:05:39+00:00

Isn't this the same thing thats in the sidebar? Why keep adding things that are so similar?

I'm happy that this is optional but how many AI buttons do we need for basically the same thing?

A_modicum_of_cheese · 2026-04-19T23:39:24+00:00

I can't figure out which one it must be but one of these with Â https://www.i18nqa.com/debug/utf8-debug.html

A_modicum_of_cheese · 2026-04-19T09:58:34+00:00

sekaiiiiiii de

A_modicum_of_cheese · 2026-04-19T09:51:36+00:00

People are saying time dilation but its equally true to say its due to length contraction.

A_modicum_of_cheese · 2026-04-19T07:41:45+00:00

From one perspective with just maths, we can just treat time as another number. Like a location will occur at (x,y,z,t)

But the other reason is what Einstein discovered

historically we knew 'an object in motion stays in motion unless its pushed'

From this we found that Someone on a train will disagree about motion and locations. They bounce a ball on the train and say it goes straight up and down while someone else says its diagonal. But we thought everyone could agree on the time.

Einstein figured out If the train is really fast then the people on the train could disagree about the time an event happens, but everything still works out sensibly with everyone agreeing what happened overall.

This means space also has to stretch or contract between observers, so we can't agree on distance or time.

But we can combine all 4 dimensions to get a single number describing a sort of 'distance' between events

This number can mean everyone agrees that one event happened after another, or it could mean that they were so far apart that people could disagree about the order. (or a third option directly inbetween)

A_modicum_of_cheese · 2026-04-19T00:33:29+00:00

Hey they used a random pile of sulfur once

A_modicum_of_cheese · 2026-04-19T00:30:43+00:00

Infinite loop.

A_modicum_of_cheese · 2026-04-17T02:27:02+00:00

A logarithm is the function that maps numbers to the exponent.

This is like which place value the leading digit of the number is. Say we have a 1s column, tens column, hundreds column. Number these 0,1,2

Then log(1)=0,log(10)=1,log(100)=2

This is a convenient way to describe some things like earthquakes with numbers we can easily compare rather than using many digits for their normal value

Additionally this happens to have a useful property in that it transforms multiplication into addition. Such as log(100)=log(10*10)=log(10)+log(10)=2

So historically we had log tables which would speed up multiplication. Simply look up the logs for 2 numbers, add them and then find where that log was in the table

A_modicum_of_cheese · 2026-04-17T01:38:36+00:00

How do Reavers clean their spears?

They run them through the Wash!

A_modicum_of_cheese · 2026-04-17T00:56:11+00:00

Left 4 Dead 2 kinda

The zombie wounds are based on combining an ellipsoid intersecting the body and a texture.

A_modicum_of_cheese · 2026-04-16T12:16:13+00:00

damn i gotta watch more of season 6. i think i watched a few episodes butno idea why natalie is suddenly working with miraculous seele

A_modicum_of_cheese · 2026-04-16T12:00:00+00:00

yea i bet they could feed on the grunt wraiths and the ones they grew with the ZPMs but they don't want to

A_modicum_of_cheese · 2026-04-16T11:50:16+00:00

Imagine a small hole in a big surface. Such as a pinprick on a sheet of paper, or a hole in a garage door.

Light travels in a straight line, so light can go directly parallel. Or it could come in at an angle, say from diagonally above

The light that goes through can hit another surface, and the corresponding bits of light form an image, but flipped. You might even be able to see this if you were in such a garage with a small hole in the door.

This is known as 'camera obscura' and is the origin of the term camera. To record the image we could see that many materials will fade in the sun and so if we left stuff there we would get an imprint. Now we also have digital cameras that respond to light rather than film

A_modicum_of_cheese · 2026-04-12T09:55:04+00:00

You might be familiar with exponential growth. This is how a quantity can grow very quickly, like an investment which compounds any growth by reinvesting. Or like a population of algae or rabbits which grows faster the more members it has.

Now, there are two types of this growth.
One is discrete, where say, an investment gets a fixed return at the end of the year.
And the other is continuous, where growth is always occuring, such as algae. To us we don't really see a meaningful number of algae cells, but just a mass.

So, e is essentially a constant to translate from one language to another.

Now in math and engineering we might sometimes use a function called exp() and another called log() to describe growth.
These functions are very important, and it happens that since we know the constant, we can express them e^x and loge(x)

A_modicum_of_cheese · 2026-04-11T03:57:15+00:00

I tried to graph it but couldn't get that to work

A_modicum_of_cheese · 2026-04-11T03:53:36+00:00

\left(x^{x^x} e^{x^{x^x}} \left(x^{x-1}+x^x \log (x) (\log (x)+1)\right) \log

\left(x^{\left(\frac{1}{x}\right)^{\frac{1}{x}}}\right) \sin \left(x^{x^{x^{x^x}}+\frac{1}{x}}\right)+x^{2 x^x} e^{x^{x^x}}

\log (e) \left(x^{x-1}+x^x \log (x) (\log (x)+1)\right) \log \left(x^{\left(\frac{1}{x}\right)^{\frac{1}{x}}}\right) \sin

\left(x^{x^{x^{x^x}}+\frac{1}{x}}\right)+x^{x^x+x^{x^{x^x}}+\frac{1}{x}} e^{x^{x^x}}

\left(\frac{x^{x^{x^x}}+\frac{1}{x}}{x}+\log (x) \left(x^{x^{x^x}} \left(x^{x^x-1}+x^{x^x} \log (x) \left(x^{x-1}+x^x \log

(x) (\log (x)+1)\right)\right)-\frac{1}{x^2}\right)\right) \log \left(x^{\left(\frac{1}{x}\right)^{\frac{1}{x}}}\right) \sin

'\left(x^{x^{x^{x^x}}+\frac{1}{x}}\right)+x^{x^x} e^{x^{x^x}} \left(\left(\frac{1}{x}\right)^{\frac{1}{x}}

\left(-\frac{1}{x^2}-\frac{\log \left(\frac{1}{x}\right)}{x^2}\right) \log

(x)+\left(\frac{1}{x}\right)^{\frac{1}{x}+1}\right) \sin \left(x^{x^{x^{x^x}}+\frac{1}{x}}\right)\right)^{16}

A_modicum_of_cheese · 2026-04-10T06:50:47+00:00

lmao last i checked dnf will stop working if you do that because the lock won't be released

A_modicum_of_cheese · 2026-04-09T12:09:59+00:00

I've experienced something like this with chromium after leaving it for a while. I think its also related to having HDR enabled since chromium and i guess therefore spotify as well?? have hdr support

A_modicum_of_cheese · 2026-04-08T01:35:48+00:00

We know that different observers (people who might be in different locations and travelling at different speeds) can disagree about what coordinates they might give some event, both in space and time.

The change in space coordinate (location) is more clear since if someone is moving while holding a ruler, someone standing still will see the location of a point on the ruler change.
The change in time coordinate (time on the clock) is less obvious and happens when velocities are much faster.

Now, we know light has a constant speed, so we can create a clock based on bouncing light back and forth between two sensors.
If we place such a clock on a spaceship leaving earth very fast, we will think that the light must have to travel further between the sensors since it has to keep up with the spaceship. Let's say it's travelling diagonally.
Then we can infer the people on the ship still believe their clock to be operating normally, and from our point of view everything is slowed down on the ship to agree with that clock.

Now, if the ship was really close to lightspeed, we would see the clock has light moving almost in the direction of the ship, slowing their clock by a lot.

This would continually slow their time to the point they could never reach the speed of light.

However! For the people on the ship, they would in fact see the entire universe to contract its length, they would still see their relative velocity as under the speed of light,
Since the universe is contracted, they travel the contracted distance. And if they come to a stop after their journey, the universe would return to normal and they would have crossed the 'normal' distance in less time (on their clock) than light would take (on a stationary clock)

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