https://youtu.be/cHEOsKddURQ

Here is an excelent Kurzgesagt video.

It’s the slowest in speech and the one that conveys information the slowest too.

Brazil

My S21 FE has automatic call recording natively, you only have to go to the settings and enable it.

I’ll add Spanish! “Alfil”, taken from arabic “(al-)fil”, taken from persian “pil”, meaning “the elephant”, since at some point in the past the piece was, evidently, an elephant.

States are defined by sovereignty over territory and a group of people. They are what we commonly call countries. [1] The United States, Great Britain, and Nigeria are all examples of states

https://chass.usu.edu/international-studies/aggies-go/nation-states

No, it’s correct. You define the operation by it’s properties. It’s not saying that “a plus 0 = a” but “the result of applying the binary operation ‘+’ to any number with 0 should give the original number.”

• is just a symbol. You could instead write it as +(a,0)=a and +(a,S(b))=S(+(a,b)).

You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.

Thanks for your reply!

I hate having to cater to the lowest common denominator, I had to struggle with un-engaging classes all throughout elementary and middle school. I’ve seriously thought about becoming a teacher so I’d like to ask, in your experience, what happens to the children that are able to process more advanced information? Can something be done to keep them engaged and nurture their development too?

Edited an unfortunate typo

Commenting to check later.

The system works perfectly, it just looks wonky in base 10. In base 3 0.333… looks like 0.1, exactly 0.1

Do you know what an irrational number is?

Sure, let’s do it in base 3. 3 in base 3 is 10, and 3^(-1) is 10^(-1), so:

1/3 in base 10 = 1/10 in base 3
0.3… in base 10 = 0.1 in base 3

Multiply by 3 on both sides:

3 × 0.3… in base 10 = 10 × 0.1 in base 3
0.9… in base 10 = 1 in base 3.

But 1 in base 3 is also 1 in base 10, so:

0.9… in base 10 = 1 in base 10

Carbohydrates are the ones with (H20)n

https://en.wikipedia.org/wiki/Supertask

I really like that description! The study of choice. I think that under that lens I’ll be able to appreciate art in a new way. Thanks.

But snakes are legless lizards. Link to youtube

Edit: Wrong link, I’ll leave the previous one anyways because it’s also fun https://youtu.be/_5jNZyoSszE

Both of you should look up AdGuard. It’s the only adblocker I use and it works system-wide.

So we can see the where this weirdness comes from when we look at the energy for a photon, E=hf=hc/λ

When we integrate we sort of slice the function in fixed intervals, what i called above df and dλ. So let’s see what is the difference in energy when our frequency interval is, for example, 1000 Hz, and use a concrete example with 100 Hz and 1100 Hz. Then ΔE = E(1100 Hz) - E(100 Hz) = h·(1100 Hz - 100 Hz) = h·(1000 Hz) = 6.626×10^-31 joules. You can check that this difference in energy will be the same if we had used any other frequencies as long as they had been 1000 Hz apart.

Now let’s do the same with a fixed interval in wavelength. We’ll use 1000 nm and start at 100 nm. Then ΔE = E(100 nm) - E(1100 nm) = hc·(1/(100 nm)-1/(1100 nm)) = 1.806×10^-18 joules. This energy corresponds to a frequency interval of 2.725×10^15 hertz. Now let’s do one more step. ΔE = E(1100 nm) - E(2100 nm) = 8.599×10^-20 joules, which corresponds to a frequency interval of 1.298×10^14 hertz.

So the energy emitted in a fixed frequency interval is not comparable to the energy emitted in a wavelength interval. To account for this the very function that is being integrated has to be different, as in the end what’s relevant is the result of the integral: the total energy radiated. This result has to be the same independent of the variable we use to integrate. That’s why the peaks in frequency are different to those in wavelength: the peaks depend on the function, and the functions aren’t the same.

https://www.scielo.br/j/rbef/a/mYqvM4Qc3KLmmfFRqMbCzhB/?lang=en

This is something that bothered me when I was in undergrad but now I’ve come to understand. The article above goes through the math of computing different Wien peaks for different representations of the spectral energy density.

In short, the Wien peaks are different because what the density function measures in a given parametrization is different. In frequency space the function measures the energy radiated in a small interval [f, f + df] while in wavelength space it measure the energy radiated in an interval [λ, λ + dλ]. The function in these spaces will be different to account for the different amounts of energy radiated in these intervals, and as such the peaks are different too.

(I typed this on a phone kinda rushed so I could clarify it if you’d like)