It’s 0, since ∂t/∂x = 0.

I can get two whoppers for about 5 dollars and they are full of flavor over here (Brazil).

There are two very different things that take the form •'s:

1. as the clitic version of a verb, is, has, and sometimes was and does; 2) as the genitive/possessive case marker.

2. can be attached at the end of all noun phrases, even when the noun phrases is a single pronoun, like it: it’s=it is, it has (or it was and it does in some dialects).

3. can be attached to all noun phrases except to personal pronouns. These inflect, they change their forms: I>my, mine; you>your, yours; he>his; she>her, hers; it>its; we>our, ours; they>their, theirs.

Historically, the genitive case marker •'s originated from inflectional morphology in the form of •es. Different classes of nouns would have different case markers but the •es version ended up prevailing over the others as english shed its case system. The apostrophe that turned •es into •'s seems to have come from imitating the french practice of using an apostrophe where a vowel wasn’t pronounced anymore.

The word has always had a t sound since Old English, and it’s part of the reconstructed language Proto-Germanic in the form *ufta. Every other Germanic language displays a t in the corresponding word:

Scots oftin (“often”), North Frisian oftem (“often”), Saterland Frisian oafte (“often”), German oft (“often”), Pennsylvania German oft (“often”), Danish ofte (“often”), Norwegian Bokmål ofte (“often”), Norwegian Nynorsk ofte (“often”), Swedish ofta (“often”), and Icelandic oft (“often”).

Source

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.

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)

The research you are basing your third paragraph on was actually never published and its claims have remained controversial.

I recommend you check this great video on both grammatical gender and Boroditsky’s article: https://www.youtube.com/watch?v=1q1qp4ioknI