Dimensionless Quantity Puns

The only thing I’m confused about tbh

So while i was studying about arc length
why does arc length when theta is used in radians has unit metre and not metre raidians.

I've done my fair share of reading and seem to still lack some basic understanding that is inhibiting me from grasping why pi or e are dimensionless. Does this have to do with SI or is something dimensionless because it lacks previous or subsequent quantities?

Thanks!

I'm aware that elasticities were introduced to economics by Alfred Marshall. Formally, elasticity of a function is the derivative times the input variable divided by the original function:

[;\text{E}\left[g(x)\right]=\frac{x\cdot g'(x)}{g(x)};]

I've never seen this concept used in any other field, be it pure mathematics, statistics, or physical science. It seems to differ quite substantially from the concept of elasticity used in physics.

The justification used by Varian in Intermediate Microeconomics is that it allows us to see dimensionless (percentage) changes. This seems to work fine for monomial functions, but behaves quite oddly when dealing with most other functions.

I don't think I understand how this works, and I would welcome any good intuition pumps.

In terms of "data types", the sine function is supposed to take in an angle and return a number. This shouldn't depend on whether we use radians or degrees or something else -- sin(pi radians) should be the same as sin(180 degrees). But in a lot of places I see it interpreted as taking a number and returning a number. The input number is assumed to be radians in this case, so that sin(1) == sin(1 radian). But is this fundamental, or is this arbitrary? Can I say that I'm representing my angles in some other dimensionless quantities? Like multiples of a circle, so that sin(1) == sin(360 degrees) == 0.

This becomes important when we consider data types. I often see people writing something like sin(x) / x. For us to be able to take a sine of x, x needs to be an angle. So sin(x) / x is dividing a number by an angle -- why does this work, is it not a mismatch in data types? One way we can fix this is to assume that the sine function converts a number to an angle "under the hood", so to speak, so that the resulting function takes a number and returns a number. But for this to work, we need to define how exactly a number is converted into an angle. We can say it interprets the number as the amount of radians, or we can say that it interprets the number as the amount of multiples of a circle. Sin(1) takes up different values depending on how exactly we convert a plain number into an angle. So -- I'm not sure if I'm making sense here, correct me if I'm wrong -- there isn't a single sin function, there is a family of sin-like functions that differ in how exactly they convert a number into an angle. Sin_radians(1) is 0.84, sin_degrees(1) is 0.02, and sin_multiples_of_circle(1) is 0.

So the question is -- is sin_radians special in any way, for us to consider it the "default" sine function in our applications?

There's Euler's formula: e^(ix) = cos(x) + isin(x). X is clearly a number, because it's used as an exponent. Is it important how exactly it gets converted into an angle on the right side of the equation? What kind of sine and cosine function does the formula use? Would the formula look different if we conventionally measured angles in multiples of a circle rather than in radians? Euler's formula is used to define complex exponentiation -- does that mean that the way complex exponentiation works depends on an arbitrary choice of measuring stick? Or is the radia

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

I hope this is helpful:

tl/dr; you can subtract the cable loss from your dBi value in the app, but only because the math happens to work out that way, not because it actually changes the dBi value of your antenna

 

#deciBels and logarithms

 

The base unit here is the Bel (named after Alexander Graham Bell) and deci means 1/10^th (like how centi means 1/100^th in centimeter), so 1 dB = 0.1 Bel.

When we express a number in Bels or dB, we are just choosing a logarithmic representation, i.e., to express numbers as 10 to some power. For example, 2 = 10^0.3 = 0.3 Bels = 3 dB so we are just choosing to represent the number "2" as 3 dB because 10^0.3 = 2 instead of just saying "2". We can express any number this way. This implies that every 3 dB represents a factor of 2, and every 10 dB represents a factor of 10 (because 10^1.0 = 10). The reason we do this is because it allows us to cover a much larger range of values using small numbers (e.g., 100 dB is much more compact than 10000000000). It also allows us to add quantities instead of multiplying because 10^x * 10^y = 10^x+y.

 

#What's the difference between dB, dBm, and dBi?

Because logarithms and, therefore, dB, are dimensionless quantities, they must be expressed relative to something to have any physical meaning. For example, dBm stands for deciBel-milliWatts and is in reference to 1 mW. If the Bobcat miner has a power rating of 25 dBm, for example, we can express it in a more familiar quantity using the above relations: 25 dBm = 2.5 Bel * 1 mW = 10^2.5 * 1 mW = 316 mW.

dBi stands for deciBel-isotropic and is relative to an ideal, isotropic source (i.e., it emits radiation uniformly in all directions). Antennas are passive devices, so this gain actually describes the shape of the radiation pattern (i.e., it's deviation from an isotropic sphere). It's not actually a single value but rather a function that depends on direction; when a single value is given, it is taken to be the maximum, which occurs perpendicular to the axis of the antenna (the radiation is identically zero along the axis of the antenna for a real source).

Side note, dBd stands for deciBel-dipole and is relative to an electric dipole, which is much more physcially meaningful because these are dipole antennas and perfect isotropic radiators do not really exist. You simply add 2.15 dB to convert from dBd to dBi, so it is actually sometimes frowned upon when manufacturers

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

How the hell am I suppose to know when it’s raining in Sweden?

They were cooked in Greece.

I'm surprised it hasn't decade.

Don't you know a good pun is its own reword?

Two muffins are in an oven, one muffin looks at the other and says "is it just me, or is it hot in here?"

Then the other muffin says "AHH, TALKING MUFFIN!!!"

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

And now I’m cannelloni

Because she wanted to see the task manager.

But that’s comparing apples to oranges

And boy are my arms legs.

Heard they've been doing some shady business.

but then I remembered it was ground this morning.

Edit: Thank you guys for the awards, they're much nicer than the cardboard sleeve I've been using and reassures me that my jokes aren't stale

Edit 2: I have already been made aware that Men In Black 3 has told a version of this joke before. If the joke is not new to you, please enjoy any of the single origin puns in the comments

BamBOO!

They’re on standbi

A play on words.

My daughter, Chewbecca, not so much.

Now that I listen to albums, I hardly ever leave the house.

Pilot on me!!

Christopher Walken

Nothing, he was gladiator.