Stuff I just don't understand, post here yours.

[Mightymosy]

Logarithms. I know how to read a logarithmic graph and they are helpful in displaying information in some cases. But the math behind it always flew past my head.



"You'll find that many of the truths we cling to depend greatly upon our own point of view."

Worse with me. I find it very hard to read logarithmic graphs, which is partially because I don't understand why you need them in the first place.
Yes, they show exponential functions in way that they look linear - but isn't the whole point of exponential functions that they grow faster than linear functions, and thus should look like they grew faster?

Logarithmic graphs, for me, have the charm of someone painting a square like a circle, because circles look nicer.

All that, and I even like math very much like a true nerd :ashamed:

[Mith]

Worse with me. I find it very hard to read logarithmic graphs, which is partially because I don't understand why you need them in the first place.
Yes, they show exponential functions in way that they look linear - but isn't the whole point of exponential functions that they grow faster than linear functions, and thus should look like they grew faster?

Logarithmic graphs, for me, have the charm of someone painting a square like a circle, because circles look nicer.

All that, and I even like math very much like a true nerd :ashamed:

In my experience, it compresses information on the graph better, and allows you to more easily pull information from.

Instead of needing a huge Linear graph to account for orders of magnitude, you have a smaller log plot that you take your points off a linear equation, and convert as needed.

[Knaight]

Worse with me. I find it very hard to read logarithmic graphs, which is partially because I don't understand why you need them in the first place.
Yes, they show exponential functions in way that they look linear - but isn't the whole point of exponential functions that they grow faster than linear functions, and thus should look like they grew faster?

What if you want to quickly compare different exponential functions? There them being linear makes the comparison easy. Similarly, what if you have something not quite exponential, where you want to see the particulars? On a normal graph it often looks pretty similar, but a logarithmic graph can show the differences clearly.

[Grey_Wolf_c]

One excellent reason to use the log scale:

Spoiler: Spoilered for size

Show

Xkcd has done a couple

GW

[Fyraltari]

Logarithms. I know how to read a logarithmic graph and they are helpful in displaying information in some cases. But the math behind it always flew past my head.

Maths?! Alright let me try.
I will try to make this as simple as possible and not include proofs (just explanations) starting from the basics (since I don't know what you are familiar with)

*Cracks knucles*

First let's talk about functions, those are basically transformation machines: you give a number a number x to the function f it gives you the number y : f(x)=y

When you map that function on two-way graph you get a continuous (not always but that is beside the point) courb where every point on the X-axis has a single counterpart on the Y-axis (but each point on the Y-axis may have any number of counterparts from zero to infinity).

Now, let's talk about derivatives. A derivative is a function (f') which indicates how "fast" another function (f) changes. On the courb it is the incline of the courb of f.
So if f(x) = 1 then f'(x)=0: the courb never evolves.
if f(x) = x then f'(x)=1: the courb changes at a constant rate and for any given numbers a and b f(b)-f(a) = b-a.
if f(x) = 2x then f'(x)=2: the courb changes at a constant rate and for any given numbers a and b f(b)-f(a) = 2(b-a).
if f(x) = x² then f'(x) = 2x: the courb will climb twice as fast as x.
etc etc.
Keep in mind: the higher the value of the derivative the faster the courb climbs. Which means that if f'(x)>0 then the courb does climb, f(x)=0 it is static, f'(x)<0 it decreases.


Now, given a derivative and the value of f(x0) where x0 is any single real only one function has this value at this point and this derivative: this is enough todefine a function.

Let us consider a function (that we call the exponentional) defined like this:
exp(0) = 1 and exp'(x)=exp(x) ie the fuction that equals 1 in zero and is its own derivative

Spoiler: Here it is

Show

Let us observe this for a moment.
Exp(x) never equals 0 or less, and indeed if it did its derivative would, and exp would eternally decrease or be static and we know that its derivative is more than 0 at one point meaning that it increases.

Since its derivative is always >0 then it always increases in value which means that
1) it never stops growing (its limit in positive infinity is positive infinity).
2) going the other way when x becomes an ever greater negative, exp becomes closer to zero (without ever reaching it (its limit in negative infinity is zero)
3) given any real b and a, if b>a then exp(b)>exp(a) and if exp(b)=exp(a) then a=b.


That means that exp is a bijective function from R to R₊^*, or in everyday english: every real positive or negative has a real positive counterpart when processed through exp and for any and all real positive (except zero) there is one and only one real (positive or negative) which when processed through exp gives that real positive.

This means that ther is a function, called the natural logarithm (ln) such that ln=exp^-1 or if exp(x)=y then ln(y)=x for every (x,y).
So we have exp(ln(x))= ln(exp(x))= x

Spoiler: Here is ln:

Show

Spoiler: Note the symmetry

Show

Like exp, ln is always increasing but it tends toward negative infinity when x tends towards 0 and increases much more slowly. (In fact ln and exp are the slowest and fastest increasing functions respectively.)

But we are not done with exp. See one its properties is this one:
exp(a+b) = exp(a)*exp(b) this in turns means exp(2a) = exp(a+a) = exp(a)*exp(a) = (exp(a))²
The same is true if you replace 2 with any other real:
exp(a*b) = (exp(a))^b = (exp(b))^a
Now this is interesting because powers have the exact same properties:
2^2*3 = (2³)² = (2²)³ = 64
Basically it looks like exp(x) is a power of a number e, which is why you often see it written e^x. e is an irrational which equals 2.7182...

Okay we've done the concept-heavy part, now comes the calculation-heavy part but bear with me:

Let's look at the powers of ten: 10⁰=1, 10¹=10, 10²=100, 10³=1,000, 10⁴1=10,000.
Doesn't it look like a function to you? with f(x)=10^x? But we can only use that when x is a natural but how can we calculate 10^2.3? We'd have to multiply by ten 2.3 times.
Well what if we wrote 10 as exp(ln(10))?*
10^2.3 = (exp(ln(10))^2.3 =exp(2.3*ln(10)).
And done, we have a continous function on R₊ for the powers of ten.

So now if we want to compress very great numbers (or expands very small numbers) on a readable scale we can just process everything through ln to get much more manageable numbers. Well almost.
ln(10^x) = x*ln(10) and ln(10) = 2.3025... and I don't know about you but I'd rather have my scale read 1km, 10km, 100km, etc rather than 2.302km, 23.02km, 230.2km etc.

So let's define log₁₀ like this log₁₀(x)=ln(x)/ln(10) this way we have log₁₀(10^x) = x and (10^log10(x)) = x and all is well.


Aaah, aren't maths beautiful?

I used the powers of 10 here because they are commonly used but it works with any power (except 1) . For example computer scientists will use log₂.

[ve4grm]

All the info!

Wow... ok, that's quite an info dump. It's right, and very thorough, but it goes through calculus to reach the answer. I'm going to try to simplify it a bit more.

A log graph is literally a exponential graph with the x and y switched!

If you take the graph of:

y = a^x you get the first graph that Fyraltari posted.

If you switch that x and y you get

x = a^y

which is the same graph, but mirrored across the line x = y. Look at Fyraltari's third graph, you can see both graphs and the line (45 degree line) they're mirrored across.

But we like writing equations in certain ways. y = formula.

So just as if we had

3y = x

we would rewrite it as

y = x/3

we want to do the same with the above formula. But we don't have a way to invert a^y (we can say a = the y root of x, but that doesn't help since both y and x are on the same side now)

so we make one up.

y = log_a(x)

The log base (in this case, a), to the value of y, = the number you're taking the log of. Basically, Log asks, what exponent would this base need to be to to get this result.

Hopefully that explains it alright without going into calculus?

[Knaight]

I used the powers of 10 here because they are commonly used but it works with any power (except 1) . For example computer scientists will use log₂.

Though if we're talking about common use here natural log deserves particular recognition, using a base of e (which I'm sure you know). The math works out so nicely with e^x, particularly with calculus that it just makes sense to map most things to it, pulling natural log along for the ride.

[Vinyadan]

Why chicken curry, instead of curry chicken?

[Sinewmire]

Why chicken curry, instead of curry chicken?

Because the curry is the dish, the chicken is the variety of the dish.
Beef stew, lobster á la greque, and so forth.

If you asked for dinner, and were told it was chicken you might me quite surprised to find it was curried chicken. If you were told it was curry, you wouldn't be surprised to find it was chicken curry.

[Grey_Wolf_c]

Because the curry is the dish, the chicken is the variety of the dish.
Beef stew, lobster á la greque, and so forth.

Or, put in language terms, because "chicken" is the adjective, and in English, the adjectives are placed before the noun.

GW

[factotum]

Also, you *could* describe the dish as "curried chicken" if you wanted to--I don't know anybody who actually does that, but the option is there.

[Lord Joeltion]

Also, you *could* describe the dish as "curried chicken" if you wanted to--I don't know anybody who actually does that, but the option is there.

Like, burgered meat? In another language (say, Romance?), probably "chicken a la curry" or something similar might make more sense than "curried chicken".

[Grey_Wolf_c]

Like, burgered meat? In another language (say, Romance?), probably "chicken a la curry" or something similar might make more sense than "curried chicken".

No, I feel that "burgered" (or "minced") beef would make more sense than "beef a la burger", because "a la" means "in the style of", and neither curry nor burger is a cooking style, but a preparation. A curry might at one point have meant "cooked with the leaves of the curry tree", but in English it means "spicy stew". And just like you can say beef stew or stewed beef but not beef a la stew, "burgered" could be used that way, I feel, even if it is not (although, as I said, I have used "minced (ingredient) often.

Now, yes, "Hamburger" could have originally been used as "beef a la Hamburg", but it has been quite some time since "burger" meant "meat prepared in the style connected to a Hanseatic city", if it ever did (a quick wikipedia check suggests its origins are disputed).

Grey Wolf

[Lord Joeltion]

No, I feel that "burgered" (or "minced") beef would make more sense than "beef a la burger", because "a la" means "in the style of", and neither curry nor burger is a cooking style, but a preparation. A curry might at one point have meant "cooked with the leaves of the curry tree", but in English it means "spicy stew". And just like you can say beef stew or stewed beef but not beef a la stew, "burgered" could be used that way, I feel, even if it is not (although, as I said, I have used "minced (ingredient) often.

Now, yes, "Hamburger" could have originally been used as "beef a la Hamburg", but it has been quite some time since "burger" meant "meat prepared in the style connected to a Hanseatic city", if it ever did (a quick wikipedia check suggests its origins are disputed).

Grey Wolf

The burger part was referring to curried chicken making as much sense to me as burgered meat. That is, I have a harder time conceptualizing it, than the regular form.

The other part was because in other cultures, "stew" can be considered a cooking style, depending on context/wording*. Therefore, I think "stew style prepared (main ingredient)" might make sense for that culture, even if it doesn't translate well.

*In my native language, I can think some five or six different things when thinking about "stew". The concept ain't that different though

[Fyraltari]

Like, burgered meat? In another language (say, Romance?), probably "chicken a la curry" or something similar might make more sense than "curried chicken".

That is the case in French (well "au curry" because curry is masculine, but whatevs).
Both actually:
If you eat the dish curry using chicken meat you are eating "un curry de poulet" (a curry [made] of chicken).
If you eat some chicken with curry on it you are eating "un poulet au curry" ("au" is masculine for "à la", meaning here "chicken with curry")
but it should be noted that this is not the "à la" that English borrowed from French, that one is short for "à la manière [X]" (in the [X] way) where X is place or a person or whatever.
Thaat's because in French, and I strongly suspect this is true of all Romance languages, you cannot just use a noun as if it were an adjective.

[Some Android]

Awesome. Now I just need an explanation of "waifu," "husbando," "desu," and "doki doki."*

*For the record I know what all those things mean, but if anyone wants to give a joke answer I might find it amusing.

I also forgot to ask about "kawaii."*

*Yes I know what that means. I'm just bored and looking for a funny explanation.

[Random Sanity]

I also forgot to ask about "kawaii."*

*Yes I know what that means. I'm just bored and looking for a funny explanation.

Obviously, it's where you end up when your flight to Hawaii makes a wrong turn.

[Some Android]

Obviously, it's where you end up when your flight to Hawaii makes a wrong turn.

Makes sense. I kind of want to go there now. What's their main export? Magical girls?

[Lord Joeltion]

I also forgot to ask about "kawaii."*

*Yes I know what that means. I'm just bored and looking for a funny explanation.

Isn't Kawaii a motorcycle brand?

[Vinyadan]

Now I can't help but think that I have never eaten actual curry, because all the curry stuff I have eaten was normally cooked or roasted + some spice or mix at the end called curry.

[factotum]

Now I can't help but think that I have never eaten actual curry, because all the curry stuff I have eaten was normally cooked or roasted + some spice or mix at the end called curry.

An actual curry is a spicy dish of meat and/or vegetables cooked in a sauce, AFAIK. Spicy meat or veg that's not in a sauce is something else.

[Random Sanity]

Makes sense. I kind of want to go there now. What's their main export? Magical girls?

That and stuffed animals.

[Some Android]

That and stuffed animals.

The kind of stuffed animals that run a school and try to have its students kill each other off or whatever happens in this game series?

[Sajiri]

I don't understand people who litter when there is a trash can right there.

My main gripe working in a high school right now when I do playground duty. The kids who sit near the trash are the worst offenders, they just leave it all right there on the ground instead of just reaching their arm over and dropping it in.

[Florian]

Now, yes, "Hamburger" could have originally been used as "beef a la Hamburg", but it has been quite some time since "burger" meant "meat prepared in the style connected to a Hanseatic city", if it ever did (a quick wikipedia check suggests its origins are disputed).

Do you know what you actually get when ordering a dish "hamburg style" in Germany? A sunny side up egg on top of the meat, no matter if it´s a burger or not....

[Grey_Wolf_c]

Do you know what you actually get when ordering a dish "hamburg style" in Germany? A sunny side up egg on top of the meat, no matter if it´s a burger or not....

Best way to have a hamburger, so I'm fine with that. Weirdly, I've often come across that as "American style Hamburger" in various bars of Europe (Americans, as far as I have determined, definitely do not think it belongs there)

What style do I need to request if I want a pineapple slice on the meat instead?

GW

[Fawkes]

Best way to have a hamburger, so I'm fine with that. Weirdly, I've often come across that as "American style Hamburger" in various bars of Europe (Americans, as far as I have determined, definitely do not think it belongs there)

What style do I need to request if I want a pineapple slice on the meat instead?

GW

Go full Australian and top it with egg, pineapple, and beetroot.

[Peelee]

Best way to have a hamburger, so I'm fine with that. Weirdly, I've often come across that as "American style Hamburger" in various bars of Europe (Americans, as far as I have determined, definitely do not think it belongs there)

What style do I need to request if I want a pineapple slice on the meat instead?

GW

The nicer places tend to have the fried egg option. Of course, I might consider a place nicer by virtue of having that option to begin with, so there's that.

As for the pineapple... Hawaiian? They're definitely have to offer it on the menu, I don't know many places that keep whole pineapple slices in their repertoire.

[Grey_Wolf_c]

The nicer places tend to have the fried egg option. Of course, I might consider a place nicer by virtue of having that option to begin with, so there's that.

As for the pineapple... Hawaiian? They're definitely have to offer it on the menu, I don't know many places that keep whole pineapple slices in their repertoire.

There was a pub, about ten minutes' walk down from my office when I was in England, that had a £5 entry in their menu that was a slab of meat with a pineapple ring on top and a few fries. I'm sure there were other nice things in the menu, but the combination was perfect, and the cheapest option, and I never felt the need to explore beyond it.

Maybe it is a British dish, but since it was edible, I suspect not.

(Also, the "Hawaiian" in Hawaiian pizza refers to the source of the pineapple, as it turns out)

GW

[Peelee]

There was a pub, about ten minutes' walk down from my office when I was in England, that had a £5 entry in their menu that was a slab of meat with a pineapple ring on top and a few fries. I'm sure there were other nice things in the menu, but the combination was perfect, and the cheapest option, and I never felt the need to explore beyond it.

Maybe it is a British dish, but since it was edible, I suspect not.

(Also, the "Hawaiian" in Hawaiian pizza refers to the source of the pineapple, as it turns out)

GW

Huh. I always figured it was pineapple (tropical, indicative of Hawaii) and ham and bacon (indicative of luau) that lent the name. Regardless, I'd wager few Hawaiian pizzas would use Hawaiian pineapples anymore.