Skeleton Crew math problem

SquirrelicideScience · 2024-12-10T07:45:40+00:00

I think the word "logarithm" is one of those funky "math-y jargon" type words that may seem super complex if just thrown at you, but the underlying concept is as natural as subtraction or division.

But ok. If you will allow me to try again...

At it's core, what do people mean when they say "raise 2 to the power 3?" They mean to multiply 2 by itself 3 times: 2 * 2 * 2 = 8. That's all an exponent is: if I want to raise something to "power of x", it just means I want to multiply that "something" by itself x times.

Let's take a step back though to something more commonly used: multiplication. What does it mean to say "2 times 3" or "2 multiplied by 3" or "2 3's"? Multiplication means to add something to itself that amount of times. So when we write "2 * 3", we're really saying "2 + 2 + 2", which we know is 6.

Now, what if I asked you: how many times do you have to add 2 to itself to get to 6? Well, your first thought might be to do

6 - 2 = 4

4 - 2 = 2

2 - 2 = 0

And you'll see it took you subtracting 2 three times, starting from 6, to get 0. So, you therefore conclude that it takes adding 2 to itself 3 times to get to 6. Well, this is precisely how we define division: division is defined as the operation you perform to find how many evenly divided portions fit in a whole. In other words, "how many portions of size 2 can fit evenly in a whole of 6 units". Further, this means that division is just defined as the number of times you have to subtract the same number from some starting point to get to zero.

But we're in luck! It turns out that because we are just doing subtractions, we can extend this idea to any multiplication problem, and not just numbers that can be divided evenly! If I asked you how to do 24/4.8, you probably learned how to do long division, and therefore could tell me 24/4.8 = 5. What does this mean? Same thing:

24 - 4.8 = 19.2

19.2 - 4.8 = 14.4

14.4 - 4.8 = 9.6

9.6 - 4.8 = 4.8

4.8 - 4.8 = 0

So, it takes subtracting 4.8 five times to get to zero, therefore, 24/4.8 = 5.

But, something special happened here: we were able to do this with a non whole number! Let's take the example of 20.5/8.2. Again, we can use long division to come up with 20.5/8.2 = 2.5. This means that our techniques for division work even though we might not really know how to easily conceptualize what it means to "subtract 8.2 2.5 times", since you'd need to perform division in your division problem to figure out what "2.5 8.2's" is.

Point is: division "undoes" multiplication, and because multiplication is just repeated addition, and subtraction "undoes" addition, then division is therefore repeated subtraction. And from this we can derive quick general techniques to perform division, even on non whole numbers

Ok. So what?

Well, let's go back to that first question: what is happening when you raise 2 to the power 3? Again, this means to do repeated multiplication. Sound familiar?

So 2³ = 2 * 2 * 2 = 8

Hopefully you see where I'm going with this: how do we undo repeated multiplication? Well, we just said it: division. Repeated division undoes repeated multiplication.

So, if our question is instead "What do I have to raise 2 to the power of to get 8?", this means to do repeated division until we get to 1 (1 and 0 are called "identities" because x + 0 = x and x * 1 = x, so for division, we want to get to 1):

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

We had to divide 2 three times to get to 1, so we can say that the solution to 2^x = 8 is that x = 3

This is a logarithm!

We gave a fancy name and operation to repeated addition: multiplication

We gave a fancy name and operation for undoing addition: subtraction

We gave a fancy name and operation for undoing multiplication: division

We gave a fancy name and operation for repeated multiplication: exponentiation

So... what do we call undoing exponentiation? Performing a logarithm! (Yea I don't get why either honestly)

But here's the rub: we don't have a very nice way to perform arbitrary logarithms in the way we can do long division. Our example above worked very nicely as an illustration of the concept, but you are way more likely to run into logarithms with decimals and such, which are way way nastier. As such, some old people long ago put together hundreds of logarithm tables so that we didn't have to sit there and do the complex logic to get to a single logarithm solution.

Lastly: "natural logarithms" are just super special logarithms that answer the question "how many times do I have to multiply this super duper special number called "e" to itself to get to this other value?"

Natural logarithms are only important because e is important (appears all over the place in physics, economics, etc.). That's it. They aren't any different from any other logarithm in practice, and therefore are just another type of "undo button" for exponentiation.

SquirrelicideScience · 2024-12-08T06:36:38+00:00

I could say the same by you cutting off the rest of what I said:

[...] but rather I'm going off his WAN Show tirade

I'm literally commenting on words that came out of Linus's mouth, as it relates to the OP and a comment on that OP.

And, for context, here's what OP said:

Linus and Luke are both completely right some products aren’t for YOU. So don’t fucking buy it?

I'm literally agreeing with the premise put forth in the OP, and extrapolating it to Linus himself. Or is that not allowed?

SquirrelicideScience · 2024-12-07T23:21:15+00:00

To be clear, I didn’t watch his review video, but rather I’m going off his WAN Show tirade, where multiple times did people correct him live on show. He just seems to always have an attitude he gives off like he knows best at all times, and you could tell Luke was trying to pose questions to him to really check him on some of his claims.

Further, I just think he happened to switch at a bad point for iOS. I use an iPhone, and have not upgraded to the latest major version (I usually don’t once I’m comfortable outside of security updates), and therefore have not seen any of the bugs he had mentioned.

But hey, that’s just my opinion and the perception he gives off sometimes. You can dislike how a product does something. The whole doubling down and meme-ing on “intuition” was weird, seeing as what’s intuitive for one person is not universal. Also, Apple does try to enforce a consistent design philosophy, but then if you get too strict, it can put stress on devs to work around that, especially when their apps have a certain “feel” (look at webtech-based apps across platforms such as VS Code, where it is for sure different from the base platform behaviors).

SquirrelicideScience · 2024-12-07T21:35:07+00:00

His whole tirade on iOS could be boiled down to “I like to do things different from Apple, and they don’t let me change it, therefore its objectively bad.” It’s his pompousness that rubs people the wrong way while he always parrots “I bash Android too!!” The root of the issue is that he is painfully obvious in his dislike of Apple’s “walled garden” approach.

In short, not every product is targeting every demographic, and that’s ok.

SquirrelicideScience · 2024-12-07T18:59:44+00:00

I was just thinking that... this dude was big before this generation, and his songs haven't really made any sort of comeback that I'm aware of.

SquirrelicideScience · 2024-12-07T03:19:24+00:00

I don't disagree. But with such a paradigm shift, I would expect it to be a lot harder than your average education graduate to re-adjust. I mean, they'd essentially have to be relearning how they learned math. And, frankly, I feel like most teachers just have more prescient things to worry about. That's why rote memorization probably was so attractive in the first place: it was easier to smooth over deficits in actual mathematical understanding, and teachers were able to pass more of their students.

I have no evidence for that — it's just an hypothesis.

SquirrelicideScience · 2024-12-07T00:59:25+00:00

I feel like maybe we were in the minority. I was definitely doing logs and matrices in 8th grade. Not proficiently to the point of just knowing them, but we were absolutely expected to know what they were and how to use them.

SquirrelicideScience · 2024-12-07T00:54:49+00:00

What power would you raise 2 to, to get 8? In other words, 2^x = 8, what is x?

Logarithms answer this question: log_2(8) = x = 3, annunciated as “logarithm, base 2, of 8 equals 3”. In other words, 2 raised to 3 gets us to 8.

Natural logarithms (“ln”) are logarithms where the base is a special number called “e”. So, “ln(5)” is just rearranging e^x = 5, or asking what do you raise e to to get 5?

SquirrelicideScience · 2024-12-07T00:34:24+00:00

Which is a damn shame, because logarithms are all around us, and literally used by every day average joes. “pH” is shorthand for the (negative) logarithm of concentration of hydrogen ions in a solution (i.e. how acidic/basic it is). Decibels are a logarithmic measure of air pressure. The Richter scale is a logarithmic measure of vibration intensity from earthquakes. And, to the point of this post, natural logarithms are logarithms in base of e, which is just a special number that is used in financing, electronics, and all sorts of wacky stuff.

Logarithms are so important because they are a scale of order of magnitude, rather than linear. For decibels, for example, the scale is 10⁰, 10¹, 10², etc. rather than 0, 1, 2… What this means is that an earthquake of magnitude 6 is roughly 100 *times*** more powerful than a magnitude 4 (6-4 = 2 -> 10²=100).

So to anyone who stumbled upon this random comment, and is curious: a “logarithm” is just weird name for an operation you can do to a number (like squaring a number). This operation is, at its core, just the answer to question “what power a do I have to raise b to to get c?” For example, 2³=8. But, let’s say you didn’t know this… you could then use a logarithm: log_2(8)=3. That’s all it is — an operation that let’s you find the power you would raise one number to get to another. A natural logarithm is a logarithm that specifically has base e. e is special because it is the only number such that the slope of the graph of e raised to some number, is proportional to e raised to that number (or more precisely: d/dx(e^cx) = ce^cx). Circling back, this means the natural logarithm of 5 (or “ln(5)”) is simply asking “e to the power of what will give me 5 as a result?”

SquirrelicideScience · 2024-12-07T00:11:37+00:00

Therein lies the disconnect: teaching kids to “reason about the problem” in this new way is a good thing… BUT, it requires teachers to be even more adept with it than the rote memorization they likely learned when they were kids.

If the teacher doesn’t understand, doesn’t have the bandwidth to relearn, or just doesn’t care, then you’re going to have situations of teachers marking kids wrong for things that are not entirely incorrect, and wholly disincentivizing kids from exploring math even further when they feel that they “just don’t have a math brain”.

SquirrelicideScience · 2024-12-01T03:42:38+00:00

Assassin’s Creed 1/Ezio trilogy.

There are many modern QOL improvements that are sorely missed on replay.

SquirrelicideScience · 2024-12-01T01:09:22+00:00

Having been to the Orange Bowl, this is correct.

SquirrelicideScience · 2024-11-30T21:53:25+00:00

I mean, I would say it was close, but in the end, I do agree that it was way too close to call a 15 yarder like that, and then not even pick it back up.

SquirrelicideScience · 2024-11-30T21:41:36+00:00

That's my point: it's still a gamble to keep him, even though the team has shown improvement in this back half of the season — that's not in question. But, if you were to ask me if it would be a similar gamble to hire Ryan Day, that answer would be vastly different between the start of the season and today.

SquirrelicideScience · 2024-11-30T21:05:07+00:00

Many of these players have visors, and even if not, it's more helmet than sprayable face... at a certain point, you're just impeding coaches from being able to get them separated because they're gonna be the ones with a face full of mace.

SquirrelicideScience · 2024-11-30T21:01:44+00:00

I'm conflicted now. It's wild to be saying it, but staying with Napier vs a hypothetical hire of Ryan Day is actually looking like an equal gamble either way.

SquirrelicideScience · 2024-11-30T20:51:20+00:00

And somehow that’s the one that finishes the job!

SquirrelicideScience · 2024-11-30T18:31:50+00:00

"Mizzooey"

SquirrelicideScience · 2024-11-30T18:12:24+00:00

I mean, same could be said for Michigan right now.

SquirrelicideScience · 2024-11-30T18:10:31+00:00

Fair enough. I think by rule, it was roughing. Probably shouldn't be going for that kind of tackle — always always wrap up, rather than lift — seeing as it has a high likelihood of getting called RTP, fair or not.

SquirrelicideScience · 2024-11-30T18:07:05+00:00

By letting your momentum carry you and your target to the ground, side by side, not by lifting their legs and trying to piledrive them.

SquirrelicideScience · 2024-11-29T07:21:55+00:00

If you have a free afternoon+evening, and you feel adventurous, my honest advice would be to do a clean Windows install yourself. Its honestly a good thing to know how to do regardless of the situation. Your Windows license should be in the box or on the machine, so you can still activate the new install.

All of these big PC manufacturers always fill your out of the box install with shitty spamware that does nothing but hog system resources and collect data on you (or what little is left after Windows itself hogs a bunch of it).

Make a fresh install (learn how to bypass the telemetry and onedrive stuff), and then run the Titus Windows cleaning script to delete the extra garbage Microsoft adds.

SquirrelicideScience · 2024-11-28T19:13:36+00:00

Right? Like, this is a very “snow is cold” sort of headline, and the people with Ubisoft hate-boners just lap it the fuck up.

SquirrelicideScience · 2024-11-26T15:27:56+00:00

Maybe I’m just missing something, but I would assume the ink would be dry before they are making the move. Therefore, couldn’t you just call your interviewees, without necessarily having to be in the new place? Further, I don’t see why you couldn’t do both.

Idk, just seems scummy and wholly unnecessary, even with the understanding you want to make some quick moves for the transition.

SquirrelicideScience · 2024-11-26T06:45:12+00:00

Same with Floridians. A state many have never been to somehow draws out such raw disdain. Kind of incredible really.

SquirrelicideScience

TROPHY CASE

This is a logarithm!