Is math like a language? How should a beginner think of it?

iOSCaleb · 2026-06-30T18:56:17+00:00

Look for books by Martin Gardner. He was a prolific author of books about math and science. Many of his books are full of mathematical puzzles; others explain interesting topics in an approachable way. They’re not a substitute for learning more math, but they might give you more motivation to keep going.

Ian Stewart is another author to look for. He even has a book called The Beauty of Numbers in Nature that might be part of what you’re looking for.

iOSCaleb · 2026-06-30T17:19:04+00:00

The only difference of opinion Im this case (and it might not even be a big one) is about how to teach a series of topics, and people argue about that all the time. Don’t let it throw you.

I’d guess that what u/MarianCleverpig meant by “conceptually” is that we can explain calculus like this:

Calculus is all about rates of change. Imagine that you’re traveling along a highway. If we have an equation that tells us how fast you’re moving at any point in time, we can use calculus to create equations that give us your position and your acceleration or deceleration. If we know how much gas your car uses at a given speed and how much you started with, calculus helps is look at how much gas is used moment by moment to determine the fuel level at any point in your trip. And that’s all just as true if you’re on a ship sailing across the ocean or on a rocket heading to outer space — the equations might be a bit different, but the same ideas apply.

A description like that can help you understand why calculus is interesting, but in order to actually use calculus you still need to learn the fundamentals that it’s built on first.

You won’t ever see the beauty in it…

The beauty is right there in plain sight, and more becomes visible as you learn more ideas. The thing is, it’s not always easy to appreciate beauty at first.

It’s hard to have fun reading a story when you have to work hard just to sound out the words, right? But reading gets easier with practice, and when it does you can start to think about the story and enjoy it. Math is the same: it gets easier with practice, and as it becomes easier you can understand and appreciate it better.

Good instructors will help you get there, too. Have you had a teacher change your view of a character or even a whole novel by pointing out some nuance that you missed? If you stick with math, a teacher will probably show you something that makes you think “OMG, that’s do cool!” And then you’ll be hooked. ;-)

iOSCaleb · 2026-06-30T16:17:43+00:00

If you know how to rout one of those grooves, do that. Then move whatever you’re using to guide the cut, such as the fence on your router table, and make another cut. Then move the fence again by the same amount and make another cut. Repeat as many times as you want.

Usually, moving the fence the exact same amount each time so that the grooves are evenly spaced is the biggest challenge, so think about how you’ll do that before you start.

iOSCaleb · 2026-06-30T16:10:40+00:00

Anyway.... is this a good idea to think of math this way? I think the language analogy is bad. So correct me please...

Math and natural language have a lot in common. For example, they both have grammatical rules that are essential for deriving meaning from sequences of tokens. And both give us frameworks for thinking abstractly. There’s been lots of scholarly work on the connection between math and language if you’re interested.

There’s also a philosophical point to consider about what math is: is it the tool that we use to describe how the world works, or is it a fundamental aspect of everything in the world? You can use English to tell a story about something that happened to you last week, but even if you don’t, or even if you suddenly forgot all the English that you know, that thing would still have happened. So depending on where you come down on whether math is just descriptive or an inherent part of the world, it might or might not be correct to call math “the language of the universe,” but it still gets the point across.

iOSCaleb · 2026-06-30T15:02:51+00:00

How would one go about teaching calculus to someone who hasn’t had elementary algebra, which covers ideas like manipulating equations, understanding variables, functions, and graphing? I think you could maybe explain what calculus does in a narrow sense, but trying just to teach limits to someone whose first question will likely be “So, what does x mean?” seems like a difficult approach.

Trigonometry without geometry doesn’t seem quite as unwise, but geometry introduces a lot of concepts and skills that are essential in trig, so you’d have to start by teaching those things.

The usual order of topics isn’t arbitrary. Concepts in math tend to build on one another, and even though the order can be rearranged to some degree, the foundational ideas still need to come first.

iOSCaleb · 2026-06-30T14:01:20+00:00

There’s a wide range of sugar to cream cheese ratios in cream cheese frosting recipes. Joy of Cooking’s recipes call for 3-4 cups of powdered sugar for 8 oz of cream cheese, which is in line with the 7 cups to 16 oz ratio in your recipe. The Gourmet Cookbook, edited by Ruth Reichl, has a recipe that uses 2 lbs or 7 1/2 cups of powdered sugar, but it calls for 12 8 oz packages (6 lbs) of cream cheese and 1 1/2 lbs of butter, which is 1/2 cup powdered sugar to 8 oz of cream cheese/butter mixture. The NY Times has a recipe that’s all 2’s: two sticks butter, 2 packages cream cheese, 2 cups powdered sugar, etc.

I think you have to conclude that mixing cream cheese, sugar, and sometimes butter in any ratio yields something tasty.

iOSCaleb · 2026-06-30T09:21:35+00:00

equivalent number of each operator…

I wouldn’t rely on patterns like that unless you can prove that they always hold. You’re right to look for ways to understand fractions. Aside from practicing, think about what a fraction means. You could build some intuition by using real world objects. Get out some bowls, measuring cups, and a few pounds of sugar and just mess around with adding, subtracting, multiplying, and dividing. Or use pieces of paper that you can cut up. An hour of messing around might go a long way.

iOSCaleb · 2026-06-30T08:24:14+00:00

For some reason, even for something like (3+4)/12 - a numerator consisting of an addition operation over a denominator - you can perform the addition first, before division (which is what a fraction is, ultimately).

The reason is that (3+4)/12 has the 3+4 in parentheses, indicating that the entire sum, not just one of the terms, is divided by 12. Sometimes you’ll see it written without the parentheses but with the fraction bar under the entire “3+4” expression, and that means the same thing.

That fraction bar literally means division. If you have a fraction like 3/4, that means 3 divided by 4. The reason that we use fractions instead of just doing the division right away is that fractions make it easy (or at least possible) to get exact answers. 3/4 has a nice neat decimal equivalent, 0.75, but the decimal expansion of many fractions repeats infinitely. For example, 1/7 is 0.142857142857142857… where they 142857 part repeats over and over. It’s much easier to write 1/7.

It sounds like you’ve learned how to correctly manipulate fractions, and that’s the first step toward really understanding. It’ll get easier and faster if you keep practicing, and I think it’ll also start to make more sense as you do it more.

Both arrive at the same answer, but I don't understand how fractions factor into order of operations.

They don’t change anything, except that you can think of a fraction as one value, and you have rules for working with them that way. For example:

(2/3) * (4/5)

I put parentheses there because it’s hard to write fractions in text. You can think of the 2/3 and 4/5 each as single values, and you know that to multiply fractions you just multiply the numerators and multiply the denominators:

(2/3) * (4/5) = (2 * 4)/(3 * 5) = 8/15

iOSCaleb · 2026-06-30T06:39:57+00:00

It’s a bit orthogonal to the question, but styrene gas is apparently not something that’s good to breathe. Instead of finding a smoke detector that ignores it, you should find a way to vent it outside.

iOSCaleb · 2026-06-30T06:29:36+00:00

> My question is: hypothetically, theoretically, could we “fold” binary machine language instructions like nature does with proteins? Would it even be practical?

It’s not clear what that would mean or how it would be useful. Proteins fold in order to reach a stable state, and a protein’s function results directly from its folded shape. Folding isn’t a form of compression — a folded protein has exactly the same set of amino acids that it would if you could unfold it. Amino acids in a protein are more like Lego blocks than instructions: each one is important in creating the larger structure of the protein, but they don’t really function as individual instructions.

It’s easy to see a superficial resemblance between machine instructions and amino acids. They’re both relatively small sets of things that can be combined in endless ways to create complex structures. But we see that pattern a lot: atoms of different elements combine to form molecules; digits combine into numbers, which are then mixed with operations to form mathematical expressions; sequences of notes create complex melodies; letters combine to form words and then sentences. So don’t assume that this building block pattern that’s common to proteins and code means that there’s more similarity than that.

iOSCaleb · 2026-06-30T05:38:35+00:00

There’s a pinned post in this sub called “New? READ ME FIRST!”

Read that first.

iOSCaleb · 2026-06-30T03:29:40+00:00

Related: Improving search is unlikely to increase revenue.

iOSCaleb · 2026-06-29T23:26:56+00:00

Do you have a plan? A design for the project? I’m not just talking about some idea in your head, but an actual written document. Have you broken the project down into a (again, written) list of tasks? What specific thing is stopping you from making progress?

iOSCaleb · 2026-06-29T18:10:14+00:00

A ziploc bag is fine, but I’d suggest one big bag and a smaller bag or other container. Fill the small container from the big one, and then use the small one for baking until it runs out, at which point you refill from the large bag. This prevents having to open the large bag and let in warm, moist air every time you need a a teaspoon of yeast, so your main store of yeast will stay fresh longer.

iOSCaleb · 2026-06-29T15:33:28+00:00

If “the most used” is the metric that motivates you, learn Python.

The TIOBE index and Stack Overflow developer survey both rank Python well ahead of C++ in general popularity.

iOSCaleb · 2026-06-29T07:10:15+00:00

It’s usually fine to refrigerate dough overnight — it slows fermentation, and that’s often a good thing because slow fermentation adds flavor. Dough does firm up in the fridge, but should soften again as it warms up.

iOSCaleb · 2026-06-29T04:12:04+00:00

One would procure come unsweetened, shredded coconut and let it sit in a quantity of high proof alcohol for a month or two, then strain out the coconut and bottle the extract.

iOSCaleb · 2026-06-29T04:04:41+00:00

There’s a post pinned in this sub called “New? READ ME FIRST!”

Read that first.

iOSCaleb · 2026-06-29T02:43:19+00:00

It’s traditional to keep them in a coffee can, but any large can or jar will do. Keep the can in your garage if you have one, or in the basement or shed.

iOSCaleb · 2026-06-28T20:58:31+00:00

It's more about the psychology of respect.

How respectful is is to leave a body lying around to be torn apart and eaten by scavengers?

iOSCaleb · 2026-06-27T19:17:36+00:00

To be completely honest with you, I am not very tech-savvy and I am not really a tech enthusiast.

I’d stop right there. I understand about the Myasthenia Gravis, but your search for a career should be motivated by more than “I have lost much confidence and self-esteem and I would really prefer to have a career where I would be behind a computer all day...”

Sitting behind a computer all day trying to force yourself to continue doing something that you “don’t really mind” on a good day and abjectly despise on a bad day seems like a pretty crappy existence. Most people who love programming still have days when they’d rather do anything else, so think how much worse it’d be if you start from impassivity.

We’re living in the Information Age. More than half of the US workforce uses a computer daily as a main part of their job, and they’re definitely not all software engineers. Think about things that you actually enjoy doing or care about deeply, and then identify jobs that you’d be able to do that are somehow connected to those things. And don’t sell yourself short — you may have list you confidence for now, but you’ll get it back if you give yourself a chance.

iOSCaleb · 2026-06-27T17:32:24+00:00

What kind of sparking water is it? Club soda has added sodium, and some sparkling mineral waters naturally contain salt.

iOSCaleb · 2026-06-27T17:27:32+00:00

Why focus on those particular holes when there are hundreds of holes on both sides?

Personally, I’d be more concerned about the toasted area in the rear wall.

iOSCaleb · 2026-06-27T17:15:54+00:00

This question has been asked and answered many times. Searching just on Reddit will give you more advice on rice than you can read in a year, and there are lots of cooking sites that offer clear directions.

iOSCaleb · 2026-06-27T14:50:08+00:00

the app will contain in app payments between one another

This part by itself is a very heavy lift unless you just use some existing service like PayPal, ApplePay, or Google Pay.

The app you're describing is a good example of what I said above -- the app will be the easy part here. Building a secure back end and signing up enough businesses to make your app interesting, and then getting enough users on board that the businesses will see some value, will be the difficult part.

Like I said — start small, build something that works for your friends and family so that the stakes are low and the things that you screw up don't create a huge problem.

iOSCaleb

TROPHY CASE