# Incredibly useful math concepts that everyone should know how to use

I have aphantasia. I can’t see pictures in my mind unless I’m dreaming. You guys who can do big math problems or “rotate this figure in your head”’ because you can “see” them? To me that’s like you’re cheating.

I can do the math problems but not rotate figures. With the latter I have enough trouble when it’s in front of my face.

We’ve had this discussion somewhat before. Most of the people, as I understand it, like me, do not see any literal images in our heads like we do using our eyes or like during dreaming. At least I sure as hell don’t. It’s more like what happens when you hear music in your head, or imagine a smell or something like that. I wouldn’t be surprised if some people get more concrete visuals, but it’s not like dreaming for most (I believe.) Of course, there is a big range of how well people can do this even without concrete visuals.

LIke when I do mental math, I often have to “refresh” my memory often to keep track of what’s going on and what numbers are where for more complicated problems. Kind of like how some computer memory (DRAM) requires constant pulsing of electricity to keep the capacitors charged and the data alive.

When you stated this in another thread I was surprised knowing that you are a photographer. Then I realized unlike a painter or sculptor you are creating images from reality, your perception of what you can see with your eyes may be greater than those who can form mental images. My wife has done a lot photography and I think she works that way also, she can select angles, background, and pose people in a way that produces pictures pleasing to the eye and complimentary to the subject. Then she also edits the images to improve them more, something much easier in this century with PhotoShop. OTOH I don’t see her operating on a purely conceptual level that well.

I do think most people have aphantasia to some degree except for those rare people, often artists who can visualize something in detail purely within their “mind’s eye”. I know I can visualize many things ‘geometrically’ while missing much of the real world detail of color, texture, and even perspective angles.

Rearranging formulas

I=E/R I can mentally rearrange to calculate Voltage or Resistance.

P=I*E is the power formula. I can easily calculate the approximate current. (wall voltage varies slightly from place to place)

A fridge rated at 475W draws approximately 475/115 or about 4Amps

Simple Algebra is always useful.

I’ve forgotten derivatives and integrals. I used them for years in electronics. But time has slipped by.

It bothers me that money math is no longer understood by younger cashiers. My ticket is \$9.14. I give the cashier a ten and 14 cents. l get surprised looks at Target and Walmart when the computer register tells them to give me a dollar bill.

Trig comes in really handy when making things.

This is especially true in machining. Most machining I do can be sorted out quickly with a pencil and paper and a calculator. If I’m feeling particularly lazy, an online triangle solve will do the job, but you still need to know what it is doing.

For a contrived example, imagine you want to make a bolt circle with 6 evenly spaced holes, each 10mm from the center…there’s a bit of trig to work out the triangles and distances, giving you X, Y coordinates for each hole.

There are always multiple ways to skin the cat, and bolt-circle tables and formulae in Machinery’s Handbook would also be a good option.

I once had a girlfriend who, as a schoolgirl, had a Saturday job on a market stall that sold greeting cards.

There were a lot of different prices and the stall had no fancy till. She was expected to calculate the total in her head, ring it up, take the cash and make change - fast. It was a skill that never left her.

Going back a lot further, before decimalisation we had a system where there were 12 pennies in a shilling. I went to a baker to buy a gross of penny buns and the assistant started to ring them up on his till one at a time. After less than a minute, I dropped the 12 shillings on the counter and left him to it.

Indeed. I don’t quite count as ‘lying with statistics’ a politician choosing to emphasize numbers that make things look good over numbers that make things look less good–in your example, the fact that inflation has slowed down will ultimately benefit consumers, but those consumers SHOULD be aware that the benefit won’t show up for quite a while, and ask the politician for more information.

The ‘lying’ outright by politicians often comes in the form of claims about correlations–claims that the correlations indicate causation. ‘Don’t vote for [insert Candidate] because murders happened when Candidate was in office!!!1!!!’

An example of lying with statistics, with “significance” being misinterpreted:

In my senior year in college in electrical engineering, we had a test that mixed English and metric units. One student didn’t complete one of the four questions, saying it was because the test didn’t include the conversion from mm to inches. He complained when the prof marked the question wrong, but the professor shook his head, saying you should know the basics like that at this point in your studies. The other students agreed with with the professor .

Yea, there are certain things that are permanently burned into my brain. 25.4 mm = 1 inch (or 2.54 cm = 1 inch, if you prefer) is one of them, but that’s because I am always doing unit conversions in Excel. Another is 273.16 K = 0.01 °C, but that’s only because I used to make water triple point cells all the time.

If you’re not using a conversion formula all the time, then I can understand how you wouldn’t have it memorized. It’s more important, IMO, to know how to perform a conversion after looking up the proportionality constant or formula (°F ↔ °C formula as an example of the latter). So I sorta disagree with his professor.

If a student had used 1 inch = 2.5 cm, or even 1 inch = 2.64 cm, and had consistently worked through using those numbers, well, that’d be a penalty, but a small one. But when a student just says “I can’t finish this problem because I don’t know how to convert inches to millimeters”, that’s a big penalty.

Here’s a real horror story that happened to a friend of mine during a power failure. He was buying something that cost \$1.99. He handed the clerk \$2 and expected her to give him a penny. Instead, she took out a pencil and paper and wrote down 2.00 and under it 1.99 and proceded to painfully subtract. 9 from 0, have to borrow 1 and to do that you have to borrow 1 from the 2 and she wrote down 1. Then 9 from 9 is 0 and then 1 from 1 is 0. She carried it out correctly, but was astonished to see the answer was \$0.01.

There is a difference between useful things some people should know, and useful things you feel everyone should know (because there are times you found them useful).

Obviously many things taught in math class have practical applications. If you are in science, engineering, computers, research or pure math you will probably use many more of these things than those who are not. But businessfolk, tradespeople or accountants still need many skills, and everyone would benefit from a few.

Calculations, basic algebra, basic statistics, money mathematics, understanding units and quick mental approximations really are important for almost everybody. You could add a lot to the list. Not that many people really need to be able to figure out what formula represents the curve made by one point on a rolling ball going along a flat surface, or that of a telegraph wire under gravity. or the intricacies of complex calculus.

The California school system once asked for Richard Feynman’s advice on its curricula. He felt too many children were taught too much “pure math”. You can criticize that view but there is some truth to it too.

In primary school we had ‘times tables’ games. I was really good at my times tables and I find them very useful even today. Any calculations up to about 30x30 I can basically do almost without thinking, and up to 100x100 within 5-10 seconds. I tend to break the complicated ones into ‘chunks’ which I can do easily, and then add together.

Totally unrelated to anything at all, but Richard Feynman was also once asked to advise on the school system in Brazil.
In the process of doing his day job he happened to stumble across a Escola de Samba, the organizations that perform in parades during Carnival, and joined them for their practice sessions, playing in the drum section. I don’t remember if he performed during Carnival, but it was super cool to imagine this uber physicist out there after work with the common folks from the favela just having a good time playing samba music.

I learned multiplication up to the 12’s. 12*11 is 132. I still entertain myself in waiting rooms by doing math in my head. Helps make the time go by faster.

I too learned multiplication as a game. I had a relative that quizzed me forwards and backwards. 6x7. and later 7x6=42

So one doesn’t have walk around all day long with a calculator in one’s pocket, let’s start with basic arithmetic. No, I’m not joking. We have many adults who can’t divide because they don’t know their times tables and can’t multiply. Next, it’s business math. People should understand ratio, proportion, and percent, and they should also have a basic understanding of probability and statistics. I’ve never a day in my life needed any of my post graduate math, so I think that is sufficient.

Almost everyone I know walks around with a calculator in their pocket.

Because it’s on your phone! LOL

It was my way of saying that they would be totally dependent on one if they didn’t know basic math.

Mental arithmetic in general is surely an “incredibly useful” skill. I think many people who work with numbers (or handle money— I cannot recall the last time I encountered an innumerate cashier) just do it automatically without thinking. For a simple example, if a mixture of A and B is 43% A, then it has to be 57% B.