This! We have tools and use them when needed for timeliness and accuracy. As long as you know HOW to arrive to the solution or solve the problem, you’re good.
I would agree with you, but I wouldn’t call this a useless skill. Small calculations like these are pretty frequent, and being able to do it quickly without pulling out a calculator can be an advantage, but by no means is it a necessary skill.
I would agree if it was something like the cube root of 2197, but a quarter of 512? Come on that should be almost instant for any high school educated human.
This thread is confusing to me. Isn't it pretty standard to say "the cube root" in place of "the principle cube root" (or even, "the real cube root") when talking about mental arithmetic?
Why are you getting down voted but dcterr isn't, when they're being pedantic in a way that isn't at all useful or relevant.
(Just to make myself unpopular with everyone, I don't agree with you that 512/4 is too simple to get rusty on, but I don't see why you're getting down voted - they're absolutely being a smartass)
>Isn't it pretty standard to say "the cube root" in place of "the principle cube root" (or even, "the real cube root") when talking about mental arithmetic?
Yep.
When I was in elementary school, in like fourth (american) grade, so like seven years old, we had to take these arithmetic tests. They were these sheets of cardboard with two digit addition, then subtraction, then multiplication, then division problems, with a little square cut out below the written problem to write your answer on a sheet of paper placed below the cardboard.
I, the entire year, never managed to pass the multiplication test. Not for lack of trying, I drilled and I drilled, but I just couldn't do that shit quickly. It was traumatic. I had been *good* at math, worked ahead, skipped a grade, but, couldn't do that shit. My parents were pissed, things got tense, things are *still* tense, looking back, that was the start.
I ended up staying in school 22 years, studying math, differential geometry and topology. I'm now a principal machine learning engineer. I made mathematics a (acceptable part of) my career.
You're projecting your skills, what you feel is important, on others. You don't have to be like that, you don't gain anything from it.
Okay, that was 22 years ago. Could you do those problems now? Is 512 x 0.25 in your head a skill that takes an unreasonable amount of time and practice to solve quickly, or is it the simplest application of the distributive law (500 x 0.25 + 12 x 0.25), a horse we beat to death in rings and fields?
No, I cannot comfortably do it in my head. I have a very weak mental eye, and cannot hold image details in my imagination for a sustained amount of time. I cannot "picture" the numbers in my mind and manipulate them. I need paper and pencil to do anything of this sort.
I draw lots and lots of pictures. I was quite good at analysis because the images don't need to have tons of detail, and they don't need to be manipulated dynamically. I can hold very simple static, abstract, images, but I cannot manipulate them. Low dimensional topology, knot theory, were indeed almost impossible for me.
I'm just trying to understand. Say you have a difficult assignment problem, work on it for a few hours and step away to take a break. You go for a walk or whatever. Are you able to continue thinking about the problem, or do you need paper in front of you to imagine possible solutions?
It depends. If the problem is very visual: show these two knot diagrams are isotopic, then the answer is a hard no, I cannot. I struggle with things in these domains that are obvious to others. I've just had to accept these topics are not for me.
In other cases, like in abstract algebra, my weak visual imagination is not so much of an impediment. If I'm thinking in pictures in these domains, they're very basic and abstract, rectangles lined up that represent cosets, something like that.
In the middle, say analysis, it helps to have sat down and drawn pictures beforehand, then I can kind of "take them with me". The act of physically drawing things helps me maintain them.
In all cases, if it is required to *dynamically* manipulate an image in my mind, as is the case with arithmetic, keeping track of intermediate results, I'm quite weak, and below the curve of I would suspect all people, not just mathematicians. If the pictures are simple, static, and abstract, I can manage. I can picture basis vectors of a vector space, I can't picture the curve of intersection of two surfaces embedded in three space.
This is the fastest mental math. If numbers were way more hugely complicated, you round to easy to compute numbers and compute the small differences separately.
Yes, Minecraft uses powers of 2 intentionally, reflecting common practices in computer science and game development. Here are a few key areas where powers of 2 are evident in Minecraft:
1. **Chunk Size**: Minecraft's world is divided into chunks, each measuring 16x16 blocks. The number 16 is 2^4, a power of 2. This chunk size helps in efficiently managing and rendering the game world.
2. **World Height and Depth**: The default world height limit in many versions of Minecraft is 256 blocks (from -64 to 319 in more recent versions), which is 2^8.
3. **Block IDs and Data Values**: Originally, block IDs and data values were designed around powers of 2 for efficient storage and processing.
4. **Textures**: The game's textures are often 16x16 pixels (again, 2^4), which allows for optimized memory usage and processing speeds.
Using powers of 2 aligns well with the binary nature of computer systems, allowing for more efficient computation and memory use. This is a deliberate design choice by the developers to enhance performance and scalability.
Edit: That response was from ChatGPT b/c I was too lazy to type. Minecraft was originally developed as a project to learn Java through self instruction by making a game. The developer happened to stumble onto one of the best sandbox games of all time.
Faster if you realise 512 = 2^9 and 4 is 2^2 so you just need 2^7 which you can possibly recall so O(1)😂. Especially if you're in CS. These are special numbers because of their significance in the binary system.
I’d suppose the opposite. OP has done areas at a very advanced level, so I’d deduce he’s definitely smart. And it’s a trait of smart people to get mad at getting things wrong, especially when they think it ought to be trivial
>And it’s a trait of smart people to get mad at getting things wrong
It's a trait of obsessive and competitive people. Although obsessive and competitive people do also tend to be smarter (because they put more effort into things that develop intelligence).
I once heard that the more a person goes deep on maths the worst they get o basic calculus (Like you did, things like 7*29 - 256/8) etc and i couldnt agree more seeing some teachers in my life just unravel some crazy hard questions and when it comes to the end for them to do some "667 + 148 + 319" to solve the question they take like 2 minutes lol
I've always been pretty good at math. And as I went through things like linear algebra and multivariable calculus, the only points I ever got taken off my exams were things like forgetting negative signs and fucking up basic arithmetic like 6x7.
One of my all-time favorite quotes from an undergrad math professor of mine: “I have forgotten more math than most people will ever know.” You’ve made mental space for better and more complicated things; sometimes that comes at the price of quick arithmetic, so be it.
I personally know a lot of people who can’t do mental calculations like they used to (myself included). It sucks to feel like you’ve lost the skill, but it’s super common and is in no way indicative of a loss of intellect or greater ability.
Like others have said, you retain the knowledge that you use and practice frequently. If anyone in any academic environment judges you based on your ability to do elementary school math, that’s much more telling about them.
OP, you don’t have to worry about this at all.
The people who quickly do arithmetic in their head are the people who frequently do arithmetic in their head.
It’s also true that not everyone does math in their head. An engineer recently talked about struggling with it. I struggled with it, and I struggled with 0.25 times 512.
Anyone who says you’ve gotta be able to do some purity test is a poser.
*does a kickflip and skates away*
Yeah its just practice, I was studying for quant jobs and got pretty quick at it, before I studied I was really slow. You can learn certain techniques to make it easier as well.
For me it was learning mental math shortcuts, picking a couple of favorite ones, and then doing them a lot. Frankly, you can get pretty far practicing doubling and halving numbers. Start with even numbers then practice it with odd numbers. Also, turning decimals back to fractions whenever possible. People go into vapor lock when they see 0.25, as opposed to realizing oh that's just half of a number and then half that.
When I was young and had to take exams that calculators are not allowed, I trusted my calculations by my hands. but now it is a different story, I usually write codes and let computers do all the arithmetics. My engineering background makes me very realistic and I only care about how to do things correct, not thinking much about the way to do it.
For example when I take elementary level solid mechanics course. They usually ask you to calculate the stress and strain, which is basically using formulas involving forces, displacements, and material properties. The Young’s modulus is usually in GPa and length is usually in cm, but sometimes it could be messier when they give you imperial units and you will have fun canceling the units such as inch and pound before doing the calculations, which it is possible that you make mistakes. To be lazy why not just convert everything to SI and you don’t need to worry about the units at all. I usually do this and find the answer by the calculator or python, whatever is allowed for the exam.
I do think my ability to do basic arithmetic gets weakened, but I am not too worried about it.
well you can try and force yourself to do mental calculations instead using python for even the simple ones, that practice will make you faster.
also, both 512 and 0.25 are powers of two, so computer people who has powers of two memorized can tell the answer in 1-2 seconds
Learn the powers of two up to 2^10 by heart . It will save you time.
The calculation you mentioned is simply 512/4 = 512/2/2 = 256/2 = 128
But yes. It's frequent for people that have invested in higher mathematics to be rusty in calculations. It's just a matter of practice and converting the initial calculation to easier ones.
During one of my favorite classes, the professor said something along the lines of "what is 26 - 43, well I'm not sure, but it is negative, so the theorem is true."
I never memorized all the times table in elementary school. During tests in high school through grad school that didn't allow calculators I often would find it helpful to write out some large number and add it to itself multiple times until I had a list of that number times everything up to 10 so I could do multiplication and division with that number quicker.
Being able to do quick mental arithmetic has very little to do with how good you are at math. Most of Math has very little to do with multiplying numbers quickly in you head.
Perhaps it is time to go back to basics. I am an EE so 2^n from N=0 to 24 I know by heart. 0.25 means divide by 4.
It is patterns like these that keep us curious. Machine learning about recognizing pattern. Mathematics about recognizing patterns. Keep this in mind and it will help you in a long run.
I'm more the opposite as far as math goes. I'm like a human calculator. I can multiply two three-digit numbers in my head, but I have a hard time with abstract concepts unless I can visualize them. I guess that just goes to show that our brains are all wired differently, even among mathematicians.
Think about it this way. Would you rather be good at doing the same thing as simplest calculator, be good at all the topics you listed you have been through, or be good at both and give up the entire rest of your life because you have to spend all your time practicing?
I want to be good at things that come up in my life. If I go for grocery shopping, I want to able to calculate the discounts easily. If I attend a conference lecture, I want to understand the lecture to a decent level. So, an optimal trade-off between simple calculations and advanced math. Of course, I am not perfect and I don’t want to be perfect in everything in life. But, at least near perfect level in things I choose to be in life.
Simplify and solve, it's the way of mathematics. take 512 and halve it, 250 plus 6, 256, right? Not very hard or time consuming. Now halve it again, 125 plus 3, again easy and fast. So, in about 5 seconds, the answer is 128. The trick is in recognizing that .25 is a quarter, which is half of a half.
It’s more about practice than anything. I’m pretty sure 3rd graders would annihilate me at this type of stuff even though I’m a prof at the university level. No shame at all.
Nice to know this, remember we too were once the third graders with god level computational prowess.
Seems like kids are better than adults in math and chess.
Let me tell you the only reason I was able to do it in under 20s (not impressive by any means) is because I'm cs student and I touch computers a lot and repaired and replaced a lot of ssds
If you tutor high school students or freshman, without using calculators, your skills will come back quickly. Even volunteer G tutoring once a month can bring you back up to speed.
Sometimes the very low, trivial things get lost in the process of expanding and evolving to accommodate more advanced techniques. Imagine how dumb I feel forgetting words like “microwave” and “vacuum” as I explain to people the algorithmic theories behind machine learning. It’s all relative.
Definitely not for ML. But you’d be surprised how often needing to know those words when communicating with humans. So it’s more an issue for continued human interaction before I end up just talking to AI. Lol
it's funny, but it's kinda true. it seems like people lose the ability to perform simple tasks. for example, my memory became a bit slower(the speed of recall). I don't think it's bad, though
512 is a power of 2. Computer nerds often recognize the first ten or so:
1 2 4 8 16 32 64 128 256 512 1024
And often 65536
25% means divide by 2 then divide by 2 again, so all I have to do is go back to powers of 2
Math in your head is a cognitive task that requires far more attention than people think. If you're under stress because you're in a bad environment or put on the spot folding like this is perfectly normal.
This is probably almost all in your head, the worry you can't do the math is making you focus on that negative feeling instead of doing the math.
I knew the answer to that about 3 seconds after I read it because I don't have to do math. I've memorized the typical decimal progression of binary numbers. .25 is divide by four. I just walk thru the list real fast in my head and notice it's 1/4 which is 128.
Doing fresh l each individual number like a calculator does not work well for humans we need to use mnemonic tricks to calculate fast. Most people aren't even aware they do it.
You gotta practice! Math is a use or lose it thing.
I do inventory a lot, my counts have to be right. Simple math has to be double checked and it just becomes habit.
Don't laugh and take this seriously. But give looking into common core math that's taught to grade schoolers today. Try Kahn Academy. You'll feel silly but it will give you problems to practice on.
Common core gets a bad wrap due to politics and ignorance. The core methods behind it provide the number tools for people to find ways to do math in their head without resulting to brute force calculation. Very few people do that.
i mean thats what doing theory does to u. i was the arithmitics champ in elementary scchool out of 180+ kids now i need 10 seconds to subtract 3 digit numbers
Do you walk from your car to work? Take dumps? Just squeeze in some mental math during times you got nothing better to do. There are apps and such or you can jus come up with problems in your head and verify your answer with a calculator. I do mental math because it keeps my brain sharper and quicker and I’m a naturally slow person
Used to have fun with number plates of cars, but life has become harsh that I am not the carefree teenager anymore. Used to be like this number is prime, oh no this is a sum of two squares... And now how much is that Honda ? Shall I go for a second hand Ford 🙃
As pointed out in the other answers, you need to write the numbers as powers of 2. And this works quote well in general for mental multiplications. For example, take 61\*43. This is still easily doable mentally in the conventional way, but it does require you to memorize a few intermediary results and then add those up. But you can also decompose one of the factors into powers of two as follows. For example:
61 = 64 - 3 = 2\^6 - 2\^2 + 1 = (2\^4 - 1)\*2\^2 + 1
So, multiplying 43 by 61 can be done by doubling 43 4 times, subtract 43 from that and then double that two times and then add 43. So, you see that you now don't need to remember multiple results from different intermediate computations. You only need to remember the outcome of a computation and that is then the input for the next step. So, the proces is linear, it's not branching out, which makes it easier for mental computations.
Also 512 is a common number, for computing at least, and it’s likely that he knew the quick math on this like most of us know the 0-10 multiplication table.
Possibly this is from computers/bytes (powers of 2), I don't think I can literally do 512 x 0.25 very quickly anymore (in my 30s now and have lost some mental quickness for sure), but I've seen it so much I know half of 512 is 256, half again is 128. Also seems reasonable to recognize 2^9 / 2^2 = 2^7
Yes, I agree; In school I used to do multi-step evaluations in my head, and teachers used to take points off of my test until they eventually just accepted that I simply did it in my head…though of course in higher Math branches, that is hardly possible and a calculators (computers in general) can do the rest and one must simply understand the concepts and have the ability to solve or evaluate it (with the use of computers to assist), though I may not have to tell you or the person that made the post this since they survived…a lot lol.
Though I was never arrogant about it. I used to try to explain to people how I was able to do it and also help people that aren’t as good at math as others may be
I mean you can do it in under 10 seconds(or even 5) if you take a quarter of 500(125) and a quarter of 12(3) and sum them. I think the exponent thing is unnecessarily convoluted, but thats just my take.
Don't feel too bad. I've heard that when Einstein was in grade school, he tried to convince his math teacher that 1 + 1 = 1, because if you add one bag of sand to another one, you're still left with one bag!
Yup. And just the binary stuff in general. I'm not a CS major but work with computers and have effectively memorized powers of two up to 8192 so that particular example would have been quick for the CS folks.
Bro I understand quantum physics without explanation but math beyond simplicity I can relate to goes past my grasp for knowledge. However, my wisdom overflows.. Pls dont feel stupid
Hmmm - I knew the answer instantly, but I think that is only because of familiarity with powers of 2, which was taught in my elementary school, along with the times table up to 25x25. Most of us top out with things we never learned well or with which we once had facility but have recently had little cause to use.
As an older guy, I can remember that, when I was a child, any unimpaired adult could reasonably be expected to look at a page with a column of three to five digit numbers and sum them nearly as fast as they could scan the page. As a child, I could do this as well, but I am certain I would be much slower and more error-prone now, as this is just not a task anyone has generally needed to do since the invention of the calculator and the spreadsheet.
We lose what we never use. I think this has little relationship to how many complex abstractions we have mastered. If you want to get good at basic arithmetic, you will likely need to do some now and then. ;-}
It's really a rather enjoyable exercise and fun rabbit trail - just recall that working with much more than integers and ratios was broadly unknown up until the mid 1700s, even later in many places, yet people managed to solve all kinds of problems for which we would now use more advanced methods. It can also revive a little of the zest for math when you reacquaint yourself with the properties of numbers.
Just for fun, here is the first such problem which I was given as a pre-school child: Add up all the numbers from 1 through 100. You have ten seconds. What is the answer?
For what it is worth, I didn't succeed the first time I tried this as a child, but once I understood what was at play, I succeeded at the next question, which is: Add up the value of the digits (i.e. the number 15 has a digit value of 6) in all the numbers between one and one billion. You have one minute. What is the answer?
;-}
Yes. I grew up in an area where arithmetic and logic puzzles were common, and were an everyday teaching tool. This is what we had \*instead\* of kindergarten or Pre-K.
This particular puzzle is really a quite simple task, which most kids around six who can count, play cards, dominos, or similar games, but who have not yet been introduced to multiplication would fail at initially, until they puzzled out (or were gently led to) a successful way to approach it, at which point it is typically a real insight for them and generally cements the understanding far more than simply being taught a rule or procedure.
Typically it goes something like this:
Adult: presents puzzle
Child: starts to add then has a moment of pure panic as they realize there is no way they are going to add all those numbers individually in the next few seconds
Adult: lets the child work at it
Persistent Child: works at it for a long time, generally comes up with a wrong answer, but is praised for their persistence
or
Less Persistent Child: tries for a while then asks for help
Adult: Well, what if we took the 1 from the beginning and the 100 from the end, and added those how much would that be?
Child: 101
Adult: Hmm, well, what if we took the 99 and the 2, or the 98 and the 3?
Child: Oh!
Adult: How many times can we do this?
etc...
Some children who can count well will get to the point of 50 sets of a 101 and be able to understand how move the 50 over a couple of places and then add in another 50. Some may not. But nearly all will get an understanding of the principle involved along with a real power charge out of the feeling that they have a secret insight into how to do something that just moments before they believed to be flatly impossible for themselves.
The 'Persistent Child' then gets the next puzzle. The 'Less Persistent Child' is given more variations of the same puzzle over the next days/weeks.
By the time they went to their first year of school, nearly every child could do most basic arithmetic tasks proficiently, and had a handle on some of the basics of geometry, set theory, combinatorics, and knew how to solve a variety of everyday rural problems, like calculating how much garden space was needed for a crop of particular yield, how to square off a new building, how to calculate time and season from the stars, etc.
The intent of the first question is to get a child to think in sets. 101*100/2* is obviously correct but perhaps a bit much to expect of a six year old, but 50 sets of 101 is not.
Now, let's assume our six year old doesn't have a calculator or a slide rule, and hasn't yet been introduced to exponents...
You sure you understood that second puzzle? ;-}
oh ghosh! did fast reading and realised how much my answer is wrong. You're asking about the digits while I calculated all the numbers. For the second puzzle: there is A = {1,..,9} single digit numbers which sum to 45. Then, there is {11,...99} where each digit in A occurs 20 times in each place, so the digit value sum A \* 20 \* 2. And so on Is my reasoning right?
Not sure but what you might get there using your approach, but there is a much simpler way; which is much more analogous to how to solve the first puzzle using sets.
At first I thought you were bragging then I did it in under 3 seconds not having taken math past Gr. 10. For the good of humanity it is imperative you not spread your moronic genes. I am sorry.
You are quick at what you practice. Don't lament being bad at mostly useless skills.
This! We have tools and use them when needed for timeliness and accuracy. As long as you know HOW to arrive to the solution or solve the problem, you’re good.
I would agree with you, but I wouldn’t call this a useless skill. Small calculations like these are pretty frequent, and being able to do it quickly without pulling out a calculator can be an advantage, but by no means is it a necessary skill.
Most people are only good at useless skills.
I would agree if it was something like the cube root of 2197, but a quarter of 512? Come on that should be almost instant for any high school educated human.
You realize that there are three cube roots of 2197, don't you?
You got me, Einstein
There are three complex cube roots of every nonzero complex number - basic complex arithmetic.
When you punch 2197 to the power 1/3 into a pocket calculator, does it give you three roots or are you just being a smartass for no reason?
You’re gonna feel silly when you google this
You should feel silly for leaving this comment. I'm not saying this person is wrong, I'm saying they're being pedantic for no good reason.
This thread is confusing to me. Isn't it pretty standard to say "the cube root" in place of "the principle cube root" (or even, "the real cube root") when talking about mental arithmetic? Why are you getting down voted but dcterr isn't, when they're being pedantic in a way that isn't at all useful or relevant. (Just to make myself unpopular with everyone, I don't agree with you that 512/4 is too simple to get rusty on, but I don't see why you're getting down voted - they're absolutely being a smartass)
He’s being pedandic because the other guy is being an asshole
How does that help though? Now there's just two assholes
Sometimes you just want to make an asshole feel stupid for being an asshole I guess
>Isn't it pretty standard to say "the cube root" in place of "the principle cube root" (or even, "the real cube root") when talking about mental arithmetic? Yep.
When I was in elementary school, in like fourth (american) grade, so like seven years old, we had to take these arithmetic tests. They were these sheets of cardboard with two digit addition, then subtraction, then multiplication, then division problems, with a little square cut out below the written problem to write your answer on a sheet of paper placed below the cardboard. I, the entire year, never managed to pass the multiplication test. Not for lack of trying, I drilled and I drilled, but I just couldn't do that shit quickly. It was traumatic. I had been *good* at math, worked ahead, skipped a grade, but, couldn't do that shit. My parents were pissed, things got tense, things are *still* tense, looking back, that was the start. I ended up staying in school 22 years, studying math, differential geometry and topology. I'm now a principal machine learning engineer. I made mathematics a (acceptable part of) my career. You're projecting your skills, what you feel is important, on others. You don't have to be like that, you don't gain anything from it.
wow you're an inspiration!
Okay, that was 22 years ago. Could you do those problems now? Is 512 x 0.25 in your head a skill that takes an unreasonable amount of time and practice to solve quickly, or is it the simplest application of the distributive law (500 x 0.25 + 12 x 0.25), a horse we beat to death in rings and fields?
No, I cannot comfortably do it in my head. I have a very weak mental eye, and cannot hold image details in my imagination for a sustained amount of time. I cannot "picture" the numbers in my mind and manipulate them. I need paper and pencil to do anything of this sort.
How did you pass analysis exams if you cannot hold an image in your head (eg. counterexamples)?
I draw lots and lots of pictures. I was quite good at analysis because the images don't need to have tons of detail, and they don't need to be manipulated dynamically. I can hold very simple static, abstract, images, but I cannot manipulate them. Low dimensional topology, knot theory, were indeed almost impossible for me.
I'm just trying to understand. Say you have a difficult assignment problem, work on it for a few hours and step away to take a break. You go for a walk or whatever. Are you able to continue thinking about the problem, or do you need paper in front of you to imagine possible solutions?
It depends. If the problem is very visual: show these two knot diagrams are isotopic, then the answer is a hard no, I cannot. I struggle with things in these domains that are obvious to others. I've just had to accept these topics are not for me. In other cases, like in abstract algebra, my weak visual imagination is not so much of an impediment. If I'm thinking in pictures in these domains, they're very basic and abstract, rectangles lined up that represent cosets, something like that. In the middle, say analysis, it helps to have sat down and drawn pictures beforehand, then I can kind of "take them with me". The act of physically drawing things helps me maintain them. In all cases, if it is required to *dynamically* manipulate an image in my mind, as is the case with arithmetic, keeping track of intermediate results, I'm quite weak, and below the curve of I would suspect all people, not just mathematicians. If the pictures are simple, static, and abstract, I can manage. I can picture basis vectors of a vector space, I can't picture the curve of intersection of two surfaces embedded in three space.
If it helps, do it like 512/4 = (400 + 100 + 12) ÷ 4 = 100 + 25 + 3 = 128
Faster. .25 is half of half. So just half 512 twice. 256. 128. Done
This is the fastest mental math. If numbers were way more hugely complicated, you round to easy to compute numbers and compute the small differences separately.
Oh yeah, this is how i did it. And every minecraft player know half of 128, the stack size 64 ;)
I love that Minecraft math is based on exponents of 2 like computer memory.
As a child 64 limit didn't make any sense lol. "Why not 60, 65 or 70?"
That was 100% done on purpose
They did it on purpose?
Yes, Minecraft uses powers of 2 intentionally, reflecting common practices in computer science and game development. Here are a few key areas where powers of 2 are evident in Minecraft: 1. **Chunk Size**: Minecraft's world is divided into chunks, each measuring 16x16 blocks. The number 16 is 2^4, a power of 2. This chunk size helps in efficiently managing and rendering the game world. 2. **World Height and Depth**: The default world height limit in many versions of Minecraft is 256 blocks (from -64 to 319 in more recent versions), which is 2^8. 3. **Block IDs and Data Values**: Originally, block IDs and data values were designed around powers of 2 for efficient storage and processing. 4. **Textures**: The game's textures are often 16x16 pixels (again, 2^4), which allows for optimized memory usage and processing speeds. Using powers of 2 aligns well with the binary nature of computer systems, allowing for more efficient computation and memory use. This is a deliberate design choice by the developers to enhance performance and scalability. Edit: That response was from ChatGPT b/c I was too lazy to type. Minecraft was originally developed as a project to learn Java through self instruction by making a game. The developer happened to stumble onto one of the best sandbox games of all time.
xD, I noticed from the style of writing but the effort is appreciated
Faster if you realise 512 = 2^9 and 4 is 2^2 so you just need 2^7 which you can possibly recall so O(1)😂. Especially if you're in CS. These are special numbers because of their significance in the binary system.
Check out the Minecraft thread embedded in this thread.
And if 256 didn't come instantly, 500 + 12 gives halves of 250 + 6.
I did 250 / 2 = 125 for some reason, then 12 / 4 to get the 3.
Knowing the powers of 2 helps
I used exponents which I feel like it's technically faster, but also a bit convoluted lol Just immediately recognized 512 as 2^9
That's the way I did it but it still took me longer than OC's method would've.
I guess I am biased because that particular question was computer memory based.
That's what I did.
Yes thats the easiest n fastest way. Its the way I also do.😎
What are you talking about? That just the half of the half of a power of two :)
This algo is super fun for mental math,thanks
I highly doubt someone that did those areas seriously would get upset because didnt did a quick computation (even a stupid one).
such an absurdly strange list of topics covered, too.
I’d suppose the opposite. OP has done areas at a very advanced level, so I’d deduce he’s definitely smart. And it’s a trait of smart people to get mad at getting things wrong, especially when they think it ought to be trivial
>And it’s a trait of smart people to get mad at getting things wrong It's a trait of obsessive and competitive people. Although obsessive and competitive people do also tend to be smarter (because they put more effort into things that develop intelligence).
Better put.
This! You have deduced my traits 😀
I feel things right now. Maybe this is what Sherlock felt always?
Maybe 😇
2^(9-2)
128 (minecraft math)
You have 8 stacks of items and need to separate them into 4 chests, how many items are in each chest?
I once heard that the more a person goes deep on maths the worst they get o basic calculus (Like you did, things like 7*29 - 256/8) etc and i couldnt agree more seeing some teachers in my life just unravel some crazy hard questions and when it comes to the end for them to do some "667 + 148 + 319" to solve the question they take like 2 minutes lol
Dude. Fr, as a student who likes math, my basic addition skills definitely declined while taking calculus , and I predict it will only get worse 😂
Well you should be getting plenty of practice considering the legwork of solving calculus problems is all algebra and arithmetic
Yeah but most of the time in my classes we focus on the calc concepts not the legwork.
I've always been pretty good at math. And as I went through things like linear algebra and multivariable calculus, the only points I ever got taken off my exams were things like forgetting negative signs and fucking up basic arithmetic like 6x7.
One of my all-time favorite quotes from an undergrad math professor of mine: “I have forgotten more math than most people will ever know.” You’ve made mental space for better and more complicated things; sometimes that comes at the price of quick arithmetic, so be it. I personally know a lot of people who can’t do mental calculations like they used to (myself included). It sucks to feel like you’ve lost the skill, but it’s super common and is in no way indicative of a loss of intellect or greater ability. Like others have said, you retain the knowledge that you use and practice frequently. If anyone in any academic environment judges you based on your ability to do elementary school math, that’s much more telling about them.
Thanks for the kind words 😀
OP, you don’t have to worry about this at all. The people who quickly do arithmetic in their head are the people who frequently do arithmetic in their head. It’s also true that not everyone does math in their head. An engineer recently talked about struggling with it. I struggled with it, and I struggled with 0.25 times 512. Anyone who says you’ve gotta be able to do some purity test is a poser. *does a kickflip and skates away*
Yeah its just practice, I was studying for quant jobs and got pretty quick at it, before I studied I was really slow. You can learn certain techniques to make it easier as well.
How did you practice speed? Did you consult any material? Practice questions? Did you learn Vedic maths or any tricks or is it just practice?
Zetamac and tradermTh are good websites
Thanks!
For me it was learning mental math shortcuts, picking a couple of favorite ones, and then doing them a lot. Frankly, you can get pretty far practicing doubling and halving numbers. Start with even numbers then practice it with odd numbers. Also, turning decimals back to fractions whenever possible. People go into vapor lock when they see 0.25, as opposed to realizing oh that's just half of a number and then half that.
> learning mental math shortcuts Where did you learn it from?
My favorite book was Arithmetricks by Edward Julius.
When I was young and had to take exams that calculators are not allowed, I trusted my calculations by my hands. but now it is a different story, I usually write codes and let computers do all the arithmetics. My engineering background makes me very realistic and I only care about how to do things correct, not thinking much about the way to do it. For example when I take elementary level solid mechanics course. They usually ask you to calculate the stress and strain, which is basically using formulas involving forces, displacements, and material properties. The Young’s modulus is usually in GPa and length is usually in cm, but sometimes it could be messier when they give you imperial units and you will have fun canceling the units such as inch and pound before doing the calculations, which it is possible that you make mistakes. To be lazy why not just convert everything to SI and you don’t need to worry about the units at all. I usually do this and find the answer by the calculator or python, whatever is allowed for the exam. I do think my ability to do basic arithmetic gets weakened, but I am not too worried about it.
I now let python do all the calculations even the elementary ones 😂
well you can try and force yourself to do mental calculations instead using python for even the simple ones, that practice will make you faster. also, both 512 and 0.25 are powers of two, so computer people who has powers of two memorized can tell the answer in 1-2 seconds
Learn the powers of two up to 2^10 by heart . It will save you time. The calculation you mentioned is simply 512/4 = 512/2/2 = 256/2 = 128 But yes. It's frequent for people that have invested in higher mathematics to be rusty in calculations. It's just a matter of practice and converting the initial calculation to easier ones.
buddy he probably only knows from minecraft being in stacks of 64. 25% of 512 is just divided by 4 which is 100 is so 128
Remember that a full passage through the academic system takes you from knowing nothing about everything to know everything about nothing.
During one of my favorite classes, the professor said something along the lines of "what is 26 - 43, well I'm not sure, but it is negative, so the theorem is true."
Once Grothendieck assumed 57 is a prime 😂
I never memorized all the times table in elementary school. During tests in high school through grad school that didn't allow calculators I often would find it helpful to write out some large number and add it to itself multiple times until I had a list of that number times everything up to 10 so I could do multiplication and division with that number quicker. Being able to do quick mental arithmetic has very little to do with how good you are at math. Most of Math has very little to do with multiplying numbers quickly in you head.
Um, write an algorithm to do it in PC, simplifying arithmetics. So your age won't drag you back
A python for loop is easier to execute though 😂
Need a whole algorithm to sort all of those when you get older(# Till a point we look like high tech SF film(#
Perhaps it is time to go back to basics. I am an EE so 2^n from N=0 to 24 I know by heart. 0.25 means divide by 4. It is patterns like these that keep us curious. Machine learning about recognizing pattern. Mathematics about recognizing patterns. Keep this in mind and it will help you in a long run.
Thanks a lot for the advice 😀
I'm more the opposite as far as math goes. I'm like a human calculator. I can multiply two three-digit numbers in my head, but I have a hard time with abstract concepts unless I can visualize them. I guess that just goes to show that our brains are all wired differently, even among mathematicians.
Think about it this way. Would you rather be good at doing the same thing as simplest calculator, be good at all the topics you listed you have been through, or be good at both and give up the entire rest of your life because you have to spend all your time practicing?
I want to be good at things that come up in my life. If I go for grocery shopping, I want to able to calculate the discounts easily. If I attend a conference lecture, I want to understand the lecture to a decent level. So, an optimal trade-off between simple calculations and advanced math. Of course, I am not perfect and I don’t want to be perfect in everything in life. But, at least near perfect level in things I choose to be in life.
I'm feeling the same way too. But I didn't even know which mathematical subjects you're talking about.
Simplify and solve, it's the way of mathematics. take 512 and halve it, 250 plus 6, 256, right? Not very hard or time consuming. Now halve it again, 125 plus 3, again easy and fast. So, in about 5 seconds, the answer is 128. The trick is in recognizing that .25 is a quarter, which is half of a half.
Maybe stress of friend’s expectation leading to dissapointment (obviously hyperbolizing) played a role in your performance
definitely that played a role too
I have a formal math education and I can barely do 7*9. Arithmetic is not mathematics!
is it 69 ? 😅🤓
I would just do the following: 512*0.25=2^9 * 2^(-2) = 2^7 =128
I only know that from Minecraft lol
It’s more about practice than anything. I’m pretty sure 3rd graders would annihilate me at this type of stuff even though I’m a prof at the university level. No shame at all.
Nice to know this, remember we too were once the third graders with god level computational prowess. Seems like kids are better than adults in math and chess.
python -i Google it.
Let me tell you the only reason I was able to do it in under 20s (not impressive by any means) is because I'm cs student and I touch computers a lot and repaired and replaced a lot of ssds
If you tutor high school students or freshman, without using calculators, your skills will come back quickly. Even volunteer G tutoring once a month can bring you back up to speed.
Oh I plan on refreshing that a bit
512 is the Integral from 0 to 512 of 1, so just integrate from 0 to 512/4 and you get 128, duh.
Wholesum way to do it
Sometimes the very low, trivial things get lost in the process of expanding and evolving to accommodate more advanced techniques. Imagine how dumb I feel forgetting words like “microwave” and “vacuum” as I explain to people the algorithmic theories behind machine learning. It’s all relative.
Unless you need physics, why do you need to remember “microwave” or “vacuum” though for ML ?
Definitely not for ML. But you’d be surprised how often needing to know those words when communicating with humans. So it’s more an issue for continued human interaction before I end up just talking to AI. Lol
This is so common, there's a [meme](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTlS-fkSDKqQIIBlwEM0dH4Hm1hSWho5vBVNg&s) dedicated to this.
Oh wow 😂😂
I did this 1/4 (500) = 125 1/4(12) = 3 ergo 1/4 (512) = 128
Nice
it's funny, but it's kinda true. it seems like people lose the ability to perform simple tasks. for example, my memory became a bit slower(the speed of recall). I don't think it's bad, though
I just did 512/2 = 256, 256/2 = 64... And now I feel your mood
Join the company 😂
Err easy 512 256 128... Base 2
What would you do if it was 0.15*516
51.6 + 25.8 77.4
512 is a power of 2. Computer nerds often recognize the first ten or so: 1 2 4 8 16 32 64 128 256 512 1024 And often 65536 25% means divide by 2 then divide by 2 again, so all I have to do is go back to powers of 2
Math in your head is a cognitive task that requires far more attention than people think. If you're under stress because you're in a bad environment or put on the spot folding like this is perfectly normal. This is probably almost all in your head, the worry you can't do the math is making you focus on that negative feeling instead of doing the math. I knew the answer to that about 3 seconds after I read it because I don't have to do math. I've memorized the typical decimal progression of binary numbers. .25 is divide by four. I just walk thru the list real fast in my head and notice it's 1/4 which is 128. Doing fresh l each individual number like a calculator does not work well for humans we need to use mnemonic tricks to calculate fast. Most people aren't even aware they do it. You gotta practice! Math is a use or lose it thing. I do inventory a lot, my counts have to be right. Simple math has to be double checked and it just becomes habit. Don't laugh and take this seriously. But give looking into common core math that's taught to grade schoolers today. Try Kahn Academy. You'll feel silly but it will give you problems to practice on. Common core gets a bad wrap due to politics and ignorance. The core methods behind it provide the number tools for people to find ways to do math in their head without resulting to brute force calculation. Very few people do that.
i mean thats what doing theory does to u. i was the arithmitics champ in elementary scchool out of 180+ kids now i need 10 seconds to subtract 3 digit numbers
lol 😂
Do you walk from your car to work? Take dumps? Just squeeze in some mental math during times you got nothing better to do. There are apps and such or you can jus come up with problems in your head and verify your answer with a calculator. I do mental math because it keeps my brain sharper and quicker and I’m a naturally slow person
Used to have fun with number plates of cars, but life has become harsh that I am not the carefree teenager anymore. Used to be like this number is prime, oh no this is a sum of two squares... And now how much is that Honda ? Shall I go for a second hand Ford 🙃
As pointed out in the other answers, you need to write the numbers as powers of 2. And this works quote well in general for mental multiplications. For example, take 61\*43. This is still easily doable mentally in the conventional way, but it does require you to memorize a few intermediary results and then add those up. But you can also decompose one of the factors into powers of two as follows. For example: 61 = 64 - 3 = 2\^6 - 2\^2 + 1 = (2\^4 - 1)\*2\^2 + 1 So, multiplying 43 by 61 can be done by doubling 43 4 times, subtract 43 from that and then double that two times and then add 43. So, you see that you now don't need to remember multiple results from different intermediate computations. You only need to remember the outcome of a computation and that is then the input for the next step. So, the proces is linear, it's not branching out, which makes it easier for mental computations.
Well I do it differently 61*40=2440 61*3=183. Now add these two, I get 2623.
Also 512 is a common number, for computing at least, and it’s likely that he knew the quick math on this like most of us know the 0-10 multiplication table.
Don't feel stupid about not being able to do the arithmetic. However, the fact that you didn't realize you can just divide by 4 is another matter.
It didn't occur to me at that moment
Possibly this is from computers/bytes (powers of 2), I don't think I can literally do 512 x 0.25 very quickly anymore (in my 30s now and have lost some mental quickness for sure), but I've seen it so much I know half of 512 is 256, half again is 128. Also seems reasonable to recognize 2^9 / 2^2 = 2^7
Ohh interesting…I did it in two seconds.
Different people different mental computing powers
Yes, I agree; In school I used to do multi-step evaluations in my head, and teachers used to take points off of my test until they eventually just accepted that I simply did it in my head…though of course in higher Math branches, that is hardly possible and a calculators (computers in general) can do the rest and one must simply understand the concepts and have the ability to solve or evaluate it (with the use of computers to assist), though I may not have to tell you or the person that made the post this since they survived…a lot lol. Though I was never arrogant about it. I used to try to explain to people how I was able to do it and also help people that aren’t as good at math as others may be
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I mean you can do it in under 10 seconds(or even 5) if you take a quarter of 500(125) and a quarter of 12(3) and sum them. I think the exponent thing is unnecessarily convoluted, but thats just my take.
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Ah I see, thats impressive you have that memorized. Goes to show how in math how many niches can be applicable. I appreciate the explanation!
if you're in computer science for long enough you just kinda passively learn the powers of two via osmosis. or at least that's how it happened to me
Same. Powers of two are everywhere in programming because they are necessary for computing the values of binary representations of numbers.
Whats your undrgrad major
Mathematics
yep sounds like ur dumb or something idk
Don't feel too bad. I've heard that when Einstein was in grade school, he tried to convince his math teacher that 1 + 1 = 1, because if you add one bag of sand to another one, you're still left with one bag!
if you need 60 seconds to solve this you are not somewhere „higher“ in the academic hierarchy, as you say. That’s all good though welcome to the club.
At the spur of the moment it felt like 60sec but when I am doing the calculations with focus, it might be 20 sec
controversial but people who are super fast at arithmetic are nearly always midwits
Maybe or maybe not
This sort of arithmetic means nothing.
Raw computational skills also decrease with age, and are not correlated with doing actual maths
Probably would have answered faster if you were a CS Major.
Why specifically CS though ?
RAM.
Yup. And just the binary stuff in general. I'm not a CS major but work with computers and have effectively memorized powers of two up to 8192 so that particular example would have been quick for the CS folks.
Bro I understand quantum physics without explanation but math beyond simplicity I can relate to goes past my grasp for knowledge. However, my wisdom overflows.. Pls dont feel stupid
Hmmm - I knew the answer instantly, but I think that is only because of familiarity with powers of 2, which was taught in my elementary school, along with the times table up to 25x25. Most of us top out with things we never learned well or with which we once had facility but have recently had little cause to use. As an older guy, I can remember that, when I was a child, any unimpaired adult could reasonably be expected to look at a page with a column of three to five digit numbers and sum them nearly as fast as they could scan the page. As a child, I could do this as well, but I am certain I would be much slower and more error-prone now, as this is just not a task anyone has generally needed to do since the invention of the calculator and the spreadsheet. We lose what we never use. I think this has little relationship to how many complex abstractions we have mastered. If you want to get good at basic arithmetic, you will likely need to do some now and then. ;-} It's really a rather enjoyable exercise and fun rabbit trail - just recall that working with much more than integers and ratios was broadly unknown up until the mid 1700s, even later in many places, yet people managed to solve all kinds of problems for which we would now use more advanced methods. It can also revive a little of the zest for math when you reacquaint yourself with the properties of numbers. Just for fun, here is the first such problem which I was given as a pre-school child: Add up all the numbers from 1 through 100. You have ten seconds. What is the answer? For what it is worth, I didn't succeed the first time I tried this as a child, but once I understood what was at play, I succeeded at the next question, which is: Add up the value of the digits (i.e. the number 15 has a digit value of 6) in all the numbers between one and one billion. You have one minute. What is the answer? ;-}
Bro what... you had to sum 1 thru 100 in 10 seconds before pre-K!?
Yes. I grew up in an area where arithmetic and logic puzzles were common, and were an everyday teaching tool. This is what we had \*instead\* of kindergarten or Pre-K. This particular puzzle is really a quite simple task, which most kids around six who can count, play cards, dominos, or similar games, but who have not yet been introduced to multiplication would fail at initially, until they puzzled out (or were gently led to) a successful way to approach it, at which point it is typically a real insight for them and generally cements the understanding far more than simply being taught a rule or procedure. Typically it goes something like this: Adult: presents puzzle Child: starts to add then has a moment of pure panic as they realize there is no way they are going to add all those numbers individually in the next few seconds Adult: lets the child work at it Persistent Child: works at it for a long time, generally comes up with a wrong answer, but is praised for their persistence or Less Persistent Child: tries for a while then asks for help Adult: Well, what if we took the 1 from the beginning and the 100 from the end, and added those how much would that be? Child: 101 Adult: Hmm, well, what if we took the 99 and the 2, or the 98 and the 3? Child: Oh! Adult: How many times can we do this? etc... Some children who can count well will get to the point of 50 sets of a 101 and be able to understand how move the 50 over a couple of places and then add in another 50. Some may not. But nearly all will get an understanding of the principle involved along with a real power charge out of the feeling that they have a secret insight into how to do something that just moments before they believed to be flatly impossible for themselves. The 'Persistent Child' then gets the next puzzle. The 'Less Persistent Child' is given more variations of the same puzzle over the next days/weeks. By the time they went to their first year of school, nearly every child could do most basic arithmetic tasks proficiently, and had a handle on some of the basics of geometry, set theory, combinatorics, and knew how to solve a variety of everyday rural problems, like calculating how much garden space was needed for a crop of particular yield, how to square off a new building, how to calculate time and season from the stars, etc.
1 to 100 is easy though, innit? Because of the great Gauss, we have 101*100/2 = 5050. For sum upto 1B, it’s 1B*(1B+1)/2 = 5 * (10^8) * [1+(10^9)]
The intent of the first question is to get a child to think in sets. 101*100/2* is obviously correct but perhaps a bit much to expect of a six year old, but 50 sets of 101 is not. Now, let's assume our six year old doesn't have a calculator or a slide rule, and hasn't yet been introduced to exponents... You sure you understood that second puzzle? ;-}
oh ghosh! did fast reading and realised how much my answer is wrong. You're asking about the digits while I calculated all the numbers. For the second puzzle: there is A = {1,..,9} single digit numbers which sum to 45. Then, there is {11,...99} where each digit in A occurs 20 times in each place, so the digit value sum A \* 20 \* 2. And so on Is my reasoning right?
Not sure but what you might get there using your approach, but there is a much simpler way; which is much more analogous to how to solve the first puzzle using sets.
At first I thought you were bragging then I did it in under 3 seconds not having taken math past Gr. 10. For the good of humanity it is imperative you not spread your moronic genes. I am sorry.
Congrats on solving the problem. Sorry, everyone is not like you and that’s not exactly how genes work though.