He must be a real joy during parent-teacher meetings hahaha

Man I feel bad for the 6th grade math teacher who doesn’t realize Sally Greene’s dad is Dr Brian Greene. Yikes.

This is how I learned - PEMDAS. I am an elderly, arm-chair physicist now, and what I have learned from physicists, such as yourself, is to apply thought; to look, and see numbers differently; to be playful with equations, etc. I have found 'the beauty of wonder' in mathematics and physics that I never realized I had the capacity for. You, Dr. Greene, sparked my beginning interests. Thanks!

Feynman was asked to review secondary school text books with a similar madness. If professional mathematicians and scientists had a platform to crowd source real working methods, we would have more students excited about STEM topics. I had to supplement and correct textbook material for my kids.

I've been a software engineer my whole adult life and when I started every byte you could save in your source code listing was important so back then the order of operations did matter, however with today's computers and even phone and tablets it's not that important anymore, memory is cheap. Code is written once (well, not counting the numerous refactoring) but read many, many times. So source code shouldn't be ambiguous, it should be easy to read the code. Therefor using parentheses is very important, especially since besides the regular arithmetic operators we also have a bunch of logical operators, and comparison operators, and the order of precedence of these can differ from one language (or compiler) to the next.

As a software engineer, I prefer making the order explicit via parens. Relying on rules that might be different from one language/compiler to the next is asking for trouble.

@stephenkamenar

4 жыл бұрын

pemdas is never different.

@stephenkamenar

4 жыл бұрын

@@chriswarburton4296 okay sry i wasn't born when people used those

@michaelsommers2356

4 жыл бұрын

@@chriswarburton4296 APL goes right to left, and has no parentheses.

@joba1560

3 жыл бұрын

I learned these rules in school in germany and always thought they are a given and useful for professionals, but always been specific with parentheses myself. Nice to know I'm in good company. P.S.: hope you're doing good over the big pond!

@davidbrisbane7206

Жыл бұрын

Indeed.

Oh Brian, I LOVED this episode, you made me laugh and cry at the same time... I learned math using parenthesis, and that was when I got it. I had a love hate relationship with mathematics at school, and it always depended of the teacher!! I HATE when they are are arbitrary and they love to make you suffer... sometimes they seem to make up things that do not match nor make sense to any purpose. I just got an insight to apply math to my life, if math shows up patterns that happen and we can create formulas to solve and resolve and discover these patterns and create order and get results. Using a simple mathematical equation to reduce overwhelm in my life sounds like the magical solution LOL It makes so much sense to look at life in this way, from a mathematical perspective! You've no idea the train of thoughts this episode has started... I follow you every morning, I have breakfast with your episodes while being quarantined in Italy. I hope this series will go on and on!! Thank you Brian for your time and dedication. BTW, I'm an artist who loves to make sense of things introducing concepts from different areas :)

I'm a computer programmer. I always use parenthesis in my math code for the same reason Brian stated, it has to be readable and clear. If your code can't be formatted in such a way that it becomes clear to another programmer of what your intention was when writing those lines, then your code might work but it could become a pain in the ass to deal with on large projects.

@RemikPi

4 жыл бұрын

Have you ever plaid a code golf? :D

@RemikPi

4 жыл бұрын

I bet you don't care about the esoteric languages! ;-)

@grayaj23

4 жыл бұрын

And then there's perl.

@gorankraljevickoehler4381

4 жыл бұрын

@@RemikPi Lol, I used to simplify my C++ code so much It would become very optimized but really hard to read which I didn't mind because It was usually on my own projects and it was a fun exercise, but experience has taught me that doing that all the time is not always good when working on a project with multiple people and due dates. It's is a very general programming lesson I've learned over the years, but of course, it doesn't apply to all situations or all languages.

@gorankraljevickoehler4381

4 жыл бұрын

@@grayaj23 true hahahaha

Great episode. I loved math. Public school knocked that notion out of my head really quick. “Show your work!” “Solve it how the book says to solve it!” Don’t you dare be creative!!

Omg! Thank you, Dr. Greene! I don’t have children of my own, but I have been tasked with tutoring many nieces, nephews, or pseudo-nieces and nephews, and have encountered this very concept!! It’s frustrating from my point of view, because as a language, mathematics can be much more elegant and easier to express. And I always stress that it is the NECESSARY language of science, engineering, and technology, so however one gains fluency is penultimate to success. Your endorsement of my alternative helps my arguments immensely!

It goes a fair bit further in computer programming. For example, multiplication (*) and division (/) and modulus (%) are higher precedence than addition (+) and subtraction (-), which are higher precedence than bit-wise "and" (&) operations which are higher precedence than bit-wise "or" (|) operations, which are higher precedence than logical "and" (&&) operations, which are higher precedence than logical "or" (||) operations, which are higher precedence than assignment (=), etc. A programmer uses a significantly expanded variation of "PEMDAS" when interpreting (and fixing with parentheses) ambiguous expressions that contain bitmasks or conditions. That's not even all, I left out several other operators that are probably not familiar to everyone.

@cesarmoya7

4 жыл бұрын

Yep, all the more reason to use parenthesis to ensure the meaning is clearly and unequivocally conveyed to future developers. we're humans, it's too easy to miss one little operation over there and then the plane crashes!

Couldn't agree more, Prof. Greene ! I graduated decades ago , I have been a teacher and a researcher in Mathematics, never used PEMDOS or anything like it. How could I?? On the contrary, always insisted in very very clear when writing equations or inequalities . Also, as Julia said in the chat,using the dividing line between the = sign is a simple but very useful practice!

What we were taught in elementary (in Canada) was to follow BEDMAS-brackets, exponents, division, multiplication, addition, and subtraction. It was always clear that being precise was important and very straightforward. However, it was not made clear the fluidity of mathematics. Thank you, Prof. Greene.

Thank you Professor Greene for your much-appreciated positive efforts in doing The 'Daily' Equation which I am loving ! I'm catching up on the back catalogue of YDE and 'Live' discussions- brilliant stuff. re : Daily Equation #22. I agree absolutely with Professor Greene. I believe order of execution within an expression such as [ 8 - 2 ÷ 2 x 3 + 4 = ? ] is not ambiguous when following PEMDAS ( in UK, we sometimes learn the equivalent BODMAS-- Brackets, Order [ i.e. power ] , Division= Multiplication, Addition=Subtraction ) and means consistency when entering large equations on a calculator if, and only if, operations of equal priority ( add=subtract, multiply=division) are carried out strictly left-to-right. This teaches us to be able to predict the output of a calculator and be assured of consistency. e.g. If I use BODMAS, then the division of 2/2 is left of the multiplication, so divide first, then multiply, then add/subtract left-to-right gives 9. When entering the expression [ 8-2/2*3+4 ] on my calculator, it gives 9, as expected. 'As expected' is the key point here. It's important that if you buy a calcuculator, then it's output will always be as expected. Note 1 : many modern calculators display 2/2 as a fraction automatically, which is a visual clue as to the fact that it is 'doing PEMDAS/BODMAS. left to right. Note 2 : Polish Notation calculators ( I believe Sharp make them still ) is a completely different kettle of fish-- good videos on KZread by various people already there if you're interested in following *that* up ! Please keep up your magnificent efforts ! How about a YDE on conversion of units by including the units as algebraic symbols and using multiplication of the start value by unity expressed as a a ratio of the units to be converted to and from... e.g. to convert 1km to m : ( 1 * km ) * ( (1000 * m ) / ( 1 * km ) ) = 1000 * m = 1000m ? I find including units always is desirable to avoid ambiguity or mistakes, and think you could teach it in a clear way. Thank you.

Thank you Dr. Brian Greene! You are saying all of the things I wish education programs would realize.

As a computer programmer for over 40 years I agree with you completely. If a programmer brought a program to me that contained an equation like the one without the parenthesis, I would give it back to him and tell him to write it properly. If a teacher gave me a problem like that, or a textbook, I'd tell them to take back their test (or book) and rewrite it properly.

Very enjoyable video, Brian has passion. Great to watch.

Thank you Dr. Greene. You have given me some insight on how to teach my 5th grade nephew about order of operations. Maybe you could show us some more basic arithmetic ideas, for young math learner's. Possibly how to introduce the idea of variables to the uninitiated.

As a Bachelors Degree Mechanical Engineer who spent 10 years teaching Intermediary and college algebra and various other subjects at a community college to students just trying to get through the class and finished with the semester, I most certainly agree with you.

Simpler and clearer. It’s the way. 👍 That PEMDAS is like a secret code for emotionally unbalanced mathematicians. 😃 I like this so much. This is about philosophy of thinking and of life! Great stuff. 🌷

a programmer should make the code readable... so adding parentheses is good style

@ricardodelzealandia6290

4 жыл бұрын

As a coder, if one of my staff was flooding the code with parentheses that were unnecessary because they weren't aware of operator precedence or thought that it was somehow clearer to plaster these all over the code, I'd probably take them off the project or at least have some stern words with them. If coders are doing this they may be simply putting too much stuff into a single statement. Thankfully modern IDEs can remove all this with functions like "clean up code", etc. Still, it shouldn't be done in the first place. Learn your language.

@nikitaelizarov7444

4 жыл бұрын

@@ricardodelzealandia6290 I bet you hate lisp :)

@ricardodelzealandia6290

4 жыл бұрын

@@existenceisillusion6528 I find it interesting that there is a fairly large group of developers (it appears from this video's comments) who prefer unneeded parentheses. From my experience, in any given team, there aren't many who prefer it. In any case, the worst part of using parentheses in an expression in code is that in order to read the expression, you need to click on one of the parentheses within it to find the corresponding (using the IDE parenthesis matching) one in order to make sense of the expression. Without parentheses, you can rely purely on operator precedence to read the expression, which is less effort.

@jonathanwilson7957

3 жыл бұрын

@@ricardodelzealandia6290 As a software engineer I completely disagree with your argument. If it makes the code more readable, which parens would, then the better. A few arbitrary parens is of no issue to the performance of the operation, so have at it. As long as it is not absurdly unseeded. "Pull them off the project", sounds a bit harsh...

Excellent video. What are your thoughts on teaching prefix/Polish notation or other unambiguous notations to avoid the problem altogether?

I'm with you Brian. Trained as a physicist and professional engineer for the past 40 years, and I've never seen PEMDAS or whatever they call it used professionally. Or course the operator hierarchy as used in polynomials is used all the time (exponention->multiplication->addition/subtraction), but the ambiguity in the order of applying division is always made explicit with parentheses or other layout cues.

Finally! An equation I can understand! And even without the brackets! :D

Reminds me of Richard Feynman‘s comments on textbooks in California. Love it!

So true, finally, thanks for that Professor Greene!

Thanks for explaining Dr. Brian

I agree with this so much. Math in school is about memorizing silly rules and not thinking in the language of mathematics. Thanks Dr. Green.

I totally agree although, from a pedagogical perspective, I've always wondered whether order of operations discussions couldn't be a starting point for a discussion of associative, commutative properties that would be more mathematically engaging. I'd be interested to hear from teachers whether that's a reasonable approach.

Thanks, love the videos! Yes precision is also quite important in written communication, as evidenced by the emails we sometimes get! I’ve never become comfortable with math, I plan to go back and watch this entire series again! At university my symbolic logic prof took pity on me and gave me a ‘D’, as I tried- just didn’t get it. Calculus was a bust too on paper, but in the real world I regularly ‘calculated’ the speed of the semi in front of me , the speed of the oncoming car, and whether or not my motorcycle has enough acceleration to pass the semi and tell the story afterwards. I was actually going to ask you to do operation orders - so you’re psychic too! Nice!

Thank you, Brian!

These are great, EVERY one of them! Thank you!!!!

I completely agree with the general sentiment, 100%, and I also hate when problems like the one you broke down go viral online. However, PEMDAS is very cleanly applied in situations like polynomials, which would be very cumbersome with parentheses/brackets around every operation. It is useful to know that 5x^2 - 3x + 4 is not the same as [(5x)^2-3]x + 4, which it would be just going left to right without the standard implied order of operations, [5(x^2)] - (3x) + 4. At the elementary level though, I agree that clarity and simplicity should be taught, which would mean removing ambiguity by using parentheses, and then later students can learn to drop parentheses in commonly-understood formats, for example exponentiation before multiplication before addition as in a polynomial. Thank you for the video! I'll save it to post next time somebody shares one of these annoying problems.

I am so glad that Brian said that is this ambiguous. I taught myself both semesters of college algebra (to save money) and then went on to 2 semesters of calculus. Never heard of PEMDAS and found the above equation pretty crazy. I was so happy to see I was correct. No punctuation in that sentence.

@immigrationcanada1802

3 жыл бұрын

Let me explain real world situation which needs PEMDAS rule. Suppose I own a shop. I enter each transaction into computer and then at the end of every week, I check the amount of money I have. I do following 2 main things: 1) Purchase items wholesale from a dealer. 2) Sell items to the individual customers of my shop. Total Money Left = Money earned(Selling to my shop's customers) - Money Spent(Buying wholesale from a dealer) I need all 4 operators for doing following things: 1) Division - I need to know price of individual item. So I need to divide number of items(purchased in bulk) by total price which I paid to dealer. 2) Multiplication - I need to calculate money I earned. So Multiply individual price by number of items sold to customer 3) Addition - Adding money which I earned by selling to customers 4) Subtraction - Subtracting money which I paid for buying from wholesale dealer Now suppose I do 50 transaction each day for 5 days in a week. And I keep on entering each transaction's data to computer. At end of week, computer has to tell me money left. So computer has (50 transactions x 5 days) = 250 numbers. And it has to apply all 4 operator types. So there are 250 numbers and 249 operators. Now should I keep typing brackets for so many numbers and operators ! MESSY ! IMPOSSIBLE ! What's the use of computer then ! So I teach computer the PEMDAS rule and now computer can do all calculations without need mentioning brackets. IMAGINE THOUSANDS of numbers and thousands of items - IMPOSSIBLE WITHOUT PEMDAS. Computer SHOULD KNOW PEMDAS ! ! !

9:42 Facts sir. I got goosebumps when i heard that from you. I felt the same way and now I'm sure .

I was so happy to hear this lecture, thanks.

Prof. Greene, I am older than you, and studied math in the 60’s and 70’s. We were never taught PEMDAS, but were taught the order of operations along with other principles like commutative and associative. We didn’t spend a lot of time up on them, however. It’s true that they could’ve made the bigger picture clearer to us, but at least we weren’t being trapped with tricky rules. Girls were not expected to do well in math; as a senior in high school, I got the highest SAT score in math our high school had ever had, and my math teacher told me he was really surprised because he didn’t realize I was that good in math. Well, he had not paid much attention to me. The bias against girls in math always annoyed me, especially because I saw it continued in the 90’s with my own daughters!

Another great episode. As a student I was NOT taught PEMDAS. 20 YEARS later as a teacher I was required to teach it. I had never heard any reasoning behind the PEMDAS pedagogy, so when kids asked 'WHY' I finally gave them my only reason. "Some old DEAD guys wrote the rules a thousand years ago and now WE are stuck with these rules. I agree .. more parenthesis would be a much better solution. The person making up the problem should make the problem understandable by all.

@immigrationcanada1802

3 жыл бұрын

Let me explain real world situation which needs PEMDAS rule. Suppose I own a shop. I enter each transaction into computer and then at the end of every week, I check the amount of money I have. I do following 2 main things: 1) Purchase items wholesale from a dealer. 2) Sell items to the individual customers of my shop. Total Money Left = Money earned(Selling to my shop's customers) - Money Spent(Buying wholesale from a dealer) I need all 4 operators for doing following things: 1) Division - I need to know price of individual item. So I need to divide number of items(purchased in bulk) by total price which I paid to dealer. 2) Multiplication - I need to calculate money I earned. So Multiply individual price by number of items sold to customer 3) Addition - Adding money which I earned by selling to customers 4) Subtraction - Subtracting money which I paid for buying from wholesale dealer Now suppose I do 50 transaction each day for 5 days in a week. And I keep on entering each transaction's data to computer. At end of week, computer has to tell me money left. So computer has (50 transactions x 5 days) = 250 numbers. And it has to apply all 4 operator types. So there are 250 numbers and 249 operators. Now should I keep typing brackets for so many numbers and operators ! MESSY ! IMPOSSIBLE ! What's the use of computer then ! So I teach computer the PEMDAS rule and now computer can do all calculations without need mentioning brackets. IMAGINE THOUSANDS of numbers and thousands of items - IMPOSSIBLE WITHOUT PEMDAS. Computer SHOULD KNOW PEMDAS ! ! !

7:00 listening your this experience and feeling it is Amazing

Hi Prof. Greene, When I went to school (a long time ago), we were taught about BODMAS. Bearing in mind that in Britain / England we tend to call them "brackets" rather than "parentheses", which in the UK, usually mean square or curly "brackets". However, my Maths teacher at the time emphasised the same point that you made in the video - the expression should always be clear & consistent in its ordering. Then, if the expression was clear, BODMAS showed the order in which to perform the various operations. To give you some idea of when I did elementary maths at school, we were still taught to use Log Tables and Slide Rules !! Honestly. All the best, Paul C.

This may come up when using an electronic calculator. It's why "reverse Polish notation" was standard on a lot of them, because entering parentheses wasn't possible on some of the simpler ones, and even if it's available, you end up having to write out the expression so you get them in the right places. Since most don't display the formula as a whole, but calculate on the fly, it's easy to make errors.

@Warguard9

Жыл бұрын

Those HP...with RPN was a must have!

ok I know i am coming into this conversation way late but i do agree whole heartedly with you Dr. Greene. i would also like to add my own perspective which has been driving me crazy and i been arguing with mathematicians for a few years. This Idea of 1=0.999... and simply that one divided by 3 equals 0.333...I wrote this response to a mathematician in regards to our argument 1/3. Hello Professor Ely, Robert It is Rolin Bankus again, I hope this finds you well, and not too busy to reply. I understand with School in session that your time is very important. I thought long and diligently about our last conversation we had in your office; I wasn't even sure if I was going to respond but then with as frustrated as I got, I knew if I didn't that it would drive me crazy. As always, I must apologize first. I am sorry for two reasons one this will be quite long, and two if I offend you in any way then I am sorry I mean no disrespect. When we were talking in your office about 0.3 + .1/3 and 0.33 + .01/3 etc. you had told me to forget about the remainder part of this (which I think mathematicians do too often) well now I am going to throw this back at you because I think you will see where I am coming from if I do. Ok in the proof that 0.999... =1 you set 0.999... = to x and multiply by ten etc. (which I am going to write out SRY.) x = 0.999... 10x = 9.999... 10x = 9.999... - x = 0.999... = 9x = 9, 9x/9 = 9 /9, = x = 1. well, you already know that I have a problem when you multiply by ten and like you told me in your office someone already wrote a book about how the values are not equal etc. So, like I told you in your office if I add 1/3 and 2/3 in their decimal form my way then I can come to a value 0.999 + .003/3 well now here is where I throw this back at you, forget the remainder value set it equal to x and prove it is equal to one. because the only difference in my value and your value of 0.999... is your ... and so, they must be both equal to one, correct? I know you're not going to but we both also know what happens if you did. it would look something like this. x = 0.999 then multiply by ten so 10x = 9.99 and when you subtract you would get 9x = 8.991 so, what I am saying is that 1/3 does not equal 0.333... because this ... is a poor example of what the value is. for example, if you take out your phone divide one by three then it is 0.3333333333 my phone only goes out ten decimal places but then if I erase this and put that same value in and multiply by three, I do not get one. when I am doing math, I was always told if you find the answer stop. well, 1/3 = 0.3 + .1/3 because like I said in your office you can only divide 1 by 3 once. If you continue you are only seeing how small you can make the remainder so that if you were then to multiply by three it still equals one. because 0.3+.1/3 is the same value as 0.33+.01/3 you cannot just simply forget the remainder and say that if you do the value is bigger. Because yes 0.33 is bigger than 0.3 but see neither of these two values are a product of 1/3. They are either 0.99/3 or 0.9/3. you know it was Einstein who said that the definition of crazy is doing the same thing over and over again and expecting a different result. I also do not think that I am arguing over semantics because with my value you never get an incorrect value and is simple to explain. See without your special little ... you cannot explain how your value is equal. Well as always, I appreciate all your help and look forward to your response. Sincerely Rolin Bankus.

Great episode!

Thank you for saying this Dr. Greene. Part of the problem, maybe, is that non-mathematicians are often teaching mathematics, and a certain social belief that prescribing steps may make mathematics, physics, abstraction, or complex ideas accessible, and they mean usable and useful, to anyone even without understanding. I find this type of thinking even in community college "developmental" courses ... and is there any wonder people repel away from math!

I thoroughly concur with your sentiments about the beauty of math to encapsulate wondrous patterns found in the natural world and think it applies to chemistry as well. On a technical note, what software do you use to record your video with handwritten notes.

OMG Because of this video i have learned how to do math operations ! It is unbelievable what they were teaching us in school...I knew how to them but never understood why do the math has to be so weird that it lets me do so many different operations with that single equation...what you did for me today....you just made math more interesting for me ! Thank you for that !

@immigrationcanada1802

3 жыл бұрын

Let me explain real world situation which needs PEMDAS rule. Suppose I own a shop. I enter each transaction into computer and then at the end of every week, I check the amount of money I have. I do following 2 main things: 1) Purchase items wholesale from a dealer. 2) Sell items to the individual customers of my shop. Total Money Left = Money earned(Selling to my shop's customers) - Money Spent(Buying wholesale from a dealer) I need all 4 operators for doing following things: 1) Division - I need to know price of individual item. So I need to divide number of items(purchased in bulk) by total price which I paid to dealer. 2) Multiplication - I need to calculate money I earned. So Multiply individual price by number of items sold to customer 3) Addition - Adding money which I earned by selling to customers 4) Subtraction - Subtracting money which I paid for buying from wholesale dealer Now suppose I do 50 transaction each day for 5 days in a week. And I keep on entering each transaction's data to computer. At end of week, computer has to tell me money left. So computer has (50 transactions x 5 days) = 250 numbers. And it has to apply all 4 operator types. So there are 250 numbers and 249 operators. Now should I keep typing brackets for so many numbers and operators ! MESSY ! IMPOSSIBLE ! What's the use of computer then ! So I teach computer the PEMDAS rule and now computer can do all calculations without need mentioning brackets. IMAGINE THOUSANDS of numbers and thousands of items - IMPOSSIBLE WITHOUT PEMDAS. Computer SHOULD KNOW PEMDAS ! ! !

Looking through old maths books history, reasoning and recognizing principles was more important that teaching a lot of routines.

Love it! 😎👍

I am a similar age to you and was taught the equivalent of PEMDAS at school in the UK. I have always used parenthesis to remove ambiguity though.

Genuinely, the rules of math given by instructors were aggrevating as a child. Understanding why said rules were implemented was more useful. I failed math because of teachers that didn't take enough time giving the reason behind why we do these things. They would always mention in the next class you'll understand. By the time I reached trigonometry (27 yrs old), retaking it a third time, I started reading on why calculus was created and it made learning square root trees easier. Mind you, I worked as a Network Engineer mentee and was studying Embedded Systems during this time too. My comment is more so a thank you for the validation. Equally it sparked the question, why PEMDAS? Why this order? Similar to the question I had while learning C++.

I believe this is more about learning pre requisite to designing a computer than math or physics. Prof. Brian the world revolves around other subjects too!

Late to the game, but really enjoying the Daily Equations. As a retired engineer and volunteer high school math and physics tutor I couldn't agree more with your comment on order of operations and avoiding ambiguity. In Canada the in word is BEDMAS, but the different letters solve nothing.

Yes Professor, you are damn true. Teachers in my school focus on the rules and tells us the rules that guide the mathematics. But I am trying to get our of this rules and understand the mathematics as a whole. Thank you professor it is very kind of you for taking me further into the magical and wonderful universe of mathematics.

@prabirkumardash653

4 жыл бұрын

Out of these rules**********

that is a great method of encryption your order of operation!

To be honest after years on passing different courses of math and physics in school and then university, I could never imagine there would be a day I start to look at math and physiscs with all my heart not only the brain. That is the point: all the beauties of math can be revealed deep down in physics and physics in math. If from the first step, instead of "just" math or "just" physiscs, the authors of the school books start to join the building blocks of both sciences together and describe the very complicated math subjects by the help of physiscs, maybe there start a revolution in students point of view regarding both scienses. For sure the subject will be more understandable and will not seem to be rigid and though for students any more.

Spot on Prof!

Point before line (Punkt vor Strich)... one of the first things we learn at school in Germany. At least in my time.

Absolutely! No ambiguity. Also learned as in engineer to ALWAYS include units. Not everyone does, but it often saved my bacon. If the units don't fall out properly, then something somewhere is wrong.

Dr Greene i think that since you start by requiring a set of parentheses to begin with, maybe you actually apply this PEMDAS rule, given that the rules apply in that order after P. Anyway i agree with you on the general context. I am Greek and remember back in school that time we were taught the sequence of operations, i was really frustrated.

I never heard of pemdas. We always learned to use Parentheses in 1970s Ireland :)

Conputer programmer here, unfortunately ambiguous operator order is legal in math and in many languages. You can use code analysis to enforce a rule of no ambiguity, using parentheses, which is certainly recommended. I've encountered bugs in the wild more than once that came down to this ambiguity. I think the real fix would be to totally disallow ambiguity both in languages and in math. So that your example wouldn't even be well-formed syntactically to begin with.

As a pogrammer with a university maths degree I always use parentheses in my code. The result after compilation would be the same with the compiler applying PEMDAS, but I prefer code that is easier to interpret and thus maintain. Just another way math is like language studies, you have elaborate constructs you don't use in everyday conversation either

@immigrationcanada1802

3 жыл бұрын

Let me explain real world situation which needs PEMDAS rule. Suppose I own a shop. I enter each transaction into computer and then at the end of every week, I check the amount of money I have. I do following 2 main things: 1) Purchase items wholesale from a dealer. 2) Sell items to the individual customers of my shop. Total Money Left = Money earned(Selling to my shop's customers) - Money Spent(Buying wholesale from a dealer) I need all 4 operators for doing following things: 1) Division - I need to know price of individual item. So I need to divide number of items(purchased in bulk) by total price which I paid to dealer. 2) Multiplication - I need to calculate money I earned. So Multiply individual price by number of items sold to customer 3) Addition - Adding money which I earned by selling to customers 4) Subtraction - Subtracting money which I paid for buying from wholesale dealer Now suppose I do 50 transaction each day for 5 days in a week. And I keep on entering each transaction's data to computer. At end of week, computer has to tell me money left. So computer has (50 transactions x 5 days) = 250 numbers. And it has to apply all 4 operator types. So there are 250 numbers and 249 operators. Now should I keep typing brackets for so many numbers and operators ! MESSY ! IMPOSSIBLE ! What's the use of computer then ! So I teach computer the PEMDAS rule and now computer can do all calculations without need mentioning brackets. IMAGINE THOUSANDS of numbers and thousands of items - IMPOSSIBLE WITHOUT PEMDAS. Computer SHOULD KNOW PEMDAS ! ! !

@flemlion13

3 жыл бұрын

@@immigrationcanada1802 I think you are confusing a calculator with a computer. But either way, a calculator has a memory for intermediate results, and that is what you would use instead of trying to get it to calculate the total in one go. A computer has registers, which are similar, but there are more of them. On top of that, a computer can store register values in memory and load them back as needed, so the number is close to unlimited. Also a computer is programmed with an algorithm. That is like the recipe to get to the result. You only need to program each level of calculation at a time and you can give each level a name in what is called a function (or method). If in such a function you would have a single line with more than three levels of brackets, you can consider that bad programming and should introduce another function. There are exceptions of course, as the programming language LISP is just full of brackets, even when not doing calculation.

I am a teacher and can't wait for a fresh explanation!

I agree with you! If I'm a graduate student, and if I learned how to solve differential equations why should I be tested on PEMDAS? What we know should be tested and not if we make a accidental mistake!

From one physicist to another; I think you're simply awesome, Dr. Greene.

Love it!

This strikes a real pet peeve as well. I am a computer programmer and over the years I have programmed in many languages so I always use parenthesis to ensure my formulas are interpreted correctly. One of my first languages was APL that is strict right to left, MUMPS is strict left to right, FORTH was (is) RPN, lots of equations involve conditionals NOT, AND, OR and XOR etc that are not covered explicitly by PEMDAS and often even different implementations of the same language do it differently so why take the chance. Long live the parenthesis !

Preach! lol, well lucky for me I was taught not to apply that rule PEMDAS so extensively but to rather sharpen it up in a precise manner.

I learned this too but no acronym for it, just that multiplication and division were associative as were addition and subtraction. But we learned this early in school, while we were doing arithmetic, long before algebra.

Every time I hear the phase "small business owner" I think of Danny Devito running a shop.

That's what i was expecting Thanks for this

A very good and important point!

I'm a maths graduate and computer programmer of many years standing and share your views and frustrations. I only became aware of these acronyms when all these "Try this - 99% get it wrong!" "PEMDAS" / "BODMAS" memes started appearing on (e.g.) FB. We were never taught that way (why would we have been?). Yes we were taught PRECEDENCE - but surely this took at most an afternoon. From what I've seen, an awful lot of those who have been taught these acronyms apply them blindly (why wouldn't they?) and often get the wrong answer as a result - insisting that multiplication ALWAYS comes before division (if "PEMDAS"-trained; conversely if "BODMAS"-trained) rather than applying operators of equal precedence in left-to-right order. They should at least have taught it as "PE(MD)(AS)" or "BO(DM)(AS)". This misguided teaching is now showing up in computer code - with who knows what consequences.

Professor I am a chemistry prof and tutor math in high school. Your comments on ambiguity and no brackets is right on. I will use your idea next time i have to teach this concept. thanks!...

30 years ago in Poland I learned that multiplication and division is stronger than addition and subtraction. The rest must be explained by parentheses. So when I saw the title equation, I found it ambiguous and its value could not be determined without parentheses.

Dr .Greene ,please make a video on laws of motion.

Even if we use parentheses/brackets, we still are doing PEMDAS but putting the "MD" and sometimes "AS" into P. Which just shortens it to PEAS. Right?

it took quarantine for him to realize this 🙏🌌

Who's gonna tell these people that there's no such thing a 'division' in a Field

@black_jack_meghav

3 жыл бұрын

Lol

I just remember it like this: ×, ÷ just more important so I do them first. And parentheses- makes it easy to see. Of course when you have all black board written with formulas. You have to make it easy to see.

As a software developer with a maths degree, I absolutely agree - no mathematician or programmer ought to be writing expressions like that, and kids ought to be taught not to. A mathematician would have the possibility of using layout to make their intention unambiguous, of course. A programmer should use parentheses - or even well-named variables for the intermediate results. But PEMDAS isn't even right - doing multiplication before division and addition before subtraction is just wrong. Maybe it should be written PE(MD)(AS).

I agree. An intelligent use of parentheses and brackets will tell you the order of operations. That is much simpler to learn and is also more intuitive than some silly acronym. Period.

Here in the UK we were taught BODMAS, which amounts to the same thing but at least the BS is more obvious in our acronym. Your final point about coding is pertinent for me. As a former coder, I would never have left the opportunity for ambiguity in any code that I was prepared to expose to others.

PEMDAS matters when you're using a calculator. You can do things a lot more quickly if you use PEMDAS. The ambiguity in your equation isn't with the plus and minus sign but with the division and multiplication signs. It's ambiguous whether it means 2/(2x3) or (2/2)x3. I think that division sign is what makes it unclear, which is why it's better to use a fraction to represent it so we know where the 3 goes.

I absolutely agree. The order of operations can be arbitralily decided by us mortal humans. No big meaning behind it. It is a waste of time to spend more than a day on it. As you say, bracketing clearly shows you what you mean. So have that dealt with quickly and talk about something more interesting than made up rules.

I encountered riddles in my math classes at school. I took Accounting as an undergraduate. Same thing, riddles.

I heard PEMDAS when I was in my elem year and most of my friends use it until now that we're already in college, i don't know why but i still never really paid attention to it and never use it even thought they sometimes encourage me. Thankyou professor now have more reason to continue ignoring it.

@immigrationcanada1802

3 жыл бұрын

Let me explain real world situation which needs PEMDAS rule. Suppose I own a shop. I enter each transaction into computer and then at the end of every week, I check the amount of money I have. I do following 2 main things: 1) Purchase items wholesale from a dealer. 2) Sell items to the individual customers of my shop. Total Money Left = Money earned(Selling to my shop's customers) - Money Spent(Buying wholesale from a dealer) I need all 4 operators for doing following things: 1) Division - I need to know price of individual item. So I need to divide number of items(purchased in bulk) by total price which I paid to dealer. 2) Multiplication - I need to calculate money I earned. So Multiply individual price by number of items sold to customer 3) Addition - Adding money which I earned by selling to customers 4) Subtraction - Subtracting money which I paid for buying from wholesale dealer Now suppose I do 50 transaction each day for 5 days in a week. And I keep on entering each transaction's data to computer. At end of week, computer has to tell me money left. So computer has (50 transactions x 5 days) = 250 numbers. And it has to apply all 4 operator types. So there are 250 numbers and 249 operators. Now should I keep typing brackets for so many numbers and operators ! MESSY ! IMPOSSIBLE ! What's the use of computer then ! So I teach computer the PEMDAS rule and now computer can do all calculations without need mentioning brackets. IMAGINE THOUSANDS of numbers and thousands of items - IMPOSSIBLE WITHOUT PEMDAS. Computer SHOULD KNOW PEMDAS ! ! !

As a German I never saw the PEMDAS rule. We have "Punkt vor Strichrechnung". Roughly translated "point ahead of dash calculation", where point calculation means multiplication or division and dash calculation addition or subtraction. The german rule is incomplete in the sense that it does not mention exponents and parenthesis. However, it clearly points out that multiplication and division (point-operations) have the same precedance and have to be evaluated from left to right, while PEMDAS suggests that multiplication takes precedance over division, which is wrong. For instance: 24:2*3 = 36 = (24:2)*3, while PEMDAS could misslead students to believe 24:2*3 = 24:(2*3) = 4 I agree that parenthesis are helpful to make the order clear. But I would not set parenthesis, when a left to right evaluation is identical to the evaluation according to the operator precedence. Hence I would not write ([(8-2):2]*3)+4. I think ((8-2):2)*3+4 is sufficiently clear. In scientific papers one almost never find the division operator. Most often a division is handled by writing down a fraction which implicitly parenthesize the enumerator and denominator expressions

Your daughter's math class sounds just like my math classes as a kid in the 90s. Thanks for this rant.

Writing code here.... yes, definite use of parentheses for both logical and mathematical operations. Even when I can reliably assume the language 'knows what I meant' there's no benefit to risking ambiguity.

I had BODMAS drummed into me over and over in High school, I got into arguments a lot as to the interpretation could be very much different without brackets - thank you very much for demonstrating the ambiguity of expressions where brackets and parenthesis are omitted I remember telling a teacher once that I was not a mind reader lol

I agree totally. In primary school, I would *always* put brackets (sorry not saying paren..ehhh) around everything that needed them to show the order of calculations. However, my teachers did not agree with this unambiguous representation of a mathematical equation, and would mark me down for using brackets when I "didn't need" them. The real issue here is some (not all of course) teachers are so rigid and don't think for themselves about what they are teaching.

Not from the US (Or any other country that use this method), did not know PEMDAS was a thing, that is super arbitrary, I always used (), [], {} If you don't use them like this on College you pretty much gonna have a 1 (where I live notes goes from 1 to 10). I love math, I'm not that super good with it, but it is so beautiful... specially when you start with Calculus. To think Sir Isaac Newton had to "invent" his own math's to explain things he observed is astonishing, he was, no doubt, a genius.

Considering division is interchangeable with fraction, I think the answer could be; P | [(8-2) ÷ (2×3)] + 4 = [(8-2)/(2x3)] + 4 Express as (6 ÷ 6) + 4 = (6/6) + 4 E | Not applicable but just for fun, can change 4 to √16 M | Parenthesis supercedes multiplication D | 1 + 4 A | 5 S | End of equation By Order, PEMDAS

Cannot believe that you did an episode on this question as well. Love you man. Thanks for explaining in a lucid way.

Hello, Brian! I never heard of PEMDAS. In my country, I was taught that you do parentheses first, then multiply or divide, and only then add or subtract. So, the bit that confused me was the order of the operations in the middle. Adding or subtracting first was never an option, but what to do with 2/2x3 - no idea. To top it all, this expression does not exist anywhere else. I agree with you - why make maths complicated and abstract, rather than allow its students to enjoy its relentless logic? Thank you for what you do and who you are!

@davidharris8904

3 жыл бұрын

Yes exactly! I learned PEMDAS/BEDMAS in school but must not have been paying attention when they said you must go left to right. In my mind the question is ambiguous because of the part you mention

If i was given this equation, i might be inclined the proceed to calculate from left to right (as in reading English). The problem can be simply entered into a calculator while proceeding from left to right, giving 9 as the solution. Agreed that parentheses should be included if another order was intended. Should a person whose language reads from right to left do similarly (-1)? ;-)

Fully support the goal, although I have a suspicion that the mundane world works on PEDMAS (or BODMAS as I learnt - I do appreciate the addition of exp into it though) and it's unlikely to change anytime soon. And I agree that *mostly* math-professionals use parentheses and implied-parentheses (like a large fraction to group a division) to make the OoO clear. But there's one operator where I suspect every professional still uses what I think is an abritrary OoO without concern, and it's the one we don't even bother to write at all, being multiplication. acosx+bsinx still implies multipliers that occur before the addition (not to mention the functions). Similarly for ab+cd. So I don't know that anyone's a real purist here.

Totally agree

As a writer of compliers I couldn't take Brian's route and say "don't do this," although I almost did. If I had to group "by rule" I gave a "Warning, ambiguity resolved as: ." Consider A*B! PEDMAS doesn't say whether (A*B)! or A*(B!) is correct. All unary operators have a similar issue, scope of unary. Unary negation is not covered by PEMDAS so -3^2 is ambiguous. Converted to (-3)^2 [by applying unary minus first to the one item to its right] or 0-3^2 for PEDMAS evaluation depending on the complier/spreadsheet/calculator. e^(-x^2) -- ambiguous. The thread end is always the same: Always parenthesize in real life.