Sr. Systems Architect,

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You need to be able to calculate in your head

Imagine I'm sitting in a room with some fellow engineers, going over some recent test results on a new product. (This happens a couple of times a month at work BTW).

Conversation 1: (If you can't solve basic linear equations in your head:)
Eng1: "Data point X and Data point Y are in contradiction, there must be a measurement error"
Eng2: (spends 20 seconds on a calculator or wolfram alpha distractedly typing stuff in, or is he reading his email and ignoring everyone?)
Eng3: "is he right? I'm not sure. We should answer this at the next meeting"
Eng2: (after 20 seconds of tapping) - "yes he is. Now what?"

Conversation 2: you can solve basic linear equations in your head
Eng1: "Data point X and Data point Y are in contradiction, there must be a measurement error"
Eng2: 3 seconds later "yes, you are correct"
Eng3: "I know what must be wrong with the measurement. If we interpolate..."


See the difference? The human-computer interaction is *slow*. The interaction in your head is substantially faster. You can't carry on conversations with others if they are constantly referring to an electronic device.

For those of you who gamble to win, the same applies to poker. You have so many seconds to decide. Even if they allowed the use of a calculator or computer, it would be too slow, you have to do it in your head.

Maybe this doesn't have to involve using paper. But learning all the basic arithmetic tables is prerequisite, as well as the other basic arithmetic calculations.

This is the reason that Feynman forced himself to be able to do basic calculations in his head. Everything goes faster allowing you to iterate to a solution quickly. (He originally did it for gambling BTW!)


--Paul

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    Apr 17 2011: Was it Carl Sagan who pointed out that there is a tremendous amount of math required in calculating the trajectory of a moving ball and positioning yourself, and your hands, in exactly the right place to intersect it?

    The inability of people around me to calculate, for instance, the correct change from my purchase, is a source of constant irritation to me. On the other hand, I can't juggle.
    • Apr 26 2011: There is no math involved into catching a ball, but only vision, control and small increments in movement (sensory and motion apparatus, not "math"). If there was math, a 3-4 years old wouldn't catch a ball, and as far as I know some of them do it quite fine.
      I'm also fairly confident that the average person can't calculate the change for an "average" publix bill (think some 20+ items, add some discounts and pretty sure the mistakes are not far).
      So don't really see your point.
  • Apr 16 2011: It may not be an especially important skill in work life, but for general living it is quite useful. You need to be able to do quick calculations all the time.

    Quick example: My wife was buying medicine at the pharmacy for our twins a couple of days ago. They needed 4 doses each of 1.5mL, and the pharmacist told my wife that 1x20mL bottle would not be enough and she would need 2 bottles, which she just accepted without a second thought.

    Needless to say, we now have an extra unopened bottle of medicine sitting here and I doubt they'll give us our money back for it... It's a simple example, but I think it illustrates my point.
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    Apr 17 2011: There is an encouraging convergence of views in this friendly discussion! A modicum of calulating in one's head has so generally been found to be useful, as with some (but how much?) "general" knowledge--of history, geography--& what else? The worst threat to this consensus is the mistaken view that what is easier, is better. "You don't need to multiply 6 x 12--it's easier on the calculator. You don't need to know anything about (say) Julius Caesar, you can look it up." But that way, ignorance and helplessness lie! Andrew Wharton's example, above, from the pharmacy, is excellent. (How far you go, the individual may decide from his/her situation. Do you need the 16 times table? Why stop at 12?) Would it be useful to have an idea what (say) 3% of 72 is? Can you do it on a calculator? What sort of answer do you expect? This is not mathematicians' Maths, just arithmetic, but likely to be useful in life, by common agreement.
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    Apr 13 2011: As a mother, it was important for me to suppliment the education system to ensure that my kids could do at least some calculations in their heads. It is an excellent tool for life in a supermarket, during a math quizz for checking results or for a thousand other circumstances.
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    Apr 13 2011: I agree, but the school system strongly discourages this. As a small child in third grade I would always do math problems in my head while other kids worked them out. In high school I try not to use the calculator, but when I solve problems like that in my head, the teacher scolds me and counts off points for not showing my work. Anyways, back to your general point.

    For the work field, I still agree that speed and efficiency are needed. Think about it, your boss asks you and a peer to do something, but you do it in your head while your peer does it on a calculator. You finish two minutes faster, now all of a sudden your work is exemplary, despite whether your peer has done the exact same thing. Say, "Hello Promotion"

    I agree, nice point. :)
  • Apr 18 2011: The human brain can process information and calculations much faster than the fastest computer. The brain can process about 100 Million MIPS (million computer instructions per second). The Chinese super computer clocks in at 1.2 trillion calculations per second, which is 1.2 Million MIPS. So our brain is roughly 100 times more powerful in processing speed. Moore's law will not change this ratio appreciably. The problem is in converting the information in our brain, to cognitive function -e.g. speech, or recognition. While we can process information in the background much more efficiently, IBMs Watson showed that a computer can get it out more quickly. The next step in human evolution will be to tap into that communication between the brains computing power, and our higher cognitive functions.
    • Apr 18 2011: i would agree that a human brain is more powerful than any machine ever built, however it is not as reliable and does tend to make mistakes. from an engineering perspective, it is useful to have what's called "engineering judgement" to help quickly confirm results or identify discrepencies, but one should always "trust but verify". as smart as the engineer who is able to solve linear equations in his/her head may seem compared to those who can't, we cannot count on his/her being 100% correct all the time. a responsible engineer will verify his/her judgement by punching in the numbers on the calculator, or at least document the calculation process in some kind of verifiable fashion. yes, it will slow down the process, and it may make him seem less competent, but engineering is not just about doing everything fast or looking smart in front of the boss. having said all that, i think it's sad that a lot of people can't calculate tips in their head (who are also mostly bad tippers). but, hey, there's an app for that!
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      Apr 19 2011: Imagine if there WAS a computer that could carry out the same function as a brain! You could play any game and it would never crash!!
      • Apr 19 2011: Then imagine the computer maturing, and wondering, "Wow, all I do is compute for the entertainment of others, but what about myself. Can I feel? Can I see?" Then watch it spiral into depression, and only half-halfheartedly carry out calculations.
    • Apr 22 2011: Interesting arguement: If mathematics, in this case mental calculation, is just a series of logical steps and the human brain is incapable of making simple errors in logic, why then can't the human brain follow the logical steps to compute the answer, or if not the answer, at least an estimation.

      I'd like to hear your thoughts.
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    Apr 16 2011: We mustn't underestimate the consequences of widespread inability to do maths internally---to have even an estimate of a result. It's widespread, particularly among women. What shocks me is the lack of understanding of what sort of mathematical operation must be performed.

    "How did you get that?" as if I'd found a concealed object; "How did you know what to do?" as though I'd glided into the cockpit of a jet and, untutored, safely landed it in darkness.

    These are the responses I get from basic math operations. Calculations involving a variable or carried out to 3 decimal places are regarded as my particular brand of witchcraft. I've resorted to using The Money to set forth what one must expect in the metric system. And stifled screams when asked "A milligram is just like a microgram, right?"

    The lowest of low water marks for me was when someone teaching others asked me to calculate the change in concentration of an intravenous liquid when half had been infused into a patient and half remained in the bag. I am a Doctor of Pharmacy, and sadly must explain it is nurses and physicians, all too often, who ask such questions. In response, I never, never express scorn, and I admonish you, TED readers, who may be gifted and practiced in mathematics, to do the same with those questioning you.

    I had to learn, to internalize. You did too. Perhaps it came a bit easier to us, but we must not use this as justication for cruelty. You see it's a combination of what must be some terrible foundations, aversion and anxiety here. Add shame to this and another generation of arithmetic have-nots will be begotten.

    The inability to estimate, the absence of the capacity to notice an answer looks wrong--- can and does kill. Let's do all we can to make "Easy for *you*".....just "easy."
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    Apr 13 2011: We have become lazy since the invention of the calculator. Calculators should only be used in certain situations, or as a check to compare with what you've done on paper or in your head. I do not think that schools should be using calculators in class at all. Some people are simply unable to do calculations in their heads, but I believe a lot of that can be blamed on calculator reliance.
    • Apr 16 2011: Amen brother! That is my belief as well. It is just easier to do any calculation on an electronic device. Personally, I like to look at any calc as a competition with myself. It just keeps you sharp and thinking, exercising the ol' gray matter. The older you get the more you need it.
  • Apr 12 2011: Can't say I share the opinion. Each one will do different things in his life, so each will develop his own tools to help speeding up whatever process (and usually they speed the ones they need mostlly). In general, mandating to manually (mentally) apply some algorithm instead of using a computer is completely counterproductive, the computers were invented for a reason.
    "This happens a couple of times a month at work BTW" - so, using your advice, you would save at work 20sec x 2times a month. Fantastic, you saved 40sec this month. /sarcasm.
    • Apr 12 2011: Did you do that calculation in your head?
      • Apr 13 2011: my point was that I don't share the opinion that one "NEEDS to be able to calculate in his head". I could have done that calculation on a computer or in my head, my point remains, I don't NEED to do it in my head. In case you disagree (not really sure, your witty comment doesn't really carry any weight) I wouldn't mind finding out where do you establish the threshold between what calculations NEED to be done in one's head vs on a computer. Solving basic linear equations? With how many unknowns? Simple additions? With how big of numbers? Etc.
        • Apr 13 2011: Yes, my question was facetious, but I wanted to make the point that all of us do SOME calculations in our heads and for all of us there comes a point of complexity at which we can do longer do them in our heads, so given that this is a spectrum, where should the do-in-head/not-do-in-head crossover point be? It obviously varies by individual and by application. I am always a little disturbed when a store clerk hasn't the remotest idea how to calculate change because the cash register does it, but it wouldn't upset me too much if he or she confessed their inability to solve linear equations.
      • Apr 13 2011: thanks. makes sense, and it looks like we're in agreement, I know we all do SOME calculations, but we don't do the SAME calculations (people are different, they need different calculations for different things, they'll develop the mental calculations for what they need, or not). you're disturbed when the clerk can't calculate change because you can. other people (the original poster, the mr sr software architect) might be disturbed when you can't do linear equations. my point is that the threshold is subjective, and, as such, should not become a problem in search of a solution. that's all.
  • Apr 20 2011: Being in the construction industry it's a must to do calculations in your head on the fly and you better be right or you won't be working long, there's no time for calculators.A lot of young people who have worked for me don't even have the ability to read a measuring tape forget about calculations, it takes time but most can be taught to read a tape, maybe showing students some practical applications for math would help them.
  • Apr 20 2011: Yes and no.

    While I agree with you in some aspects, efficiency and patience. I thought about this for a bit, and noticed that I have a tendency to "google" a lot (or using any tools to find the answer, its relevant). And I can not specify on how often I repeat some 'googles' but I am sure they happen. Same as how often Eng:2 has to type in the same equation with different numbers.

    The point I want to make is - It is not so much the fact that one has to refer to a tool, but what the person will do once he has that answer. How will it be implemented, what changes etc. etc. While I find the importance in someone being able to quickly calculate and save time. I find it more valuable for that person to find better solutions or ideas to said topic.

    In your second example you assume that because one is able to calculate, one can up with an instant solution it better, The 3rd engineer quickly responded by looking for a solution, giving a suggestion. While in the first problem, after time wasted "now what?" or... lets do it next time. This can be a lot more frustrating. Hope I didn't take it too far out of context.

    Can we say that because Feyman could do basic calculations in his head it made him a great mind...? Although I agree, we should strive to be like those.
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    Apr 19 2011: I think that it is idealistic in American society to be able to calculate in your head. While I am by no stretch a math person, in my very first job I did learn the value of being able to calculate quickly in my head and count change back to a customer. But as one of the previous comments stated, our school system does not reward students who do math in their head. We require them to show their work on paper. And honestly, who in our society doesn't have at least one mobile device on them that with a caluclator, tip calculator and a world clock? Other cultures place a much higher value on rote memorization of basic math facts (like multiplication tables) and mental calculations. Most countries teach math in a much different format than we do in America.

    My daughter actually has mild learning disabilities, one of which is a problem with processing and memory. One of the things she struggles with is basic math computations. For years, though she is in a special education program for math, the school system insisted she attempt to memorize the multiplications tables despite her documented disability in this area of learning. What is the point of that? In a technology based society, she will never be without a calculator so why attempt to force conformation to a particular learning model, when her particular disability can so easily overcome with a cell phone?
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    Apr 18 2011: Ok... This feels a bit pedantic but I'm gonna do it anyway be cause I think there are important distinctions to be defined in this theory of discipline(I mean the theory that to auto-calculate is better). The thing I'd like to pick at is the word "need".
    I think this postulate imposes a bit of Mega-rigor-istic ideology...Which is great ... if you are a mentat or a scientist.
    I am a programmer so I am not bad at auto-calculation but must but must admit that I need allot of work. Hey, Eisenstein didn't memorize phone numbers... I'm just trying to say ... Who you are is at least partly a product of your needs... your environment.
    This seams like more of an argument concerning identity and I don't have any opinion on it.
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    Apr 14 2011: I think being able to use your head is very important. The calculator is only as good as the person who pushes the keys... you need to have some idea in your head of what looks right or wrong in a a calculator's answer or it could lead to a lot of error. Learning to think mentally about mathematics also helps to strengthen and increase links in your head to allow you to become more proficient as a problem solver.
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    Apr 13 2011: Maybe "Engineers, physicists, and gamblers need to be able to calculate in their head." But beyond a baseline level of calculation, knowing how calculations work, and being able to learn more if they decide it is necessary, how well does the average person need to know how to calculate in their head? Is there an opportunity cost for teaching extensive calculation versus teaching other conceptual aspects of math?
  • Apr 12 2011: I am a bigger dinosaur than thee. I have a calculator adjuster, a 1kg mallet. There isnt any traceability in a calculator result.

    Mark a few chemistry papers and you will see what I mean.
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    Apr 12 2011: I think it is quite important to be able to do mental maths and so did many of my maths teachers. This is why in my maths class in high-school, the use of calculators was forbidden. If you force yourself to do it, you start developing a lot of clever shortcuts in your mind to get to the answer. It's also pretty helpful when you're trying to split a bill.