back to article Yay, more 'STEM' grads! You're using your maths degree to do ... what?

There's a good reason why the big brains at the top of science in Australia are suddenly singing hosannas to entrepreneurs. Someone's finally pointed out to chief scientist Ian Chubb and CSIRO (federal agency the Commonwealth Scientific and Industrial Research Organisation) boss Larry Marshall that the STEM (science, …

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  1. Anonymous C0ward

    Someone who understands statistics

    will know the difference between relative and absolute risk, so probably more likely to eat bacon and not be taken in by scaremongering.

    1. Martin Gregorie

      Euclid is not outdated, worthless knowledge

      Mental Euclidian arithmetic is also rather useful for anybody who needs navigation skills: think pilots and many sailors. Calculating drift, or working out your heading from a map is purely Euclid in action. Think a modern pilot doesn't need these skills because GPS? How about emergencies caused by electric power failures or when a CME takes out the GPS, Glonass and Galileo constellations?

      1. 404

        Re: Euclid is not outdated, worthless knowledge

        Considering the US Navy has gone back to teaching the use of sextants for navigation again should tell you something...

      2. Steven Roper

        Re: Euclid is not outdated, worthless knowledge

        You also need a good grasp of Euclidean geometry if you want to get into any of these fields: game design, 3D modelling, graphic design, architecture, or photography (think projecting 360° panoramas etc) among others. So for one thing all those budding wannabe game developers better have their 3D trigonometry down pat if they hope to get anywhere in that field.

        It still amazes me how dismissive some people are of geometry. They don't realise how much they use it in everyday life without even thinking about it: things like deciding whether it's worth driving to the shop or walking to the corner store, figuring out the best route to take to a friend's place, finding north without a compass, working out if your car will fit into that parking space - all this entails a near-instinctive use of geometry.

        As far as I'm concerned, if you can't even guesstimate the diagonal distance between two points given their x and y coordinates by the time you finish high school, you haven't finished school and you sure as hell aren't ready for any skilled position.

        1. Vic

          Re: Euclid is not outdated, worthless knowledge

          You also need a good grasp of Euclidean geometry if you want to get into any of these fields: game design, 3D modelling, graphic design, architecture, or photography

          Years aog, I worked for a company that provided quite a bit of the MediaHighway platform to Canal+[1].

          My first task was to write the ellipse rendering stuff. At the briefing with the head tekkie, I was asked if I knew how to do ellipses. I replied that I understood the maths, but didn't know how to do it *quickly*[2].

          He then proceeded to walk me through the O-level maths that describes an ellipse. I don't think he understood me...

          Vic.

          [1] We were later bought by Canal+, but at that point, we were the startup that knew how to do stuff in digital TV...

          [2] I knew quite a few people from Quicksilva. They'd given me assorted rapid ways of doing trigonometric functions which were slow on Sinclair machines.

    2. Syren Baran
      Mushroom

      Re: Someone who understands statistics

      "will be less likely to play the pokies, smoke cigarettes, deny climate change or eat bacon."

      The same holds true for zombies. What's the point again?

  2. Grikath

    "It's a stupid position to take, because Euclidian geometry is only a "basic" mathematical skill for a subset of STEM disciplines, and it typifies the belief that students are best served by rote-learning tasks that wouldn't tax the processing power of a Nokia 3210."

    Funny you should say that... Last time I checked, the people who are mostly responsible for what we now call "the internet age" were expected to be able to handle euclidian geometry, basic calculus, elementary statistics, and several other odds and ends, without a calculator before even being allowed to enroll into University. But hey...

    1. Anonymous Coward
      Anonymous Coward

      Elementary statistics

      How can you draw a pie chart if you don't understand how to divide up a circle?

      1. Bob Dole (tm)

        Re: Elementary statistics

        >>How can you draw a pie chart if you don't understand how to divide up a circle?

        Excel.

    2. phil dude
      Pint

      depends on....

      the university!

      If you've ever had a "white board" interview, you'll know what I mean...

      P.

    3. DropBear

      "...were expected to be able to handle..."

      Not that they have actually ever used them during their entire adult lives, within or without the activity of creating said "internet age", mind you. But sure, they were expected to be able to...

  3. Stevie

    Bah!

    If you can't calculate the internal angles of a coin you also stand little chance of doing the same for a roof truss, making you a non-carpenter either.

    The problem isn't that the country (any country) doesn't need STEM types, it is that those countries cannot remunerate them in the industries that do need them to a level commensurate with the cost of the education required.

    So how about a return to the apprentice/journeyman model? The government pays for your degree and you in turn agree to work for X years for the government (or until you pay off the balance of the debt).

    You could give an education as part of a job too, so the degree is earned while the student is working for the people paying for it.

    Either way, I think this is the only way to resolve the dichotomy and bring the needed skills to where they are required while also reining in spiralling education costs and defusing the inevitable mass defaulting and economy crash waiting in the wings.

    1. Anonymous Coward
      Anonymous Coward

      Re: Bah!

      "If you can't calculate the internal angles of a coin you also stand little chance of doing the same for a roof truss, making you a non-carpenter either."

      What kind of coins do you use? I have a few seven sided ones (20p and 50p) in my pocket but they have curved sides as well and the corners are chamfered as well. Where do I measure the angles and to what degree of accuracy? Now: assume a spherical cow err idealized 50p coin (no not one made of platinum), it's a flat septahedron so 360/7 degrees is the internal angle.

      A first fix chippie wacking up a set of roof trusses for a standard build house on site should only need a long level and a (measuring) tape and absolutely no maths. A plumb bob, straight edge (side of saw), pencil (or a spare screw point) might be handy. Oh and lots of wood. They will have to know the standard sizes and what to use where. Note that routine standard sizes eg "6 bee 2" (6 inches by 2 inches) aren't those dimensions - they are the rough sizes. However its funny to see metric sizes being precisely noted on the packaging but you never use those sizes.

      Everyone (should) knows that 2x2 is slightly thinner in one direction and slightly fatter at 90deg (when it doesn't fit, try twisting) and it's not really 2" x 2".

      1. Anonymous Coward
        Anonymous Coward

        Re: Bah!

        "it's a flat septahedron so 360/7 degrees is the internal angle." - ??????

        The internal angles of regular 2d shapes are (180 * (number of sides - 2))/number of sides

        so 900/7 for a heptagon. :-P

        1. Tom 13

          Re: Bah!

          Ah! The SUM of the internal angles. Got it.

          Thank-you very much.

      2. Michael Wojcik Silver badge

        Re: Bah!

        Note that routine standard sizes eg "6 bee 2" (6 inches by 2 inches) aren't those dimensions - they are the rough sizes

        They're nominal sizes, not "rough" sizes. The nominal sizes are exact, and with modern milled lumber, the actual sizes are quite consistent.

        Now, if you're talking about hand-milled lumber, or reclaimed old lumber, or something like that, then sure, you're dealing with rough sizing. But not for the dimensional lumber you pick up in the home center.

      3. Stevie

        A first fix chippie wacking up a set of roof trusses

        Gambrel roof?

        It is disappointing to see how many commentators cannot "do the math" on this issue.

        Or even the math itself in some cases. It's pythagorean trig for Euclid's sake. Humans have had the secrets of that for centuries.

      4. Alan Brown Silver badge

        Re: Bah!

        "A first fix chippie wacking up a set of roof trusses for a standard build house on site..."

        ... is an oh so typically english waste of fucking time and money.

        If it's a standard build then it can take a standard truss, made by the hundred in a factory, at ground level and under cover, then trucked out to the site and lifted on in an hour or so, meaning the entire roof can be finished in a day or less.

        The UK is full of the kinds of attitudes and practices which helped the shipyards compete so well against japanese builders and gave us the likes of British Leyland - whose management seem to have spontaneously migrated into the real estate industry (substandard builds of substandard designs, only this time there are no floods of better designs coming in to show them up for being as bad as they are, the odd Huff House notwithstanding)

        "But it's traditional" doesn't fly. So was dying young from a preventable bacterial infection.

    2. a_yank_lurker

      Re: Bah!

      The key for all STEM fields is to reach the necessary mathematical literacy to understand the math in physics, chemistry, engineering, etc. Have the math skills and with some effort and time any STEM field is accessible. Whether you would get hired in that field, another topic.

    3. Paul Hargreaves

      Re: Bah!

      > So how about a return to the apprentice/journeyman model? The government pays for your degree and you in turn agree to work for X years for the government (or until you pay off the balance of the debt).

      Here's a better one. How about regardless of the government paying for a degree or not you spend the rest of your life working for them.

      That's called income tax. About 40% of my time is spent working directly for the government.

      The primary reason education should be free is that it pushes the potential income of an individual up for life, and hence the government is repaid via increased tax revenue. This assumes that the quality of degrees being offered are marketable and valuable and that having achieved a degree there is suitable employment related to that degree.

      So remove funding and loans for all the non-valuable degrees e.g. history, literature, 'american studies' (wtf?), languages in general, ethics, films, religion, 'gender analytics in economics' (wtf?) etc, basically anything that either doesn't have an actual paid outcome or where 'on the job' would have been a better use of time.

      Make sure the number of places offered for a course resemble the market for a skill. Pretty pointless training 100,000 people in Forensic Science if there are only 4,000 jobs and those are mostly filled by stable candidates.

      And when people want to study 'american studies', more power to them. Go fund your own way or persuade an employer to fund it. No need for a loan from any government.

      1. GrumpenKraut

        Re: Bah!

        > So remove funding and loans for all the non-valuable degrees...

        That is a very slippery slope. Education is never a bad thing. Everybody will be able to name fields he/she doesn't appreciate very much (my choice: gender-anything), still I suggest to let the academia "market" sort itself out. Keep in mind that where I named "gender" someone else will name "mathematics".

        1. Primus Secundus Tertius

          Re: Bah!

          'Education' is indeed bad if it makes classics graduates think they can pontificate on statistical questions using their 'generalist, rounded, people-handling abilities'.

          Boris Johnson is a rare exception among classicists: I have read articles by him that actually do understand statistics. That is a rarity in any policial party.

      2. MonkeyCee

        Re: Bah!

        It's a good idea, but the actual "value" of a degree can vary greatly from it being an entry to a new profession where your study and day to day work line up closely (eg. engineering, medicine), or the general research and presentation skills you learnt on your BA in Bugger All are adaptable to another job in the "real world" which is now gated by a requirement you have a degree.

        So picking which degrees should get the axe is tough, because you can't just pick by direct content -> job (unless it's marketed as a vocational course). Some of the ire against "dumb" courses is simply because you can't see the total value of them. I'm studying AI, the amount of papers from literature, language and anthropology that I read and apply into code are often more than the mathematical ones. Well, depends a bit on the area, but I'm doing word stuff rather than number stuff at the moment.

        As for "gender analytics in economics" that's an academic way of saying "the analysis of economic decisions by gender", which seems a sensible area of study, as it applies to things like setting minimum wages/benefits. It's behavioral economics, so you can add that to your bin list too if you like :)

        I think history is a valid degree, met quite a number of history graduates doing non-history stuff. Thorough, thoughtful types, often called Nigel. And as they say, those that study history are doomed to watch those who didn't repeat it.

        Languages seems an odd one to pick, since it's pretty unusual to be completely mono lingual these days. Well, maybe the kiwis. Anyway, I live in the Netherlands, my course mates and professors speak some combination of Dutch, German or Italian in addition to English, and most people also manage a bit of French. Oh, and a zillion dialects that get spoken around here (Flemish and Limburgish). Linguistics can seem a bit abstract and "useless" but how we use and process language is perhaps our most useful "tool" as a tool using species

        I've also seen the absolute abuse of government funds by "educational" groups running computer courses. It's got computers! It'll make us silicon <feature>! Don't check anything! Millions of bucks spent, students either got passed with doing no work, or could sign up and get living costs, while not having to do anything. 19 year old "computer apprentices". But it's STEM, so it's all cool.

        My general point is that implementing a mechanism for culling courses is tricky, and ripe for abuse. I would hope that the MinEd or whatever equivalent has some sort of vetting for institutions.

        As for cost, I pay about 2k euro a year for fees, and if I wanted a longer commute I could change to a German university to study for free. Whilst not living in, nor paying taxes in Germany.

      3. Naselus

        Re: Bah!

        "So remove funding and loans for all the non-valuable degrees "

        Yes, that's pretty much what Stalin did in the USSR. And that turned out really really well.

      4. veti Silver badge

        Re: Bah!

        Do you really want the government to dictate what is and isn't "acceptable" content for degree courses?

    4. DropBear

      Re: Bah!

      "The problem isn't that the country (any country) doesn't need STEM types, it is that those countries cannot remunerate them in the industries that do need them to a level commensurate with the cost of the education required in any other job than salesman or burger flipper." TFTFY...

      1. tesmith47

        Re: Bah!

        i agree with you except for the one word "CANT" remunerate , i think it is more a case of capitalist WONT remunerate. the capitalist expect that enough bright folks will fin a way to invent or discover that they need not invest any capital or effort neither theirs directly nor theirs indirectly (I.E. the governments tax money!!) yeah the capitalist own everything and all the money!!!

    5. Tom 13

      Re: Bah!

      Sorry, I'm not understanding your shorthand here. What exactly do you mean by "calculating the inside angles of a coin"? Granted I'm exceedingly rusty on my geometry, but I'm pretty sure I could do it if I understood what was being asked. I'm guessing it's an across the pond cultural misunderstanding.

      The apprentice/journeyman model isn't a bad one. Truth be told, it is the one I've used to learn IT (and I'm rather glad I had such a capable master helping me learn the craft). But it does rather eliminate the opportunity for government controlled indoctrination, which is actually the point of public education.

  4. Anonymous Coward
    Anonymous Coward

    Huh?

    At least people who leave high school with decent statistics will be less likely to play the pokies, smoke cigarettes, deny climate change or eat bacon.

    Which is a comment on the authors own (lack of) education, and bigotry..

    It is indeed the statistics that show that climate change is not happening the way the models predict, and that bacon is not that dangerous compared with many other things.

    Climate change alarmism depends on the offices of a mass of people who think they are intelligent and educated, but dont do maths or indeed science very well at all.

    One suspects the author is amongst their number.

    1. Anonymous Coward
      Anonymous Coward

      Re: Huh?

      Just a tick-- if it's on The Register and it is in any way suggesting that eating bacon is bad, it's sarcasm. (I got a new detector after that Apple hypegasm parody)

    2. TheOtherHobbes

      Re: Huh?

      Considering the fact that climate scientists are far more alarmed about the science than the public is - at least the ones I know are - your comment is disingenuous at best, and ignorant nonsense at worst.

      1. nijam Silver badge

        Re: Huh?

        > ... climate scientists are far more alarmed about the science than the public is

        Are they worried about science in the sense that it doesn't support the political theory generally known as climate change, so their jobs are at risk? Or are they not worried about the science at all, but about about the climate? The former seem substantially more likely, all things considered.

        1. Tom 13

          Re: Huh?

          Actually none of them are really worried about this. Trust me on this, I work with far more of them than Hobbes does. I mean yes, they SAY they are when asked directly, but when you watch their actual behaviors it is quite another matter.

          They do however all exhibit a rather profound tendency toward group think and adherence to priestly authority. If you offend their Warmist religion by asking an actual scientific fact they WILL try to excommunicate you from among The Chosen. And the bewildering look in their eyes when you tell them that the Greeks proved that the melting of the Arctic ice caps won't change sea level even a tenth of a millimeter is priceless.

          1. veti Silver badge

            Re: Huh?

            That "bewildered look in their eyes" is called pain. It's what you get when you realise you're talking to someone who doesn't know the difference between the floating Arctic ice cap, and glaciated land masses, such as most of Antarctica, much of Greenland, Alaska, bits of Canada, Russia...

        2. Alan Brown Silver badge

          Re: Huh?

          "Or are they not worried about the science at all, but about about the climate? "

          In my experience, the latter - although some are starting to concede that sea level and temperature may not matter that much as a global oceanic anoxic event is looking increasingly likely to take out a large chunk of the planet's megafauna before too many cities are drowned.

          (The parallel to this is Apollo13. Their oxygen tanks might have exploded and everyone might have been concentrating on making sure they didn't suffocate or die of CO2 poisoning, but the overlooked thing that came closest to killing them was plain old hypothermia - and long before the oxygen ran out.)

    3. Alan Brown Silver badge

      Re: Huh?

      FWIW anyone who does understand statistics will avoid horses and take ecstasy. One is _much_ safer than the other.

      As for bacon: just about everything that's fried is bad for you at some level, so choose the best fried things and don't eat the rest. I'll keep my bacon.

  5. Charles Manning

    Well duh!

    One of the reasons I've heard put forward by philosophy grads is that phylosophy teaches you to think and companies like that.

    Well try something like chemstry. Chemistry requires you look at tiny little clues and slowly figure out what things are made of and figure out how to make more useful things from those. That sort of analytical capability is very valuable when applied to any business.

    Maths too. Risk assessment (actuarial) has always bee an important part of the insurance industry. Over the last decade or so, those skills and methods are getting used far more mainstream in business decision making. Plug in the mathematicians and the statisticians.

    Just as we see with any field of expertise, just being vaguely familiar with a bit of theory is not enough.

    When I got into programming 35 years ago, "programmers" were not graduates, they were filing clerks who were up-skilled in a 3 month COBOL training program. Now you need a whole lot of training and a few years of experience to be any use.

    I fear the "soft science" people like Business Sciences have run out of puff. More rigorous skillsets are needed for business development.

  6. Anonymous Coward
    Anonymous Coward

    Right livelihood?

    The Law and MBA degrees are glutted too, manufacturing is done overseas and the trades have been de-unionized and replaced by immigrant visa labor. What's a bloke to do for a living?

    1. Anonymous Coward
      Anonymous Coward

      Re: Right livelihood?

      exploit them?

    2. DropBear
      Trollface

      Re: Right livelihood?

      "What's a bloke to do for a living?"

      Pinpoint the goldrush-du-jour, resist temptation to participate at all costs, and start selling shovels, pickaxes and booze.

  7. Mark 85

    So, by what the article indicates is that the government is deciding that logical and rational thinking are NOT to be taught? Only teach what the marketplace currently needs/wants? Learning science and scientific method as well as maths, an understanding of engineering and tech is not a waste. At some point, they should be allowed to specialize, but for incoming 1st and 2nd year, the Unis should insist on a well-rounded, thought provoking education including tech, science, the arts, etc.

    The alternate is to end up with those who follow blindly as they've never learned to think things through in a logical and rational manner. Part of many countries' problems stem from an education that only teaches what the masters want them to learn and not what they need to think outside of whatever box they've put into by their degree.

    And in the long term, if a country wants a tech based economy, train them in this, not in philosophy or art appreciation or how to flip a burger. If you have the workforce, the jobs will come or those with the skills will create their own jobs via startups. I've known engineers who became house painters because they liked the work but I've never known of a house painter who became an engineer without getting the schooling.

    1. Tom 13

      Re: those who follow blindly

      The truth is, even with that exposure many people follow blindly anyway because that's what they are prone to do by nature. And most of the ones who don't resist indoctrination anyway because that is their nature. What it leaves is a small middle who might learn to think for themselves.

      That being said, if we could get back to what you propose, I'd be all for it. While the numbers who learn to think for themselves might be small compared to the whole, they're worth it. The problem as I said up-thread is that today's education system is about the reverse: government indoctrination.

  8. Displacement Activity

    If you can't calculate the angles on a 50-cent coin...

    Then you probably don't know how many sides it has. I don't know what a year 12 student is, but anyone in the UK who couldn't answer this question at GCSE (16-year-olds) is unlikely to end up as a radio astronomer, or a statistician.

    Your entire argument is nonsense. This is nothing to do with rote learning - it's a basic concept with almost-zero mathematics involved. Once you've got your head around this, you can move on to vectors and matrices. For a professional mathematician or scientist there's no such thing as an optional subset which can be ignored - would you have a problem writing articles if you weren't allowed to use the letters 'a', 's', or 'd'?

    1. Destroy All Monsters Silver badge
      Holmes

      Re: If you can't calculate the angles on a 50-cent coin...

      THIS!

      Of course it's not absolutely necessary. But it's definitely a strong indicator that sciency and engineering stuff is not for you and you may want to go into sociology, comparative literature or opening a hamburger stand.

    2. Cuddles

      Re: If you can't calculate the angles on a 50-cent coin...

      So very much this. Basic maths like geometry and algebra are used constantly not just in a huge variety of professions, but also throughout the everyday lives of most people. They simply don't realise that's what they're doing most of the time; you don't need to be writing down a solving a big pile of xes and ys for the underlying concepts to be used. The idea that these skills are only relevant to a small number of professional scientists is utterly ridiculous.

      Of course, this is not a new thing. Richard Feynman lamented that students he was teaching were unable to answer a question that was nothing more than a rewording of one they'd just answered, because while they'd been taught the maths they hadn't been taught how to actually relate it to anything. And unfortunately, this is what's still missing from a lot of education - it's not enough to just teach people something, you need to also teach them why you're doing so and how it's relevant to them. See the author of this article for a perfect example of the latter part being missed.

      1. nijam Silver badge

        Re: If you can't calculate the angles on a 50-cent coin...

        > ... throughout the everyday lives of most people...

        Absolutely. Maths is the "power tool" of thought. (Philosophy, not so much.)

        Heinlein had one of his characters say "a person who can't do maths is not fully human" (I think). Maybe a little extreme... or maybe not.

        1. Primus Secundus Tertius

          Re: If you can't calculate the angles on a 50-cent coin...

          You raise a good question: what is it that makes us uniquely human? And is that important?

          1. We are talking bipeds.

          2. Many of us can do arithmetic. Note that arithmetic is not the same as recognising that a bunch of items has five of them. It is knowing that 4+1 = 3+2.

          Is that important? Item 2 certainly is; it is evidence of an ability to go beyond immediate facts.

          @Dropbear: If you play darts, someone has to keep score. Good arthmetic test, that, even if afer a while you will 'know' the result from experience.

          1. Michael Wojcik Silver badge

            Re: If you can't calculate the angles on a 50-cent coin...

            @Dropbear: If you play darts, someone has to keep score.

            And how is that "beyond bog-basic addition", as Dropbear asked? A bit of mental arithmetic is not a compelling argument for STEM education.

            I like mathematics myself. I'm no mathematician, but I've done my share of calculus and linear algebra and group theory and the like.

            I don't believe the vast majority ever comes up in my mundane activities, unless I decide to do some recreational math. I do a lot of DIY stuff but, somehow, I simply don't find myself integrating any functions or finding near-optimal graph traversals in the process. Very simple geometry once in a blue moon, perhaps.

            On rare occasions, it comes up during work, which is nice. But that's because I chose a field where it's sometimes relevant.

            Exposure to mathematics - that is, to formal systems and their applications - is, I think, useful for anyone with normal cognitive abilities. It teaches concepts like abstraction and symbolic manipulation, and reveals some of the aspects of one of the critical intellectual tools of civilization. But this idea that everyone unknowingly uses math all the time in their daily lives is bullshit.

        2. JDKelley

          Re: If you can't calculate the angles on a 50-cent coin...

          It may have been in a few places, but I seem to recall it best from _Starship_ _Troopers_ - "... a man who doesn't know maths isn't a man, he's merely a domesticated animal who has learned to wear shoes and not make messes in the house." (Or something in that vein.) This was given as the reasoning for the protagonist to continue to study - at least his maths - when he was sure he's muffed his 'prentice cruise as a "Temporary Third Lieutenant" and was heading back to post.

          While I am somewhat inclined to argue that philosophy is wholly useless (it depends on just what sort of philosophy we are talking about here - logic, symbolic or otherwise, is always useful; and solipsism makes for wonderful extended sessions of mental gymnastics...) my mother and grandfather (her father) were of two different - yet related - schools of thought on basic education:

          - (Mum) If you can read, you can figure out anything else you need to know. (For this reason, I was taking the newspaper to /kindergarten/ on a daily basis, because I never have napped well. The teacher stopped quizzing me the third day, because I was reading, understanding, and retaining.)

          - {Granddad) If you can do maths, you can figure out anything else you need to know (he'd kickstarted me, extended sessions in his workshop with his textbooks or in the city library saw me working my way through first-year calculus by age twelve.)

          Another quote from Heinlein, speaking in the person of Lazarus Long: "A man should be able to: " (at which followed some two pages of disparate tasks which a man ought to be able to do well. This was closed with what I have come to call 'Heinlein's Dictum') "Specialization is for insects."

          This last has been a guiding principle of life for me.

      2. DropBear
        Devil

        Re: If you can't calculate the angles on a 50-cent coin...

        "The idea that these skills are only relevant to a small number of professional scientists is utterly ridiculous." [Citation needed. Badly.]

        I'd like to hear how and where does any sort of math (past bog-basic addition / multiplication etc. and even that with small numbers only) get used in the daily course of a mundane job like 99% of us have (like a plumber / clerk / supermarket drone / cab driver / insurance salesman / bouncer / hair dresser / car mechanic / cook or waitress in a restaurant / any number of paper shuffling bureaucratic administration / etc. you name it). Even where geometry might seem to apply, it's actually just a measuring tape and a straight edge and / or sheer learned numeric experience ("you need that size there"). And please do try to refrain from contrived "examples" like "well if you see a brick falling from the roof you need to be able to predict the parabola before it hits you..." (and no, a driver doesn't "calculate" anything about how he drives his car) or else I won't be responsible for my actions...

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