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Spud’s maths lessons

Now let me pose a question I often put on the board when starting a discussion of maths in the context of the political economy of data with second year undergraduates. It was this:

2 + 2 = ?

I have never yet had a student give the right answer.

They all say 4.

It isn’t.

It’s 5. Both those figures written as 2 were 2.49 rounded to the nearest whole number. The sum of the two is 4.98, which rounded to the nearest whole number is 5. The answers the students gave me were almost 25% out in all cases.

And these wrong answers came despite children being taught about rounding to whole numbers in primary schools, just about anywhere in the world.

Holy Shit that’s bad.

Because the thing you’re taught about rounding numbers is that you don’t round numbers during a calculation – for this very reason – and only do so with the final answer.

Well, they did at the LSE, Downside, Worth, the Air Force school in Naples and St Alphege’s anyway.


46 thoughts on “Spud’s maths lessons”

  1. “Both those figures written as 2 were 2.49 rounded to the nearest whole number. ”

    If those figures were written as 2, then how are the students to know that they were “really” 2.49?

    Figures are just figures.

    Oh, and cunts are just cunts.

  2. I knew that “academia” was fraying at the edges with identity overriding intelligence but this is amazing. What disguise could Spud possibly wear that would make someone think there were a couple of synapses linked up in that dome?

  3. “I have never yet had a student give the right answer.”

    The correct answer to 2+2 is 4. The correct answer to “Let x,y be real numbers which, when rounded to zero decimal places, both equal 2. Then what is x+y when rounded to zero decimal places?” then the correct answer is “x+y \in {3,4,5}”. A better mathematician than me will phrase this more formally.

    The students have answered the question correctly as set. The question setter has not phrased the question accurately to reflect what they want to test. This would be successfully appealed if it turned up in an exam (although a proper external examiner wouldn’t let it show up in the first place).

  4. Similarly much of the climate science-cum- propaganda involves taking averages in the middle of the calculation and using them as input to the next steps. Climate grifters seem unaware of the traps involved. Such as, you take an areal average of temperature ranges? What exactly is that? It’s a number but not a value of anything. You can’t just use it as if it meant something.

  5. Who would have guessed that today the polymath of Ely would solve number theory.

    All he’s saying is that the answer to 2 + 2 is anything that he deems it to be.

    How the fuck is this man employed as a professor and pity the poor bastards paying for this

  6. A few years ago, a young engineer came to me with a ‘problem’. The standard stipulated a minimum factor of safety of 1.6 and his calculations returned an answer of 1.58, which of the costly options should we implement to increase the FoS? I told him to round it to one decimal place, just like in the standard. I also took the opportunity to educate him on factors of safety and probabilities of failure when your data are variable and uncertain. Something that I imagine would also be a significant problem in economics.

  7. “When I use a number,” Murphy said in rather a scornful tone, “it means just what I choose it to mean–neither more nor less”

  8. +50% -20% = +20% (e.g. start with 100, gain 50% in year 1, lose 20% in year 2, the result is you’re 20% ahead)
    Divide by 10 and move the negative number across and we have
    So we’re all wrong lol. Every ex accountant knows this shirley.

  9. Dick Murphy, Genius

    Now let me pose a question I often put on the board when starting a discussion of maths in the context of the political economy of data with second year undergraduates. It was this:

    When was the Battle of Hastings?

    I have never yet had a student give the right answer.

    They all say 1066.

    It isn’t.

    It’s 1993, when I fell out with my wife during a coach trip to Sussex.

    Tory neoliberalism has making are children stupiderest.

  10. It does remind you of that old joke, where you ask a mathematician, an engineer, and an accountant what 2+2 equals. The mathematician says 2, the Engineer says 2, +/- your uncertainties, and the Accountant says…well, what do you want it to be…

  11. decnine,
    If the figure was 2.51 then I suspect even the Professor would be able to round that to 2.5!
    I wouldn’t bet the house on that, mind.

  12. And then I go and misread decnine’s comment as 2.51 instead of 1.51 !!
    Candidly, I need to attend a Murphy lecture.

  13. As in Tim’s previous submission, if Spud had ever done anything in his life but be an overblown book-keeper he might have a firmer grasp on reality.

  14. Murphy’s wrong.

    2+ 2 = 6.

    The 2s in the question were 2.99 rounded down to the nearest whole number.

  15. I sneeze in threes

    Rounding to x decimal places is a pain in the arse for accountants when preparing stats accounts. The balance sheet doesn’t balance. All that matters is cash is king. You fudge a rounding adjustment (often in the fixed assets note) but then you’ll need to restate opening balances in the subsequent year when that year’s closing balance rounds too high.

  16. Surely there’s some kind of quality control at the University Level? If he is teaching that 2+2 = 5 can’t he be removed from his position on grounds of incompetence?

  17. Hate to say this but there are other types of rounding apart the “standard” rounding.

    Rounding options include up/down, to value, nearest, multiples and ranges.

    Depends what you are trying to achieve.

  18. Had an oh so clever prof do this trick in my first math lecture at college. Showed us an algebra “proof” that was, or so he claimed, not a valid proof. We had to identify which line of the proof was invalid. None of us said it was the line 1 + 1 = 2. “But what if we are working in characteristic 2?” he says, “then 1 + 1 = 0 not 2!” Not that he had given any indication what “characteristic” we were working in, hadn’t taught us what a “characteristic” was, and by the end of the course we still hadn’t been told. I assume it’s something similar to modular arithmetic. The answer to 7 + 7 is 2 if you’re figuring out the time on a clock 7 hours after 7 o’clock, I get that much. I remember this episode, and little if anything else he taught, only because I thought this was such a stupid trick if you aren’t even going to explain what it means.

  19. Professor
    What’s the average train time from Ely to Liverpool street on a weekday using the quickest trains?
    about 1hr 30 mins
    Wrong. It’s 10 hrs 50 mins. I take the train from Ely to Peterborough, then Peterborough to Kings X, walk to St Pancras. take the Eurostar to Gare du Nord, take the next train back to St P, then to Manchester Piccadilly. From there to Cambridge and on to Ely.

  20. …rounded to nearest odd, rounded to nearest even, rounded towards zero, rounded away from zero… loads of fun.

  21. Take two numbers at random, as Murphy seems to have done.
    The probability that they are both exactly 2.49 strikes me as very low.
    There’s accounting fraud software designed to detect this sort of thing.

  22. @Anon…

    Much like the old “There are 10 sorts of people in the world… Those who understand binary and those who don’t!”.

  23. Because the thing you’re taught about rounding numbers is that you don’t round numbers during a calculation – for this very reason – and only do so with the final answer.

    and further to @rhoda klapp, June 3, 2024 at 8:17 am

    Some many years ago I downloaded the Fortran source code of the NASA GISS climate model, I don’t know if it’s still available but I somehow doubt it. They didn’t so much round in the middle of calculations as manage to lose significance by cheerfully swapping between long and short precision numbers. The old versions of Fortran assigned the precision and type of a variable based on its name!! and it looked like whoever wrote some of the model didn’t realise it. That was only a relatively minor fault compared to some of the others I saw. This was considered to be the premier model at the time so I can’t say I’ve had much faith in climate models since!

  24. Bloke in North Dorset

    Well you’re all wrong:

    2+2=10 or in Spud world it would be 11

    (I’m applying Spud’s trick of expecting you all to be clairvoyant and realise we’re working in Base4)

  25. Murphy torturing logic in the same way that the party does in Nineteen Eighty-Four.

    Murphy is O’Brien in this case.

  26. Dennis, Neither Retired Nor From Wandsworth

    There are few things more repulsive than Richard Murphy when he thinks he’s being clever.

  27. Dennis, Pointing Out The Obvious

    One thing Murphy has highlighted is this: “Political Economy” is a large sack of bullshit.

  28. There’s accounting fraud software designed to detect this sort of thing.
    I’ve always presumed that.
    There was guy asked me recently about doing a bank transfer that was basically money laundering. So I produced a figure that with 21% VAT added was a number with cents on the end close to what he wanted to shift & told him to make up an invoice number & stick it in the reference box. I would imagine round number transfers in thousands ring alarm bells for bank compliance IT.
    It’s also the thing that puzzles me about the Horizon thing. You’d think if the system was accepting incomplete transfers as complete & therefore listing duplicate transactions, two identical numbers in a short interval from the same source should stick out a mile. Sort of thing they should have been looking for anyway as part of fraud protection.

  29. Why would any lecturer want to do this?. Set a question that you know they’ll fail because you formulated the question wrong ? -Is his ego so big and he’s so sad that he has to do this? I bet the students if they have any sense would be muttering cunt under their breathe. I know when i was at Poly if one of our lecturers had been so petty i would have done followed by a quick trip to my year tutor to put in a complaint.

  30. Person in Pictland

    “There’s accounting fraud software designed to detect this sort of thing.”

    I once detected an accounting fraud by noticing that one number, for expenses, was exactly 10% of another number elsewhere in the accounts.

    I don’t think the silly sod was set on stealing: I suspect he’d lost a receipt and made a lousy decision on what number to report in its absence. But they sacked him all the same. I suppose that might have been wise; once they’d lost confidence in him …

    Or maybe they’d gone through older accounts to see if there was a pattern of being cavalier about accuracy.

  31. @Ed Snack

    Reminds me of the other engineer/mathematician joke

    A mathematician and an engineer die and are sent to hell.
    They wake up behind a line. A short distance away is an attractive, sexy lady for each man. Satan appears and informs them that every ten minutes the distance between them and the women will half every ten minutes.
    The mathematician cries out in anguish, knowing that he will never get to touch the woman.
    The engineer is excited and starts celebrating.
    The mathematician looks at him and asks why he’s happy since the distance between them will never get to zero.
    The engineer responds that that may be the case, but soon he will be close enough for all practical purposes…

  32. Have had to point out to people on a few occasions where people have been concerned about a bug or issue that Excel does calculations on the actual numbers not the displayed rounded numbers so it is entirely possible that if you add up the rounded numbers you have a different answer

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