8 ms·

Would you notice if your calculator was lying? Research says probably not

64 points by EndXA 7y ago

perl4ever 7y ago
On a related note, I was listening to a talk on information security the other day when the speaker gave "balancing your checkbook" as an example of a control/check on a process. And the funny thing was he didn't ask the audience "do you balance your checkbook?", he asked "how often do you balance your checkbook?" Anyway, this is why Fermi estimation is worthwhile; I never understood why people hate it or think it's pointless. Anything you don't check on for not being absurd will eventually get absurd enough for you to notice. Also, when it comes to phishing, the paragraph on why we can't train people to recognize phishing ignores (as usual) the elephant in the room - corporate and government environments are plagued with legitimate emails that are full of red flags, thus training people to ignore things like misspellings, weird source addresses, and so on. You'll never make any progress on a problem when you're studiously ignoring the important factors...and assuming people balance their checkbooks.
- deleted 7y ago
  [deleted]
- foxyv 7y ago
  To add to this, even if you don't own a checkbook, keeping a tracking budget with something like YNAB, Mint Wallet, or Personal Capital makes a huge difference. I've caught so many weird charges on my credit card that way. It also let me know when my bank decided to start charging a "Checking Fee" on their "Free" checking account >_<
  - perl4ever 7y ago
    I have a bad habit of reading the agreements, and I can't stomach the ones for services like that. Lots of stuff about power of attorney...
    - foxyv 7y ago
      Yeah that's part of why I don't use the account imports and do everything manually. Plus it's pretty limited. For example, from YNAB: "FOR PURPOSES OF THIS AGREEMENT AND SOLELY TO OBTAIN AND PROVIDE THE ACCOUNT INFORMATION TO YOU AS PART OF THE SERVICES, YOU GRANT THE COMPANY A LIMITED POWER OF ATTORNEY,"
EndXA 7y ago
The original study that's mentioned here: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223736 https://journals.plos.org/plosone/article?id=10.1371/journal... Abstract: > Calculators are often unnecessary to solve routine problems, though they are convenient for offloading cognitively effortful processes. However, errors can arise if incorrect procedures are used or when users fail to monitor the output for keystroke mistakes. To investigate the conditions under which people’s attention are captured by errant calculator outputs (i.e., from incorrectly chosen procedures or keystroke errors), we programmed an onscreen calculator to “lie” by changing the answers displayed on certain problems. We measured suspicion by tracking whether users explicitly reported suspicion, overrode calculator “lies”, or re-checked their calculations after a “lie” was presented. In Study 1, we manipulated the concreteness of problem presentation and calculator delay between subjects to test how these affect suspicion towards “lies” (15% added to answers). We found that numeracy had no effect on whether people opted-in or out of using the calculator but did predict whether they would become suspicious. Very few people showed suspicion overall, however. For study 2, we increased the “lies” to 120% on certain answers and included questions with “conceptual lies” shown (e.g., a negative sign that should have been positive). We again found that numeracy had no effect on calculator usage, but, along with concrete formatting, did predict suspicion behavior. This was found regardless of “lie” type. For study 3, we reproduced these effects after offering students an incentive for good performance, which did raise their accuracy across the math problems overall but did not increase suspicion behavior. We conclude that framing problems within a concrete domain and being higher in numeracy increases the likelihood of spotting errant calculator outputs, regardless of incentive.
mindB 7y ago
At the bottom of the article, it links to [1] as the original article. Could we please update the link? [1] https://theconversation.com/would-you-notice-if-your-calculator-was-lying-to-you-the-research-says-probably-not-126027 https://theconversation.com/would-you-notice-if-your-calcula...
kevinmchugh 7y ago
My cousin lived in rural Moldova from 2002-2004. She said at many markets, vendors had both calculators and abaci. The vendors mostly totalled bills with an abacus, because customers assumed the calculators were built to cheat them, and they could follow the summing when performed on an abacus. I wonder how it goes now, with more penetration of technology. What would a calculation interface designed for verification look like? How could you build a calculator app that's as trusted as an abacus?
- pg_is_a_butt 7y ago
  make it look like an abacus, duh.
- CamelCaseName 7y ago
  If people are unwilling to do the math themselves, then it becomes a question of what can you trust? Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion. Something digital (an iPhone app) could silently do the same. But what if you make it really easy for the user to do the math themselves, by explicitly breaking down the calculation into a video of smaller steps where the numbers move to show the calculation. E.g. $19 + $25 + $28 on such an app: 19 25 +28 --- 10 20 14 +28 --- 10 20 10 20 +12 --- 30 10 20 +12 --- 40 20 +12 --- 60 +12 --- 72
  - catalogia 7y ago
    > "Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion." That's true, but people often overestimate their ability to see through such ploys. That's why the shell game (https://en.wikipedia.org/wiki/Shell_game https://en.wikipedia.org/wiki/Shell_game) is thousands of years old and still going strong, across the world.
  - judge2020 7y ago
    I think they need some registers that print receipts.
  - nkrisc 7y ago
flybrand 7y ago
In 1998 my first job involved manually checking very large xl sheets for government cases to confirm that the math was right. If there are $s involved, someone will notice.
- tehlike 7y ago
  It might be too late when they notice, though.
- jmkni 7y ago
  Was the maths ever wrong on the Excel spreadsheets? What was the cause when that happened?
  - flybrand 7y ago
    Yes - at that time there were two common errors that we would find about once per week that were known issues. (Can’t remember specifics - but we were thrilled when an old WSJ article noted them.) They were a combination of multiplication / exponential and some basic if-then statements. Easier items - where rounding resulted in paper errors were common.
  - nwallin 7y ago
    The fdiv bug in the Pentium x87 unit was discovered because someone was manually checking their Excel spreadsheets. https://en.wikipedia.org/wiki/Pentium_FDIV_bug https://en.wikipedia.org/wiki/Pentium_FDIV_bug
    - jmkni 7y ago
      Waow, nuts/interesting. Thanks
- papln 7y ago
  1998 is a bit late, but in the 1970s people commonly did this professionally as a fallback/verification for these newfabngled machines (and of course also there were similar jobs as the primary source of results in the age before machines). Those people's job roles were called "computer", before the machines took over the name.
deleted 7y ago
[deleted]
orionblastar 7y ago
I had a calculator from 1985 a TI Scientific SLR solar powered. I did not know it had a bug in the square root function. It was enough to flunk Algebra and get a C in Statistics. I bought a more modern calculator later on when I went back to college and learned the older one had a square root bug. I never learned to do the math in my head, that would have been a neat trick.
- nullc 7y ago
  Arbitrary precision sqrt in your head: There are two ways to do it, one is via a process that looks like long division, the other is via newtons method. I find the latter more useful because I for me its easier to remember and even a single step of it gives a pretty good result. First guess get an initial guess. If you're good with base-2, you can crop off half the number's binary digits. Otherwise, think of the number in scientific notation and take the sqrt of the mantissa and halve the exponent. Alternately, guess and check some nearby squares. Now we apply newton's method using the derivative of sqrt() to refine your guess: guess_n+1 (x) = 0.5 * (guess_n + x/guess_n) That division is a PITA mentally, so don't be a chump-- keep your intermediate results in rational form and keep multiplying up the denominator (the rapidly bloating denominator also gives you an idea of how fast the precision of this process increases-- very fast...). Sometimes I get the sign wrong, but that or any other mistake I've encountered obvious really fast.
  - SamReidHughes 7y ago
    That algorithm should be called square rootus horribilis. Let's say we're square rooting a 3-4 digit number (or you can multiply/divide out the exponent accordingly). I recommend starting with the (x + .5)^2 = x(x+1) + .25 shortcut, multiplied by 100, to be able to compute all multiple-of-five squares 5, 10, 15, 20, ..., 95. Then, from some multiple of 5 that is x, with k in {-2,-1,0,1,2}, use (x+k)^2 = x^2 + 2xk + k^2 to tweak that to a particular perfect square. E.g. 42^2 = 1764 = 1600+160+4. Now, we're square rooting a number, so find the two nearest perfect squares. Depending on how close you are to halfway between them, and depending on if you're in the mood for that sort of thing, poke it up by <0.25 to account for the quadratic factor of whatever you're square rooting (because (x+.5)^2 is 0.25 less than the average of x^2 and (x+1)^2), and then linearly interpolate between the two perfect squares. (You don't really have to calculate both neighboring squares to interpolate, because the difference is about 2x, and you probably already calculated that when you did the 2xk calculation.) So for example, what's the square root of (types randomly) 5719? Why, 56 is 7*8, so 5625 is 75^2. We're like, 95 more than that, out of 150? So, 75.6 and change. Or more exactly, 94/151? That's like a +4% -.6% adjustment of .6 [1], so maybe 75.62. Or even closer, you might use 94.2/151, sure. [1] (a+n%)/(b+m%) can be approximated (a/b) + n% - m%, for small percentages.
jbarham 7y ago
I've personally witnessed scammers using people's trust in calculators being correct to cheat them. It was at the Zambia-Zimbabwe border at Victoria Falls in 1999. We needed to change USD into Zimbabwe dollars and were approached by an informal money changer who ostentatiously did the calculation on his calculator in full view. We knew roughly what the exchange rate should be and confirmed that the money changer was using close to that on the calculator. However, the final result of the multiplication on the calculator was fraudulently low. I thought the result was "off" but given the relatively high exchange rate (this was pre-hyperinflation), by the time I'd done the math in my head he'd taken our USD and disappeared. Not a huge deal as we were only out by maybe tens of USD, and we had to grudgingly admit that it was a very effective scam.
- jlg23 7y ago
  > I've personally witnessed scammers using people's trust in calculators being correct to cheat them. Whenever people shove a calculator into my face, I expect a scam. One of the oldest, used a lot in restaurants: 50+0 (showing customer the zero) + one coffee + ...
  - achow 7y ago
    Without calculator how would one calculate things in places like Zimbabwe or any Mom-Pop place where there are no computers. Apart from building 'trust', calculator plays important job of communication - people in places like Zambia probably do not know how to write in numbers in English (or are not very fluent) and also probably do not know how to say the numbers in English. Being traders however they would recognize numbers readily, so they communicate via calculator by punching out the numbers. That is, calculator is used even when there is no calculation involved. [Edit - Corrected the Roman numerals to English numbers]
    - jlg23 7y ago
      Yes, when they are mere displays, no problem. The scam I talked about only works when adding up larger number of items (like a table of 4 at a restaurant) but there it is pervasive. With honest traders I never had a problem, neither in Africa nor in South America: Calculator on the table, reset in front of me, slowly, step by step, add up the items so I have time to punch it into my own calculator/phone.
perilunar 7y ago
I bought a QAMA calculator to improve my estimating abilities, but then put it in a drawer and forgot about it. http://qamacalculator.com/index.html http://qamacalculator.com/index.html
maaaats 7y ago
Reminds me of when I was TA for calculus at university. Lots of people got one answer wrong, having done the calculations correctly. Found out roughly half of the calculators gave the answer in a different than expected quadrant. Found the picture: https://imgur.com/a/Ve8DVXu https://imgur.com/a/Ve8DVXu
- roelschroeven 7y ago
  Unless I'm missing something the right half of that picture is simply wrong, not just another quadrant. tan(-1/3 pi) = -sqrt(3), so arctan(sqrt(3)/-1) = arctan(-sqrt(3)) = -1/3 pi != 1/3 pi Why do they use sqrt(3)/-1 instead of simply -sqrt(3)? I have the impression something else is going on. Are we seeing the last line of a multi-line expression? Why do we see the bottom curls of the parentheses but not the top curls?
  - maaaats 7y ago
    Yeah, I meant that by some thought one should have realized the answer was unexpected/off, but as the article states one does not really think about that when using a calculator. The parantheses are just how it looks on that model, I tried inputing the exact same sequence on multiple calculators.
  - papln 7y ago
    Despite convention, it is reasonable to consider sqrt(3) to have ambiguous sign since inverse(square) is a multi-valued function (as is arctan). So you can have arctan(-sqrt(3)) = arctan(sqrt(3)) = pi/3 (allowing for arbitrary selection from multi-valued functions) This is a problem in general with the design of calculators and single-result algorithms in general. The -1 might be needed to trigger the bug. The Citizen calculator has a reputation for bad math: https://forum.kerbalspaceprogram.com/index.php?/topic/119681-stupid-calculators/ https://forum.kerbalspaceprogram.com/index.php?/topic/119681...
WalterBright 7y ago
I recall this being researched in the 1970s. The calculators had to be off by a factor of 2 before people became suspicious.
codeulike 7y ago
Would you notice if your calculator was lying? Well no, because thats the point of calculators, right? You trust them to get it right but if its something important you run it through twice just in-case you made a mistake. Its like saying "Would you notice if your coffee machine was adding a bit of alcohol to your coffee?" . We're obviously not expecting mundane appliances to do weird shit to us, and it would mostly be a waste of time and energy to worry about things like that.
- mkl 7y ago
  Calculators generally don't lie [1], but people do frequently make mistakes pressing their buttons. Calculators' accuracy cannot be trusted, because people's accuracy cannot be trusted. I think this experiment is really simulating things like entering mistakes, and you should pay attention and notice when the numbers seem off. I just finished marking an exam question that depended heavily on calculator work, and quite a few people need to work on their calculator mistrust... [1] Well, they do! But only things like small rounding errors that usually don't matter.
  - codeulike 7y ago
    Dealing with operator error is different from having doubts about the accuracy of an appliance. For quite a lot of things done on a calculator, trying to judge whether the numbers seem 'right' is going to be difficult. A more reasonable way to reduce operator error is to key the calculation through the device a couple of times and make sure you get the same answer.
    - mkl 7y ago
      For purely keying errors, yes, but at least as big a problem are errors in translating formulas to the calculator, like leaving out parentheses, and these errors will probably just be repeated.
pimmen 7y ago
I work in data engineering, and we have multiple systems built by other people talking to our pipeline. Just one of them being off by a little might send the KPIs, the machine learning models and much more into a spiral where they end up completely wrong. This has unfortunately made me paranoid and uncertain of anything data or calculation related. I cross check all my day to day calculations and, annoyingly, my friends' calculations too. Any known remedies from people with similiar problems would be appreciated.
goatinaboat 7y ago
Back in the day it was not uncommon to do important calculations twice, once on HP and once on TI, just in case of bugs.
cellular 7y ago
Once my friend wrote a program for an hp48sx that would add 1 to any calculation. He tried to let people borrow his calculator.
- copperx 7y ago
  Did he teach them how to use RPN before letting them borrow it?
  - cellular 7y ago
    Most of us geeks already knew rpn. He was an uber geek. :-)

64 points by EndXA 7y ago

On a related note, I was listening to a talk on information security the other day when the speaker gave "balancing your checkbook" as an example of a control/check on a process. And the funny thing was he didn't ask the audience "do you balance your checkbook?", he asked "how often do you balance your checkbook?" Anyway, this is why Fermi estimation is worthwhile; I never understood why people hate it or think it's pointless. Anything you don't check on for not being absurd will eventually get absurd enough for you to notice. Also, when it comes to phishing, the paragraph on why we can't train people to recognize phishing ignores (as usual) the elephant in the room - corporate and government environments are plagued with legitimate emails that are full of red flags, thus training people to ignore things like misspellings, weird source addresses, and so on. You'll never make any progress on a problem when you're studiously ignoring the important factors...and assuming people balance their checkbooks.

deleted 7y ago
[deleted]
foxyv 7y ago
To add to this, even if you don't own a checkbook, keeping a tracking budget with something like YNAB, Mint Wallet, or Personal Capital makes a huge difference. I've caught so many weird charges on my credit card that way. It also let me know when my bank decided to start charging a "Checking Fee" on their "Free" checking account >_<
- perl4ever 7y ago
  I have a bad habit of reading the agreements, and I can't stomach the ones for services like that. Lots of stuff about power of attorney...
  - foxyv 7y ago
    Yeah that's part of why I don't use the account imports and do everything manually. Plus it's pretty limited. For example, from YNAB: "FOR PURPOSES OF THIS AGREEMENT AND SOLELY TO OBTAIN AND PROVIDE THE ACCOUNT INFORMATION TO YOU AS PART OF THE SERVICES, YOU GRANT THE COMPANY A LIMITED POWER OF ATTORNEY,"

EndXA 7y ago

The original study that's mentioned here: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223736 https://journals.plos.org/plosone/article?id=10.1371/journal... Abstract: > Calculators are often unnecessary to solve routine problems, though they are convenient for offloading cognitively effortful processes. However, errors can arise if incorrect procedures are used or when users fail to monitor the output for keystroke mistakes. To investigate the conditions under which people’s attention are captured by errant calculator outputs (i.e., from incorrectly chosen procedures or keystroke errors), we programmed an onscreen calculator to “lie” by changing the answers displayed on certain problems. We measured suspicion by tracking whether users explicitly reported suspicion, overrode calculator “lies”, or re-checked their calculations after a “lie” was presented. In Study 1, we manipulated the concreteness of problem presentation and calculator delay between subjects to test how these affect suspicion towards “lies” (15% added to answers). We found that numeracy had no effect on whether people opted-in or out of using the calculator but did predict whether they would become suspicious. Very few people showed suspicion overall, however. For study 2, we increased the “lies” to 120% on certain answers and included questions with “conceptual lies” shown (e.g., a negative sign that should have been positive). We again found that numeracy had no effect on calculator usage, but, along with concrete formatting, did predict suspicion behavior. This was found regardless of “lie” type. For study 3, we reproduced these effects after offering students an incentive for good performance, which did raise their accuracy across the math problems overall but did not increase suspicion behavior. We conclude that framing problems within a concrete domain and being higher in numeracy increases the likelihood of spotting errant calculator outputs, regardless of incentive.

mindB 7y ago

At the bottom of the article, it links to [1] as the original article. Could we please update the link? [1] https://theconversation.com/would-you-notice-if-your-calculator-was-lying-to-you-the-research-says-probably-not-126027 https://theconversation.com/would-you-notice-if-your-calcula...

kevinmchugh 7y ago

My cousin lived in rural Moldova from 2002-2004. She said at many markets, vendors had both calculators and abaci. The vendors mostly totalled bills with an abacus, because customers assumed the calculators were built to cheat them, and they could follow the summing when performed on an abacus. I wonder how it goes now, with more penetration of technology. What would a calculation interface designed for verification look like? How could you build a calculator app that's as trusted as an abacus?

pg_is_a_butt 7y ago
make it look like an abacus, duh.
CamelCaseName 7y ago
If people are unwilling to do the math themselves, then it becomes a question of what can you trust? Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion. Something digital (an iPhone app) could silently do the same. But what if you make it really easy for the user to do the math themselves, by explicitly breaking down the calculation into a video of smaller steps where the numbers move to show the calculation. E.g. $19 + $25 + $28 on such an app: 19 25 +28 --- 10 20 14 +28 --- 10 20 10 20 +12 --- 30 10 20 +12 --- 40 20 +12 --- 60 +12 --- 72
- catalogia 7y ago
  > "Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion." That's true, but people often overestimate their ability to see through such ploys. That's why the shell game (https://en.wikipedia.org/wiki/Shell_game https://en.wikipedia.org/wiki/Shell_game) is thousands of years old and still going strong, across the world.
- judge2020 7y ago
  I think they need some registers that print receipts.
- nkrisc 7y ago

flybrand 7y ago

In 1998 my first job involved manually checking very large xl sheets for government cases to confirm that the math was right. If there are $s involved, someone will notice.

tehlike 7y ago
It might be too late when they notice, though.
jmkni 7y ago
Was the maths ever wrong on the Excel spreadsheets? What was the cause when that happened?
- flybrand 7y ago
  Yes - at that time there were two common errors that we would find about once per week that were known issues. (Can’t remember specifics - but we were thrilled when an old WSJ article noted them.) They were a combination of multiplication / exponential and some basic if-then statements. Easier items - where rounding resulted in paper errors were common.
- nwallin 7y ago
  The fdiv bug in the Pentium x87 unit was discovered because someone was manually checking their Excel spreadsheets. https://en.wikipedia.org/wiki/Pentium_FDIV_bug https://en.wikipedia.org/wiki/Pentium_FDIV_bug
  - jmkni 7y ago
    Waow, nuts/interesting. Thanks
papln 7y ago
1998 is a bit late, but in the 1970s people commonly did this professionally as a fallback/verification for these newfabngled machines (and of course also there were similar jobs as the primary source of results in the age before machines). Those people's job roles were called "computer", before the machines took over the name.

deleted 7y ago

[deleted]

orionblastar 7y ago

I had a calculator from 1985 a TI Scientific SLR solar powered. I did not know it had a bug in the square root function. It was enough to flunk Algebra and get a C in Statistics. I bought a more modern calculator later on when I went back to college and learned the older one had a square root bug. I never learned to do the math in my head, that would have been a neat trick.

nullc 7y ago
Arbitrary precision sqrt in your head: There are two ways to do it, one is via a process that looks like long division, the other is via newtons method. I find the latter more useful because I for me its easier to remember and even a single step of it gives a pretty good result. First guess get an initial guess. If you're good with base-2, you can crop off half the number's binary digits. Otherwise, think of the number in scientific notation and take the sqrt of the mantissa and halve the exponent. Alternately, guess and check some nearby squares. Now we apply newton's method using the derivative of sqrt() to refine your guess: guess_n+1 (x) = 0.5 * (guess_n + x/guess_n) That division is a PITA mentally, so don't be a chump-- keep your intermediate results in rational form and keep multiplying up the denominator (the rapidly bloating denominator also gives you an idea of how fast the precision of this process increases-- very fast...). Sometimes I get the sign wrong, but that or any other mistake I've encountered obvious really fast.
- SamReidHughes 7y ago
  That algorithm should be called square rootus horribilis. Let's say we're square rooting a 3-4 digit number (or you can multiply/divide out the exponent accordingly). I recommend starting with the (x + .5)^2 = x(x+1) + .25 shortcut, multiplied by 100, to be able to compute all multiple-of-five squares 5, 10, 15, 20, ..., 95. Then, from some multiple of 5 that is x, with k in {-2,-1,0,1,2}, use (x+k)^2 = x^2 + 2xk + k^2 to tweak that to a particular perfect square. E.g. 42^2 = 1764 = 1600+160+4. Now, we're square rooting a number, so find the two nearest perfect squares. Depending on how close you are to halfway between them, and depending on if you're in the mood for that sort of thing, poke it up by <0.25 to account for the quadratic factor of whatever you're square rooting (because (x+.5)^2 is 0.25 less than the average of x^2 and (x+1)^2), and then linearly interpolate between the two perfect squares. (You don't really have to calculate both neighboring squares to interpolate, because the difference is about 2x, and you probably already calculated that when you did the 2xk calculation.) So for example, what's the square root of (types randomly) 5719? Why, 56 is 7*8, so 5625 is 75^2. We're like, 95 more than that, out of 150? So, 75.6 and change. Or more exactly, 94/151? That's like a +4% -.6% adjustment of .6 [1], so maybe 75.62. Or even closer, you might use 94.2/151, sure. [1] (a+n%)/(b+m%) can be approximated (a/b) + n% - m%, for small percentages.

jbarham 7y ago

I've personally witnessed scammers using people's trust in calculators being correct to cheat them. It was at the Zambia-Zimbabwe border at Victoria Falls in 1999. We needed to change USD into Zimbabwe dollars and were approached by an informal money changer who ostentatiously did the calculation on his calculator in full view. We knew roughly what the exchange rate should be and confirmed that the money changer was using close to that on the calculator. However, the final result of the multiplication on the calculator was fraudulently low. I thought the result was "off" but given the relatively high exchange rate (this was pre-hyperinflation), by the time I'd done the math in my head he'd taken our USD and disappeared. Not a huge deal as we were only out by maybe tens of USD, and we had to grudgingly admit that it was a very effective scam.

jlg23 7y ago
> I've personally witnessed scammers using people's trust in calculators being correct to cheat them. Whenever people shove a calculator into my face, I expect a scam. One of the oldest, used a lot in restaurants: 50+0 (showing customer the zero) + one coffee + ...
- achow 7y ago
  Without calculator how would one calculate things in places like Zimbabwe or any Mom-Pop place where there are no computers. Apart from building 'trust', calculator plays important job of communication - people in places like Zambia probably do not know how to write in numbers in English (or are not very fluent) and also probably do not know how to say the numbers in English. Being traders however they would recognize numbers readily, so they communicate via calculator by punching out the numbers. That is, calculator is used even when there is no calculation involved. [Edit - Corrected the Roman numerals to English numbers]
  - jlg23 7y ago
    Yes, when they are mere displays, no problem. The scam I talked about only works when adding up larger number of items (like a table of 4 at a restaurant) but there it is pervasive. With honest traders I never had a problem, neither in Africa nor in South America: Calculator on the table, reset in front of me, slowly, step by step, add up the items so I have time to punch it into my own calculator/phone.

perilunar 7y ago

I bought a QAMA calculator to improve my estimating abilities, but then put it in a drawer and forgot about it. http://qamacalculator.com/index.html http://qamacalculator.com/index.html

maaaats 7y ago

Reminds me of when I was TA for calculus at university. Lots of people got one answer wrong, having done the calculations correctly. Found out roughly half of the calculators gave the answer in a different than expected quadrant. Found the picture: https://imgur.com/a/Ve8DVXu https://imgur.com/a/Ve8DVXu

roelschroeven 7y ago
Unless I'm missing something the right half of that picture is simply wrong, not just another quadrant. tan(-1/3 pi) = -sqrt(3), so arctan(sqrt(3)/-1) = arctan(-sqrt(3)) = -1/3 pi != 1/3 pi Why do they use sqrt(3)/-1 instead of simply -sqrt(3)? I have the impression something else is going on. Are we seeing the last line of a multi-line expression? Why do we see the bottom curls of the parentheses but not the top curls?
- maaaats 7y ago
  Yeah, I meant that by some thought one should have realized the answer was unexpected/off, but as the article states one does not really think about that when using a calculator. The parantheses are just how it looks on that model, I tried inputing the exact same sequence on multiple calculators.
- papln 7y ago
  Despite convention, it is reasonable to consider sqrt(3) to have ambiguous sign since inverse(square) is a multi-valued function (as is arctan). So you can have arctan(-sqrt(3)) = arctan(sqrt(3)) = pi/3 (allowing for arbitrary selection from multi-valued functions) This is a problem in general with the design of calculators and single-result algorithms in general. The -1 might be needed to trigger the bug. The Citizen calculator has a reputation for bad math: https://forum.kerbalspaceprogram.com/index.php?/topic/119681-stupid-calculators/ https://forum.kerbalspaceprogram.com/index.php?/topic/119681...

WalterBright 7y ago

I recall this being researched in the 1970s. The calculators had to be off by a factor of 2 before people became suspicious.

codeulike 7y ago

Would you notice if your calculator was lying? Well no, because thats the point of calculators, right? You trust them to get it right but if its something important you run it through twice just in-case you made a mistake. Its like saying "Would you notice if your coffee machine was adding a bit of alcohol to your coffee?" . We're obviously not expecting mundane appliances to do weird shit to us, and it would mostly be a waste of time and energy to worry about things like that.

mkl 7y ago
Calculators generally don't lie [1], but people do frequently make mistakes pressing their buttons. Calculators' accuracy cannot be trusted, because people's accuracy cannot be trusted. I think this experiment is really simulating things like entering mistakes, and you should pay attention and notice when the numbers seem off. I just finished marking an exam question that depended heavily on calculator work, and quite a few people need to work on their calculator mistrust... [1] Well, they do! But only things like small rounding errors that usually don't matter.
- codeulike 7y ago
  Dealing with operator error is different from having doubts about the accuracy of an appliance. For quite a lot of things done on a calculator, trying to judge whether the numbers seem 'right' is going to be difficult. A more reasonable way to reduce operator error is to key the calculation through the device a couple of times and make sure you get the same answer.
  - mkl 7y ago
    For purely keying errors, yes, but at least as big a problem are errors in translating formulas to the calculator, like leaving out parentheses, and these errors will probably just be repeated.

pimmen 7y ago

I work in data engineering, and we have multiple systems built by other people talking to our pipeline. Just one of them being off by a little might send the KPIs, the machine learning models and much more into a spiral where they end up completely wrong. This has unfortunately made me paranoid and uncertain of anything data or calculation related. I cross check all my day to day calculations and, annoyingly, my friends' calculations too. Any known remedies from people with similiar problems would be appreciated.

goatinaboat 7y ago

Back in the day it was not uncommon to do important calculations twice, once on HP and once on TI, just in case of bugs.

cellular 7y ago

Once my friend wrote a program for an hp48sx that would add 1 to any calculation. He tried to let people borrow his calculator.

copperx 7y ago
Did he teach them how to use RPN before letting them borrow it?
- cellular 7y ago
  Most of us geeks already knew rpn. He was an uber geek. :-)