You lost me on the section when you started going into different calculators, but I read the rest of the post. Well written even if I ultimately disagree!
The reason imo there is ambiguity with these math problems is bad/outdated teaching. The way I was taught pemdas, you always do the left-most operations first, while otherwise still following the ordering.
Doing this for 6÷2(1+2), there is no ambiguity that the answer is 9. You do your parentheses first as always, 6÷2(3), and then since division and multiplication are equal in ordering weight, you do the division first because it’s the left most operation, leaving us 3(3), which is of course 9.
If someone wrote this equation with the intention that the answer is 1, they wrote the equation wrong, simple as that.
There has apparently been historical disagreement over whether 6÷2(3) is equivalent to 6÷2x3
As a logician instead of a mathemetician, the answer is “they’re both wrong because they have proven themselves ambiguous”. Of course, my answer would be RPN to be a jerk or just have more parens to be a programmer
The calculator section is actually pretty important, because it shows how there is no consensus. Sharp is especially interesting with respect to your comment because all scientific Sharp calculators say it’s 1. For all the other brands for hardware calculators there are roughly 50:50 with saying 1 and 9.
So I’m not sure if you are suggesting that thousands of experts and hundreds of engineers at Casio, Texas Instruments, HP and Sharp got it wrong and you got it right?
There really is no agreed upon standard even amongst experts.
Hi, expert here, calculators have nothing to do with it. There’s an agreed upon “Order of Operations” that we teach to kids, and there’s a mutual agreement that it’s only approximately correct. Calculators have to pick an explicit parsing algorithm, humans don’t have to and so they don’t. I don’t look to a dictionary to tell me what I mean when I speak to another human.
Thanks for putting my thoughts into words, that’s exactly why I hate math. It was supposed to be the logical one, but since it only needs to be parsed by humans it failed at even that. It’s just conventions upon conventions to the point where it’s notably different from one teacher/professor to the next.
I guess you can tell why I went into comp-sci (and also why I’m struggling there too)
No, those companies aren’t wrong, but they’re not entirely right either. The answer to “6 ÷ 2(1+2)” is 1 on those calculators because that is a badly written equation and you(not literally you, to be clear) should feel bad for writing it, and the calculators can’t handle it with their rigid hardcoded logic. The ones that do give the correct answer of 9 on that equation will get other equations wrong that it shouldn’t be, again because the logic is hardcoded.
That doesn’t change the fact that that equation worked out on paper is absolutely 9 based on modern rules of math. Calculate the parentheses first, you then have 6 ÷ 2(3). We could solve from here, but to make the point extra clear I’m going to actually expand this out to explicit multiplication. “2(3)” is the same as “2 x 3”, so we can rewrite the equation as “6 ÷ 2 x 3”. All operators now inarguably have equal precedence, which means the only factor left in which order to do the operations is left to right, and thus division first. The answer can only be 9.
If you’d ever taken any advanced math, you’d see that the answer is 1 all day. The implicit multiplication is done before the division because anyone taking advanced math would see 2(1+2) as a term that must be resolved first. The answer still lies in the ambiguity of the way the problem is written though. If the author used fractions instead of that stupid division symbol, there would be no ambiguity. It’s either 6/2 x 3 = 9 or [6/(2x3)] = 1. Comment formatting aside, if someone put 6 in the numerator, and then did or did NOT put all the rest in the denominator underneath a horizontal bar, it would be obvious.
TL;DR It’s still a formatting issue, but 9 is definitely not the clear and only answer.
I did this at the interview for the power plant I’ve been working at for the past 2.5 years. There was a 3 person panel interviewing me and I think they were impressed that I not only asked this but kept asking it through vague bullshit answers. They initially just said “the previous guy left.” And I just sat there for about 10 seconds, waiting for more info than that. Then I said “okay, did he quit, get fired, put in his notice, retire, get demoted, get promoted, become disabled, die off site, die while here…?” He had gone to a different company, but I was uneasy from their hesitance to be forthcoming, so I dug into questions about the culture there, work/life balance, advancement opportunities, safety record, management style, and (maybe my favorite) “what does success in this role look like and how are your feedback and expectations of that communicated to employees?”
They seemed uncomfortable and impatient, but because I already had a decent job at the time I had nothing to lose by swinging my dick around and cutting the bullshit. I highly recommend applying and interviewing for jobs while you’re already reasonably well-employed. It’s great practice, it keeps your resume up to date, you learn real negotiation tactics, and you get to decline offers that aren’t a substantial step up. About a year and a half ago, I did a video interview in my underwear where the manager and supervisor running the interview couldn’t hear me so I was live troubleshooting and resolved their issue. I got an offer, rejected it by telling HR to come back with a higher offer, got the same offer a week later, asked the HR lady why she wasn’t capable of listening to my instructions and was wasting my time with greedy negotiation tactics (which really annoyed her), asked for her name and the name of her supervisor while wholeheartedly rejecting any offer that would come from her, reported the experience to her supervisor, got a call back from the HR lady full of apologies (which I didn’t forgive but thanked her for), and emailed the supervisor I had interviewed with to thank him and let him know that everything sounded great but I couldn’t work for a company whose HR department was that shitty to me before I even verbally accepted an offer. Because of the nature of my industry and our relatively young ages, I told him I wouldn’t be surprised if I wound up working with him somewhere within the next ten years anyway, and I looked forward to that within a company that respects its employees as much as he seems to.
For those who don’t already know, HR exists to fuck the workers in order to benefit the company. Do not trust a goddamn thing HR says. Get everything documented. Record everything they say if it’s legal to do so in your state. If not, draft immediate, timestamped memos (like an email to yourself) of everything that just happened and was said, and be objective with your phrasing.
Capitalism acts like a car hurtling down a highway with no brakes, powered by the roaring engine of industry.
Its insatiable thirst for growth and profits accelerates industrial activity to reckless speeds, steamrolling environmental concerns in its pursuit of relentless expansion.
Industry isn’t the villain; it’s merely the engine being pushed to its limits by capitalism’s uncontrolled, destructive momentum.
Happened to me today. Turns out MIUI optimized the Clock app.
I allowed it to autostart, I disabled battery optimization, I locked it in recent apps.
It may still occur.
But hey, I only woke up 30 minutes later. “Something isn’t right.”
I loved how my xiaomi went EOL after a major update that broke receiving calls, also the battery saver thing.
Never buying anything off them again, especially after GDPR notifications on everything, like why the fuck do you need this data (I know. Xi Jinping wants to know the good furry fetish porn)
Sounds like my Moto G5s Plus. I updated it to Android 8.1 and it started having issues like lagging, completely freezing up, randomly restarting, battery drain, overheating, etc.
Oh, well. It ran PixelExperience 11 just fine. It also allowed me to use the notification LED that Motorola disabled in software for reasons unknown.
Edit: I just like this part from bootloader unlock license agreement on what doing so may cause:
Cause the Device to overheat, explode and/or catch fire, exceed SAR values, exceed safe volume settings, and otherwise be unsafe, including creating the potential to cause serious bodily injury, including death
A32 5G costs anything from $150 to $300. Trust me, I know what it means to be on a budget - I’ve never owned a phone that costed over $250. However, at that price I’d much rather get something like OnePlus 6 - an old phone with amazing community support (in fact, the new OnePlus 6 I bought from China costed $150) and specs that frankly are probably going to be better than newly released “budget” phones.
They aren’t readily available here either, so I’m ordering it online. Unless you want to tell me you have less online purchase options than people in Russia.
I’ve read your comment history and you said you live around Balkans, fwiw back when I was in Montenegro in 2017 I ordered Zuk Z2 from Aliexpress, it stays well supported to this day, you should be able to do something similar.
Unfortunately not all features are always available on those ROMs.
One example is GrapheneOS and Google Wallet which I cannot use due to GrapheneOS not being considered “certified software” by the app and therefore not being trusted.
spoof safety net or sth
there are ways to get gpay to work. also you may have more luck with lineageos and full system install of official, proprietary google services instead of graphene (but of course you’ll be sacrificing your privacy)
Hi! Nice blog post. Since you asked for feedback I’ll point out the one thing I didn’t really understand. You explain the difference between the calculators by showing excerpts from the manuals and you highlight that in the first manual, implicit multiplication is prioritised. But the text you underlined only refers to implicit multiplication involving special expressions(?) like pi, e, sqrt or log, and nothing about “regular” implicit multiplication like 2(1+3). So while your photos of the calculator results are great proof that the two models use a different order of operations, to me the manuals were a bit confusing since they did not actually seem to prove your point for the example math problems you are discussing. Or maybe I missed something?
You are right the manual isn’t very clear here. My guess is that parentheses are also considered Type B functions. I actually chose those calculators because I have them here and can test things and because they split the implicit multiplication priority. Most other calculators just state “implicit multiplication” and that’s it.
My guess is that the list of Type B functions is not complete but implicit multiplication with parentheses should be considered important enough for it to be documented.
What he means is, if you want to download the document from ISO that describes the standard, you have to pay a fee. Here’s their store page: click.
It’s about 190 USD for a 38 page document describing the rules of the standard. There’s another document with extensions for a similar price. Quite pricey for a PDF file obviously, and the RFC is free to download.
On the other hand, no one in the history of time has gone “hmm, I don’t know how ISO-8601 works, let me go buy this document from the ISO store to figure it out.” Most people just call datetime.isoformat() or whatever their library function is called.
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