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Comment by happytoexplain | Hacker News Reader

>For those of us who did maths this is obvious, but for those for whom maths was just a list of formulas and processes, applied without any real understanding, I can see that this can come as a surprise.

This comes off as obnoxiously superior. I was excellent at math in school. I was the guy who understood the theory and could extrapolate. And yet this surprised me. Not because the theory is surprising, but because I just hadn't thought about it before - or maybe I did, and it didn't stick. I don't work with percentages every day.

It's sort of like implying that only people who are bad at programming don't know about a particular API or pattern. That's not what makes somebody good or bad at something.

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I don't think the author explained it well. What % means, is, "out of 100" so like X% is X out of 100. % is a unit, just like meter or candela. You can do dimensional analysis with %. To remove a % you do like, X % * 1 / (100%) and then the two % (remember % is a unit) cancel out so you get X % = X / 100.

This dimensional analysis makes more sense with multiple terms, for example X % * Y = X % * 1 / 100% * Y = X * 1 / 100 * Y = X * Y / 100. (And note "of" means "times")

It's the same thing as saying, 5 * 2cm = 10cm = 5cm * 2 (hopefully the statement 5 * 2cm = 5cm * 2 qualifies as "obvious")

If this entire explanation is as automatic to you as breathing (which yes it is if you did a significant amount of technical courses as a student, although admittedly dimensional analysis tends to come up in chemistry not math) then the statement "X% of Y = Y% of X" is vacuously true and I would feel comfortable saying this is more or less "By definition of %" with no further explanation, if I were talking to someone who I know has an equivalent background to me.

Doing the conversion can often be helpful. For example say I'm thinking to myself, "what is 4% of 50" and I'm like ugh idk but half of 4 is 2 so the answer is 2

Agreed. The writing is quite prolix, affected, and pretentious, too. This is apparent even in the first sentence, where the author inexplicably puts quotation marks around "social network feeds" (while incorrectly failing to hyphenate the compound adjective).

This would, of course, be obvious to anyone who has studied languages or writing. For those for whom language is a mere instrument or vehicle of thought, while receiving no thought or appreciation itself, I can see why this may come as a surprise.

I expected there to be something interesting in this loveliness. Instead, I found boredom. I wanted to share in the joy, but found despair in both the original comment and the shocked responses.

Understanding the definition of percentages and expecting them to commute is more basic than some random API. For someone trained in math it's like a "programmer" not understanding what a function is, and vibecoding their way through.

I had to stare at Euler's identity for a while to recover from this.

> I had to stare at Euler's identity for a while to recover from this.

It's pronounced "YEW-ler," right?

And the Greek mathematician is pronounced OY-clid ;)

Anyone, anyone, Yewler?

Maybe they meant that, if you were to sit down and figure out whether that statement is true, someone with a math education would find it is and not be particularly surprised. Not necessarily that you should know it beforehand.

A person who has a degree in math ought to be able to easily understand the result and the “why” behind it the first time they see the result.

And a mature adult should be able to communicate this without treating it, or seeming to treat it, as a marker of superiority.

Agreed. And they didn’t do this. If a physicist says that A is obvious to physicists then this isn’t an insult to others. It’s expected that having expert level knowledge in something indicates that some things are obvious after all the training that are not obvious to those without training.

Your comment convinced me to revisit the quotation. It's even worse than I thought. The author contrasts people who 'understand' because they 'did maths' (i.e. studied maths formally in school) with those who don't understand because they haven't. The implication: formal study in school is the only, and a guaranteed, path to understanding.

Clearly they were not saying this. It is a fact that the overwhelming majority of people who grok mathematics were trained to do so. The set of people who are self taught in math is small enough that one ought to be forgiven for assuming this. Similar to how people who know how to perform brain surgery almost certainly got that knowledge from training.

> Clearly they were not saying this.

It's the meaning of what the author wrote. Even if the author doesn't believe it, I think I'm accurately interpreting the overall posture and attitude. Given the pretention of the rest of the post, I'm not willing to cut the author slack or give the benefit of the doubt

As a person who has a degree in math, I can claim that I easily understand it.

Yet I wasn't aware of it, and I've never used it (as a mental math trick). It was definitely surprising that it is true--and I wasn't aware of it.

You really weren't aware that x% of y = y% of x?

I find that very surprising.

Maybe it was just the way I was taught percentages ( "% means /100, 'of' means multiply), but it seems too trivial a result to even be something worth commenting on.

Yes, I really wasn't aware.

> but it seems too trivial a result to even be something worth commenting on.

Yes, but I also think it is memetic and lovely enough to remembered it if you've encountered it. Calculating 52% of 25kg of something as 52/4=13 sparks joy.

I have training in math and wasn’t consciously aware of this a few years ago when I first saw this. I didn’t then and don’t now think the language used was insulting.

I feel that categorizing people into math-doers and people that just merely apply formulas is insulting in general. Mathematicians can too use other people's theorems without working out all the details, not just people the working in other fields. (Also mathematicians use results from other fields in their daily lives all the time without understanding.)

Also using this random factlet to sort them out seems especially weird, since

    - as I am an example, people with education in math might find it surprising
    - it is standard middle-school stuff, so everyone *understands* it, regardless of a degree in math

- - -

.. this is just a reasoning of why

    > For those of us who did maths this is obvious, but for those for whom maths was just a list of formulas and processes, applied without any real understanding, I can see that this can come as a surprise.

is not lovely.

Okay, I'm done. I've probably spent too much time on a random 2 sentences on a random internet stranger's blog, I don't find this topic that interesting.

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