The most important maths lesson in my life wasn't actually that hard. It wasn't even really about maths.

Back in the primary school we had the following problem to solve:

There's a guy who likes his coffee... strange. He gets a cup of black coffee, drinks half of it, then fills the empty half of the cup with milk. Drinks half of it and fills back up with milk. His coffee gets whiter and whiter that way, until after the eighth time he just drinks it whole. How much coffee and how much milk did he drink overall?

We've spent the entire lesson calculating this shit. An entire class of primary school kids trying not to make a mistake in their fractions. And not just regular kids – it was an extracurricular for pupils gifted at maths.

At first he drank ½ a cup of coffee. Then he drank a half of this half-coffee half-milk mixture. So now it's ½ + ½⋅½ = ¾ cup of coffee, and ½⋅½ = ¼ cup of milk. Then he drank a half of the ¼-coffee ¼-milk mixture, or something... Then five more times...

Our young brains, that had just learned about fractions in the first place, were now melting, basically trying to calculate the 8^{th} power of some messy fractions. Everyone got a different result. We were tired, disappointed and ready to give up.

So then the teacher gave us the answer. It's one cup of coffee and 4 cups of milk. Simple as that. Not ^{507}/_{512} cups of coffee and ^{1034}/_{256} cups of milk, or whatever we came up with.

Why were we so wrong and tired, while she managed to calculate the correct result in her head in a second?

Because we were calculating how much he drank (exactly what the question was), while she calculated... how much he poured into the cup. He drank everything he had poured, so why not?

He poured in a full cup of coffee and 8× half of cup of milk, and then drank it in an overcomplicated way. That's it.

So here's my math lesson: if you're stuck solving a problem (any problem, not just primary school maths problems), but it gets increasingly harder and harder to solve – don't keep plowing like an idiot, and stop being so sure you're gonna solve it if only you just work hard enough. Instead, take a step back, take a deep breath and try to find a totally different way around it.

Sometimes it's way better to work smart than hard.

The whole class (including the teacher who kept pretending to help us all along) has spent an entire hour calculating boring and complex stuff, while we could have just spent a minute to think about it first.

We didn't *waste* that hour. It might have been one of the most valuable hours of my early life.

This post is not about gays. It's about maths.

Some guy online told me that queers don't deserve rights (or at least the attention of lawmakers), because they make up only 0.03% of the population. Which is ridiculous. Both the argumentation, and the number itself. Human rights are inherent and inviolable, human dignity doesn't depend on numbers of specific minoritiesed groups.

But it shows how important it is to properly estimate how many queer people are there in society. Usually, homophobes are trying to prove it's as low as 0.5% to make homosexuality sound like an aberration, some totally marginal oddity that can be ignored, laughed at or hated. Meanwhile, some studies go as high as 52%! That's a number that should make every homophobic politician worry about their reelection unless they change their hateful policies. Where are such huge discrepancies coming from?

This study treated sexual orientation as a spectrum, and not just gay/bi/straight. 52% is the number of people who say they aren't 100% straight. Also, it's among teenagers in the US, which shows that younger people in countries where the taboo on homosexuality is lower are more open to embrace their queer side and to admit it in a questionnaire.

But let's come back to that ridiculous figure of 0.03%. If it were true, that would mean there's only 12 000 queers in Poland – while last year's Equality Parade gathered around 50 000 people attending in Warsaw alone.

That would also make my hometown of Szczecin, population 400k, a home to just 120 gays, bisexuals, lesbians and trans people. Assuming half of them are female and like a third is a proper age — my dating pool would have been just 30 people. I probably slept with more than that before I'd moved out of the city.

Looking at my high school class, there were 4 people (out of 28) that I know to be LGBTQ (and probably some more that I don't know about), making it around 14%.

But neither of those methods of trying to estimate this number from my personal experience has even a hint of scientific rigour. Most importantly, the sample sizes are laughably small, making them not representative at all.

Proper scientific studies, albeit probably pretty reliable, are easily dismissed by homophobes – those surveys were done by some random people they don't trust, the respondends didn't have to tell the truth about their orientation, etc. etc.

But I think I came up with a way to very roughly estimate the number of gay, lesbian and bisexual people that everyone^{[1]} can do for themselves and see with their own eyes that there's a lot of us.

I went on PlanetRomeo, a very popular gay hookup app that shows you profiles of other guys sorted by distance.

I scrolled down until the 780^{th} person until I've reached the first person to be “1 km away”. This means that in a circle with the area of πr² = 3.14 km² there are at least 780 gays and bisexual guys (and probably some girls, and trans people, and couples with a joint account – but those numbers should be neglectable for the purpose of this rough estimation).

It's hard to estimate, how many gays in here use this particular app, how many use a different one, how many use multiple, and how many don't use any... — so keep in mind that 780 is the lowest estimate. In the radius of 1 km from me there are *at least* 780 guys, actively looking for another guy to meet.

I think it's safe to assume that the number of lesbians and bisexual girls would be similar, if not higher (studies suggest girls tend to be more bisexual than guys, which makes it a low estimate as well), so let's double our number: there's at the very least 1560 queer people in the 3.14 km² area around me.

The population density of the district I live in is 6966 people/km². That means queers are at the very least `1560 people / (3.14 km² * 6966 people/km²) ≈ 7%`

of the population in here.

Seven percent! Plus those who aren't using hookup apps. Plus those who use a different one. Plus the asexual people. Plus the aromantic people. Plus trans people. Plus nonbinary people. Plus all the other queers...

I know, I know. There's so many unknowns in my process. But! For the purposes of proving in a *simple and reproducable* way that the number of queers is orders of magnitude higher than what some homophobes are claiming – I think this process does a great job, doesn't it?

I never would have thought that one day I'll be using hookup apps not to hook up, but to do maths and to fight for human rights 😅

^{[1]} Well, ok, not everyone... there's still a lot of places where queers have to stay so deep in the closet that using apps might not help...