> mathematical intuition ... is indeed a real superpower.
What is this power used for?
Say you're at a restaurant, and you and your other both ordered $25-ish dollar entrees, and $10-ish drinks, and split a $15-ish appetizer, and the bill comes closer to $150 than $100, something was probably mixed up.
That kind of quick approximation gives you a nudge to check real numbers.
On the other side of the spectrum, many people don't even understand percent. So if an article says "1% of corona patients died", they don't understand what that actually means. They understand some people died, but not really what the probabilities are or if they should be worried. They don't really understand much at all about the world as even the simplest of analytical articles are beyond their understanding. They can pick up the emotions in the article and understand that 1% dying is bad, but if you told them that 1% dying isn't a big deal they would trust you as well, as the number doesn't tell them anything its just how you say it.
A worryingly (to me) large number of people can't tell you what 3% of 200 is.
Should we care? Should people have a clue about this? Rates of interest are quoted in percentages. Deaths from diseases are quoted in percentages. Growth rates of economies are quoted in percentages.
If you have no idea about them, how can you make properly informed decisions?
And yet people survive, so maybe it really doesn't matter.
They survive thanks to people who knows math. We can't run modern society without a lot of people who knows math, we would regress centuries, every natural science requires people who are good at math. There is a reason why the people who are decent at math are valued in every modern society, even soviet understood that part.
I think we should care if kids can't do it because they learned it recently, but who cares if an adult does it in their head vs. uses a calculator correctly?
> "being able to do quick approximations in mid-conversation is a superpower."
So here's something to think about:
* People who can do quick, rough estimations in their heads say that they find it useful, and that the experience is that they have a sort of superpower.
* People who can't do it say that there's nothing special about it, and using a calculator is just as good.
Perhaps people in the second group don't have the information needed to make an accurate assessment.
The math doesn't add up for me, and I'm hesitant to believe anyone who says it feels like a superpower because that sounds like an exaggeration. What does that comparatively make people who use calculators to do estimates? Simple primates using an iPhone?
Plus the article's reasoning is really bogus to me too: "When I’m on Zoom with a client, I can’t say “Excuse me a second. Something you said gave me an idea, and I’d like to pull out my calculator app.”"
This feels like a forced problem to justify his conclusions. It goes away if the other party is willing to wait for you.
But we're repeating ourselves. I'm saying I agree with the submitted post, that it's everywhere, and in everything, and feels like a superpower. You're saying you don't understand, therefore it can't be that important. That's fine, the post (and my replies here) have tried to give you an insight into this experience ... you don't have to believe it.
Back in a previous job we'd be in a meeting and people would be discussing strategies. The ability to sketch out options, choices, rough costs, and expected benefits on the fly meant that it all flowed without pause, without hesitation. Pulling out calculators and working out the numbers would have made things horribly staccato ... I've been in meetings where that happened.
> What does that comparatively make people who use calculators to do estimates? Simple primates using an iPhone?
It makes them ordinary people (in this sense) without this superpower. They may have other skills that people find extraordinary and don't understand, they might not.
I think the issue that we're leaving out is how right were those calculations? You can throw out a number to move the conversation on, but if you have to double back because you got something wrong, you lost time there maybe some further conclusions were also wrong. I'd rather just try to get it right the first time, and I know I'm flawed as human, which is why I rely on devices rather than gray matter. But I feel like this is optimizing for the wrong thing: flow of conversation vs. accuracy of calculations. That really starts to seem like the same tradeoffs as experience vs. raw speed.
Part of this entire thing is to know when a number is "right enough". Anyone can choose to just throw out random numbers ... we're talking about being able to come up with numbers that are right enough.
Otherwise the whole thing is genuinely pointless.
I don’t know if the calculations are essential (tho I guess they are) but having the feeling for the numbers and the ways things become inevitable because of numeric truths and relationships is essential for understanding reality.
x% of y = x/100 * y
= y/100 * x
= y% of x
For instance, a job offer. One job offers you $28/hr, the other offers you $55,000 a year with 2 weeks paid vacation time
Simple math shows that $28/hr, with 2 weeks unpaid vacation time, is $56,000/year. ($28*2000), and can be ~$2.3k more if you don't take vacation.
Understanding of the world and yourself may make you realize that earning $1k-~$3.3k less a year would be worth it to have a set income that doesn't change even when you take vacations, but it's nice to be able to quickly compare the stark math so that you don't immediately think "big number better".
That's not the best allegory to explain the utility of math, but the basic concept has rung true in many situations anecdotally in my life.
Knowing roughly what the value will come out to be if your priors are ~10, ~100, or ~1000x apart is very helpful when trying to discern if you're just being led down a wrong path.
Generally speaking doing Monte-Carlo simulations in your head would be nothing more than a stress test on your brain, but the simple multiplications and divisions used in reasoning under uncertainty can take you quite far, and with very little effort. You can even double check your work in the future if you really felt you did a bad job, and you'll be able to point out exactly where the error was (to yourselves or others) because it's more formalized than "I had a gut feeling."
Then you of course have to check before you say something. But without that intuition you would not checked.