Napkin Math Tool | Hacker News Reader

Napkin Math Tool

taylor.town

134 pointssurprisetalk33 comments

How do you make use of it? Is it basically logarithms of values? So add them together to multiply them? I don't know if I quite understand how the units would work.

As an example, "how long would it take for everyone in a large high school to microwave their meals if they all did it sequentially?".

People in a large high school is *4* (let's say about 3000 people).

Microwaving a meal is *2* (let's say 5 minutes).

So by Napkin Math we get 4+2=*6* which is a *large metropolitan area*.

Oops. I mean 11.6 days.

And with normal multiplication, 3000 * 5 = 10.4 days, so 11.6 days is a pretty good estimate.

So I think the answer is indeed "add the numbers together to multiply them", and be careful that you understand what units you're using.

Yeah, 'tool' here is a little generous. "list of order of magnitude of some things" is more like it

If notation is a tool of thought, seems reasonable to say a cheat sheet works as a tool too. It's like downloading more RAM for your brain.

How did you get 11.6?

Under the "Time (seconds)" section, I looked up "6", which is my result from 4+2:

> 6 11.6 days, two-week vacation, waiting for a passport, healing from minor surgery

11.6 days is what's listed for time 6, along with two-week vacation and some other examples.

>How do you make use of it?

It could be useful for Fermi estimation, where you generally only care about orders of magnitude.

https://en.wikipedia.org/wiki/Fermi_problem

It is generally a good mental tool.

Yet, without explicitly saying it's about (base-10) logarithms, it is preaching to the choir - either you already know that, or won't learn either.

Pet peeve - while most numbers make sense, this not, by a quite a large number:

> -10 practically impossible, every atom in your body quantum tunneling simultaneously one foot to the left

I don't want to do maths here, but for a single particle to happen that, it would be a totally different scale (I don't know, maybe closer to -10^10^10).

Agree that having something in there for how to use it will make it make sense for 10^1 times more people. Show one simple calculation. I don't know: Probability that at least one person on Earth gets struck by lighting twice in a year.

Yeah I'm not too sure what they should be but the lower probabilities are way off.

For -9 it lists 'shuffling a deck and getting cards in perfect sequential order', which is closer to -68. Also being dealt a royal straight flush is more like 10^-6 unless you get more than 5 cards.

Not that I don't understand why, low probabilities are very tricky to get a grip on. And 'winning the lottery' sounds a lot more likely to people than it should, while having the exact same birthday as someone at work is a lot more likely than you might think.

Great catch! I'll fix those rows later today

Any suggestions for stuff I can put in the probability rows?

I think the problem is that below 10^-6 there's a pretty broad range of magnitudes that are effectively 'happens to n people every k years (if they try very hard)'. Which makes them rare but not impossible, which is annoying because you can't rule it out but you can't expect to easily reproduce it either.

That does tend to be the best way to think about those probabilities. For any probability you can make it happen If you try enough times or with enough people you can try to force it to happen. Below -6 is a pretty wide range of stuff you can just barely make happen if you have enough people, enough tries and enough time.

It's only once you get to the 'wouldn't happen to 10^10 people in a million years' that you get to the stuff that you can be fairly sure has never happened. Matt Parker has quite a good video on it [1]. He settles on 10^-19 as something that you can be fairly sure has never happened (deliberately).

As for other stuff in the probability rows, maybe include a couple of well known paradoxes like the birthday paradox. And be clear what you're saying, things like getting dealt a royal flush depends a lot on the type of poker game.

[1]: https://www.youtube.com/watch?v=8Ko3TdPy0TU

>Not that I don't understand why, low probabilities are very tricky to get a grip on.

They are harder to intuitively guess maybe, but it's still trivial to verify. I don't understand why the article would have so many mistakes, unless either the author just chose whatever numbers felt right (but then why write them down as a reference?) or just used chatGPT.

The one that doesn't make sense to me is "Days per $1000," because it's the only one (that I saw) where each line has an order of magnitude plus an addition unit, and that unit is often different from the one in the heading.

    -2 hours minimum wage day's work, small coffee shop daily revenue    
    -1 days entry-level weekly salary, independent contractor daily rate    
    0 weeks average monthly rent payment, typical car payment

Is the difference in order of magnitude between the first two just one (-2 to -1) or 2 (E-2 hours vs E-1 days)?

And how is "0.1 days per $1000" an entry-level weekly salary? Now we have days and weeks in the same sentence.

Thanks! Definitely something funky going on there. I'll double-check my math and clean that up

Can I ask what what was the process of coming up with this list?

Pretty sure it was "Ask ChatGPT". I wouldn't really rely on it. Too many mistakes.

Reminds me of the Jeff Dean "Numbers you should know" schtick about latency.

Other people are asking about how to use this "tool", I think it's just a rough reference. I almost see it as a kind of art/poetry, the way it's presented.

From the source (and https://bsky.app/profile/taylor.town/post/3lkl4rbfmnc2e):

  <meta name="description" content="Logarithmic tables for estimations.">

Always thought something like this would be really nifty if paired in real-time with quantities we interact with in a daily basis.

Oh, it was a large scam? Hundreds of people participated? Basically if an extended family reunion or apartment building full of people. Not as hard to imagine.

The hope would be to better calibrate our own magnitude of reactions against the numbers we see

It would be an interesting website if formatted like wikidata. Anyone can make/edit a magnitude, and the goal for moderation is keeping like-items in a context comparable. (Stadium Attendance has at least some commonality with Stadium Size)

You'd end up with this big graph of values, that in theory you could traverse as deep as you want by just using the right units and multiplying. "[1-person's joules burned per hour by standing] x [1-standium's worth of people] x [4-football game's length in hours]"

I work with storage, and "how long does it take" questions come up a lot - filling an HDD, wearing out an SSD, etc.

A day is about 10^5 seconds. 10^6 seconds is about a fortnight. A year is about 10^4 hours, or 310^7 seconds, so a billion seconds is about 30 years.

Typically the numbers you're multiplying are vague enough that these numbers are more than accurate enough - e.g. if you want to support 20MB/s for a year, back of the envelope says 600TB, exact says 630.72. You typically picked "20" out of thin air, and unless you have a very* specific use case (e.g. fixed-rate video streams) it's probably only accurate +/- 50% at best.

Two **s or \* to have a literal asterisk in your text.

Some of those are way off, IMO:

- What CPU makes a thousand cycles per second?

- How is fastest electronic switching slower than fastest computer operation?

- AFAIK, DDR5 access time is -8 or -7, not -6.

- Earth rotation frequency is -5, not -1.

- Infrared frequency is more like 14 or 13, not 12.

Whoops -- I'll fix those up later today. Sloppy work on my end. Thanks!

An unforgettable anecdote from an electrical engineering professor I had, some 20 years ago.

Engineering math works like this: if it's an order of magnitude bigger, round it to infinity. If it's an order of magnitude smaller, round it to zero.

Prior to teaching, he'd spent a career working on missile guidance systems.

It’s the same in (mathematical) physics: I routinely say something like “let’s look very far away, say z=10” to my workgroup. :P

If I remember right Isaac Asimov wrote down similar notes on scale and they were publish but I can’t remember what the book was called. I used to do the same think when I was a kid. A teacher saw me doing it and mentioned the book. It haunts me to this day.

Is "Measure of the Universe" the book you're thinking of?

Alternatively, chapter 8 of "Realm of Numbers" touches on logarithms, and "That's about the size of it" chapter from Assimov on Numbers" includes a log-scale table of animal weights (from blue whale at 8.08 to Rotifer at -8.22)

Could be, I’ll check it out. It’s probably on of those childhood memories lost in time. Thanks though.

-1 for Hertz is listed as "earth rotation cycle, tide changes, circadian rhythm", but 1e-1 hz is just a cycle time of 10 seconds. More like how often waves crash on the beach.

Great catch! Super helpful. Thank you

    2.8 hr, watching a movie trilogy

Dune: Part Two

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