5 ms·

All good points, and the only thing I'll add is that, for me, the utility of mental math (and putting it into practice often) is that it strengthens your mathem

All good points, and the only thing I'll add is that, for me, the utility of mental math (and putting it into practice often) is that it strengthens your mathematical intuition--you start to know, and even feel how numbers work. Having strong mathematical intuition that is reinforced by even basic/rudimentary mental math abilities is indeed a real superpower.

gowld 5y ago
> you start to know, and even feel how numbers work. > mathematical intuition ... is indeed a real superpower. What is this power used for?
- thomascgalvin 5y ago
  Math is all around us, and it's nice to have a gut-level check on whether or not something makes sense. 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.
- jihadjihad 5y ago
  Good question. For me, in my line of work, it allows me to very quickly and on the spot (similar to John's blog post) confirm or deny if something passes the sniff test. If someone says "but that will cost X!", it is a superpower to easily refute or corroborate that. Along those lines, if someone throws out that doing Y will easily provide Z amount of value, simply being able to work through the assumptions the person made when coming up with Z, and offering up your own Z' if necessary, is very advantageous in a live, synchronous setting like a meeting with a client.
- peteradio 5y ago
  Error spotting during otherwise very quick meetings.
- mkr-hn 5y ago
  The replies suggest a need to separate mental math from mental arithmetic. I can't do mental arithmetic despite a lifetime of trying to develop the ability, but still have no trouble with the mathematic intuition based on expected costs described in other comments. It's easy enough to round things to 0 or 5 and sum it up for comparison even if doing the actual numbers in my head just won't happen.
- thrashh 5y ago
  Saving you a shit ton of work down the road because you on a quick glance caught a weirdness.
- spaetzleesser 5y ago
  For deciding if it makes sense to buy a house or finance a car. Or if a high deductible health plan makes sense. It also helps with cooking. Math is all around you.
- ajkjk 5y ago
  Everything, oh my god. (imo, it changes the whole way you think about the world).
  - lanstin 5y ago
    I think that is just called understanding the world.
    - Jensson 5y ago
      We primarily understand the world in terms of numbers and equations. Human intuition for people only sees individuals, it doesn't see the scale of a population or a country. For example the war in Ukraine, people talk a lot about Putin and Zelenskyy and the emotional parts, but the best way to see what really happens is to look at a lot of logistics spreadsheets and how the numbers evolves. Then you understand better what Russia can do, how reasonable their threats are, get a feeling for timeframes etc. 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.
      - ColinWright 5y ago
        > ... many people don't even understand percent. 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.
        5y ago
- ThatGeoGuy 5y ago
  If you can get used to applying Bayes Theorem in your head as a second nature, it helps greatly as a quick dummy check with reality. Obviously this doesn't mean calculating hundreds of probabilities in your head at once, but it can be very useful as a litmus test for all manner of things. 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."
- teawrecks 5y ago
  Once you are familiar with Fourier series expansion, you start seeing everything as a signal that can be broken up and manipulated in interesting ways. From silly stuff like a talking piano (https://youtu.be/-6e2c0v4sBM https://youtu.be/-6e2c0v4sBM), to more complicated and useful inventions like jpeg, real time dynamic light rendering (spherical harmonics), and countless others.
- watwut 5y ago
  Basically, you will be able to "feel" when numbers are wrong - without doing calculations or making an effort. Then you of course have to check before you say something. But without that intuition you would not checked.

gowld 5y ago

> you start to know, and even feel how numbers work. > mathematical intuition ... is indeed a real superpower. What is this power used for?

thomascgalvin 5y ago
Math is all around us, and it's nice to have a gut-level check on whether or not something makes sense. 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.
jihadjihad 5y ago
Good question. For me, in my line of work, it allows me to very quickly and on the spot (similar to John's blog post) confirm or deny if something passes the sniff test. If someone says "but that will cost X!", it is a superpower to easily refute or corroborate that. Along those lines, if someone throws out that doing Y will easily provide Z amount of value, simply being able to work through the assumptions the person made when coming up with Z, and offering up your own Z' if necessary, is very advantageous in a live, synchronous setting like a meeting with a client.
peteradio 5y ago
Error spotting during otherwise very quick meetings.
mkr-hn 5y ago
The replies suggest a need to separate mental math from mental arithmetic. I can't do mental arithmetic despite a lifetime of trying to develop the ability, but still have no trouble with the mathematic intuition based on expected costs described in other comments. It's easy enough to round things to 0 or 5 and sum it up for comparison even if doing the actual numbers in my head just won't happen.
thrashh 5y ago
Saving you a shit ton of work down the road because you on a quick glance caught a weirdness.
spaetzleesser 5y ago
For deciding if it makes sense to buy a house or finance a car. Or if a high deductible health plan makes sense. It also helps with cooking. Math is all around you.
ajkjk 5y ago
Everything, oh my god. (imo, it changes the whole way you think about the world).
- lanstin 5y ago
  I think that is just called understanding the world.
  - Jensson 5y ago
    We primarily understand the world in terms of numbers and equations. Human intuition for people only sees individuals, it doesn't see the scale of a population or a country. For example the war in Ukraine, people talk a lot about Putin and Zelenskyy and the emotional parts, but the best way to see what really happens is to look at a lot of logistics spreadsheets and how the numbers evolves. Then you understand better what Russia can do, how reasonable their threats are, get a feeling for timeframes etc. 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.
    - ColinWright 5y ago
      > ... many people don't even understand percent. 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.
      - 5y ago
ThatGeoGuy 5y ago
If you can get used to applying Bayes Theorem in your head as a second nature, it helps greatly as a quick dummy check with reality. Obviously this doesn't mean calculating hundreds of probabilities in your head at once, but it can be very useful as a litmus test for all manner of things. 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."
teawrecks 5y ago
Once you are familiar with Fourier series expansion, you start seeing everything as a signal that can be broken up and manipulated in interesting ways. From silly stuff like a talking piano (https://youtu.be/-6e2c0v4sBM https://youtu.be/-6e2c0v4sBM), to more complicated and useful inventions like jpeg, real time dynamic light rendering (spherical harmonics), and countless others.
watwut 5y ago
Basically, you will be able to "feel" when numbers are wrong - without doing calculations or making an effort. Then you of course have to check before you say something. But without that intuition you would not checked.