13 votes

Problems of scale: How to get a better grasp on numbers?

Inspired by the post about "petty reform" platforms, I noticed a trend, that matched with my own brain musings.

People have an inherent problem with number conceptualization(Poor natural magnitude conception?).

I recall this being a problem as old as time. Things that have helped me grapple with this are things like Fermi Problems and someone who used a grain of rice to represent the scale of wealth discrepancy in the world, using Bill Gates or Elon Musk as an example (can't find the original video, all the derivatives have been turned into TikTok-esque drivel).

I ask the people of Tildes, what types of scale descriptors, demonstrations, etc. have you found moving in your life? Really putting something into perspective. I will give bonus points for "positive" examples, not just doom and gloom, but welcome anything that tickles your fancy.

6 comments

  1. doors_cannot_stop_me
    Link
    A million seconds is about a week and a half. A billion seconds is about 31 and a half years.

    A million seconds is about a week and a half. A billion seconds is about 31 and a half years.

    17 votes
  2. kru
    Link
    I've thought a bit about this from time to time. It's interesting to me. Humans struggle with non-linearity, both in terms of magnitude of scale and magnitude of change (ie exponential change...

    I've thought a bit about this from time to time. It's interesting to me. Humans struggle with non-linearity, both in terms of magnitude of scale and magnitude of change (ie exponential change being difficult to naturally intuit).

    I think one of the driving factors of this is the way that most of us are initially taught numbers. We're introduced to larger numbers via an exponential scale (the 10's digits), but have them drawn out in a very linear fashion on a blackboard. We see that the difference between 10 and 100 is just another zero, and zero is the smallest number there is. 10 and 1000 is only two zeroes apart. It's understandable that we might mistakenly intuit that larger numbers are closer together than they truly are.

    Just to drive the point home. When seeing them on a blackboard for the first time, the difference between 1 and 1,000 is just 3 zeroes. The difference between a 1,000,000 and a 1,000,000,000 is also just 3 zeroes. So, really, how far apart can they be? Right?

    It's similar to how we show kids pictures of our solar system with Jupiter and Saturn barely an inch away from each other, and the Earth about half the diameter of the sun, and so forth. It's valuable to have all of that information presented in a clean visual package, so a kid can learn about the planets and Earth's place in the order. But it definitely does skew the perception of just how vastly far apart everything is in reality.

    11 votes
  3. first-must-burn
    Link
    The long black strip Montessori lesson. They did this in my daughter's class last year and it made a big impression on her.

    The long black strip Montessori lesson. They did this in my daughter's class last year and it made a big impression on her.

    A few weeks later, after enlisting the help of a local seamstress, Montessori invites the boy and his classmates to meet her. Following Dr. Montessori's instructions, two teachers on bicycles position between them a long wooden dowel, upon which is rolled a huge spool of narrow black cloth. Without a word the teachers begin to unroll the black strip of fabric, laying it on the ground, as they slowly ride their bicycles down the street. Montessori and the inquisitive children follow behind and many neighborhood children join the procession, asking, "What is this? What is it for?"

    Montessori is very quiet. Perhaps she says "Wait and see." Perhaps she does not say a word until the end, when the long black strip has been completely unwound and now at the very end there appears a surprise: a narrow strip of white cloth.

    Montessori finally speaks: "This little white part represents the entire time that human beings have been on Earth. Compare it to the black strip, which represents the age of Earth."

    5 votes
  4. [2]
    SloMoMonday
    (edited )
    Link
    Not exactly massive numbers, but it's so difficult to properly calculate, understand and communicate probability. You're taking an insane amount of specific data points, applying expertise and...

    Not exactly massive numbers, but it's so difficult to properly calculate, understand and communicate probability. You're taking an insane amount of specific data points, applying expertise and technical information and abstracting them down to a limited range. The only practical way to explain these values to non-experts is in broad descriptive terms.

    Unless you have solid frames of reference, most people default to a few arbitrary values when given an exact value.
    Like I can look at my RA dashboard right now and tell you that there is about a 4% chance of the monthly analytics being junk data because it's been a messy few weeks. And it's happened before: a ton of different services managing hundreds of processes across a dozen sites run by hundreds of humans who are not immune to an innocent mistake. I'm not going to say that 4% to everyone, because people will round it down to a 0% impossibility and that number will shoot up dramatically.

    So I'm just sure to remind people that there's a small chance of their mistakes causing a major issue. We all have our own ideas of a "low chance". Maybe its constantly rolling 1s or catching that big fish or an underdog team winning the championship. Yes I'm exaggerating the odds, but it keeps people in the mindset that the outcome can happen.

    1 vote
    1. sparksbet
      Link Parent
      THIS. I work in data science and communicating things like these to people who don't work with these kinds of stats is really difficult if you want to actually use the numbers involved. 1% of hits...

      THIS. I work in data science and communicating things like these to people who don't work with these kinds of stats is really difficult if you want to actually use the numbers involved. 1% of hits being false positives could be thousands or even millions of false positives depending on how many hits you have to begin with. The impact of something like that isn't necessarily something that jives with the average person's intuitive understanding of likelihood and probability.

      2 votes
  5. X08
    Link
    I remember a video of a guy having his notepad open and having tons of 'millions' listed as 100k per block. Then showcasing how much it actually is to a billionaire to buy stuff say, a few...

    I remember a video of a guy having his notepad open and having tons of 'millions' listed as 100k per block. Then showcasing how much it actually is to a billionaire to buy stuff say, a few expensive cars, a few houses and just taking away some lines. And then utter nonsense it seems that it doesn't even worry people in such postions. It's beyond me how people can live like that.

    I'm off the opinion that ethical billionaires don't exist. But that's me getting sidetracked a little.

    Video here https://www.youtube.com/watch?v=0J6BQDKiYyM