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The full post (non-twitter) is better and has the full explanation: https://thepalindrome.substack.com/p/how-did-the-babylonians-know-2-up https://thepalindrome

The full post (non-twitter) is better and has the full explanation: https://thepalindrome.substack.com/p/how-did-the-babylonians-know-2-up https://thepalindrome.substack.com/p/how-did-the-babylonians... I didn’t realize Babylonians had a system for “decimals” in sexagesimal. Edit: another comment pointed out the post is an extrapolation of this paper: https://www.sciencedirect.com/science/article/pii/S0315086098922091?via%3Dihub https://www.sciencedirect.com/science/article/pii/S031508609...

polygamous_bat 4y ago
It has the full explanation behind a paywall, which may as well be non-existent. No, thank you.
- imglorp 4y ago
  This is the first substack I've seen with a full paywall, not just an engagement nag.
  - Tams80 4y ago
    You missed the whole Domonic Cummings UK thing then. Journalists were moaning about 'having to' subscribe to his SubStack. It was actually the first I heard of the place and I thought it was the norm to charge.
  - sbierwagen 4y ago
    Substack authors can choose which posts to paywall, and how far into the post to end the preview. It's interesting in that the paywall can be trivially circumvented... by asking a paid subscriber to forward the email of the full post. Costs nothing, but in practice, almost never happens.
    - matheusmoreira 4y ago
      > Costs nothing, but in practice, almost never happens. Any information people consider important enough to share with the whole world will not be paywalled. Consequently, any paywalled information must not be important.
- wanderingstan 4y ago
  Strange—I don’t get a paywall and I don’t even have a substack account.
  - AkshatJ27 4y ago
    It cuts off at "Here is how they did it." for me. Had to enter (made up) credit card details to access the rest of the post. http://web.archive.org/web/20221229110741/https://thepalindrome.substack.com/p/how-did-the-babylonians-know-2-up http://web.archive.org/web/20221229110741/https://thepalindr...
    - rootusrootus 4y ago
      Your archive.org link still shows the same paywall for me.
      - nobody9999 4y ago
        Here you go... https://archive.vn/vkHFU https://archive.vn/vkHFU
  - aaws11 4y ago
    same here: NO paywall and I don’t have a substack account. Is it a regional restriction? edit: Thanks to the author for removing the paywall!
- TivadarDanka 4y ago
  Hi there, author here. I have removed the paywall for this and all future posts. I am new to Substack, and still experimenting with the proper format. This change has been in my mind for a while, so I went and removed the paywall from all of my posts, and left the paid subscription as a supporting option.
  - hackernewds 4y ago
    Thank you for doing this and also somehow popping in here
  - nextaccountic 4y ago
    Hey, just wanted to chime in that your post is nice. Now, I wish substack had support for math. Adding formulas in images isn't that bad (and practically unavoidable if you want to draw functions - unless you write js), but, still.
AkshatJ27 4y ago
The only thing extra in the post is the relation between this method and the Newton-Raphson method. You can find the method here: https://en.wikipedia.org/wiki/Newton%27s_method#Square_root https://en.wikipedia.org/wiki/Newton%27s_method#Square_root
- bee_rider 4y ago
  There’s also a bit more historical info in: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Heron's_method https://en.wikipedia.org/wiki/Methods_of_computing_square_ro... It would seem we don’t know exactly what method they used. I would like to propose: really, really long and accurate ruler, just because the mental image is funny. The Greeks hadn’t come around yet to make everybody’s homework harder by insisting on compass and straight-edge (Note: this comment is not historically accurate).
  - justsomehnguy 4y ago
    I would agree on the long and accurate ruler. The actual problem here is understanding what the square root is (and how it can be used), not finding it's value for some arbitrary number. And despite all even 4000 years ago our ancestors could make a very precise tools.
    - Sharlin 4y ago
      It’s ridiculously more likely that they found the approximation by calculating rather than via any experimental means.
      - a9h74j 4y ago
        Without multiplying non-integers, you could seek the square root of 200,000,000 using bisection. Sort of a "long ruler" story.
        jacquesm 4y ago
        Your first guess of that should be within .5% of the actual value.
layer8 4y ago
It's why we have 360 degrees in a circle, and 60 minutes and 60 seconds. (For why the day has 24 hours though, see https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi....)
- hackernewds 4y ago
  Thanks for sharing. that did bit of information. I do not understand though. how is that related? because they are multiples of six? They are also multiples of four and two and three
  - jasonjmcghee 4y ago
    Because the Babylonians used base 60 for their numeric system.

polygamous_bat 4y ago

It has the full explanation behind a paywall, which may as well be non-existent. No, thank you.

imglorp 4y ago
This is the first substack I've seen with a full paywall, not just an engagement nag.
- Tams80 4y ago
  You missed the whole Domonic Cummings UK thing then. Journalists were moaning about 'having to' subscribe to his SubStack. It was actually the first I heard of the place and I thought it was the norm to charge.
- sbierwagen 4y ago
  Substack authors can choose which posts to paywall, and how far into the post to end the preview. It's interesting in that the paywall can be trivially circumvented... by asking a paid subscriber to forward the email of the full post. Costs nothing, but in practice, almost never happens.
  - matheusmoreira 4y ago
    > Costs nothing, but in practice, almost never happens. Any information people consider important enough to share with the whole world will not be paywalled. Consequently, any paywalled information must not be important.
wanderingstan 4y ago
Strange—I don’t get a paywall and I don’t even have a substack account.
- AkshatJ27 4y ago
  It cuts off at "Here is how they did it." for me. Had to enter (made up) credit card details to access the rest of the post. http://web.archive.org/web/20221229110741/https://thepalindrome.substack.com/p/how-did-the-babylonians-know-2-up http://web.archive.org/web/20221229110741/https://thepalindr...
  - rootusrootus 4y ago
    Your archive.org link still shows the same paywall for me.
    - nobody9999 4y ago
      Here you go... https://archive.vn/vkHFU https://archive.vn/vkHFU
- aaws11 4y ago
  same here: NO paywall and I don’t have a substack account. Is it a regional restriction? edit: Thanks to the author for removing the paywall!
TivadarDanka 4y ago
Hi there, author here. I have removed the paywall for this and all future posts. I am new to Substack, and still experimenting with the proper format. This change has been in my mind for a while, so I went and removed the paywall from all of my posts, and left the paid subscription as a supporting option.
- hackernewds 4y ago
  Thank you for doing this and also somehow popping in here
- nextaccountic 4y ago
  Hey, just wanted to chime in that your post is nice. Now, I wish substack had support for math. Adding formulas in images isn't that bad (and practically unavoidable if you want to draw functions - unless you write js), but, still.

AkshatJ27 4y ago

The only thing extra in the post is the relation between this method and the Newton-Raphson method. You can find the method here: https://en.wikipedia.org/wiki/Newton%27s_method#Square_root https://en.wikipedia.org/wiki/Newton%27s_method#Square_root

bee_rider 4y ago
There’s also a bit more historical info in: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Heron's_method https://en.wikipedia.org/wiki/Methods_of_computing_square_ro... It would seem we don’t know exactly what method they used. I would like to propose: really, really long and accurate ruler, just because the mental image is funny. The Greeks hadn’t come around yet to make everybody’s homework harder by insisting on compass and straight-edge (Note: this comment is not historically accurate).
- justsomehnguy 4y ago
  I would agree on the long and accurate ruler. The actual problem here is understanding what the square root is (and how it can be used), not finding it's value for some arbitrary number. And despite all even 4000 years ago our ancestors could make a very precise tools.
  - Sharlin 4y ago
    It’s ridiculously more likely that they found the approximation by calculating rather than via any experimental means.
    - a9h74j 4y ago
      Without multiplying non-integers, you could seek the square root of 200,000,000 using bisection. Sort of a "long ruler" story.
      - jacquesm 4y ago
        Your first guess of that should be within .5% of the actual value.

layer8 4y ago

It's why we have 360 degrees in a circle, and 60 minutes and 60 seconds. (For why the day has 24 hours though, see https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi....)

hackernewds 4y ago
Thanks for sharing. that did bit of information. I do not understand though. how is that related? because they are multiples of six? They are also multiples of four and two and three
- jasonjmcghee 4y ago
  Because the Babylonians used base 60 for their numeric system.