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In many locations in the Mishna, it is mentioned what should be done if something has an exact measurement. For instance in Shekalim:

Coins which were found between the [chest inscribed] “shekels” and the [chests inscribed] “freewill-offerings: Nearer to [the chest inscribed] “shekels”, they go to the shekels; [Nearer to the chests inscribed] “freewill-offerings”, they go to freewill-offerings; Half way in between, they go to freewill-offerings. [Coins which were found] between [the chest inscribed] “wood” and [the chest inscribed] “frankincense”: Nearer to [the chest inscribed] “wood”, they go to the wood; [Nearer to the chest inscribed] “frankincense”, they go to frankincense; Half way in between, they go to frankincense. [Coins which were found] between [the chest inscribed] “bird-offerings” and [the chest inscribed] “young pigeons for burnt-offerings”: Nearer to [the chest inscribed] “bird-offerings” they go to bird-offerings; [Nearer to the chest inscribed] “young pigeons for burnt-offerings”, they go to young pigeons for burnt-offerings; Half way in between, they go to young pigeons for burnt-offerings. [Coins which were found] between non-sacred [money] and [second] tithes [money]: Nearer to the non-sacred [money], they go to common [money]; Nearer to the [second] tithes [money], they go to [second] tithes; Half way in between, they are considered [second] tithes. This is the general rule: the go to that which is nearer [even if this] is lenient; but if half way in between, [they must go] to that which is the more stringent.

Also, in Taharot or Makhshirin there are many discussions of what happens when congealed Tamei liquid that is exactly the size of an egg becomes liquid again (it is Tahor, but if it is even a tiny bit larger it is Tamei)

But if space is continuous, there is no such thing exactly halfway in between two objects or exactly the size of an egg. Is there some point at which we say the measurement is exact even if a precise measurement might show it is a bit bigger or smaller? Or is there some other way of understanding this?

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  • sefaria.org/Bekhorot.17b.2?lang=bi&with=all&lang2=en
    – H. Eugene Walters
    Aug 31, 2020 at 18:33
  • In general, halakhah doesn't deal with scientific empirialism, but with the world as observed. If a human being cannot see a tardigrade with the naked eye, it's not a bug and water is kosher. Similarly, R Dovid Lifshitz zt"l applied the same idea to louse and maggot eggs. Neither bug reproduces through visible means, and the halakhos that allows you to kill that kind of louse on Shabbos or eat maggots that emerge from within the meat don't change. So, I would think here too -- if the difference in distance isn't big enough to be observed without instruments, it's precisely enough to midway.
    – Micha Berger
    Sep 1, 2020 at 16:30
  • Thanks! Can you bring a source to indicate this also applies to discussions like this? I think in the cases you cite there is no 'half-and-half' case in the halacha. Or is there?
    – Daniel Kagan
    Sep 1, 2020 at 16:45

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