My Analysis Takes a Bath

As all new fathers do, I ponder calculus problems when I give my son a bath. OK you wash the kid's hair, so now the bath water is soapy. There are two things you can do to try to reduce the soapiness (specifically, soap units divided by volume of water in tub). (A) You can pull the plug so the tub starts to drain. (B) You can turn the faucet on so fresh water pours into the tub.

What is the fastest way to reduce the soapiness? (A), (B), or both? (HINT: I originally convinced myself that one of the techniques was "obviously" in the answer, but then I later reversed myself. I.e. I think one of the techniques is irrelevant.)


  1. And all this time I thought you were keeping an eye on Clark while bathing him.

    I'm not sure I understand why you need to reduce soapiness in the tub, since it's the supergentle baby soap, and since we rinse him off before we take him out.

  2. I'm preparing for homeschooling! And of course one needn't reduce the soapiness, but it happens when Clark pulls out the plug (and tries to eat it) while the water is still running. So, when Clark puts the plug back in, does that change the rate at which the soapiness decreases?

    I.e. if you had to drink a cupful of tub water in 30 seconds, would you leave the plug in or out, or would it not matter?

  3. P.S. What I mean is, if 30 seconds from now you have to at that point fill the cup and drink it, in the meantime do you want the plug in or out, and do you want the water running or not?

  4. How 'bout
    1. pull the plug
    2. rinse child
    3. remove rinsed child to drying location.
    4. don't drink the water

  5. If you want to avoid calculus, teach Clark proper dental hygiene early on.

  6. BTW, if you want to be sure to reduce soapiness, it's best to leave the plug in and just pour fresh water in. There is no way that the percentage of soapiness will not be reduced by that method. If you pull the plug, there is a possibility that you might be pouring most of that fresh water if not all down the drain--depending on the relationship of the faucet to the drain--and not reducing soapiness at all.

  7. I think the more pressing concern is the amount of peepee in the tub, not the amount of soap. That's why I wouldn't want to drink the baby's bathwater.

  8. Anonymous5:31 PM

    What's a soap unit? The fastest way to reduce soapiness would likely be to remove these soap units.

  9. Anonymous7:59 PM

    What's a soap unit? The most obvious way to lower the proportion of soap units is to remove soap units.

  10. Well Margaret is the only one with the courage to tackle the issue, and yes her answer is what I settled on myself. At first I had thought that pulling the plug out would surely help, since it "gets rid of the soapy water." But by the same token, it lets out clean water too.

    If you weren't running the faucet at all, then obviously pulling the plug would have no effect on the soapiness; i.e. the water wouldn't get clearer as it drained. And if the plug is in, then running the faucet obviously helps.

    So I conclude that running the faucet always helps, but the plug is irrelevant. (This assumes that the tub water is equally soapy--i.e. not patches of clear and patches of soapy.)

  11. I think pulling the plug could make things worse, since soap tends to float on water.

  12. Austrians don't know the answer to such questions. (That's my story and I'm sticking to it.)

  13. I.e., it all depends on the subjective valuations of the soap, the water, and the drain. (Clark's and Bob's opinions are irrelevant.)

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