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My nephew recently received this as a piece of homework (he is seven):

"How many grains of sand are there in the world?"

Obviously he Googled the question and it came back with "It is incalculable". Knowing that I'm `into' maths, he asked me if there is a symbol to mean incalculable'. I am not aware of one (I do Pure maths, so it doesn't come up very often). I told him that I do't know, but that I will ask the lovely people of Stackexchange to help me.

Does anyone have any idea if there does exist such a symbol?

Asaf Karagila
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GerrySmith
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  • What would be the value of the symbol, precisely? There are many things that don't have symbols, but rather have words associated to them. Incalculable for example, or maybe "group" which is a set together with a binary operation, blah blah blah. The idea is that a symbol may not be necessary when a simple sentence may suffice. On the other hand, if your symbol indicates an operation, it may actually prove useful. For example a plus b plus c is much more easily seen as $a+b+c.$ – Chickenmancer May 05 '17 at 20:02
  • Absolutely no value (so I guess that means $0$). It was just a mildly interesting thought. – GerrySmith May 05 '17 at 20:06
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    I am sure he is a bright seven-year-old. The point of such questions is not so much what the answer is, or how closely it is calculable, but to get a young person thinking about what they might need to know to have a good go at such a question and to make some defensible estimates of those factors in the absence of accurate knowledge. Saying "it is incalculable because ..." is a good answer, but adding "the best estimate I can give based on ..." adds to it. – Mark Bennet May 05 '17 at 20:07
  • I didn't mean to belittle the thought. I remember when I first started to learn mathematics, and I was very inspired by the symbols. Once I started to learn about mathematical formalism, I realized that the symbols were arbitrary. I suppose that was what I had hoped to convey, and maybe you could inspire your nephew to think of the idea more, rather than finding a symbol to replace it. – Chickenmancer May 05 '17 at 20:16
  • Culture corner: Archimede's Sand reckoner (https://en.wikipedia.org/wiki/The_Sand_Reckoner) – Jean Marie May 05 '17 at 20:55

3 Answers3

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There is no symbol that means incalculable. Probably the closest you'll get is $\text{DNE}$ for "does not exist" and that's not applicable here.

Is "it's incalculable" really all that was found in the google search? I just googled How many grains of sand are there in the world? and got results much more interesting than that.

I think it's clear (although perhaps not to a 7-year-old, and understandably so) that an exact answer is not expected. Rather, the point of this seems to be an exercise in estimating very large quantities. Some of the results in my search talked about comparing the number of grains of sand to the number of stars in the universe. An interesting read but may not be a good starting point. I suggest also googling stuff about how to estimate large quantities, and perhaps, more specifically, how to estimate the number of grains of sand in the world. The key word here being estimate.

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"Incalculable" is not a symbol. It is an adjective, which means "cannot be calculated" and, as such, a false response to the question. (Probably a prank or a software place holder from Google programmers.)

Back to your nephew's homework, the teacher probably wanted an order-of-magnitude estimate. Something like,

(total area on Earch covered by sand) * (average thickness of the sand) / (average volume of a sand grain).

avs
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  • There are many estimates of the number, although to me it seems a little pointless considering the margin of error. I image you are right with what the teacher is asking - that is what my nephew has answered. – GerrySmith May 05 '17 at 20:08
  • I once was asked, "How many piano tuners are there in New York?" by a physics instructor.:) – avs May 05 '17 at 20:09
  • I think the teacher actually is looking for an answer closer to "its incalculable." Along with and explanation why. "if you tried to count it, more sand would be created while you counted." Or, "if a heap of sand less a grain is still a heap, how many grains can be removed for a heap to still be a heap?" – Doug M May 05 '17 at 20:18
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    The piano tuners question is famous because of Enrico Fermi. – Doug M May 05 '17 at 20:20
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If you count them, i am sure you will forget at least one grain. the number of grains is a function of time $$N (t) $$ which depends on many parameters and whose evolution equation is very complicated.

Your question has not to be asked. i have been downvoted cause i answerd a bad philosophic question.

hamam_Abdallah
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