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Mathematicians, and esp. number theorists, are used to working with big numbers. I have noted on several occasions that lots of people don't have a clear understanding of big numbers as far as the real world is concerned. I recall a request for a list of all primes of less than 500 digits.

Another example is homeopathic dilutions. I understand they use dilutions like 200C, which is 1 in $10^{400}$. An absurd number in view of the fact that the total number of particles in the universe is estimated (safe margin) to be less than a googol.

How would you give people insight in big numbers? I'm not talking about Skewes' Number or Graham's Number; for most practical purposes $10^{20}$ is equal to infinity.

edit
To whoever voted me down: if you vote this down, please also tell me why. Thanks

  • 2
    Stuff like "real world", (effectiveness of) "homeopathy" and "practical purposes" sounds more like engineering than mathematics so I don't think this is on topic. Although I quite liked [this poster](http://images.etacuisenaire.com/view/1/eta/product-thumbnails/noimage.gif/2/eta/product-large/1809eta.jpg).2010-08-28
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    This question seems too vague as written. I would appreciate a more focused question.2010-08-28
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    If you really want to feel small (in the context of numbers), [watch this short](http://vimeo.com/819138).2010-08-28
  • 1
    Here is one disconnect I see between laypeople and those with scientific training: for scientists, one merely needs to show the number in scientific notation, and only a look at the exponent is needed to appreciate the magnitude. The lay, on the other hand, needs (or seems to need) to have all the number's digits written in full, zeroes and all, just to grasp how big or tiny a quantity is.2010-08-28
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    The sci.math link was very amusing :)2010-08-28
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    Out of nowhere, ask a classroom of kids "Who's Number One?" Bring some One forward and announce to the confused others, "Well, that means you're all a bunch of Zeroes!" Explain that this One kid represents only himself. Then bring up a Zero kid; together, as "10", they represent a portion of the class. Another Zero kid makes "100", representing roughly an entire grade level; another Zero kid, the whole school; a few more Zero kids, the town, state, country, planet. By the time you've run out of kids, you've represented a Real Big Number. Then ask: "What if *everyone* (except #1) is a Zero?"2011-01-22
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    $10^{20}$ is infinity?! Compared to the smallest infinity cardinal, aleph-null,the set of all natural numbers, $10^{10^{10^{\dots}}}$ ($10^{20}$ times), or any other bigger natural numbers, such as Graham's number, is approximate equal to zero.2014-03-28
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    @user136774 - That's why I say **for most practical purposes**. I remember a quote by a professor: "In theory the summation goes to infinity, but in practice infinity is five." When was the last time you needed Graham's Number in a real-life application? Or even 10^20?2014-03-30
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    This [video](https://www.youtube.com/watch?v=GoW8Tf7hTGA) of the size of stars is helpful for understanding the magnitudes of distance.2016-10-19
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    Finitist? Ultrafinitist?2017-02-12
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    See [this video](https://www.youtube.com/watch?v=QXliQvd1vW0&list=PL3A50BB9C34AB36B3&index=1).2018-07-20

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