A number NOBODY has thought of - Numberphile

Comments · 1.8K

• RI

  @RickSanchez78-d2v · 4 years ago

  A ten digit number could just be somebody's phone number

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• PS

  @Pseudo___ · 9 months ago

  i thought of a number. no one else think of it

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• MP

  @mphayes98 · 4 years ago (edited)

  I think Tony mis-stated the question and I think that&apos;s why Brady was so confused. So he stated that if you pick a number larger than 10^67, there is a 99% chance that it has never been thought of before. But in the mathematics, he then shows that there is a 99% chance that NOT A SINGLE number above 10^67 has EVER been thought of before when thinking of numbers according to that 1/n^1.3 distribution. That&apos;s a big difference. The 99% isn&apos;t a probability for that exact number, it&apos;s the probability that every number ever thought of following that distribution is less than that number.<br><br>At <a href="https://www.youtube.com/watch?v=KdZrxkix9Mk&amp;t=658">10:58</a> he states this. But then he says &quot;so if you go farther, there&apos;s a 99% chance you&apos;ll find a number that&apos;s never been thought of before.&quot; But really what the math means is &quot;if you go farther, there&apos;s a 99% chance that you&apos;ll never again come across a number that has been thought of by following the distribution&quot;

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• HY

  @Hyproxious · 4 years ago

  For those that wondering, the spike on the graph at <a href="https://www.youtube.com/watch?v=KdZrxkix9Mk&amp;t=429">7:09</a> is 2004, the year the data was gathered. The reason 2003 isn&apos;t as high, is many pages are updated to the current year

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• DU

  @dumnor · 4 years ago (edited)

  I like that Brady doesn&apos;t just accept 99% probability at face value.

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• TO

  @TomMalufe · 2 years ago

  I&apos;m getting out 74 d10s from my dice box and I&apos;m going to come up with my own number today

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• AL

  @alansmithee419 · 4 years ago (edited)

  <a href="https://www.youtube.com/watch?v=KdZrxkix9Mk&amp;t=335">5:35</a><br>But then the question you asked at the start is different to the one you just answered.<br>Start: &quot;How big a number do you have to generate for it to be likely to be <b>different to</b> any other number ever thought of?&quot;<br>Answered: &quot;How big a number do you have to generate for it to be likely to be <b>bigger than</b> any other number ever thought of, ignoring anomalous occurrences?&quot;

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• TR

  @trentgraham465 · 4 years ago

  Seems like there is a really big difference between &quot;no one has ever thought of this number&quot; and &quot;all the numbers that have ever been thought of are less than this number&quot;. &nbsp;I think the latter is an amazingly loose bound on the former.

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• GT

  @gtziavelis · 4 years ago (edited)

  the shape in the thought bubble at <a href="https://www.youtube.com/watch?v=KdZrxkix9Mk&amp;t=256">4:16</a> is a Calabi Yau manifold. some physics theories postulate at least 10^500 different ones of those (a number with 501 digits).

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• EP

  @EpicGamerScout · 4 years ago (edited)

  I think I&apos;ve solved this in a fairly reasonable method, starting from the same assumptions and formula that Tony used. I might be slightly bodging the explanation but this should explain the ideas for anyone that wants to quickly replicate my math:<br>With N being his 1.5e18 estimate, and p(x) calculating the percentage of numbers above x<br>And &apos;amount of numbers&apos; meaning some defined portion of N because I don&apos;t want to write &apos;amount of numbers thought of by humanity&apos; every time<br><br>Calculating the amount of numbers BELOW some N* is simply the total N minus the fraction of N above N*, so N-(p(10)*N)<br>So below 10 would be N-(p(10)*N)<br><br>With the ability to calculate the number above and below some range of N*, you can then get the amount of numbers in that range by subtracting the number below the minimum and the number above the maximum from the original N<br>Or Calculate the number above the minimum, and subtract the amount above the maximum. This is how I actually implemented it in the test spreadsheet.<br><br>And the &apos;normal size&apos; of any range its maximum-minimum.<br><br>So I think it&apos;s fair to propose that you can roughly estimate the likeliness of a random number in some range being unique &nbsp;by simply dividing the &apos;amount of numbers&apos; in a range into the &apos;size&apos; of that range. Of course to be REALLY precise about this you&apos;d want to do some further stats to account for the birthday-paradox type errors that my simple estimation leaves in.<br><br>Using a spreadsheet to test these formulas on power of 10 ranges(0-10,10-100,100-1000,etc) gives fairly intuitive results: <br>For a 15 digit number the amount of numbers that land there is 47.2 trillion, and the size of that range is 900 trillion, so you&apos;d be at ~5% odds that your number has never occurred in that N dataset before.<br>For a 16 digit number the amount of numbers that land there is 23 trillion, and the size of that range is 9 quadrillion, so you&apos;d be at ~.2% odds that your number has never occurred in that N dataset before.<br>17 digit - .013%<br>20 digit - .00000165%<br><br><br>So Brady&apos;s 10 digits is definitely an underestimation, especially considering other commenter&apos;s examples such as ip addresses and phone numbers. But you definitely don&apos;t have to go too much further to reach near-certainty even from these assumptions.

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• ST

  @stephenandrusyszyn3444 · 4 years ago

  10^67 is a huge over estimate. Consider a 30 digit number. To have a greater than 1% chance of repeating a 30 digit number, then more than 10^28 of those 10^30 numbers would have to been &quot;thought of&quot;. With a total population of 10^11 people, that would mean that every person would have to have thought of 10^17 30 digit numbers in their lifetime. So if everyone lived for 80 years, then you would have to come up with 40 million 30 digit numbers every second of your life (60 million if you want some sleep).

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• OV

  @overestimatedforesight · 4 years ago (edited)

  The Doomsday argument always makes me laugh. Imagine a particularly intelligent cro-magnon figuring it out and concluding that humans will go extinct in the next few hundred years. It&apos;s basically &quot;well if we&apos;re roughly in the middle then we must be roughly in the middle.&quot;

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