Sir Roger Penrose has quantified the "very special" nature of the big bang as being "1 part in 10 to the 10 to the 243", but I do not understand what this really means - my apologies but I cannot even write the figure properly, either using notation, as my phone only copes with 1 line of superscript, or by employing solely regular numerals, as apparently even if I could fit each zero onto it's own proton there would still not be enough protons in the observable universe for me to complete it, (or have I misconstrued Sir Roger here? Presumably he at least understands the basics of scientific notation!)

  • $\begingroup$ Is your question what does something like '10 to the 10 to the 243' mean? $\endgroup$ Commented Jul 15, 2021 at 13:48
  • 1
    $\begingroup$ MathJax: $10^{10^{243}}$ yields $10^{10^{243}}$. $\endgroup$ Commented Jul 15, 2021 at 13:50
  • $\begingroup$ Yeah, that's not scientific notation. Just a power tower. $\endgroup$
    – DKNguyen
    Commented Jul 15, 2021 at 13:51
  • $\begingroup$ Indeed. You can interpret the number as '1 with $10^{243}$' zeros behind it, where $10^{243}$ is 1 with 243 zeros behind it. It's a very big number. E.g. even $10^{10^2}$ is 1,000,000,...[94 more zeros]. $\endgroup$ Commented Jul 15, 2021 at 13:55

1 Answer 1


You can interpret the number you mentioned, $10^{10^{243}}$, as '1 with $10^{243}$' zeros behind it, where $10^{243}$ is 1 with 243 zeros behind it. It's a very big number. E.g. even $10^{10^2}$ is 1,000,000,...[with 94 more zeros].

  • $\begingroup$ Hi Ben, thanks for answering my question. I'm sorry that I'm a bit late getting back to you, I just had to duck-out... you know, for a few years! I think I've almost wrapped my head around it, but something still isn't quite meshing for me yet. If 10³ is 1,000, then wouldn't that be the same as 10¹⁰2? With 10² being 100, and then multiplying that by 10? Sorry, I'm sure that I was born with a natural number deficiency or something! $\endgroup$ Commented Apr 4 at 10:42
  • $\begingroup$ NB. The number is Roger Penrose's calculation for the odds that our universe just happened to have been born in the low-entropy state that it was - such that complexity, and ultimately ourselves, could exist within it. $\endgroup$ Commented Apr 4 at 10:48
  • $\begingroup$ That's an important number! For your example, think of $10^3$ as $10\times10\times10$ (Three 10s, all multiplied together). Then think of $10^{10^2}$. Since $10^2 = 100$ then $10^{10^2} = 10^{100} = 10\times10\times10\times10\times ...$. (One hundred 10s, all multiplied together). This second number is much larger than $10^3 = 1000$. In your reasoning for this same example, it looks like you want to multiply instead of raise to the power of. E.g. $10^{10^2}$ is not $10\times 10^2$, as I think you claimed. $\endgroup$ Commented Apr 5 at 15:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.