<p>Seth Lloyd has a <a href="http://arxiv.org/abs/quant-ph/9908043">paper</a> on the subject. You need energy to compute, but if you put too much energy into a small region, it forms a black hole. This slows down time (making the time it takes for the computation to complete relatively longer), and any computation done in the interior of a black hole is wasted, as the results cannot be extracted from the black hole and used. Seth calculates the limits on the amount of computation possible, and shows that for some measures of computation, the most computationally intensive environment possible in the universe would be that surrounding a black hole. </p>

CC BY-SA 3.0
2014-01-26T16:42:45.643Z
@AaronRoth I was stuck in a black hole.  Accepted now.
Good Person
CC BY-SA 3.0
2011-02-26T11:29:10.637Z
2015-07-18T09:15:19.987Z
2015-07-18T09:15:19.987Z
Peter Shor 
<p>I understand that Turing completeness requires unbounded memory and unbounded time.</p>
<p>However there is a finite amount of atoms in this universe, thus making memory bounded. For example even though <span class="math-container">$\pi$</span> is irrational there is no way to store more than a certain number of digits even if <em>all</em> the atoms in the universe were used for this purpose.</p>
<p>What then are the limits of computability of an <em>implemented</em> Turing machine (which could use all the resources of the universe but no more) based on the limits of the universe? What is the maximum number of digits of <span class="math-container">$\pi$</span>? Are there any papers on this subject that might be interesting to read?</p>

CC BY-SA 2.5
2011-02-26T08:32:24.933Z
Possibly related topic: [Can a computer simulate itself as part of a simulated world](http://cstheory.stackexchange.com/q/2894/873).
Sadeq Dousti
CC BY-SA 2.5
2011-02-26T08:57:01.180Z
There is a fun essay by Scott Aaronson on this: http://www.scottaaronson.com/writings/finite.html
Artem Kaznatcheev
CC BY-SA 2.5
2011-03-26T17:11:31.717Z
You might be interested in the discussion around [this question](http://cstheory.stackexchange.com/questions/2758/how-much-computational-power-fits-into-a-cubic-centimeter).  Yarosloav Bulatov posted a link to a popular-science version of the Lloyd paper Peter Shor linked to below, but, unfortunately, the link appears to be broken now.  I read that paper at the time, but didn't save it, and don't remember the exact title.
Aaron Sterling
CC BY-SA 4.0
2020-08-17T13:13:32.717Z
How do you know there is a bounded amount of atoms in the universe?
Andrej Bauer
<computability><upper-bounds>
What are the limits of computation in this universe?
Good Person
# What are the limits of computation in this universe?

(Asked by: username_0 on 2011-02-26)

I understand that Turing completeness requires unbounded memory and unbounded time.

However there is a finite amount of atoms in this universe, thus making memory bounded. For example even though $\pi$ is irrational there is no way to store more than a certain number of digits even if *all* the atoms in the universe were used for this purpose.

What then are the limits of computability of an *implemented* Turing machine (which could use all the resources of the universe but no more) based on the limits of the universe? What is the maximum number of digits of $\pi$? Are there any papers on this subject that might be interesting to read?

**Tags:** computability, upper-bounds
> **Comments:**
> **username_1**: Possibly related topic: [Can a computer simulate itself as part of a simulated world](http://cstheory.stackexchange.com/q/2894/873).  
> **username_2**: There is a fun essay by Scott Aaronson on this: http://www.scottaaronson.com/writings/finite.html  
> **username_3**: You might be interested in the discussion around [this question](http://cstheory.stackexchange.com/questions/2758/how-much-computational-power-fits-into-a-cubic-centimeter).  Yarosloav Bulatov posted a link to a popular-science version of the Lloyd paper Peter Shor linked to below, but, unfortunately, the link appears to be broken now.  I read that paper at the time, but didn't save it, and don't remember the exact title.  
> **username_4**: How do you know there is a bounded amount of atoms in the universe?  

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## 1 answers

### Answer by username_5 on 2011-02-26. Score: 37 | Accepted answer

Seth Lloyd has a [paper](http://arxiv.org/abs/quant-ph/9908043) on the subject. You need energy to compute, but if you put too much energy into a small region, it forms a black hole. This slows down time (making the time it takes for the computation to complete relatively longer), and any computation done in the interior of a black hole is wasted, as the results cannot be extracted from the black hole and used. Seth calculates the limits on the amount of computation possible, and shows that for some measures of computation, the most computationally intensive environment possible in the universe would be that surrounding a black hole.

> **Comments:**
> **username_0**: @AaronRoth I was stuck in a black hole.  Accepted now.  

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