sanil
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Very interesting question!
My observations:
| Problem Complexity | Scaling |
|---|---|
| O(log(n)) | 10^10¹² |
| O(n), O(n log(n)) | 10^12 |
| O(n^2) | 10^6 |
| O(n^3) | 10^4 |
| O(n^4) | 10^3 |
| O(n^6) | 10^2 |
| O(n^12) | 10 |
| O(10^n) | 12 |
Hence, we should expect exponentially complex brute force problems to perform 10 times better. With this, you'd only need 1 year to simulate something that would have taken 10 years. Quite nice for problems like quantum... (read 384 more words →)
Why limit ourselves to our planet? 12 OOMs is well within reason if we were a type 2 civilization and had access to all the energy from our sun (our planet as a whole only receives 1/10^10 of it).
Encryption wouldn't really be an issue - we can simply tune our algorithms to use slightly more complicated assumptions. After all, one can just pick a problem that scales as O(10^(6n)), where n could for example be secret key length. If you have 12 orders of magnitude more compute, just make your key 2 times larger and you still have your cryptography.
Thought of how small computers (phones etc) would scale also came to me.... (read more)