3 ms·

The Infinity Machine (2017)

17 points by luu 8y ago

lostmsu 8y ago
Very amateurish. Why even talk about clockspeed of a machine, that can run any countable set of Turing programs in a single tick? That does not make any sense. Also, claim, that such a machine is physically impossible in our Universe is unsubstantiated (thought very likely).
- jandrese 8y ago
  It's not hard to conceive of an algorithm that, when using the smallest possible unit of energy per step, requires more energy than exists in the known universe.
  - lostmsu 8y ago
    I don't understand your suggestion. Where does the assumption, that each "step" directly maps to energy consumption of some physical machine? Does not that basically rest on the assumption, that no machine can run infinite Turing machine steps with finite energy?
    - jandrese 8y ago
      It seems self evident that you can not run an infinite process in a finite universe. The laws of entropy are your enemy. In this case the process is not "infinite", but is larger than your universe. An example is trying to brute force an encryption algorithm. You figure out the minimal amount of energy that could be used to compute each step, in terms of electron state changes or some other fundamental unit. Then you calculate the quantity of energy in the universe (assuming mass gets converted into energy as per E=MC^2 and all energy is put in some form you can use) and compare that against the energy per step * problem space. If the latter is larger then you can say that even though the problem is finite, there is not enough resources in the universe to discover the solution.
      - lostmsu 8y ago
        Now you are assuming, that the Universe has countable size.
yters 8y ago
If we can talk about infinity, does that mean our minds are infinity machines? For example, it is impossible to derive the axiom of infinity from any set of finite axioms. https://math.stackexchange.com/questions/155380/why-accept-the-axiom-of-infinity https://math.stackexchange.com/questions/155380/why-accept-t...
- skh 8y ago
  By definition, all axioms are not derivable within the axiom system they define. We can talk about sand but that does not mean our minds are sand or sand machines. We can talk about infinity within a set theory that contains that concept. A very large majority of mathematicians use infinite sets and have no problem with them. There are mathematicians that don't like the existence of uncountable sets or of uncountable choice but almost all of them accept countably infinite sets. For instance, I've never heard of a mathematician who believes that there are finitely many primes.
iosDrone 8y ago
"Even symmetric algorithms with a shared secret key aren't safe - with an appreciable amount of ciphertext and only a vague idea of the nature of the data ("ASCII text" for example), the Machine can try all possible decryption keys and see which potential plaintexts fall within the description of the real plaintext. There will probably be few enough left that choosing the right one is a matter for only a moment's thought!" This is just clearly wrong as long as you append an appropriately long number of random bits to your plaintext before encrypting. There will be a virtually infinite number of candidate plaintexts with randomly appended bits to choose from (think: Borges's Library of Babel)

17 points by luu 8y ago

Very amateurish. Why even talk about clockspeed of a machine, that can run any countable set of Turing programs in a single tick? That does not make any sense. Also, claim, that such a machine is physically impossible in our Universe is unsubstantiated (thought very likely).

jandrese 8y ago
It's not hard to conceive of an algorithm that, when using the smallest possible unit of energy per step, requires more energy than exists in the known universe.
- lostmsu 8y ago
  I don't understand your suggestion. Where does the assumption, that each "step" directly maps to energy consumption of some physical machine? Does not that basically rest on the assumption, that no machine can run infinite Turing machine steps with finite energy?
  - jandrese 8y ago
    It seems self evident that you can not run an infinite process in a finite universe. The laws of entropy are your enemy. In this case the process is not "infinite", but is larger than your universe. An example is trying to brute force an encryption algorithm. You figure out the minimal amount of energy that could be used to compute each step, in terms of electron state changes or some other fundamental unit. Then you calculate the quantity of energy in the universe (assuming mass gets converted into energy as per E=MC^2 and all energy is put in some form you can use) and compare that against the energy per step * problem space. If the latter is larger then you can say that even though the problem is finite, there is not enough resources in the universe to discover the solution.
    - lostmsu 8y ago
      Now you are assuming, that the Universe has countable size.

yters 8y ago

If we can talk about infinity, does that mean our minds are infinity machines? For example, it is impossible to derive the axiom of infinity from any set of finite axioms. https://math.stackexchange.com/questions/155380/why-accept-the-axiom-of-infinity https://math.stackexchange.com/questions/155380/why-accept-t...

skh 8y ago
By definition, all axioms are not derivable within the axiom system they define. We can talk about sand but that does not mean our minds are sand or sand machines. We can talk about infinity within a set theory that contains that concept. A very large majority of mathematicians use infinite sets and have no problem with them. There are mathematicians that don't like the existence of uncountable sets or of uncountable choice but almost all of them accept countably infinite sets. For instance, I've never heard of a mathematician who believes that there are finitely many primes.

iosDrone 8y ago

"Even symmetric algorithms with a shared secret key aren't safe - with an appreciable amount of ciphertext and only a vague idea of the nature of the data ("ASCII text" for example), the Machine can try all possible decryption keys and see which potential plaintexts fall within the description of the real plaintext. There will probably be few enough left that choosing the right one is a matter for only a moment's thought!" This is just clearly wrong as long as you append an appropriately long number of random bits to your plaintext before encrypting. There will be a virtually infinite number of candidate plaintexts with randomly appended bits to choose from (think: Borges's Library of Babel)