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Have another account here but don't want to take the karma hit for being a crank. I published this 2-page proof that the EMH is false: https://arxiv.org/abs/1

Have another account here but don't want to take the karma hit for being a crank. I published this 2-page proof that the EMH is false: https://arxiv.org/abs/1011.0423 https://arxiv.org/abs/1011.0423 (didn't set the date so in the document it's wrong, this was published 2010.) It doesn't depend on P = NP, it's simply a rigorous proof that EMH is false. Let's switch gears a second. Here's a famous elementary proof[1] that there are infinite primes. Suppose there are just finite primes, up to some largest. Multiply them together and add one. No prime divides the new number (because "every" prime leaves a remainder 1), so you've just produced a new prime. This new prime is larger than the largest prime in your finite set because you multiplied that by the rest of them and added one to get it. So this is a contradiction, you couldn't have had finite primes up to some largest. Anyway if you think there might be a largest prime after what you just read, it just means you don't understand the proof. If you believe EMH might be true it just means you don't understand the proof that it is false. Of course, nobody ever even hypothesized that academia was efficient :) [1] https://en.wikipedia.org/wiki/Euclid%27s_theorem#Euclid's_proof https://en.wikipedia.org/wiki/Euclid%27s_theorem#Euclid's_pr... -- EDIT: no mistake in my comment

csomar 8y ago
> Have another account here but don't want to take the karma hit for being a crank. Stop worrying about karma and what some random dudes think about you/your comments on HN or whatever online board. If you think it is wrong simply don't do it.
- zeth___ 8y ago
  You get silenced by karma when you have unpopular opinions. You know, just how people used to tell homosexuals to not be gay when other people thought they were freaks because of it.
  - csomar 8y ago
    What I’m saying is stop worrying about karma and talk your opinions. Karma is not money or air. Your opinion matters.
    - zeth___ 8y ago
      And what I'm saying is that you literally can't when you get enough negative karma. I have three HN accounts and two of them have negative karma and can't post without mod approval. Or it just says: You're posting too fast. Please slow down. Thanks.
      - deleted 8y ago
        [deleted]
      - csomar 8y ago
        Then you must be doing something wrong. I, always, speak my mind. This sometimes backfires karma wise but on the long run i think it was minimal.
        zeth___ 8y ago
        It's called having unpopular opinions. That you're conventional enough to never stand out of the herd says more about you than anything else.
  - simias 8y ago
    Individual comments effectively get silenced (or at least buried) by downvoting, changing the account you post with won't change that. You can get an account shadowbanned however which does reduce the visibility of all its comments but that's a different issue, I don't think you can trigger a shadowban automatically by downvotes alone (or maybe only in extreme cases).
babypistol 8y ago
I haven't heard of EMH before today and can't really comment on that. But it seems to me that even in the example from your note the stock price will tend to reflect the the correct price. As you realease new information the factorization becomes more feasible and once it's feasible enough the stock price will get the correct value. Maybe we should amend EMH to say that asset prices fully reflect all the facts that are feasible to compute from the available information. Anyway, the reason I'm writing this comment is to say that you should no be so sure of your proofs, especially because your proof of the infinitude of primes is wrong. This proof does not show that the new number (the product of primes + 1) is prime. It shows that none of the primes are factors in this new number and from that it follows that there must be more primes, but it does not follow that the new number is necessarily prime (it might be a product of another unknown primer and the others).
- viraghr 8y ago
  Sure, but you can't "amend EMH" to fully reflect all the facts that are "feasible to compute" any more than you can amend it to say that that asset prices fully reflect the "best feasible analysis". That's not EMH. For the prime proof, the new number is prime as long as as it has no prime factors < itself, which we assumed at the start. This guarantees it's prime under our assumption and this falsifies the assumption. Doesn't matter if it's really prime.
ayepif 8y ago
Maybe I'm being super pedantic and possibly confrontational (I apologise in advance) but it jumped out on me here. I think you've misunderstood the 'famous elementary proof' that there are infinite primes. You do not create a new prime as you have suggested (quoted below). "Multiply them together and add one. No prime divides the new number (because "every" prime leaves a remainder 1), so you've just produced a new prime. This new prime is larger than the largest prime in your finite set because you multiplied that by the rest of them and added one to get it." Instead you have created a number that may or may not be prime but definitely requires a new prime number (not in your set) to factorise it. Counter example: Take your set of prime numbers to be {2,3,5,7,11,13} then (2.3.5.7.11.13)+1 = 30031 30031 factorises into 59.509 so you have found two prime numbers that are not in your original set. EDIT: Responding to the edit above. The problem is that you claim that you make a new prime number by multiplying them all together and adding one. You didn't multiply all the numbers and added one to get the prime number, you multiplied all the numbers and added one to get a number (POSSIBLY NOT PRIME) whose FACTORS are prime numbers not in your original 'supposed' finite set. Your proof essentially lacks the step: IF new_number is prime: proof finished ELSE: factor new_number and show that at least one of the factors is not in your finite set. EDIT 2: Counterexample number 2. Suppose your finite set of primes is {2,7} (2.7)+1 = 15 So you have found 3 and 5 as primes that are not in your original set and are SMALLER than the largest prime in your original set. This is now a second mistake in your proof. Whether you are trolling or just too arrogant to see the mistake/error I do not know.
- n4r9 8y ago
  You're entirely correct. A very ironic mistake/misunderstanding for the parent post to make. Edit: I've thought about this a bit more, and you can save the parent post by prepending a result like "Every number larger than one is either prime, or divisible by a prime smaller than itself". In this case you can then assert that your constructed number is prime. However, this result requires its own proof and was not mentioned by the parent post.
  - deleted 8y ago
    [deleted]
- deleted 8y ago
andrewla 8y ago
Your proof for the EMH hinges on a very specific technicality -- whether the secret prime, P, is public knowledge, or to what degree it is public knowledge. I think if we were to approach the EMH from a constructive or computability approach, we'd have to make that definition much crisper. That is, the feasibility of computing the factorization based on limited information determines whether the information is actually "available" in the sense of the EMH. In the real world we can see things like drug trials that will determine the success of a pharmaceutical company. The information that the drug works or doesn't work, or has side effects, would be "apparent" to a hypothetical "ideal" expert in human biochemistry -- so simply knowing the chemical formula for a new drug, the information about its working is "available" in that sense.
- viraghr 8y ago
  If you can show an inefficient market experimentally whenever you want, that's good enough to disprove EMH. The EMH doesn't say, "All information is normally factored into the price, except for technicalities." I like your drug trial example but a "hypothetical ideal expert" isn't assured to exist. Do you have an existence proof? On the other hand, unique prime factorization is assured, we know that given infinite time anyone can factor any large number.
  - andrewla 8y ago
    The EMH is usually restricted to "available information". This hinges on what "available" means. I would argue that until the search space was reduced to the point where it would be feasible to factor the secret before another digit is revealed, the information is not "available" in any useful sense. So maybe, in some sense, this helps us narrow down a definition of what "available" means, but since real-world price signals are rarely something that is deterministically computable, I'm not sure that this would help to clarify the EMH. In my drug trial example, such an expert does not exist, but if we're dealing with mundane real-world stuff, then the assurances that the proposed $1B gift to a random company would actually go through would have to be factored into any strategy -- why would I bother committing computing resources to factoring the number when in all likelihood the billion dollars would not handed over because why would anyone actually do that?

csomar 8y ago

> Have another account here but don't want to take the karma hit for being a crank. Stop worrying about karma and what some random dudes think about you/your comments on HN or whatever online board. If you think it is wrong simply don't do it.

zeth___ 8y ago
You get silenced by karma when you have unpopular opinions. You know, just how people used to tell homosexuals to not be gay when other people thought they were freaks because of it.
- csomar 8y ago
  What I’m saying is stop worrying about karma and talk your opinions. Karma is not money or air. Your opinion matters.
  - zeth___ 8y ago
    And what I'm saying is that you literally can't when you get enough negative karma. I have three HN accounts and two of them have negative karma and can't post without mod approval. Or it just says: You're posting too fast. Please slow down. Thanks.
    - deleted 8y ago
      [deleted]
    - csomar 8y ago
      Then you must be doing something wrong. I, always, speak my mind. This sometimes backfires karma wise but on the long run i think it was minimal.
      - zeth___ 8y ago
        It's called having unpopular opinions. That you're conventional enough to never stand out of the herd says more about you than anything else.
- simias 8y ago
  Individual comments effectively get silenced (or at least buried) by downvoting, changing the account you post with won't change that. You can get an account shadowbanned however which does reduce the visibility of all its comments but that's a different issue, I don't think you can trigger a shadowban automatically by downvotes alone (or maybe only in extreme cases).

babypistol 8y ago

I haven't heard of EMH before today and can't really comment on that. But it seems to me that even in the example from your note the stock price will tend to reflect the the correct price. As you realease new information the factorization becomes more feasible and once it's feasible enough the stock price will get the correct value. Maybe we should amend EMH to say that asset prices fully reflect all the facts that are feasible to compute from the available information. Anyway, the reason I'm writing this comment is to say that you should no be so sure of your proofs, especially because your proof of the infinitude of primes is wrong. This proof does not show that the new number (the product of primes + 1) is prime. It shows that none of the primes are factors in this new number and from that it follows that there must be more primes, but it does not follow that the new number is necessarily prime (it might be a product of another unknown primer and the others).

viraghr 8y ago
Sure, but you can't "amend EMH" to fully reflect all the facts that are "feasible to compute" any more than you can amend it to say that that asset prices fully reflect the "best feasible analysis". That's not EMH. For the prime proof, the new number is prime as long as as it has no prime factors < itself, which we assumed at the start. This guarantees it's prime under our assumption and this falsifies the assumption. Doesn't matter if it's really prime.

ayepif 8y ago

Maybe I'm being super pedantic and possibly confrontational (I apologise in advance) but it jumped out on me here. I think you've misunderstood the 'famous elementary proof' that there are infinite primes. You do not create a new prime as you have suggested (quoted below). "Multiply them together and add one. No prime divides the new number (because "every" prime leaves a remainder 1), so you've just produced a new prime. This new prime is larger than the largest prime in your finite set because you multiplied that by the rest of them and added one to get it." Instead you have created a number that may or may not be prime but definitely requires a new prime number (not in your set) to factorise it. Counter example: Take your set of prime numbers to be {2,3,5,7,11,13} then (2.3.5.7.11.13)+1 = 30031 30031 factorises into 59.509 so you have found two prime numbers that are not in your original set. EDIT: Responding to the edit above. The problem is that you claim that you make a new prime number by multiplying them all together and adding one. You didn't multiply all the numbers and added one to get the prime number, you multiplied all the numbers and added one to get a number (POSSIBLY NOT PRIME) whose FACTORS are prime numbers not in your original 'supposed' finite set. Your proof essentially lacks the step: IF new_number is prime: proof finished ELSE: factor new_number and show that at least one of the factors is not in your finite set. EDIT 2: Counterexample number 2. Suppose your finite set of primes is {2,7} (2.7)+1 = 15 So you have found 3 and 5 as primes that are not in your original set and are SMALLER than the largest prime in your original set. This is now a second mistake in your proof. Whether you are trolling or just too arrogant to see the mistake/error I do not know.

n4r9 8y ago
You're entirely correct. A very ironic mistake/misunderstanding for the parent post to make. Edit: I've thought about this a bit more, and you can save the parent post by prepending a result like "Every number larger than one is either prime, or divisible by a prime smaller than itself". In this case you can then assert that your constructed number is prime. However, this result requires its own proof and was not mentioned by the parent post.
- deleted 8y ago
  [deleted]
deleted 8y ago

andrewla 8y ago

Your proof for the EMH hinges on a very specific technicality -- whether the secret prime, P, is public knowledge, or to what degree it is public knowledge. I think if we were to approach the EMH from a constructive or computability approach, we'd have to make that definition much crisper. That is, the feasibility of computing the factorization based on limited information determines whether the information is actually "available" in the sense of the EMH. In the real world we can see things like drug trials that will determine the success of a pharmaceutical company. The information that the drug works or doesn't work, or has side effects, would be "apparent" to a hypothetical "ideal" expert in human biochemistry -- so simply knowing the chemical formula for a new drug, the information about its working is "available" in that sense.

viraghr 8y ago
If you can show an inefficient market experimentally whenever you want, that's good enough to disprove EMH. The EMH doesn't say, "All information is normally factored into the price, except for technicalities." I like your drug trial example but a "hypothetical ideal expert" isn't assured to exist. Do you have an existence proof? On the other hand, unique prime factorization is assured, we know that given infinite time anyone can factor any large number.
- andrewla 8y ago
  The EMH is usually restricted to "available information". This hinges on what "available" means. I would argue that until the search space was reduced to the point where it would be feasible to factor the secret before another digit is revealed, the information is not "available" in any useful sense. So maybe, in some sense, this helps us narrow down a definition of what "available" means, but since real-world price signals are rarely something that is deterministically computable, I'm not sure that this would help to clarify the EMH. In my drug trial example, such an expert does not exist, but if we're dealing with mundane real-world stuff, then the assurances that the proposed $1B gift to a random company would actually go through would have to be factored into any strategy -- why would I bother committing computing resources to factoring the number when in all likelihood the billion dollars would not handed over because why would anyone actually do that?