You can certainly do it to some extent. Thus for example, just because their are innovations in physics that are ongoing doesn’t mean I can’t safely dismiss perpetual motion claims. And while there’s constant research in my own field (number theory) I can dismiss a lot of claims of proofs of major theorems by crackpots even though there’s ongoing research. Moreover, people in some fields are able to evaluate claims as having very low probability even though they are technically possible given what we have today. Thus for example, I have a friend who is a physicist who considers it extremely unlikely that we will ever have room temperature superconductors. If some random individual came up to him claiming to have a way of constructing them, he’d be completely justified in giving this a low confidence. I don’t know if you’d label that evidence as posteriori or not given that he has zero data about the individual claim, just the type of claim in general.
Now, as you mentioned your field, I have a crackpot idea to evolve a divisor of a big number.
How much points on the crackpot scale from 0 to 99 I’ve earned with this? Zero means no quacking at all, while 80 is something like “I have an UFO in the basement, and a private zoo with the captured aliens”. I can’t imagine 99.
I’m not sure. I’d say it would depend on if you’ve got an actual procedure to do it. If yes, pretty close to 0. If not, maybe around 40 or so. Although the term “evolve” isn’t used, there are some procedures that try to do similar things.
Consider for example primitive roots. A primitive root an integer g such that g^k runs through every possible non-zero remainder when divided by p. Thus, for example, 2 is a primitive root modulo 5, since 2^1=2 (mod 5), 2^2=4 (mod 5), 2^3=8 = 3 (mod 5) and 2^4=16=1 (mod 5) so 1,2,3, and 4 are all accounted for. 2 is not a primitive root mod 7 since one only can get as remainders 1,2 and 4. (Most people here probbably already know about primitive roots but it seemed like a good idea to just go over the basics for readers who might know. Also my assumption that most people will know may be some form of projection and I’m assuming a much higher degree of knowledge about my field than can be reasonably expected). Now, it turns out that number theorists care a lot about primitive roots. Aside from intrinsic mathematical interest, they turn out to be useful in a number of practical algorithms such as the Diffie-Hellman algorithm which is a simple to implement key exchange procedure useful in cryptography.
It turns out that every prime has a primitive root (a non-obvious fact first proved by Gauss) but for a given prime, finding a primitive root is tough in general. However, some of the procedures used to find primitive roots work off of picking a set of random numbers, checking if any is a primitive root and if not combining them in a certain way to get a number whose powers run through more remainders. One can iterate this process to eventually get a primitive root. In some sense, this is evolving an answer to the problem, although that terminology would never be used. And there are procedures to find factors which rely on not so far off procedures (although calling them evolution would be more of a stretch). So the rough idea isn’t intrinsically crackpottish. It would depend a lot on the details.
You’d be applying a weak optimization process to the problem instead of using your built-in much stronger one, and hoping that its different set of biases will let it hit on a useful algorithm that you yourself wouldn’t.
Intuitively, math-space is too big and twisted for evolution to work, and it’d suffer horribly from getting stuck on local maxima. I don’t know this for certain, however, and even if you fail you’ll still have learned something.
Thus for example, just because their are innovations in physics that are ongoing doesn’t mean I can’t safely dismiss perpetual motion claims.
Yes, but a perpetual machine would be an innovation par excellence, wouldn’t it be? Especially for you and me and everybody else, who are almost certain, it’s not possible.
And while there’s constant research in my own field (number theory) I can be dismiss a lot of claims of proofs of major theorems by crackpots even though there’s ongoing research.
Yes, again. But whatever is quite familiar for you, what you can easily grasp, is not a big innovation for you. Maybe important, but not that innovative. You have thought similar thoughts already.
Thus for example, I have a friend who is a physicist who considers it extremely unlikely that we will ever have room temperature superconductors.
I tend to agree with him. Anyway, superconductivity would be a very important but not a very innovative thing. Unless based on some completely unexpected principles. Then it would be innovative too.
I’m still not clear on this definition as it applies to what the top-level post discussed. Everything in the top level post are ideas that aren’t unprecedented. Many of these ideas have been around for a very long time. So only talking about ideas which are unprecedented and mainly unexpected seems unhelpful. Also, I’m not sure what constitutes unprecedented in this context.
You can certainly do it to some extent. Thus for example, just because their are innovations in physics that are ongoing doesn’t mean I can’t safely dismiss perpetual motion claims. And while there’s constant research in my own field (number theory) I can dismiss a lot of claims of proofs of major theorems by crackpots even though there’s ongoing research. Moreover, people in some fields are able to evaluate claims as having very low probability even though they are technically possible given what we have today. Thus for example, I have a friend who is a physicist who considers it extremely unlikely that we will ever have room temperature superconductors. If some random individual came up to him claiming to have a way of constructing them, he’d be completely justified in giving this a low confidence. I don’t know if you’d label that evidence as posteriori or not given that he has zero data about the individual claim, just the type of claim in general.
Now, as you mentioned your field, I have a crackpot idea to evolve a divisor of a big number.
How much points on the crackpot scale from 0 to 99 I’ve earned with this? Zero means no quacking at all, while 80 is something like “I have an UFO in the basement, and a private zoo with the captured aliens”. I can’t imagine 99.
I’m not sure. I’d say it would depend on if you’ve got an actual procedure to do it. If yes, pretty close to 0. If not, maybe around 40 or so. Although the term “evolve” isn’t used, there are some procedures that try to do similar things.
Consider for example primitive roots. A primitive root an integer g such that g^k runs through every possible non-zero remainder when divided by p. Thus, for example, 2 is a primitive root modulo 5, since 2^1=2 (mod 5), 2^2=4 (mod 5), 2^3=8 = 3 (mod 5) and 2^4=16=1 (mod 5) so 1,2,3, and 4 are all accounted for. 2 is not a primitive root mod 7 since one only can get as remainders 1,2 and 4. (Most people here probbably already know about primitive roots but it seemed like a good idea to just go over the basics for readers who might know. Also my assumption that most people will know may be some form of projection and I’m assuming a much higher degree of knowledge about my field than can be reasonably expected). Now, it turns out that number theorists care a lot about primitive roots. Aside from intrinsic mathematical interest, they turn out to be useful in a number of practical algorithms such as the Diffie-Hellman algorithm which is a simple to implement key exchange procedure useful in cryptography.
It turns out that every prime has a primitive root (a non-obvious fact first proved by Gauss) but for a given prime, finding a primitive root is tough in general. However, some of the procedures used to find primitive roots work off of picking a set of random numbers, checking if any is a primitive root and if not combining them in a certain way to get a number whose powers run through more remainders. One can iterate this process to eventually get a primitive root. In some sense, this is evolving an answer to the problem, although that terminology would never be used. And there are procedures to find factors which rely on not so far off procedures (although calling them evolution would be more of a stretch). So the rough idea isn’t intrinsically crackpottish. It would depend a lot on the details.
Umh.. twenty?
You’d be applying a weak optimization process to the problem instead of using your built-in much stronger one, and hoping that its different set of biases will let it hit on a useful algorithm that you yourself wouldn’t.
Intuitively, math-space is too big and twisted for evolution to work, and it’d suffer horribly from getting stuck on local maxima. I don’t know this for certain, however, and even if you fail you’ll still have learned something.
At least not always. At least.
Yes, but a perpetual machine would be an innovation par excellence, wouldn’t it be? Especially for you and me and everybody else, who are almost certain, it’s not possible.
Yes, again. But whatever is quite familiar for you, what you can easily grasp, is not a big innovation for you. Maybe important, but not that innovative. You have thought similar thoughts already.
I tend to agree with him. Anyway, superconductivity would be a very important but not a very innovative thing. Unless based on some completely unexpected principles. Then it would be innovative too.
Could you expand on what you mean by innovative then? How do you define something as innovative?
Done on a new way. Unprecedented and mainly unexpected. It doesn’t mean that it is very important then, only a surprise for almost everyone.
http://wordnetweb.princeton.edu/perl/webwn?s=innovativeness
Check!
I’m still not clear on this definition as it applies to what the top-level post discussed. Everything in the top level post are ideas that aren’t unprecedented. Many of these ideas have been around for a very long time. So only talking about ideas which are unprecedented and mainly unexpected seems unhelpful. Also, I’m not sure what constitutes unprecedented in this context.