The sad thing is that already anyone who points these things out is derided as a nut.
I don't think that is true. For example, I think that if you had simply put the first two paragraphs of your post, and no other, they would be completely reasonable.
But once you start comparing having to get a driver's license to anything the Gestapo did, and refer to "the State", then things start sounding a little nutty. Sorry, but it's true.
Does that make you a nut, or everyone else in the world a nut? I don't know, you could be right and the rest of the world wrong; as Winston Smith said, "Sanity is not statistical." But if you want to convince anyone else of your position, you need to not sound like an ideologue.
I'm imagining that over the next few hours, we'll see the traditional/. backlash that we're expecting, hear the words "Big Brother" about a thousand times, etc.
But my question is, what is new here?
For example, in every state that I've lived and gotten a driver's license in, I was required to submit all of this information. I had to give biometric information, my NY state driver's licence has my height and eye-color, and other states have required my weight, and so on. Also, every driver's license I've ever had has a picture on it, which was digitized and entered into a database.
I can understand your position if you think that it's a violation of privacy for you to have to submit to a picture, and to give basic biometric information. I disagree, but I can understand where you're coming from... But, if this is your position, then it must be true that the current situation was intolerable to you. Anyone who thinks that this new development is somehow different than the current situation is just having a knee-jerk reaction.
"The Sacramento Bee reports about custom-tailored molecules and spray-on plastic could someday create the next generation of solar cells -- more flexible, more efficient and much less expensive than existing sources of solar power.
Quantum encryption and quantum computing may be just around the corner!
Unfortunately, this is a pretty lossy algorithm, because if you wanted to recreate the article from your compression, you couldn't. This is simply because just about anything in the New Scientist will be compressed, using your algorithm, to the same thing... heh.
No, read my proof more carefully. In the proof, we assume that there is no prime larger than p_n. Your example of 30031 is of course not prime, but under the assumption that the only primes are {2,3,5,7,11,13}, it is. This is because although it is divisible by a smaller number (59 and 509), these numbers cannot be prime by assumption, thus they each must have been divisible by a smaller number.
As you've pointed out, in either case you get a contradiction, and therefore the statement is true.
I think you've actually made the problem worse. I don't know what the complexity of GCD is, but you're giving it a factorial input, which is significantly worse that exponential, because n! is asymptotically the same as n^n, which is even worse than e^n. And GCD will be at least linear in the size of its argument.
On the other hand, you've not really done anything there. All you're roughly saying is, find the greatest common divisor of r and all numbers less than r, which is intuitively even worse than just factoring the damn thing.
The first thing that would happen after creating such a solution would be the FBI showing up at your door without a warrent and arresting you under the DMCA.
>If a person could find an function f(x) that returns the xth prime number, [blah blah]
Actually, you can. Anyone proficient in a programming language can code one easily enough, and anyone with any math experience can write out a description of said function. I think you meant a "simple" function f(x) (i.e., non-recursive), which I think has been proven impossible (although don't take my word for it).
Well, if you want to define function in any way you want, then of course, I can find a function which returns the primes. I define f so that f(n) is the nth prime. Woo.
Of course, this function is completely meaningless. The poster was of course saying that it would interesting to find a function which allowed you to compute the nth prime without knowing the primes already. This has not been found. Of course, you can't prove that it's not possible, because our conditions are pretty vague. I mean, there are certainly many smooth functions whose value at n is the nth prime. And for any finite number N, there is even a polynomial whose values at 1,2,...,N are the 1st, 2nd,... , Nth prime. But unless you could say something about these functions, then they are useless.
For example, there is a function whose value at 0 is the time of my birth,at at 1 is the time of my death. Claiming there is such a function doesn't tell me much.
>If only it was easy to find any decimal of PI with a simple formula, [blah blah]
It is. See other replies to your post.
I was going to reply to this elsewhere, but since I'm already typing...There is a result where one can calculate the nth digit of \pi in hex (and I think in any base which is a power of 2), but, surprisingly, there is no analogous algorithm for base 10. So you might say, well, the hell with it. Just compute the nth digit in hex, and then convert. But, to convert from hex to decimal to find the nth digit, you would need all of the preceding digits. A funny little Catch-22. Although, it's certainly possible that there is an analogous base 10 algorithm, just noone knows it.
Similarly, we know there are an infinite number of primes, just that nobody has been able to prove it.
Other posters have pointed out that this was proved clasically (and by classically I don't mean last century, I mean like 500BC or whenever Euclid was around), but not only is this a classically known fact, I will reproduce the simplest proof I know here:
We will prove this by contradiction. We will assume that there are a finite number of primes, i.e. that there is a largest prime. Let's number them p_1,...,p_n.
To show N is prime, it suffices to show that it cannot be divided by any smaller number (except for 1). Even better, it suffices to show that N cannot be divided by any smaller prime (since if a smaller number divided N, so would its prime factors). Consider the number
N = p_1p_2...p_n + 1
by which I mean that I multiply all of the primes together, and then add one. If I can show that this is not divisible by any of the primes, I am done. But consider what happens if I divide N by any p_k. Looking at the formula, p_k certainly divides the product evenly, so therefore if I divide N by p_k, I always get a remainder of 1.
Thus N is not divisible by any p_k. But thus it is not divisible by any smaller number, and therefore is prime. But since N > p_n, our "largest" prime, this is obviously a contradiction. Therefore there can be no largest prime, and thus there are infinitely many.
As I said, this proof is due to Euclid. There are many sources for this proof, and there are many other elegant proofs. There is a realtively advanced book called Proofs from the Book which gives elegant proofs to some well-known (and perhaps not so well-known) results. This is a nice little book, and, anyway, there are no fewer than six proofs that there are infinitely many primes. Not being a number theorist, I don't get all stiff about primes personally, but it's good stuff.
Ok, maybe this is a bit off-topic, but if anyone reads any Harry Turtledove, the name is somewhat amusing... one of the major characters in the WorldWar series is named Heinrich Jaeger.
I used to read the NS a bit, it is entertaining. But so is Harry Turtledove and Dan Simmons. I'm not passing that off as reality.
In the department I used to be in, we'd have some cool arguments over what was going on in NS articles... it was usually 6 dudes saying "that's bullshit", and then 4 dudes saying, "well, if it were true, then we could build, etc., etc., and that would be cool". Very cool conversations, sometimes, but, frankly, worthless from a scientific point-of-view. Good for lunch conversation, tho'...
I agree with you to a point, but I think there is an added complication. It is certanly true that the amount of pay increases as the number of peope who can do a job decreases.
On the other hand, I do think the economic value of the product is a factor. For example, there aren't many people who can, say, sew a quilt, like those 100-year-old Quaker things. And they're very nice. But they aren't worth a whole lot, certainly not compared to M$ Office. So programmers will make more than quilters, in general.
I think hgh pay comes from a combination of lack of qualified workers, and a product which can generate revenue.
Wow you have the view of business economics way wrong.
your employer pays you as little as possible to keep you working.
This last statement is of course true. Why would they pay you more than you're willing to work for? This is a good answer to the poster who asked why certain types of workers make less; when there are more people willing to do a certain job, then the salary falls, because there is more competition for the spot. This is, again, why programmers make more than garbage collectors.
And I'll be honest... I'm not sure I would trust someone who is willing to pay me more than I'm worth. I don't know about you, but I get email from random companies all of the time telling me they'll hire me for twice what I'm getting paid. When I see this, I'm inherently suspicious. Perhaps, once in a blue moon, this sort of offer is made in good faith, but it's usually just bullshit. Maybe I'm cynical, but whenever I see someone in the business world proporting to not be looking out for their own interests, I get very suspicious...
no, in the real business world, if company profits were to triple, employee salaries will go up by 3% if they are lucky
This is not true. For example, what is the average starting salary of someone graduating with a BS in CS? Now, graph that from the period '90-'00. I don't have the numbers in front of me, but are you going to say that this grew at 3% per year?
I guess it just saddens me that access is so unaffordable, when the resource itself is so rich. Am I being unreasonable?
Maybe you are, maybe you're not. But let me put it in a context for you.
I think it's a bad idea to compare it to coding, open/closed-source, etc. This is not the right paradigm. I think this is more like an academic work. For example, if you write a scholarly article, you submit it to some journal or another. They don't pay you anything, and they even take the copyright. Then they turn around and sell these journals for tons of money. For example, it is common for mathematics journals to cost an institution US$1000 or more a year. The authors of the papers get nothing from this.
Of course, if you're associated with a reasonable university, you'll be able to gain access to these journals as a scholar. So it seems to me that contributing to the OED is completely analogous to scholarly publication.
Slightly off-topic now, but I'm curious. Who decides that a long series of ones and zeros is worth so much more than the service of a garbage collector or artist?
Presumably, the people willing to pay so much more for it. It's pretty much the Law of Supply and Demand. There are not many people who can program, so they can ask their price much more so than can a garbage collector.
It's certainly true that our society would be in trouble without garbage collection, but, that being said, it's not so hard to find people to pick up the garbage. You would agree with me that the vast majority of people (certainly all able-bodied individuals) are capable of filling this job. On the other hand, there are much fewer people who can program.
Just for interest's stake, I'm an artist and a writer, so I have no reason to say this other than my own belief that the values society places on certain things are fundamentally twisted.
You're talking about society like it's some homogenous entity which makes these decisions in a vacuum. That's not really accurate. Also, I think you're confusing two concepts here: just because something is necessary doesn't mean it is more expensive. I need to eat, I don't need computers. But I bet you I've spent more on silicon in the last year than food.
I'm not an expert in this, but there's got to be some rules and explanations about life where there is no atmosphere.
Speaking theoretically, I don't see why there would have to be an atmosphere. For example, to most of the sea-dwelling creatures on Earth, it just as soon not have an atmosphere.
First and foremost, what kind of long-term injury are you potentially causing with the exercise/workouts?
I guess it depends on the workout. But there are certainly workouts which don't lead to injuries, in general. Certainly if you do all kinds of running, or lifting all kinds of sick weights, you're asking for some sort of injury. But if someone does a good amount of swimming, or walking, the chances of incurring an injury are small. And, actually, in fact, certain types of injury (say, in the back) are actually much less likely amongst those who are athletic. So, as long as it's reasonable, it's a good idea.
The only effect it has, is on Bill Gates Salary. You must be a programmer. What? You think they will pay you more if piracy didnt exsist? Hell no, You'll make the exact same amount of money that you make now. The people who will get paid more are, Steve, Bill, and upper level management. NOT YOU!!!!!
This is insane. By your logic, the amount of money entering an industry does not affect the salary of the people working in it. Therefore programmers make as much as artists, garbage collectors, ditch diggers, etc? No, of course not. Programmers can make tons of money for not so much work simply because the product they produce is worth a lot of money. End of story.
Now, what you're saying is true, in the sense that once you've worked on a project, the amount of sales of that product in the future won't affect the amount of money you make now. But this is a horrendously simplistic viewpoint. When you work for a company, they're not paying you out of the money they will get selling the product you're working on. They don't have it yet. They're paying you the money they've made on previous products. And yes, me pirating M$ software today will affect the job prospect of M$ programmers in the near future.
Here's a question, though - Do we still live in an age where we can postulate these types of ideas and questions, or do we demand hard-core applications to come directly from speculative science?
Well, I guess for a good answer to that question, you need to know who the "we" are. I think that most people in the country as a whole are interested in science inasmuch as it can produce applications, and, in particular, applications which will affect their everyday life. For example, IMHO most people wouldn't consider what NASA does as "applied", since they don't see how they would benefit from it directly.
On the other hand, there is a large class of people who care about asking questions in a pure sense, and answering them without a lot of thought given to their applications. These people are the academics. For example, with few exceptions, academics fall into these this category. As a professor of (say) mathematics, one is rarely interested in commercial applications of the math one is doing, and depending on the field, not interested in whether the mathematics applies to anything at all. This is true of most academic fields. Historians ask those questions because they're the right questions to ask, not because it'll build a better motherboard.
Now... do you think XYZ Genetic Corp. has any right to prevent me from either having children or selling one of my super kidneys to the highest bidder?
There's fundamentally no difference between me and a plant.
The law certainly recognizes the difference between plants and humans. It even recognizes the difference between animals and humans.
For example, you can buy and sell most plants and most animals. But, in the US at least, it is not legal to buy and sell humans. You can forcibly breed plants and animals now, without genetic engineering, to get better strains. You can't do this with humans. We do all kinds of medical research on all levels of animals, but, again, this is illegal to do on humans.
In general, the law has heretofore recognized a significant difference between humans and non-human life. There's no reason to expect this will be any different.
Let me also point out, aside from any legal precendent, most people would disagree with your final statement in every sense. I see what you're saying, but in most Americans' worldview, there is a qualitative difference between humans and plants. Aside from a few radicals, almost everyone would disagree with your last statement on political, ethical and even spiritual grounds.
I do not think we need to fear any scenario such as that you described. Or, let me amplify: we shouldn't fear corporations violating humans' rights simply because they can do it to plants.
I have to agree. This can turn out really well for the rest of the world.
As I see it, we are running into a bit of a problem (which is certainly not a novel viewpoint) in that we have a lot of people, and the number is growing quickly. What makes this problem somewhat worse is that both people and food are distributed asymmetrically, but in different ways.
Ok, nothing new, too many people, not enough food. Everyone knows this. I think, though, the standard reaction to this is to be, essentially, very pessimistic, and takes the viewpoint "We're screwed". But I think that science can solve these problems. It's had a pretty good track record so far.
And if there's one thing technology development has taught us, that's that if you make something profitable to implement, it will be implemented. Patenting foods is a good step in this direction. And I think we really need to hit this problem with new technology, because what else do we do?
Slashdot Mirror
2*(sandwich)*c^2
I don't think that is true. For example, I think that if you had simply put the first two paragraphs of your post, and no other, they would be completely reasonable.
But once you start comparing having to get a driver's license to anything the Gestapo did, and refer to "the State", then things start sounding a little nutty. Sorry, but it's true.
Does that make you a nut, or everyone else in the world a nut? I don't know, you could be right and the rest of the world wrong; as Winston Smith said, "Sanity is not statistical." But if you want to convince anyone else of your position, you need to not sound like an ideologue.
But my question is, what is new here?
For example, in every state that I've lived and gotten a driver's license in, I was required to submit all of this information. I had to give biometric information, my NY state driver's licence has my height and eye-color, and other states have required my weight, and so on. Also, every driver's license I've ever had has a picture on it, which was digitized and entered into a database.
I can understand your position if you think that it's a violation of privacy for you to have to submit to a picture, and to give basic biometric information. I disagree, but I can understand where you're coming from... But, if this is your position, then it must be true that the current situation was intolerable to you. Anyone who thinks that this new development is somehow different than the current situation is just having a knee-jerk reaction.
Quantum encryption and quantum computing may be just around the corner!
Unfortunately, this is a pretty lossy algorithm, because if you wanted to recreate the article from your compression, you couldn't. This is simply because just about anything in the New Scientist will be compressed, using your algorithm, to the same thing... heh.
And maybe you're not.
Calm down there, my man... That's some pretty harsh language.
Driving drunk is irresponsible.
Shooting guns into the air on New Year's Eve is irresponsible.
This, on the other hand, isn't that big a fucking deal at all.
As you've pointed out, in either case you get a contradiction, and therefore the statement is true.
On the other hand, you've not really done anything there. All you're roughly saying is, find the greatest common divisor of r and all numbers less than r, which is intuitively even worse than just factoring the damn thing.
Now that is a /. post!
Actually, you can. Anyone proficient in a programming language can code one easily enough, and anyone with any math experience can write out a description of said function. I think you meant a "simple" function f(x) (i.e., non-recursive), which I think has been proven impossible (although don't take my word for it).
Well, if you want to define function in any way you want, then of course, I can find a function which returns the primes. I define f so that f(n) is the nth prime. Woo.
Of course, this function is completely meaningless. The poster was of course saying that it would interesting to find a function which allowed you to compute the nth prime without knowing the primes already. This has not been found. Of course, you can't prove that it's not possible, because our conditions are pretty vague. I mean, there are certainly many smooth functions whose value at n is the nth prime. And for any finite number N, there is even a polynomial whose values at 1,2,...,N are the 1st, 2nd, ... , Nth prime. But unless you could say something about these functions, then they are useless.
For example, there is a function whose value at 0 is the time of my birth,at at 1 is the time of my death. Claiming there is such a function doesn't tell me much.
>If only it was easy to find any decimal of PI with a simple formula, [blah blah]
It is. See other replies to your post.
I was going to reply to this elsewhere, but since I'm already typing...There is a result where one can calculate the nth digit of \pi in hex (and I think in any base which is a power of 2), but, surprisingly, there is no analogous algorithm for base 10. So you might say, well, the hell with it. Just compute the nth digit in hex, and then convert. But, to convert from hex to decimal to find the nth digit, you would need all of the preceding digits. A funny little Catch-22. Although, it's certainly possible that there is an analogous base 10 algorithm, just noone knows it.
Other posters have pointed out that this was proved clasically (and by classically I don't mean last century, I mean like 500BC or whenever Euclid was around), but not only is this a classically known fact, I will reproduce the simplest proof I know here:
We will prove this by contradiction. We will assume that there are a finite number of primes, i.e. that there is a largest prime. Let's number them p_1,...,p_n.
To show N is prime, it suffices to show that it cannot be divided by any smaller number (except for 1). Even better, it suffices to show that N cannot be divided by any smaller prime (since if a smaller number divided N, so would its prime factors). Consider the number
N = p_1p_2...p_n + 1
by which I mean that I multiply all of the primes together, and then add one. If I can show that this is not divisible by any of the primes, I am done. But consider what happens if I divide N by any p_k. Looking at the formula, p_k certainly divides the product evenly, so therefore if I divide N by p_k, I always get a remainder of 1.
Thus N is not divisible by any p_k. But thus it is not divisible by any smaller number, and therefore is prime. But since N > p_n, our "largest" prime, this is obviously a contradiction. Therefore there can be no largest prime, and thus there are infinitely many.
As I said, this proof is due to Euclid. There are many sources for this proof, and there are many other elegant proofs. There is a realtively advanced book called Proofs from the Book which gives elegant proofs to some well-known (and perhaps not so well-known) results. This is a nice little book, and, anyway, there are no fewer than six proofs that there are infinitely many primes. Not being a number theorist, I don't get all stiff about primes personally, but it's good stuff.
WooOOo
I used to read the NS a bit, it is entertaining. But so is Harry Turtledove and Dan Simmons. I'm not passing that off as reality.
In the department I used to be in, we'd have some cool arguments over what was going on in NS articles... it was usually 6 dudes saying "that's bullshit", and then 4 dudes saying, "well, if it were true, then we could build, etc., etc., and that would be cool". Very cool conversations, sometimes, but, frankly, worthless from a scientific point-of-view. Good for lunch conversation, tho'...
On the other hand, I do think the economic value of the product is a factor. For example, there aren't many people who can, say, sew a quilt, like those 100-year-old Quaker things. And they're very nice. But they aren't worth a whole lot, certainly not compared to M$ Office. So programmers will make more than quilters, in general.
I think hgh pay comes from a combination of lack of qualified workers, and a product which can generate revenue.
your employer pays you as little as possible to keep you working.
This last statement is of course true. Why would they pay you more than you're willing to work for? This is a good answer to the poster who asked why certain types of workers make less; when there are more people willing to do a certain job, then the salary falls, because there is more competition for the spot. This is, again, why programmers make more than garbage collectors.
And I'll be honest... I'm not sure I would trust someone who is willing to pay me more than I'm worth. I don't know about you, but I get email from random companies all of the time telling me they'll hire me for twice what I'm getting paid. When I see this, I'm inherently suspicious. Perhaps, once in a blue moon, this sort of offer is made in good faith, but it's usually just bullshit. Maybe I'm cynical, but whenever I see someone in the business world proporting to not be looking out for their own interests, I get very suspicious...
no, in the real business world, if company profits were to triple, employee salaries will go up by 3% if they are lucky
This is not true. For example, what is the average starting salary of someone graduating with a BS in CS? Now, graph that from the period '90-'00. I don't have the numbers in front of me, but are you going to say that this grew at 3% per year?
Maybe you are, maybe you're not. But let me put it in a context for you.
I think it's a bad idea to compare it to coding, open/closed-source, etc. This is not the right paradigm. I think this is more like an academic work. For example, if you write a scholarly article, you submit it to some journal or another. They don't pay you anything, and they even take the copyright. Then they turn around and sell these journals for tons of money. For example, it is common for mathematics journals to cost an institution US$1000 or more a year. The authors of the papers get nothing from this.
Of course, if you're associated with a reasonable university, you'll be able to gain access to these journals as a scholar. So it seems to me that contributing to the OED is completely analogous to scholarly publication.
Presumably, the people willing to pay so much more for it. It's pretty much the Law of Supply and Demand. There are not many people who can program, so they can ask their price much more so than can a garbage collector.
It's certainly true that our society would be in trouble without garbage collection, but, that being said, it's not so hard to find people to pick up the garbage. You would agree with me that the vast majority of people (certainly all able-bodied individuals) are capable of filling this job. On the other hand, there are much fewer people who can program.
Just for interest's stake, I'm an artist and a writer, so I have no reason to say this other than my own belief that the values society places on certain things are fundamentally twisted.
You're talking about society like it's some homogenous entity which makes these decisions in a vacuum. That's not really accurate. Also, I think you're confusing two concepts here: just because something is necessary doesn't mean it is more expensive. I need to eat, I don't need computers. But I bet you I've spent more on silicon in the last year than food.
Speaking theoretically, I don't see why there would have to be an atmosphere. For example, to most of the sea-dwelling creatures on Earth, it just as soon not have an atmosphere.
Hell, if people will watch NASCAR, they'll watch damn near anything...
I guess it depends on the workout. But there are certainly workouts which don't lead to injuries, in general. Certainly if you do all kinds of running, or lifting all kinds of sick weights, you're asking for some sort of injury. But if someone does a good amount of swimming, or walking, the chances of incurring an injury are small. And, actually, in fact, certain types of injury (say, in the back) are actually much less likely amongst those who are athletic. So, as long as it's reasonable, it's a good idea.
This is insane. By your logic, the amount of money entering an industry does not affect the salary of the people working in it. Therefore programmers make as much as artists, garbage collectors, ditch diggers, etc? No, of course not. Programmers can make tons of money for not so much work simply because the product they produce is worth a lot of money. End of story.
Now, what you're saying is true, in the sense that once you've worked on a project, the amount of sales of that product in the future won't affect the amount of money you make now. But this is a horrendously simplistic viewpoint. When you work for a company, they're not paying you out of the money they will get selling the product you're working on. They don't have it yet. They're paying you the money they've made on previous products. And yes, me pirating M$ software today will affect the job prospect of M$ programmers in the near future.
Sorry, kid, it's the way the world works.
Well, I guess for a good answer to that question, you need to know who the "we" are. I think that most people in the country as a whole are interested in science inasmuch as it can produce applications, and, in particular, applications which will affect their everyday life. For example, IMHO most people wouldn't consider what NASA does as "applied", since they don't see how they would benefit from it directly.
On the other hand, there is a large class of people who care about asking questions in a pure sense, and answering them without a lot of thought given to their applications. These people are the academics. For example, with few exceptions, academics fall into these this category. As a professor of (say) mathematics, one is rarely interested in commercial applications of the math one is doing, and depending on the field, not interested in whether the mathematics applies to anything at all. This is true of most academic fields. Historians ask those questions because they're the right questions to ask, not because it'll build a better motherboard.
There's fundamentally no difference between me and a plant.
The law certainly recognizes the difference between plants and humans. It even recognizes the difference between animals and humans.
For example, you can buy and sell most plants and most animals. But, in the US at least, it is not legal to buy and sell humans. You can forcibly breed plants and animals now, without genetic engineering, to get better strains. You can't do this with humans. We do all kinds of medical research on all levels of animals, but, again, this is illegal to do on humans.
In general, the law has heretofore recognized a significant difference between humans and non-human life. There's no reason to expect this will be any different.
Let me also point out, aside from any legal precendent, most people would disagree with your final statement in every sense. I see what you're saying, but in most Americans' worldview, there is a qualitative difference between humans and plants. Aside from a few radicals, almost everyone would disagree with your last statement on political, ethical and even spiritual grounds.
I do not think we need to fear any scenario such as that you described. Or, let me amplify: we shouldn't fear corporations violating humans' rights simply because they can do it to plants.
As I see it, we are running into a bit of a problem (which is certainly not a novel viewpoint) in that we have a lot of people, and the number is growing quickly. What makes this problem somewhat worse is that both people and food are distributed asymmetrically, but in different ways.
Ok, nothing new, too many people, not enough food. Everyone knows this. I think, though, the standard reaction to this is to be, essentially, very pessimistic, and takes the viewpoint "We're screwed". But I think that science can solve these problems. It's had a pretty good track record so far.
And if there's one thing technology development has taught us, that's that if you make something profitable to implement, it will be implemented. Patenting foods is a good step in this direction. And I think we really need to hit this problem with new technology, because what else do we do?