> They're doing something right if the show has gone on this long
Davies is responsible only for 4 years of that success. Note that I'm not criticising the series as a whole, but the finale (and other Davies writing). The best episodes of each series are almost universally recognised as not being those written by Davies. I have to credit Davies with resurrecting the series, but the best thing Davies did was hire Moffat and others as writers.
As usual, it was a Russell T Davies campy almost-but-not-quite musical cheesefest. Just about any fact about Doctor Who that you thought was canonical was blatantly ignored. The greatest sin of all was throwing away a regeneration. For god's sake. Regenerations are probably the most precious thing in the Doctor Who universe and Davies thought he'd end his Who career (after all, he doesn't have to fix the plot holes he made) by simply throwing one away for a completely dumb plot twist. Of course it doesn't matter now that no rules are followed any more. And could anything have been more sickly that seeing all of the Doctor's wannabe lovers (and their pathetic families) fawning after him? The whole finally was nothing but laughable. The scene of the Tardis towing the Earth was beyond laughable. The faster Stephen Moffat takes over, the better.
> The proof for that is the fact that sex roles differ from one culture to another
That just demonstrates that the specifics of sex roles vary from society to society. It doesn't show that humans aren't born with an instinctive drive to acquire sharply differentiated sex roles. Similarly, the fact that people in different countries speak different languages doesn't prove that language is cultural. It shows that the specifics of individual languages are cultural, but that humans may still be born with 'hardwired' language skills. It could well be that women, for example, have an instinct, from birth, to find out what other women do, find out what men do, and make sure they do more of the former than the latter.
> The goal should be to give one computer to each and every student
Why? To make sure they all have myspace accounts and can watch youtube videos? That is, after all, what kids do with them. Households with computers often result in kids being less educated because they have more distractions from homework.
Other things being equal, companies prefer to recruit younger people meaning that as I get older it'll be harder and harder for me to find new work. So this is great news because as long as I can outthink the next generation I have a steady stream of income. At this rate, when I'm old and senile I'll still be gainfully employed.
We think straight lines on the ground are man-made because we know man-made processes that can produce them, but not natural ones. If a geologist discovered a natural method for producing straight lines wed rethink our interpretation of straight lines visible from a plane. Simplicity has nothing to do with it. Of course if youre the kind of person who likes to reduce things to a single axis this is all very confusing, but most people arent that stupid. The smart SETI people arent looking for simplicity, theyre looking for signals that cant be produced by any known natural process.
> An excellent Physics book that is very math heavy but assumes no prereqs is Penrose's Road to Reality
You're joking, right? You can't go from no prereqs to graduate level physics in just a handful of pages. The truth is - Penrose's book flies through the physics faster than it can be explained. This means that every reader either understands the whole book before they start, or hit a wall with no possible way to proceed at some point in the book, even if you have a PhD in mathematics or physics. Did you read it all? Really? Understanding the theory well enough to make physical predictions of your own?
Road to Reality is a terrible way to learn any physics. And when someone wants to learn about physics for differential equations they'd better start with fluid dynamics or electrostatics before they get onto twistor theory.
> getting paid for actual work just seems more honest.
Who cares what's honest? The goal is to get your client to willingly part with their money and give it to you. I couldn't care less what seems 'actual' or 'honest'.
Not sure what the relevance of that answer is anyway. The picture I just glanced at on my desk holds a lot of meaning for me. Is the writer you're replying to trying to say that Ockham's razor implies that actually this picture doesn't mean anything?
A hammer is a collection of electrons, neutrons and protons. But that's a completely useless point of view except in very special contexts. A hammer is a tool for knocking nails into wood. But it doesn't become a hammer because you add something to those particles. There is no essence of malleosity you have to sprinkle on its molecules to make it into a hammer. So you've completely lost me with equations like "Cosmology + n = Purpose".
I also have no idea what you mean by "Cosmology and evolutionary biology don't need any such entity". Presumably you intend 'need' as a metaphor of some sort, but it needs unpacking. Hammers serve a purpose, but a physicist can quite happily describe the physics going on inside a hammer without ever touching on its purpose. So what does cosmology have to do with the purpose of the universe?
Now I admit that there was a time when meaning and science were bound up. For example Aristotle talked of final purposes and derived physics from such things. But those days have long gone.
> Science says...that the universe serves no particular purpose or has any meaning for its existence,
Tell me, which exact branch of science deals with meaning and makes such statements?
Science has nothing to say about meanings and values. These fall completely outside of its domain. The world is full of people who somehow read the message "the universe serves no purpose" into cosmology and "people have no purpose" into evolutionary biology but that message is being put there by those people, it's not part of cosmology or evolutionary biology.
Thank you for pointing out my egregious errors. So let me say what I should have said: every proposition of *propositional calculus* is provably true or false. That is a counterexample to the incorrect statement of Godel's first incompleteness theorems above. I've no idea how I drifted from propositional calculus to first order logic and on a good day I'm fully aware that Godel uses two different sense of completeness - after all, I've read the same book as you.
A sad story about that book. I read it on the recommendation of the author himself. He said I should get back to him if I had any questions. So I compiled my list of questions and got ready to send it to him. And then I found he'd died of bone cancer. It's a great loss to the world.
> it's kind of a cheat to have infinitely many axioms without a production rule...
Absolutely. That's the whole point of Godel's (incompleteness) theorems. If you fail to mention the production rule then you're talking about the wrong thing.
> I'm not sure S is a set at all, it just might be to big.
How can it be too big? Propositions are just *finite* strings of characters. There's nothing mysterious about them. Not only do they form a countable set, it's a few minutes work to write a computer program to enumerate them all.
You don't need a set of all sets to make the set of all propositions.
The axioms of set theory are not finite. Look up the 'axiom' of comprehension. It's an infinite axiom schema. Even in simple arithmetic the 'axiom' of induction is an infinite collection of axioms.
Propositions are very simple things. They're just strings of characters. You can easily write a computer program to generate all propositions and there's no problem working with the set of all propositions. Given any set, the set of all subsets exists. This is the Power Set Axiom. This set contains every possible set of propositions, so it certainly contains the set of all true propositions.
An important part of Godel's incompleteness theorems that is often overlooked is that the set of axioms has to be recursively enumerable (r.e). In other words it has to be possible to write a computer program that lists the axioms, and no other propositions. My example fails because even though the set of all true propositions exists, it's not r.e. So it's not the kind of axiom set that Godel's theorems talk about. That's why these theorems can coexist with the example axiom set I talked about.
The other example I gave was first order logic. The incompleteness theorems don't talk about this either because you can't do arithmetic in first order logic. The theorems only apply to formal systems in which you can do arithmetic. Check out the wording at wikipedia.
A consequence of the incompleteness theorems is that we can't write a program that systematically lists all true mathematical propositions. But that's *not* what the original article is about. It's about machines checking human-generated proofs, and maybe filling in details. Godel's incompleteness theorems provide no objection to this at all. In principle, checking human proofs is really easy, you just check the axiom or derivation step that was used at each step in the proof. It's an undergraduate programming exercise to do this. The problem is more human than logical: complete formal proofs of non-trivial results are very very long and so don't correspond to what mathematicians actually write.
We already know that a statement like the continuum hypothesis can be proved neither true nor false from ZFC. We don't need Godel's theorem to prove "incompleteness or inconsistency" when we have lots of practical examples of its incompleteness. So your claim of "don't know" is false.
First order logic is consistent and complete. In fact, Godel proved this. Additionally, consider the set S of all possible propositions of set theory. Somewhere in the power set of S must lie the set of all true propositions. Just take these as your axioms. Voila, a formal system that is both complete and consistent. Your characterization of Godel's theorem is incorrect.
> Godel of course proved that you can never have a complete list of all true statements in mathematics
It doesn't need Godel to figure out that you can't make a list of all possible true statements in mathematics. Given that even a child knows that there are an infinite number of true statements I can only think that you cite Godel in an attempt to give your trivial observation an exaggerated air of authority.
But what they lack in the third leg of a triad they more than make up for with harmonic richness generated by the nonlinear effects of distortion. In effect, they have as many overtones as any true chord and so, unlike power cords, fully deserve the appellation 'chord'.
Slashdot Mirror
Davies is responsible only for 4 years of that success. Note that I'm not criticising the series as a whole, but the finale (and other Davies writing). The best episodes of each series are almost universally recognised as not being those written by Davies. I have to credit Davies with resurrecting the series, but the best thing Davies did was hire Moffat and others as writers.
As usual, it was a Russell T Davies campy almost-but-not-quite musical cheesefest. Just about any fact about Doctor Who that you thought was canonical was blatantly ignored. The greatest sin of all was throwing away a regeneration. For god's sake. Regenerations are probably the most precious thing in the Doctor Who universe and Davies thought he'd end his Who career (after all, he doesn't have to fix the plot holes he made) by simply throwing one away for a completely dumb plot twist. Of course it doesn't matter now that no rules are followed any more. And could anything have been more sickly that seeing all of the Doctor's wannabe lovers (and their pathetic families) fawning after him? The whole finally was nothing but laughable. The scene of the Tardis towing the Earth was beyond laughable. The faster Stephen Moffat takes over, the better.
Sheesh!
That just demonstrates that the specifics of sex roles vary from society to society. It doesn't show that humans aren't born with an instinctive drive to acquire sharply differentiated sex roles. Similarly, the fact that people in different countries speak different languages doesn't prove that language is cultural. It shows that the specifics of individual languages are cultural, but that humans may still be born with 'hardwired' language skills. It could well be that women, for example, have an instinct, from birth, to find out what other women do, find out what men do, and make sure they do more of the former than the latter.
Why? To make sure they all have myspace accounts and can watch youtube videos? That is, after all, what kids do with them. Households with computers often result in kids being less educated because they have more distractions from homework.
Don't forget how they cloned Dirk Benedict's cheesy smile from the original and grafted it onto Katee Sackhoff.
Other things being equal, companies prefer to recruit younger people meaning that as I get older it'll be harder and harder for me to find new work. So this is great news because as long as I can outthink the next generation I have a steady stream of income. At this rate, when I'm old and senile I'll still be gainfully employed.
We think straight lines on the ground are man-made because we know man-made processes that can produce them, but not natural ones. If a geologist discovered a natural method for producing straight lines wed rethink our interpretation of straight lines visible from a plane. Simplicity has nothing to do with it. Of course if youre the kind of person who likes to reduce things to a single axis this is all very confusing, but most people arent that stupid. The smart SETI people arent looking for simplicity, theyre looking for signals that cant be produced by any known natural process.
So just how many near Earth objects come from atop Haleakala?
> An excellent Physics book that is very math heavy but assumes no prereqs is Penrose's Road to Reality
You're joking, right? You can't go from no prereqs to graduate level physics in just a handful of pages. The truth is - Penrose's book flies through the physics faster than it can be explained. This means that every reader either understands the whole book before they start, or hit a wall with no possible way to proceed at some point in the book, even if you have a PhD in mathematics or physics. Did you read it all? Really? Understanding the theory well enough to make physical predictions of your own?
Road to Reality is a terrible way to learn any physics. And when someone wants to learn about physics for differential equations they'd better start with fluid dynamics or electrostatics before they get onto twistor theory.
> getting paid for actual work just seems more honest.
Who cares what's honest? The goal is to get your client to willingly part with their money and give it to you. I couldn't care less what seems 'actual' or 'honest'.
Not sure what the relevance of that answer is anyway. The picture I just glanced at on my desk holds a lot of meaning for me. Is the writer you're replying to trying to say that Ockham's razor implies that actually this picture doesn't mean anything?
Of course it's a technology story. It's people like this that have driven technologies like Bayesian filtering of email.
A hammer is a collection of electrons, neutrons and protons. But that's a completely useless point of view except in very special contexts. A hammer is a tool for knocking nails into wood. But it doesn't become a hammer because you add something to those particles. There is no essence of malleosity you have to sprinkle on its molecules to make it into a hammer. So you've completely lost me with equations like "Cosmology + n = Purpose".
I also have no idea what you mean by "Cosmology and evolutionary biology don't need any such entity". Presumably you intend 'need' as a metaphor of some sort, but it needs unpacking. Hammers serve a purpose, but a physicist can quite happily describe the physics going on inside a hammer without ever touching on its purpose. So what does cosmology have to do with the purpose of the universe?
Now I admit that there was a time when meaning and science were bound up. For example Aristotle talked of final purposes and derived physics from such things. But those days have long gone.
> Science says...that the universe serves no particular purpose or has any meaning for its existence,
Tell me, which exact branch of science deals with meaning and makes such statements?
Science has nothing to say about meanings and values. These fall completely outside of its domain. The world is full of people who somehow read the message "the universe serves no purpose" into cosmology and "people have no purpose" into evolutionary biology but that message is being put there by those people, it's not part of cosmology or evolutionary biology.
So that's what my parents have been trying to stop me accessing all these years! But I don't see what the big deal is.
Thank you for pointing out my egregious errors. So let me say what I should have said: every proposition of *propositional calculus* is provably true or false. That is a counterexample to the incorrect statement of Godel's first incompleteness theorems above. I've no idea how I drifted from propositional calculus to first order logic and on a good day I'm fully aware that Godel uses two different sense of completeness - after all, I've read the same book as you.
A sad story about that book. I read it on the recommendation of the author himself. He said I should get back to him if I had any questions. So I compiled my list of questions and got ready to send it to him. And then I found he'd died of bone cancer. It's a great loss to the world.
> it's kind of a cheat to have infinitely many axioms without a production rule...
Absolutely. That's the whole point of Godel's (incompleteness) theorems. If you fail to mention the production rule then you're talking about the wrong thing.
> I'm not sure S is a set at all, it just might be to big. How can it be too big? Propositions are just *finite* strings of characters. There's nothing mysterious about them. Not only do they form a countable set, it's a few minutes work to write a computer program to enumerate them all. You don't need a set of all sets to make the set of all propositions.
> You want your set of axioms to be finite
The axioms of set theory are not finite. Look up the 'axiom' of comprehension. It's an infinite axiom schema. Even in simple arithmetic the 'axiom' of induction is an infinite collection of axioms.
You're overthinking the problem. Just borrow a few drivers from California and you can have *real* traffic jams anywhere with little or no effort.
To be frank, I replied to your post because it was the first one to make sense. The parent posts didn't seem to say anything coherent at all.
Propositions are very simple things. They're just strings of characters. You can easily write a computer program to generate all propositions and there's no problem working with the set of all propositions. Given any set, the set of all subsets exists. This is the Power Set Axiom. This set contains every possible set of propositions, so it certainly contains the set of all true propositions.
An important part of Godel's incompleteness theorems that is often overlooked is that the set of axioms has to be recursively enumerable (r.e). In other words it has to be possible to write a computer program that lists the axioms, and no other propositions. My example fails because even though the set of all true propositions exists, it's not r.e. So it's not the kind of axiom set that Godel's theorems talk about. That's why these theorems can coexist with the example axiom set I talked about.
The other example I gave was first order logic. The incompleteness theorems don't talk about this either because you can't do arithmetic in first order logic. The theorems only apply to formal systems in which you can do arithmetic. Check out the wording at wikipedia.
A consequence of the incompleteness theorems is that we can't write a program that systematically lists all true mathematical propositions. But that's *not* what the original article is about. It's about machines checking human-generated proofs, and maybe filling in details. Godel's incompleteness theorems provide no objection to this at all. In principle, checking human proofs is really easy, you just check the axiom or derivation step that was used at each step in the proof. It's an undergraduate programming exercise to do this. The problem is more human than logical: complete formal proofs of non-trivial results are very very long and so don't correspond to what mathematicians actually write.
We already know that a statement like the continuum hypothesis can be proved neither true nor false from ZFC. We don't need Godel's theorem to prove "incompleteness or inconsistency" when we have lots of practical examples of its incompleteness. So your claim of "don't know" is false.
First order logic is consistent and complete. In fact, Godel proved this. Additionally, consider the set S of all possible propositions of set theory. Somewhere in the power set of S must lie the set of all true propositions. Just take these as your axioms. Voila, a formal system that is both complete and consistent. Your characterization of Godel's theorem is incorrect.
It doesn't need Godel to figure out that you can't make a list of all possible true statements in mathematics. Given that even a child knows that there are an infinite number of true statements I can only think that you cite Godel in an attempt to give your trivial observation an exaggerated air of authority.
But what they lack in the third leg of a triad they more than make up for with harmonic richness generated by the nonlinear effects of distortion. In effect, they have as many overtones as any true chord and so, unlike power cords, fully deserve the appellation 'chord'.