In fact, you can do that in almost any country; all of those measurable characteristics will still be met, but they'll be called something different...
Are you thinking of the Hilbert Program http://plato.stanford.edu/entries/hilbert-program/? A really interesting idea, but it ultimately failed due primarily to Goedel's incompleteness proof (though in a talk I recently heard, Saul Kripke shows that Goedel's proof wasn't necessary to bring about its demise--the program fails due to internal inconsistency).
Yeah, this sort of thing has definitely happened before. When Frege published his (groundbreaking) account of set theory, everyone thought it was the greatest thing since sliced bread--until Russell showed that it entailed a fatal paradox (namely, that there is a set, call it R, that contains all and only those sets that don't contain themselves. Hence, R contains itself if and only if R doesn't contain itself). Similarly, Kurt Goedel proved in 1931 that the Russell/Whitehead language for first-order logic (and, indeed, any language complex enough to express simple arithmetic) is incomplete if consistent--despite the completeness proofs which were already published. Plenty of other cases abound. By (simple) induction on the history of mathematics, it appears probable that some results which we currently take as proved are actually false (or unproven, at least). So where does this leave us? Must we embark on a Cartesian quest for Absolute Certainty? I think that's probably not the best way to proceed. I like Otto Nuerath's analogy better: we are (epistemically) like people afloat on a raft at sea. As we discover leaks in the raft, we fix them and then move on; it's not as if it would be wise, upon discovering a leak, to destroy the entire raft and start over with a better engineering design (i.e. begin with something like Cartesian foundations).
I mostly agree with your comment--the sentiment is definitely right. I'll just add that there is a field called formal semantics, which consists in building models of and, importantly for the discussion here, making rules that describe the semantics of languages. Now, this is most easily accomplished with artificial languages, where the semantics are clear and precise (and usually quite a bit more orderly than in natural languages) but there has been work in using this with natural languages as well. Long story short, you're right that "You can't get semantics from syntax" but, and I take it this is the project of the semantic web, "You can *model* semantics with syntax." (Consider (e.g.) proofs of soundness and completeness for derivation systems in first-order logic--the whole point of these proofs is to show that the syntax of the formal derivation system is, in fact, a good model of the semantics of first-order (informal) logic.) That said, I agree with the sentiment that the project is overblown and that they're nowhere near as close to coming up with a good model as their press releases might indicate.
Science provides a falsifiable test of itself? I'd like to see how this would go. What observation could we possibly make that would impugn the entire body of theory, evidence, experimental technique, etc. that we call science? I think you're right to say that there's no "faith" required to, as it were, believe in science, but there's certainly something faith-like. You might think its inference to the best explanation (i.e. the best explanation for the tremendous predictive and manipulative power of science is that its theories are (at least approximately) true), but notice that there's no obvious reason to think that something's being the best explanation guarantees that it is actually correct (since, note, the best explanation is always chosen from among those we *currently have available*). Put crudely, the point is that there's no such thing as an argument with no premises (i.e. no starting point). Some skeptics will call the premises of science "faith", but I don't think this is right. Better, I think, to think of them as reasonable, but unproven (and perhaps unprovable) assumptions, which may one day be rejected. An honest attitude about science is, I think, fallibilist.
As to your final remark: For any statement (hence, including the one you quote) it's either true or not true, right? So what's this business about being "taken to an absurd level"? Is this just a claim about how we should understand the domain over which the quantifiers (i.e. "everyone", "something") range? If so, then your statement just reads: "The statement: "Everyone has something they believe in that they can't prove," is not true, unless the domain of the quantifiers is interpreted in to be wide enough (i.e. ranging over the entire domain of a persons' beliefs) such that it is true." That looks tautologous, and hence lacking content, to me. If it's not a claim about how the quantifier domains should be interpreted, then it's just false. Goedel proved in 1933 that, for any consistent language powerful enough to express basic arithmetic, there are true statements expressible in that language that are not provable in it. This is the so-called "Incompleteness Theorem" (I'll give you a link to Wikipedia on it, but I haven't had time to see if what's on there is accurate, so I'll just warn you to take it with a grain of salt, which I'm sure you would have anyway: http://en.wikipedia.org/wiki/Incompleteness_theorem).
I have to admit that I'm a little bit puzzled by all the fuss over this. As the article notes, theory retraction is not an uncommon phenomenon. Furthermore, many, many theories and findings published that long ago (60+ years!) have been shown to be false (or, if you prefer, not part of our best overall picture of the workings of the world). In a way, this would tend to invalidate the claims made by, in particular, recent ID supporters, who purport to be scientists. No actual scientist would base her arguments on a single paper published that long ago (unless it was an exceptionally groundbreaking paper, of course, but it doesn't seem that this paper was). Furthermore, this reliance of the ID people here on Science (note capital 'S') as an established body of immutable truths or some such thing again indicates how out of touch they are with actual scientific practice. Most scientists (if they are being honest) are fallibilists--they recognize that it's quite likely that our current theories aren't strictly true, yet are probably at least approximately true (since this explains (e.g.) their tremendous predictive power, practical applicability etc.). It is a hallmark of biblical (little 'b' to indicate "text-based") religions that they tend to take their sacred writings as a body of eternal, immutable, permanently established truths. That they would treat relatively old articles in scientific journals the same way suggests a religious, rather than scientific, approach even to scientific texts. Interesting.
Long story short: What's the big deal? Let the ID people cite the article--in so doing they only expose how non-scientific their practices actually are.
This is essentially a real-life, large scale version of the much discussed "Trolley Problem" (originally posed by Philippa Foot). (See http://en.wikipedia.org/wiki/Trolley_problem for a more-or-less accurate sketch.)
I'm quite aware that this is completely off-topic, but "Flip-Flops"? This locution, imported from contemporary political discourse, no doubt, irritates me to no end. Why not just say what you mean--namely: "changes its (or, in the case of persons, his/her) mind"? Or is this neologism supposed to mean something else that I'm not aware of (I doubt it, but who knows)?
Interestingly, at least some Burmese (generally younger people) are using the internet as a way to further their education (via online correspondence courses in other countries) since it is essentially illegal to go to college in Burma unless you are the child of a member of the military elite. Further, the idea behind this education is that they can hopefully use it to bring about social change in Burma, which need not involve the use of the internet to disseminate information.
I probably shouldn't go into any further detail about how I know this, though...
Great post, parent. Your penultimate paragraph especially is right on the money. The falsifiability criterion always struck me as a bizarre one anyway. I know that Popper (its inventor) was motivated to come up with a criterion whereby enterprises like experimental physics would be classes as "science" and enterprises such as Freudian psychology would be classed as "non-science", which is fine, but the principle cannot extend that far.
For one thing, as the parent points out, there are scientific "axiomatic" statements that cannot be shown to be false. In fact, this problem (if you think it is a problem) is not as isolated as the parent's post may suggest. The model of falsification that we have in mind looks something like this: We have a theory T that we want to test, so we derive from T some prediction about observable phenomenon O, and then we perform a test and see if O occurs. If O does not occur then, we conclude, T must be incorrect. Schematically, the model is just a modus tollens argument:
If T, then O (derived prediction)
Not O (we observe that the predicted phenomenon does not occur)
Therefore, not T
However, the problem is that no theory (excepting possibly some toy examples) is sufficient to entail, all by itself, any observational prediction. In order to derive any such observational prediction we will have to make additional assumptions about (e.g.) the way our instruments work, how the formulae of the theory are to be calculated and applied, the system of logic that we use to derive the predictions, etc. So, going back to the model, what we really have is something more like:
If (T & A1 & A2 & A3 &...) then O
Not O
Therefore, not (T & A1 & A2 & A3 &...)
But all this tells us is that at least one of those conjuncts is false (i.e. either T or A1 or A2 or...), but it can offer no insight as to which conjunct(s) is (are) the false one(s). Hence, if falsifiability requires that there be an observation that can deductively show that a theory is false, no theory is falsifiable. At best, we might say that *entire theoretical groups* can be falsifiable, but this is not particularly helpful since such theoretical groups will almost certainly include mathematics and logic as well.
Additionally, even if the above problem (the so-called "underdetermination" problem) can be overcome, there is an additional serious problem with the falsifiability criterion; namely that it is not at all clear which observations are possible and which are not. It may seem that the only handle we have on possibility (other than what we've already done, of course) is what we can conceive of--if something is imaginable, or makes sense on imagining, then we might be inclined to say that it is possible. But notice that this involves a rather strange claim for a Popperian to make, namely that we somehow have this amazing facility of mind such that if we can imagine something, it really is possible and, if we cannot imagine it, then it isn't possible (because, recall, this is how we show that things like psychoanalysis are not science--we cannot conceive of any observation which would falsify it). But why should we suppose that we have such a tremendous faculty of mind? For one thing, the claim that conceivability entails possibility certainly isn't itself falsifiable...
Right, fair enough. What I should have said (and what I really just meant to point out) was that, even amongst the philosophy programs I was looking at, only MIT did not ask for a GRE score. You're quite right to point out that I shouldn't generalize this to the whole school (which I didn't mean to imply).
The parent's post is a good one. Also, I think it's worth noting that MIT (graduate programs, anyway) seems to put less stock in standardized test scores than most. I was considering applying to their graduate program in philosophy, and noted that they don't ask for a GRE score as part of your application package.
"if you can't compete on price or service, just paralyze the competition by limiting the ability to shop elsewhere."
Good idea, in principle, but I don't think it would work in this case. Frankly, I think this is an idiotic decision by the book store, and here's why: When I was an undergraduate, I would go to the bookstore at the beginning of the term to write down the prices of the books that I needed for my classes, so that I could compare them to prices that I could find online. Sometimes the price difference would be negligible (or the bookstore price might actually be cheaper--it was rare, but it happened), in which case I would go back and buy those books from the bookstore. However, most of the time I could find better prices online (even including shipping). So, what would I have done had they kicked me out for writing down prices? I would have assumed (quite reasonably, given the tendencies) that I could find better prices online for *all* of my books and thus just not bought any of them at the bookstore. At least if the store allows me to comparison shop, they have a chance at getting my business--if they won't let me compare prices, I'll just assume that it's because their prices aren't the lowest and buy all of my books elsewhere.
I think it would be better to interpret blank cells as null, actually (if you interpret blanks as zeros, that could really bork your calculation of (e.g.) the average of a data set). Better, I think, to write your formulas with a clause to handle what to do if the referenced cell is blank. I don't know how to do this in Symphony, but I bet it's similar to what you can do in Excel: =IF(ISBLANK(myCell),"",$formula).
Yeah, I've looked into getting AmaroK working on OSX, but I got a bit balled up in installing the KDE libraries and I haven't had a chance to look into it further. I hope those apps are useful for you.:)
"Seriously, why would you want to buy a Mac if you can have Ubuntu, apart from Adobe/Macromedia products?"
First off, I'm typing this post on my Ubuntu Fiesty desktop. That said, I've also got a MacBook running OSX, which I absolutely love. The reason why I have a Mac? It's all about the apps. Most of the apps that I use on a regular basis in my workflow are free, awesome, and Cocoa or otherwise Mac-only. I'm thinking particularly of Quicksilver, Journler, iGTD, and Skim. There just aren't apps of these types that work this cleanly (and work *together* this cleanly) available for Ubuntu (at least, afaik--I'm happy to be proven wrong).
That said, there are some apps that I run on my Ubuntu box that beat the pants off of anything with a similar function for OSX. Amarok, for instance, so far outstrips iTunes (and anything else I can find for OSX) that it's not even funny. Long story short? As to the question: "Why buy a Mac when you can have Ubuntu?" The answer is: Get the best tools for the job. It just so happens that, for many of the jobs that I do (and the way I like to do them) the best tools I've found are available only for OSX.
There are plenty of alternative tuning systems, though I don't know if a "metric" tuning has been done (though I wouldn't be surprised at all if someone had already tried it). Just as an example, Javanese Gamelan music uses two different tuning systems, both of which (iirc) divide the octave unevenly between five pitches. In any event, I think that our current tuning system is really quite a reasonable one. Ignoring the fact that A is the note commonly tuned (this, I think, is more of a historical accident based on the fact that this is an open string on a violin) the frequencies of the "home note", C, are actually all powers of 2. Middle C is 512Hz, an octave above it is 1024Hz, an octave below it is 256Hz etc. That strikes me as being a lot neater than a "metric" system anyway.
Oh, and I think that the reason it's called an octave has to do with the fact that the eighth note of the traditional Western scale is the repeated one. E.g. C D E F G A B C
These debates may have been the place where ideas were put forwards once, but these days they are more like a boxing match in which each candidate tries to land knockout punches on the others, and a panel of pundits awards them points for style. Fact and logic don't stand a chance.
That's absolutely dead-on, sadly. That's a large part of the reason why I just can't pay too much attention to politics any more--it's all just so infuriatingly idiotic. I hate to be so apathetic, but I guess it's better than being enraged and frustrated all the time.
But school should not simply be job training centres, despite what some in business would like. We also need well rounded people. Techies needs to be familiar with art and literature. And artsies needs to know how to change the oil on their car. We need more renaissance men and women, not simple robots trained to do one job. Only then can we better understand each other and think outside the box to solve problems.
Well put, and absolutely correct in my opinion. If only more people thought that way...
I found your proof very interesting, though I'm not quite sure about the first definition you offer (and on which the reasoning is crucially based). According to this definition, A is evidence of B iff P(B|A) > P(B|~A) (I'm using '~' instead of the corner symbol since it is easier to type).
This definition has a few interesting features. First, it implies that there can be no evidence for a proposition whose (unconditional) probability is 1. (i.e. if P(B)=1, then P(B|A)=1 and P(B|~A)=1 so P(B|A) !> P(B|~A) so, by definition 1, A is not evidence of B (and this of course generalizes to any proposition A)).
That limit case is not a huge deal, though, but I thought I would point it out.
Second, what if the probability of A is very low (or even 0)? In this case, it may well turn out that P(B|A) > P(B|~A), but should this really mean that A *is* evidence of B? I think the indicative mood used in the definition doesn't square with how we normally think about evidence in our investigative practices (now, if you're offering a proposed *revision* of how we should think about evidence, that's another matter). I think the subjunctive mood might be better: "A, if its probability were sufficiently high, would be evidence of B". (Obviously "sufficiently high" would need to be given a rigorous, and hence probably arbitrary, treatment here for a workable definition.)
Here's the larger issue, though: Even if your proof works, and establishes that "absence of evidence is evidence of absence" we need to ask how good this evidence really is. The biggest part of the problem here is in how we might go about determining the conditional probability of the claims in question. Built in to your proof is the assumption that, if there is evidence to be found, we can eventually find it (this assumption does the work in the argument that our continued inability to find evidence of (e.g.) UFOs makes it more likely that there aren't any). But why should we be so confident in our current investigative techniques? Why not suppose instead that "absence of evidence is evidence that we're not looking hard enough (or looking in the wrong place, or in the wrong way etc.)"?
Slashdot Mirror
In fact, you can do that in almost any country; all of those measurable characteristics will still be met, but they'll be called something different...
Are you thinking of the Hilbert Program http://plato.stanford.edu/entries/hilbert-program/? A really interesting idea, but it ultimately failed due primarily to Goedel's incompleteness proof (though in a talk I recently heard, Saul Kripke shows that Goedel's proof wasn't necessary to bring about its demise--the program fails due to internal inconsistency).
Yeah, this sort of thing has definitely happened before. When Frege published his (groundbreaking) account of set theory, everyone thought it was the greatest thing since sliced bread--until Russell showed that it entailed a fatal paradox (namely, that there is a set, call it R, that contains all and only those sets that don't contain themselves. Hence, R contains itself if and only if R doesn't contain itself). Similarly, Kurt Goedel proved in 1931 that the Russell/Whitehead language for first-order logic (and, indeed, any language complex enough to express simple arithmetic) is incomplete if consistent--despite the completeness proofs which were already published. Plenty of other cases abound. By (simple) induction on the history of mathematics, it appears probable that some results which we currently take as proved are actually false (or unproven, at least). So where does this leave us? Must we embark on a Cartesian quest for Absolute Certainty? I think that's probably not the best way to proceed. I like Otto Nuerath's analogy better: we are (epistemically) like people afloat on a raft at sea. As we discover leaks in the raft, we fix them and then move on; it's not as if it would be wise, upon discovering a leak, to destroy the entire raft and start over with a better engineering design (i.e. begin with something like Cartesian foundations).
I mostly agree with your comment--the sentiment is definitely right. I'll just add that there is a field called formal semantics, which consists in building models of and, importantly for the discussion here, making rules that describe the semantics of languages. Now, this is most easily accomplished with artificial languages, where the semantics are clear and precise (and usually quite a bit more orderly than in natural languages) but there has been work in using this with natural languages as well. Long story short, you're right that "You can't get semantics from syntax" but, and I take it this is the project of the semantic web, "You can *model* semantics with syntax." (Consider (e.g.) proofs of soundness and completeness for derivation systems in first-order logic--the whole point of these proofs is to show that the syntax of the formal derivation system is, in fact, a good model of the semantics of first-order (informal) logic.) That said, I agree with the sentiment that the project is overblown and that they're nowhere near as close to coming up with a good model as their press releases might indicate.
Science provides a falsifiable test of itself? I'd like to see how this would go. What observation could we possibly make that would impugn the entire body of theory, evidence, experimental technique, etc. that we call science? I think you're right to say that there's no "faith" required to, as it were, believe in science, but there's certainly something faith-like. You might think its inference to the best explanation (i.e. the best explanation for the tremendous predictive and manipulative power of science is that its theories are (at least approximately) true), but notice that there's no obvious reason to think that something's being the best explanation guarantees that it is actually correct (since, note, the best explanation is always chosen from among those we *currently have available*). Put crudely, the point is that there's no such thing as an argument with no premises (i.e. no starting point). Some skeptics will call the premises of science "faith", but I don't think this is right. Better, I think, to think of them as reasonable, but unproven (and perhaps unprovable) assumptions, which may one day be rejected. An honest attitude about science is, I think, fallibilist.
As to your final remark: For any statement (hence, including the one you quote) it's either true or not true, right? So what's this business about being "taken to an absurd level"? Is this just a claim about how we should understand the domain over which the quantifiers (i.e. "everyone", "something") range? If so, then your statement just reads: "The statement: "Everyone has something they believe in that they can't prove," is not true, unless the domain of the quantifiers is interpreted in to be wide enough (i.e. ranging over the entire domain of a persons' beliefs) such that it is true." That looks tautologous, and hence lacking content, to me. If it's not a claim about how the quantifier domains should be interpreted, then it's just false. Goedel proved in 1933 that, for any consistent language powerful enough to express basic arithmetic, there are true statements expressible in that language that are not provable in it. This is the so-called "Incompleteness Theorem" (I'll give you a link to Wikipedia on it, but I haven't had time to see if what's on there is accurate, so I'll just warn you to take it with a grain of salt, which I'm sure you would have anyway: http://en.wikipedia.org/wiki/Incompleteness_theorem).
I have to admit that I'm a little bit puzzled by all the fuss over this. As the article notes, theory retraction is not an uncommon phenomenon. Furthermore, many, many theories and findings published that long ago (60+ years!) have been shown to be false (or, if you prefer, not part of our best overall picture of the workings of the world). In a way, this would tend to invalidate the claims made by, in particular, recent ID supporters, who purport to be scientists. No actual scientist would base her arguments on a single paper published that long ago (unless it was an exceptionally groundbreaking paper, of course, but it doesn't seem that this paper was). Furthermore, this reliance of the ID people here on Science (note capital 'S') as an established body of immutable truths or some such thing again indicates how out of touch they are with actual scientific practice. Most scientists (if they are being honest) are fallibilists--they recognize that it's quite likely that our current theories aren't strictly true, yet are probably at least approximately true (since this explains (e.g.) their tremendous predictive power, practical applicability etc.). It is a hallmark of biblical (little 'b' to indicate "text-based") religions that they tend to take their sacred writings as a body of eternal, immutable, permanently established truths. That they would treat relatively old articles in scientific journals the same way suggests a religious, rather than scientific, approach even to scientific texts. Interesting.
Long story short: What's the big deal? Let the ID people cite the article--in so doing they only expose how non-scientific their practices actually are.
This is essentially a real-life, large scale version of the much discussed "Trolley Problem" (originally posed by Philippa Foot). (See http://en.wikipedia.org/wiki/Trolley_problem for a more-or-less accurate sketch.)
I'm quite aware that this is completely off-topic, but "Flip-Flops"? This locution, imported from contemporary political discourse, no doubt, irritates me to no end. Why not just say what you mean--namely: "changes its (or, in the case of persons, his/her) mind"? Or is this neologism supposed to mean something else that I'm not aware of (I doubt it, but who knows)?
I agree with your point, but I'm not so sure about the choice of example--the Bavarian Radio Orchestra has produced some damn fine recordings, actually. I recently found this (http://www.amazon.com/Shostakovich-Symphony-No-Sergey-Aleksashkin/dp/B0007D0AUU/ref=sr_1_1/002-3144820-4888024?ie=UTF8&s=music&qid=1192111144&sr=8-1) recording of Shostakovich's 13th Symphony ("Babi Yar") which is really wonderful and (and this underscores your point) it was a steal too since it's not from a "big name" orchestra.
Wow, that's great--now if only someone could convince them to sell the files in FLAC format too; it would be the perfect music store (for me anyway)!
Interestingly, at least some Burmese (generally younger people) are using the internet as a way to further their education (via online correspondence courses in other countries) since it is essentially illegal to go to college in Burma unless you are the child of a member of the military elite. Further, the idea behind this education is that they can hopefully use it to bring about social change in Burma, which need not involve the use of the internet to disseminate information.
I probably shouldn't go into any further detail about how I know this, though...
Great post, parent. Your penultimate paragraph especially is right on the money. The falsifiability criterion always struck me as a bizarre one anyway. I know that Popper (its inventor) was motivated to come up with a criterion whereby enterprises like experimental physics would be classes as "science" and enterprises such as Freudian psychology would be classed as "non-science", which is fine, but the principle cannot extend that far.
For one thing, as the parent points out, there are scientific "axiomatic" statements that cannot be shown to be false. In fact, this problem (if you think it is a problem) is not as isolated as the parent's post may suggest. The model of falsification that we have in mind looks something like this: We have a theory T that we want to test, so we derive from T some prediction about observable phenomenon O, and then we perform a test and see if O occurs. If O does not occur then, we conclude, T must be incorrect. Schematically, the model is just a modus tollens argument:
If T, then O (derived prediction)
Not O (we observe that the predicted phenomenon does not occur)
Therefore, not T
However, the problem is that no theory (excepting possibly some toy examples) is sufficient to entail, all by itself, any observational prediction. In order to derive any such observational prediction we will have to make additional assumptions about (e.g.) the way our instruments work, how the formulae of the theory are to be calculated and applied, the system of logic that we use to derive the predictions, etc. So, going back to the model, what we really have is something more like:
If (T & A1 & A2 & A3 &...) then O
Not O
Therefore, not (T & A1 & A2 & A3 &...)
But all this tells us is that at least one of those conjuncts is false (i.e. either T or A1 or A2 or...), but it can offer no insight as to which conjunct(s) is (are) the false one(s). Hence, if falsifiability requires that there be an observation that can deductively show that a theory is false, no theory is falsifiable. At best, we might say that *entire theoretical groups* can be falsifiable, but this is not particularly helpful since such theoretical groups will almost certainly include mathematics and logic as well.
Additionally, even if the above problem (the so-called "underdetermination" problem) can be overcome, there is an additional serious problem with the falsifiability criterion; namely that it is not at all clear which observations are possible and which are not. It may seem that the only handle we have on possibility (other than what we've already done, of course) is what we can conceive of--if something is imaginable, or makes sense on imagining, then we might be inclined to say that it is possible. But notice that this involves a rather strange claim for a Popperian to make, namely that we somehow have this amazing facility of mind such that if we can imagine something, it really is possible and, if we cannot imagine it, then it isn't possible (because, recall, this is how we show that things like psychoanalysis are not science--we cannot conceive of any observation which would falsify it). But why should we suppose that we have such a tremendous faculty of mind? For one thing, the claim that conceivability entails possibility certainly isn't itself falsifiable...
Right, fair enough. What I should have said (and what I really just meant to point out) was that, even amongst the philosophy programs I was looking at, only MIT did not ask for a GRE score. You're quite right to point out that I shouldn't generalize this to the whole school (which I didn't mean to imply).
The parent's post is a good one. Also, I think it's worth noting that MIT (graduate programs, anyway) seems to put less stock in standardized test scores than most. I was considering applying to their graduate program in philosophy, and noted that they don't ask for a GRE score as part of your application package.
"if you can't compete on price or service, just paralyze the competition by limiting the ability to shop elsewhere."
Good idea, in principle, but I don't think it would work in this case. Frankly, I think this is an idiotic decision by the book store, and here's why: When I was an undergraduate, I would go to the bookstore at the beginning of the term to write down the prices of the books that I needed for my classes, so that I could compare them to prices that I could find online. Sometimes the price difference would be negligible (or the bookstore price might actually be cheaper--it was rare, but it happened), in which case I would go back and buy those books from the bookstore. However, most of the time I could find better prices online (even including shipping). So, what would I have done had they kicked me out for writing down prices? I would have assumed (quite reasonably, given the tendencies) that I could find better prices online for *all* of my books and thus just not bought any of them at the bookstore. At least if the store allows me to comparison shop, they have a chance at getting my business--if they won't let me compare prices, I'll just assume that it's because their prices aren't the lowest and buy all of my books elsewhere.
I think it would be better to interpret blank cells as null, actually (if you interpret blanks as zeros, that could really bork your calculation of (e.g.) the average of a data set). Better, I think, to write your formulas with a clause to handle what to do if the referenced cell is blank. I don't know how to do this in Symphony, but I bet it's similar to what you can do in Excel: =IF(ISBLANK(myCell),"",$formula).
Yeah, I've looked into getting AmaroK working on OSX, but I got a bit balled up in installing the KDE libraries and I haven't had a chance to look into it further. I hope those apps are useful for you. :)
"Seriously, why would you want to buy a Mac if you can have Ubuntu, apart from Adobe/Macromedia products?"
First off, I'm typing this post on my Ubuntu Fiesty desktop. That said, I've also got a MacBook running OSX, which I absolutely love. The reason why I have a Mac? It's all about the apps. Most of the apps that I use on a regular basis in my workflow are free, awesome, and Cocoa or otherwise Mac-only. I'm thinking particularly of Quicksilver, Journler, iGTD, and Skim. There just aren't apps of these types that work this cleanly (and work *together* this cleanly) available for Ubuntu (at least, afaik--I'm happy to be proven wrong).
That said, there are some apps that I run on my Ubuntu box that beat the pants off of anything with a similar function for OSX. Amarok, for instance, so far outstrips iTunes (and anything else I can find for OSX) that it's not even funny. Long story short? As to the question: "Why buy a Mac when you can have Ubuntu?" The answer is: Get the best tools for the job. It just so happens that, for many of the jobs that I do (and the way I like to do them) the best tools I've found are available only for OSX.
"The world does not run on Java alone." Oh? I'm pretty sure it's the only thing that gets me moving in the morning...
Nice joke--that got a good chuckle out of me. I'd mod you up if I had any points...
Haha yeah. And yes, you're right--middle C is 256Hz. My bad.
There are plenty of alternative tuning systems, though I don't know if a "metric" tuning has been done (though I wouldn't be surprised at all if someone had already tried it). Just as an example, Javanese Gamelan music uses two different tuning systems, both of which (iirc) divide the octave unevenly between five pitches. In any event, I think that our current tuning system is really quite a reasonable one. Ignoring the fact that A is the note commonly tuned (this, I think, is more of a historical accident based on the fact that this is an open string on a violin) the frequencies of the "home note", C, are actually all powers of 2. Middle C is 512Hz, an octave above it is 1024Hz, an octave below it is 256Hz etc. That strikes me as being a lot neater than a "metric" system anyway. Oh, and I think that the reason it's called an octave has to do with the fact that the eighth note of the traditional Western scale is the repeated one. E.g. C D E F G A B C
These debates may have been the place where ideas were put forwards once, but these days they are more like a boxing match in which each candidate tries to land knockout punches on the others, and a panel of pundits awards them points for style. Fact and logic don't stand a chance.
That's absolutely dead-on, sadly. That's a large part of the reason why I just can't pay too much attention to politics any more--it's all just so infuriatingly idiotic. I hate to be so apathetic, but I guess it's better than being enraged and frustrated all the time.
But school should not simply be job training centres, despite what some in business would like. We also need well rounded people. Techies needs to be familiar with art and literature. And artsies needs to know how to change the oil on their car. We need more renaissance men and women, not simple robots trained to do one job. Only then can we better understand each other and think outside the box to solve problems.
Well put, and absolutely correct in my opinion. If only more people thought that way...
I found your proof very interesting, though I'm not quite sure about the first definition you offer (and on which the reasoning is crucially based). According to this definition, A is evidence of B iff P(B|A) > P(B|~A) (I'm using '~' instead of the corner symbol since it is easier to type).
This definition has a few interesting features. First, it implies that there can be no evidence for a proposition whose (unconditional) probability is 1. (i.e. if P(B)=1, then P(B|A)=1 and P(B|~A)=1 so P(B|A) !> P(B|~A) so, by definition 1, A is not evidence of B (and this of course generalizes to any proposition A)).
That limit case is not a huge deal, though, but I thought I would point it out.
Second, what if the probability of A is very low (or even 0)? In this case, it may well turn out that P(B|A) > P(B|~A), but should this really mean that A *is* evidence of B? I think the indicative mood used in the definition doesn't square with how we normally think about evidence in our investigative practices (now, if you're offering a proposed *revision* of how we should think about evidence, that's another matter). I think the subjunctive mood might be better: "A, if its probability were sufficiently high, would be evidence of B". (Obviously "sufficiently high" would need to be given a rigorous, and hence probably arbitrary, treatment here for a workable definition.)
Here's the larger issue, though: Even if your proof works, and establishes that "absence of evidence is evidence of absence" we need to ask how good this evidence really is. The biggest part of the problem here is in how we might go about determining the conditional probability of the claims in question. Built in to your proof is the assumption that, if there is evidence to be found, we can eventually find it (this assumption does the work in the argument that our continued inability to find evidence of (e.g.) UFOs makes it more likely that there aren't any). But why should we be so confident in our current investigative techniques? Why not suppose instead that "absence of evidence is evidence that we're not looking hard enough (or looking in the wrong place, or in the wrong way etc.)"?
Interesting read, though.