once they start getting the local weather 2 days out correct on a consistant basis THEN I will start to believe their long term forcasts Useful climate predictions are currently usually over the next 50 years or century. You see it is easier to predict long term behaviour averaged over long time scales than it is to deal with the short term fluctuations. It remains very hard to predict exactly when and how the next wave is going to break on the beach, but predicting where the high tide mark will be, averaged over all the various waves washign ashore, that's a little easier. Short term climate prediction is still very young. They are currently making a big fuss about a new climate model in England that can predict in terms of a decade instead of a century by incorporating a lot of the nasty short term variability that can be averaged out of longer term predictions. Predicting climate in terms of a year ahead as you're suggesting? That's simply not possible yet.
The correction is the US (lower 48 states even) temperature data only, so yes, the effects on data for global temperatures is fairly small. 1998 remains the hottest year on record globally. There is also the fact that this is the US (via NASA GISS) historical temperature record data, there's also the HadCRUT series from the Climatic Research Unit and the UK Met. Office Hadley Centre, which is independently compiled, and shows much the same trends. It's also worth noting that the IPCC tends to use the HadCRUT data rather than GISS (as far as I am aware).
From an outsider's point of view (I'm from Finland myself), it seems that one of the problems is that everything in the US gets turned into a dichotomy between the democrats and the republicans. Indeed, these days that is how you identify people from the US. To quote Fisher's Deduction:
The more issues a person manages to crudely shoehorn down into an artificial liberal/conservative dichotomy, the more certain you can be that the person is an American.
But I've sort of realized that form follows emotion and in a world where Math is not consider cool (not in India though), something like this which stands away from the boring beige world of mathematics would get more eyeballs into the basic subject. The catch is that in doing so you tend to dilute the actual math content. Math can be interesting, but we tend to spend too much time (which is to say 100% of the time) on the nitty gritty details without ever bothering to properly survey the big picture. As I wrote in an essay, if we taught English and literature in the same way you would spend 100% of your time memorising spelling and diagramming sentences, and absolutely no time actually reading novels, or poetry, nor discussing what any of ti means. This is a pervasive and corrosive approach, and it has polluted the general perception of math to the point where people have trouble realising what mathematics really is -- they mistake math for the long array of facts about math, and have no idea what doing math actually means. As hard as it may be, finding the part of math that is actually interesting, rather than dressing it up in fancy clothes, is a better way to go. I'm not averse to a little window dressing to initially get people to pay any attention to the subject, but you fairly quickly have to drop that, or else they'll mistake the window dressing for the subject itself.
Your best bet is to learn a bunch of sci fi swear words and use them in common speech. I've always been rather amused by the apparent success of the approach taken by various SciFi shows which substitute in different words ("frak", "frell", etc.) The thing is that they aren't just used as an exclamatory/expletive, but are often used to refer to various bodily excretions and sexual acts. That is, the exact parallel meaning is easy to discern by context, and as such the words used are every bit as "indecent" as "fuck" and "shit" etc. That this substitution approach works as a legitimate loophole does a fine job of showing up the complete absurdity of trying to proscribe words in the manner they do. For all intents and purposes they may as well be saying "fuck" instead of "frak" so why not quit being childish and just let them say "fuck"; it is clearly what they mean> .
It would be nice to have some hybrid app that by default, added text boxes for the header, footer, and a reflowing text box for the body. Then allowed you to flip to a desktop publishing mode to resize those boxes and add graphics and figures. It wouldn't be too hard to throw together a way to do this with TeX. I know it's not exactly what you're looking for (which would presumably be a nice user-friendly application), but with just a little work I wrote a system that lets you do essentially this (draw text bounding boxes, position text and mages etc. as a template) in inkscape, and convert the result into a TeX style file. Now in my case I was interested in presentations rather than documents, and only really did as much work as was required to scratch my itch, so it's neither feature rich, nor particularly friendly; still the code is straightforward and in python, and the core layour conversion material is all there, so anyone who was keen could build a more advanced document templating system pretty easily.
$500M isn't that much, you know. We spend that for three days in Iraq. Sure, but it is symptomatic (and in this case emblematic because of the relative extravagance -- I'm sure there are many other cities with larger populations that could grow far more with a $500 million infrastructure investment) of federal pork being suffled off in earmarks. Each individual item isn't that much, but after every state has had their little piece of pork pie, year after year, it tends to pile up. To quote Senator Everett Dirksen:
"A billion here, a billion there, pretty soon it adds up to real money."
STM always struck me as the half-assed solution designed to let programmers not have to think. In that sense I see it is rather akin to C++ when it first came out. You could go with a proper language that was designed for OO from the ground up like Smalltalk or Eiffel, or you could stay in your happy little comfort zone and go for the half-assed kluge that was C++. Naturally, most programmers, being lazy bastards, chose the latter option because it didn't involve actually having to think; they could essentially stick with their old C style ways and sort of work in OO in a hacky sort of way where required. STM does the same thing; there are good solutions out there that make concurrency much easier (generally I'm thinking CSP/Actor model type stuff, such as Erlang here) but that would actually involve thinking about concurrency properly. Instead you can use STM which is pretty clunky and not the pleasant, but you can continue to write serial code as before and pretend that you don't really have to think about concurrency.
Thus I predict that STM will win out as the option for how to handle concurrency, but it will do so to the detriment of us all.
You can discuss the content of the food all you want, but as a foreigner who has visted the US many times I can say that what you need to look into is your portion sizes. As a rule, when I go to a restaurant in the US, I order an appetizer; if I'm really lucky I might have room for dessert after that, but usually not. The only time I ever consider ordering an entree/main is when I am with someone else non-American who is willing to split it with me. So as far as I can tell the average American meal is enough to feed two people comfortably (as long as they're both non-American). In that case, is it really a surprise that you gain weight?
"Software as a Service" died back in 2000... why does MSFT keep insisting on bringing it back up? Software as a service is alive and well, just not in quite the form it was originally brought up as. I mean let's face it, isn't Ubuntu essentially software as a service, where you "cache the software locally", but ultimately have access to a vast library of software via a service (apt-get, which suitable graphical front-ends). It's certainly easy enough to use that way. Need a program to do X right now? Click a button and it's ready to use. Done doing X and don't need the software for a while? Click a button and it's gone, but is ready and waiting to be pulled down from the service the next time you need it. Sure you're not using a foreign server to run the applications (and certainly aren't paying "per use" fees), but you are using a foreign server to store your applications, and only bothering to keep local copies of what you need and want ready access to at the moment. Ubuntu without a network connection is really just a pale shadow of the system attached to the network. And the same goes for most other ditributions these days. There's even Click'n'Run which introduces the pay part of the service.
This project has the potential to be meaningful, but it has a long way to go yet. They need a hypothesis, a rigorous way to test it, and repeatable results. Luckily other people have already studied these effects. Historical temperature reconstructions, such as NASAs GISS instrumental temperature record, account for urban effetcs; in the GISS case this is done by normalising urban temperatures against temperatures from surrounding rural areas. There have also been studies done [1][2], [3], that show that such urban effects are insufficient (by a large measure) to account for the observed warming. Indeed, the relative effect averaged across all stations was found to be negligible.
The first two caucuses that can give a candidate enormous momentum are in Iowa and New Hampshire. How amazing is that? We had presidential elections turn on the outcomes of voting in Florida and Ohio. For me that's evidence that the Electoral College system works. No, it's evidence of how the electoral college system has created a battle between states to be the most influential. Just look at primaries. Right now everyone is battling to have their primaries earlier than everyone else, because whoever goes first carries significant influence (which in and of itself is solly, but hey). The electoral college system and the fight for influence also manifests itself in the fact that hardly any states bother to split their electoral college votes proportionally with regard to vote returns in the state (that is, if the vote in the state splits 60-40, then the state splits the EC votes 60-40 accordingly). You see if a state does that, then it isn't as influential in comparison to states that follow a winner takes all mentality.
The population of my entire state is similar to the number of people just in the San Francisco metro area. That shouldn't make our votes worthless, guarantee that we never get a chance to meet candidates, or reduce or access to government. It doesn't make your vote any more worthless than a Democrat in Utah, or a Republican in New York (or and Independent or third party voter pretty much anywhere). Your vote would count, while someone who votes Democrat in Utah won't get their vote counted at all (Utah will go Republican, and thus all EC votes from Utah will be Republican); the same holds in reverse for a Republican voter in New York. Your vote would count, while an Independent or third party voter is going to have their vote scrubbed no matter where they are, since they'll never get enough votes to win an entire state outright, so they'll never get a single EC vote, even if nationally they polled at 20% or even 30%. What you fear nationally ith your vote not being counted is exactly what happens, only in an even more extreme fashion, to everyone at the state level who isn't in a swing state.
Which is why the government just loves running our school system. Dumb 'em down right so they will be nice sheeple when they grow up, more concerned with buying the latest tech toy or fashion than in anything real going on in the world. Yeah, we should have an entirely private run school system. That way sponsoring corporations can dumb kids down right so they'll be nice sheeple when they grow up, more concerned with buying products of the sponsoring corporations than products from other corporations, or even caring about how manipulated they are. That would be much better. And as a side benefit you'd probably have a large swathe of poor voting public that will either have been educated at the McDonald's Fry Academy or not at all, which will really help us avoid those bought and paid for populist candidates.
Public schooling is not ideal, but by providing a guaranteed basic minimum level of education for everyone it helps ensure a minimum level of education amongst the voting public. The fact that the US public school system is a bizarre, broken, fucked up mess doesn't mean public education doesn't work (just try looking at some of the top performing countries in the world, such as Finland or South Korea, which both have public education systems) it just means the US public education system doesn't work.
Look it up and get educated. Don't just assume that a certain set of people who call themselves a "scientific consensus" (even though most of them are NOT scientists) are correct simply because they are "enlightened liberals." Anthropogenic global warming is about as correct as epicycles. The thing is, I have looked it up. I've read a number of primary source material. I've even has the chance to discuss the issues with at least two scientists (William Connolley, and Raymond Arritt -- I'm presuming the academic qualifications and long lists of publications will suffice to show they are indeed scientists) who work in the given field. Hell, I've even searched out a variety of published data and done my own (admittedly simplistic) analysis and graphs based on it: [1], [2], [3]. The result is that AGW appears to be a very well supported theory, while solar based explanations for the current warming (last 50 years or so) have proved to be quite insufficient. Perhaps you should actually go to some of the source material yourself. You can start with the most recent IPCC WGI report which provides a summary of a large number of papers -- all of which are sourced, so you can track them down for further detail on any particular points you are interested in. Finally, here are a couple of papers addressing your specific points that you might find interesting: on solar irradiance varation, and on cosmic rays.
I, of course, see your point. But you have to picky about typefaces at some level to note any significant difference in quality between Arial and Vera Sans (of the two I perfer Sans, but then I prefer Optima and Cronos to both by a waide margin).
Why won't the fonts look beautiful by default? Because good fonts are expensive. If you want beautiful fonts then I suggest you head on over to Adobe, or Monotype or ITC and buy some. For sans-serif Cronos Pro, Gill Sans and Optima are all excellent. For serif fonts there's always the classics like Caslon, Garamond, or New Baskerville. Of course some of those cost a fair amount of money for the complete font set, but you'll end up with far more beautiful fonts than Windows fonts give you. If you're not actually willing to pay for nice typefaces then you'll probably find that, relatively speaking, the Bitstream Vera fonts, which are provided with most distros these days, are actually quite nice. But in the end the reality is that if you want nice fonts you have to pay for them. If you have such refined sensibilities that you prefer Arial to Vera Sans, then you'll truly appreciate having Cronos or Optima instead, which are far far better than either of those, and the cost won't bother you.
But gravity is a human creation. Things will behave as they will, but the abstraction fo some overriding process that makes things behave that way, that's a human model; an abstraction from what is there into a model that allows us to predict (quite accurately I might add) how things will behave; the model is not the reality however. Without us things will continue to behave as they do; that doesn't mean that the concept of gravity as a description of that behaviour will exist; there may well be completely different ways of viewing and describing that behaviour that doesn't invoke what we would describe as gravity. What matters for us is that, for all practical purposes gravity may as well exist, since things seem to behave as if it does. That doesn't make gravity (* pound the table *) "real"; it just makes it an effective abstraction.
Electrons are universal? Well, we think so, but ultimately electrons are our model of how we percieve the universe to work. Now it's damn good model in that it makes suprisingly good predictions, but that doesn't make it "true", just useful. There may well be other perfectly effective ways of describing such things; who knows. What matters to us is that for all practical purposes electrons may as well exist, because things behave as if they do according to our models. That doesn't make them concrete or "real" in some absolute sense, but it does make them good enough that for any practical purpose we don't care.
I think we're talking about different things. A decently expressive type system provides checks for a lot of errors, and with things like type inference and higher order constructs your code size doesn't bloat as much as you seem to imply. If you experience with static types is C++ and Java then I can understand your concern. Static types are more than just that however. I strongly suggest you look further afield. As long as your type system is expressive enough to allow to actually express "producing the right results" then type correctness, while not a guarantee to of absolute correctness, provies strong assurance of a high degree of correctness. Again, it is not about being correct, it is about assurance.
Don't worry, I like dynamically typed languages too; each has their place. If you want assurances of correctness then strongly staticly typed are a good way to go, particularly if they actually have a good expressive type system (see Haskell or the ML family, or Coq, for example), are definitely the way to go. That doesn't mean you can't write correct code in a dynamically typed language as just easily as you can in a staticly typed one; it means you can't get the same assurance with regard to correctness as easily with type free languages.
But questions like, "How the hell did you think *that* was readable", "How can I turn a bunch of requirements into something that isn't crap", "How do I get 10 guys working on a project and have a single vision", etc, etc, etc; those questions I ask every day. Well you could try converting the vague requirements into something precise and unambiguous so the whole team has a clear an unambiguous idea of what is meant. Sure, the first pass at it might not be that great, since there will be details, or specific requirements that aren't thought of immediately, or otherwise not covered. Not a problem, you cna take the original requirements specification and use that to see what might need refinement and, well, refine it.
And lo, there are even languages specifically designed to help you write requirements out in that sort of clear and unambiguous manner; to help you make sure everyone is working on the same page, that all the different bits will interact within expected ranges, and to give a high level overview specifying what each chunk of code is supposed to be doing. They are languages like the Z specification language, which takes it's name from Zermelo-Frankel set theory, since it is firmly grounded in set theoretic mathematical notation (that being a good way to be clear an unambiguous). If you don't like set theory you can always try something like OBJ or CASL, which are firmly grounded in abstract algebra. You see, math has an annoying habit of cropping up everywhere.
For instance there *are* *two* apples. Even if no sentient species ever came into existence and recognized that fact, it is still true. Those two apples are embodiments of a universal truth that there is a discreet quantity of 'something'. Things, in this case the apples, exist, but that doesn't mean that the number 2 does. Try and point out the number 2 to me, and you'll only ever point out specific examples of things about which we (hopefully) agree have the property we would describe as "two". The actual number two, the abstract property which is universal to all such examples, that transcends the examples and is something that exists in our minds. Two has no physical existence, but is, rather, an abstraction we have drawn across a vast array of examples; it is a mental synthesis that we make to categorise. To say that the number two exists, really (* pound the table *) exists, is to claim that there is some realm out there, some platonic world with a real existence, which this abstract property inhabits. That's really quite a spiritual belief. There are, of course, people who believe that, but to me it seems a little absurd.
Please note, by the way, that I am a mathematician. Feel free to read my blog for my thoughts on mathematics, and philosophy of mathematics. I feel mathematics has a great deal of value and meaning; I just don't require a belief that it has some sort of physical embodiment, nor meaning beyond that which we grant it, to have value and meaning. Mathematics is a lens through which to see the world, and it is a lens which lets you see clearer and further than our native perception; don't mistake the lens for the reality you are viewing however.
Math is inherent to the universe and is universal. Math is universal, in that by abstracting away detail it provides a framework that can speak broadly and universal, but I think the assumption that math is inherent to the universe is rather hard to support. It is a stretch to say that the universe is behaving mathematical laws; it is clear, at least, that the mathematical abstractions we develop provide a good framework and language with which to model the behaviour we see, but that doesn't mean the mathematics is inherent in the behaviour. We see the world through a lens, through our perceptions, and through the story our minds construct from that. By abstraction we can create lenses that see fairly clearly, and that can transcend our narrow perceptions; don't mistake the lens for what you see through it though.
2 apples are still two apples even if nobody counts them. Again, we did not invent the concept of an integer. Did we not? What you have is a pair of apples, which is not the same thing as the number 2. The number 2 is an abstract concept, a property that is universal to all things that have "twoness" about them. It is not a physical thing, and you can't point to it anywhere; you can only ever point to pairs of things, which are examples of things that have the requisite property, but are not property itself, which transcends above all the particular examples. The number 2, as opposed to examples that have the property we describe as "two", exists in our minds, not out in the world.
Perhaps a better way to consider this is to look at transfinite numbers, which, in ZFC, are every bit as real and concrete as integers. So the question is, does the number between aleph_0 and aleph_1 exist, or not? The answer is neither -- its existence is contingent, just a choice we make. Integers are the same, its just that the choices that lead to them are far more ingrained and subconcious. This makes them more "real" to us because they are closer to the way we percieve the world, but they are no more concrete, no more absolute and "out there" as transfinite cardinals.
None of this is to say that math is useless, or can't say anything about the universe; it is the best lens through which we can view and accurately describe the universe, and its ability to layer abstractions allows us to stretch our minds into worlds of pure possibility, and escape the shackles that nature and evolution has hobbled our intuitions and perceptions with. Math is a wonderful and powerful way to see beyond our own narrow horizons. That is why I study and write about mathematics. I don't spend the better part of my life getting advanced graduate degrees in subjects that I feel are without meaning. But you don't need some concrete absolute platonist world for things to have meaning. The truth of mathematical and logical assertions rests clearly and firmly on the assumptions you make, and ultimately those assumptions are a matter of efficacy, and convenience, not some absolute "truth".
...you're using Mathematics (DeMorgan's Law from Boolean Algebra, to be precise). Actually it gets even more interesting than that. If you're willing to delve into the mathematical philosophy here, you can find proofs that DeMorgan's law (as a statement of pure logic) is, in fact, equiavlent to the pretty much purely mathematical statement "Every maximal ideal in a commutative ring is prime". What this really means is that, at a very deep and fundamental level, what we think of as "mathematics" and what we think of as "logic" are deeply intertwined, and in essence the same. Keep in mind, by the way, that the effort to show that mathematics is just logic (the logicism program of Frege and Russell) failed; ultimately Russell required axioms (most notably the axiom of infinity and the axiom of reducibility) that you really can't describe as fundamental laws of logic. Mathematics is not logic; rather it is more accurate to say that logic is just mathematics -- especially when you come to topos theory and local set theory which let you work in different logics within a mathematical framework.
Of course none of this is likely of interest to the programmer who simply makes the required DeMorgan's law style transformation by rote without really understanding the underlying theory (is there a need to understand underlying theory to be able to apply it?), but then that only speaks to programming: to actually study and develop new ideas regarding such things does require understanding -- and that's CS research.
Rather, if I was to point a programmer to mathematics that may well be worth learning and understanding for his day job, I would point to process algebra/calculi. To really understand and use those well it helps to have a decent grasp of abstract algebra. The benefit is that you cna reson about and write concurrent code far more easily. Alternatively, as more of a future investment, you might like to look into abstract algebra and category theory for the ongoing influence they are having in cutting edge type theory. The programming languages of the next decade may well make use of mch of this deep theory to provide far more powerful, expressive, and robust type systems.
Slashdot Mirror
The correction is the US (lower 48 states even) temperature data only, so yes, the effects on data for global temperatures is fairly small. 1998 remains the hottest year on record globally. There is also the fact that this is the US (via NASA GISS) historical temperature record data, there's also the HadCRUT series from the Climatic Research Unit and the UK Met. Office Hadley Centre, which is independently compiled, and shows much the same trends. It's also worth noting that the IPCC tends to use the HadCRUT data rather than GISS (as far as I am aware).
STM always struck me as the half-assed solution designed to let programmers not have to think. In that sense I see it is rather akin to C++ when it first came out. You could go with a proper language that was designed for OO from the ground up like Smalltalk or Eiffel, or you could stay in your happy little comfort zone and go for the half-assed kluge that was C++. Naturally, most programmers, being lazy bastards, chose the latter option because it didn't involve actually having to think; they could essentially stick with their old C style ways and sort of work in OO in a hacky sort of way where required. STM does the same thing; there are good solutions out there that make concurrency much easier (generally I'm thinking CSP/Actor model type stuff, such as Erlang here) but that would actually involve thinking about concurrency properly. Instead you can use STM which is pretty clunky and not the pleasant, but you can continue to write serial code as before and pretend that you don't really have to think about concurrency.
Thus I predict that STM will win out as the option for how to handle concurrency, but it will do so to the detriment of us all.
You can discuss the content of the food all you want, but as a foreigner who has visted the US many times I can say that what you need to look into is your portion sizes. As a rule, when I go to a restaurant in the US, I order an appetizer; if I'm really lucky I might have room for dessert after that, but usually not. The only time I ever consider ordering an entree/main is when I am with someone else non-American who is willing to split it with me. So as far as I can tell the average American meal is enough to feed two people comfortably (as long as they're both non-American). In that case, is it really a surprise that you gain weight?
Public schooling is not ideal, but by providing a guaranteed basic minimum level of education for everyone it helps ensure a minimum level of education amongst the voting public. The fact that the US public school system is a bizarre, broken, fucked up mess doesn't mean public education doesn't work (just try looking at some of the top performing countries in the world, such as Finland or South Korea, which both have public education systems) it just means the US public education system doesn't work.
I take it you didn't actually read my message closely, nor the actual papers I linked to. Try reading the papers, then get back to me.
I, of course, see your point. But you have to picky about typefaces at some level to note any significant difference in quality between Arial and Vera Sans (of the two I perfer Sans, but then I prefer Optima and Cronos to both by a waide margin).
But gravity is a human creation. Things will behave as they will, but the abstraction fo some overriding process that makes things behave that way, that's a human model; an abstraction from what is there into a model that allows us to predict (quite accurately I might add) how things will behave; the model is not the reality however. Without us things will continue to behave as they do; that doesn't mean that the concept of gravity as a description of that behaviour will exist; there may well be completely different ways of viewing and describing that behaviour that doesn't invoke what we would describe as gravity. What matters for us is that, for all practical purposes gravity may as well exist, since things seem to behave as if it does. That doesn't make gravity (* pound the table *) "real"; it just makes it an effective abstraction.
Electrons are universal? Well, we think so, but ultimately electrons are our model of how we percieve the universe to work. Now it's damn good model in that it makes suprisingly good predictions, but that doesn't make it "true", just useful. There may well be other perfectly effective ways of describing such things; who knows. What matters to us is that for all practical purposes electrons may as well exist, because things behave as if they do according to our models. That doesn't make them concrete or "real" in some absolute sense, but it does make them good enough that for any practical purpose we don't care.
I think we're talking about different things. A decently expressive type system provides checks for a lot of errors, and with things like type inference and higher order constructs your code size doesn't bloat as much as you seem to imply. If you experience with static types is C++ and Java then I can understand your concern. Static types are more than just that however. I strongly suggest you look further afield. As long as your type system is expressive enough to allow to actually express "producing the right results" then type correctness, while not a guarantee to of absolute correctness, provies strong assurance of a high degree of correctness. Again, it is not about being correct, it is about assurance.
Don't worry, I like dynamically typed languages too; each has their place. If you want assurances of correctness then strongly staticly typed are a good way to go, particularly if they actually have a good expressive type system (see Haskell or the ML family, or Coq, for example), are definitely the way to go. That doesn't mean you can't write correct code in a dynamically typed language as just easily as you can in a staticly typed one; it means you can't get the same assurance with regard to correctness as easily with type free languages.
And lo, there are even languages specifically designed to help you write requirements out in that sort of clear and unambiguous manner; to help you make sure everyone is working on the same page, that all the different bits will interact within expected ranges, and to give a high level overview specifying what each chunk of code is supposed to be doing. They are languages like the Z specification language, which takes it's name from Zermelo-Frankel set theory, since it is firmly grounded in set theoretic mathematical notation (that being a good way to be clear an unambiguous). If you don't like set theory you can always try something like OBJ or CASL, which are firmly grounded in abstract algebra. You see, math has an annoying habit of cropping up everywhere.
Please note, by the way, that I am a mathematician. Feel free to read my blog for my thoughts on mathematics, and philosophy of mathematics. I feel mathematics has a great deal of value and meaning; I just don't require a belief that it has some sort of physical embodiment, nor meaning beyond that which we grant it, to have value and meaning. Mathematics is a lens through which to see the world, and it is a lens which lets you see clearer and further than our native perception; don't mistake the lens for the reality you are viewing however.
Perhaps a better way to consider this is to look at transfinite numbers, which, in ZFC, are every bit as real and concrete as integers. So the question is, does the number between aleph_0 and aleph_1 exist, or not? The answer is neither -- its existence is contingent, just a choice we make. Integers are the same, its just that the choices that lead to them are far more ingrained and subconcious. This makes them more "real" to us because they are closer to the way we percieve the world, but they are no more concrete, no more absolute and "out there" as transfinite cardinals.
None of this is to say that math is useless, or can't say anything about the universe; it is the best lens through which we can view and accurately describe the universe, and its ability to layer abstractions allows us to stretch our minds into worlds of pure possibility, and escape the shackles that nature and evolution has hobbled our intuitions and perceptions with. Math is a wonderful and powerful way to see beyond our own narrow horizons. That is why I study and write about mathematics. I don't spend the better part of my life getting advanced graduate degrees in subjects that I feel are without meaning. But you don't need some concrete absolute platonist world for things to have meaning. The truth of mathematical and logical assertions rests clearly and firmly on the assumptions you make, and ultimately those assumptions are a matter of efficacy, and convenience, not some absolute "truth".
...you're using Mathematics (DeMorgan's Law from Boolean Algebra, to be precise). Actually it gets even more interesting than that. If you're willing to delve into the mathematical philosophy here, you can find proofs that DeMorgan's law (as a statement of pure logic) is, in fact, equiavlent to the pretty much purely mathematical statement "Every maximal ideal in a commutative ring is prime". What this really means is that, at a very deep and fundamental level, what we think of as "mathematics" and what we think of as "logic" are deeply intertwined, and in essence the same. Keep in mind, by the way, that the effort to show that mathematics is just logic (the logicism program of Frege and Russell) failed; ultimately Russell required axioms (most notably the axiom of infinity and the axiom of reducibility) that you really can't describe as fundamental laws of logic. Mathematics is not logic; rather it is more accurate to say that logic is just mathematics -- especially when you come to topos theory and local set theory which let you work in different logics within a mathematical framework.Of course none of this is likely of interest to the programmer who simply makes the required DeMorgan's law style transformation by rote without really understanding the underlying theory (is there a need to understand underlying theory to be able to apply it?), but then that only speaks to programming: to actually study and develop new ideas regarding such things does require understanding -- and that's CS research.
Rather, if I was to point a programmer to mathematics that may well be worth learning and understanding for his day job, I would point to process algebra/calculi. To really understand and use those well it helps to have a decent grasp of abstract algebra. The benefit is that you cna reson about and write concurrent code far more easily. Alternatively, as more of a future investment, you might like to look into abstract algebra and category theory for the ongoing influence they are having in cutting edge type theory. The programming languages of the next decade may well make use of mch of this deep theory to provide far more powerful, expressive, and robust type systems.