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KipIngram last won the day on June 18

KipIngram had the most liked content!

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About KipIngram

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    Houston, Texas
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    Photography, history, science, digital privacy, beer brewing, genealogy, astronomy, cycling, movies / books, ...
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    PhD - Engineering, The University of Texas at Austin, 1992
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    Senior Engineer, IBM

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  • koti

  1. Correct - the quotient of any two rational numbers is always a rational number. Say we have r1 = a/b and r2 = c/d, where a..d are integers. That's the definition of a rational number (quotient of two integers). So now r1/r2 = (a/b) / (c/d) = (a/b) * (d/c) = (ad)/(bc). The products ad and bc are both the products of integers, and thus are integers. The quotient of those two products is thus a rational number. The previous answers point out the misstep in your original reasoning.
  2. Well, I think there's truth in those words, but caution is in order. On the one hand, you have people like Einstein, whose imagination leads them to things that turn out to be right. Then on the other hand you have people who uncork the most ridiculous things. I don't think Einstein's words should be taken to defend anything that someone coughs up, because some people's imagination leads them thoroughly out into the weeds. I have no doubt that Einstein's imagination tended to stay "in bounds" because he also had knowledge. So I absolutely do not think he was saying "imagination is all that matters." Knowledge is very important too. To say that a different way, imagination without knowledge doesn't get you there. Knowledge is a necessary pre-requisite, but then having imagination as well makes all the difference in the world to how much you can contribute to new understanding.
  3. It is a mess, and the software industry is as well. A large fraction of working programers don't, in fact, have familiarity with what's really going on under the hood of the systems they work on and also don't have familiarity with those "core" things I mentioned, like algorithm theory, basic data structure concepts, and so on. A lot of programming these days involves relying heavily on software libraries that hide all of that, and which have their own bugs and quirks which the programmer is likely unfamiliar with. On top of that, a lot of the day to day work involves either modifying software written by someone else, or working in a very small niche of some large system in collaboration with hundreds or even thousands of other programmers. These hoards of programmers will generally have no idea what one another is doing and wind up creating pieces that, when brought together, lead to more bugs or security vulnerabilities. When evaluating the performance of programmers, management usually rewards speed of execution (which may later turn out to have led to bugs or vulnerabilities) rather than taking the time to develop the deep understanding required to do a better job. Said managers are often in no way technical themselves, and yet they are expected to lead and evaluate technical staff. It's no wonder we wind up with a world full of buggy, sloppy products that make very poor use of the underlying power of the hardware.
  4. There are components of a (good) computer science education that don't change. Algorithm complexity theory, data structures, standard classic algorithms like searching, sorting, hashing, and so on - those things don't change as technology changes. Proper application of them depends on the underlying technology, and so that changes. You are right up to a point, though - languages come and go, hardware changes, and so on - the usefulness of knowledge of that sort is ephemeral.
  5. I don't know if that's entirely fair - studying computer science does require you to think rigorously and logically. I think it does involve an "intellectual mindset" similar to that you bring to bear studying science and mathematics. The key difference, that makes it math in my eyes rather than science, is that you don't apply the scientific method to make new discoveries. You start with axioms and you build a logically correct structure on that foundation. That's more akin to math than science.
  6. Yes, I'm basically of the same opinion. I can't do such things right now, because I have family responsibilities and the government would "slap my risk" if they caught me experimenting with such things. But I'm very curious about some of them - particularly mescaline - and may get around to a little tinkering once the kids are all gone and such a wrist slap wouldn't affect so many other people.
  7. Well, it is pointless to haggle over it, really. Words aren't always used exactly right, but I guess it really doesn't make any difference. YES. I could not agree more. The bulk of my career was in "embedded system design," and I would wind up responsible for the hardware architecture, the detailed hardware design, and the layers of software that were most intimately connected to the hardware. I always thought of the whole thing as a fully unified design effort. Deciding exactly how to split functionality between hardware and software, exactly how to break the hardware into subassemblies (keeping in mind not only the economic and performance efficiency of the the product at hand, but also how useful those subassemblies will be for future products, and son on) was all just part of doing the job right. So when you have people that are too specialized in hardware or software keeps them from being able to bridge that chasm. I do think that's a fault of how we approach education in that area in America. You always wind up with some people who self-train in a way that lets them cross over, but it's not as formally structured into the program as it should be.
  8. I want to say that it sounds like you are off to a great start and I think the attitude you're bringing to the table already has you destined for success! Most high school kids in my region are thinking more right now about how many parties they can manage to go to this summer. So kudos to you. I'm not a chemist, but my father was (organic). On my own I've come to realize that knowing the basics of quantum theory as applied to electron structure in atoms ties in very strongly with how the periodic table works. However, it may be possible to just start with the periodic table and get the same capabilities without that. But it's something you might consider as part of this quest. Regarding organic chemistry, I also know that understanding the nomenclature really well is important. I spent a bit of time looking at that and it looked like a fair amount of memorization was in order. Just to inject a bit of humor here, I feel I must recommend that you keep your study sessions and your exploration of mind altering drugs well-separate from one another. That's all I have to offer, but I really wish you a lot of luck and I hope you'll let us know from time to time how things are going!
  9. I've said often in this and similar threads that it is wrong to blame all members of a religion for the misbehavior of a few, and I stand by that. However, in response to your last post, Handy andy, I do have to say that if you're talking about a formal organization like the Roman Catholic Church, then the fact that the organization does a lot of good does not excuse those running it from responsibility for their wicked deeds. To whatever extent the sitting authorities of the church have directed the machinery of the organization to do bad things, they should be held responsible. However, "millennia" are not relevant - no one involved with the organization today was around more than a few decades ago. History is done and behind us - it's no more appropriate to hold today's Church leaders responsible for atrocities committed during the Crusades than it is to hold you or me responsible for the fact that our great-great-great-great grandparents perhaps owned slaves. I don't really trust big religion (I don't really trust "big" anything - religion, government, business, whatever). But before you take aim at someone you really need to show that that person committed the wrong you're complaining about.
  10. Yes, absolutely. I read a very good article recently that said exactly that - that false information can spread faster than true information because it can be tailored without regard for facts to maximize it's propagation speed as a meme. Fascinating idea, and when you combine it with generalized Darwinism it's frightening because it says that ultimately most people are going to believe incorrect information. I hate people who preach against vaccines. It is SO CLEAR that they do good, and yet these people have chosen that as their "path to prominence," and that's all they care about - getting attention for themselves. Very astute observation, koti!
  11. I think several of you are confusing "computer science" (which is really about things like Turing machine theory and computational complexity and is a type of mathematics) with "computer architecture" (which is a branch of engineering and studies the architecture, design, fabrication, and operation of real computers and is a branch of engineering). Quite a bit of science is relevant in computer architecture, including EM theory (transmission line effects on circuit boards), semiconductor physics, and so on. But "computer science" as it's generally used in the US is in the math arena. Your typical CS graduate couldn't tell you very much at all about how computers are built, in terms of things like transistor circuits and so on. Many of them couldn't even design a simple hardware state machine out of gates and flip flops. That's studied in electrical engineering. Of course, some CS majors learn some engineering, and some EEs (like me) learn some computer science. But you can make it through the graduation line in either case without doing so. By that definition history and literature are science as well. Yes, and I do say that. Computer science teaches you how to use computers (including how to program them). That doesn't mean just knowing a nice variety of languages, it also means understanding which one is fit for various purposes, understanding various algorithms for solving the classic problems that show up over and over again (searching, sorting, etc.), and knowing which algorithm to pick for which application and why, and so forth. But like I touched on above, CS doesn't talk about how computers work in terms of circuitry and so forth. The capabilities of the computer are presented in much the same way the behavior of numbers and algebraic structures are presented in math, and you prove logically how to do various things. Compiler design, for instance, is very much an exercise in the mathematical theory of rigorous language structure. An IRC friend of mine and I often lament the fact that there is not more "crossover training" between the CS of computers and the EE of computers.
  12. Holy cow, I had to go back a page or two to get any clue as to what this discussion is about...
  13. Sorry if I sounded contentious at all - several threads in play this morning and some of them are somewhat contentious. That tone really had no place here in this thread.
  14. You can't do accounting without mathematics either, but math isn't a part of accounting.
  15. Those words are there, but the provide a reason for the main clause of the sentence, which is what I quoted. It does not say "the right of the people to form militias shall not be infringed." It says what it says. This is an endless argument, though - I think you're completely wrong and I won't be changing my mind - you think I'm completely wrong and you won't be changing your mind. I'll note again that the Supreme Court has repeatedly taken the position that the amendment does, in fact, describe some sort of individual right. I'll tell you where I think this gets hardest and thorniest. Interpreted directly, the amendment places no limitation on the right. An individual in the 1700s who owned a cannon could have claimed constitutional protection. And I imagine there were at least some people who did own cannons. Probably a small minority, but I imagine you could have found some. We just can't let it be that broad today - it's not ok for my neighbor to own a nuke. In other words, no one in their right mind would really claim that there should be no limitations on "arms bearing" in today's world. But the amendment doesn't provide for any limitations, so once you admit a single limitation of any kind you've breached the integrity of the amendment. So no one (in their right mind) is really calling for a 100% literal and total application of the 2nd amendment. Once you've admitted one limitation (citizens can't bear nukes), then there's no really good way to decide when to stop. What about tanks? RPGs? Etc. We are not helped in any way by the Constitution to decide where to draw that line. Someone who takes the position that it's ok to own a handgun for home defense but not ok to own a fully automatic military assault rifle doesn't find that opinion defined for them in the Constitution. But to get back to the OP of this thread, Rand's remark was not incorrect - it remains true that the whole point of the second amendment was to ensure that a government gone sour could be resisted with force of arms. Things may have changed such that the likelihood of success of such resistance would be a lot lower today than back then, but the right to try still remains. And it remains true now, just as it would have been then, that having things come to that (an armed uprising) would represent an utter failure of the system to work the way it's supposed to. Anyway, the whole business about then vs. now and nukes vs. cannons just means that we are no longer able (because of our advanced technology) to make this a clean and simple debate about the Constitution. All of us except nuts agree that some degree of limitations, in violation of the strict words of the Constitution, are necessary. So instead of that clean logical debate we're left with a public opinion debate about "how much" do we break the Constitution. What should be a matter of Constitutional law becomes a matter of public opinion.