I've never come across a keypad lock that would be vulnerable to this. You either have to press # at the end of the code, or the codes are significantly longer than 4 digits. Of course, even in the first category, entering 24 codes (50% chance of entering 12 or fewer) isn't a huge barrier once you know the four digits.
before someone gets up from their desk and walks down the hall, Mars is able to sell that person the idea of a 50cent Snickers. While this is not completely realistic - many times that snickers slot will be empty - it's enough to convince someone to get out of their chair, walk down the hall and 'check' the machine. At the machine, they've not only decided that they probably want something, they've begun to exert effort to achieve their goal. Upon finding the machine out of snickers, they either have to walk back disappointed (and now maybe slightly hungry, by suggestion) or they can get some other similarly priced snack to fulfill the need they created for themselves.
If, instead, at the beginning of the decision tree it was a 75cent guaranteed snickers bar then it would be a simple, rational decision - do i want to pay 75cents for this? The argument the marketing department makes is that there are are fewer people who rationally want that 75cent snickers bar vs. the people who can be sold on the dream of a 50cent snickers bar (that strangely looks and tastes more like a high-margin cookie).
And then there are people like me, who are hungry and desperate for real food (not milk chocolate and corn syrup) who pass by a vending machine, despair at every single product on offer, and just drink some water.
Happy that I live somewhere where "fast food" includes very very healthy options (like made-that-day rice balls with red beans).
I use Google Gears, so I can still access all of my mail. I'm sending e-mails from a mail server on my laptop, but I could just as easily use a different e-mail service while gmail is down. Yes, Google is a big company with lots of technical prowess, but you can't reasonably expect 100% uptime. If it's that important to you, you should have a backup plan.
To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does.
Now, on the other hand, linear algebra is almost universally important and is probably easier for a programmer to grasp. I would also suggest picking up a Number Theory or Combinatorics text; they're practically useless, but they're fun and interesting, they'll give you a better idea of what mathematicians do, and you don't need much education to get into them.
My usual advice for building skills is to work on contest problems. See if you can find some AMC12 problems. If those are too easy, you can work your way up. AIME and Putnam would be good next steps (those can be found here: http://web.archive.org/web/20080205091131/http://www.kalva.d... ).
Saying the Putnam is a next step from AMC12 problems is like saying the NBA is a next step from pickup basketball with friends in middle school! There are people who can do Putnam problems for fun, but those people generally know who they are already.
Solving problems 1-4 on each day of the Putnam with an "unlimited" amount of time is not a ridiculous expectation. Putnam's difficulty is partly due to its time format.
Putnam problems are not considerably harder than AIME problems, and AIME is definitely the next step from AMC12. Anybody who can solve a few AIME problems can certainly solve A1 on the Putnam of almost every year.
> I would also suggest picking up a Number Theory or Combinatorics text; they're practically useless
Useless? I dear to say that number theory is currently the most lucrative field of mathematics. Without number theory, modern day cryptography would not exist and thus everything that depends on secure communication of information would not exist. So forget about commerce over the Internet, bank wire transfers, credit cards, administrating computers remotely and, most importantly, hiding your huge porn collection from your wife.
And, combinatorics is useful for the study of algorithms. It is pretty much the foundation of computer science.
I'm aware of their applications; by "practically", I meant "almost". There are certainly compelling uses for number theory and combinatorics (though I'm not convinced the study of algorithms is one of them), but they're nothing compared to calculus.
No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. Topology does, too, depending on which area you study and what you consider calculus. Sure, there are obviously fields that do rely heavily on calculus, as well as certain branches in the above fields, but my point was that it's nowhere near universally needed. I'm a graduate student at UCSD, and I can't remember the last time I used calculus in my research.
This is terrible, wrongheaded advice. It's like Pablo Picasso, in the middle of his Blue Period, trying to convince younger painters that red isn't a useful color for serious artists.
If you want to study graph theory or combinatorics [1], then calculus will be pretty much useless to you, and you'll naturally go years without using it.
Calculus is also useless in some situations in abstract algebra (which are said to have combinatorial character). There are other parts of abstract algebra, e.g. Differential Galois Theory [2], in which calculus is pretty important.
Topology is similar. Elementary topology is part of the foundation supporting calculus, while algebraic topology is one of the tools that's useful when we try to do calculus (or solve differential equations) in non-Euclidean spaces.
Fields making heavy use of calculus include differential geometry, differential equations (ordinary or partial), dynamical systems or control theory. That subsumes most of physics. Fields underpinning (and largely inspired by) calculus include real and complex analysis, measure and integration theory (aka axiomatic probability theory). Also functional analysis, which is a generalization of linear algebra, which is the bookkeeping methodology of calculus in higher dimensions.
That post does not contain any advice. It contains facts, none of which were contradicted by your post (a typical property of facts). I never told him not to study calculus. Given our current education system, that would be impossible anyway. I guided him more toward real analysis and suggested some other areas of math that might interest him. Since his only background is high school math, I felt it would be best to introduce him to something where proofs play a central role. If he can't stand that, then he probably shouldn't go into math.
> calculus isn't that important for mathematicians
> Many pure math classes require no (or very little) calculus.
These are not the same thing (hence my confusion.) Your initial comment seemed to indicate that nobody does analysis anymore, which is just not true at all (look at the most recent fields medal.)
Nope. I'm well aware that people still study analysis. I just meant that one doesn't necessarily need to learn calculus before taking the plunge into serious mathematics. Even in analysis, there's quite a bit you can do without knowing the stuff from a standard calculus class (though it certainly helps).
I would claim that Calculus isn't that important for engineers / scientists / programmers either. Real Analysis is important if one needs to understand thing deeper. In the real world, problems can't be solved analytically... and many of the tools one learns in Calculus are kind of useless. I think Linear Algebra is much, much more important than Calculus. Linear Algebra is the arithmetic of higher mathematics, like Bellman said.
I'm not willing to concede his point yet, but even if he's right, this should be implemented by the browser, not the website. And if you consider taking his advice, I suggest masking the password as soon as the input field loses focus.
Me too, but I use more like 20 minutes per month. (Seriously, who needs a phone? That's what the internet is for.) The great part is that I can buy $10 worth of minutes at the end of the year, and all my minutes last another year. So, after four years or so, I will have paid maybe $160 including the phone. You can't come close to that kind of deal with any other provider.
> ah right, judging someone from grammar is a very rational thing to do
I think you just turned "rational" into a label. Apart from your attempt at sarcasm, this statement is probably true. Like it or not, your ability to structure sentences reflects your ability to structure thoughts.
I agree, up to perhaps a log-log scale. My grammar isn't likely to be significantly better in 30 years. However, when comparing among groups with similar English experience, grammar is likely to have a reasonable correlation with well-structured arguments. Also, the amount of time since learning English is not under your control; adherence to the rules of grammar is.
Perhaps more importantly, it wasn't actually grammar that I criticized. It was erratic use of punctuation (which was clearly for effect and to catch attention rather than clarity), lack of appropriate capitalization (which negatively impacts readability, and definitely doesn't require extreme English skills to get right), aggressive tone (which I find annoying pretty much anytime I see it on the Internet, as it provides no value), and sounding like a self-righteous teenager (which everybody older than ~24 finds irritating). Though one could argue that capitalization and punctuation are components of grammar, I used specific terms rather than a general one for a reason. I tend to be quite forgiving of grammatical mistakes that can be attributed to native language differences and different levels of skill with English. But, I'm less forgiving of things that are very easy to control and get right, even for non-native speakers, and that negatively impact my ability to read and understand. When wrapped in negativity and an aggressive tone, I tend to feel negative towards the person. So, I explained why his tone made me feel negative towards him, and why I thought people were voting him down.
I thought I was providing a helpful suggestion for how he could better present himself and his ideas on HN, but one can only do so much to be helpful.
[15] By this I mean you'd have to become a professional controversialist, not that Noam Chomsky's opinions = what you can't say. If you actually said the things you can't say, you'd shock conservatives and liberals about equally-- just as, if you went back to Victorian England in a time machine, your ideas would shock Whigs and Tories about equally.
Well, I stupidly did not follow the link to the notes, and hence missed that. In my defense, I think pg would have done better to pick a different example. The context, indeed the whole essay, is about "what you can't say". For the reasons stated, Chomsky either says things that a lot of people in the world agree with or things that are horrific (praise of Hezbollah). Neither of these puts me in mind of Galileo.
My suggestion to pg: use George Orwell as an example.
