The Riot Act was read in 1854 in Ballarat, Victoria, Australia. Many Australians (though not all) consider the battle that followed to be the birth of democracy in this country. Note that in this case the At was used principly as a political weapon, and not as a means of restoring order in a time of calamity.
I have to point out that for people like myself who live in constant pain drugs like oxycontin are one of the few options we have other than jumping in front of trains.
The biggest reason oxy is a major crime and health problem is the illegality of opioids makes the black market so profitable. A further reason is linked to the hysteria that the Power Brokers use in the "War on Drugs", where every person who uses opioids is painted as a monster about to explode into a frenzy of violent crime.
I've had lots of well meaning persons who offer to advise me about treatment centers to lick my "oxy problem". They have nothing to offer for my neuropathy problem though. Oxy is not a problem, it's a solution for many people who otherwise suffer unbearable pain. Equating these people with raving drug addicts is ignorant and insulting. A society that paints people as potential killers and thieves because they're trying to find some way of having a somewhat "normal" life is disgusting. Here endeth the rant.
Re:For those interested in a modern intro to the m
on
Charles Darwin Online
·
· Score: 1
In fact Darwin's Origin said nothing about the origins of life - only of species. Later in his life he did publish some papers about a hypothesis of panspermia, but he also wrote that he was very uncomfortable with the fact that he had, for the first time, published an idea without any experimental observations to support it. His panspermia work was published in response to the religous right of the day, who were confusing the idea of speciation with the origin of life. Some things haven't moved on much.
But diden't publish. His work was "rediscovered" 30 years later, when someone found and understood his notes. So unless Darwin used Astral Travelling, he wouldn't have known about Mendel's work on inheritance.
Why is it so difficult for people to accept that culture and technology are part of natural humanity? It's this whole "we're not part of nature" crap that leads to a trashed planet. Our future evolution will continue, albiet "natural selection" now includes that part of "human nature" we call technology, whereas previously other parts of culture affected the selction pressures.
Australia has a net +ve population growth, and is a 1st world country. I'm pretty sure that you'll find our growth is probably not that different to yours, with the difference being that race is not such a big deal here in general (although that is changing to our detriment IMHO).
The western half country now known as Libya was a major part of the Carthagian empire, in fact the term Punic Empire specifically refers to that part of the Empire based on the Three Cities ("Tri Polis" or "Tripolis"). The Western half of Libya is still primarily a Berber homeland, known to the anciant Greeks as "Lebu", from which we get the term Libya. Tunisia became a country in the latter half of the 18th century. Libya (the country, not the place where Berbers live) was created just before WWII. One of it's major regions was Tripolitania - the same region previously known as "Tri Polis". Tri Polis was a breadbasket (along with the lakes whose exact position is uncertain these days) for Carthage, with major irrigation works. Ruins of the irrigation systems were still there during WWII, when the aqueducts were used for target practice by the British.
So yes, Carthage has been in Tunisia for about 125 years. It was in Libya for nearly 2500 years before that. In my previous post I didnt actually say that Carthage was in Libya you'll note - yet you knew exactly what civilisation I was talking about. The fact remains that there is enough money from oil that the Libyan Government (Gaddafi) could restore the Three Cities area to agricultural productivity if he chose - or more likely if his "Desert Voices" told him to.
Conversely, Libya was once a marvellous place full of fruit and food. Then a superpower invaded, genocided them and destroyed their civilisation with chemical weapons (sodium cloride). If Libya chose to, they could put in the infrastructure to restore their lost fields and orchards, using some of the oil money. IF...
David Hicks has never fired a shot at a human being. He has never bombed a building. Exactly how is he an "enemy combatant". He has never been to or applied for a visa to the US. The closest he's ever been to the US is being held in custody without charge for years on end. Your presumption about the inmates of Gitmo is flawed.
Don't get me wrong, there may well be terrorists who were actively involved in committing and/or performing terrorist acts against the USA in there, in fact there probably are. But at least one isnt, and there may be more.
I have to ask, are you using stable? If so, then the "6 months to a year" is what you're asking for.
Software in testing is only 2 weeks behind the release of the upstream IF (a) software doesnt contain egregious bugs, and (b) doesn't depend on software that isn't in testing. This is reasonably close to the edge if you like software that works very well.
If you really want up-to-the-moment software, use debian unstable, which is typically updated 50 or more times a day. Personally I don't like such an exciting life. I use Testing.
But the question begs itself again, what are these patches that should only be found in a certain distro. Security patches that only apply to debian? Sounds like a problem in debian somewhere else up the tree, not in FF itself. If it's in FF itself, it should be submitted to the tree.
Debian supports very old versions of their "stable" distribution, which include very old versions of "firefox". When a Security issue is identified with current versions of Firefox/Mozilla, the Debian maintainers checks to see if that issue affects the versions shipped with the old versions of stable. If so they back-port these fixes. Usually the version of Mozilla being patched is no longer supported by Mozilla Foundation/Corporation.
So Debian has to either say "Sorry, but this distribution we support has software in it we no longer support" or it has to back-port fixes into versions of Moz/FF that Mozilla no longer supports. Do other distributions support their releases of 4+ years ago? The problem with Debian is that it supports its' users' Freedom.
I don't see that "Iceweasel" is in any way intended as an insult. I mean, we're talking about a distribution that called its three last stable releases "sarge", "woody" and "potato". They just like silly names.
Ah, the sounds of ignorance!
Once upon a time Bruce Perens was very involved with Debian. At the time he was working on this cult film called "Toy Story". All the releases of Debian are named after characters in the movie. In the film the nasty kid next door who broke toys was called sid (debian unstable). Other characters were bo (Bo Peep), hamm (the piggy bank), buzz (Buzz Lightyear, Space Ranger), rex (A T. Rex dinosaur), slink (A slinky spring dog), potato (Mr Potato Head), etch (an etch-a-sketch), woody (The cowboy doll hero of the film), sarge (The leader of the plastic toy soldiers). We still havent seen squeaky, bullseye, stinky, zurg, the girl cowboy doll, and many other toys from the show. The silly names are things like "Hoary Hedgehog" and "Fedora Core" (the core of a hat - isn't that just empty space?).
The "h" formula is a view of the derivative that is specific to real valued functions over reals. It does not help the OP's quest of understanding the language of mathematics, versus the "more general" (and quite fluffy) view of the limit of the average rate of change, which has meaning wherever the terms "function", "ratio", "limit" (in particular consider how limit's are not just as per Wierstrasse, consider point valued functions such as Cauchy sequences where the "h" formula simply has no meaning, yet a derivative does exist) and "difference" make sense.
The whole "maths is just a set of formulae and definitions" approach doesn't help you learn problem solving (it does let you learn "cookie cutter" "fill-the-blanks" style solving problems in text-books though). It doesn't reveal the simplicity and beauty that underlies maths. Give someone two pencils and 6 inches of string and they can measure the height of trees and towers, or the width of plains and rivers, if they understand basic geometry and can do a little mental arithmetic. The person who thinks it's all "formulas" will be looking for trig books or a calculator. It's important to know the formulas, but without some kind of understanding what they describe and how that happens then they're dry black boxes. Everything in maths makes sense. I've had thousands of students tell me that "maths doesnt make any sense to me - I don't get it", and I've never seen anyone who really tries fail to improve on that. They don't all love maths now, but they're not intimdated by it, and they understand what the point is.
Look at what things mean and do, and then the "rest" of maths (the actual doing sums) will make a lot more sense, and you'll feel more confident that you can understand what you're doing.
Wow, there are just so many ill-informed and probably very unwise pieces of advice here.
Let me make this clear to start with - I've worked teaching Maths to people struggling with it for many many years, starting with private tuition, through the Education Department and as a University Tutor/Lecturer. I've seen teaching of maths at all levels above primary. And I'm damn good at it, as I've only had a handfull out of hundreds of students over 20+ years who didnt show marked improvement, in their grades and in general life as they've realised that they're not stupid after all.
The things that are most important to get a "unified" and "intuitive" understanding of maths are the simple rules you met at primary school. You didn't meet their names back in Primary School (commutivity, reflexivity, transitivity, associativity) but these properies (and their abscence) are what make all the different algebras different (or the same). If we wish to be very technical we could say these properties allow us to identify isomorphisms and homeomorphisms between spaces, but that's not what matters. What matters is that by the end of primary school you have learn't all the basic principles that "higher maths" is made up of, it's all just a matter of putting it into perspective.
As another example, consider garden variety subtraction over the positive integers. This gives us a lovely view of the ideas of openness, closedness, a non-commutative operation. We have to "borrow" to perform some subtractions in primary school - and we use exactly the same technique when solving a quadratic equation by "completeing the square". Later you can use exactly the same idea to solve hairy beasties using tensors and Kroneker's Delta.
Multiplication, division, addition and subtraction of the integers is isomorphic to the algebra of the Polynomials over the Integers - anything you want to do to polynomials is EXACTLY the same as you did to integers in grade 4.
Understanding your Calculus I & II courses is easy if you forget the "formulae" and look at the geometry and
the quanitities. Most people get terrified by hairy looking "formulae", to the extent that they develop "formulitis" where maths has degenerated into a mass of formulae to be applied (or mis-applied) on demand. A better approach is to learn what is happening to the quantities being discussed, and then learning how the formulae are just generalisations and shorthand for exactly the same things. For example, look at using increasing numbers of rectangular strips to find the area of a squiggly closed curve, using paper and scissors (try this!!). Then you can see there's a way of writing this down in terms of the 1st rectangle, the last rectabgle, and a huge number of "arbitrary" rectangles that go between them. At that point you've got yourself about to take a Reimann Sum, and you've almost understood the definate Integral - but you haven't got any scary expressions with capital sigmas, lower case epsilons and trying to count an infinitely large number of infinitely small things and get your head around how it's not the same as 0+0+0+...+0+0 being something that isn't zero.
I've heard the "don't try to understand this, it won't make sense to 99.9% of people, and even if it will make sense don't expect it to do so for a few years yet" excuse for mediocrity many many times. My experience is that it's not true. In particular there's nothing you'll meet in maths in an engineering degree that can't be reduced to a series of operations you met at primary school. The wonderful thing is that as you overcome the Fear and Loathing, you will start to see the lovely patterns, and you'll start to see that the different methods and techniques are all just different approaches to essentially the same problem - describing the realtionships between observable quantities.
The most productive acts you can do to improve your maths skills are:
1) Always do a back-of-envelope estimate before you punch the (hopefully correct) butt
Most of what you say is excellent advice. I have to point out that the formula you present as the "definition of the derivative" is nothing of the kind. The derivative is simply lim[delta x -> 0] (delta y / delta x) where y=f(x). For real valued functions of real numbers that is the same thing as you write from a purely numerical point of view, but it's the shorter (and more general) definition that allows you to see what it is, how it works, and why we can interpret it as the slope of the curve, or the rate of change, or the bounds of the error, according to the problem at hand. Avoid formulitis!
Sorry, the grandparent is right. Think of catching a ball (baseball, basketball - doesnt matter which). Most people learn to intuitivly allow for differences in elevation, wind speed, relative velocities of thrower and catcher, movement of the ball, spin on the ball, bouncing off uneven surfaces (in cricket at least) etc reasonably well. Much better than a Patriot Missile battery. The equations needed are pretty hairy compared to the gool old v=u+at stuff from High School. Yet almost all humans do it intuitively.
As a parent it is my responsibility to do my best to ensure that my kids (I have 5 by the way, so I've done it at least 5 times with another person, which is more than most/. readers can manage without money changing hands...) grow up to be happy, productive, self-actualised human beings, at the same time trying not to force too many of my prejudices and neuroses on them.
I know from experience as a Cranky Old Bastard that I fialed to recognise people who I should not of hung out with when young, and I did many things as a teenager that I regret deeply now. I was a pretty bitter and angry kid though, from a very nasty family. Now I have no doubt that my environment made me more vulnerable to scum, but I have no doubt that part of the problem was simpply my age.
For example, a classic situation is adult says "Don't do drugs they're really really bad for you". I got to see at the age of 13 people tripping on the local fungi, and they certainly seemed to be having a great time. They weren't running round with axes, or jumping off roofs trying to fly, although they were falling over laughing a lot. So I ate shrooms. In fact, the best shroom paddock in the Tweed Valley was my front yard, so I ate a LOT of shrooms, many many times. Take it from me, they are NOT good for young teenagers. You get a perspective that is just a bit warped.
Now let's step back to this century. a few months back, I discovered that over half my eldest son's friends were turning into potheads. This isn't that rare amongst 13 year olds, but it certainly makes success at school a challenge. Not only this, the boy started to talk stoner talk. Okay, time to explain the truth about Uncle Murray (in jail due to an attempt to run over his ex whilst speeding), and why people in our family have to be very very careful of mood altering drugs as we seem to have a weakness in that area. This talk got quite gruesome, with details about Glen (junkie friend who the boy hadn't seen since he was 6 years old, who has since died very horribly of AIDS), Gary (father of one of the boy's mates, who suffers from the worst kind of paranoid speed psychosis, and is now in gaol after nodding off whilst driving. The 2yo passenger is in critical condition, the kids mum is in an induced coma as we speak). Now I don't want to fill my kid's head with these kinds of details, but I'm sure as hell he's going to have all the facts about the things he's hanging around. If I didn't care enough to know who he hangs out with, what they do, where they do it, and when, then I wouldn't bother with letting my son know the horrible details. This way he can make an informed decision, rather than an uninformed one like I did.
As for the CIA, I live in a country that respects its citizens (although that seems to be eroding). We don't have a CIA here.
Exactly. But if he thinks "Wow I could get in deep shit for looking at this" then he's not likely to come to me, as against my saying "hey boy, I see you've been looking at dirtychickswithbaseballbats.com. Did you know that most of those chicks are drug addicts modelling porn for smack money, and not because they're really enjoying that shit?". "Wow Dad" says my son. "so these pictures are like totally using those girls". "yep son, not a lot of respect for human beings there".
Yes, but until such a time as my kids have developed all the skills you mention (and that is a process that takes many, many years) I'll do everything I can to try to understand what they do and why, so that I can best help them BEFORE they fall into a very deep hole they've dug for themselves.
Yes, they'll try to circumvent some measures _if_ they're up to no good. But my kids know that if they do that I'll see that they've taken those steps, and I'll just keep moving the goalposts. If they're not doing evil deeds, then my steps for protection are overkill, but won't affect them much.
You are assuming that a kid will alwys be able to recognise inappropriate behaviour. They can't, simply because they're kids. In exactly the same way that a 10 year old kid doesnt understand the importance of paying taxes. Trust between a kid and his parents is vital. But until I'm sure they have all they need to identify "safe" and "unsafe" I'll monitor, block, log and re-direct their Internet usage.
It's a bit like giving someone who can drive a car the controls of a 747 - the principle of "push the stick" is pretty simple, but the damage caused by a mistake is terrible.
Starting sex education at 12 is too late. I was a bit surprised to here my 7 year old daughter talking about the male guinea pig to here friend "he's in a seperate cage because he just wants to do it to Zelda [ed: a female guinea pig] and she's just had babies". After a little discussion with her we found that she knows a lot more than we expected - the combination of owning guinea pigs and schoolyard talk. Look at the figures - puberty is happening earlier. Talk to your kids by 10 or you'll be far too late.
Slashdot Mirror
You mean like Service Pack 4? or DOS 4.0?
The Riot Act was read in 1854 in Ballarat, Victoria, Australia. Many Australians (though not all) consider the battle that followed to be the birth of democracy in this country. Note that in this case the At was used principly as a political weapon, and not as a means of restoring order in a time of calamity.
You're correct, that Bill was passed to appease Senator Harradine in return for him supporting the "Anti-terror" laws.
I have to point out that for people like myself who live in constant pain drugs like oxycontin are one of the few options we have other than jumping in front of trains.
The biggest reason oxy is a major crime and health problem is the illegality of opioids makes the black market so profitable. A further reason is linked to the hysteria that the Power Brokers use in the "War on Drugs", where every person who uses opioids is painted as a monster about to explode into a frenzy of violent crime.
I've had lots of well meaning persons who offer to advise me about treatment centers to lick my "oxy problem". They have nothing to offer for my neuropathy problem though. Oxy is not a problem, it's a solution for many people who otherwise suffer unbearable pain. Equating these people with raving drug addicts is ignorant and insulting. A society that paints people as potential killers and thieves because they're trying to find some way of having a somewhat "normal" life is disgusting. Here endeth the rant.
In fact Darwin's Origin said nothing about the origins of life - only of species. Later in his life he did publish some papers about a hypothesis of panspermia, but he also wrote that he was very uncomfortable with the fact that he had, for the first time, published an idea without any experimental observations to support it. His panspermia work was published in response to the religous right of the day, who were confusing the idea of speciation with the origin of life. Some things haven't moved on much.
But diden't publish. His work was "rediscovered" 30 years later, when someone found and understood his notes. So unless Darwin used Astral Travelling, he wouldn't have known about Mendel's work on inheritance.
Why is it so difficult for people to accept that culture and technology are part of natural humanity? It's this whole "we're not part of nature" crap that leads to a trashed planet. Our future evolution will continue, albiet "natural selection" now includes that part of "human nature" we call technology, whereas previously other parts of culture affected the selction pressures.
Australia has a net +ve population growth, and is a 1st world country. I'm pretty sure that you'll find our growth is probably not that different to yours, with the difference being that race is not such a big deal here in general (although that is changing to our detriment IMHO).
The straight facts are as follows:
The western half country now known as Libya was a major part of the Carthagian empire, in fact the term Punic Empire specifically refers to that part of the Empire based on the Three Cities ("Tri Polis" or "Tripolis"). The Western half of Libya is still primarily a Berber homeland, known to the anciant Greeks as "Lebu", from which we get the term Libya. Tunisia became a country in the latter half of the 18th century. Libya (the country, not the place where Berbers live) was created just before WWII. One of it's major regions was Tripolitania - the same region previously known as "Tri Polis". Tri Polis was a breadbasket (along with the lakes whose exact position is uncertain these days) for Carthage, with major irrigation works. Ruins of the irrigation systems were still there during WWII, when the aqueducts were used for target practice by the British.
So yes, Carthage has been in Tunisia for about 125 years. It was in Libya for nearly 2500 years before that. In my previous post I didnt actually say that Carthage was in Libya you'll note - yet you knew exactly what civilisation I was talking about. The fact remains that there is enough money from oil that the Libyan Government (Gaddafi) could restore the Three Cities area to agricultural productivity if he chose - or more likely if his "Desert Voices" told him to.
Conversely, Libya was once a marvellous place full of fruit and food. Then a superpower invaded, genocided them and destroyed their civilisation with chemical weapons (sodium cloride). If Libya chose to, they could put in the infrastructure to restore their lost fields and orchards, using some of the oil money. IF...
David Hicks has never fired a shot at a human being. He has never bombed a building. Exactly how is he an "enemy combatant". He has never been to or applied for a visa to the US. The closest he's ever been to the US is being held in custody without charge for years on end. Your presumption about the inmates of Gitmo is flawed.
Don't get me wrong, there may well be terrorists who were actively involved in committing and/or performing terrorist acts against the USA in there, in fact there probably are. But at least one isnt, and there may be more.
I have to ask, are you using stable? If so, then the "6 months to a year" is what you're asking for.
Software in testing is only 2 weeks behind the release of the upstream IF (a) software doesnt contain egregious bugs, and (b) doesn't depend on software that isn't in testing. This is reasonably close to the edge if you like software that works very well.
If you really want up-to-the-moment software, use debian unstable, which is typically updated 50 or more times a day. Personally I don't like such an exciting life. I use Testing.
No, Debian didn't want the different name and logo, the Mozilla people did.
Like David Hicks?
But the question begs itself again, what are these patches that should only be found in a certain distro. Security patches that only apply to debian? Sounds like a problem in debian somewhere else up the tree, not in FF itself. If it's in FF itself, it should be submitted to the tree.
Debian supports very old versions of their "stable" distribution, which include very old versions of "firefox". When a Security issue is identified with current versions of Firefox/Mozilla, the Debian maintainers checks to see if that issue affects the versions shipped with the old versions of stable. If so they back-port these fixes. Usually the version of Mozilla being patched is no longer supported by Mozilla Foundation/Corporation.
So Debian has to either say "Sorry, but this distribution we support has software in it we no longer support" or it has to back-port fixes into versions of Moz/FF that Mozilla no longer supports. Do other distributions support their releases of 4+ years ago? The problem with Debian is that it supports its' users' Freedom.
I don't see that "Iceweasel" is in any way intended as an insult. I mean, we're talking about a distribution that called its three last stable releases "sarge", "woody" and "potato". They just like silly names.
Ah, the sounds of ignorance!
Once upon a time Bruce Perens was very involved with Debian. At the time he was working on this cult film called "Toy Story". All the releases of Debian are named after characters in the movie. In the film the nasty kid next door who broke toys was called sid (debian unstable). Other characters were bo (Bo Peep), hamm (the piggy bank), buzz (Buzz Lightyear, Space Ranger), rex (A T. Rex dinosaur), slink (A slinky spring dog), potato (Mr Potato Head), etch (an etch-a-sketch), woody (The cowboy doll hero of the film), sarge (The leader of the plastic toy soldiers). We still havent seen squeaky, bullseye, stinky, zurg, the girl cowboy doll, and many other toys from the show. The silly names are things like "Hoary Hedgehog" and "Fedora Core" (the core of a hat - isn't that just empty space?).
The "h" formula is a view of the derivative that is specific to real valued functions over reals. It does not help the OP's quest of understanding the language of mathematics, versus the "more general" (and quite fluffy) view of the limit of the average rate of change, which has meaning wherever the terms "function", "ratio", "limit" (in particular consider how limit's are not just as per Wierstrasse, consider point valued functions such as Cauchy sequences where the "h" formula simply has no meaning, yet a derivative does exist) and "difference" make sense.
The whole "maths is just a set of formulae and definitions" approach doesn't help you learn problem solving (it does let you learn "cookie cutter" "fill-the-blanks" style solving problems in text-books though). It doesn't reveal the simplicity and beauty that underlies maths. Give someone two pencils and 6 inches of string and they can measure the height of trees and towers, or the width of plains and rivers, if they understand basic geometry and can do a little mental arithmetic. The person who thinks it's all "formulas" will be looking for trig books or a calculator. It's important to know the formulas, but without some kind of understanding what they describe and how that happens then they're dry black boxes. Everything in maths makes sense. I've had thousands of students tell me that "maths doesnt make any sense to me - I don't get it", and I've never seen anyone who really tries fail to improve on that. They don't all love maths now, but they're not intimdated by it, and they understand what the point is.
Look at what things mean and do, and then the "rest" of maths (the actual doing sums) will make a lot more sense, and you'll feel more confident that you can understand what you're doing.
Wow, there are just so many ill-informed and probably very unwise pieces of advice here.
Let me make this clear to start with - I've worked teaching Maths to people struggling with it for many many years, starting with private tuition, through the Education Department and as a University Tutor/Lecturer. I've seen teaching of maths at all levels above primary. And I'm damn good at it, as I've only had a handfull out of hundreds of students over 20+ years who didnt show marked improvement, in their grades and in general life as they've realised that they're not stupid after all.
The things that are most important to get a "unified" and "intuitive" understanding of maths are the simple rules you met at primary school. You didn't meet their names back in Primary School (commutivity, reflexivity, transitivity, associativity) but these properies (and their abscence) are what make all the different algebras different (or the same). If we wish to be very technical we could say these properties allow us to identify isomorphisms and homeomorphisms between spaces, but that's not what matters. What matters is that by the end of primary school you have learn't all the basic principles that "higher maths" is made up of, it's all just a matter of putting it into perspective.
As another example, consider garden variety subtraction over the positive integers. This gives us a lovely view of the ideas of openness, closedness, a non-commutative operation. We have to "borrow" to perform some subtractions in primary school - and we use exactly the same technique when solving a quadratic equation by "completeing the square". Later you can use exactly the same idea to solve hairy beasties using tensors and Kroneker's Delta.
Multiplication, division, addition and subtraction of the integers is isomorphic to the algebra of the Polynomials over the Integers - anything you want to do to polynomials is EXACTLY the same as you did to integers in grade 4.
Understanding your Calculus I & II courses is easy if you forget the "formulae" and look at the geometry and the quanitities. Most people get terrified by hairy looking "formulae", to the extent that they develop "formulitis" where maths has degenerated into a mass of formulae to be applied (or mis-applied) on demand. A better approach is to learn what is happening to the quantities being discussed, and then learning how the formulae are just generalisations and shorthand for exactly the same things. For example, look at using increasing numbers of rectangular strips to find the area of a squiggly closed curve, using paper and scissors (try this!!). Then you can see there's a way of writing this down in terms of the 1st rectangle, the last rectabgle, and a huge number of "arbitrary" rectangles that go between them. At that point you've got yourself about to take a Reimann Sum, and you've almost understood the definate Integral - but you haven't got any scary expressions with capital sigmas, lower case epsilons and trying to count an infinitely large number of infinitely small things and get your head around how it's not the same as 0+0+0+...+0+0 being something that isn't zero.
I've heard the "don't try to understand this, it won't make sense to 99.9% of people, and even if it will make sense don't expect it to do so for a few years yet" excuse for mediocrity many many times. My experience is that it's not true. In particular there's nothing you'll meet in maths in an engineering degree that can't be reduced to a series of operations you met at primary school. The wonderful thing is that as you overcome the Fear and Loathing, you will start to see the lovely patterns, and you'll start to see that the different methods and techniques are all just different approaches to essentially the same problem - describing the realtionships between observable quantities.
The most productive acts you can do to improve your maths skills are:
1) Always do a back-of-envelope estimate before you punch the (hopefully correct) butt
Most of what you say is excellent advice. I have to point out that the formula you present as the "definition of the derivative" is nothing of the kind. The derivative is simply lim[delta x -> 0] (delta y / delta x) where y=f(x). For real valued functions of real numbers that is the same thing as you write from a purely numerical point of view, but it's the shorter (and more general) definition that allows you to see what it is, how it works, and why we can interpret it as the slope of the curve, or the rate of change, or the bounds of the error, according to the problem at hand. Avoid formulitis!
Sorry, the grandparent is right. Think of catching a ball (baseball, basketball - doesnt matter which). Most people learn to intuitivly allow for differences in elevation, wind speed, relative velocities of thrower and catcher, movement of the ball, spin on the ball, bouncing off uneven surfaces (in cricket at least) etc reasonably well. Much better than a Patriot Missile battery. The equations needed are pretty hairy compared to the gool old v=u+at stuff from High School. Yet almost all humans do it intuitively.
I call bullshit.
/. readers can manage without money changing hands...) grow up to be happy, productive, self-actualised human beings, at the same time trying not to force too many of my prejudices and neuroses on them.
As a parent it is my responsibility to do my best to ensure that my kids (I have 5 by the way, so I've done it at least 5 times with another person, which is more than most
I know from experience as a Cranky Old Bastard that I fialed to recognise people who I should not of hung out with when young, and I did many things as a teenager that I regret deeply now. I was a pretty bitter and angry kid though, from a very nasty family. Now I have no doubt that my environment made me more vulnerable to scum, but I have no doubt that part of the problem was simpply my age.
For example, a classic situation is adult says "Don't do drugs they're really really bad for you". I got to see at the age of 13 people tripping on the local fungi, and they certainly seemed to be having a great time. They weren't running round with axes, or jumping off roofs trying to fly, although they were falling over laughing a lot. So I ate shrooms. In fact, the best shroom paddock in the Tweed Valley was my front yard, so I ate a LOT of shrooms, many many times. Take it from me, they are NOT good for young teenagers. You get a perspective that is just a bit warped.
Now let's step back to this century. a few months back, I discovered that over half my eldest son's friends were turning into potheads. This isn't that rare amongst 13 year olds, but it certainly makes success at school a challenge. Not only this, the boy started to talk stoner talk. Okay, time to explain the truth about Uncle Murray (in jail due to an attempt to run over his ex whilst speeding), and why people in our family have to be very very careful of mood altering drugs as we seem to have a weakness in that area. This talk got quite gruesome, with details about Glen (junkie friend who the boy hadn't seen since he was 6 years old, who has since died very horribly of AIDS), Gary (father of one of the boy's mates, who suffers from the worst kind of paranoid speed psychosis, and is now in gaol after nodding off whilst driving. The 2yo passenger is in critical condition, the kids mum is in an induced coma as we speak). Now I don't want to fill my kid's head with these kinds of details, but I'm sure as hell he's going to have all the facts about the things he's hanging around. If I didn't care enough to know who he hangs out with, what they do, where they do it, and when, then I wouldn't bother with letting my son know the horrible details. This way he can make an informed decision, rather than an uninformed one like I did.
As for the CIA, I live in a country that respects its citizens (although that seems to be eroding). We don't have a CIA here.
Exactly. But if he thinks "Wow I could get in deep shit for looking at this" then he's not likely to come to me, as against my saying "hey boy, I see you've been looking at dirtychickswithbaseballbats.com. Did you know that most of those chicks are drug addicts modelling porn for smack money, and not because they're really enjoying that shit?". "Wow Dad" says my son. "so these pictures are like totally using those girls". "yep son, not a lot of respect for human beings there".
Yes, but until such a time as my kids have developed all the skills you mention (and that is a process that takes many, many years) I'll do everything I can to try to understand what they do and why, so that I can best help them BEFORE they fall into a very deep hole they've dug for themselves.
Yes, they'll try to circumvent some measures _if_ they're up to no good. But my kids know that if they do that I'll see that they've taken those steps, and I'll just keep moving the goalposts. If they're not doing evil deeds, then my steps for protection are overkill, but won't affect them much.
You are assuming that a kid will alwys be able to recognise inappropriate behaviour. They can't, simply because they're kids. In exactly the same way that a 10 year old kid doesnt understand the importance of paying taxes. Trust between a kid and his parents is vital. But until I'm sure they have all they need to identify "safe" and "unsafe" I'll monitor, block, log and re-direct their Internet usage.
It's a bit like giving someone who can drive a car the controls of a 747 - the principle of "push the stick" is pretty simple, but the damage caused by a mistake is terrible.
Starting sex education at 12 is too late. I was a bit surprised to here my 7 year old daughter talking about the male guinea pig to here friend "he's in a seperate cage because he just wants to do it to Zelda [ed: a female guinea pig] and she's just had babies". After a little discussion with her we found that she knows a lot more than we expected - the combination of owning guinea pigs and schoolyard talk. Look at the figures - puberty is happening earlier. Talk to your kids by 10 or you'll be far too late.