I just realized that the formula you gave is identical to the area of a trapezoid - where A and B are the lengths of the parallel sides, and (A + B - 1) is the distance between the sides... which makes sense if one sees a trapezoid as the result of a "triangle minus a triangle," so to speak.
In a reply to an earlier post, I asked about the sum of the integers from A to B. My proposed solution was to take the "triangular number" formula - the sum of (1,2,3,...,n) is equal to:
n * (n + 1) / 2.
In that case you'd be taking the triangular number for B, and then subtracting the triangular number for (A - 1). Thus you'd have:
(B * (B + 1) - (A - 1) * A) / 2, or
(B^2 - A^2 + B + A) / 2
Either way, both are pretty high-level reasoning for a grade school student.
And you're probably right about the story being apocryphal. I rather thought it smacked too much of urban legend to be absolutely true - <wry grin> not that I let that stand in my way when I'm on my soapbox. </wry grin>
Good points, all of them. I was lucky - in my case, a lot of my enthusiasm was beaten out of me, and I'm willing to bet that a bit of it was due to my being an asshead, to use your awful-sounding and highly-appropriate term. (I'll bet the hyphenation above shows that it didn't totally work.)
Still, I had teachers who were trying to keep all of us from using our heads for ashtrays, who hadn't had their enthusiasm beaten out of them by obnoxious kids, hostile or indifferent parents, and school administrations who didn't want their own "superiority" challenged.
I don't think that such teachers are dead, or even hunted to the point of endangerment, but the stresses involved probably have managed to drive some of these highly worthwhile souls into managing a Burger King.
So, I think I have had an answer, which suggests that I've been a little hasty.
However, having two children who are extremely bright, I sometimes fear for their future. It probably comes with the territory...
The story is (and how accurate this is I'm not entirely certain) that when Gauss was a child in school, he was acting up in class, and his teacher assigned him the task of adding up all of the numbers between 1 and 100. 2 minutes later, he had the answer, and he showed the teacher that he had figured that 100 + 1 = 101, 99 + 2 = 101... and thus cut it down to 50 pairs of numbers that added up to 101. He then multiplied 50 by 101 to get the answer of 5050.
I mention this because if little Freddy Gauss had done something similarly in our current school system, he'd have gotten one of three responses from the teacher:
1 - "Class, look at what Freddy figured out! Isn't he smart?" This bit of gushing praise would get him pegged as a "teacher's pet," and after his "not-smart" classmates managed to re-arrange his face during recess, he'd decide better than to open his mouth.
2 - "That smart-ass attitude just earned you a trip to the principal's office!" This attitude of "you just made ME look not-smart, so you're going to pay!" will also convince him to shut up next time.
3 - "OK. In that case, add up the numbers between 100 and 200." (Tricky one, that - it's an odd number of elements!) Freddy would be kept busy, while the teacher figured out how to contact Mr. and Mrs. Gauss and suggest that they get their holy terror signed up for advanced math.
Would anyone care to estimate the percentage chance of each response? I'd say that no matter the school, there'd only be a 5% chance of the third option being taken... (and it's predicated on the idea that the teacher would be knowledgeable enough in math to throw a curveball like that last one).
Most of the places where I've worked I've been treated decently - at least as decently as the situation allowed. I also had a clueful manager at the majority of these places. At one, I had a manager who knew when to keep our noses to the grindstone when we had some slack time to fix an intermittent problem... and then took our noses off the grindstone and saw to it we got more slack when we solved the problem. Another one was the sort who, to paraphrase Heinlein's description, would look through the rulebook to find the clause that would let you get what you needed, instead of finding the clause that would keep you from getting what you deserved.
My point? Keep these people happy when you leave, by leaving cleanly. Don't leave deliberate time bombs, try to prevent accidental ones by either fixing them or by documenting the living s**t out of them, and do your best by the person they're bringing in to replace you. Leaving nasty good-bye presents only comes back to haunt you, one way or another.
I've done that at all the places I've left, and although I'm not making as much as I'd like, I sleep pretty well... and I do like my sleep.
I am one of those people who can communicate much better with a computer than with other people until I get relaxed. At one company I interviewed, I met the CIO, and we talked about my technical experience. I was able to write the pseudocode for what I'd done before, and the CIO was pretty happy. He then took me in to talk to the owner of the company. The owner later told the CIO that I seemed to stutter and stammer a bit. The CIO said that I didn't stammer to the computers, which he thought was more important.
I got the job.
Looking back, I was lucky - but once I got relaxed enough to be able to discuss opera with the owner (a big supporter of the arts in this town), he was convinced that I was the perfect person for the job.
I wonder if they considered the effect of the deploying plane's jetwash on the opening of the first chutes.
I know, it sounds silly, but just remember the aircraft windshield tests that failed until someone remembered to thaw the turkeys that they were shooting at the mockups. Sometimes the obvious does get overlooked.
Truer and truer. When the Founding Fathers put "ex post facto" laws on their not-to-do list in the Constitution, they had unfortunate prior experience driving them. They'd seen people arrested for retroactive violations of sedition laws (and then getting a no-expenses-paid trip to England for their trials), and they knew that a government needed checks to keep from excesses in the name of "keeping the civil peace."
<sigh> The price of freedom doesn't seem to be getting any easier to meet, and the alternative is cheaper, but I'm kind of attached to the neat extra features.
Hey, I'm all down with the Catholic church coughing up the New World assets as soon as the Islamic world reverts the middle east to the Roman Christian states they were before hand Islamic expansion.
Let's go further than that! Join the Gondwanaland Reunification Movement!
You see, the other costumed heroes were just that - some had improved capabilities (like Ozymandias), and some had neat devices (like Nite Owl), but in the end they were all people whose costume was primarily aimed at concealing their identities.
Dr. Manhattan was different... since he was no longer entirely human he was no longer affected by human norms and values (watch how his clothing becomes sketchier from his early days to the "present").
I thought it was a pretty cool way of showing how much he'd diverged from his original self without blabbing it out loud.
Let's leave out the legal ramifications here, and let's not go to the hysteria of "he's being thrown to the wolves to protect management" or "he's an evil hacker who shut down the city government networks."
When it comes down to it, one has to ask what Childs' job was. He was supposed to manage the network for the San Francisco city government.
As a result, he was supposed to implement policy as communicated to him by his bosses... but he also had the latitude to take actions to support the spirit of those policies where the right action was unclear. And yes, this is a Pollyanna-esque (is that a word?) view of the situation, but it leaves out the concept of malice as the driving force for either side - because it didn't start out as a plan to shut down the city.
Somehow it morphed into him becoming the sole support for the network routers, be it through arrogance ("I can't believe anyone else would do this right!") or being the only one available ("There's nobody else who works here who even understands the need!"), and at that point this became an incident waiting to happen.
So, either he refused to do his job (at which point he would have deserved to be fired), or his job was such that he was prevented from doing it (at which point professional ethics would have suggested his resignation - or at least, that's what engineering associations would have recommended in similar scenarios).
Instead, he stayed on and we have the current state of affairs.
I sent an E-mail to my representative, and here's what it said:
Representative Moore,
I have read the results, and saw that you voted "Yea" for the FISA amendment act of 2008 (HR 6304).
I don't understand how you could have supported a bill that provided a blanket immunity for the telecommunications companies when they provided warrantless wiretapping at the request of the Justice Department.
I don't comprehend how you could hold these entities as blameless when they knew that the warrants for the wiretaps were not forthcoming, and provided them anyway. At the very least, I believe that a lawsuit would have forced them to defend their actions, indicate whether they were putting in some safeguards of their own, and possibly to exonerate them as actually yielding under protest. Instead, once this bill passes the conference committee and is signed by President Bush, it quietly absolves them without determining whether they did, in fact, break the law.
I don't understand how you could have decided in favor of this compromise, considering that it only succeeds in compromising the 4th Amendment's guarantee against unreasonable search and seizure.
I have been a Kansan for close to 20 years now, and I have been proud of your representation of us in this district. Like most Kansans, I have put your achievements ahead of party affiliation, and I considered you a prime example of how some people could put partisan advantage behind the good of the country.
I am bitterly disappointed in your decision, and am now finding myself in a position of having to consider how I can continue to support you in light of this decision.
Again, I am sorry to see this decision of yours. I don't think it was your best one.
Sincerely...
It may have the same effect as shouting into a vacuum, but as citizens, we need to let our displeasure be known - now and at the ballot box.
When they call this a "compromise" bill, they aren't kidding. It will compromise our civil liberties, by letting the telecoms know that they can get away with helping illegal actions scot-free.
I worry that this will receive strong bi-partisan support, because a future Democrat administration will see the advantages of this, and want it in place in advance.
1) The case of Megan Meier is an anomaly. A pair of PARENTS decided to put this kid through an emotional wringer to screw up her life.
Detestable, contemptible, and atrocious? Yes. A widespread case? I don't think so. A sound basis for a law making it illegal? I doubt it.
2) Knee-jerk reactions, especially in an election year, are to be expected, particularly by a legislature that is sharply divided along partisan lines. Either party will want to use this as a tool to stay in office.
Detestable, contemptible, and atrocious? Yes. A widespread case? Yes - along with anti-flag-burning amendments, laws requiring the rating of video games and bills proposing convicted sex offenders to be put on 24-hour electronic surveillance for life. A sound basis for a law making it illegal? Don't I wish.
While losing his license was not directly responsible for his current status, if he had never lost his license, he likely would never have done anything more than be a local shrink.
"If you strike me down, I shall become more powerful than you can possibly imagine."
... Ruining other lives because you're on a mission for some sort of revenge is never a good thing, never.... Why not? It's been good for the Bush administration...
This was a well-written article about a good experiment.
I went through a similar situation where I tried to introduce my mom to Linux by setting her up with Mandrake 8.1. It was a good distro - at least for me, a software developer - but Mom tends to be somewhat terrified of high tech, and after valiantly trying to do things, she just got fed up and asked me to install Windows.
One of her biggest problems was that Mandrake installed 3 different web browsers, 2 mail clients, and the proverbial "partridge in a pear tree." The availability of these browsers was fine for me, but Mom got confused, flustered, and finally gave up.
I'm thinking of trying again in the next couple of months - but this time with SymphonyOne, which offers her more of a "here's what you do," rather than a "what do you want to do?" approach. I'd feel like I was in a strait-jacket, but it'll probably work much better for her... and (hopefully) will get her using her computer more.
Slashdot Mirror
I just realized that the formula you gave is identical to the area of a trapezoid - where A and B are the lengths of the parallel sides, and (A + B - 1) is the distance between the sides... which makes sense if one sees a trapezoid as the result of a "triangle minus a triangle," so to speak.
Dear God! I'm reverting to being a math nerd! :)
An elegant solution!
In a reply to an earlier post, I asked about the sum of the integers from A to B. My proposed solution was to take the "triangular number" formula - the sum of (1,2,3,...,n) is equal to:
n * (n + 1) / 2.
In that case you'd be taking the triangular number for B, and then subtracting the triangular number for (A - 1). Thus you'd have:
(B * (B + 1) - (A - 1) * A) / 2, or
(B^2 - A^2 + B + A) / 2
Either way, both are pretty high-level reasoning for a grade school student.
And you're probably right about the story being apocryphal. I rather thought it smacked too much of urban legend to be absolutely true - <wry grin> not that I let that stand in my way when I'm on my soapbox. </wry grin>
Good points, all of them. I was lucky - in my case, a lot of my enthusiasm was beaten out of me, and I'm willing to bet that a bit of it was due to my being an asshead, to use your awful-sounding and highly-appropriate term. (I'll bet the hyphenation above shows that it didn't totally work.)
Still, I had teachers who were trying to keep all of us from using our heads for ashtrays, who hadn't had their enthusiasm beaten out of them by obnoxious kids, hostile or indifferent parents, and school administrations who didn't want their own "superiority" challenged.
I don't think that such teachers are dead, or even hunted to the point of endangerment, but the stresses involved probably have managed to drive some of these highly worthwhile souls into managing a Burger King.
So, I think I have had an answer, which suggests that I've been a little hasty.
However, having two children who are extremely bright, I sometimes fear for their future. It probably comes with the territory...
Fine, then, smarty-pants. Figure out the sum of the integer numbers between A and B (inclusive).
The story is (and how accurate this is I'm not entirely certain) that when Gauss was a child in school, he was acting up in class, and his teacher assigned him the task of adding up all of the numbers between 1 and 100. 2 minutes later, he had the answer, and he showed the teacher that he had figured that 100 + 1 = 101, 99 + 2 = 101... and thus cut it down to 50 pairs of numbers that added up to 101. He then multiplied 50 by 101 to get the answer of 5050.
I mention this because if little Freddy Gauss had done something similarly in our current school system, he'd have gotten one of three responses from the teacher:
1 - "Class, look at what Freddy figured out! Isn't he smart?" This bit of gushing praise would get him pegged as a "teacher's pet," and after his "not-smart" classmates managed to re-arrange his face during recess, he'd decide better than to open his mouth.
2 - "That smart-ass attitude just earned you a trip to the principal's office!" This attitude of "you just made ME look not-smart, so you're going to pay!" will also convince him to shut up next time.
3 - "OK. In that case, add up the numbers between 100 and 200." (Tricky one, that - it's an odd number of elements!) Freddy would be kept busy, while the teacher figured out how to contact Mr. and Mrs. Gauss and suggest that they get their holy terror signed up for advanced math.
Would anyone care to estimate the percentage chance of each response? I'd say that no matter the school, there'd only be a 5% chance of the third option being taken... (and it's predicated on the idea that the teacher would be knowledgeable enough in math to throw a curveball like that last one).
"Random speculation? That's what slashdotters does best!"
Most of the places where I've worked I've been treated decently - at least as decently as the situation allowed. I also had a clueful manager at the majority of these places. At one, I had a manager who knew when to keep our noses to the grindstone when we had some slack time to fix an intermittent problem... and then took our noses off the grindstone and saw to it we got more slack when we solved the problem. Another one was the sort who, to paraphrase Heinlein's description, would look through the rulebook to find the clause that would let you get what you needed, instead of finding the clause that would keep you from getting what you deserved.
My point? Keep these people happy when you leave, by leaving cleanly. Don't leave deliberate time bombs, try to prevent accidental ones by either fixing them or by documenting the living s**t out of them, and do your best by the person they're bringing in to replace you. Leaving nasty good-bye presents only comes back to haunt you, one way or another.
I've done that at all the places I've left, and although I'm not making as much as I'd like, I sleep pretty well... and I do like my sleep.
I can attest to this.
I am one of those people who can communicate much better with a computer than with other people until I get relaxed. At one company I interviewed, I met the CIO, and we talked about my technical experience. I was able to write the pseudocode for what I'd done before, and the CIO was pretty happy. He then took me in to talk to the owner of the company. The owner later told the CIO that I seemed to stutter and stammer a bit. The CIO said that I didn't stammer to the computers, which he thought was more important.
I got the job.
Looking back, I was lucky - but once I got relaxed enough to be able to discuss opera with the owner (a big supporter of the arts in this town), he was convinced that I was the perfect person for the job.
Interesting you should use that phrase.
Here's a link that shows the origin of the phrase.
The included graphic seems particularly apt.
I wonder if they considered the effect of the deploying plane's jetwash on the opening of the first chutes.
I know, it sounds silly, but just remember the aircraft windshield tests that failed until someone remembered to thaw the turkeys that they were shooting at the mockups. Sometimes the obvious does get overlooked.
In short, the cure is likely to be worse than the disease.
Truer and truer. When the Founding Fathers put "ex post facto" laws on their not-to-do list in the Constitution, they had unfortunate prior experience driving them. They'd seen people arrested for retroactive violations of sedition laws (and then getting a no-expenses-paid trip to England for their trials), and they knew that a government needed checks to keep from excesses in the name of "keeping the civil peace."
<sigh> The price of freedom doesn't seem to be getting any easier to meet, and the alternative is cheaper, but I'm kind of attached to the neat extra features.
Let's go further than that! Join the Gondwanaland Reunification Movement!
I have to agree.
You see, the other costumed heroes were just that - some had improved capabilities (like Ozymandias), and some had neat devices (like Nite Owl), but in the end they were all people whose costume was primarily aimed at concealing their identities.
Dr. Manhattan was different... since he was no longer entirely human he was no longer affected by human norms and values (watch how his clothing becomes sketchier from his early days to the "present").
I thought it was a pretty cool way of showing how much he'd diverged from his original self without blabbing it out loud.
Let's leave out the legal ramifications here, and let's not go to the hysteria of "he's being thrown to the wolves to protect management" or "he's an evil hacker who shut down the city government networks."
When it comes down to it, one has to ask what Childs' job was. He was supposed to manage the network for the San Francisco city government.
As a result, he was supposed to implement policy as communicated to him by his bosses... but he also had the latitude to take actions to support the spirit of those policies where the right action was unclear. And yes, this is a Pollyanna-esque (is that a word?) view of the situation, but it leaves out the concept of malice as the driving force for either side - because it didn't start out as a plan to shut down the city.
Somehow it morphed into him becoming the sole support for the network routers, be it through arrogance ("I can't believe anyone else would do this right!") or being the only one available ("There's nobody else who works here who even understands the need!"), and at that point this became an incident waiting to happen.
So, either he refused to do his job (at which point he would have deserved to be fired), or his job was such that he was prevented from doing it (at which point professional ethics would have suggested his resignation - or at least, that's what engineering associations would have recommended in similar scenarios).
Instead, he stayed on and we have the current state of affairs.
What's the difference, Professor Falken?
I sent an E-mail to my representative, and here's what it said:
It may have the same effect as shouting into a vacuum, but as citizens, we need to let our displeasure be known - now and at the ballot box.
When they call this a "compromise" bill, they aren't kidding. It will compromise our civil liberties, by letting the telecoms know that they can get away with helping illegal actions scot-free.
I worry that this will receive strong bi-partisan support, because a future Democrat administration will see the advantages of this, and want it in place in advance.
"Overreaction is what governments do best!"
I spoke in a different post about "detestable, contemptible, and atrocious." Here's a prime example.
1) The case of Megan Meier is an anomaly. A pair of PARENTS decided to put this kid through an emotional wringer to screw up her life.
Detestable, contemptible, and atrocious? Yes. A widespread case? I don't think so. A sound basis for a law making it illegal? I doubt it.
2) Knee-jerk reactions, especially in an election year, are to be expected, particularly by a legislature that is sharply divided along partisan lines. Either party will want to use this as a tool to stay in office.
Detestable, contemptible, and atrocious? Yes. A widespread case? Yes - along with anti-flag-burning amendments, laws requiring the rating of video games and bills proposing convicted sex offenders to be put on 24-hour electronic surveillance for life. A sound basis for a law making it illegal? Don't I wish.
"If you strike me down, I shall become more powerful than you can possibly imagine."
... Ruining other lives because you're on a mission for some sort of revenge is never a good thing, never.... Why not? It's been good for the Bush administration...Actually, you won't get modded down. What will happen will be even more depressing: you'll get modded up... as "+4, Funny."
This was a well-written article about a good experiment.
I went through a similar situation where I tried to introduce my mom to Linux by setting her up with Mandrake 8.1. It was a good distro - at least for me, a software developer - but Mom tends to be somewhat terrified of high tech, and after valiantly trying to do things, she just got fed up and asked me to install Windows.
One of her biggest problems was that Mandrake installed 3 different web browsers, 2 mail clients, and the proverbial "partridge in a pear tree." The availability of these browsers was fine for me, but Mom got confused, flustered, and finally gave up.
I'm thinking of trying again in the next couple of months - but this time with SymphonyOne, which offers her more of a "here's what you do," rather than a "what do you want to do?" approach. I'd feel like I was in a strait-jacket, but it'll probably work much better for her... and (hopefully) will get her using her computer more.