>> Pro tip: If I can answer 20 long-division questions correctly, I can
>> probably answer 2,000 long-division question correctly. It'll just take
>> me 100 times longer. :-P Thus, there's no real point to actually
>> *making* me answer 2,000 questions...
>
> Yes, but if you (ok, well, some other poor sod) can answer only 10 out
> of 20 long-division questions correctly, then doing 2000 of them might
> help to push that ratio to maybe 19 out of 20.
>
> And because even maths teachers don't usually base their way of teaching
> on stochastical methods, they'll just let every pupil do the 2000.

More like "it keeps the students quiet so we don't have to think up any 
*real* tasks for them to do".

>> I was just having a chuckle about my science teacher whining about how I
>> "don't apply myself" in class. His final comment was "more effort
>> required". I notice he was the only teacher who forgot to actually fill
>> out the performance ratings in the school report. MORE EFFORT
>> REQUIRED! :-P
>>
>> This amuses me, of course, because I got a B grade for my science, a
>> grade which is apparently unprecedented in the history of the school.
>> Yeah, I really need to "apply myself" more. :-P Self-important idiot of
>> a teacher...
>
> Heh, maybe he only tried to keep up the morale of the other pupils.
>
> "Why do we have to do all the homework when Andrew doesn't?"

No, he told everybody they were doing really badly, regardless of how 
good or bad their work was.

And when I went over and told him I got a B, he was all like "see, I 
always said you'd do well". NO YOU DIDN'T! You told me I would likely 
fail! "I only said that to motivate you." WTF? Telling people they're 
hopeless is NOT MOTIVATION!

Self-important dick... Man, everybody hated that guy.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 21/08/2011 10:37 AM, Orchid XP v8 wrote:
> And when I went over and told him I got a B, he was all like "see, I
> always said you'd do well". NO YOU DIDN'T! You told me I would likely
> fail! "I only said that to motivate you." WTF? Telling people they're
> hopeless is NOT MOTIVATION!
>
> Self-important dick... Man, everybody hated that guy.

Recurring dream: Going back in time to school with the knowledge and 
confidence I have now. But then I would probably see what sad examples 
of humanity the male teachers were and give up in disgust.
At least you probably weren't belted (beaten with a leather belt).

-- 
Regards
     Stephen

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>> What part of
>>
>> | U x V | = |U| * |V| * cos a
>>
>> do you *not* understand? :-P

> Would be a lot simpler if the damn stuff you have to use it in
> "understood" all that shit, natively. The problem I always run into is
> that you can find a perfectly comprehensible form of something some
> place, but it is only applicable is you a) do it by hand, or b) know how
> to derive some completely bloody different set of equations, that the
> damn computer will understand. Its like knowing, sort of, how to speak
> some obscure Chinese dialect, but then finding out that you need to
> *write* the information down in German, which for which the only work
> you know is the one applying to yourself, Dummkopf.
>
> Well, not exactly the same case, but if you don't have all the other
> stuff in between the two concepts, understanding what the math is doing
> in the "human" version won't get you any closer to understanding how the
> hell the computer needs to deal with it.

I'm having difficulty following what you're trying to say here.

> The original post in this, describing deriving the two equations needed
> for Mandelbrot, from the original non-computer usable one, is a perfect
> example. My reaction is, "Show the math, step by step, because WTF?" lol

Yeah. All the textbooks advanced enough to talk about complex dynamical 
systems assume that you *already* know everything there is to know about 
complex numbers (a much less advanced topic, comparatively speaking).

The first equation *is* useable in some software packages. But usually 
you need to expand out the real and imaginary parts seperately - a step 
which isn't mentioned anywhere and isn't described in any detail because 
it's presumed to be "obvious".



I assume that was a rhetorical question, but I'll answer anyway...

Start with Z^2 + C. Assume that Z = X + Y i, and C = A + B i. For that 
is what complex numbers are: a real part, and an imaginary part. 
(Explaining *that* is a whole /other/ essay...)

Substituting into the original formula, we have

   (X + Y i)^2 + (A + B i)

We can open the second pair of brackets without changing anything:

   (X + Y i)^2 + A + B i

Now, the first pair of brackets. The binomial theorem tells us the 
answer in canned form, but it's perfectly easy to do it all by hand. 
Since K^2 means the same thing as K * K, we can say

   (X + Y i) (X + Y i) + A + B i

Opening the first pair of brackets, we have

   X (X + Y i) + Y i (X + Y i) + A + B i

Opening the first pair of brackets, we get

   X X + X Y i + Y i (X + Y i) + A + B i

Obviously X X becomes X^2:

   X^2 + X Y i + Y i (X + Y i) + A + B i

Do the same sort of thing with the last pair of brackets:

   X^2 + X Y i + Y i X + Y i Y i + A + B i

The Y i X term is of course the same thing as X Y i:

   X^2 + X Y i + X Y i + Y i Y i + A + B i

Since there are two X Y i terms, we can gather them together:

   X^2 + 2 X Y i + Y i Y i + A + B i

The Y i Y i term is the same thing as Y Y i i. And that's obviously the 
same as Y^2 i^2. Now, BY DEFINITION, i^2 = -1. And Y^2 * -1 = -Y^2. So 
we have

   X^2 + 2 X Y i - Y^2 + A + B i

If we now put all the terms containing "i" into one pair of brackets, 
and everybody else in other pair of brackets, we get

   (X^2 - Y^2 + A) + (2 X Y i + B i)

This is still the same formula, we've just added some redundant brackets 
and rearranged the order a bit. Now, if we take everything in the left 
set of brackets and divide through i, we get

   (X^2 - Y^2 + A) + (2 X Y + B) i

This is still the same formula. (If we open the brackets, we get back 
what we had a few lines ago.) But now we have two purely real 
subexpressions, which a computer can calculate:

   X := X^2 - Y^2 + A
   Y := 2 X Y + B

QED.



I saw pictures in books of the "cubic Mandelbrot", and tried all sorts 
of modifications of the formula to make it cubic instead of quadratic. 
Of course, I didn't know about the binomial theorem yet. In order to get 
a cubic, you need to do this:

   (X + Yi)^3 + (A + Bi)
   (X + Yi)(X + Yi)(X + Yi) + A + Bi
   X(X + Yi)(X + Yi) + Yi(X + Yi)(X + Yi) + A + Bi
   X^2(X + Yi) + XYi(X + Yi) + Yi(X + Yi)(X + Yi) + A + Bi
   X^3 + X^2 Yi + XYi(X + Yi) + Yi(X + Yi)(X + Yi) + A + Bi
   X^3 + X^2 Yi + X^2 Yi + X Y^2 i^2 + Yi(X + Yi)(X + Yi) + A + Bi
   X^3 + X^2 Yi + X^2 Yi - X Y^2 + Yi(X + Yi)(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + Yi(X + Yi)(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + XYi(X + Yi) + Y^2 i^2(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + XYi(X + Yi) - Y^2(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + X^2 Yi + X Y^2 i^2 - Y^2(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + X^2 Yi - X Y^2 - Y^2(X + Yi) + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + X^2 Yi - X Y^2 - X Y^2 + Y^2 i + A + Bi
   X^3 + 2X^2 Yi - X Y^2 + X^2 Yi - 2 X Y^2 + Y^2 i + A + Bi
   X^3 + 2X^2 Yi - 3 X Y^2 + X^2 Yi + Y^2 i + A + Bi
   X^3 + 3X^2 Yi - 3 X Y^2 + Y^2 i + A + Bi
   (X^3 - 3 X Y^2 + A) + (3 X^2 Y i + + Y^2 i + Bi)
   (X^3 - 3 X Y^2 + A) + (3 X^2 Y + Y^2 + B)i

   X := X^3 - 3 X Y^2 + A
   Y := 3 X^2 Y + Y^2 + B

As you can see, the result looks *nothing like* the quadratic case. If 
you didn't know what the derivation procedure was, you would have no 
idea why this is so.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>> Can you imagine anything more MIND-NUMBINGLY BORING than staring at a
>> sheet of 40 long division problems? YES, I GET IT! I KNOW HOW LONG
>> DIVISION WORKS! STOP BUGGING ME ALREADY! >_<
>>
> Uh, no. The reason you have to do sheet after sheet of utter bullshit
> like that was because your school, like mine, catered to the one idiot
> in the room that didn't grasp the idea after the first 3 times.

That still doesn't make sense. We each got given a textbook. We each 
work through that textbook as quickly or slowly as we please. (Although 
if you're too slow, you get yelled at.) If you get too much stuff wrong, 
they make you redo it, or redo something from a similar textbook.

Which should *still* mean that you only have to do 2,000 questions if 
you're actually that slow at getting it. But noooo...

When math is treated as some kind of punishment, why is anybody 
surprised that nobody wants to do it?

> I refused to do any more of them, they sent me to a school psychologist,
> where they then jumped to several screwed up conclusions, based on, of
> all things, the fact that crayons got handed out alphabetically, so I
> always ended up with the black one (they later adjusted this so people
> got the chance to use other colors, but one wonders how many others
> where misdiagnosed with some sort of disorder over that silly thing),
> and my house **actually** had boxes around the trees and windows, so I
> was "disturbed", because I, "drew boxes around things and used black to
> do it". By the time the idiots figured out that the real problem was
> that I was bored to death of the crap they kept handing me to do, they
> had managed to put me a whole year behind in math. Luckily, I was like
> 6-7 years *ahead* in reading. lol

Did you just say "the education system is fundamentally broken"?

I remember seeing a psychologist. Part of the conversation went like this:

"What were you thinking about just now?"
"Crystals."
"OK. Tell me about crystals."
"Nah, you wouldn't really be interested. I can tell."
"How can you tell?"
"The frames of your glasses are grey."

Now, considering I was, like, 9 years old, most people would have just 
laughed that off. This guy looked actually terrified that I was able to 
READ HIS MIND just by the colour of his glasses. Literally, he was 
desperately trying to figure out how I knew. Obviously, I didn't "know" 
anything. I was just being daft.

It's like nerd-sniping. http://xkcd.com/356/ Apparently psychologists 
are really, *really* easy to confuse.

>> I was always quite bad at arithmetic. I still am. The difference is that
>> today, I use a frigging *computer* to do the work for me. :-P My job is
>> to figure out what the actual calculation is; the computer does the
>> mundane work of actually *running* it.
>>
> Yeah. Same here, more or less. I can't do math in my head worth shit,
> and I hate doing it by hand on paper.

I find doing /arithmetic/ on paper to be trivially easy. It's just not 
particularly interesting. I quite often do /math/ on paper - mainly due 
to the difficulty of typing most of the notation on a computer.

> Shortcuts would help, but you don't get those in school.

I haven't been to school in a long time. I hear they no longer teach 
"mathematics". They teach "numeracy". And it doesn't involve knowing how 
to add and subtract and multiply and divide. They only teach you how to 
/estimate/ results.

I have no idea whether this is true, or just what the media tells us.

>> I spent almost all of my time at
>> college sat in the library, absorbing everything I could lay my hands on.
>>
> Should probably do that myself. The problem is figuring out where the
> hell my gaps are to start with, then finding something that doesn't bore
> the hell out of me reading it

My problem is that I know a lot of quite advanced (i.e., interesting) 
mathematics, but I don't know some of the stuff that comes before that. 
Normally you would learn the simple stuff first, gradually moving on to 
the more advanced stuff. Which means there are books full of simple 
stuff, and books full of advanced stuff. And to fill the gaps in my 
knowledge, I'd have to read one of the "introductory" books where I 
already know 95% of what it says, just to learn the 5% that I haven't 
stumbled across yet.

> like, I don't know, something directed at
> "application" of the math, not just how the hell you write the
> equations. I think this is a huge damn failing in "text books", and
> classes in general. Its one thing to hand someone a formula, or even a
> stupidly simply thing you want someone to do, like graphing a line, but
> give no possible context for why the hell anyone would bother to do so,
> save maybe some historical context. Its quite a bit different when you
> "need" to know, for your own purposes, how thick a rope will get, wound
> onto a spindle, and thus how big the spindle needs to be, versus just
> having someone hand you a problem, and ask you to give them a result,
> when your only thought is likely to be, "Why the hell do I need this?"
> Mind, that was physics class, while the normal math classes don't even
> give you problems that come even remotely close to that interesting. In
> any case, I don't remember the equations. lol

It depends.

Sometimes I just want to solve a specific problem. But I do also enjoy 
reading about mathematical objects and their properties just for the 
hell of doing so. It's interesting. (I suspect if you had to do this for 
an actual *test*, it would become much less interesting...) For example, 
reading about polynomials and all the patterns and symmetries they have. 
And /then/, when you find yourself needing to solve some problem that 
happens to involve polynomials, you already know quite a bit about them, 
and therefore where to start looking for a solution.

> Nah.. Stupidity desirable? How could that ever be the case. I mean, its
> not like, at least in the US, there are politicians banking on it,
> products sold based on playing fast and loose with as little information
> as possible, or active attempts to undermine education. That is just
> absurd! Or, in reality, as I put it a bit ago when talking about the US
> version of libertarianism - "The concept is simple, lower taxes,
> resulting in poorer schools, resulting in closed schools, and since its
> everyone's 'right' to choose to be ignorant, the fact that 90% of the
> population is stupid has nothing to do with the failure of the system,
> its entirely the fault of people not moving to where the only two
> schools still open are located."

WOW. O_O

> Dear old Madison would be having a
> heart attack at this shit, if he hadn't had the sad misfortune of dying
> in 1836.

...irony...

> I seems only fitting that by 2036 the US might be so fucking stupid that
> they couldn't build a log cabin from his time, let alone work out why
> living in one would be preferable to huddling under a tree, or wearing
> animal skins in a cave... Or, so it sometimes seems the trajectory of
> some of this stupid shit is headed.

I think sometimes it's hard to tell whether the entire world is stupid, 
or just a vocal minority.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>> Self-important dick... Man, everybody hated that guy.
>
> Recurring dream: Going back in time to school with the knowledge and
> confidence I have now. But then I would probably see what sad examples
> of humanity the male teachers were and give up in disgust.

There was a kid at school who used to bully me constantly. I used to 
dream about doing terrible things to him.

And then one day I thought to myself "Wait a minute. Your dad is an 
alcoholic, your whole family lives on welfare in a rundown council 
flat... there is basically NOTHING I COULD DO that would make your life 
anybody miserable than it already is. HAVE A NICE DAY!" :-D

> At least you probably weren't belted (beaten with a leather belt).

I do remember two kids got the slipper. (You're probably not allowed to 
do that, but they did.) The first kid stood there and took it like a 
man. The second was a screaming wreck.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 8/21/2011 0:41, Le_Forgeron wrote:
> Below IP is not a network (in IT terminology), but links.

It depends on what IP travels over. If it's IP-over-ATM, there's most 
certainly a network there. If it's IP over dial-up, less so.

> (such as video distribution: better skip a frame than freezing.

Sure. And the point I was trying to make is that it's better to reserve 
bandwidth than skipping a frame, but IP doesn't support that.

> TCP covers 95% of applications, but there is more than TCP under the sun.

Yep. And I'm saying that the primary reason people don't use TCP is to 
compensate for a lack of things like bandwidth allocation and routing 
assurance. Nobody used TP4 over a network that will work fine with TP0.

-- 
Darren New, San Diego CA, USA (PST)
   How come I never get only one kudo?

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On 8/21/2011 2:37, Orchid XP v8 wrote:
> More like "it keeps the students quiet so we don't have to think up any
> *real* tasks for them to do".

I will say that I never had an art class before grad school that actually 
wasn't of the busywork type. Very few of those sorts of classes actually 
taught anything. I would have loved to go to music class where they actually 
taught some music theory or something, or an art class where they talked 
about the proportions for drawing people or the golden rectangle or 
something like that.

-- 
Darren New, San Diego CA, USA (PST)
   How come I never get only one kudo?

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On 8/21/2011 3:38, Orchid XP v8 wrote:
> NOTHING I COULD DO that would make your life anybody

Sounds like a Holly Lisle book.

Gabriel: "But God, the devils are breaking their contract. Thay're cheating!"

God: "Of course they are, Gabriel. They're devils."

Gabriel: "But ... but ... you should punish them!"

God: "They're already damned to hell, Gabriel. What would you have me do?"

A very amusing book, overall. I recommend at least the first 2 or 3 for 
silly light reading.

-- 
Darren New, San Diego CA, USA (PST)
   How come I never get only one kudo?

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On 21/08/2011 04:06 PM, Darren New wrote:
> On 8/21/2011 2:37, Orchid XP v8 wrote:
>> More like "it keeps the students quiet so we don't have to think up any
>> *real* tasks for them to do".
>
> I will say that I never had an art class before grad school that
> actually wasn't of the busywork type. Very few of those sorts of classes
> actually taught anything. I would have loved to go to music class where
> they actually taught some music theory or something, or an art class
> where they talked about the proportions for drawing people or the golden
> rectangle or something like that.

In our music class, they made us play musical instruments.

Oh, until the old teacher left and we got that *other* person, who 
couldn't make kids do stuff for toffee...

We didn't even *have* art classes. Though we did have pottery classes, 
where we actually made pots. I still have some of them.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Le 21/08/2011 17:04, Darren New nous fit lire :
> Nobody used TP4 over a network that will work fine with TP0.

Unless the "network" is only a part of the path.
(Interconnecting 2 Lan/Ethernet with pair of X.25 links: the system on
the lan are probably better using TP4 and the X.25 gateways just have to
push the clnp packets in the X.25 links. On these gateways, it's
probably simpler to have the application use also a TP4, even if they
could simplify the connections crossing only X.25 to use only a TP0).

Now, if I could have convinced the customer to use IS-IS on the
redundent four gateways per lan, that would have saved a few nightmares
about the routing table on the lan... and less money for my company on
the long run ;-)

Regarding IP-over-ATM, it depends from where you look (as you are
smashing the model inside another instance):
From IP (layer 3), ATM is simply a link (or set of links) (layer 2)
From ATM, it is providing nearly level 4 service. (and even more)

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