On 20/08/2011 1:30 PM, Orchid XP v8 wrote:

> Doing arithmetic "without thinking" is how we ended up with Verizon Math
> Fail.
>

Straw man, straw man.


>>
>> You don't know how to do mental arithmetic, then?
>
> Nobody ever needs to compute the exact quotient of two 4-figure numbers
> mentally. It's not necessary. You just need to be able to estimate the
> answer with sufficient accuracy.

True.

> (Something which apparently a great
> many people can't do for some reason...)
>

Again true.


>
> Practising something you're going to need to do every single day of your
> life is worth while. Practising something which you will never, ever
> need to actually do is pointless.
>

Well it surprises me that you never need to calculate something when you 
are away from some form of calculator.

> Nobody computes 6-figure quotients mentally. Nobody needs to.
>

True.

>> And BTW adding, subtracting, dividing and multiplying is arithmetic
>> not maths.
>
> ....which was the entire point of my rant, yes. Our "maths" class
> covered *only* arithmetic, and nothing else.
>

You have said before that your school was not a particularly good one. 
But then I was taught arithmetic in primary school and we did not 
progress to mathematics until secondary school.

-- 
Regards
     Stephen

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On 8/20/2011 4:11, Warp wrote:
>    Drawing an accurate antialiased line (of certain width) is not a trivial
> problem. Basically for each pixel you need to calculate how much of it is
> covered by the line. Doing this accurately with integer math only can be
> complicated.

I am not sure you can do it accurately with integer math at all, given that 
there's a "portion of a pixel" involved in there somewhere. At best you'd be 
working in scaled fixed-point.

That said, the AA equivalent of bressenham is Wu:

https://secure.wikimedia.org/wikipedia/en/wiki/Xiaolin_Wu%27s_line_algorithm

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

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On 8/20/2011 2:45, Orchid XP v8 wrote:
>>> OK. Is that for legacy reasons, or because ATM is actually good at
>>> something?
>>
>> ATM is a lot less legacy than IP is. Yes, of course it's actually good
>> at something.
>
> Well, you know, RS232 is a pretty sucky design. But it's still here. That
> *isn't* because it's good at anything. It's because it's widely implemented,
> i.e. legacy.
>
>>> "Yeah, IP really sucks, except for being really flexible." Yes, because
>>> flexibility is a really sucky thing to have.
>>
>> I didn't say that. I said it sacrifices other things in preference to
>> being flexible. There's no resource allocation. There's no way to force
>> a particular route thru the network (well, there is, but nobody actually
>> implemented it in their switches), the addressing sucks for large
>> networks, the address space (in IPv4 at least) is exceedingly limited,
>> remote management of hardware is extremely limited, there's no access
>> control, admission control, or decent rate regulation other than
>> actually dropping packets, etc etc etc.
>
> Most of this sounds like "IP is sucky for managing network hardware". Well,
> no, that's not what IP is for. It's deliberately hardware-neutral.

Well, yes, that's what I said. IP really sucks, except for being 
hardware-neutral. You didn't seem to understand what I was saying before I 
gave the list of many things IP sucks at.

Oh, and it also sucks at things like bandwidth allocation, sophisticated 
routing, and isochronous connections, so it's not just the management part 
that sucks.

 > The idea
> is that you have some infrastructure for controlling your hardware, and then
> run IP on the top. IP is for moving data from A to B.

IP is for moving data from one port on your network to the next port on your 
network, as long as you don't care how long that takes or how quickly it 
gets there.

There's no reservation, no connection control, no access control, and no 
routing control. Even if the hardware fails, you have no way of determining 
how to route around that failure efficiently and promptly.

> If you asked me what was "sucky" about IP, the one I'd probably pick is that
> the entire design philosophy fundamentally assumes that everybody will
> follow the rules.

That too. But tell me how you tell whether the reason you lost your 
connection is whether the remote machine went down, or just some router in 
the middle is rebooting? Tell me how to ask, in IP, whether there's enough 
bandwidth to carry your 64Kbps conversation in each direction with a maximum 
of 85ms delay in each direction. OK, I'm going to start displaying a digital 
movie from the producer to a theater for the next two hours seven minutes: 
How do I pick a route that guarantees me enough bandwidth that the audience 
doesn't see stutters?

You're looking at the things IP does well, and saying "well, it's a bit 
limited here and there." You're not even looking at the stuff that ATM or 
SONET does that IP is never even asked to do.

>> Heck, it doesn't even do roaming, which cell phones have been managing
>> for 10 years.
>
> Cell phones do that by being controlled by a single central authority.

If they were controlled by a single central authority, you wouldn't need 
roaming agreements, now would you?

>> See above. Every packet has the full source and destination address, and
>> there's no information anywhere about the physical network.
>
> Ooo, 64 bits, bit deal.

Well, yes, when you're transporting voice packets a couple dozen bytes long, 
96+ bits of routing information is indeed a big deal.

> It sounds like you're basically complaining that IP isn't
> connection-oriented.

That's one of its failings, yes.

 > You know, if what you're trying to do isn't
> connection-oriented, that's an advantage, right?

Yep. How much of your networking isn't connection oriented? Here's a hint: 
all networking is connection oriented. IP layers non-connection-oriented 
networking on top of that, and then layers TCP to turn it back into 
connection-oriented, poorly. If IP wasn't connection oriented, you wouldn't 
need routing tables on each machine.

> I'm unfamiliar with the data protocols that enable this to be possible. (I
> was under the impression that everybody runs their voice data over IP now
> anyway, so they only need to maintain one big IP network for their voice
> services *and* their broadband offerings...)

In the last mile, that might be true. I'm fairly sure it isn't IP that's 
running on the undersea fibers or bouncing off satellites.  Know how I know? 
There aren't enough IP addresses.

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

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On 8/20/2011 3:49, Orchid XP v8 wrote:
> Seriously though. I was awful at maths when I was at school. Then again,
> when I was at school, "maths" consisted of doing endless arithmetic.

We did that in second grade. What "school" were you in when you were doing this?

> 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! >_<

You realize that most people aren't that smart, right?  I always got crap in 
school for only doing one homework problem of each type, and then I'd say 
"No, I get it, OK."  And everyone would make fun of me, and then I'd be the 
only one to ace the test.

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

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On 20/08/2011 03:58 PM, Darren New wrote:
> On 8/20/2011 3:49, Orchid XP v8 wrote:
>> Seriously though. I was awful at maths when I was at school. Then again,
>> when I was at school, "maths" consisted of doing endless arithmetic.
>
> We did that in second grade. What "school" were you in when you were
> doing this?

Admittedly it was a school for mentally retarded people such as myself...

>> 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! >_<
>
> You realize that most people aren't that smart, right?

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...

> I always got crap
> in school for only doing one homework problem of each type, and then I'd
> say "No, I get it, OK." And everyone would make fun of me, and then I'd
> be the only one to ace the test.

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...

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

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Orchid XP v8 <voi### [at] devnull> wrote:
> The slanted area cut by the line actually has the same area as a 
> rectangle with the same center hieght. (This is why the trapezoidal rule 
> for numerical integration works.)

  That takes care of the situation where the edge of the line crosses the
opposite sides of the pixel. However, you have to take into account
separately the cases where the edge crosses two adjacent sides of the pixel
(in which case the cross-section is a triangle rather than a trapezoid).
And of course the triangle can be either the inside or the outside of the
line, so that has to be taken into account.

  Then there's the special case where *both* edges of the line cross the
*same* pixel. This can happen even if the line width is that of one pixel,
when the line crosses the pixel diagonally (but can also more obviously
happen when the width of the line is less than a pixel). In this case you
have to calculate the area covered by one edge, then the area *not* covered
by the other and subtract them.

  So no, you don't get it "almost for free". Not if you want a high degree
of accuracy.

> A more "interesting" problem is what happens when multiple 
> different-coloured lines overlap...

  What's the problem in that? Just draw them one at a time (taking the
transparency of the antialiased pixels into account).

-- 
                                                          - Warp

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On 8/20/2011 3:49 AM, Orchid XP v8 wrote:
> At the start of the book, you get to do really easy stuff like 3+7. They
> would have several pages of adding, and then a few pages of subtracting,
> then a few pages explaining how multiplication works, and then some
> pages of multiplication, then how long multiplication works, and then
> several pages of progressively harder long multiplication questions.
> Then they might get you to do sums involving multiple numbers of
> increasing size. Then they have a couple of pages explaining about
> negative numbers, then you do progressively more complicated sums
> involving multiple negative and positive quantities. Then they might
> talk about long division, and get you to do a few hundred of those. And
> then division and multiplication with negative quantities as well. Then
> maybe they start talking about fractions...
>
> 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! >_<
>
> Seriously. If you know how it works, do you really need to do it 200
> times over just to *prove* that you know how it works? It's not even
> like it's particularly important to be able to *do* long division; it
> isn't something you're going to need to do every day of your adult life.
> You just need to have a firm grasp of /how/ it works and /why/ it works.
> Once you've got that, practising it on endless question sheets is just
> an utter waste of time.
>
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. 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

> 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. Shortcuts would help, but you 
don't get those in school. You are lucky if you a) stumble over one 
yourself, or b) pass the class while still having difficulty 
remembering, by rote, certain parts of the times tables. The ones that 
"are" good at math, tend to be the ones that do (a), or just have 
stupidly good memories.

> It wasn't until I got to college that I discovered, mainly due to DKJ,
> that "mathematics" consists of something other than just doing hundreds
> of identical long division calculations over and over again. Mathematics
> provides a systematic way of solving puzzles and problems. It lets you
> manipulate and analyse hypothetical entities who's identity (or, indeed,
> existence) is as-yet unknown. Through tools like FractInt, I discovered
> that mathematics can be beautiful. 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, 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

> I suspect it's some combination of math being taught badly, a cultural
> expectation that math is impossible to understand, and a society where
> stupidity is seen as desirable.
>
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." Dear old Madison would be having a 
heart attack at this shit, if he hadn't had the sad misfortune of dying 
in 1836.

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.

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On 8/20/2011 3:55 AM, Orchid XP v8 wrote:
> On 19/08/2011 11:23 PM, Patrick Elliott wrote:
>
>> No wonder I can't even figure out some "basic" stuff
>> I need for some 3D math.
>
> What part of
>
> | U x V | = |U| * |V| * cos a
>
> do you *not* understand? :-P
>
>
>
> Only teasing. ;-)
>
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.

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

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On 8/20/2011 11:55, Warp wrote:
>    So no, you don't get it "almost for free". Not if you want a high degree
> of accuracy.

Actually, I think you do, if you keep the slope of the line positive and 
below 45-degrees. Then you use basic rotations of the algorithm to handle 
other cases. The trick is the line will never go through more than 2 pixels 
in the same column, so whatever doesn't go into the first pixel does go into 
the second picture.

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

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Am 21.08.2011 00:26, schrieb Darren New:
> On 8/20/2011 11:55, Warp wrote:
>> So no, you don't get it "almost for free". Not if you want a high degree
>> of accuracy.
>
> Actually, I think you do, if you keep the slope of the line positive and
> below 45-degrees. Then you use basic rotations of the algorithm to
> handle other cases. The trick is the line will never go through more
> than 2 pixels in the same column, so whatever doesn't go into the first
> pixel does go into the second picture.

Not true - unless you accept diagonal lines to appear thinner than 
horizontal or vertical ones; 45 degree lines of proper width can 
(partially) cover up to 4 pixels per column.

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