On 8/19/2011 5:00 AM, Invisible wrote:
> As part of the drive to empty our house of useless crap, I was going
> through some of my old college work last night. Ah, the memories.
>
> I still chuckle at my first few programming assignments. We were
> learning to use Borland Turbo Pascal 5.5 for MS-DOS. The guy teaching us
> only found out two weeks earlier that we was taking the class, so he had
> two weeks to learn Pascal out of a book. Frankly, they should probably
> have just given us that book! (Also, his name was Frank.) He wasn't
> /bad/ at teaching, but it was somewhat baffling to walk into a classroom
> and discover that I know more about the subject than the lecturer does.
>
> The comments on my first assignment indicated that it works well, "and
> you've even added a few extra procedures you weren't asked for" (in
> other words, I factored the problem more thoroughly), "but comments are
> rather sparse". Considering that the entire source code print out was
> literally 3 pages long, there's not a hell of a lot to comment on. No
> non-obvious design decisions or tricky invariants to document. If you
> understand Pascal, the code is pretty much self-explanatory. It's a
> first-year college assignment FFS!
>
> My second assignment is even more amusing. The actual phrase the
> lecturer used was "...the program works, but is a little overly complex
> for mere mortals like me to understand." Oh, I'm sorry, I thought you
> were supposed to be the frigging *expert* that we've all paid good money
> to be taught by! :-P
>
> In fairness, as well as writing the code for the actual assignment, I
> did also write an entire library module that's triple the size of the
> main program, and which allows me to print nicely formatted output. (I
> forget the exact details now. I think it was just number alignment so
> all the decimal places line up.) But I put it in a separate source file
> and made it really easy to read the main program without having any idea
> how the library actually works. And I put comments in the library
> explaining what each procedure does (not that the names didn't make it
> self-evident anyway).
>
> Then again, splitting a program into more than one module was beyond the
> scope of our course. (!) We were never taught the syntax for doing this.
> (It's not like C where you just write more files. In Pascal the main
> program source file has a different structure to library modules. You
> have to declare the public interface, for one thing...)
>
> This experience of knowing what the lecturer is going to teach us before
> he even opens his mouth turned out to be a recurring theme of my path
> through college and university. At the time I just felt smug for being
> better at Pascal than Frank was. By the time I was in my 3rd year at
> university, I was beginning to feel frankly a little outraged that I was
> being charged vast sums of money (tens of thousands of pounds, more
> money than I will ever own) to listen to lecturers who can't speak
> English properly and/or don't have a damned clue WTF they're talking about.
>
> (Not /all/ the lecturers were this bad, of course. But some of them
> were...)
>
> In one of Frank's other classes, we learned all about binary and
> floating point. The former was of course no longer news to me. Spend 10
> years poking bytes into the control registers of the 6581 (that's the
> MOS Technology Sound Interface Device [S.I.D.] to you) and you learn a
> thing or two about binary, computers, processors, addressing modes, and
> so on. Floating point was all new to me though.
>
> Then there were the lessons on logic gates. (You had to know what they
> are. You weren't required to know what to do with them or why they
> exist.) Again, old news to me, having already spent years playing with
> physical 7400 chips. Taking a harddrive apart was fun though. (And
> probably ****ing expensive, I should think. This is the era when "4 gig
> drives don't grow on trees".)
>
> And then there were the Quants lessons. ("Quantitative Methods") This,
> as best as I can tell from my lecture notes, was simply an orgy of
> mathematics. It's all in the bin now, but I skimmed through pages and
> pages of statistics, polynomials, linear algebra, fractal geometry, 3D
> graphics, Polish reversed lists, chaos theory, cryptography, sound
> synthesis, and God-only knows what else. I should note that only about
> half of this stuff is directly related to anything in the syllabus. The
> other half is just me doodling while bored in class. (Something that
> DJK, our lecturer, seemed to actively encourage.)
>
> I actually found the sheets of paper where I first performed the
> derivation of the binomial theorem from first principles. You cannot
> simply /tell/ me that (A + B)^2 = A^2 + 2AB + B^2. I have to know /why/
> this is true. And why is it that (A + B)^3 isn't A^3 + 3AB + B^3? There
> must be a pattern. And damnit, I'm going to find it.
>
> This apparently involved drawing a grid:
>
> +------+---+
> | | |
> | A^2 |AB | A
> | | |
> +------+---+
> | AB |B^2| B
> +------+---+
> A B
>
> I think you can see where this leads. Next I drew the same thing, but in
> 3 dimensions. That took me a bit longer. After that, I wanted 4
> dimensions, but was forced to abandon geometry and simply shift algebra
> by hand. The final expression may be small, but some of the intermediate
> terms are quite large, and it's easy to make mistakes as you repeatedly
> copy and manipulate the terms step by step.
>
> After laboriously tabulating the expansions up to (A + B)^9, it became
> quite obvious what the general pattern was. But what the hell are the
> coefficients? Where do they come from? It took at least another hour of
> shifting algebra around and scrutinising my work before I discovered
> that collecting like terms caused the coefficients to be computed in a
> way exactly matching the definition of Pascal's triangle.
>
> DKJ offhandedly told me that I had discovered "the binomial theorem".
> Consulting the library, I learned that this little puzzle had been
> solved over a century ago. AND FOR NEGATIVE EXPONENTS! >_<
>
> This again is a typical experience in mathematics. Any problem which you
> can imagine has either been solved several hundred years ago, or else is
> impossible to solve. There are no easy unsolved problems. I had the
> feeling of being in the centre of a field of ideas, looking at all the
> familiar, well-known stuff. All the new, unknown stuff would be at the
> far reaches of the field, involving problems so complicated I wouldn't
> even understand the language.
>
> The first time we were in the computer lab, DKJ got us to graph some
> trivial polynomials which supposedly represented various things. (E.g.,
> rather than give has a data set representing the company's monthly
> income, he would think up a cubic off the top of his head and get us to
> tabulate and graph that - an easy task for Excel.) I of course was
> bored, and so I ended up graphing my standard incantations. The harmonic
> expansion of various waveforms. The chaotic behaviour of the logistic
> and lambda maps. And so forth. As I recall, it caused quite a stir among
> the chavs I shared a classroom with. For five minutes.
>
> I recall on another day, we had one formula which yields the company's
> income for each month, and another that yields the expenses for each
> month. We were using this to understand the concepts of profit, loss,
> break-even, etc. This was a classroom exercise, so everybody sat
> laboriously tabulating these formulae by hand.
>
> Obviously, I immediately realised that I could directly tabulate the
> company's monthly profit simply by subtracting one formula from the
> other, simplifying the algebra, and then tabulating that. But then DKJ
> wanted us to compute the profit growth rate. I duly tabulated the first
> few months of profit and computed the difference between consecutive
> rows. But I couldn't help feeling that there ought to be a /pattern/ to
> the results.
>
> After about 15 minutes of experimentation, I managed to successfully fit
> a quadratic curve to my data. Literally, I had a formula that produced
> the exact same numbers as the curve I was laboriously tabulating. And
> it's the damnedest thing: the coefficients of this new formula seemed to
> be /related/ to the original formula. Well, it seemed obvious to me that
> such a relationship /should/ exist, but what exactly was its nature?
>
> While everybody else continued the tabulation of growth rate that I had
> long since finished by halving my workload, I picked formulae at random,
> tabulated their growth, and tried to fit curves to them. This is quite a
> lot of work, and I never did figure out exactly what the relationship
> was. At this point, DKJ came over and informed me that I had just
> invented differential calculus, and showed me the general formula for
> the derivative of any polynomial.
>
> I remember being quite suspicious of the perfect constants in the
> expression. "Is that really 3? Or is it 2.986 or something?" No, it's
> *exactly* 3. Needless to say, I went and found a book which explained
> all this in far more detail than the 5 minute conversation I had in
> class, and now I understand /why/ all of these beautiful patterns are so.
>
> While sorting through all this paperwork, there was one assignment I
> felt compelled to keep. The assignment, quite simply, was to write a
> program to "do graphics". Literally, any sort of program you write which
> produces pretty graphics is OK. While DKJ was explaining on the board in
> excruciating detail how to draw a simple rotating square, I was typing
> away at my computer, which I had already got drawing a rotating
> wireframe 3D cube.
>
> It was around this time I was playing with complex numbers. For years
> I'd been baffled by the descriptions telling me that the Mandelbrot
> formula is z := z^2 + c, but the formula is /also/ x := x^2 - y^2 + a, y
> := 2xy + b. Clearly z = x + yi and c = a + bi. But how do you get from
> one formula to the other? It made no sense, and nothing anywhere
> explained it.
>
> One fateful day, I tried applying the binomial theorem to (x + yi)^2 +
> (a + bi). The result is obviously x^2 - 2xyi + y^2i^2 + a + bi. If you
> replace i^2 with -1 (for that is its defined value), you get x^2 - 2xyi
> - y^2 + a + bi. And if you gather all the terms containing i in one
> group and all the others in another, you get x^2 - y^2 + a and 2xyi +
> bi. Divide the latter through i and its 2xy + b.
>
> Suddenly, it clicked. (No, not my spine!) I spent the rest of the day
> deriving complex arithmetic from first principles. Perhaps the single
> most significant moment was in class the next day. I wrote out the
> Taylor series for exp(yi). Replacing i^2 with -1, I discovered that all
> the terms now alternate between negative and positive. And between real
> and imaginary. And collecting all the reals and all the imaginaries, I
> was shocked to find myself looking at the Taylor series for the sine and
> cosine functions.
>
> At which point DKJ informed be that Euler figured that out almost 300
> years ago. Damnit! >_<
>
> Following our lecture on Polish reversed lists, I wrote a small Pascal
> interpreter. It takes a String containing a Polish reversed list, and
> executes it. You can only include purely real constants and the variable
> names "A", "B", "C", "D" and "Z". The values of these variables are
> passed as arguments to the interpreter function. The interpreter
> executes the expression, and returns the result. It even correctly
> handles complex exponents. (Although they would have to be variables.)
>
> Using this, I added to my graphics assignment a fairly large collection
> of fractal types. I don't think I ever got as far as implementing
> Dijkstra's shunting algorithm (to turn normal algebra into Polish
> reversed lists). But I implemented the usual Mandelbrot and Julia
> fractals, with multiple colouring options (escape time, Z-magnitude,
> epsilon cross, binary decomposition, etc.) And also several other
> fractal types; cubic Mandelbrot, lambda, logistic, lambda-exp and
> lambda-sin.
>
> I read in a book about Floyd-Steinberg error distribution dithering. Now
> remember, we're talking about the era where one of my assignments
> actually asked me about the differences between MGA, CGA and EGA. (For
> you youngsters: That's what we had *before* VGA.) We all did our
> graphics work in VGA mode. So, 16 hard-coded colours available. So I
> went ahead and wrote an FS dithering algorithm, and then adapted my
> Mandelbrot renderer to generate images in 24-bit colour and then dither
> them into 4-bit colour. The results at 640x480 were... well, grainy.
> (Plus I think I had a bug somewhere. The algorithm never worked
> /exactly/ right.) But it was still kinda neat.
>
> I actually /sold/ the code for the Mandelbrot fractal to Graham. Not for
> very much money. And, actually, I didn't give him any code. I just sat
> next to him and told him what steps had to happen, and he coded it. I
> can still remember the conversation. "Now run that loop for every
> pixel." "Wow, for EVERY PIXEL?" "Yep. Now you know why it's so slow!"
> (Mine of course did fancy tracing operations to speed it up...)
>
> My rotating cube went on to acquire hidden line removal. *ahem* OK,
> back-face cull. Which took some considerable research and discussions
> with DKJ to get right. Finally I discovered that it wasn't working
> because it /actually matters/ what order you list the coordinates in.
> O_O Once I fixed that, it worked much better. I then went on to add
> surface illumination calculations, using a simple point source and Phong
> lighting. (Each surface is one flat colour.) With only 4 shades of grey
> to play with, it didn't look so hot. But it was quite neat animated.
>
> I vaguely recall that I did implement something with /real/ hidden line
> removal, but I don't know if it made it into my assignment. I'll have to
> read the sources.
>

> animated spirals and so forth. Needless to say, I got a Distinction for
> that. (The highest mark possible.)
>
> It still makes me chuckle that I enrolled for a computing diploma and I
> spent two terms learning how double-entry accounting works. I've got
> Sage printouts and everything. (That's Sage for MS-DOS, mind you.) I
> still remember the login password. It was "letmein".
>
> Then there's heaps of stuff about the relative merits of Ethernet verses
> Token Ring verses something else. As far as I can tell, that's a format
> war that has long since been won my Ethernet. Does *anybody* still use
> token ring? How about ATM, is that still used?
>
> (Come to think of it, *all* of the networking stuff at college was done
> by Novel Netware. Now there's a name I haven't heard in a long time...)
>
> There was one assignment called "computers in society". I didn't
> actually read the assignment, but the lecturer's comments were amusing.
> "A wonderful, almost poetic report. I would be delighted to receive
> writing of this calibre in my professional life." He then goes on to
> offhandedly mention that I didn't actually cover all of the required
> aspects. And yet, I got a Distinction? LOL!
>
> I briefly flicked through the report I wrote. Obviously produced with MS
> Word 6. One sentence has been highlighted and the guy wrote next to it
> "beautiful!" The sentence reads:
>
> "The computer is to information as the power loom is to fabric."
>
> Aside from that, the report isn't well written at all. The tone is very,
> very informal. Like, if you imagine being given a topic, and just
> monologuing about it to your friend off the top of your head,
> videotaping that, and then rearranging the sentences into a more
> coherent order with a word processor... that's what I wrote.
> Distinction. Heh, well I guess it *is* only college...
>
> Also: If you think my spelling is bad *now*, you have literally no idea
> how abysmal it used to be! (E.g., I can spell "abysmal" now. :-P ) And
> that was when I was a teenager, obviously.
>
> Some of the lecturer's comments weren't so friendly. (Actually, some of
> them weren't legible at all. That has to be some kind of fail, right
> there!) Deanna wrote something about "Task A shows technical brilliance,
> however task B is still not acceptable, even on this second attempt, and
> even though I told you which research sources to use. This just isn't
> good enough Andrew. You simply must improve in this area."
>
> Oh? Oh really? You think so? Do ya? Yeah? Well let's see how you like my
> SHREDDER!!! Muhuhuhuh!!! Take THAT, Selby! Yeah, you like that?! Not so
> smug *now*, are we? Now that your acidic little smartypants voice has
> been minced into a thousand tiny pieces. EAT METAL!!! >:-]
>
> Ahhh. To quote H. Granger, "that felt good".
>
> In summary, all the assignments to do with programming computers or
> solving equations gave me exemplary marks. Everything else brought me
> dismal failure. A pattern that was to be repeated at university, come to
> think of it. Well I guess that's tomorrow's tidying task.
>
> I'm particularly proud of the grade I got for my second programming
> module at uni. I got a D for that. (On an A - F scale.)
>
> You see, due to the faculty secretly moving the notice board and not
> bothering to tell me about it, I missed all of my exams that term. Every
> single one of them. And that meant I failed all my modules and had to
> retake them.
>
> Well, all except one. You see, for my programming module, my coursework
> grades were *so* damned awesome that I actually PASSED THE MODULE
> OUTRIGHT WITHOUT EVEN TAKING THE EXAM. And not only did I pass, I got a
> D. Not an F. Not an E. But a D. Without even sitting the exam. I'm *that
> good*, bitch! ;-)
>
> And then there was that database class. The one where Ian says "There
> are various levels of normalisation. I mean, you've got 2NF, 3NF, 4NF
> and even higher ones. But generally, you only really need to worry about
> Boyce-Codd normal form, which says, ANDREW..."
>
> I stand up from my seat in the front row and enunciate "...every
> determinate must be a candidate key..."
>
> "...thank you Andrew. Now as you can see[...]"
>
> That was a feel-good moment. When even the lecturers know you're a
> damned walking encyclopaedia. ;-)
>
> ...and now I'm feeling all nostalgic about the long-lost days when I
> could just sit in a corner reading about Gaussian elimination or
> something while the lecturer blathers on about the role of middle
> management or whatever. I could do crazy math stuff, and people would be
> *impressed* and stuff. My college notes are literally a fermenting sea
> of equations. Serious work mixed up with doodles and advanced math. I
> have nobody to impress anymore. :'{
>
> (Although... I wonder how much of the praise I received was actually
> justified. Especially at college, when I was in a class full of chavs
> who went out and got drunk *every day*. They'd be hung over for the
> morning classes, and mildly drunk for the afternoon ones. Is it any
> wonder the lecturers though I was brilliant?)
>
>
>
> Go on, admit it. You thought this was going to be about SRAM vs DRAM,
> didn't you? :-P
>
You do realize that about half the people here, including me, read this 
and thought, "Man I really hate this guy for being able to do that 
shit!", right? lol No wonder I can't even figure out some "basic" stuff 
I need for some 3D math. The most I ever derived was some non-standard 
way of multiplying two, two digit, numbers, so it wasn't necessary to do 
all the complicatedly silly stuff the teacher insisted we screw with. :p

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