Friday, September 30, 2005

Algebra Eats Trignometry

If trigonometry and algebra got in a fight, who would win?

Ever since the ancient Greeks codified these disciplines, the answer to this question has been unknown. Now it would seem we have an answer. And things don't look good for old trig.

This story at caught my eye because how often do you see an incredible breakthrough in a subject you were taught in JUNIOR HIGH SCHOOL? You know when that happens, something major has gone down.

But if the claims being made in a new book are true, trigonometry classes the world over may be looking at dark days. An Australian mathematician has re-analyzed trigonometry starting from the most basic premises, and has discovered that we've been working with a flawed framework all this time. Trig doesn't need sin, cos, tan or any of those other weird little keys on your calculator. Nope, nor does it have to be as hard as it is. It only has to be as hard as algebra. (I always found trig and geometry a walk in the park compared to algebra, so this is not personally the greatest news.)

As an avid - though amateur - mathophobe, I'm in no position to evaluate the following statements for correctness, but the new book by NJ Wildberger claims:

The new form of trigonometry developed here is called rational trigonometry, to distinguish it from classical trigonometry... An essential point of rational trigonometry is that quadrance and spread, not distance and angle, are the right concepts for metrical geometry (i.e. a geometry in which measurement is involved). Quadrance and spread are quadratic quantities, while distance and angle are almost, but not quite, linear ones. The quadratic view is more general and powerful...

When this insight is put firmly into practice, a new foundation for mathematics and mathematics education arises which simplifies Euclidean and non-Euclidean geometries, changes our understanding of algebraic geometry, and often simplifies difficult practical problems.... although the actual definitions used in this text are independent of distance, angle and the trigonometric functions. They are ultimately very simple, based on finite arithmetic and algebra as taught in schools.

New laws now replace the Cosine law, the Sine law, and the dozens of other trigonometric formulas that often cause students difficulty.... The derivation of these rules from first principles is straightforward, involving some moderate skill with basic algebra. The usual trigonometric functions, such as cos θ and sin θ, play no role at all.

Rational trigonometry deals with many practical problems in an easier and more elegant fashion than classical trigonometry, and often ends up with answers that are demonstrably more accurate. In fact rational trigonometry is so elementary that almost all calculations may be done by hand. Tables or calculators are not necessary, although the latter certainly speed up computations. It is a shame that this theory was not discovered earlier, since accurate tables were for many centuries not widely available.

The mind (at least my mind) reels. I wonder what else we've gotten wrong? I'm hoping some English professor will check in soon reporting the long-theorized existence of the verbless sentence. (If so, then I happy.)

Tuesday, September 20, 2005

"High end productivity at your fingertips!"

Hand in hand with my love of old technology is my love of cheap technology. Now, I have plenty of experience that tells me that cheap gadgets are worth what you pay for them, often less, but that never seems to dull the siren song of some gizmo that does X Y and Z all for the low, low, price of...

Anyway, being a cheap tech aficionado, I've encountered the iConcepts line of PC products a few times. iConcepts is a low-cost line of peripherals from a Chinese company called Sakar (which I believe must be an Asian-inflected form of the English word "sucker"). Sakar makes nifty little gizmos that are too cheap to resist, but alas, are also too cheap to do what you bought them for.

My first run in with iConcepts was when I was in the market for a digital camera. I wanted something in the 1 megapixel range with a few extras, like webcam ability, and possible audio & video recording. I picked up their slim-line digicam and spent a couple of days trying to get it to work with any version of Windows I could get my hands on before giving up and returning it to the outlet store for my $20 back. (I eventually wound up getting a BenQ mini cam - the DC1300 - that is still serving me faithfully.)

Buying ultracheap tech is a little bit like walking into CompUSA. You know that no matter how simple and straightforward your needs are, they are going to find a way to disappoint you. There's that breathtaking micro-moment when you are both wondering whether this time might be the time you actually get what you wanted, and wondering how exactly they are going to keep you from getting what you wanted. It's the way I imagine Charlie Brown must feel every time he sees Lucy holding that ol' football.

So that's what I was feeling today when I plunked down my debit card for an iConcepts Wireless Optical Keypad Mouse. I'd been wanting a wireless optical mouse to use with my laptop, and although this one was bigger than I'd wanted, the built-in keypad made it irresistible. As with most laptops, there's no built-in numeric keypad on my Latitude. If you need a keypad, you have to use the main keyboard keys with Num Lock on, which puts about half your keyboard out of commission for anything other than numeric entry, yet still sucks as a numeric entry tool.

I've been learning Blender, the open-source 3-D modeling program, and they say the best way to use the program is with one hand on the keyboard and one on the mouse. Blender uses the numeric keypad for really essential and frequently used commands, so this device seemed like the perfect tool. I could use the mouse and click the keypad buttons with one hand, while still having access to the full keyboard with the other hand. I'd be stylin'!

So I get the wireless optical keypad mouse back to my desk, pry it out of the "everyone's a crook!" blister, and plug it in. Nada. The little red light on the bottom doesn't come on. So I change the batteries, thinking that maybe the ones that came with it are just dead. No dice. Then I see it:

There's a plastic shield that covers the keypad. The top part of the plastic shield is clear. The bottom part is textured, so it's more translucent than transparent. And hidden behind the translucent section is a tiny switch, with two labels: "Mouse" and "Keypad." I pry off the cover, flip the switch from "keypad" to "mouse," and the little red light comes on. After that, the mouse works fine.

So you can't use the keypad and the mouse at the same time. There goes my anticipated Blender workflow, and truthfully, the whole reason I bought this particular unit in the first place.

I guess what bugs me the most about this incident is how much of a science modern companies have made out of caveat emptor. Just because I saw device that had both a keypad and a mouse, why did I expect I'd be able to use both devices at the same time? I can almost hear Sakar's justification for thwarting my expectation:

"Certainly we are under no obligation to point out this 'feature' of the product anywhere on the package! Why, you can see the switch right there, albeit hazily, behind the clear plastic cover that suddenly becomes not-clear where it covers the switch! You say the pictures on the package of the product being used also hide the switch from view? Merest coincidence! Do you think we designed the product and packaging this way just to obscure this glaring flaw... er, feature... as much as possible? Oh, all right, we did. But it worked! We've got your money! Woo hoo!"

I will say this for Sakar - whoever writes the copy for the packages may be a little less than forthcoming with important technical details, but he or she has the soul of a poet. Truth be told, once I read the package's declaration that the wireless
optical keypad mouse "makes your cursor glide across the screen like butter on ice" there was just no way it wasn't ending up in my briefcase.

BTW - I'd include a picture of the product from Sakar's website, but the wireless optical keypad mouse (Part # M07017) does not currently exist on their website. Neither Google nor I could find it. Supposedly this is just another example of them living by their motto: "Setting New Standards of Quality."

Friday, September 16, 2005

Cross-Eyed Mice

The computer I use most these days is my trusty Dell Latitude LS sub-notebook, a slim and light 500MHz PIII machine. It's still running Windows ME, which helps ensure I keep up with my daily dose of pain and suffering.

I installed ME because at the time I bought the computer I was still using a scanner that had no drivers for anything but Windows 9X. (But that's a story for another time.) Also, I was worried that the machine was under-powered to run W2K, XP was not officially supported, and I had heard that ME was the best of the 9X line for dealing with digital video. I wanted to be able to tinker with video stuff on this machine. Curiously, while I can capture DV and edit it just fine,
a bug in Windows ME prevents me from getting back out onto tape. Oh well.

Anyway, the notebook, like many others, has a VGA out port on the back. I wanted to use this port to see if I could run the machine with a dual display. When I'm at home or the office, it would be nice to plug in a monitor and have the expanded desktop of a dual display to work with.

For a while, I thought it wasn't possible, but then I discovered a driver from Dell that actually supported the two displays! For once I thought I was in luck - one of my older devices not only did exactly what I wanted, but it was something supported by the manufacturer.

So I installed the driver, fiddled with it, and got the dual-display up and running.

There's just one little catch.

The display driver has a bug in it. Windows and icons can be moved from one screen to the other, but the MOUSE POINTER always stays on the main screen. If I try to move it onto the second screen, it wraps around and appears back on the main screen at the opposite side. In this weird state, the mouse actually ACTS on the second screen - I can work with windows, move things, click & drag, etc. - but I have to guess at where the mouse is positioned, based on the pointer's position on the main screen.

In practice, this makes the second screen impossible to use. Just like the old Howard Jones song... "You can look at the menu / but you just can't eat, you can feel the cushion / but you can't have a seat..."

And like the song says, no one ever is to blame. Think there's any way to get a fix in a 3rd party device driver for a machine that's past 5 years old? There isn't. But then, that's life on the edge... the SUPERANNUATED edge.

The reason I bring all this up is that today I discovered something that gives me new hope I can get this to work. It's called Powerstrip from a company called Entech. These guys are like the uber-gurus of display driver technology. I found them while searching for a quick way to switch screen resolutions on my laptop when moving between the built-in display (800 x 600 max) and an external monitor, which I do several times a day. They make a tool called Multires, which is like an enhanced version of the old Windows power toy that gave you a system tray icon for one-click resolution switching. They also have a free screen-rotator utility called iRotate, but I haven't tested that out yet.

Even if Powerstrip doesn't solve my problem, it's a cool utility - it lets you do all kinds of stuff with your display adapter, even if the manufacturer didn't specifically build the capabilities into the driver. Don't know if I'll pay for it though if it doesn't fix the mouse pointer bug.

I'm experimenting with Powerstrip now to see if it will do any good on my laptop. I'll keep you posted.