Tenkeyless keyboards and the Golden ratio

[spremino]

While I was wondering why so many people find tenkeyless keyboards much more aesthetically pleasant, it striked me that dimensions of tenkeyless keyboard are closer to the Golden ratio:

The golden ratio is ... approximately 1.6180339887.

Source: http://en.wikipedia.org/wiki/Golden_ratio



I haven't got neither a tenkeyless keyboard nor a ruler handy, but those members who do, can check how much I'm right.

[itlnstln]

Dimensions: 356 x 135 x 33mm (14.0 x 5.3 x 1.3in)

This is for the Filco Tenkeyless.

[spremino]

Therefore:

Golden ratio: 1.6
Topre Realforce 86u (14.4 x 6.65): 2.2
Filco Tenkeyless (14.0 x 5.3): 2.6

Well, they are not that close. What about the Model M Space Saver?

EDIT: Model M Space Saver (15.3 x 7): 2.2

Not that close either. Well, I failed to find the secret of tenkeyless' beauty. Thanks anyway.

[itlnstln]

The Golden Rule is:

"Get A Ruler!"

Wait.  Somehow I think I'm doing it wrong.

[elbowglue]

Therefore:

Golden ratio: 1.6
Topre Realforce 86u (14.4 x 6.65): 2.2
Filco Tenkeyless (14.0 x 5.3): 2.6

Well, they are not that close. What about the Model M Space Saver?

EDIT: Model M Space Saver (15.3 x 7): 2.2

Not that close either. Well, I failed to find the secret of tenkeyless' beauty. Thanks anyway.

I got one that has ratio of 1.85, and it's probably the most beautiful keyboard out there.



Sorry for the eyeball burn.

[Phaedrus2129]

The G84-4100 has a ratio of ~2... It's certainly easier on the eyes than my full size Model M.

[Rajagra]

Damn. Now I HAVE to buy a Realforce 23U numpad. At 93x152mm that's a ratio of 1.63, which is pretty darn close to the golden ratio of 1.62 (rounded to 2 decimal places.)

[kode]

The Golden Rule is:

"Get A Ruler!"

No it isn't. Mr. T says it is "The man with the gold... rules".

[didjamatic]

The Tekgadget KP-701 is pretty close.

[itlnstln]

Damn. Now I HAVE to buy a Realforce 23U numpad. At 93x152mm that's a ratio of 1.63, which is pretty darn close to the golden ratio of 1.62 (rounded to 2 decimal places.)

Yep.  It looks pretty golden sitting on my desk.  Well, black gold, maybe.

[ricercar]

Why isn't it: "The man with the gold treats others as he treats himself"?

[illegalsurgeon]

As a mathematician, I can assure you this is not aesthetically pleasing ratio at all, and all the hype is pseudoscientific at best. Just like how there is a conspiracy because Steinway, Yamaha, and all companies make pianos with 88 keys.

Sorry about that. But too many people asked me about how beautiful fractals are (no they are not) and how chaotic chaos is (no it isn't), and this is sort of natural response.

[illegalsurgeon]

But fractals aren't so colourful. :biggrin:

[HaaTa]

Noo, my eyes, they burn!

Grew up near Nelson BC, hippie capital of Canada (well at least for western Canada). As well as popular spot for US war deserters.

[Mental Hobbit]

As a mathematician, I can assure you this is not aesthetically pleasing ratio at all, and all the hype is pseudoscientific at best.

How do mathematicians determine what's aesthetically pleasing?

[illegalsurgeon]

How do mathematicians determine what's aesthetically pleasing?

Sorry, should have clarified further. There are researches done to show that people do not feel this ratio makes "better" rectangles than others.

From mathematics side, it's because many claims about the ratio is quite -- horrible. There are a LOT of numbers, so why (1+sqrt(5))/2? There are many other numbers that have as many interesting (and useless) property as this one. People point to natural patterns but lot of numbers occur in nature, and this is how golden ratio became famous. Also lot of numbers are really close to golden ratio and they could be used for so many arguments, but people don't care about them.

[elbowglue]

Sorry, should have clarified further. There are researches done to show that people do not feel this ratio makes "better" rectangles than others.

From mathematics side, it's because many claims about the ratio is quite -- horrible. There are a LOT of numbers, so why (1+sqrt(5))/2? There are many other numbers that have as many interesting (and useless) property as this one. People point to natural patterns but lot of numbers occur in nature, and this is how golden ratio became famous. Also lot of numbers are really close to golden ratio and they could be used for so many arguments, but people don't care about them.

Are you saying you don't believe in numerology?

[illegalsurgeon]

Indeed. Me, I prefer the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function".

Don't think that one's proven yet, but yes. That number does pop up everywhere. :biggrin:

[Mental Hobbit]

Did you know that after Health Care passes they are putting Obama's eyeball on the back of the 1 dollar bill?

Nonsense. Americans will have to pay with yuan bills then.

[kishy]

Did you know that after Health Care passes they are putting Obama's eyeball on the back of the 1 dollar bill?

Show Image

It'll be the Amero, don'tcha know?

[Phaedrus2129]

As a mathematician, I can assure you this is not aesthetically pleasing ratio at all, and all the hype is pseudoscientific at best. Just like how there is a conspiracy because Steinway, Yamaha, and all companies make pianos with 88 keys.

Sorry about that. But too many people asked me about how beautiful fractals are (no they are not) and how chaotic chaos is (no it isn't), and this is sort of natural response.

Fractals are beautiful...

After an artist goes and paints them.

[ricercar]

Fractals are gross. Remind me of dendrites growing from a cancer.

[itlnstln]

Fractals are pretty lame.  They look like crappy screen savers from Windows 3.1.

[DreymaR]

I'll settle for "graphical representations of fractals can be beautiful"! In themselves, they're just sets of numbers.
 However, I've studied enough mathematics to find the sets themselves and their production aesthetically pleasing...

What makes us link numbers and beauty is our perception. Human perception has a lot of inherent postprocessing mechanisms from the lower levels to quite advanced stuff. And I do think the golden ratio works for our perception in a good many cases. I also agree that it's been hyped as well though.

The classical example is how the Fibonacci sequence approaches the golden ratio. The Fibonacci sequence is found a lot in nature (I just picked up a snail shell with a perfect Fibonacci sequence in my garden!), and a friend of mine who's a designer told me they usually use fibonacci ratios when determining how much larger a headline font should be than a bread text font for instance. Da Vinci's drawings of the human body show that he was very aware of the many golden ratios in a well-proportioned body.

If you insist that the human mind doesn't in fact perceive applications of the golden ratio as aesthetically pleasing in a great many cases, you're going to be quite lonely on your side of the line. And I think you should feel silly there as well.

When it comes to keyboard ratios, keep in mind that you'll be viewing them at an angle! I've heard that the Japanese Go board makers don't use squares but slightly taller rectangles because when you sit down by the board these will be perceived as more square! So adjusting for the cosine of the viewing angle minus a little for your brain's total perception, what do we end up with?

[illegalsurgeon]

I'll settle for "graphical representations of fractals can be beautiful"! In themselves, they're just sets of numbers.
 However, I've studied enough mathematics to find the sets themselves and their production aesthetically pleasing...

What makes us link numbers and beauty is our perception. Human perception has a lot of inherent postprocessing mechanisms from the lower levels to quite advanced stuff. And I do think the golden ratio works for our perception in a good many cases. I also agree that it's been hyped as well though.

The classical example is how the Fibonacci sequence approaches the golden ratio. The Fibonacci sequence is found a lot in nature (I just picked up a snail shell with a perfect Fibonacci sequence in my garden!), and a friend of mine who's a designer told me they usually use fibonacci ratios when determining how much larger a headline font should be than a bread text font for instance. Da Vinci's drawings of the human body show that he was very aware of the many golden ratios in a well-proportioned body.

If you insist that the human mind doesn't in fact perceive applications of the golden ratio as aesthetically pleasing in a great many cases, you're going to be quite lonely on your side of the line. And I think you should feel silly there as well.

I must disagree here. Fibonacci is another thing. It does not really show up in nature. Once you tolerate the errors, something like (4/pi)^2 tends to be lot closer than golden ratio. And if you don't... there is no golden ratio.

And it's a misunderstanding that Da Vinci used golden ratio in his human body drawings, because they are quite off golden ratio. People used to claim that Gutenberg bible was in golden ratio. Too bad it turned out to be 10% off. (Very close to sqrt(2) though!)

There is a reason why fractals are not really mentioned among mathematicians. People think it's a mathematical concept -- well, I would love to know if it was, because there is no definition of fractal. Mathematicians just say some things "look like" fractals, but no sane mathematician would ever put that on a paper. But probably to mathematicians Cantor set is one of the most popular "fractals". Unfortunately, it really cannot be seen. It's just uncountable number of points scattered around. But we don't care, because it is what it DOES that makes it interesting, not because it is a "fractal" (whatever that means.)

Mathematicians do mathematics because fortunately there are countless things more pleasing than golden ratio. If golden ratio was as pleasing as mathematics, no one would be doing mathematics. Even for art -- I really like Escher paintings, because I can see so much that is pleasing and surprising. But drawing human proportional to 1.618:1? It's just a rectangle.

[DreymaR]

I think you're full of it. The Fibonacci sequence showed up in my garden yesterday. And lots of mathematicians talk a lot about fractals. I've been to lectures about the Haussdorff dimensions of various mathematical constructs and physical phenomena for instance, and the word was used incessantly. Just because you're tired with them doesn't mean you get to pull the world of mathematics with you.

Thanks for correcting my misconception of Da Vinci's works. Do you have a link to that point, please?

Let me guess: Are you having problems with your English? You seem a bit unclear at points. That might be it.

[itlnstln]

*Grabs popcorn for the geek fight*

[DreymaR]

You're right - I probably came off much sharper than I... naaah.  

[didjamatic]

Must see movie: Pi - 1998

Golden Ratio, Fibonacci sequence, Number Theory, Weird Computer Stuff, Genius... it's all there.

[Rajagra]

Pi is exactly three!!



Sorry. I had to say that to get your attention. Now calm down everyone.

©Futurama.

[illegalsurgeon]

I think you're full of it. The Fibonacci sequence showed up in my garden yesterday. And lots of mathematicians talk a lot about fractals. I've been to lectures about the Haussdorff dimensions of various mathematical constructs and physical phenomena for instance, and the word was used incessantly. Just because you're tired with them doesn't mean you get to pull the world of mathematics with you.

Thanks for correcting my misconception of Da Vinci's works. Do you have a link to that point, please?

Let me guess: Are you having problems with your English? You seem a bit unclear at points. That might be it.

No, mathematicians do not talk about fractals. Just because third year grade school students learn addition in math class doesn't mean that's what mathematicians do. Do you really think mathematicians get together to talk about fractals? Why would we talk about something we don't even have an definition of? Do you know a fractal when you see one?

There is a good reason why Hausdorff dimension is not generally taught to undergraduates. Because to make sense of it you would need to define Hausdorff measure, and measure is not an easy concept. Do you know what it's used for? It was defined long time before there was word "fractal".

Do you know what "world of mathematics" is?
http://www.mathunion.org/activities/icm/icm-2010-program-structure/

This is 2010 international congress program. Do you see anything related to fractals?

About Da Vinci:
http://www.umcs.maine.edu/~markov/GoldenRatio.pdf
http://www.maa.org/devlin/devlin_05_07.html

[kishy]

This is worse than when people talk about touchpads and I react adversely.

[trievalot]

kaliedascopes are pretty.

[Nonmouse]

Nope.  Based purely upon math.  If you have a line segment a+b, compose of tow shorter line segments, a and b, if the ratio of a+b to a is the same as the ratio of a to b, that is the Golden Ratio.  Mathematically: IFF (a+b)/a = a/b, then a/b  (or (a+b)/a) = the Golden Ratio.  Depends on space time curvature, I suppose (it's likely different very near to a black hole), but not much of anything else.  

The aethestics  of it are another matter...

I believe in a golden ratio, although this number is kind of arbitrary. But just like a good model of something more complex, it probably gets it right. The golden ratio depends on the amount of hydrogen and amount of other gasses in the cloud that collapsed to form our star and in particular our planet, and the distance between this planet and this star. This defines the gravity pull and climate. The gravity pull define the length/width proportions of the carbon based life forms, the climate defines other visual characteristics. The brains of these life forms, and the way they process visual input, is based on pattern repetition. See: visual illusions. These beings replicate based on regenerated DNA by mixing two DNA patterns, and thus the carriers will look for the best possible DNA partner for replication. There are many ways for such a life form to determine the best partner, and many are based on visual pattern recognition. The proportions must be right. Eyes too far apart? Strange short legs? Your subconscious brain has made its mind up, because it is trained by patterns, defined by gravity. You will look ugly to the natives on a planet with a different gravity pull. The golden ratio is nothing more than something which triggers such a subconscious reaction. Hayao Miyazaki, legendary Japanese story teller and movie maker, is a true master in understanding and triggering these subconscious reactions, on many levels (not only gravity). No, I won't get into what Fraud would say, that little bastard.