Math: Fibonaci Sequence Video Fallacy

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Math: Fibonaci Sequence Video Fallacy

Xah Lee, 2011-09-10

Beware of Math Fallacies Spreading on The Net

Recently this video is spreading fast on the net.

“The Fibonacci Suite in It's All Beauty” [sic]

A beautiful video indeed, but filled with fallacies.

It would be good for math teachers to use this vid as a intro, then proceed to go into detail of every piece of math shown in the video, and point out the parts that are false.

First, there's the Fibonacci sequence: {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …}. This is formed by adding the previous 2 terms, starting with 0 and 1.

[0:32] The Fibonacci spiral, constructed by fitting quarter circle arcs on stacks of squares with sides of Fibonacci numbers. The spiral formed is a approximation of a spiral called the Equiangular Spiral (aka logarithmic spiral).

The Fibonacci spiral isn't a true spiral. That is, it has kinks at every place the square connects (to see the kinks, think of a circle. A circle is a curve that has constant curvature at any point on the curve. Different sized circle have different curvatures. So, by connecting arcs of 2 circles from different sizes, the curvature will suddenly jump at the connection point. Although, such connection will be superficially smooth, but on a second level it is not smooth (this is the idea of derivative). You cannot design roads, train tracks, or roller coasters by just connecting circles of different sizes.).

Here, you should remember that the stacking of circular arcs as done by Fibonacci spiral is only a approximation to a particular equiangular spiral, called Golden Spiral.

equi spiral def
A example of equiangular spiral with angle 80°.

A easy way to understand equiangular spiral is that it's a spiral such that its growth rate is constant. (For much more and many pictures, see: Equiangular Spiral.)

The equiangular spiral is a family of spirals, with a constant angle as parameter. The Fibonacci spiral is a approximation of just one of them, called the Golden spiral.

then, they fit this spiral to the nautilus shell. Note again that it's the equiangular spiral the shell is based on, not the Fibonacci stacks of circular arcs, and nor is the shell shaped like the particular equiangular spiral that Fibonacci spiral is approximating.

Here's a quote from Wikipedia Nautilus:

The nautilus shell presents one of the finest natural examples of a logarithmic spiral, although it is not a golden spiral.

[1:30] then, they draw a rectangle outline of the shell, then cut it in half, then take a diagonal and sweep it down... as if to show that a rectangular hull of the shell has the right proportions to construct the golden rectangle. This is pure garbage.

[1:41] then, they sweep a circle and spit out speeds at every angle of (2*π - 2*π/φ) radians to show how it forms the sunflower pattern. This is also borderline of pseudoscience. You can spit out seeds in such a regular way but using just about any other constant angle and still be able to show the result being similar to the patterns of sunflower seed's arrangement.

[2:53] then, they pick out certain dots of the sunflower seeds, connect lines, to form the pattern on dragonfly's wings. This is again purely fairy tale. Am not quite sure what rule they used to pick out the dots. But it doesn't matter. The closest real math this part of vid is trying to show the the idea of Voronoi diagram and Delaunay triangulation.

voronoi diagram
A Voronoi Diagram. img src

Here's how it works. Given a bunch of dots on a paper, suppose you need to draw lines as to form borders between all the dots (think of each dot as a person, and you want to create a fair personal space among all people). One way, is to have the border such that any point on the border is equal-distant between the 2 neighboring dots. Such a border is called the Voronoi diagram. So, some plant's cell patterns, insect wing patterns, might be based on this principle because the equal-distance property is optimal under the circumstances of physical or biological constraints. Also remember, you have to start with placement of dots first. If the dots are arranged regularly, then the Voronoi diagram would also be regular. For example, if the dots are arranged in a square grid, then the Voronoi diagram is just a square grid. If the dots are arranged in a triangular grid, then its Voronoi diagram is a honeycomb tiling.

Even if we suppose that the pattern of a dragonfly's wings is a Voronoi diagram (which, clearly it is not just by observing photos, except in some artificially limited regions), that still leaves the more essential question of how the dots are arranged.

dragonfly wing pattern
Dragonfly Wing Pattern. Source Bob Moul www.pbase.com

In summary, it is possible to make a convincing animation that suggests false relations or proofs between any math number or curve. Mathematicians never relied on visual illustration as proofs, and the fallacy caused by visual illustrations has moved many mathematicians to completely avoid using figures at all in serious publications since about ~1700s or was it ~1800s.

The Fibonacci sequence is a rife source of math mysticism. There are lots of websites telling you how it connects to everything in nature, art, or god. The good news is, starting in about 2007, articles debunking the Fibonacci myth started to appear. For more and links, see: Math Mysticism: is Hurricane Shape a Fibonaci Spiral?.

Shakespeare vs Dr Seuss Rap Battle

New. over at Wordy English blog: Shakespeare vs Dr Seuss Rap Battle

Karmin - Look at Me Now

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Karmin - Look at Me Now

Xah Lee, 2011-09-10

Karmin - Look at Me Now


Yellow model chick
Yellow bottle sipping
Yellow Lamborghini
Yellow top missing
Yup yup
That stuff looks like a toupée
I get what you get in 10 years, in two days

Ladies love me I'm on my cool J

If you get what I get what would you say
He wax it on and off, Mr Miyagi
And them suicide doors, Hari Kari

Look At Me Now, Look At Me Now
Oh, I'm getting paper
Look At Me Now
Oh, Look At Me Now
Yeah, fresh than a mu-what?

Lil jigga bigger than gorilla
Cause I'm killing every jigga that
Try to be on my stuff
Better cuff your man if you with him
I can get him
Cuz he accidentally slip fall on my crack
Oops, I said on my crack
I aint really mean to say on my crack
But since we talking about my crack
All of you haters say hi to that
I'm Done… No really though i'm not done

Lets goooo

cause I feel like I'm running
and I'm feeling like I gotta get away, get away, get away
better know that I don't and I won't ever stop cause
you know I gotta win everyday day
see they don't really really wanna pop me
just know that you will never stop me
and I know that I can be a little cocky, ohhhh
you aint never gonna flop me

everytime I come a jigga gotta set it then I got it going
then I gotta get it, than I gotta blow, and than I gotta shudder any little thing
the jigga think that he be doing cause it doesnt matter cause I'm gonna dadadadada

then I'm gonna murder every thing and anything a badaboom a badabing
I gotta do a lot of things, and make it clearer to a couple jiggas
that I'm always winning and I gotta get it again and again and again
and I be doing it to death and now I move a little foul
a jigga better call a ref, and everybody know my style
and jiggas know that I'm the best

when I come to doing this and I be banging on my chest
and I bang in the east and I'm bangin' in the west
and I come to give you more and I will never give you less
you will hear it in the street or you can read it in the press
do you really wanna know whats next

see the way we on, when we all up in the race and you know
we gotta go, don't try to keep up with the pace
we struggling and hustling and sending in and getting in
and always gotta do it take it to another place
gotta taste it and I gotta grab it
and I gotta cut through all this traffic
just to be at the top of the throne
better know I gotta have it

Look At Me Now, Look At Me Now
Oh, I'm getting paper
Look At Me Now
Oh, Look At Me Now
Yeah, fresh than a mu-what?

Man forget these haters how yall doin?
I'm Lil Tunechi, I'm a nuisance, I go stupid, I go dumb like the 3 stooges
I dont eat sushi, I'm the stuff, no pollution, no substitution
Now i'm chilling play in movies in my jacuzzi, fruit is juicy
I never give a damn about a hater got money on my radar
Dress like a skater, got a big house, came with an elevator
You jiggas aint eatin, go tell a waiter

Marley said shoot em, and I said ok,
You on that bullsh- I'm like ole'
Dont care what you say, so don't even speak
Your boyfriend a freak like Cirque Du Soleil
That's word to my flag, and my flag red
I'm out of my head, yo I'm outta my mind from the bottom I climb
You aint hotter than mine, nope, not on my time and I'm not even trying
Whats poppin Slime? nothin five, and if they trippin forget em five
I aint got no time to shuck and jive, these jiggas as sweet as pumpkin pie

Ciroc and sprite on a private flight
Yo I been tight since guiding light, and my pockets white my diamonds white and my mommas nice and my daddy's gone
You please be scared cause I'm too wild, been here for a while
I was like no trial I puts it down
I'm so young money you got eyes look at me now oh

Look At Me Now, Look At Me Now
Oh, I'm getting paper
Look At Me Now
Oh, Look At Me Now
Yeah, fresh than a mu-what?

ok! ok! Is that right? I'm fresh than a mu-what?

The piece is performed by Karmin (band), made up of the twain Amy Heidemann and Nick Noonan.

The song is a cover of Look at Me Now (Chris Brown song).

Karmin Suicide Roll Hair Tutorial

Internet is For Porn

due to Google's Ad Sense policy, please view the post at the following url instead: http://xahlee.org/Periodic_dosage_dir/internet_is_for_porn.html


Project Gutenberg Founder Died (Michael S Hart, 1947‒2011)

Michael S Hart (1947‒2011) died on Sept 6. Cause of death is not mentioned.

Here's the news sources:

I benefited from Project Gutenberg. Specifically, i used it to get the original text for the following 3 annotated work:


2 artworks

2 Artworks

Murasame Maru street 2 dummies-s
Seems to be a cover art for a japanese pregnant porn magazine. Author seems to be Murasame Maru 村雨丸.
half elf
author unknown.

Please comment if you know any info about these artwork.


T-Mobile Commercials: Hottie Carly Foulkes

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T-Mobile Commercials: Hottie Carly Foulkes

Mobile phone commercial featuring the hottie Carly Foulkes (b1988).

Monthly Mugging
T-Mobile myTouch 4G “New Ride”

Look above, she's got elf ears.

Step Up to Nationwide 4G Without Losing Your Shirt
A Special Greeting for T-Mobile Fans

Look at the make up, the attire, the body languages, the script, it's all engineered to precision with the science of psychology.

T-Mobile commercial dissected.


Photography is High Art?

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Photography is High Art?

Xah Lee, 2011-09-04

Starting to take photographers out of my circle.

As a class of human animals on this earth, with respect to my taste and propensities of academic and humanity issues, i find photographers — shallow. In particular, those loud on the blogsphere (e.g. Trey Ratcliff). And, there's also the googler photo community manager Brian Rose. On g+, they are running the show. (note: if you are looking for photographers to add, just check out the above twain's posts. There are posts that collect all the pop photographers on g+, each got a myriad followers.)

The word photographer is loaded. It is this quasi-artist type of folks, of which requires little imagination compared to a painter, and little skill compared to a craftsman, similar to “designer” class or other post-modernistic “artists”. If you have fingers, you are a photographer material to begin with. (contrast this with, say, pianist)

Photographers, like designers (e.g. typographer. Also, calligraphers), when successful (e.g. Annie Leibovitz (see a big list here Category:American photographers)), are heightened out of proportions, gilded with theories of esthetics, exhibited in art museums and galas. (you know? there are artistic charlatans that peddle the idea that a splash of paint on canvas is fine art, or randomly piled up cubes as sculpture, and there is a award-winning composer whose magnum opus is silence. It is this type of phenomenon, that made me despise the word photography as a art form. I wonder now whether there has been photographers who have propounded that a photo of a white wall constitute a art)

I've always thought, that photographer as a profession is dying. Some 20 years ago, a pro photographer means you really need to have the equipment. Those bulky lenses carried on shoulders, with understanding of optics and technical know-how of complex optical equipment and film chemistry, and means of traveling, prop setup, etc. Today, all these fell by the wayside. On photo sites such as flickr, there are giga billions of photos, and a significant percent of them are great photography. These are done not by some professionals with years of training in photo school or under apprenticeship, but by “accident”. Google, with its Google Map, has taken a systematic approach where it runs cars around every road of major cities, with cameras that automatically take photos in all directions every few meters, producing a world of photos. These are functional photography, where you get to see things and people as they are, sans the artificial artistic touch, and it's really great and amazing, a real treasure to anthropology for the masses. (not that artistic touch is bad, just overvalued.)

If i were to spend 30 min a day gazing at photos, i'd rather goto Google Map's street photos of the world. If i were to spend time on visual art, i look for those whose production took a mastery of skill with imagination. If i were to look at photos of pretty faces, i have my porn collection.

Funny Video: Cat Teasing Dog

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Funny Video: Cat Teasing Dog

Xah Lee, 2011-09-04

cat teasing dog

Selena Gomez - Love You Like a Love Song

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Selena Gomez - Love You Like a Love Song

Xah Lee, 2011-08-27

Love You Like a Love Song (2011), sung by Selena Gomez (b1992)

Selena Gomez - Love You Like a Love Song

The repeat-peat-peat stuttering is a parody of Max Headroom (character), a fictional animated talking-head character that drew a craze in ~1988.

The lyrics “musical, lyrical, magical”, reminds me of Supertramp's The Logical Song.

Fan video featuring “Supertramp - The Logical Song”