I watched a program on Tuesday evening on my local Public TV Station. It was called “Hunting the Hidden Dimension,” and was on the Nova series of programs.
The subject of the broadcast was “Fractal Geometry.” (First aired in October 2008.)
Fractal is a word coined by mathematician Benoit Mandelbrot (Left.) who published his findings as recent as the 1970s.
Up until that point, throughout history geometry was all about straight lines, triangles, pyramids, circles and cylinders, etc.
This geometry applied to everything man-made, buildings, bridges and other engineering projects, and of course bicycle frames fit right into this category, being made up of straight lines and triangles. Up until Mandelbrot’s findings, everything outside of that which is man-made could not be explained by geometry and mathematics.
Mandelbrot changed all that when he discovered that shapes and forms in nature. For example cloud formations, trees, mountains, river flow and even blood vessels in our bodies, were a series of repeating irregular shapes, which could be recreated and proven mathematically.
Benoit Mandelbrot was at first scoffed at by other experts, but now with improvements in computing his theories are being proved mathematically. Now taken seriously, fractals is being studied and used in the medical and the environmental fields.
One of the places we also see fractal geometry in practice is in special effects for movies. Not only are images of nature being created, like landscapes, plants, trees, and even human and animal forms, but fire and explosions can be created and animated on a computer.
This subject has always fascinated me, because on the one hand you have the bicycle which is traditional man-made geometry, and the task of the frame builder is to match that to the human body, so the two become one, and the bicycle becomes an extension of its rider.
The human body, like all forms in nature, appears to be chaotic and infinite in its makeup. Yet it was possible for me to build a series of production frames, the Fuso for example, in a range of sizes that would fit just about anybody.
From as far back as the late 1960s I found I could fit someone to a frame “Intuitively.” I did not let this be widely known for fear of being labeled a crack-pot. I was basing my estimation of frame size primarily on a person’s height.
Long after I left the bike business, and therefore the effect of the “Crackpot” label had diminished, I wrote an article here in February 2006, stating that frame size could be estimated around a person’s height.
I came to this conclusion, not so much by what I could do in sizing a person, but more by what I could not do. A person who is six feet tall would normally fit on a frame around 58 or 59 centimeters (Measured center to top.)
However, it is quite a common occurrence to find a person six feet tall (183 cm.) with a 30 inch (76 cm.) inside leg measurement. You cannot put a person like that on a 51 centimeter frame as his inseam would suggest then build a long top tube to accommodate his long body.
I would simply drop the frame size down to a 56 or 57 centimeter because of the short legs, and leave the top tube as standard for that size frame. (55cm. or 55.5 respectively.) This same frame would also suit a person 5’10” tall, (178 cm.) with an inseam around 33 inches.(84 cm.) The difference being the taller guy with short legs would have his saddle lower and possibly use a longer stem.
I knew this was so, but never knew why; it all became clear to me on watching the Nova episode. Towards the end of the program a group of environmentalists were studying rainforests. They cut down a large tree, then measured and documented the dimensions of all its branches, overall height etc.
They then found that a seemingly random pattern of trees of all sizes growing throughout the rest of the rainforest followed the same pattern as the branches of the one tree they had documented; both in the position of their branches, and their position in the forest relative to other trees.
Watching this, it occurred to me that if you took a large group of humans all the same height, you could fit them all to the same size bicycle frame. (Within a centimeter or so.) This is why this theory works; although on the surface it appears that my group all the same height are each different in every other way, they are no different than the trees in the rainforest. They all follow the rule of fractals that can be plotted mathematically.
Just a little something for you to think about, to agree or shoot down. If you haven’t seen the hour long program, you can watch it here. It is fascinating stuff.
Talisman
Tal-is-man (noun) an object believed to give magical powers to somebody who carries or wears it, e.g. a stone or jewel.
The talisman has been around throughout history, whether it be the Native American medicine bag, or a religious symbol like a Crucifix, or St. Christopher medallion, or something similar. Usually, in these cases the talisman is said to protect the wearer from bodily harm.
For years there have been copper bracelets and others that incorporate magnets said to cure rheumatism. Some eastern philosophies maintain there is a flow of energy throughout the human body and indeed the universe that can somehow be controlled and directed by certain objects.
I remember some years ago helping a female friend move into a new apartment. The first thing she did was to hang a crystal in the widow, and remark, “Can’t you just feel the energy that it draws into the room.” I was thinking, We could use some energy to get the rest of this shit moved in here.
One could accept that a copper or magnetic bracelet might actually do something; copper being an excellent conductor of electricity, and magnets actually producing and electrical or magnetic field.
But how about a plastic bracelet? I find that a stretch. However, since 2007 a group of athletes have managed to sell the “Power Balance” bracelet (Pictured above.) at $30 a pop, said to work with the body’s natural energy field.
Used by certain professional cyclists, and other top athletes, the makers of the Power Balance bracelet claim that it can make you go faster, and of course it can’t be detected in a dope test.
What supposedly makes this plastic bracelet work is that it incorporates a “Hologram.” I have a hologram of a little bird on my Visa credit and debit cards; it symbolizes my money flying away.
There is also one on my driver’s license; so if I carry these items while riding my bike, I should be covered in the Hologram/Energy field department. There is no need to shell out $30 for a Power Balance bracelet.
Now I read that the Australian government has stepped in to stop the producers of the Power Balance bracelet from claiming that the product does anything except relieve you of $30 and look cool when you are wearing it.
Actually the talisman does work. However, it has nothing to do with the object actually doing anything, but everything to do with the wearer’s belief that it does. It is the wearer’s mind that cures the rheumatism, or makes him go faster on his bike. The mind is a powerful thing.
People go to Lourdes, France and are cured of all manner of illnesses and diseases; this is well documented. They are not cured by their visit to this one particular place; it is their unshakable faith that such a trip will cure them.
It could be that the Power Balance bracelet actually did help cyclists go faster, although the Australian government has now killed that idea stone dead.
When I ride my bike I have an invisible “Energy Field” that extends three feet all around me. It weighs nothing and it cost me nothing, because it is invisible. It protects me and keeps me safe.
I have completely dispensed with the talisman, and just use my mind. I am currently working to get the energy field to rotate counter clockwise on the left, and clockwise on the right, so it will actually push me along.
You might try it, only please be like me and not tell anyone, or people might think you are loony-tunes. On the other hand, apparently many people thought the Power Balance Bracelet was legit, and a government had to step in to save people from themselves