No Wheels In Nature

Your avatar is "Waterfall." In an earlier exchange, I confused it with "Belvedere." These two, plus "Ascending and Descending" (the monks on the Penrose staircase), "Flatworms," and others, are sometimes collectively described as "the impossible houses."

M.C. Escher worked largely in obscurity until Martin Gardner's 1959 "Mathematical Games" column in Scientific American introduced his work to a larger viewership. In those days, prints were priced very modestly. In the U.S., the Vorpal Gallery negotiated an exclusive distributorship. They husbanded the oeuvre well, and it increased in value until about the late 1980s. There were a few piracies of images for psychedelic record albums.

Sometime around the late 1980s or early 1990s, the Dutch heirs of Escher's estate disrupted this appreciating picture, whereupon there emerged the plethora of posters, neckties, sweatshirts, and socks imprinted with Escher's images. That pretty much killed the fine art market, which by then had been recognized by the premier art publisher Abrams.

I still have "Flatworms" 1/53^II. From a semi-inside view, it has been quite a ride.

I am highly gratified that you have become an Escher enthusiast. I enjoy many varieties of art, ancient to classic to modern. Escher did not fit in to some of the artistic movements of his time, and remained unrecognized for quite a while. Eventually this obscurity was overcome by the interest of mathematicians, scientists, engineers, and psychedelics.

If you have not yet seen it, I strongly recommend that you obtain Douglas R. Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid. This book may not be to everyone's taste, but it is an amazing tour de force. (As is Hofstadter's Metamagical Themas, which I recommend next.) I am sure you will be delighted with both of these.

I enjoyed every page from Gardner's Mathematical Amusements, in the 60's. I remember all those symmetry drawings. My daughter has won the first prize in a computer science fair, organized by Compaq, with a html web site having as first page the Escher's Snakes. It is only now that I found out about the picture (including the title), when I googled the mentioned the artist. I owe you a good link

I believe that "Snakes" (1973) was Escher's last work. Martin Gardner passed away a month or so ago, at age 95. I am sure that his long-running column brings well loved memories to many. His column was succeeded by Douglas Hofstadter's "Metamagical Themas", which was gathered into a book (same title) after Godel, Escher, Bach: An Eternal Golden Braid. I highly recommend Metamagical Themas as well.

Congratulations to your daughter!

I suggest you start a thread on "The art and geometry of... "

It seems there is a lot of interest, and is a blend of geometry, art and perception.

The hydraulic system I theorized could supply oxygen and nutrients dissolved in the fluid, with the cells extracting them from the fluid as it flows in and spins the wheel organ around. At the same time, waste products can be excreted back into the fluid to be disposed by the organism's excretory system. However, it does also mean that the creature's wheel organs are essentially symbiotes even though they are actually part of the same organism.

Have you never seen a NaCl crystal, or iron pyrite, or any of a host of other natural cubes?

Yes, you are right. I thought of that myself, right after I wrote my post. In crystal grids (i.e. on molecular level) you'll find several shapes such as cubes (and others). However, on a macroscopic level such shapes are rather rare. I just wanted to show that spheres (and spheroids) are more frequent due to the physical laws.

You are right in great extent.

But nature has created not wheels, but cylinders. Snake is a cylinder. Still it doesn't use that round shape of cylinder for motion. In fact, it might have been possible to create muscular expansion and contraction in circular face of the cylinder, very similar to expansion and contraction in longutudinal direction, which snake uses for motion.

I do not know why, but nature has not selected that method though she created cylinder.

Nice tips...

Douglas Adams (Hitchhiker's Guide to the Galaxy) said that in an infinite universe there must be a planet where there are trees which produce skrewdrivers (and you can find it, provided that you have plenty of time to search for it) . In the same manner, maybe there is another planet where such wheels grow spontaneously from the ground .

Why? For the same reason man doesn't favor legged locomotives.

It's just not practical.

Nevertheless... we both have the same sail's man

Are you sure?

1. Maglev trains

2. Darth Vader

(courtesy DVader1000, thanks )

Ah yes, dumb old Pvt THX-1138. As if being ordered (by me) to wash and polish an entire division of AT-AT and AT-ST walkers in the icy cold environment of Hoth wasn't a torturous enough punishment for feeding carrots to the AT-AT, now he has to endure the ignominy of his stupidity being shown off to the entire world.

Thanks Kris. It's really not all that surprising to learn that there are actually some creatures out there that crotch and roll as a survival strategy, but one creature mentioned in the Wiki link that you provided fit my hypothesis perfectly:

Nannosquilla decemspinosa, a species of long-bodied, short-legged Mantis Shrimp, lives in shallow sandy areas along the Pacific coast of Central and South America. When stranded by a low tide the 3 cm stomatopod lies on its back and performs backwards somersaults over and over. The animal moves up to 2 meters at a time by rolling 20-40 times, with speeds of around 72 revolutions per minute. That is 1.5 body lengths per second (3.5 cm/s). Researchers estimate that the stomatopod acts as a true wheel around 40% of the time during this series of rolls. The remaining 60% of the time it has to "jumpstart" a roll by using its body to thrust itself upwards and forwards.^[8][12]

Now, has nature ever produced a wheel and axle for the purposes of carrying loads? Umm no.

Not practical ? What on earth do you mean ?

GA's both. Thanks.

i get it now. Nature gave this gift to those who can handle it. Decided not to give it to Man. What a correct decision, when you look at accident statistics

My spidey sense is tingling.... (okay I don't like spiders.)

that would be cool if he turned Doc Ock and climbed a building...

It seems pretty obvious to me why there are no wheels in nature. Living organisms adapt to their conditions. If there had been roads a few billion years ago, then wheels might have evolved. Of course, brakes would have to evolve too. It would have been interesting to know if nature would have opted for driving on the left or on the right.

Nature adapted me to drive on both... in the same region.. muuauhahaha... yes.. be scared. (I also tailgate (if you are going too slow in the fast lane), and think yellow lights mean speed up...)

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Lead, Follow, or Get Out Of The Way!

How right you are my friend.. How right you are..

I think it is now very nearly possible to create "Rapid Prototyping" objects that include wheels/axles in a monolithic build, but require only a very slight impact to initialize the function of the wheel. (by breaking the sprue)

anyone seen this?

i saw a demo of a rapid prototyping machine from Z corp once. A superb video is available on their website : http://www.zcorp.com/en/Z-Corp/450-Video-and-Snapshot-Kit-Deliverables/spage.aspx

i saw this one being generated, very little post-work, as you say, breaking the equivalent of sprues...

thank you. ga. (although someone else gave you an inexplicble ot)

If the orgasm (sorry, Freudian slip), organism is in two parts and the axle is coupled with the wheel part periodically, it may be possible to inject nutrients into the wheel. The issue is that the wheel organism has to be an independent entity and not a locomotive part of a larger entity. Bioramani

No wheels in nature?!

What about Roly Poly Bugs? Any number of seeds also use rolling 'wheel' motion to further transport.

Perhaps you meant 'axle and wheel'? In that case, the examples are harder to find, but I also don't find many organisms sporting a turn signal with integrated cruise control and intermittent wiper, either.

BBB

Yes, you are right, there are wheel-like things in nature, admirably shown by the images and videos submitted by many people here. Very entertaining and enriching !

i had perhaps in mind the wheel-axle that you mention.

However, as has been said many times, if nature had intended man to fly or swim, it would have equipped him with wings and gills+fins etc. Maybe it didn't want him to drive on wheels either .....

Perhaps I'm just not thinking of wheel in the convetional sense, but it would be possible for a two "limbed" organism to exist that would work on similar principles. I will attempt to describe it using human anatomy. The torso and head at the centre, balanced about it's arms, reached straight out, with large fingers evenly spaced and faned outwards (imagine reaching out with palms open, with no legs and with giant fingers and muscle that would equate to a wheel). To cause the wheels to rotate you would pulse your fingers as though drumming your fingers on a desk, thiswould cause your entire body to rotate in one direction. To change direction you could fan out or close your hand to change the differential between each wheel/hand. In order to navigate like this, perhaps a spider like vision would need to be adopted, with evenly spaced eyes around the torso. Further limbs could be included on the torso. Perhaps i shal sketch this animal up for visualisation sakes.

Do you mean something like a starfish or an octopus or similar shape? Would be interesting to see if you can get a sketch here...thanks.

I'm not vouching for this, but Dawkins probably did his research;

"The wheel may even have been the first locomotor device ever evolved, given that for most of its first 2 billion years, life consisted of nothing but bacteria. Many bacteria, of which Rhizobium is typical, swim using thread-like spiral propellers, each driven by its own continuously rotating propeller shaft. It used to be thought that these 'flagella' were wagged like tails, the appearance of spiral rotation resulting from a wave of motion passing along the length of the flagellum, as in a wriggling snake. The truth is much more remarkable. The bacterial flagellum is attached to a shaft that rotates feely and indefinitely in a hole that runs through the cell wall. This is a a true axle, a freely rotating hub. It is driven by a tiny molecular motor which uses the same biophysical principles as a muscle. But a muscle is a reciprocating engine, which, after contracting, has to lengthen again to prepare for a new power stroke. The bacterial motor just keeps on going in the same direction: a molecular turbine." (The Ancestor's Tale)

Maybe a case could be made for flowers that turn on their stalks to track the sun.

but it doesn't really need to be a rotary device to move in a helical fashion.. just think of those artists who spin ribbions with a short stick, and can easily produce a helical motion in the ribbon. I don't know.. I've never seen a Rhizobum up close.

What about the spiral motion in maple seeds and such? Arent there any insects, worms or fish that propel themselves by spinning around? I guess nature doesn't like the brains however tiny they may be to spin around. What about things that don't have brain?