lpetrich

One category of design deficiency is designs with limited scaling; designs that do not scale all the way to whatever absolute physical limits may exist. Some examples:

Palm trees are monocot plants; following the typical monocot pattern, they have one stem (the trunk) which goes straight up with constant thickness, with leaves being continually sprouted from the end as the stem grows. Monocots seldom have side branches; this may be a basic limitation in monocot "design".

A problem with this "design" is that the trees eventually get tall enough to become top-heavy. However, conifers and dicot plants avoid this problem by growing outward as well as upward, producing more bulk in their lower trunks, and thus more strength where it is needed. This helps explain why conifers and dicots are more successful at achieving gigantism, sometimes much more.

Another example of a poorly scalable design is arthropod outer skins, which serve as the owners' skeletons, and which are periodically molted as their owners grow. Having to survive between molts can be awkward, especially on land, where one will not be buoyed by surrounding water.

By contrast, vertebrate skeletons are internal, and are not molted; vertebrates have been much more successful at achieving gigantism. The largest arthropods ever to live, some eurypterids (Paleozoic sea scorpions), were as much as 2 meters long, which is tiny by elephant or indricotherium or sauropod or cetacean standards.

Kevin Dorner

Oolon came up with the idea of the arthropod exoskeleton being a wasteful design in <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=58&t=000239" target="_blank">this thread</a>. He could probably use some evidence for it to bolster his confidence in the idea.

[ February 16, 2002: Message edited by: Kevin Dorner ]</p>

lpetrich

Here is <a href="http://library.thinkquest.org/J002415/Famous_Trees/General_Sherman/general_sherman.html?tqskip1=1&tqtime=0216" target="_blank">a nice page on the General Sherman tree, the largest one known</a>.

It has a height of 275 ft (84 m), a ground-level trunk diameter of 32 ft (10 m), and an estimated volume of 52,500 ft^3 (1500 m^3). Its age is about 2000 years.

However the tallest known tree is a <a href="http://www.vichysprings.com/montgomery.html" target="_blank">different one, the Mendocino Tree</a>; it is about 368 ft (112 m) tall, and about 700 years old.

These trees are grouped as among the family <a href="http://www.wisc.edu/botit/systematics/Phyla/Coniferophyta/Taxodiaceae.html" target="_blank">Taxodiaceae</a>; the page refers to some nice collections of pictures; check under the Sequoiadendron link to get a picture of the size of the General Sherman tree.

By comparison, the tallest palm tree known is <a href="http://www.plantapalm.com/vpe/misc/waxpalm.htm" target="_blank">the wax palm</a>, which grows up to 70 m (230 ft). However, it still grows in the palm fashion, with a tuft of leaves on top of a very long trunk (60 cm (24 in) at base; 10 cm (4 in) at top -- slightly tapered).

Here are some pictures:


The General Sherman tree and

some wax palms.

[ February 16, 2002: Message edited by: lpetrich ]</p>

Viti

Standing amongst the Sequoia's is truly awe inspiring. It is hard to wrap your mind around the size of mountains and continents and galaxies and the Universe due to limited perspective...but the Redwoods you can stand beneath and look up and touch and feel and they are alive...amazing...one of my fave places to be

lpetrich

Another example: the maximum visual acuity of various designs of eyes; using the principles of optics, it is possible to work out what is the smallest resolvable angle for some design (the smaller the better). Here's a summary for those who don't want to see my mathematical details:

Lens-camera eyes (vertebrate, squid-octopus): good.
Pinhole-camera eyes (chambered nautilus): not so good.
Compound eyes (insects): not so good, not as scalable.

Note, I'll be estimating angles in radians, a natural unit where 2*pi radians is 360 degrees; a radian ~ 57 degrees. An object of size s at distance d will have an angular size of s/d radians if s/d is much less than 1; if s/d approaches 1, it's necessary to be more careful, but s/d is still a fair approximation.

I will also be ignoring factors of 2 and pi and the like; one can often get quick approximate results if one does that.

I first start out with lens-camera eyes, with radius r and pupil diameter d. The wave nature of light limits their angular resolution to Dawes' Limit, or l/d, where l is the wavelength of visible light. For d ~ 1 mm (typical human value in daytime) and l ~ 0.5 microns (average), Dawes' limit is 1/2000 or about 2 minutes of arc -- exactly right.

There is another limit due to spherical aberration; this is a result of the difficulty of getting an exact-focus lens shape. This is approximately (d/r)^3 and since r ~ 3 cm, this limit becomes 10^-4 for daytime. In nighttime, the pupl expands, and if d gets up to 3 mm, this limit becomes 10^-3. These values are close to Dawes' limit; in fact, one the optimum pupil size can be estimated from Dawes' limit equaling the S-A limit: d ~ (r^3*l)^(1/4). Which gets about 2 mm for a human eye. Also, the resulting optimum angular resolution is (l/r)^(3/4), which is about 1 minute of arc.

Lens-camera eyes are indeed very good, with vertebrates, the squid-octopus group, and spiders having them. The first two, at least, have the same design throughout each group, suggesting separate origins and reasonably faithful copying by descendants.

Closely related to a lens-camera eye is a pinhole-camera eye; the Chambered Nautilus has such an eye. Its resolution is limited by the angular size of the pupil as seen from the eye's retina; this is d/r. Since the pupil must be large enough to allow a reasonable amount of light to enter, this forces up d, lowering the resolution. A 1 mm pupil of a 1 cm eye has a Dawes Limit of 10^-3, a SA limit of 10^-3 -- and a pinhole limit of 0.1, that is, 6 degrees. So a Chambered Nautilus does not have an eye that is as good as it could be.

I now turn to insect eyes; crustacean eyes and trilobite eyes are much like them. They consist of a large number of simple eyes, or ommatidia; each ommatidium is a light meter with directionality. Angular resolution is determined not only by Dawes' Limit (l/d for ommatidium size d), but also by the angular distance between the directions of neighboring ommatidia (d/r, where r is the eye's overall radius). The optimum ommatidium size can be estimated from Dawes' Limit equaling the separation limit; this yields d ~ sqrt(r*l) or an angular resolution of (l/r)^(1/2). The total number of ommatidia necessary is (r/d)^2 or (r/l). Since insects typically have 1-mm eyes and a few thousand ommatidia, their ommatidium size is thus optimal. However, their angular resolution is 1/45 or 1.3 degrees. By comparison, a same-sized lens-camera eye could achieve a resolution of 1/300 or 0.2 degrees -- 7 times better.

Furthermore, if one scales an insect eye to human-eye size (2 cm), the best possible resolution is 14 minutes of arc -- about 16 times worse than what the same-sized lens-camera eye could do!

To get a picture of the kinds of angular resolutions I'm discussing, a standard computer monitor has a pixel size of 1/72 in (0.35 mm), and if viewed at 2 ft distance (60 cm), each pixel has a size of 2 arcminutes.

We can see such detail, but an insect would have to be less than 1 inch away! (1.6 cm) Though a camera-eyed one could be 6 inches away (14 cm).

[ February 17, 2002: Message edited by: lpetrich ]</p>