Looks like an interesting book. For my part, it's interesting not only
that symmetry is pleasing, but *certain forms* of assymetry as well-
asymmetrical elements have to have a "balance".
IMO, the taproot, so to speak, of the phenomenon of the 'pleasingness'
quality is survivability. In nature, both smmetry, and *balanced*
assymetry, impact the survivability not only of biological organisms, but
also of structures, although it's probably easier to consider biological
organisms, as there are so many different examples.
For quadrupeds and bipeds, symmetry is important firstly because of its
impact upon locomotion, vision, and manipulation of the environment.
Picture an herbivore grazing, and the picture it being chased by a
predator. For both of them, speed is enhanced by the coordinated
movements of their four legs. Although a three-legged creature would be
stable (and possibly be able to sleep standing up - which bipeds, as far
as I know, cannot do), it's impossible for me, at elat,t o imagine how a
three-legged creature could coordinate its limbs so as to reach the
speeds of, for example, a gazelle, or a pursuing cheetah, or a horse.
Balance makes for efficiency. For humans, walking is a surprisingly
efficient means of locomotion, because of the way the human body is
(usually) balanced. A thrid arm might sometimes be "handy" (sorry for
the bad pun ;) ), but it'd have a negative effect upon balance and
therefore upon efficiency of locomotion, which doesnt' make much of a
difference in "couch potato" cultures, but does have an impact upon more
rigorous lifestyles, esp. the ancient hunting-gathering, and even manual
farming, lifestyles of our ancestors. ((Remember that the combine, for
example, only was invented and came into wide use in the late 1940's or
early 1950's.)) Inefficient locomotion generally makes for slower
locomotion, but possibly more importantly, more calorie-intensive
locomotion, since it takes more effort - and again, for the vast majority
of human history (and, really, even for a gret amhy, if not most, of
today's world population), starvation is a constant threat, so anything
that made an individual require more calories tended to be dropped from
the gene pool, due to the lowered survivability of the individual.
A lack of symmetry affects not only efficiency of locomotion, but also
perception. Given that perception is vital for both finding food and
avoiding predators, again, in a survivalist/"primitive" mode of
existence, anything that negatively impacted it would be unlikely to be
passed on to the next generation.
As for "balanced assymetry", it's obvious that the most symmetrical shape
would be a sphere (right angles being very uncommon in nature, aside from
some rock/crystal faces and formations), and equally obvious is the fact
that the closest any biological entity is to a sphere occurs in
microorganisms and jellyfish. Higher animals have separated perceptual
organs from digestive organs, and both from locomotive organs - IOW, a
head, a gut, and legs/fins/wings. However, all of these things also need
to operate in the environment of the Earth: gravity, hydrodynamics
(whether it be of air or water), temperature, and so on. If the head is
too large, the animal wouldn't be able to move forwards, and IIRC the
only animal whose main/only direction of locomotion is backwards are
squid. Most animals on Earth (and in most of Earth's history) are
laterally symmetrical, i.e. symmetrical along the long axis, but
assymetrical front-to-back. But that assymetry must be in balance, or
else the animal wouldn't be able to move efficiently. Its body, IOW, has
to balance all the forces that the animal encounters during th ecourse of
So, while mathematicians talk about 1.618 and 1.414 and other "magic"
ratios, it might make more sense to look at animals, and where their
"pivit points" are located and which rations permit, or don't permit,
them to balance.
Just my own random thoughts ;)
Sleeping right behind me is one of my dogs, 15 year old Georgie Girl, who
lost a front leg when she was about 6 months old and then last spring had a
tumor removed from a back leg that permanently damaged her muscles in that
leg. When younger she kept up with the other dogs and caught Frisbees with
ease. She still swims well and can walk at a good pace if motivated (meeting
new people or dogs). Obviously she is not symmetrical, but locomotion was
not seriously disturbed. Her remaining front leg is very heavily muscled. I
can envision a 3 legged beast because I have a well functioning one with
really 2-1/2 legs. Didn't Larry Niven (sci-fi author) write about that once?
No, I was talking about efficiency versus inefficiency and the development
of symmetry in higher animals and insects and the interplay of that with
the fact that most animals prefer mates with a high degree of symmetry.
The subject of the original post (and thread) is "WHy is symmetry
satisfying", and I was presenting, albeit in summarized form, what is known
about the animal kingdom. It's not a matter of "good" or "not good", it's
a matter of efficiency and adaptation. If someone dumped a bunch of
unwanted greyhounds onto the African savannah, they'd probalby have the
speed and agility to outrun lions and even cheetahs. (It's another matter
entirely whether they could become successful predators - I've read that
feral dogs seldom do to the extent of being able to establish a stable
breeding population.) But take a dog who has had a leg amputated, and put
it into the same situation, and sorry, but it's goign to be Dinner - being
able to "keep up with" oterh dogs in a domestic, meaning protected,
situation is completely different from whether three legs is sufficiently
efficient at *both* outrunning four-legged predators, *and* hunting prey,
so as to survive and establish a breeding population.
The point is that we do *not* live on a planet dominated by trilaterally-
symmetrical creatures - there were some, IIRC, very early on in the history
of earth, but they disappeared.
I don't understand why the point seems so obscure.
And on the planet of three legged creatures they have no idea what
were doing down here. How can you have one leg pushing, one
repositioning and another landing when you have four? Either one leg
is wasted luggage or you are duplicating motion and there's some
critical aspect of locomotion unattended.
The key to walking is lack of balance. Like those jet fighters that
are so agile because they are always THIS close to falling out of the
You ain't met my cousin Agnes.
But still, isn't it just satisfying to say "cephalopod". Say it again
now "cephalopod." Gastropod. Mmm.... gastropod...
Shouldn't take you much effort to find third party "proof" that those
very points fall within the domain of the "interesting" numbers. The
truth is out there.
Yeah, but they're the exception (exceptionally tough!) ;)
But th epoint would be to match up a three-legged critter with a
4-legged predator. I don't see that the mechanics of the 3-er could be
more efficient or even as efficient - which would mean it becomes a
No, biomechanics is an entirely differnt thing. Without continual
computer control (which is far faster than human reactions), the things
wouldn't get off the ground (or would fall from teh sky). A mroe
accurate example is birds - differnt airfoil shapes are adapted to
different purposes (c.f. goshawk, falcon, hawk, albatross, and yup,
penquins, who 'fly" underwater - air and water, hydrodynamics, the
differnce being viscosity/density). Could a three-winged bird fly?
Maybe btu the biomechanics would be a nightmare, and nature generally
tends to work like a version of Occam's Razor, favoring efficiency over
THose are lower animals. I was talking about higher animals, and
hwo.why a prefernce for symmetry, or balanaced assymetry, developed.
"Preference" implies some sort of higher brain function. Gastropods
(IIRC, snails and their ilk) don't, to my recollection, have much in hte
way of a brain.
The book referenced by the OP was, IIRC, written about math, by a
mathemetician, abotu symmetry. i added "and balanced assymetry".
I have some recollection re: the origin of Phi, but I don't know the
origin of 1.414. I've never done an analysis myself of balanced
assymetry, because I hadn't previously thought abotu the subject - uit's
always been more of an intuitive art-related thing to me. If you know
of someone else having done that sort fo study, I'd be interested in the
reference, because it'd be, well, interesting to me. As for doing it -
yikes, I already have so many other projects going on...and the
electronics bits are enough math for me to handle at any one time ;)
And on the planet of three legged creatures the point would be to
match up a four-legged critter with a 3-legged predator. They don't
see that the mechanics of the 4-er could be a more efficient or even
as efficient - which would mean it becomes a meal.
Yes. Your discussion of computers and eventual side project on three
winged birds has no relevance to my point.
Nature tends to work like a human, continually reusing the same
solution and rarely thinking outside the box. See "history since the
Those are lower animals. I was talking about how fun it is to say the
I can't imagine that we prefer symmetry because it helps us run from
wolves rather than we prefer symmetry because we are symmetrical. We
may be symmetrical because it helps us run from wolves (and quite
possibly are not) but our emotions aren't that scholarly.
Square root of two. Has some fun properties.
Don't know if "The Origins Of Architectural Pleasure" gets in to
discussion of such, but imagine that it might touch on the symmetry/
It seems, on quick glance, to be easier to find stuff showing people
prefer stuff with "pretty numbers" than that God designed stuff that
way. Color me surprised.
Only if they are inherently more efficient. I'm not an expert in
biomechanics, but IIRC, four or two is more efficient than three.
huh? You're the one who brought computer-controlled machines to the
question of possible explanations why symmetry is pleasing.
You're saying "we"/humans, I'm also including other animals. But
whatever. It's not even my own theory - I might have come across it in
the journal "Nature" but can't recall at this point. Do you have a
better/more sensible theory?
As above, I don't know what those are; just haven't looked into it
WHat does that have to do with what you quoted where I said I've too
many projects going on to get, at least currently, into a study of
Not "if you recall". If you'll recall, you "can't imagine". There's a
big difference there. Are you imagining your argument or are you
recalling somebody elses?
It's beside the point. My point is merely that when you say you 'can't
imagine' that's pretty much the root of the discussion about symmetry
and preference. We like what we know. What we don't know is odd and we
"can't imagine" how it might work. My point - on the 3 planet, they
have the exact same problem when they look at us. My point - that by
limiting ourselves to your imagination we get very suspect answers.
If I understand your statement correctly:
I make no mention of computer controlled machines as a possible
explanation for why symmetry is pleasing. I will make no such mention.
I do not think I have any belief that such a thing might be true.
Why do you think it's impossible to do both? (1) From what I recall, X,
AND (2) attempts to think of unresearched situations where "not X" is
equally viable were unsuccessful in the time I gave to the endevor.
Who can recall the point, with this ever-widening arc of tagents off of
No, there *is* data gathered from research showing that, if given a
choice, one of the major preferences for a mate is one who is symmetrical
(along the linear axis).
Once again, you've massaged what I said and used the incomplete result to
claim that I said something which I did not. I can *of course* imagine
how three legs might work anatomically biomechanically (duuuh!); but I
couldn't think of a way in which a three-legged animal could compete in
terms of speed, strength, or agility with a 4-legged predator (or
conversely for a predator, prey animal).
And if you went to the planet odf three-legged animals, bring a bunch of
4-legged animals, and released them, would they outcompete the three-
legged ones - I think they would, based upon what I recall (yes, RECALL)
of anatomy (which, yes, I did study as part of my University coursework),
and what I can deduce from it regarding the biomechanics.
Look, you mentioned the jet fighters - which you yourself quote above.
And the plain and simple facts are that (1) one cannot consider them
without also considering the fact that advanced computer systems are
required for tehm to fly, unlike walking, which can be handled (normally
at least) by the animal brain; (2) walking is a controlled fall, which
isn't the same thing as lacking balance. Anyone can see that I mentioned
birds merely because you mentioned jets, because flying is more akin to
flying, than it is to walking - IOW, you made an analogy, and I mentioned
what is a more apt analogy (flight to flight, rather than flight to
IMO, all you're doing is quibbling, trying to drum up an argument using
red herrings drawn across various points, and incomplete quotes carefully
selected in an attempt to make your target appear dimwitted.
I'm in the middle of trying to learn some electronics (to make solar-
lights for my stained glass scuptures/constructs), and learn what I need
to finish several other projects as well, so, although I enjoy real
discussion and information exchange, excuse me if I don't have the time
or energy to spend on meaningless polemics and drummed-up contention.
My point, rather, was that I think you are changing your story not
merely telling the parts that suit you at certain times.
Yes, exactly. Look carefully at who is doing the chosing. See below.
Yes, I know. My point is that that is an expectable shortcoming in you
and in no way indicative of the truth of the matter.
Yes, I know you think so. And _I_ think you may well be wrong.
Your coursework in biomechanics should have left you well able to
understand what I meant.
Yes, yes I did. So what?
The plain and simple facts are that you can not read.
I'll leave you and somebody else to argue the compare/contrast between
"advanced computer systems" and the apparently sluggardly backward
incompetent human brain.
Irrelevant. I told you that in the last post and yet you keep arguing
about it. I see your point. I argee. And it is utterly irrelevant to
what I said. What I meant. What I was illustrating. Yet you fall all
over it even after being told that it is not in the least bit relevant
and you are barking up your own tree. I can not make your life any
easier for you if you insist on making it so hard.
The interesting point you seem to have missed about the unstable
aircraft is that w/o the control systems they fail. Same too humans.
See, you can read! One sentence out of pages of irrelevance and wrong
accusatory snideness (see below). Thanks be to Don.
Well phrased. You're right. We don't walk because we lack balance, we
push ourselves "off balance" and use our balance to recover.
Let's think about the planes... they are being pushed by engines and
held up by wings. People are being pushed by legs and held up by long
stiff bones (the mechanics of the two are different by far, but I
think the analogy should suffice for our purposes. We'll see soon
enough). A paper airplane, pushed, will tend to glide forward, nose
first in a pleasant manner. A person, pushed, will tend to fall over.
An X-29, pushed, being unstable, will tend to turn around and do all
sorts of ugly things for a plane. A person, pushed, being unstable,
will tend to fall over and do all sorts of ugly things for a person.
The behaviour seems the same, but
The _key_ to walking is not lack of balance, you are right. The X-29
relies on instability to increase agility. The human may use a moment
of instability as a transition point (at "best" here) as a stage in
the system of walking, but no, the analogy I was thinking of just
doesn't cut it. Sorry.
Of course, that doesn't mean three legged beasts couldn't kick four
Yes, I could see that. And it was a very poor reason. It underscored
that I didn't manage to convey my point to you in the least. Perhaps
because it was such a poor analogy (mine) you found yourself grasping
at straws to answer it. A simple "I'm sorry, I don't follow." or
today's nice summary of what walking is would have been a better
It was more apt to what you were thinking. Incredibly unrelated to
what I was trying to say.
No, not at all. I'm trying to make sure you know that I am not saying,
trying to say, implying or even thinking about the many things you
ascribe to me when you talk to yourself in reply to my tiny little
observations. That, and I was trying to get you to see that your
argument about the inferiority of three legged beasts and their lack
of bilateral symmetry was baseless bigotry born of "ethnocentrism" and
lack of imagination. AND that this bigotry ties in exactly with the
human preference for symmetry. I repeat, did you ever address? - we
like what we are. I add - that's sort of a survival trait right there.
I add - and we fear that which we are not.
That's pretty Internet 101 of you.
Regarding "real discussion," I was trying very hard to keep to real
discussion of those things I was discussing. You can't have enjoyed it
because you kept trying to drag me off into places of your own
concern. I told you "I'm not talking about that and I don't care."
Never once did you say "oh, oops. What are you talking about?" No,
rather, you kept (no doubt (and in contradiction to your above
protestation), keep) going on about shit I don't care about in this
context, shit I'm not talking about in this context, and long tedious
paragraphs responding to... stuff I never said, in ways that make it
abundantly clear you aren't understanding the most simple of my
statements and aren't interested in so doing.
So, say "whatever," and pretend you win because you've got IMPORTANT
AND REAL things to do.
I know that I, for one, have clearly "lost".
An expected shortcoming? Or your own misinterpretation?
Flight is a more of a matter of mechanics interacting with fluid dynamics
than is walking, or even running - air resistance is a crucial factor in
flight, but insignificant in walking, and not very significant in
As above. The analogy was a thin comparison.
Right, I can't read.
I know. I made the error of trying to get back to the main point, which
was mentioning some theories (the impication being evolutionary theories,
tho' I supposed I ought to have stated that more obviously)of why animals
(including humans) might prefer certain physical arrangements.
Which was why I brought in birds, which you claimed to be irrelevant, but
is not. The point was about "why symmetry", and more specifically, What
is efficient about bilateral symmetry. Symmetry makes for a smoother,
more efficient interaction with air (expressed using similar math to that
which is used to study underwater movement).
I wasn't "grasping at straws", I simply brought in the more appropriate
Tactic? So, uh, what, you thought I was picking on you or something?
I don't talk to myself more than anyone else, including you.
No, I sketched (i.e. physically, with a pencil on paper) some possible
general skeletal configurations - excuse me is that is "unimaginitive" -
and tried to imagine how the musculature would work. And I remained
unconvinced that such an anatomy would be efficient enough to compete
with animals exhibiting bilateral symmetry.
My statements were based upon what I know about anatomy and of how
animals move through their environments.
The only "baseless bigotry" seems, sorry, to be your own.
I wasn't merely talking about humans. The question of "stranger fear"
isn't the same as why there seems to be an instinct to consider symmetry
beautiful, an instinct with is observed in various animals, at least in
part, when oen studies mating preferences.
Well, if that's how you want to interpret it.
I wasn't "dragging you off" to anywhere, I was trying to keep to the
question raised by the OP.
And, just a question, but, if you don't care what someone is talking
about, why shoudl they care what you're talking about?
Well, if that's nto the pot calling the kettle black, I dunno what is.
I didn't say "important and real", I said "alot". They're important to
me but obviously not inportant to everyone else. As for "pretend", well,
if the best you can do is call me a liar, that's not even worth a
You've lost whatever respect I used to have for you. Which obviously
means nothing to you anyway, although I'm glad, in a way, that I found
out your true opinion of me - it will make for better time-management for
both of us.
Picture a pentagram (going with the most common number of appendages) -
technically, yes, you can "split it down the middle" - one point is halved,
and two whole points are on either side.
Starfish (which are invertebrates) mating choices are based upon
chemoreceptors - although they do have an eyespot at the end of each arm,
evidence indicates that these eyespots only sense general dark and light,
not acute enough to use visual cues for mate-selection. I think it can
also be said that they exhibit pentaradial symmetry. (Just to be sure, I
checked Google, and that info is readily available.)
I did some Googling - the following sites, which deal with vertebrate
locomotion, may not be of interest to you, but if they are, enjoy ;) :
http://icb.oxfordjournals.org/cgi/reprint/42/1/158 - "Stability and
Manoeuvrability of Terrestrial Vertebrates"
http://www.cs.bham.ac.uk/~txm/thesis.pdf - "Evolution, Complexity and
Progress in Natural and Artificial Systems" (long, 213 pages, I haven't yet
finished reading it)
For my money, no. Yes, you can cut a starfish, either even or odd
legged, along one axis and say "see, mirror images" but there is no
single axis of that symmetry. You can cut here OR here and get the
same answer. So we call them radially symmetrical.
And when I was a kid the plain starfish we had had one "eye" that was
asymmetrically placed. But then, I've only got one asymmetric liver
too, so maybe that arrangement of guts and stuff doesn't counts as
THis is a short but decent bit on bilateral symmetry in animals:
and where would we be without the required Wikipedia reference <g!>:
What they don't seem to address is that, although *technically* a 5-armed
starfish could be visually 'sliced' such that two approximately-mirrored
halves result, the major factor seems to be that there is a clear
"front"/head-area/direction-of-forward-movement (or maybe all of those
three?) creating a "head to butt" line.
So, for a mathematic/gemoetrical example, you could have a star-shaped
window which is divided into two mirror/equal halves by a corner or brace
or whatever. But with living organisms, the "head to butt" line (the
spine) seems to define bilateral symmetry, and the lack there of in
starfish (and other enchnoderms, and polyps, for example) seems to define
tham as not being bilaterally symmetrical, but radially symmetrical.
In a building, I think that having equually-sized windows, or at least a
limited size-range, "feels" more ordered and more balanced - most livng
organisms tend to have a size-range for their parts, and it's possible
that a preference for that srt of order could be, if not directly
instinctual, then perhaps an inherent preference for visual order; if
learning in not just a matter of acquiring facts but also of
organizing/ordering/calssifying those facts to aid in retention and
understanding, it wouldn't surprise me if that 'spilled over' so to speak
into the visual realm.
Actually "classic" window sizing usually makes the windows of the main floor
larger (usually longer) that windows of subservient floors. This identifies
the "important" areas and pleases the eye. The dimensional change need not
be large, just enough to percieve. Often the difference between a beloved
building and an awkward building lies in very subtle relationships between
elements and how the eye is pleased or not pleased by them. Remember that
"God is in the details" and "If architects built buildings without engineers
they would fall down, but if engineers built buildings without architects
they would be torn down."
True. I think that's part of what I was calling (in quotes as it
wasn't/isn't, AFAIK, a technical term) "balanced assymetry". It's
somehting you see mose of the time in nature - looking at feathers,
scales, and leaves, tehre is a variation in size between teh individual
things, usually related to their position on the creature/plant, also
usually gfalling within a certain overall range. IOW, the architectural
elements, similarly to the natural elements, vary in an ordered manner,
not just "willy-nilly".
I was thinking about 1.618 and 1.414, .75, and a few others that seem to
recur in human-made items, and why they do recur, and they seem to echo
common natural ratios.
I don't think it's only a matter of "visual habit" for lack of a more
technical term; starting at the atomic level, moving through the
reflection of of atomic and molecular shapes in crystals large enough to
be visible to the human eye, and on to the structures of plants and
animals, there is a perceivable order to the structure of things, and
it's been theorized that this order is sensed at a fundamental level by
the brain, even primitive brains, and was carried through to the human
brain. The brain seeks to impose order even upon random disorder, which
psychologists theorize is the reason that children "see a bunny in that
cloud", and why other shapes/images seem to occur in random patterns.
I don't say that visual habits don't exist, but that there is some sort
of fundamental (and subconscious) preference for order, and that ratios
such as 1.414 were (and are) part of the human visual vocabulary because
they do coincide with the organization of natural structures.
And I think it's usually subconscious. I don't know whether any study
has ever been done that takes pictures of things which are considered
beautiful, and very subtly alters the proportions/composition/etc., then
asks people to judge which version is the "most beautiful" - I'd be
interested toknow whetehr one has been done, and if one hasn't, I think
it'd be interesting to do such a study.
Anyhoo, I discoverd what you mentioned when I'd started modeling
builidngs in 3D. As you said, the difference (between, for ex., upper
storey windows and main-storey windows) is pretty small, but i's true
that, when I first modeled something and (erroneously) made all teh
windows identical, it was definitely less pleasing as a model than it was
when I fixed the error (after measuring the windows).
True, and in so many things ;)
I never hear that quote, but it's a good one to remember ;)
The next system that is used when symmetry isn't is eccentricity. The CG is
located with the building mass being used. The main entrance can be placed
at the mass CG for balance around the entrance. Of course the rest of
design properties like proportion, repetition and other properties of design
etc. needs to be considered. this system can be used for beautiful
buildings if done correctly.
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