Q:  Why don't cows, sheep, and goats have their top front teeth?  (Shannon, World)

A veterinarian bares a goat's dental pad.  Photo courtesy of Melissa Rouge of Colorado State University, used with permission.

A: Not just cattle, sheep and goats, but all 192 living species of ruminants — antelopes, giraffes, pronghorn antelopes, deer, musk deer and tiny chevrotains (mouse deer) — lack top incisors.  All these animals have a tough dental pad below their top lip instead of front teeth, and a huge gap between the dental pad and the back teeth. 

This dental arrangement helps ruminants gather great quantities of grass and fibrous plants.  A cow, for example, wraps her long, rough, dexterous tongue around a big wad of grasses, pulls the green stuff into her mouth, fits the wad into the huge gap (between front pad and back teeth), pinches the strands about six inches from the ground between her bottom incisors and her top dental pad, and, by swinging her head, neatly cuts a big swath of grass.

Tooth and jaw structure of cattle:  a top dental pad instead of top front teeth and a large gap between the pad and the back molars.  Drawing courtesy of Sarah Williams, Virginia Cooperative Extension; drawing modified by the author.

Ruminants, you may recall, have a complicated four-chambered stomach that allows them to regurgitate their food as a cud, grind it more thoroughly at their leisure, and, thereby, get a maximum amount of nutrients from a given amount of food. 

But ruminants' early ancestors did have all their teeth, just as pigs do now. The earliest known ruminant (Archaeomeryx) looked like a small deer, about hare sized, but had fully functioning front incisors.  They lived about 50 million years ago (during the Eocene epoch) in what is now Mongolia.  Over the eons, the creatures lost their front teeth.  Interestingly, these deer are still around today, dwelling in forests by streams of Southeast Asia and West Africa — little changed from their ancestral form. 

Speculating why the ancestral ruminants lost their top cutting teeth (replacing them with a tough dental pad) takes us into unmapped country.

"I think nobody has a good answer," says paleontologist Christine Janis, professor at Brown University.  But her "best guess" is "it has something to do with ruminants being highly selective feeders."  They are picky about what they jam in their stomachs, because whatever they eat goes through many lengthy, digestive processes.  They choose food of value, where they get their money's worth for the time investment. 

Moreover, ruminants use their tongues to select good food (leaves, for example, over stems), and so treat their tongues with respect.  "I can imagine natural selection acting on loss of the upper teeth, so as to not bite and injure their tongue," says Janis.   "However, that's pure speculation, not a testable hypothesis."

Her guess makes sense, though, because camels select food with tongues, have a three-chambered stomach, regurgitate their food and chew their cud.  Thus, they almost qualify as ruminants.  Moreover, they have some reduction of upper incisors.  Horses — on the other hand, who use lips, not tongues, to select food — have big, fat, front teeth.

Further Reading:

Dental anatomy of ruminants by Melissa Rouge and Richard Bowen, Colorado State University

Digestive System of the Cow by John B. Hall, Virginia Cooperative Extension, Virginia Tech and State Universities

The osteology and relationships of Archaeomeryx, an ancestral ruminant by Edwin H. Colbert, American Museum of Natural History

Motility of the gastrointestinal tract of ruminants by Dr A.L.R. Findlay, University of Cambridge

Q:  Is the image we see of ourselves in the mirror really what we look like?  (Mreason, World) 

A: Robert Burns didn't think so.

A mirror rarely, if ever, depicts us as we encounter life — thoughtful, terrified, contented, curious — ways showing what we "really look like."  Instead, it returns a bland, slightly bored look, as we check our reflection.

Through a looking glass, darkly... [Lewis Carroll]. Photo courtesy of Chris Seaton and Wikipedia.

But, aside from such philosophical matters, does a mirror accurately reflect an object placed before it?  Yes, a good plane mirror does, with minor distortions (indicating slight imperfections) we don't even notice.  We can easily check this out, though few would doubt it. 

I hold up my right hand, and look at my palm carefully.  My thumb sticks out to the right.  Now I turn it the other way to face the mirror, and check the reflected image of my palm in the mirror.  It looks the same, except it's turned about the vertical axis, because I turned it about the vertical axis to see my palm in the mirror.  My thumb in the mirror sticks out to the left.  More about this "mirror image" phenomenon in a moment.

Back to the other image characteristics:  They look the same and, consequently, my palm looks the same because we sight along lines of light to see.  The figure (left image) below shows a green-eyed man looking at a bronze ball.  He sees the ball because a ray of light reflects from the ball to his eye, as indicated by the arrow showing the line of light travel.  The right portion of the figure shows what happens when the green-eyed man places the ball in front of a mirror.  Light reflects again from the ball to his eye, so he sees the ball, but the light follows a broken path.  It reflects from ball to mirror, bounces off the mirror with the same angle that it came in, and reflects to the green-eyed man.  The man sees the ball as if it were behind the mirror, as shown by the dashed line to the ball image. 

Comparing the left with the right portion of the figure, illustrates the fact that the man sees the mirrored ball exactly as he sees the ball directly, because the mirror reflects light to his eye in a special way.  That special way is the law of reflection (click for cool animation), first discovered by Claudius Ptolemy in about 115 AD: 

A light ray incident upon a reflective surface will be reflected at an angle equal to the incident angle.

And that is the physics behind why a plane mirror shows us, maybe not as we really are, but as if we could see ourselves directly (but behind the mirror).

Minding p's and q's through a mirror. Drawing by author.

Now, let's return to the "mirror image" problem.  I hold up a card, facing me (much as I did my palm), and I read

q

p

Then I turn the card about a vertical axis (as I did my palm) so it's facing the mirror, read the card in the mirror, and I see the mirror image — a left-right reversal:

p

q

as the heavy black letters in the mirror of the figure show.

But I notice something cool.  Looking through the card (by holding it up to the light), I can simultaneously see the same letters (illustrated by the light gray letters) as I see in the mirror.  I read the same thing through the card and in the mirror.  Thus the so called 'mirror image' is strictly a matter of rotation.  With no rotation (seeing through), there's no mirror image (I read the same thing).

Moreover, I can change the 'mirror image' from left-right reversal by changing the axis of rotation.  If I rotate about the horizontal axis (instead of vertical) I get

b

d

an upside-down reversal instead of left-right.

Almost all readers commented on the fact that the mirror image is reversed.  That's why.  I must rotate the card some way or other to face it into the mirror.  When I rotate it, I reverse left and right, or up and down.  Unless,  I just look through the card with light shining through it.  Then nothing gets reversed, because I didn't turn the card. 

The same thing happens with us when we look in the mirror, as my palm example shows. 

I am indebted to MathPages.com for the card example.

Readers' Answers:

•  It's a reflection image, not altered in color, shape or any other element that may distort it.  So, in that sense, it's the same.  But, when we see ourselves in the mirror, it's backwards, and backwards is by definition, not the same as the original.  So, no.
  Kriste, Belchertown, Massachusetts
• Yes, the image we see of ourselves in the mirror is really what we look like, only it is inverted.
  Shane Seby, Muscat, Oman
• No — what you see in the mirror is not the same image others see when they look at you. What you see is a reverse image, literally a "mirror-image," of yourself!
  Crystal Ferguson, Allen, Texas
• Yes, because it looks like you and, no, because if you had raised your right-hand thumb, your mirror image would have raised its left-hand thumb.
  Gee Waman, Mumbai, Maharashtra, India.
• Some mirrors distort features, so the quality of the mirror has some bearing on just how much you actually resemble the image you are seeing of yourself.
  Lori Godby, McConnelsville, Ohio
• No, the image in the mirror has different direction or orientation.  The left hand with the watch, becomes the right hand in the mirror.  The left-right reversal depends on how you look at it.  If you choose an absolute direction, instead.  Say you stand facing North in front of the mirror, your image faces South.  It's just perception.
  Hitesh Sachan, Seattle, Washington
• I sure hope not.
  Galen, Maynardville, Tennessee

Further Reading:

What mirrors do MathPages.com

Law of reflection (animation) by Michael W. Davidson, Florida State University

Reflection and the line of sight by Tom Henderson, Glenbrook South High School, Glenview, Illinois

Conceptual Physics by Paul G. Hewitt

(Answered Sep. 5, 2006)