Go equipment is a marvel of ancient engineering for a lot of reasons.

1. Eye shaped cross section of the Go stone.

a. It's the minimal volume shape which is self stablizing and which holds an easily graspable, elevated edge horizontal. It's always right side up of course. The minimal volume matters because 181 stones have to fit comfortably in a bowl, not a bucket. Besides the stone's shape being of minimal volume, it has to fit together well with like shapes. Go stones fit together more snugly, i.e. with less airspace per stone, than do marbles for example.

b. Go stones absorb energy from board and stone collisions by rolling, and then release the energy as friction from continued back and forth rocking on the board while possibly brushing against neighboring stones.

2. The board is undersized in the latitudinal direction, why? Is it to make the board appear more square from a seated position?

No. For one thing, the stones, the focus of the game, appear less round from a seated postion. A square looking board is little consolation.

Visual overlap. Like-colored stones in a group appear more group-like when they visually overlap. Like-colored stones in longitudinal sequences tend to visually overlap because of the seated angle of view. But the seated angle of view has no affect on the appearance of a latitudinal stone sequence. By making the board too small in the latitudinal direction, the stones are forced to zigzag slightly, resulting in visual overlap from a seated position.

3. Black stones are slightly larger, why?

A gap between adjacent white stones isn't nearly as unsightly and distracting as the same size gap between black stones because of the light board color. White gives up a little of his stone diameter to Black to compensate.

4. Stones of both colors have more room than they need in the longitudinal direction, why?

Ergonomics. More room can be allowed for the easy placement of stones since the stone height is sufficient to provide visual overlap, even with a little longitudinal space between the stones.

Moreover, any zigzagging in the longitudinal direction would appear exaggerated from a seated position. Zigzagging in the latitudinal direction creates the opposite effect. Latitudinal zigzagging appears scaled down when viewed from a seated position.

When you look at the ancient design of Go equipment from the perspective of visual balance, and from the perspective of a seated player, the relative stone and board dimensions fall into place.

4. The Goban - huge block of wood. Tables and chairs of the time weren't tree stumps. Why the goban? Inertia. If you stub your toe on a goban, you get a stubbed toe. This would speak to the severity of ancient Go play. The crime of disrupting a game in progress must have been a serious one.

5. No "frame". The stones are flush with the board edge, why? Economy perhaps, in the usual sense. You'd want to make the most of the giant wood block you created. But I think economy of form would have been more important. Go is a study in minimalism. 5 faces of the block are blank and the sixth face is lines and stones - not lines, stones, and a frame.

6. Philosophical considerations were undoubtedly paramount in the ancient design of Go stones. The clam comes from the ocean. It's white and alive. Slate comes from underground, etc.

How would you improve on the Go stone? It's like the wedge. Go equipment has been optimized in every way possible, not the least of which being aesthetic and ergonomic.

ADDITIONAL NOTE

I saw the black/white stone diameter disparity explained as compensation for the optical illusion of black objects appearing smaller (witlesspedia). The problem with this theory is that there's only a difference of about .3mm out of 22mm, making black stones 1.3% larger than white stones. This minute difference is absolutely imperceptible, even between two different color stones pressed together in your fingers, never mind out on the board. However, .3mm goes a long way toward closing tiny, but conspicuous, gaps between adjacent black stones in a group, against the light wood background.

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finito ludos regula

Go equipment is a marvel of ancient engineering for a lot of reasons.

1. Single-convex stones

a. They look great
b. They don't wobble annoyingly every time somebody shakes the board
c. They don't slide all over the place at a slightest disturbance
d. You can flip them over to study variations

2. A perfect square board

a. It looks great
b. The square is a perfect shape. There's esthetic and esoteric significance to the interplay of the square board with circular stones.
c. Go is a study in minimalism
d. You don't need to worry about the "wrong side" and try to figure out which side is longer

3. The board is thick enough to look solid and be durable, but thin and light enough that you could put it in a bag and carry somewhere.

5. A xiang-qi board on the back of the go board, so you don't need to invest in two separate boards.

6. Philosophical considerations were undoubtedly paramount in the ancient design of Go stones. That's why they're black and white. And circular. Practical considerations were undoubtedly important as well. For the best quality to price ratio, I recommend single-convex Yunzi

Proving again there are no reliable answers to any of these questions, only fanciful opinions and entertaining conjecture. Thanks for not bringing up the parallax myth which is not only wrong, it's based on an incorrect usage of an optical phenomenon requiring three things, a viewpoint, a foreground object and a background object.
What about that little pyramid doodad, that cutout, on the bottom face of a traditional floor board? Is it to create a resonance? No. Removing less than 1% of the mass of dense wood will affect the sound production or sound carrying or sound modification properties of said mass of wood in no perceptible way.
I once speculated the difference in diameters between traditional slate and shell stones was simply a result of efficiency during manufacture: shell was easier to abrade than slate. When the emperor's go stone maker was asked why the white ones were smaller, he quickly made up the story about the visual appearance.

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David Bogie, Boise ID
I play go, I ride a recumbent, of course I use Macintosh.

You're welcome

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finito ludos regula

It might simply be the case that black things were expected to be larger, for some long forgotten, mysterious, unknown reason.

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finito ludos regula

here's your parallax myth
http://www.myinkblog.com/50-amazing-3d- ... an-beever/

I humbly propose my half century of woodworking observations regarding the parallax "myth." Imagine, if you will, a go board which has the same rectangular dimensions, but with the grain of the wood going in the other direction, i.e. wider on the end grain, (left to right,) and shorter in the direction along the longitudinal lines of grain forward and backward,). This is contrary to all of any craftsman's understanding of the behavior of wood, where "boards" are cut from a tree, and expand and contract width-wise to a large extent, but nearly none lengthwise. No experienced and observant woodworker in human history would orient any board of wood in this way, as it would be much likely to crack in half. Yes, the wood could be cut into a perfect square, but wood so cut would expose proportionally more of the end grain to moisture exchange which is not desirable in a shrinkage and expansion situation inherent in all blocks of wood, and would be more likely to crack as well. Added to the stability aspect, the viewpoint of the player and the parallax view factor makes for a perfect reason to make a board longer than it is wide, and to run the grain in a line between the players. Not only that, but the grain lines themselves might have been thought to connect the players in a subtle psychological or dynamic metaphysical way. Perhaps grain lines running laterally and thereby separating players would have an opposite effect, thereby placing opponents "at odds" which would be contrary to the true nature of mankind "at play."

See, but that's just an optical illusion. It only looks like they're using parallax to create an optical illusion.