Question
If vertical describes up-down & horizontal describes left-right, what word describes near-far?
Answer
The correct answer (nah, this is not a subjective question) is "temporal" but the explanation is involved.
***gulps some vodka and settles in***
Your question is conflating distance, direction and sign (negative/positive), and in a biological sense, notions of observation, orientation, measurement and movement. Things can be near-far along both vertical and horizontal dimensions.
In vertical, up/down is a direction sign indicator, while high/low (with adjectives like very or comparative forms) is a near-far distance indicator. Also note that vertical is defined by gravity, not your body. When you turn, "left" changes, but when you fall down, "up" does not. This is important.
By contrast, horizontal IS defined by your body. You are reducing it to left-right because the horizon (related to "horizontal" etymologically) goes left-right in front of you. But if you turned ninety degrees, you'd still see a horizon. Technically, you're approximating a curved space (the horizon circle) with a tangent space (left/right) locally.
*** swig of vodka, inner aerospace geek awakens, brain shifts to SO(3) ***
So what you're REALLY saying (and yes, I am putting words in your mouth) is that you want to work with an informal vocabulary for a cylindrical coordinate system consisting of a radial, arc-angle and vertical dimensions. This assumes a sober person who does not fall down frequently for instance.
In this coordinate system, vertical is defined as usual. Left-right would be the angular pan dimension, and fine, call that horizontal if you want.
You can pan vertically as well (in a spherical coordinate system those 2 pan directions would be azimuth and elevation), but that brings in 6d rigid-body geometry. We'll stick to 3D.
So what you are looking for is the radial, or "zoom in/zoom out" direction in a 3d coordinate system (pan angle defined by degrees left or right from "straight ahead" OR meters left and right on an approximate projection plane in front of you), height above/below defined in length rather than angle, and a radial dimension descriptor).
Or to boil it down, you want "near/far" in the in/out sense with respect to the direction you are currently facing.
Traditionally there is a name for this dimension, corresponding to vertical and horizontal.
It is (tantarraaa!!!!): temporal.
The analog to vertical and horizontal would be temporal.
The one-bit polarity would be neither near/far or in/out (both of which are abstract geometric pairs) but front/back.
Like left/right, front/back is relative to the geometry of the human body, not abstract geometry. Front is mapped to the future, back to the past.
The near/far measure (corresponding to high/low) would be soon/late or forward/backward (notice the movement connection here... and the fact that these words are also used to talk about time itself). We also use the up/down vocabulary for complicated reasons (a person coming up towards you grows taller due to perspective effects... stuff like that). We use time and distance measures interchangeably (the restaurant is 5 minutes ahead/2 miles away).
Most human cultures structure this particular direction via the metaphor of time and turn radial in/out into future/past. Because humans MOVE in this direction. We don't fly up like superman, and we don't scuttle sideways like crabs. Near = takes less time to get to, far = more time to get to.
("Metaphors we Live By" by Lakoff and Johnson, which I've cited many times, has lots more on this stuff, and many philosophers and anthropologists study this)
So I give you your answer: vertical (up-down), horizontal (left-right) and temporal (front-back) metaphoric space, with a near/far measure applying to all 3 (but only one of which we can move along as bipedal land mammals, we can scuttle sideways if forced to, but don't have language for it).
*** another swig of vodka ***
If you don't like sneaking in time metaphorically, you'll have to invent your own culture. And that's precisely what many scientific and engineering disciplines do. But if you want your own informal language, may I suggest:
Radiontal. As in, the radial dimension.
*** bottoms up on the vodka ***
As a bonus, I'll give you my thoughts on a full 6D spherical coordinates orientation vocabulary for a hypothetical sentient fish or flying species that does not have a neck (i.e. it always looks straight ahead towards where it is going).
So to send this alien species towards a particular star, say, you'd say things like, "alright, turn nup a bit, now turn sown a bit, now swim/fly straight ahead for 3 days).
Okay, enough vodka. I have to stop myself from working out an orientation/movement vocabulary for an articulated ball-joint neck creature that can look in a 3D space while moving in a 6D space with 2 constraints.
***gulps some vodka and settles in***
Your question is conflating distance, direction and sign (negative/positive), and in a biological sense, notions of observation, orientation, measurement and movement. Things can be near-far along both vertical and horizontal dimensions.
In vertical, up/down is a direction sign indicator, while high/low (with adjectives like very or comparative forms) is a near-far distance indicator. Also note that vertical is defined by gravity, not your body. When you turn, "left" changes, but when you fall down, "up" does not. This is important.
By contrast, horizontal IS defined by your body. You are reducing it to left-right because the horizon (related to "horizontal" etymologically) goes left-right in front of you. But if you turned ninety degrees, you'd still see a horizon. Technically, you're approximating a curved space (the horizon circle) with a tangent space (left/right) locally.
*** swig of vodka, inner aerospace geek awakens, brain shifts to SO(3) ***
So what you're REALLY saying (and yes, I am putting words in your mouth) is that you want to work with an informal vocabulary for a cylindrical coordinate system consisting of a radial, arc-angle and vertical dimensions. This assumes a sober person who does not fall down frequently for instance.
In this coordinate system, vertical is defined as usual. Left-right would be the angular pan dimension, and fine, call that horizontal if you want.
You can pan vertically as well (in a spherical coordinate system those 2 pan directions would be azimuth and elevation), but that brings in 6d rigid-body geometry. We'll stick to 3D.
So what you are looking for is the radial, or "zoom in/zoom out" direction in a 3d coordinate system (pan angle defined by degrees left or right from "straight ahead" OR meters left and right on an approximate projection plane in front of you), height above/below defined in length rather than angle, and a radial dimension descriptor).
Or to boil it down, you want "near/far" in the in/out sense with respect to the direction you are currently facing.
Traditionally there is a name for this dimension, corresponding to vertical and horizontal.
It is (tantarraaa!!!!): temporal.
The analog to vertical and horizontal would be temporal.
The one-bit polarity would be neither near/far or in/out (both of which are abstract geometric pairs) but front/back.
Like left/right, front/back is relative to the geometry of the human body, not abstract geometry. Front is mapped to the future, back to the past.
The near/far measure (corresponding to high/low) would be soon/late or forward/backward (notice the movement connection here... and the fact that these words are also used to talk about time itself). We also use the up/down vocabulary for complicated reasons (a person coming up towards you grows taller due to perspective effects... stuff like that). We use time and distance measures interchangeably (the restaurant is 5 minutes ahead/2 miles away).
Most human cultures structure this particular direction via the metaphor of time and turn radial in/out into future/past. Because humans MOVE in this direction. We don't fly up like superman, and we don't scuttle sideways like crabs. Near = takes less time to get to, far = more time to get to.
("Metaphors we Live By" by Lakoff and Johnson, which I've cited many times, has lots more on this stuff, and many philosophers and anthropologists study this)
So I give you your answer: vertical (up-down), horizontal (left-right) and temporal (front-back) metaphoric space, with a near/far measure applying to all 3 (but only one of which we can move along as bipedal land mammals, we can scuttle sideways if forced to, but don't have language for it).
*** another swig of vodka ***
If you don't like sneaking in time metaphorically, you'll have to invent your own culture. And that's precisely what many scientific and engineering disciplines do. But if you want your own informal language, may I suggest:
Radiontal. As in, the radial dimension.
*** bottoms up on the vodka ***
As a bonus, I'll give you my thoughts on a full 6D spherical coordinates orientation vocabulary for a hypothetical sentient fish or flying species that does not have a neck (i.e. it always looks straight ahead towards where it is going).
- Vertical (up/down, high/low... z-axis)
- Horizontal (left/right, more/less... theta-axis)
- Temporal (front/back, soon/late, near/far... r-axis)
- Noddingal (nup/nown, less/more... pitch angle)
- Shakingal (sup/sown, less/more... yaw angle)
- IndianNoddingal (iup/iown, less/more... roll angle... like the famous nod that my fellow Indians and I are famous for, and which no foreigner can replicate unless drunk).
So to send this alien species towards a particular star, say, you'd say things like, "alright, turn nup a bit, now turn sown a bit, now swim/fly straight ahead for 3 days).
Okay, enough vodka. I have to stop myself from working out an orientation/movement vocabulary for an articulated ball-joint neck creature that can look in a 3D space while moving in a 6D space with 2 constraints.