Note: The spatial dimensions are mostly hard scifi, but with a touch of fantasy. They provide some unique options for player abilities and advanced technology.
Humans have a very difficult time visualizing more than 3 spatial dimensions. We understand "up-down", "right-left", and "forward-backward", but cannot visualize any other direction(s). Our life experiences navigating in 3 dimensions give us a seemingly intuitive understanding of operating in our three familiar dimensions, but we have no way to visualize a 4th spatial dimension, much less any more. The math required to process additional dimensions is trivial, but we can't really visualize it in our own minds.
It will require some supporting graphics to properly explain the concept of even 1 additional spatial dimension, and i have yet to create those. Those of you who already understand the concept should agree that the 'Spatial Dimension Principles' are almost all straight sci-fi and follow logically from the existence of the additional dimension(s). For now i will not try to explain this for those who don't understand the math and simply provide the conclusions one would draw from that explanation.
The existence of additional spatial dimensions opens many game-related options that aren't possible without them.
Here are some the core definitions & principles associated with the existence of additional spatial dimensions.
Mathematically speaking, all entities have a location and size in all 7 spatial dimensions. The location and size of entities are each expressed as a comma-separated list of 7 numbers enclosed in {}, with the values listed in z,y,x,w,v,u,t order, e.g. Size = { 1, 4, 6 ,0 ,0, 0, 0 }.
Note: the reversed order places the dimensions (z/y/x) in which almost all game activities will occur at the beginning of the display. Even in games where the display of all 7 coordinates will be provided, the players will most often want to focus mostly on their unit's x/y/z coordinates
In many campaigns, there won't be mechanisms to move entities through one or more of the t/u/v/w dimensions, and even in campaigns where it is possible it will seldom be the norm. For most entities at most times, tracking only their x/y/z co-ordinates is sufficient. When the tracking of all 7 dimensions is not necessary, location and size can simply be expressed as a comma-separated list of the 3 numbers for the z/y/x values enclosed in {}. Since that number of co-ordinates is more manageable than 7, i'll use it to show an example of how to interpret location and/or size data in this documentation.
In the rare times when one would need to track specific extra-dimensional co-ordinates for any of t/u/v/w dimensions, all 7 dimensions will be tracked explicitly in the indicated order, even if not all were going to be affected. We track EITHER 3 dimensions or all 7 dimensions for entities.
Additional Note: Although the dimensions are objectively equivalent, from the perspective of the homm species the x/y/z dimensions are 'home space' or 'normal space' while the 't/u/v/w' dimensions are 'extra-dimensional space'. These are homm-centric phrases, but we ARE homms so i'm going to use them as convenient reference terms throughout the documentation.
Entities which exist in normal space have values for their x/y/z co-ordinates that correspond to their current location in whichever coordinate system is in use for the scale of the current game arena. These values change as they move.
The G.U.T.S. application tracks the size and location of the units, items, etc, to a precision of 1 cm in all 7 dimensions when using the melee arena, but the user may choose to display only x/y/z coordinates when those are all that matter. At 1 cm per pixel, a 12000 by 12000 bitmap (the largest currently supported) provides a background image for a battle field 394' * 394'. When a larger arena size is required, a higher scaling factor can be applied to the bitmap.
Entities native to our 3 dimensions are born with 0 values for their location in each of the other four dimensions and those will remain 0 unless the unit is directly acted upon by something which can exert force in one or more of the extra-dimensional directions. If the extradimensional space into which they have moved does not provide 'life support' (i.e air, a place to stand, etc.) the unit will perish and be lost forever to those who inhabit only the home space from which it moved.
This discussion would apply no matter which set of 3 dimensions one chose to be the home space for an entity. However, all examples will use the most common situation: an entity native to the x/y/z dimensions moves into one of the other 4 dimensions.
The existence of additional spatial dimensions opens many game options that aren't possible without them. The closest we can visualize this would be to imagine that we live in a 2 dimensional world from which we cannot move or look up. We can see and move only forward, backward, right, and left. An entity which could move up or down at will would have many advantages over us.
When that entity moved up it would appear to vanish completely to the entities that can sense only forward, backward, right and left directions. Entities from its native 2 dimensions do not have 'sides' in the up/down directions because these directions do not exist for them. In this example that would manifest as entities native to the 2 dimensional planes having no tops. From its vantage point in the up direction, if it can turn its senses to look back the direction from which it has moved, while looking down the entity would be able to look into and 'behind' the entities which remain in its native 2 dimensional plane.
Because entities are not bounded in the dimensions to which they are not native, an entity which has a way to move objects in any of the dimensions to which that entity is not native - by any means - would be able to extract or insert objects from/into sealed containers or 'solid' entities of any kind without breaking their surfaces in the home dimensions.
We have multiple words for motion in the directions of the x,y,z dimensions. Here are the Mind Adventures standard names for movement in all 7 bi-directional dimensions.
Game-related example:Perdido has telekinetic psy ability in multiple dimensions. He has trained himself to interpret the view of the normal world that he gets when he has moved himself into the w dimension. He sees an unknown woman approaching, so he moves himself irn 5 feet before she notices him. He is now effectively invisible to her, even if she moves to the spot directly adjacent to him in normal space. From his vantage point in the w dimension he sees that she has a sealed note in her pocket, and because he has significant practice using sight from the w dimension, he can also see inside the envelope to read its contents... all without reaching into the pocket or opening the envelope. The note is a contract to kill him. Perdido, who can see and interact with the inside of a person as easily as the inside of an envelope, inserts some slow acting poison directly into her stomach without the need to pierce her skin or have her swallow it. This occurs without her being aware of it in any way. After she walks away, Perdido moves himself ort 5 feet, which return him to his previous place. Shortly thereafter, while walking, he comes upon her corpse on the road.
All the content on this page above this point is 'hard scifi'. If additional spatial dimensions do exist and are accessible, the above discussion would all follow logically from there. Everything from here out ALSO applies in Mind Adventures, but there is no scifi justification for any of it. This section is far more fantasy based. The properties associated with each of the extra-dimensions were chosen for their convenience in creating options for Powers, magic, and advanced tech which i wanted to incorporate into Mind Adventures. You got me! :-)
The laws of math, physics, chemistry, and biology of which we are aware are not constant across extra-dimensional space. We live at co-ordinate 0 for each of the t, u, v, & w dimensions. Movement along each of those axes (or rotation around the associated axis) changes what we think of as an associated universal constant as one moves farther either direction from 0.
One does not need to fully understand matrix transformations and manipulations to understand MAMM, but for those who do know that math this should all be very easy to follow.
Translation is the first of three transformations that can be applied to entities. Translation is the formal name for 'movement'. Movement within our 3 dimensions is well understood and requires no further discussion. Movement into or within any of the additional spatial dimensions was discussed in section: "Moving Out of One's Native Set of 3 Dimensions". The discussion in that section defines the implementation of Dimensional Translation in MAMM, but it doesn't require any special postulates to function as defined. Everything in that section passes muster as hard sci-fi.
Translation exhibits inertia: an object that has been moved to a specific location will stay in that location until additional force is applied to it. This applies equally to movement in any of the t,u,v,w dimensions. An entity which has been translated outside of its normal dimensional home into one of the additional dimensions could be stranded there forever if it has no way on its own to move back in the direction that it came and no unit which does have that ability comes to its rescue.
Entities are generally able to move naturally in all three of the dimensions which comprise their home space. The most common form of translation is walking. Most animals can move fully in two dimensions. They can go forwards, backwards, right or left at will. Some can move in the third dimension of their home space as well (up/down) by climbing or flying. I suppose technically they could all move in the third dimension (down) if they stepped off a cliff, but that would be from gravity, not their inherent ability to move in that dimension :-).
Translation of a unit can occur many ways. Some chosen by the unit, some not. Vehicles can allow units to move in directions that the unit itself cannot move. Powers, magic, and/or technology can move units in any of the 7 dimensions.
Scaling increases or decreases a unit's size along the associated dimension. A unit may be scaled either direction along one or more axes.
Scaling along a specific axis is based on the scaled unit's spatial perspective. For example, scaling a unit along the y axis will increase the unit's height regardless of the unit's current stance, or relative position to the source of the scaling.
Scaling along a single axis causes the scaled entity to be 'stretched' along that axis. While that scaling is in effect, the entity will be 'out of proportion' to its normal appearance. To resize an entity in all three dimensions would require explicit scaling along each of the three dimensions simultaneously. The same effect can be achieved by a single rotation around the v axis (see below). Because the effect was more easily attainable through that Power, the lesser useful ability to scale only along a single axis isn't as commonly found.
Standard units have no existence in the t, u, v, & w dimensions, so scaling them along those axes has no effect. Similarly, the ability to scale entities in those dimensions is exceedingly rare in standard units.
Rotation changes an entity's orientation in space. We use the terms pitch, yaw, and roll to descrive rotation around our home dimension's axes. Rotations around each of the other 4 dimensions will cause the rotated unit to exhibit the associated effect. The rotated unit will not move into extradimensional space. Rotation does not cause movement. But the rotation will show a "different face" of the rotated entity for as long as the rotation remains in effect. This chart shows the effect of rotation around each of the extra-dimensional axes. Clockwise rotation increases the effect, counter-clockwise rotation decreases the effect.
Axis Effect on Rotated Entity
z The roll of the entity
y The yaw of the entity
x The pitch of the entity
w The mass (and thus weight) of the entity
v The size of the entity
u The state (solid, liquid, gas) of the entity
t The rate of passage of time for the entity
Rotation in the x, y, or z dimensions has inertia. An entity rotated in any of those dimensions will remain at that facing until the entity or some other force changes it. Rotation in any of the extra-dimensions is not permanent. An entity which has been rotated around the t, u, v, or w axis will eventually snap back to its normal facing of 0 in the associated dimension. The effect will not wear off gradually. It will be in effect for as long as it is, and then the affected entity will revert to its normal state.
The rotated entity will increase or decrease in mass. The entity will not see a meaningful change in strength from the rotation. It is common for an entity which has experienced an increase in mass to be unable to support its own weight.
The rotated entity will increase or decrease proportionally in size in all three of its home dimensions. The entity will not see a change in mass from the rotation. It is common for an entity which has experienced an decease in size while retaining their mass to put too much "pounds per sq inch" pressure on sufaces where they stand.
The rotated entity will become more or less 'solid', but retain their full mobility. Entities which become less solid will first begin to exhibit the physical traits of liquids. As they progress further in that direction, they will exhibit the physical traits of gases.
Entities which have rotated toward the less solid states will retain a degree of cohesion for their bodies and carried items. A unit's internal organs would exhibit a degree of 'surface tension' to maintain the organ whole. However, unit's in this state which cannot bring additional factors into play to maintain their cohesion may be destroyed by having their bodies 'dispersed' by hostile action.
The t dimension contains an infinite progression of spaces which exist in parallel to our own. Each space experiences the passage of time at a slightly faster or slower rate. Rotation around the t axis causes the rotated unit to 'move' faster or slower accordingly.
The effect does not make the unit explicitly *move* faster or slower. It changes the rate of the passage of time for the affected unit. Movement speed is affected, but so is the speed of any other action the unit takes, as well as the effect of potions, healing, or any other effect which occurs to that unit over time.
Each extra-dimensional rotation effect has its uses, but the usefulness of the w, v, & u effects increases when one has two of them, and even more with all three. The ability to change both mass AND size as desired is an obvious improvement. The ability to change size and state would allow a unit to resize and reshape its body at will.
As noted above, the t dimension presents as an infinite series of parallel spaces. Each space contains an entire universe like our own, but in which the rate of the passage of time is slower or faster than ours, depending on which directiona nd how far one goes.
Units which can perceive the t dimension via any means can 'see' the immediate past and most probable future of the space around them. Units canot physically move in either direction along the t axis
Looking faz or tarth allows one to see the 'next' reality in an 'infinite' array of 'reflections' of our reality. At our location in the t dimension, time passes at the familiar rate. Looking faz shows one to a reality exactly like ours, except that time passes in that reality just a bit faster than in ours so it is ahead of us. Looking tarth shows one to a reality exactly like ours, except that time passes in that reality just a bit slower than in ours. Change in that dimension is quantized, such that viewing does not register 'between the reflections'. Each view is into a universe that is one second before or after the previous universe. We think of our location in that dimension as a standard, but in truth no location is more a standard than any other.