So, how do we understand the term "dimension"? We could do the sophomoric thing and put a definition (somebody else's words) in front of us - maybe Wikipedia or Webster or whatever - and call the whole thing done. That would certainly appeal to the almost insatiable need for "closure". But, here, that would mock the point. Again, the question is how do we understand the term? It's your mind, after all. You get to decide what goes into it, what it means to you and how it gets related to the other contents of your mind and used in the physical world.
Or am i mistaken?
Yes, believe it or not, some people want to impose rules on what you do during your own information assimilation and sharing process. Amazing. If that doesn't smack of insidious, I don't know what does.
Some of us use the term "dimension" loosely to refer to refer to some kind of realm. Is that what it means? Is a "dimension" a "realm" in your understanding? You can pull-up lots of YouTube videos filled with conjecture about alien visitors or supernatural phenomena from "another dimension". So does that really mean anything to us?
To me, it sounds like a dressed-up way of saying "from some other place." Not quite as mysterious or cool sounding, is it? I guess that's why I don't write those programs.
Besides... well... if they (whoever "they" are) occupy more than one "dimension" the way we supposedly do, having physical extent in them, they don't so much "come from" another dimension (singular) but, more accurately, EXIST IN a whole set of dimensions that includes our own. They can move in one or more directions that we do not even conventionally perceive or have mobility in. At least, not at will. Already, the terminology is getting tedious. Isn't it?
Here's another usage: A dimension is a measurement. The "dimensions" of a house, for example, might be all the numbers used to define its floor plan. We might ask, "What are the dimensions of your room?" Just don't let "Pickafunnickname9-2" hear you say that.
Ok, here's another one: In some contexts a "dimension" is a degree of freedom. That might apply to a robot arm or mechanical machining tool and describe the number of "axes" the thing has that can be controlled. A "five dimensional" tool, or a "five-axis" tool isn't really a hyper tool, extending outside of our normal space. Instead, it's something whose configuration in space permits (or requires) five parameters to specify it. It could have a moving, horizontal "X - Y" stage and a vertical "Z" head, but also the ability to set the angle of attack for its drill bit or end mill, and maybe another angle, too. You can go look that stuff up on the web, if it interests you. The point I want to make with the tool example is that lots of engineers and people who make stuff consider it very useful to have a machine that they can control using more than just three spatial parameters. Otherwise it's too hard to make some complicated shapes out of blocks of metal or whatever.
How else do we use the term? In many sciences, we use the term generally to cound the number of things that coexist independently but that all conspire to create a given outcome. In other words, we use the term "dimension" to describe an abstract parameter space. that could be a "space" for describing some physical situation that has one "axis" to represent temperature, another to represent pressure, another to represent time and another to represent something else. I have personally worked on problems like these that have a parameter space with twenty-one or more dimensions! Talk about solving a Rubik's Cube! But when I have found the optimal solution in that 21-D space, the result has sometimes been patents and commercially-successful products. Crazy, huh?
How else? In mathematics, we can just MAKE-UP spaces of however many dimensions interest us and do math in them! I love it!
And what about programming? Ah, that's the one that should be on our minds. Does programming get any benefit out of the idea of a "N-dimensional* space? Yes. Absolutely. When we create "vectors" (not the geometric kind) or "arrays" or whatever term your language happens to use, you generally work with a variable name - let's call it "M" and call out its "indices". There's one "index" per dimension of the construct. So, we might have a "2D" array called "M". We could use the letters "i" and "j" to refer to its indices. So "M" refers to the whole collection of stored values. And "M(i,j)" is a way of accessing one of them. To specify a certain element or "location" inside of "M" we might say, "M(3,5)" to refer to the 3rd value of "i" and 5th value of "j" inside of "M". Let me drop the quotes. They're a pain. So, M(3,5) could have the value, 2. and M(1,1) could have the value 10 or pi or something else. Doesn't matter. What makes this USEFUL is that in a program I can use code to decide which i or j I care about or do something with and work with it by coding for M(i,j) instead of having to create a whole new variable name for each element inside of M. That, is exactly what I have done with my "4D4U" code and why I have so named it.
What makes the code significant - and what I had hoped fellow Hopscotch users might find useful - is that I came up with a way to define several variables for EACH CLONE that can (though they don't have to) have something to do with how they get displayed. So the clone is like the "M" and the referenceable properties of that clone are the "indices". That's what made it possible for me to create the illusion of each clone having a "location" in "3D space" as well as to let that location change in "time." Hence, 4 dimensions, 4 degrees of freedom, 4... whatever... indices! K? Until Hopscotch introduces the concept of arrays or provides "self" properties for clones, I submit that this is a good way to get there from here.
I will say more about the technique, if it interests anyone. Meaning, if there's a question here.
In the next post, I will treat the very specific case of spatial and time dimensions that seems to have caused some confusion. What we're talking about above is all very (beautifully and powerfully) general. In that subject, we'll be putting on our "physics" blinders and narrowing the scope of the discussion. Although, honestly, it's not that mysterious.
Hopefully the foregoing has been useful. At least a little...?