Quote from: Melan;546467Elliot already touched on the issue, but I will add that hex maps are not simply a way to figure out movement, even if that is their primary function. Hex maps are the game board for wilderness travel, abstracting a continuous stretch of terrain into discrete, identically shaped and sized units.

I think you mean "can be the game board..." Some people, including me, never used hex maps that way; for us, it was never more than a way to measure distances. I never used numbered hexes, instead relying on named locales for keying encounters in the wilderness.

Your explanation does, however, explain why a lot of people seem to like the more abstract "one terrain per hex" style of hex map, which I always thought were ugly or useless. I could never understand the enthusiasm, until now; it turns out other people were using hex maps in a different way.

Quote from: trollock;547014How do you explit that? I played some games of chess and I just don't see how one can exploit its geometry.

Movement in chess is abstracted to the point that it only means you are moving a chess piece.  You could consider lateral movement as 'political' and forward/backward movement as 'physical', it makes no difference.  Ostensibly, 3.x/4e grid movement is simulating actual movement in a physical location.  I don't recall 4e errata advising the use of the solution Mr Morrow favours, which is to count one square then two squares for diagonal movement, so 4e very much is a taxicab geometry game.  Most easily noticed by setting up a figure in one square, setting up another five squares in front of the first one, then one more five squares to each side of the second one.

You can see on the map that three of the figures are clearly standing in a line, but if you use taxicab(ish) geometry like 4e suggests, the diagonals count as one, so the line on your map is actually a semi-circle.  The lone figure is exactly the same distance from the ends of the line as from the centre, which means that can't be a line.  Unless the terrain is non-Euclidean.

Quote from: talysman;547016I think you mean "can be the game board..."

Sure, I just didn't want to go into seven paragraphs worth of disclaimers.

Quote from: talysman;547016Your explanation does, however, explain why a lot of people seem to like the more abstract "one terrain per hex" style of hex map, which I always thought were ugly or useless. I could never understand the enthusiasm, until now; it turns out other people were using hex maps in a different way.

I am not using that style either, as the image I posted demonstrates.

Quote from: trollock;547034It does a really poor job at it to the point where simulation is so bad it becomes pointless.

Exactly. That is why some folks prefer hexes, especially for outdoor adventures.

QuoteHow many orcs can stand around you beating the shit out of you? I'd say it's way less then eight or even six.

No, that would be something like correct, but they would have to be pretty co-ordinated in their attacks.  Figure two per square face on the cardinals, and on more per square on the diagonals, that's 12.  But they wouldn't have room to swing a sword or anything.  They would all essentially have to thrust into the centre with long swords or a pole weapons.  But that would be a highly unusual circumstance.

Quote from: trollock;546911Whut? It's the same amount of squares going in straight line across the chessboard as when you pass it diagonally from corner to corner. All real maps and most fantasy maps are "carricatures" (the correct word would be projections) of curved space into a plane anyway so there's no point in trying to project real distances into it as it will allwas be deformed.

Emphasis mine. Wrong. What flat maps cannot do is accurately depict angles and distances and areas at the same time. They're perfectly capable of accurately reflecting any one of the three.

QuoteBoth hex grid and square grid are graphs and the only difference is to how many other nodes is each node connected.

Grids, yes. Maps, no. The difference is that unlike a blank grid or a grid depicting some random lines, a map has a purpose pointing beyond itself: to depict, in an abstracted manner, an actual (real of imagined) landscape, layout or other thing. And since it does that, the matter of accuracy becomes relevant. And for a number of purposes that are relevant in an RPG, a hex map happens to be significantly more accurate than a square one.

Quote from: John MorrowThe 1.5 distance created by making every other diagonal move the equivalent of 2 squares a pretty close approximation of the actual distance (1.4),

Psst... the word "actual" does NOT mean what you think it means. The actual diagonal of a square is NOT 1.4 times the side but √2.[/quote]

Quote from: trollockHow do you explit that? I played some games of chess and I just don't see how one can exploit its geometry.

Imagine a dungeon drawn on a square grid with the DM and the players using chess geometry. There are rooms at A1, A8 and H8, each connected to the other two with straight corridors. The villain and the party are in A8, the fight is going against the bad guy and he's trying to escape through the diagonal corridor to H8, where he can perform some terrible magic to end the world. Imagine that the party can't follow him down the same corridor because of some traps or magic defenses or whatever. Now, with chess geometry, the party could just run to A8 and from there to H8, arriving at the same time as the bad guy and stopping his plans. In reality (or with a less irrealistic geometry), they couldn't intercept the villain in time, because they have to travel a longer path. There, an exploit.

QuoteBut hexes are as bad as squares at simulating anything even remotely realistic. Only reason to use hexes instead of squares is because it fits hand drawn map better.

WRONG. Both are inaccurate (assuming movement is restricted to boardgame-style field-to-field), but hexes are less inaccurate for all but the most specific situations (say, a dungeon where every wall is at right angles, there are no rooms, and all the corridors are so narrow that people can't pass each other).


Look, trollock, by your own admission in another thread, you're thirteen. I reckon so far you haven't studied geometry or cartography at all. (Well, to be fair, probably did at primary school level, which is one tiny step above "not at all".) It's no shame to be greatly ignorant about such subjects at your age - everyone was like that at 13 -; and if you ask normally, politely, without coming across as a grating little twerp, then people will be happy to explain things and will even think "hey, he's a cool kid, he's willing to learn". But don't try to act like you're some 13 y.o. child prodigy expert on something when in fact you have significantly less than the average layperson's knowledge and try to assert your fundamentally incorrect notions and complete lack of understanding. Being ignorant is not shameful. Not realising your ignorance is not particularly shameful, but it is rather embarassing. Being willfully ignorant, like you are with your current attitude, is shameful. (And also embarassing.)

Quote from: Telarus;546878The human mind actually uses tessellated grids (triangles) to map spaces abstractly:
http://www.sciencedaily.com/releases/2010/01/100120131201.htm

Let me quote the article for the audience...

QuoteGrid cells represent where an animal is located within its environment, which the researchers liken to having a satnav in the brain. They fire in patterns that show up as geometrically regular, triangular grids when plotted on a map of a navigated surface. They were discovered by a Norwegian lab in 2005 whose research suggested that rats create virtual grids to help them orient themselves in their surroundings, and remember new locations in unfamiliar territory.

Study co-author Dr Caswell Barry said: "It is as if grid cells provide a cognitive map of space. In fact, these cells are very much like the longitude and latitude lines we're all familiar with on normal maps, but instead of using square grid lines it seems the brain uses triangles.

Lead author Dr Christian Doeller added: "Although we can't see the grid cells directly in the brain scanner, we can pick up the regular six-fold symmetry that is a signature of this type of firing pattern. Interestingly, the study participants with the clearest signs of grid cells were those who performed best in the virtual reality spatial memory task, suggesting that the grid cells help us to remember the locations of objects."

Quote from: StormBringer;547037But that would be a highly unusual circumstance.

Alternately, it would be how the Roman heavy infantry fought for centuries.  There's an old Roman maxim that "a few inches of point is worth any amount of edge" because in a close melee, you just aren't going to have room to swing anything.

Fantasy games tend to gloss over the fact that a lot of medieval weaponry was context-dependent, and a great number of weapons that have become standard for fantasy adventurers were originally cavalry weapons and are quite inefficient when you're on foot.

Quote from: Premier;547060Psst... the word "actual" does NOT mean what you think it means. The actual diagonal of a square is NOT 1.4 times the side but √2.

I believe I mentioned that earlier, but I don't think anyone has a ruler precise enough to capture the precision of an irrational number, an actual value is more useful for making a comparison of accuracy, and given that √2 is an irrational number, I doubt that a real physical diagonal move is ever actually √2 in anything but theory, either, in the sense you want to use the word.

Were you going for irony when, after being this pedantic, you decided to lecture someone else about "coming across as a grating little twerp"?

Quote from: John Morrow;547187I believe I mentioned that earlier, but I don't think anyone has a ruler precise enough to capture the precision of an irrational number, an actual value is more useful for making a comparison of accuracy, and given that √2 is an irrational number, I doubt that a real physical diagonal move is ever actually √2 in anything but theory, either, in the sense you want to use the word.

You may work in a career where "actual value" has a highly specific meaning, and this may be confusing things, since the way you are using the term is the opposite of its common meaning. Since you contrast 1.4 with an irrational number, maybe you mean "rational value"? That would make sense, since 1.4 is an estimated value or approximate value of √2, not the actual value.

Which is what prompted Premier's crazed tirade.

Quote from: talysman;547189You may work in a career where "actual value" has a highly specific meaning, and this may be confusing things, since the way you are using the term is the opposite of its common meaning. Since you contrast 1.4 with an irrational number, maybe you mean "rational value"? That would make sense, since 1.4 is an estimated value or approximate value of √2, not the actual value.

Going for coming across as a grating little twerp, then?

Do you really think the distance of a miniature moved one diagonal square on a map board has an "actual value" of √2 using the highly specific meaning that you are using it?  If so, I recommend trying a career in manufacturing, which deals with the dimensions and positioning of real world objects, rather than mathematics or theoretical physics.

Quote from: talysman;547189You may work in a career where "actual value" has a highly specific meaning, and this may be confusing things, since the way you are using the term is the opposite of its common meaning. Since you contrast 1.4 with an irrational number, maybe you mean "rational value"? That would make sense, since 1.4 is an estimated value or approximate value of √2, not the actual value.

Which is what prompted Premier's crazed tirade.

Quote from: John Morrow;547196Going for coming across as a grating little twerp, then?

Do you really think the distance of a miniature moved one diagonal square on a map board has an "actual value" of √2 using the highly specific meaning that you are using it?  If so, I recommend trying a career in manufacturing, which deals with the dimensions and positioning of real world objects, rather than mathematics or theoretical physics.

Hey, I gave you an "out" so that you could save face and the only one who would look bad would be Premier. Do you really want to rant about how stupid people are for using "actual value" to mean "what the value really is"?

Just accept that what you are talking about is the approximate value, and that approximate values are all that we need to play a game. It will help the thread move on.

Quote from: talysman;547197Hey, I gave you an "out" so that you could save face and the only one who would look bad would be Premier. Do you really want to rant about how stupid people are for using "actual value" to mean "what the value really is"?

That's not what I'm ranting about.  The use of the word "actual" in my original quote did refer to "what the value really is" as compared to the value of 1.5 produced by alternating values of 1 and 2 squares for diagonal movement.  I provided the value 1.4 parenthetically for convenience of comparison between the two values because nobody evaluating the difference between those to values was going to do so to more than a few digits of precision, anyway.  I think my point was clear to anyone not deliberately looking for something to be pedantic about and accurate in a normal vernacular sense.

Quote from: talysman;547197Just accept that what you are talking about is the approximate value, and that approximate values are all that we need to play a game. It will help the thread move on.

How about pointing out that my use of the word "actual" for an approximation of √2 without being carefully identified as an approximation should have been good enough for a casual conversation on an Internet message board about measuring distances when pushing toy soldiers around on a game board?

Quote from: trollock;547034How many orcs can stand around you beating the shit out of you? I'd say it's way less then eight or even six.

Stand in the middle of a 15' x 15' room. How many people could easily stand in a circle around you? 6 to 8 wouldn't be an unreasonable number by any stretch of the imagination.

For example, here's a video of one guy fighting a gang of people. Notice particularly around the 0:25-0:30 mark where he gets surrounded by seven people. Notice that all of them fit comfortably into the width of a single lane of traffic (which places that distance at somewhere between 9 and 15 feet).

Positioning on a grid is still an abstraction of actual positioning. If I'm looking at a battlemap in which a single figure is surrounded by 8 guys, then he's being completely mobbed: Probably ducking back and forth between them if he's not just getting pummeled. But that whole melee is taking up a space 15' x 15'. And that's a significantly large space.

Quote from: daniel_ream;547082Alternately, it would be how the Roman heavy infantry fought for centuries.  There's an old Roman maxim that "a few inches of point is worth any amount of edge" because in a close melee, you just aren't going to have room to swing anything.

Oh, sure, in real life.    To clarify, then:  It would be unusual in a dungeon to be mobbed like that.  Kobolds or goblins, maybe; most humanoids tend to show up in numbers roughly equivalent or slightly higher than the party.

The Romans did tend to box things up a bit, though, so part of the lack of space was their own fault.  Of course, they did that because it was a devastatingly effective tactic.  I guess it evens out.

QuoteFantasy games tend to gloss over the fact that a lot of medieval weaponry was context-dependent, and a great number of weapons that have become standard for fantasy adventurers were originally cavalry weapons and are quite inefficient when you're on foot.

I have not studied it exhaustively, but I would bet there are some numbers in the AD&D 1st Edition Weapons vs AC charts that support your contention here.

Quote from: StormBringer;547212I have not studied it exhaustively, but I would bet there are some numbers in the AD&D 1st Edition Weapons vs AC charts that support your contention here.

I do seem to recall there's some stuff on how much space you need to use a particular weapon, but I know of no one who ever used those rules, and several of the values were nonsensical anyway - there's at least one polearm that only requires a 1' clearance to use.  Perhaps it's a typo.