The Genesis Of An Article

A little more than two weeks ago, as I write this, I had an unusual dream (a known side-effect of some of my medications) in which I wrote two articles for Campaign Mastery. When I awoke, I remembered them, and immediately made the appropriate notes. In the dream, one had proven easy to write, and the other difficult; but when I actually laid out the articles and saw their scope, I decided that I had it backwards. So I wrote what was supposedly the harder article two weeks ago (In My Cosmological Pocket: From Portable Holes to The End Of The Universe), leaving the easier one for last week.

I knew that this article needed some research for specifics, but that proved relatively painless and easy. I knew that it would require some complicated diagrams – and that’s where the wheels came off.

The original intention was to write and post it last Monday. If need be, I could carry it over until the Tuesday – being a day late would not be the end of the world. Several hours after “Monday posting deadline,” I finished the third of the diagrams that I would need, and felt in good shape to actually write and publish the article on Tuesday.

If only it was that easy! There was just one diagram left to do, and – much to my surprise – that ended up completely consuming my Tuesday – not helped by my being somewhat smashed after Monday’s herculean effort.

Wednesday, I spent collaborating with my Co-GM in the Adventurer’s Club campaign. That always leaves me pretty wiped out, so nothing much more was possible or expected.

But I fully expected to be able to knock the article out on Thursday, Campaign Mastery’s “alternate publication day” (instead of slugging through another session of Blogdex updates). I got as far as writing most of this introduction – to about “herculean effort,” above – and discovered (guess what!) that I needed one more diagram just in case some of my readers didn’t learn basic trigonometry in school, or have forgotten it since!

By which point it was pretty clear that there wasn’t enough time left in the day to write the actual text that will frame and cloak in meaning the five illustrations that lie at the heart of this article. Which is why this is being posted on Monday, a week late Tuesday, a week-and-a-day late – I found one more diagram that I needed – in the middle of writing the article… and then another, and another…!

Guess this wasn’t the easy article, after all – and my dream-self had it right all along! I should have listened – but who goes to dreams for professional advice?

‘Spot’ and Perception Checks

It’s one of the most ubiquitous elements of an RPG – the “spot” or “perception” check. Useful for all sorts of things, from noticing the trip-wire concealed in the underbrush to observing the thin bead of sweat rolling down the suspect’s forehead when he is closely questioned, or counting the number of bricks in a step, from spotting a charging rhinoceros that’s really hard to miss to observing the odd behavior of a hummingbird at a distance that shows it to be an illusion placed on something more threatening.

Most writers, when they consider these checks, focus on how to avoid giving the game away (even in part) – having the character make such a roll automatically tells the player that there’s something out there that they should be paying attention to.

Acting on that knowledge is, of course, the worst kind of metagaming, and universally frowned upon. Hence, a vested interest in techniques to prevent even the ‘leak’ that there’s anything to spot, whilst preserving player agency.

Okay, let’s quickly run through a couple of methods of achieving this laudable and very desirable outcome, so that I can keep this article on track.

1. Method 1: Get the player to make half a dozen ‘spot’ checks in advance and write the results down on scrap paper. The GM then consults these rolls when a roll is needed, crossing off those that have been used.
2. Method 2: Get the player to make checks as needed. Instead of announcing the DC or success/failure, the GM describes what the character has ‘spotted’ – but if the check was failed, it’s something trivial.
3. Method 3: Get the player to make checks to spot even some things that are completely obvious, concealing the significant rolls in a snowstorm of meaningless ones.
4. Method 4: Make the significance of the observation extremely transitory, so that rolls can be made on the spot as needed with minimal metagame contamination.
5. Method 5: Spot checks are made by the player to the left of the player whose character is making the ‘attempt’. The player owning the character is only informed if the result is a success.
6. Method 6: Trust the players not to abuse their meta-knowledge, backed up with editorial heavy-handedness and punishments from the GM if necessary.

For the record, Method 6 is the one that I use most of the time, with a sprinkling of Method 2, and Method 1 if and only if it is obvious that there will need to be a LOT of such rolls made in a game session (for a Sherlock-Holmes style mystery, for example).

I’m sure there are other choices out there, too. If you have one worth sharing, drop it into the comments so that others can benefit from it!

Today’s article is all about failing such rolls and what that means in terms of environmental awareness – and where the GM should position cues and warnings so that characters are far less likely to see them, perhaps to the point where no roll can even be justified, and failure should be automatic. More importantly, I’m going to look at how failure can be justified.

Okay, so we’ve established that they are used for everything from “spotting the painfully obvious” to “noticing the obscure visual clue” to “assessing another character’s mood from expressions and body language”.

Visual acuity is clearly a significant factor, and that’s another source of a steady stream of occasional articles on gaming sites – what the modifiers within a given game system should be for a variety of environments and circumstances. (In fact, you could easily write an article a week on that subject for a year. No, that is not a challenge, or an announcement!)

But where do we see? It should come as no surprise that it happens not in the eyes (as was once thought), but in the brain; the eyes simply act as the cameras. That’s the difference between ‘data’ and ‘information’ – the former has potential meaning, if analyzed correctly and placed in the correct context, the latter has meaning attached because some such processing has been carried out already.

Marvels of engineering

The human brain really is a marvel of engineering. We’re still only groping in the dark toward an understanding of how it works, what the ‘mind’ is, how sentience can emerge from the simple electro-mechanical and biological processes that have been observed, and so on.

That said, we’ve learned a lot over the last century or so. There was a time, it must be remembered, when it was thought that the purpose of the organ was to cool the blood (that’s how the expression “a cool head” derives from the concept of being “hot-blooded”)!

The brain employs dozens of processing short-cuts to achieve it’s miraculous perception of the world around it. Some of these are undoubtedly biological in nature – ‘built in’, as it were – and some have to be generated as processes from first principles in the early months of development. Not all these techniques are going to be the same – some will be more efficient in various ways than others, or more accurate – and that’s going to be a major contributor to the differences in the ways that we view the world.

One of those techniques (amongst several that will be mentioned in the course of this article) is the comparison of the current situation with archived ‘snapshots’ of normality, so that the brain can focus on the differences between that archived situation and associated events, and the current situation.

When overwhelmed by other priorities – like dispelling confusion – the brain can even assume that the current situation actually is the same as the archived ‘snapshot’, blinding and deafening the individual to anything outside of that situation. This is an extreme version of ‘confirmation bias’ that has been responsible for at least one deadly aircraft accident – the pilot became convinced that he understood what was going on, and did not react to – apparently, could not even hear or see – anything that contradicted that mental ‘picture’ of reality.

EDIT: I’m updating this article to include a reference that I wanted to include (but couldn’t find) at the time. The problem that I’ve described in the previous paragraph is called ‘fixation’ and the specific situation that I was referring to as an example of fixation is the crash of Garuda flight 200 on March 7, 2007. The pilot flying became so fixated on making his first landing succeed that he ignored repeated alarms and automated instructions, ignored his grossly excessive flight speed, ignored two requests from the co-pilot to abort the landing, and became confused just before landing by the plethora of warnings and alarms ringing in his ears – but still continued with the landing attempt, touching down 1/3 down the length of the runway with such force that the aircraft bounced, landed and bounced again close to the end of the runway, collapsing the nose landing gear. Only then did it begin to slide…

The substitution of an incorrect ‘model of reality’ for the one demonstrated around us is sometimes described as a psychosis. It’s clear that these come in all sorts of scales, from the overwhelming and complete to the trivial and minor. The first can make you dangerous to be around, something in-between can endanger lives if the person affected is operating machinery (driving a car or piloting a plane, for example), and something less is a quirk or immovably-fixed opinion. (As a side-note, it’s entirely possible that flat-earth proponents really do see the world as flat…)

What to process and what to throw away

One of the more important higher-level shortcuts employed by the brain is what to process and what to throw away, i.e. consciously ignore. This is obviously directly related to the phenomena described, possibly triggered as a ‘circuit-breaker’ to prevent overload.

You might think that higher intelligence should reduce the need to employ this shortcut; certainly, that concept is a fundamental element of many characters in literature, and that concept is inherent in the basing of Spot/Listen/Perception checks on intelligence, which is what almost every RPG that has such a roll does.

Arguing against that is the concept that NO human brain is sufficiently advanced to process the entire sensory deluge in real-time while performing abstract reasoning and any other incidental tasks like decision-making. That suggests that everyone ‘naturally’ positions their sensory input levels to the maximum that they can cope with – greater intelligent awareness of the environment simply means that there’s more to distract and divert the character, who is (as a result) as susceptible to the phenomenon as anyone else.

This line of argument is backed up by the investigation of the air crash mentioned earlier. The pilot was competent, experienced, and well-trained – all of which increases the level of input at which the person becomes overwhelmed. Compare expectations of a trainee vs someone who is experienced at their job – whatever it is – to see the inherent truth of the statement. That was what made the determination so surprising to the investigators; they didn’t expect that such an individual would become so fixated on their “picture” of the situation that they totally ignored phenomena that didn’t belong in that scenario, like alarms and warnings and even what the co-pilot was telling him.

If it can happen to him, it can happen to anyone. Intelligence adds to both sides of the equation.

The Relevance Of Illusion

“What to throw away” has been the basis of many of the most basic optical illusions, something that I have discussed in two previous articles – Leaving Things Out: Negative Space in RPGs and I See It But I Don’t Believe It – Convincingly Unconvincing in RPGs – but in both cases, the context of the discussion was rather different. I should also call out An Introduction To The Brilliance Of Derren Brown as relevant, at least indirectly.

Optical illusions have been used for years as a tool by psychologists for exploring the stranger areas of how the brain processes information. That’s because they shed light on the ‘shortcuts’ employed by the brain.

I originally presented this image in the article on negative space listed earlier. At the time, I wrote, “Human minds aren’t really equipped to deal with empty space. When we encounter it, our minds try and interpret the space as containing something. Some optical illusions rely on this to shape part of the negative space to such a degree of success that we can see something that just isn’t there, such as is the case in the Kanizsa Triangle (shown left), created by Italian psychologist and artist Gaetano Kanizsa in the 1970s. The mind creates an object – a white triangle, point-down – out of the negative space to ‘explain’ what it perceives as interruptions of the other parts of the image. In other words, it separates the negative space into two planes, one triangle-shaped and in front of everything else, and one flat and behind everything else. In fact, there is no white triangle, but this nonexistent element of the picture becomes the dominant focus of attention as soon as it appears.

“The mind extrapolates from cues within the event or scene to ‘fill in the blanks’ – which are then taken as actual fact even if they contradict what is actually seen. This effect also manifests in witness statements – people naturally try to place the event they have seen into a context, and will actually (entirely unwittingly) modify their recollection of events to conform to that context. If someone else strongly suggests an alternative context that makes more sense to the subject, they will ‘rewrite history’ in their mind to contain supporting details. The only hope an investigator has of finding out what actually took place from eyewitness testimony alone is to get those statements as soon as possible after the event, having kept the witnesses isolated from anyone and everyone else in the meantime. The Wikipedia article on Eyewitness Testimony makes fascinating reading for anyone unfamiliar with recent developments on the subject.

“Implanting subtle cues of any sort into the negative space helps give that space a context, a starting point, and the mind goes on to fill in the blanks to incorporate that context into the focus of the image.”

What all this means is that under the right circumstances, not only can the brain ignore something that is present, it can invent something that isn’t but that permits it to employ one of it’s shortcuts – even if that results in incorrect processing of the situation.

Every time you (or your players) think they should see something but don’t, flash the Kanizsa Triangle at you/them and tell yourself “I still see a white triangle”. I certainly do, and know all about how it was done – and so do you, if you’ve read the explanation quoted above. That doesn’t change the fact that you can’t look at that image for more than a second or so and NOT see something that isn’t there!

Clearly, perception of reality is far softer, objective, and malleable than we like to think…

Without the shortcuts

We can get some indications of the value of the shortcuts by considering a person processing an unfamiliar and unexpected environment, which means that the shortcuts are ‘what is thrown away’.

When the observed reality does not match the mental ‘picture’ we have of the world and how it works, the result is surprise. Surprises can be good, neutral, or bad; and the greater the separation between world-as-expected and world-as-experienced, the greater the surprise.

For example, let’s contemplate something positive: a surprise birthday party. If you’ve already got a suspicion that ‘something’s being organized’, you won’t be all that surprised. If not, you will be. If the guests include people from a long way away who you did not expect to be present, the surprise is going to be much greater. If the guest list includes a number of people you know to have passed away, the level of surprise will be so great that you will need to be convinced it’s not a trick of some kind.

We all have a different level of credulity, and if surprise exceeds this, then we are prone to react as though what we are seeing is not real.

But that’s only true of positive and neutral surprises. The negative valence of surprise – unpleasant surprises – brings about a very different effect, triggering a fight-or-flight response – which is the natural reaction to a perceived harmful event, attack, or threat to survival. This triggers the release of adrenalin, which in turn triggers other physiological and psychological effects.

In essence, the individual is now operating on instinct, with minimal conscious thought, unless they have experienced training that can take over. Because training substitutes implanted experience and prepared decisions for instinct, it actually leaves greater capacity for conscious thought and hence a more rational modification of the individual’s behavior. This takes the form of a more selective targeting of activity, most of the time – you don’t lash out blindly, you target an enemy and engage; if that’s not possible, you take cover and prepare to engage.

When instinct demands action – fight-or-flight – and no action appears possible, is when things start to get really interesting. The response, overwhelmingly, is to freeze, both physically and mentally. It is generally believed that this stems from an early animal instinct to ‘play dead’ when no other response appears possible, in hopes of blunting or abating the attack sufficiently to create an opportunity for flight or counter-attack – though there has been surprisingly little research into this area of psychology; everything to date has focused on the physiology of the phenomenon.

Why freeze mentally? i couldn’t find an answer, so here’s my personal semi-educated best-guess: we freeze mentally so that we don’t disrupt the physical freeze, either with emotional reactions (whimpering, shivering, screaming) or through other autonomic responses and reflexes. Our every mental capability is focused on processing the threat in as close to real-time as we can manage.

Other aspects of the phenomenon include tunnel vision, which I’ll discuss a little later, and a retreat to an earlier state of mental development, which implies an ordered hierarchy of processes, and that higher-order processes consume more mental capacity than lower-order ones – so that there is a survival benefit in shutting off higher-order processes while preserving lower-level ones at least preserves some intellectual capacity.

That’s why people in such situations will tend to retreat to a more elemental, more child-like state. Hiding, frozen in fear, people can find themselves sucking on a thumb, or retreating into the childlike delusion of “If I can’t see you, you can’t see me” – and screwing their eyes tightly shut to implement this ‘defense’.

So there are good psychological reasons for someone not seeing something that should be blatantly obvious.

What’s more, the human mind deceives us all – constantly.

Three Blind Spots

There are three blind spots in human perceptions – one in each eye, and one that originates in the brain that subtracts the nose from our awareness when it should be clearly visible each time we look toward our feet.

And yet, we’re never aware of any gaps in our perceptions. According to Wikipedia, “Some process in our brains interpolates the blind spot based on surrounding detail and information from the other eye, so we do not normally perceive the blind spot.” And that “some process” is about as definitive and detailed an explanation as can be provided.

We don’t notice the blind spot because our brains wallpaper over them with a best guess as to what should be there – one that may only have a nodding acquaintance with what is really there.

To The Left and To The Right Of Me

But these are as nothing compared to the biggest blind spot of all – the one that’s behind us, wrapping around our heads. Put something there, and you will never know it’s there (absent some other sensory clue, of course).

This diagram shows just how large that blind spot is – and a whole lot more. Let’s start at the back of it and work forward, and then around to the sides.

The first thing to note is that the normal range of movement of the head is 30 degrees to each side. Yes, you can usually force your head around a little further than that, to 40 or even maybe 45 degrees, but doing so can and will eventually strain neck muscles and tear tendons. We tend to subconsciously alleviate that risk by rotating our shoulders in the direction indicated, so that the head doesn’t have to turn as far. That can actually give another 60 degrees in rotation – throw in the neck’s thirty degrees, and you can look directly to the left and right.

Even then, as this very quick overlay shows, there is still a 30 degree blind spot – and you can’t turn your shoulders while moving forward at any speed, or it throws off your balance. In practice, unless proceeding with caution, the larger diagram is the correct one.

And, of course, you can still only turn your head in one direction at a time – if you are looking to your right, you can’t see to your left, and vice-versa. If you happen to visually Zig when you should Zag, you can still miss something important.

Next, we have the line of sight, which is straight ahead when viewed from the top of the head. Note also the focal point of the lines – the ones to the left point to the left eye socket, the ones to the right to the right eye socket; they don’t quite line up perfectly.

Thirty degrees to either side of the line of sight is the “limit of symbol recognition”. Research has shown that outside this central cone, we don’t bring our full cognitive capabilities to bear on what we see – which means that we either don’t recognize an abstract symbol, like words or letters of the alphabet, or road signs, or that such recognition is significantly slowed in priority. Another of our mental shortcuts is thus revealed: outside that cone, our mental processes are aimed only at recognizing what that cone should be directed next.

The next important number is 62 degrees to either side of the line of sight. That defines the range of binocular vision – the area within which both eyes can see the target. That’s important because our brains use that information to determine how far away something is. When the target is moving, you need that determination in order to target where it will be when your attack reaches that distance. I’ve seen estimates for the increase in difficulty of hitting a target moving at an angle without binocular vision that vary from 30% to 60% – I don’t know what the right number is, but whatever it is, it’s an important factor.

Beyond that line is a slim 13 degrees, which represents peripheral vision, i.e. the visual arc covered by one eye but not both – not without turning the head. That’s a total of 75 degrees to either side of the line of sight, and that’s what you can see without turning your neck and torso.

Up and Down

But that’s all fairly well known. You can figure out most of it just by putting an imaginary protractor around your head and estimating what you can see, and paying attention to the position of your muscles. You get rather more surprises when you look at the vertical range of vision.

Unlike the previous image, I didn’t incorporate the rotation of the head in the visual range – it made the image too confusing. Once again, let’s start at the back and then work forwards. The first thing that you should note is that it is not symmetrical in the same way in the way that the horizontal arc is. The head can point up about 25 degrees, but can tilt forwards 40 degrees. The other noteworthy observation included is that the line of sight is horizontal when standing, and 15 degrees downward when sitting – that’s a natural consequence of the human skeletal structure and muscularity. When moving forward at speed, the natural tendency is also to look downwards, but the amount varies somewhat, and was too complex to illustrate.

You can see the same thing on the front part of the diagram. But it’s worth noting that this 15 degree difference in line of sight doesn’t alter the angles shown, only their relative measurement. There are three distinct zones of vision depicted – a lower visual field, an arc of optimum vertical rotation of the eye, and an upper visual field. The region of optimum eye rotation runs from a standing line of sight downwards 30 degrees and upwards 25 degrees. This is as much a function of the physiology of the face as anything else – the cheeks form a relatively shallow and flat surface which doesn’t obscure downward vision greatly, but the brows jut out from the eyes (to protect the eyes with bone), and that obscures the upper field somewhat. If you’re sitting, your line of sight depresses downwards 15 degrees, the lower boundary of the optimum eye rotation arc becomes 15 degrees (=30-15), while the upper becomes 40 degrees (=25+15). This is a slight oversimplification because it assumes that the eyes are doing all the ‘work’ of adjusting the line of sight, when it’s more naturally due to neck rotation, but that’s a necessary evil, I’m afraid.

The lower visual field extends beyond the 30 degree position a full 40 degrees, giving a total arc from the standing line of sight of 70 degrees. Once again, this area functions in the same way as the peripheral vision of the horizontal arc – the priority of the brain in processing visual information is selecting targets for examination after shifting the line of sight.

The upper visual field bears the same limitation, but it only doubles the 25 degree arc from the line of sight to 50 degrees. So we are naturally more aware of things at our feet than we are of things overhead. But notice the top ten degrees of that fifty-degree arc: one of the surprises that I came across in researching this article is that our brains ignore all but the most rudimentary color information in that range, and that the fact of this is actually hidden from our awareness by our brains. Unless there is a significant difference in lightness or darkness, our vision gets progressively more desaturated and black-and-white as we approach the upper limit of the range – with color information “inferred” from lower in the arc. Of course, you can see the color information clearly by looking up at it – but not otherwise.

Ultimately then, 25 degrees up and 30 degrees down, 62 degrees to the left, and 62 to the right – that’s what we can see clearly. Our awareness extends peripherally outward further in all four directions, but that’s all subject to “degraded” processing standards aimed more at getting our attention – and, if there’s a transitory phenomenon to observe, that might not be enough. We can extend the visual field somewhat by turning our head or our body – but that’s only moving the visual field, not enlarging it. For every square degree so gained, we lost one from the other side of the field.

An exercise in Geometry

All this becomes a lot more useful when we consider the phenomenon of a character looking at focus of attention, and ask what else they can or can’t see. The horizontal doesn’t change much from the basic picture given above – point the “eye line” toward the object and consider a horizontal plane of a little more than the hemisphere (maximum) and a little less than 1/3 of that for full processing of visual information.

Outside of that 1/3, a sixty degree arc, all we know, and all we should get from a failed spot check, is that there is something to be aware of in that direction, according to a very simple (and somewhat inaccurate) standard of judgment. We don’t know what it is. And if it’s color-based information, we may not even be aware of it if the vertical angle is close to the limit – we need some contrast differentiation or motion to attract our attention.

But vertically, things get a lot more interesting, because these angles dictate whether or not something is within our field of view at all, or in what is (effectively) a blind spot. This is an exercise in simple geometry.

Let me start by admitting that if you try to measure these out, it won’t look like the example. I’ll discuss the problem a little later, and simply admit that I compromised reality to be properly illustrative in creating this diagram.

The upper part of the diagram defines the angle of the eye line, aka the line of sight. It is based on two numbers and a pair of triangles. The first number is h, the elevation of the eyes relative to the horizontal plane of the focus of attention.

That last part is a necessary complication: if the terrain is sloping upward toward the focus of attention, or it’s above ground level, it makes h smaller. The whole point is to create right-angled triangles which are susceptible to simple analysis and not the far more complicated arrangements that can result!

But the simplest situation is the one depicted – level terrain, and a focus of attention on the ground some distance away. That ‘distance away’ is also from the eyes, which is important, too – when moving, it’s normal for our point of balance to be forwarded. Walking and running are ‘controlled falls’ that are interrupted by the arrival of the other foot reaching the front of its stride, and that means that the head (and therefore the eyes) advance in the direction of the travel – how far forward of the center of gravity depends on the speed with which we are moving, and it’s something that we subconsciously process when we look at a picture, especially one that’s side-on.

Artists often think of such matters as the “center-line” of the body, which dodges all sorts of tricky questions, because then they can talk about the angle of the center-line to the horizontal. As a general rule, 0-5 degrees is about right for indicating walking, 5-10 degrees for jogging, 10-15 degrees is normal used for running, and anything more indicates a sprint. 30 degrees is a fairly extreme and exaggerated angle in art.

It should be noted that artists normally exaggerate their depictions to make the motion clear to those observing the art. The reality is less than that indicated, probably 1/2 the angle shown. The only time I’ve seen angles approaching 30 degrees in real life is when a runner is stretching for the line, deliberately extending themselves toward the tape.

It should also be noted that comic-book artists exaggerate motion even more, probably doubling the angles listed, because it makes the angle and pose more dramatic.

I suggest that under most circumstances, and assuming humanoid physiology, all this is unnecessary complication. Use the character’s height and the distance from the feet to the focus of attention. If the focus is an enemy combatant, trained fighters will watch the back or shoulders of the (potential) enemy, anyone else will focus on the eyes or the weapon-in-hand if there is one, and both will talk about assessing “intent”.

So subtract the enemy’s height from h, or subtract the character’s height from the enemy’s if the enemy is taller. Visualize the geometry of the situation in your head.

Once you know the eye line, you can calculate C, D, E, F, and G, as shown in the lower part of the diagram. 70-30-25-50 are the numbers you need to remember.

• 70° down from the eye-line is the lower limit of vision. Outside this, the character is effectively blind.
• 30° down from the eye-line is where visual processing takes over from mere “awareness”.
• 25° above the eye line is the upper limit of the visual-processing arc. If this is below the horizontal, unless the terrain is sloping down away from the character in exactly the right way, the character will not be more than aware of the horizon of the area.
• 50° degrees above the eye line is the upper limit of vision. Where this line intersects the ceiling will demark the limits of awareness of what is ‘overhead’.
• “C” is the distance from the character to the point of intersection between the floor and the 70°-down line. If anything happens within that area, the character won’t see it. If there’s anything he should have seen before it entered that area because of the character’s forward motion, they have missed their chance to spot it.
• “D” is the area ahead of the character in which they will be aware of the floor. If there’s something to see, they may become aware of the fact – but not of what it is unless the character takes their eyes off the focus of attention.
• “E” is the distance between the 30° line and the focus of attention. Normally defined by exclusion – you don’t normally need to calculate it.
• “F” gets a little trickier. It’s the distance along the ground, or up the wall, or along the ceiling, from the focus of attention to the 25°-up line.
• “G” is, similarly, the distance to the edge of the upper visual field. Outside of this area, the character is, once again, effectively blind – unless they shift their focus of attention.

So, in the example depicted, if the dashed line a little beyond the focus of attention is a wall, then F will be part-way up it, and the rest of it and some of the ceiling will be in the area defined by G. And notice how the top of the area is “grayed out” as a reminder.

The observant may comment that the 70° line looks a little shallow, relative to the eye line, and they would be correct – the actual 70° line is vertically down from the focal point, with the real C extending backwards to infinity from the feet of the character. (Told you I’d explain how I had to compromise the illustration).

Of course, actually calculating things – especially when it comes to more complex situations – requires some rules, so here they are:

These, of course, are basic trigonometry – which uses symbols like alpha, beta, and theta, because the ancient Greeks first worked out the principles of basic trigonometry (and we’ve been using them ever since).

The basic resemblance between the diagram illustrating the rules and the one given earlier should be fairly obvious!

Math? No Way!

At this point, I contemplated giving away a spreadsheet that calculated the numbers, regardless of the input values. It proved to be a lot more complicated than I expected. I thought about a worked example – but the possible permutations are so varied that I thought it might do more harm than good, especially since I wasn’t going to recommend it as a technique, anyway.

I’m including it only so that readers have the principles and techniques at their fingertips – so that they can do things the more precise (and more difficult) way if it becomes necessary.

An Array Of Examples

So, instead, here’s a set of graphical examples. Pay close attention to where the line of sight intercepts the floor, wall, or ceiling, and the effect that this has on the “blind regions” and the areas of “attention only”.

A practical method

I mentioned in the section above that I had a more practical alternative than a whole bunch of trigonometry calculations. This is a 7-step process that, with appropriate modifications for the dimensions of the room and/or the landscape, shows exactly what can be seen – and it needs nothing more than a pencil, ruler, scrap paper, and a sharp eye.

The process is in seven steps, and rather than breaking them up into separate illustrations (with discussion in between, I thought it better to illustrate the whole process in one larger image.

1. Step one is to lay out the basic dimensions. In this case, to make the process easier to follow, I’ve decided the floor is level, and the focus of interest is about 10 hexes or squares away (5′ each). I’ve also assumed that the basic character is 5’6″ tall, which sets their eyes a nice, neat 5′ above the floor.
2. Step two is to draw in the eye line at right angles to the character height marker, and the eye-line between the eye-line origin point and the target. I then guesstimate the angle that is formed – in this case, I get about 7 degrees. Some tricks: 1/3 of a 90 degree angle is 30 degrees, and 1/3 of that is 10 degrees, and half of that is 5 degrees. I make these estimates purely by eye – our assumptions are fuzzy enough that they can swallow a huge degree of error and still be usable. Once I have that, a simple calculation, 90-angle estimated, gives me the angle inside the triangle – in this example, 83°.
3. Step 3 is even simpler. Subtract 70° from the angle inside – the results tell you roughly what the angle to the edge of the lower visual range is. 83°-70°=13°, so I do the 1/3 trick to get 30 degrees, then halve the angle, and pick a result just a little less – from the vertical, it should be noted. If all I need is the lower blind spot, I’m done! But if I need the full picture, it’s on to the next step.
4. Step 4 happens in the same way, but this time I’m subtracting 30° from the eye-line angle – 83°, in this example. That gives me 43°, so I estimate a 43° angle (a shade closer than 45°) and draw another line. This defines the lower area of “poor vision”, and also – by definition – the lower part of the “good vision” area.
5. With the part below the eye-line done, it’s time in Step 5 to work out the upper boundaries. I start by adding 25° to the eye-line angle (83°), and note that the result of 108° is more than 90° which is the horizontal. So I subtract the 90° and get a smaller angle (usually much easier to work with) of 18° above the horizontal. Because I don’t want to use up more paper than I need, I’ll also roughly draw in the ceiling – in this case, about 15′ high (which is quite a high ceiling, 12′ is probably more typical – but it also happens to be about the height of the ceiling in the room in which I was doing all this, and that helps me visualize it in my head).
6. In step 6, I’ll drop a vertical line from the point where the ceiling and the 18° line intersect. That’s because my quick and dirty scale is at the bottom of the diagram, and it tells me that from four tiles ahead of the character, he has a good view of the ceiling, and therefore any wall in between the two will also be within that visual arc.
7. Step 7 starts with another calculation – the angle of the previous calculation plus another 25° degrees. In this case, we get 43° above the horizon, which is a cinch to visually estimate and draw in. That’s the boundary of the upper area of poor vision, and also identifies the area in which the character has no visual capability at all. Hey presto! It’s all done – and customized to the layout with which you have to deal. I’m good at sketching – I could do this quickly and easily even without a ruler, just with pencil and paper!

Well, almost. Using this technique, you can work out where the part of an enemy is that the character is looking (height above floor); but you need to know one or two things more before you can adjust floors for climbs and descents. Humans have no problem leaning forward, relative to the ground – but have a great aversion to leaning backwards. If the floor slopes up, the character will usually lean into it, so you have to adjust your initial vertical line appropriately; if the floor slopes down, the character will stay vertical with respect to gravity. Either way, draw in the floor and mark off the distances along that line. Once you know those tricks you can deal with the most complicated surfaces.

If only every character was 5’6″, that would be the end of it. To correct for character height, we simply need to work out the multiplier and do a new set of marks along our scale. The multiplier is the character’s height in inches divided by 66, which is 5’6″ in inches.

Let’s say that I’m dealing with a 4′ tall Dwarf. That’s 48 inches, divided by 66, or 0.727. The only thing that you have to worry about is whether or not to multiply or divide by the multiplier. If the character is shorter than your reference height, simply imagine the results if the focal point were lower; if taller, if it were higher. That should be all you need to tell you which way each measurement gets scaled.

So, if the upper zone of good vision previously started 4 squares away, for the dwarf, it will start further away – so I divide 4 by 0.727, and get 5.5. Or, I can simply take my rough sketch and (preferably in a different color) draw in a set of lines parallel to the old ones at the different focal point.

Here’s the last image from the example above, with such an adjustment shown:

As you can see, with the focal point lower, the boundaries below the eye-line intersect the “floor” sooner, so they are all shorter, but the angles have further to propagate upwards, so those are longer. It’s as though the standard character had his eye-line angled a little bit lower.

A taller character would experience the opposite effects – a smaller upper blind spot, and a larger lower one.

Cone Of Vision

So, our vision is actually a cone projecting forward, perhaps at an angle, with a notch out of the bottom and a couple of holes.

When someone’s fight-or-flight response is engaged, it’s not uncommon for the zone of processing to narrow, producing tunnel vision; however, there have been no experiments that I could find concerning the scale of this narrowing, save those on astronauts undergoing G-stress training, and I have a suspicion that the two effects are not analogous.

I am forced to pluck some numbers that “sound about right” out of thin air. I would be greatly surprised if the narrowing of an angle relative to the eye-line was by less than 1/3 or more than 2/3, on both axes. I also suspect that the “awareness” zone does not narrow by as much as the focal arc; so my rules of thumb are that narrowing may reduce the arc of “good vision” by 2/3, and the arc of “bad vision” by 1/3.

These numbers would represent a considerable diversion of significant mental capacities and their focus on the object of concern. The “blind areas” would grow considerably as a result, producing the “tunnel” effect for which the phenomenon is named. I’m not sure that anything less would result in that effect.

But these zones and blind spots are not the only limitation on perception that needs to be considered.

Technicolor Presumptions

Color differences, even substantial ones, are seriously muted by similarities in saturation level, and amplified by increases in contrast. A number of optical illusions have been generated to explore this effect. What’s more, adjacent colors can affect our perceptions of a color far more strongly than most people anticipate.

All of which means that color difference alone may not be enough to make something noticeable.

Focal Plane

Have you ever noticed how, if you are looking at a distant object, your awareness of things much closer to you is diminished, and vice-versa – even if they are within the cone of optimum sight? We live in a three-dimensional world, and the third dimension is just as important as any other in this context.

We have, in other words, a limited focal plane, but one that we can adjust.

Middle-distance focus means that both close and distant perceptions are compromised.

The focus of inattention

Focusing on some specific visual processing, such as counting the number of passes of a basketball, can leave people completely unaware of a man in a gorilla suit wandering through the shot. Don’t believe me?

It’s called the Selective Attention Test and here’s a YouTube video (1:22) to a demonstration. Don’t cheat – make sure to follow the instructions!

And here’s another (1:43).

The simple fact is that about half the population will completely miss the gorilla if they aren’t forewarned of it’s presence – and those who are distracted by watching for the gorilla will usually fail to count the number of passes correctly, or notice something else, like the curtains in video 2 changing color, or a player in black leaving the court.

It happens through another set of shortcuts in our mental wiring – by designating the counting task as of primary importance, the brain throws away unrelated visual information. You’re focusing on the players in white and how often they pass the ball, and doing your best to ignore the players in black – and completely miss the gorilla (also in black), provided that he doesn’t interrupt the path of the ball on which you are focused.

Optical Illusions

There are all sorts of optical illusions, and they all stem from the shortcuts that our brains use. There are also a number of contradictions involved in them, which is both maddening and fascinating to the psychologists who investigate the phenomena.

We’re accustomed to colors fading as they get closer to the horizon; if a mountain is faded in a picture, we consider it to be more distant than one where that’s not the case. But a somewhat-fuzzy black spot is interpreted by our brains as a hole in an object that’s much closer. So, which signifies distance to our brains: lighter or darker?

The answer: both, depending on the circumstances. Our depth perception is easily fooled.

Foreshortening and Perspective

Artists have been taking advantage of this fact for centuries to fool us into interpreting an image as possessing depth. The first known picture to make use of linear perspective was created by the Florentine architect Fillipo Brunelleshi (1377-1446). Painted in 1415, it depicted the Baptistery in Florence from the front gate of the unfinished cathedral.

The principles are fairly simple – small equals distant.

In picture 1, a couple of lines are angled toward a point, so the top of the picture seems farther away than the bottom. There’s also more white space at the bottom of the picture than the top, which reinforces the subconscious impression, because the brain assumes that the two areas are actually equal in size – so the bottom must be closer because it’s bigger. But there’s a square there which the mind finds confusing – it doesn’t have a matching context, and so the brain rebels against the illusion.

Picture 2 is worse, because a square of identical size has been added near the top of the picture. Suddenly, the lines look more like a mountain than lines on the ground. What little context the brain was manufacturing has been totally destroyed.

Picture 3 adds some horizontal lines, progressively getting closer together, in between the angled lines. Suddenly, the brain has a whole lot of new context, so much so that it assumes that the squares must conform to the overwhelming “reality” that has been created. The lines are now railroad tracks, and the box near the bottom of the image must be quite a bit smaller than the one at the back.

Picture 4 adds a horizon line that runs behind the upper box, reinforcing the “reality” being created.

Picture 5 adds a little color, some additional shapes, and fades the “distant” objects. Suddenly, the squares are box-shaped structures of some kind – one very small, perhaps six inches to a side, and one that’s more like 24′ to a side. What’s more, the mind tends to move it on the page until its scale appears to match that indicated by the tracks as making sense; the mind is now actively manufacturing supporting evidence for the illusion.

This example is hopelessly simple, very deliberately so. Because I cheated and didn’t actually define the vanishing point, then draw guide-lines from it, the “boxes” appear to be on slightly different axes of rotation to the railroad. This is a flaw that ever-so-slightly disrupts the sense that the boxes are anchored to the ground – so I added a shadow to both – but didn’t define a light-source, so these don’t look quite right either.

Nevertheless, it’s enough to convey the basic message: The brain associates details of texture, and strong contrasts, with closeness, and uses that association to decide how big the box is, and how big it appears to be, and to assign depth to the image.

Forced Perspective

Perspective mimics the way we see straight lines in real life – the sides of buildings, for example. As a general rule, the brain assumes that two lines running toward a vanishing point are parallel, and uses this assumption to estimate how far away the distant point is. Forced perspective distorts reality to manipulate the impression of distance created by this assumption. The Potemkin Stairs in Odessa appear to have far greater depth than their 142 meter depth because the stairs are wider at the bottom than at the top. There is a gallery in Rome, designed and constructed in 1632, that appears to be around four times its actual depth of 28 feet – the floor slopes up, the roof slopes down, the walls slope in, and the columns get progressively narrower.

It works in the other direction, too – the American Adventures pavilion in Epcot uses forced perspective to make a five-story building appear to be only two-and-a-half stories tall.

Forced perspective was introduced by German filmmakers in the silent movie era, and went out-of-style until resurrected for Citizen Kane by Orson Welles. Subsequent movies employed miniature sets, notably sci-fi movies such as the Incredible Shrinking Man and Attack Of The 50-foot Woman. In a lot of cases, the use of miniatures was obvious because the blur of the object or the lighting would not be quite right.

• Blur: Objects at the same distance should have identical sharpness. Fuzziness, also known as blur, should increase in accordance with the depth that the object supposedly possesses. This frequently requires the use of special lenses or optical effects. Quite often, the miniatures would look right, but their shadows would not, and would not fade in a natural manner. These technical issues could all be overcome with sufficient skill and expense, but low-budget sci-fi and horror movies rarely had the required budgets to get these effects right – the two movies cited are notable for getting it right.
• Objects that are more distant require the square of the distance ratio in greater lighting to achieve the same level of brightness on film – get the values wrong, and the miniature won’t look like it belongs, and (once again), the shadows cast as a result can be especially problematic.

But if you get it right, reality can appear to bend to your filmic will.

Some Final Observations

There are so many ways in which we can fail to observe something in the real world that by now it probably seems miraculous that we can see at all. There is always ample justification for a character failing to spot something, regardless of what their ranks in the appropriate skill appear to suggest. GMs can take a step toward reality by judicious use of penalty modifiers and the deliberate placement of things that the PCs would prefer to notice.

We couldn’t function without the processing shortcuts that our brains utilize to focus on the elements of a scene that appear to really matter – but those same shortcuts mean that we never really see anything other than an artificially-constructed mental simulation of the world around us. It’s just that we’re programmed not to notice, and reality usually doesn’t rub our noses in it.

Remember these principles when you are deciding whether or not a “spot” check is justified or required, and what modifier or DC is appropriate (depending on your game system), and what a success or failure should really mean. Don’t let a high “spot” score intimidate you, but don’t neglect to give a character who has one the benefits that they deserve, either. This article has given you the tools that you need to assert the simulation of reality within your game, but it’s like forced perspective: get it right, and the illusion can be persuasive; get it wrong, in any number of ways, and it can feel more false that it really is.

And remember, too, the effects on perceptive capabilities that result from being surprised, or in fear for your life.

Don’t be afraid to use these tricks intelligently, either. I once had a villain create a long tunnel seemingly running to his lair through a mountain range; periodically, windows would show it to be a vast city. In actuality, it was a lot smaller than it seemed, and the tunnel led to a fake that was full of deathtraps; only afterwards was it discovered that the “city” the PCs saw as they traveled were actually miniatures and paintings.

On another occasion, I convinced the players that their characters were shrinking as they approached a villain’s lair because the corridor, bricks, and fittings, all grew larger and larger. On that occasion, the PCs completely consumed their daily compliment of spells attempting to reverse the effect, without success, and eventually decided it was too risky to proceed.

The way the brain processes its perceptions were a fundamental inspiration to the way illusions worked in my Shards Of Divinity campaign, and have repeatedly been relevant to the perceptions of the world as seen by a telepath in my Zenith-3 campaign.

This article has provided the keys to the kingdom of Spot. What you do with them is up to you!