CHAPTER FIVE
It’s Better Than 11 Percent: Context Is Everything
In the Guardians of the Galaxy movie series, one of the most loved characters is Groot, a walking tree with a limited vocabulary. In fact, “limited” is a bit of an understatement. As one of the other characters, Rocket Raccoon, explains, “[Groot] don’t know talking good like me and you, so his vocabulary is limited to ‘I’ and ‘am’ and ‘Groot.’ Exclusively, in that order.” As lovable as Groot might be, he can only say one thing: “I am Groot.” So, while he’s great in the first moment of a bar pickup, the conversation goes steeply downhill from there.
But Groot is actually a better communicator than he might first seem. Part of the fun of his character is that, depending on context, Groot seems to mean quite different things by “I am Groot,” something that his friend Rocket can readily discern.
For example, sometimes “I am Groot” can even somehow amazingly mean, “It’s better than eleven percent.” In one scene the characters are arguing about a plan, and Rocket thinks it’s not at all thought through, and thus only “twelve percent of a plan.” Groot intones, “I am Groot,” to which Rocket replies, “So what if ‘It’s better than eleven percent’? What does that have to do with anything?”
Other meanings of Groot’s “I am Groot” include “save them,” “only friends we ever had,” “four of us,” and “they were looking at me funny.” In each case, Rocket can tell from context what Groot means. The moral of our arboreal friend Groot is that context can make all the difference. A seemingly teensy-weensy vocabulary repertoire can be considerably more rich and powerful than you might ever expect.
And that brings us back to our story. The emotional expressions we have introduced thus far (again see Figure 20) amount to a teensy-weensy repertoire, although not as small as Groot’s.
Now, it’s not entirely clear how many expressions we actually have, but surely we’ve got more than just those eight (not including neutral)! However, those eight emotional expressions are a lot more powerful than they at first seem. Much like “I am Groot,” they can in fact convey quite different meanings depending on context.
I Know What I’m Talking About
Suppose I were to say, “I know what I’m talking about.” I would be expressing pride (or saying I’m more confident than you suggested I am). Now let’s look at two different scenarios. In each case I’m going to express the exact same thing—“I know what I’m talking about”—but what you say beforehand will be different.
Scenario 1
You: You don’t know what you’re talking about, and so you should get less. [disdain]
Me: I know what I’m talking about. [pride]
In this case, my response might come across as a little angry. Why? Because you basically just insulted me, showing me disdain and offering me less. I’m now unhappy. And in that context, my internal emotion is something more like anger than pride.
Suppose the conversation were instead like this.
Scenario 2
You: You’re awesome and should get more. [respect]
Me: I know what I’m talking about. [pride]
In this case, my response feels quite different. I’m not unhappy at all—you just complimented me and offered me more! I’m happy, and considering that, my internal emotion of pride is colored to become something more like smug, a combination of pride and happiness.
My internal emotions associated with the negotiation expressions depend on what you just did. An emotion of pride can become smug or angry depending on whether you “made” me happy or unhappy. And respect can become something more like thankful or fearful depending on whether I’m happy or unhappy. And that depends on whether you just offered me more (conciliatory) or less (aggressive).
The meaning of my expression also gets modified. For instance, in the context of you having offered me a worse deal, you know very well that behind my pride expression there’s more. I’m unhappy inside (or at least ought to be), and so I’m probably feeling angry.
Why Tell You I’m Happy?
So what? We know our internal emotions are much richer than pride-humility and respect-disdain!
Our interest in this book, remember, is why deeply internally emotional animals broke form after vast epochs and changed their dead-eyed ways, becoming “loudly” outwardly emotionally expressive creatures. The question for our purpose is: Why not just leave the happy and unhappy emotions masked on the inside, rather than expressing them?
And we’d better have a reason! We can’t lazily hypothesize that happy emotions “leak out,” or some such answer. There is, in fact, a very crucial reason why we need some further emotional expressions in our repertoire in order to be able to negotiate: as a confirmation receipt letting you know I got the message.
Consider this little back-and-forth you might have over a used car.
Buyer: How about five grand?
Seller: Five grand? My asking price is six.
Buyer: Six grand. Are you nuts? How about five and a half, final offer?
Seller: Five hundred dollars below my asking. Sigh. Okay.
This simple negotiation was straight and to the point, and each party walked away better for it. But if you look closely at the conversation, you’ll see there’s one little extra thing, something beyond any of the negotiation “moves” we have talked about so far, and thus not something any of our response emotional expressions can actually say.
To help see the difference more clearly, let’s rewrite the little used car negotiation without the extra bits we’re hinting at.
Buyer: How about five grand?
Seller: My asking price is six.
Buyer: Are you nuts? How about five and a half, final offer?
Seller: Sigh. Okay.
This negotiation has all the same horizontal shifts in the price and vertical shifts in tension (e.g., “Are you nuts?” “final offer,” and “Sigh”) as before. But a few extra phrases have been removed.
In the original first reply, the seller said, “Five grand? My asking price is six.” And the buyer, rather than laying into him with, “Are you nuts?” actually said, “Six grand. Are you nuts?” The final seller reply originally began with “Five hundred dollars below my asking,” before wrapping it up with an agreement “Sigh. Okay.”
These initial additional phrases aren’t needed for negotiation per se. The negotiation alone demands only the compromise and tension shifts, and for that, only pride-humility and respect-disdain are needed. (Or, equivalently, only aggressive-conciliatory and serious-casual are needed.)
What these extra bits are doing is confirming that one got the right message. They’re all “let me get this straight” statements, or confirmation receipts that acknowledge having received an offer.
We don’t always do this with language. Often, it’s very clear to both parties that the offer was received and understood. But even with fairly unambiguous language, and fairly brilliant apes like us, we do a lot of acknowledging in conversation, especially negotiation, making sure we’re on the same page before going on to the next page. From academic debate, to household disputes, to asset negotiation—it’s commonplace to (at least somewhat) summarize the other party’s claim before countering it.
And if even careful academics do it in essays that each party can go back and carefully read on their own time, imagine the fleeting world of emotional expressions by our wild ancestors and wild social animals more generally! In order to talk in the ancient negotiation language evolution gifted them, they had to engage one another in some way so that they’re “tied together” in a communicative dance. By each providing a receipt that they received this offer, they are not only on the same page, but are mutually understood to be temporarily connected within the same negotiation.
My Happy-Unhappy Acknowledges Your Conciliatory-Aggressive
So, what are these confirmation receipts within our repertoire of emotional expressions? Let’s begin by considering some of the internal emotions I might have in reaction to your emotional expression.
If you emotionally express aggressive, then I’m likely to have an internal emotion of unhappiness; after all, you just suggested a better deal for yourself, and so a worse deal for me. That ancient emotion probably puts me in a bit of a defensive preparatory state, one appropriate for potentially having to fend off (your) aggression. If instead you emotionally expressed conciliatory, I’d likely be internally happy. You offered me a better deal—yeah for me! That’s a sensible internal feeling for this situation.
But why do I need to express these internal emotions I may experience to you?
I signal unhappy and happy to you to let you know I got your message. My emotional expression of happy acknowledges that you just expressed conciliatory.
Conciliatory says, “You should get a better deal.”
Happy says, “You just said I should get a better deal.” (Or “You just signaled conciliatory.”)
Unhappy, on the other hand, acknowledges receipt of your aggressive emotional expression.
Aggressive says, “You should get a worse deal.”
Unhappy says, “You just said I should get a worse deal.” (Or “You just signaled aggressive.”)
My happy and unhappy expressions serve to acknowledge that you just expressed conciliatory and aggressive, respectively. Those are the horizontal shifts in a negotiation.
As a thought experiment, if we were both 100 percent certain that I’d received your expression offering me a better deal—maybe via a mind meld from Spock, or say we just knew each other really well—then I’d have no need to express happy (even though I might be feeling happy).
My Surprised-Relaxed Acknowledges Your Serious-Casual
What about the vertical differences, or the differences between a casual and a serious negotiation? Remember that the latter is where the serious party is more likely to fight.
Before we get to what emotional expressions I might signal to acknowledge these vertical shifts, let’s just ask what internal emotion I might have if you were to emotionally express casual. If you signal casual, you’re saying you’re okay with the discussion carrying on without drama—i.e., carrying on with a lower risk of a fight. Internally, while I’m not necessarily happy or unhappy—because you didn’t offer me a better or worse deal—it does mean I can lower my level of arousal. I can relax. You’re not going to fight me.
Feeling relaxed is one thing, but the reason I emotionally express to you that I’m relaxed—i.e., express relaxed—is that it puts us on the same page. You then know that I got your signal of casual.
Instead, suppose you emotionally express serious. Now I’m definitely not relaxed. Your signal of serious means you’re more likely to fight, so I need to raise my arousal level in case I need to react. Internally, my emotion will be the opposite of relaxed, and that’s something more like surprised. I’m on my toes, reactive. I’ve emotionally expressed surprised to you to tell you I got your serious message. We’re still connected. “I’m following you. Ten-four, good buddy. You say you’re doubting this is a good deal for you, and you’re considering giving up on conversation and fighting instead.”
So, my emotional expression of surprise acknowledges that you just signaled serious.
Serious says, “I’m more likely to fight.” (Or, more simply, “I’m serious.”)
Surprised says, “You just said you’re more likely to fight.” (Or, more simply, “You just said you’re serious.”)
My relaxed expression, on the other hand, acknowledges the opposite, your casual expression.
Casual says, “I’m less likely to fight.” (Or, more simply, “You can relax.”)
Relaxed says, “You just said you’re less likely to fight.” (Or, more simply, “You just suggested I relax.”)
Staying on the Same Page
This need to “bind” to one another during discussion and ensure parties are on the same page leads to two dimensions of emotional acknowledgment expressions:
Happy-unhappy acknowledges conciliatory-aggressive, and Surprised-relaxed acknowledges serious-casual.
These parallel spaces to the two response dimensions of emotional expressions confirm receipt for any response emotional expression you might make.
Figure 22. The two-dimensional space of Mark’s emotional expressions of acknowledgment are on the outside, each next to Tim’s response emotional expression it acknowledges in the inner square. So, for example, Mark’s unhappy expression acknowledges Tim’s aggressive expression, and Mark’s surprised expression acknowledges Tim’s serious expression. Note that the inner square’s response emotional expressions are horizontally flipped compared to what we saw in Figure 20 because here we’re looking at the emotional expression Tim just signaled in response to Mark’s previous offer, and Tim favors compromises more to the right in the diagrams. Mark is now acknowledging Tim’s response. To help with the illustration, happy-unhappy is illustrated with a smile-frown face, and surprised-relaxed is illustrated with open versus closed eyes and mouth.
Figure 22 shows the two-dimensional space of acknowledgment emotional expressions we just introduced. It also places them adjacent to the response emotional expressions they acknowledge. For example, if you emotionally express pride (a combination of aggressive and serious), I can acknowledge it by signaling unhappy and surprised (or the single term worried, which comes close).
The figure also includes emotional expressions acknowledging the four corner cases for responses.
Worried-relieved acknowledges pride-humility, and Appreciated-dejected acknowledges respect-disdain.
One can think of relieved, happy, and appreciated as three distinct varieties of happy expressions. Dejected, unhappy, and worried (“Don’t worry, be happy”) are three distinct varieties of unhappy expressions.
Similarly, appreciated, surprised, and worried are three distinct kinds of expressions of surprise (basically, pleasantly, neutrally, and unpleasantly surprised). And relieved, relaxed, and dejected are three distinct kinds of relaxed expressions.
Defense to the Offense
If you recall from chapter four, the internal emotions associated with response emotional expressions were offensive preparatory states for backing up with offensive action the demands I’m making in my negotiation—if things break down. That’s why, for example, the expression of aggressive tends to be associated with the internal emotion of aggression.
Thus far in this chapter we’ve seen that there’s a second two-dimensional space of emotional expressions, one having some really important expressions such as happy and surprise. Why is it that the acknowledgment emotional expressions are connected to internal emotions? Why does my expression of happy often associate with being happy internally? Does the same basic idea connecting emotional expressions to the associated internal emotion also hold for these acknowledgment expressions?
A similar idea indeed applies for acknowledgments. Whereas my response emotional expression is related to the offense I would have to evince were there to be a fight, my acknowledgment of your response should be associated with internal emotions I might need to possess in reaction to your potential offense.
What kinds of preparatory states might be reactions to another person’s offense?
That’s just defense!
So, response emotional expressions are associated with internal emotions that prepare me for offense. And acknowledgment emotional expressions are associated with internal emotions that prepare me for defense.
The internal emotions associated with responses concern offense.
The internal emotions associated with acknowledgments concern defense.
Two Dimensions to Defense
Earlier we saw that offense actually has two dimensions, not one. There’s one for “what I’m prepared for” (associated with the horizontal component), and another for “how prepared I am for it” (associated with the vertical component).
It’s no different for defense. There are, accordingly, two dimensions to defensive internal emotions:
1.The level of defense [horizontal]: Acknowledgment emotional expressions along the happy-unhappy dimension are associated with internal emotions preparing me for some level of defense.
2.The degree of readiness to do defense [vertical]: Acknowledgment emotional expressions along the surprised-relaxed dimension are associated with internal emotions determining my level of readiness for that defense.
My level of defense is associated with my acknowledgment of your new offer (how you horizontally shifted the discussion), and my degree of readiness is associated with my acknowledgment of your new tension (how you vertically shifted the discussion).
Figure 23. Here we show the acknowledgment signals (for each response from the other party), their meaning, and the (possibly externally visible) preparatory states associated with each.
For changes along the horizontal axis, my acknowledgment that you want a better compromise for yourself induces me to prepare for a (positive) defense.
But my acknowledgment that you want a better compromise for me induces me to prepare for its opposite, an anti-defense. What is an anti-defense?
If defense is pushing you away from me, then anti-defense is pulling you toward me, or allowing you to be up close. Maybe it’s even giving you a good old bear hug! When in a good mood, friends and family are anti-defensive to one another, because they’re anti-offensive (or friendly) to one another. They would fight on each other’s behalf. More generally, where being defensive is trying to halt your offense, being anti-defensive is letting your offense happen, and perhaps aiding it.
Figure 23 illustrates the internal emotions for defense by Mark, this time shown as a reaction to Tim’s response and associated offensive preparatory state. They’re symbolized by using a shield to indicate their role as a preparatory state. Defensive preparatory states are shown with a shield facing toward Tim for defense and away from Tim (with Mark placed physically nearer to Tim) for anti-defense. Here the shield is shown as more raised to indicate an internal emotion more readied for defense.
Both Emotional Spaces
The earlier, two-dimensional space of response emotional expressions (Figure 20) was crucial for “moving the ball” in the negotiation—it was the negotiation’s steering wheel. But animals in messy real-life real communication need to confirm receipt of these “moving the ball” expressions. That requires this second two-dimensional space of acknowledgment emotional expressions. It’s not a steering wheel at all but simply an acknowledgment of the direction you just steered the negotiation.
Figure 24 shows both of these spaces. It shows the acknowledgment space first, because even though both acknowledgment and response expressions might be simultaneously signaled, the acknowledgment is about what the other party already expressed, providing the context—or color—for the response.
Figure 24. This depicts the two two-dimensional spaces of emotional expressions that we’ve come to realize are required for languageless animals to carry out negotiations. A total emotional expression would consist of an acknowledgment and response. For example, maybe I emotionally express unhappy and disdain (which conveys a total meaning more along the lines of disgust). Acknowledgment expressions are listed first, because I signal that I got your response prior to when I signal my response.
As you can see in Figure 24, these two two-dimensional spaces, while distinct, still have the same fundamental meanings in terms of the arrows. For example, the leftward arrows in the upper (acknowledgment) and lower (response) panels both have as part of their core meaning “a better offer for me.” And the northeasterly directed arrows (top right of each panel) both have “you’re more confident” at their core. In this sense, each of the two two-dimensional spaces is the same two-dimensional space, and one can imagine them as two plies (two layers) on top of one another.
Let’s look, for example, at the emotional expressions for the leftward arrows. For the acknowledgment space that’s happy, but for the response space that’s aggressive. Because they both point leftward in the space, they both mean a better offer for me.
Yet how can it possibly be that both happy and aggressive have a similar meaning?! They feel . . . so different!
While they do indeed both have the core meaning of a better offer for me, the differences come from you and me.
Happy is my expression that you signaled I should get a better deal, and Aggressive is my expression that I should get a better deal.
“I should get a better deal” is the shared core of each, and yet their meanings are utterly distinct.
And they should be different. When I say I should get a better deal, that’s totally different than when I say that you suggested I should get a better deal! It’s the difference between being given something (happy) and demanding it (aggressive)! Only a sociopath doesn’t appreciate that difference. Figure 25 shows a variety of analogous pairs.
Figure 25. Because acknowledgment and response spaces both have the same axes, we can place the two spaces on top of each other and realize that there are duals where an acknowledgment emotional expression has the same core negotiation meaning as a particular response. For example, happy and aggressive seem utterly different, but each concerns a better deal for me. They feel so different because they are so different, due to the differences between you and me, the former “my signal that you signaled I should have a better deal” and the latter “my signal that I should get a better deal.” (Note that these acknowledgments are not the acknowledgment to that response, except for the vertical axis, e.g., surprised is the acknowledgment to serious.)
Sixteen Is Not Enough
By the end of the previous chapter, we had eight emotional expressions, the steering wheel of responses. We knew that wasn’t enough to accommodate the rich variety of expressions actually available to us.
Thus far in this chapter we have seen that there are indeed more. And we’ve seen that in order for social animals to acknowledge receipt of the other’s response, there has to be a second two-dimensional space (or layer or ply) of emotional expressions, one acknowledgment for each response.
Figure 24 summarizes where we are at this point, with sixteen emotional expressions. While that’s twice as many as eight, you might get the feeling that it’s still way too few to be enough. Our expressive capability seems much richer than a mere sixteen expressions! At this point in our development, however, we have actually derived many more than sixteen emotional expressions.
Why? Because if there are two two-dimensional emotional expression spaces, and each time we express ourselves we’re choosing an emotional expression from each of these two spaces, then there are lots of distinct combinations. For example, if I express pride, but at the same time also express unhappy (acknowledging that you just signaled aggressive), the pride meaning is colored by the unhappy. My total emotional expression is, as we briefly mentioned earlier in this chapter, closer to angry. Any given response emotional expression gets colored by the acknowledgment it gets expressed with, changing its overall meaning and shifting it to a different overall emotional expression. Combining one emotional expression from one “layer” (acknowledgment) with an emotional expression from the other “layer” (response) gives a new composite emotional expression.
So, how many emotional expressions are there? Well, look again at Figure 24. Each of the two spaces has nine qualitatively distinct expressions, including the central neutral one (which has no face in that figure). Whereas we’ve covered sixteen emotional expressions thus far, there are nine by nine possible ways of combining acknowledgments with responses.
That is, there are eighty-one qualitatively distinct combinations. But what are all these new composite expressions?
The Tree of Cramming
Rather than showing the two spaces, or layers, separately as in Figure 24, what we’d really like to do is show all eighty-one emotional expressions in one diagram.
But how are we to combine both of those two-dimensional spaces in Figure 24 into a single comprehensible diagram with all their combinations? There’s a really simple way to do it, one that shows all eighty-one combinations but crams them within the diagram in a sensible fashion. To understand this simple “way,” we’ll start with Figure 26.
The task is to combine the two two-dimensional spaces on the left of the figure: the number space and the letter space. The trick is to think about the first space as a tree trunk, and the other space as leaf bunches at the various portions of the tree trunk. The right side of the figure does this and shows every combination of a number (from 1 to 8) and a letter (from a to h).
But, more than that, it preserves the directions of the numbers and letters. For example, “2” concerns a shift in the northeast direction, and you can see that all the occurrences of a “2” are up and to the right within the diagram (they’re all in the northeast leaf bunch). Likewise, “b” also concerns a shift in the same direction, and it preserves this in the sense that it is at the northeast corner of each leaf bunch.
So, for example, to get the combination that is “2h,” you start at the center of the diagram and then follow the thick gray arrow up and to the right to the upper-right leaf bunch. At that point you’re at the leaf for the number “2” (because you haven’t traveled on any thin black arrows yet). To get to “2h,” just follow the thin black arrow heading up and to the left.
To get just “h” all by itself, we would start from the very center of the diagram, and never travel along a gray arrow at all (because there is no number in the combination that is just “h”). Instead, you would just follow the upward-left black arrow to the lone “h” leaf within the central leaf bunch.
Figure 26. The two two-dimensional emotional spaces (acknowledgments and responses, as seen in Figure 24) combine to create an explosion of emotional expressions. But how are we to visualize all their combinations? That’s four dimensions! Luckily there’s an easy way. (a) On the left are two different two-dimensional spaces, each with their eight qualitatively distinct arrow directions. To combine them into one visualization, let one of them be the main “tree trunk” and the other be the many “leaf bunches.” (b) Here we’ve chosen the upper “number” space in (a) to be the “tree trunk.” If you look “underneath” the overall diagram here in (b), you’ll see thick gray arrows emanating from the center as the main branches of the tree trunk, each extending out to reach its gray-contoured circle. That’s the upper, gray-arrowed, two-dimensional “number” space from (a). Now, each of these gray-perimeter circles (each with a different number within it) at the end of each gray arrow is at the center of its own leaf bunch. Each of these leaf bunches is a copy of the lower two-dimensional “letter” space in (a), having the same solid-black arrows. The leaf bunch at the center of the diagram doesn’t combine with numbers, so it ends up with only letters in the leaves (shown in gray circles). Each of the other copies of the letter space around the tree is now combining with one of the “number” space’s branches. You can see how each combination of the numbers from 1 to 8, and the letters from a to h, are found somewhere in the space.
The Great Tree
We can use that same idea to display all the combinations of the acknowledgment and response emotional expressions (Figure 27).
The acknowledgments are the tree trunk, and the responses are the leaf bunches. You can see the same overall structure as in Figure 26, but for the moment we’re just showing you where the (pure) acknowledgments and responses are within the diagram.
The acknowledgments are at the tips of the tree trunk, meaning each is at the center of its own leaf bunch. Unhappy, for example, is at the end of the rightward-directed gray arrow. We can combine this unhappy leaf with any of the responses by following any of the eight black arrows. The acknowledgments are at the center of each leaf bunch, but the (pure, uncombined) responses are found only within the central leaf bunch (shown as shaded).
A Face for All
We’ve got our Great Tree of Expressions, with space for eighty-one emotional expressions within it. But Figure 27 is only inhabited by the sixteen we’ve introduced so far.
Figure 27. Here we are using the idea in Figure 26 to display two two-dimensional spaces together to see all the qualitatively distinct combinations. The tree trunk shows the acknowledgments. After Tim expresses his response (i.e., his offer), Mark gives the related acknowledgment, and we move from the center of the diagram out along a thick gray arrow to that acknowledgment. For example, perhaps Tim had expressed aggression, which is pushing rightward in this space. Mark’s acknowledgment of this is unhappy, and is accordingly to the right at the center of its leaf bunch. Intuitively, Mark is now pushing (giving a response) from a position in Tim’s favor. Each of the thin black arrows pushing from this unhappy spot is for a different response Mark might now make. That response, in combination with unhappy, will lead to some new expression. In this diagram, we have shown you where all the combinations are but have only put names and faces for the acknowledgments (gray-rimmed circles) and responses (gray-filled circles). The responses are in the central leaf bunch because it is that leaf bunch that combines with the neutral acknowledgment, meaning the resultant expressions are pure responses. (The thicker black arrows indicate greater bets [leftward pointing] or unbets [rightward pointing], something we’ll discuss in chapter six.)
In Figure 28, we have shown a separate face for each two-ply combination as we seek to fill our tree with combinations. All the empty circles in Figure 27 have now been given a face. But where do all the new faces in Figure 28 come from?
Recall that we devised simple rules for the emotional faces we’ve been using to help illustrate the space of signals: the brows for pride-humility and the nose for respect-disdain. And for acknowledgments, we have been exploiting the smile-frown for happy-unhappy and mouth and eye openness for surprised-relaxed.
These same rules already allow us to put faces on all eighty-one combinations, creating a unique expressive face for each. For example, the facial expression to the upper left of happy is a proud variant of happy and so has the same facial features as pride, but also with the smile. (And this emotional expression conveys something closer to smug.)
Our cartoon faces for the response and acknowledgment spaces are hardly realistic, but they do tap into some perceptual kernel of truth, which is why they at least somewhat convey an emotional expression approximating the depicted meaning. For example, pride has V-shaped brows, and humility has upside-down V-brows.
If our cartoon faces are at least mildly perceptually effective for our four response faces (pride-humility, respect-disdain) and for our four acknowledgment faces (happy-unhappy, surprised-relaxed), then combining the component visual features should perhaps lead to faces that are partially recognizable as real-life composite emotional expressions.
Figure 28. This is like Figure 27, but here we have combined the facial expressions for acknowledgments and responses. For example, suppose Mark is unhappy (because Tim was aggressive), and Mark now shows pride. The resultant face is to the upper left of the unhappy face within the unhappy leaf bunch. That face has the unhappy feature (the frown), but also the proud feature of V-shaped eyebrows. If Mark were instead to respond with his own aggression, this would be the expression just to the left of unhappy. That face has, in addition, the upturned (inverted V) nose feature. Each of the circles in the diagram now has a unique face due to how its acknowledgment component combines with its response component.
And a first observation is that each new face in Figure 28 does seem to be expressing something. If responses don’t combine with acknowledgments, then combining these might have led to non-expressive faces. But they do seem to combine.
Putting a Name to a Face
Cartoon faces are nice, but it will be really helpful to have some term in English to refer to each of the combinations. In an effort to understand the range of distinct meanings across this space of emotional expressions, we’ll give each of the composite expressions a name that roughly conveys the meaning.
We could always refer to any expression in the space using a combination of the all-capitalized expressions in Figure 28b. For example, and as we mentioned, the expression to the upper left of happy in Figure 28b can be described as happy-and-proud, but the single term smug captures the meaning much more firmly.
In Figure 29 we have the same diagram, but now with emotional expression terms that reasonably fit each of the combination cases.
A More Wordy Grand Diagram
Figure 30 shows another version of Figure 29, but without the cartoon faces, and thereby with enough room to pack in all the negotiation-related meanings everywhere within the diagram itself (rather than having to read the legend as in Figure 29).
Figure 29. This is like Figure 28, but now we have placed emotion terms that approximately fit their negotiation-related meaning. For example, for the expression in the upper-left corner of unhappy’s leaf bunch (unhappy and proud), angry fits that fairly well. We discuss a number of these combinations within the main text, and all of them in more detail in the appendix section “When I’m Sixty-Four.” The thicker black arrows indicate greater bets (pointing leftward) or “unbets,” the equivalent of taking bets off a poker table (pointing rightward), something we will discuss in the upcoming chapter. This and Figure 30 amount to our promised “Rosetta Stone”—or Periodic Table—for emotional expressions, allowing us to translate back and forth between the language of negotiation and emotional expressions.
Casual examination of some of these new emotional expressions coming from the acknowledgment-response combinations suggests all these many expressions are readily understood and appreciated by us. Furthermore, they often have reasonable emotion terms that closely fit them.
As noted in the captions, Figures 29 and 30 are each the “Rosetta Stone”—or Periodic Table—of emotional expressions we promised in chapter one to build over the course of this book.
Each qualitatively distinct situation that can happen in a negotiation is found in these diagrams. Find it, and you can then read off the emotional expression signaling that situation. Suppose, for example, that you just asked for $140,000, which is more than my earlier offer, and suppose that you added that it’s your final offer. That means you shifted the negotiation rightward (in your favored direction) and upward (which you signal with pride). I acknowledge that with worried (which is at the center of the top-right leaf bunch). Suppose that I aggressively counter with an offer of $110,000. The emotional expression signaling that is aggressive (a leftward shift), but in light of also signaling worried, that moves us leftward in the diagram to appalled. That is, appalled is the expression summarizing that I’m saying I should get a better deal after you just asked for a better deal and were serious about it.
And the other way around, for each of these eighty-one widely diverse emotional expressions within the diagram: locate it within the diagram, and you can read off what it means in negotiation terms. For example, modest (at the lower right of the left-side leaf bunch, off of happy) means that you just offered me more, and I responded by offering you more and lowering the tension. “Nah. Shucks. You should get more than that. I’m not as sure about the price as you seem to think.”
Figure 30. The entire space of emotional expressions now has each of their negotiation-related meanings (including both the acknowledgment receipt and the response) shown. The meaning of angry (right side, center panel, which is a combination of unhappy and proud) is read by first going to the center of its acknowledgment leaf bunch (unhappy), reading, “You suggested a worse deal for me . . .” and then reading the meaning in the pride direction (“but I’m more certain than you suggest”). The bet (unbet) sizes are shown by the thickness of the black (or gray) arrows (see next chapter). This and Figure 29 amount to our promised “Rosetta Stone” for emotional expressions, allowing us to translate back and forth between the language of negotiation and those emotional expressions.
Prides
We went from sixteen to eighty-one emotional expressions in a jiffy, so it will be helpful to spend some more time on some of the new emotional expressions. In the appendix section “When I’m Sixty-Four,” we have eight diagrams that walk through each of the sixty-four new emotional expression terms, something you might like to go through at your leisure.
In this and the upcoming section, we’ll walk through just a few of our favorites and get a feeling for why the term we have chosen is at least in the right ballpark for its negotiation-related meaning.
Let’s begin by pointing out some of the new expressions that have pride as their response and are therefore at the upper left within any leaf bunch.
Whereas happy-and-proud (upper left within the happy leaf bunch) is close to smug, we also hinted earlier that unhappy-and-proud (upper left within the unhappy leaf bunch) is something along the lines of angry.
How about surprised-and-proud (upper left within the surprised leaf bunch)? This would be a case where I convey I’m more confident than you suggested, but I do it after you expressed serious (that you’re more likely to fight). Intuitively, it’s a more dramatic variant on proud, and with no implication that you modified the offer itself (i.e., no implication that I’m happy or unhappy). Something like pretentious comes close. “How dare you imply I’m not taking you seriously! I should get more, and I’ve just about had enough!”
The opposite of this would be relaxed-and-proud (upper left within the relaxed leaf bunch), where I show I’m more confident, but where things are relaxed and not dramatic—sassy somewhat fits this. “Thanks for the drink, bro, but you have to admit, I’m on today!”
How about some of the cases with humble instead, which are always at the bottom right of an acknowledgment leaf bunch?
If I express happy-and-humble (bottom right of the left leaf bunch), it means you must have just offered me more, and my reply is that “I see you’re offering me more, but I’m not as confident as you suggest, and so I warrant less than what you just offered.” That’s something close to modest. “Oh, shucks. Kind of you, but I’m not worthy.”
If I instead express unhappy-and-humble, it means you must have just demanded more for yourself, i.e., less for me, and I basically further criticize myself, “I see you just offered me a worse deal. Well, I’m not even deserving of that small amount, because I’m even less confident than you imply.” That’s definitely not merely humble, and certainly not modest. It’s much closer to sad. Even the facial expression looks to be in the realm of a sad expression.
Respects
Let’s now look at the faces having respect as a component, which are always at the upper right of a leaf bunch.
If I also express unhappy (and therefore we’re at the face to the upper right within the unhappy leaf bunch) because you were just aggressive, then my total expression of unhappy-and-respectful conveys: “Even though you’re offering me a worse deal, I totally think you’re even more confident and should get an even better deal than you just suggested.” That comes across as something like fear. To a thug demanding my coat, I might reply, “Yes, sir, you can have my leather jacket. And here’s my wallet as well. I insist!”
If instead I express happy-and-respect (because you were just conciliatory), I’m saying something more like, “You just offered me a better deal, but you’re actually more confident than you’re letting on, and you should get a better deal than that.” I’m still expressing respect, but since it’s colored by happy, it becomes different than respect alone, and much different than fear. I am conveying something more like appreciative, i.e., appreciative of your nice offer. “Nice of you to offer, but it’s all yours.”
Finally, let’s peek at some disdain cases, which are always at the bottom left of a leaf bunch.
Suppose you just expressed aggressive. My disdain expression is then colored by my unhappy acknowledgment, and in total that conveys something like, “You offered me a worse deal, but you’re less confident and deserving of a worse offer than you suggest.” More than disdain, that’s closer to disgust. “Pffft. You’re out of your depth!”
If instead you had just expressed conciliatory, then my total expression would instead be happy-and-disdain (now we’re at the bottom left face of the left-side happy leaf bunch), conveying, “You offered me a better deal, but you’re even less confident than you suggest, and so I should get an even better deal than you suggest.” That kind of expression of happiness, done while basically insulting the other party, is more along the lines of sneer. “Yeah, I should get more than half as you just suggested. I should get a lot more than half because you don’t have a clue! Bwahahaha!”
A Steering Wheel and “Roger That” Colored Lamps
The steering wheel we had ended with in chapter four possessed the needed signals for making any change to a negotiation that might be required. I could ask for more—or less. And I could get “this is my final offer!” serious—or not. We had seen there were eight qualitatively different emotional expressions, one for each of the eight compass directions.
And if social animals could mind meld, those are the only emotional expressions that would be needed for finding a compromise.
But because real life isn’t one of mind melds, and animals have to ensure that they’re tightly bound in a discussion, where each “gets” what the other has just asked for, we saw in this chapter that there needs to be a second two-dimensional space of signals, allowing me to confirm receipt of any response expression you have just signaled. “Roger that; you’re asking for more, and you’re totally not kidding around.”
In a sense, what that meant was that eight differently colored lights (one for each acknowledgment—or context) could be shone upon the same steering wheel, and its color changes what each of the steering wheel directions mean. The steering wheel still does all the same stuff as before, no matter its color, in terms of how it shifts the discussion. So that part of its meaning isn’t changed by the color of the light shone upon it by the acknowledgment. But, the combination of the acknowledgment does change the overall meaning, and that means we end up with a four-dimensional space of signals. We end up with eighty-one in all, rather than the nine on the steering wheel (including the neutral position).
While that amounts to some great strides forward, there is something really big we have made an effort to (somewhat) hide from you thus far. You might even say that our failure to mention it amounts to a lie! We’ll deal with exactly that in the upcoming chapter.
Where Are the Historical Six “Basic Emotions”?
One of the most commonly used spaces for visualizing emotions is James Russell’s “circumplex structure” (Figure 31a). Russell believed that emotions were built out of a combination of two dimensions: pleasure-displeasure (valence) and activation-deactivation (arousal). Many researchers within the emotion literature like to place various emotions or their expression within this space in order to help get a sense of how they differ from one another.
Quite to our surprise, it turns out that our space has connections to the circumplex space.
First, remember that our space is four-dimensional not two, so there’s quite a bit more going on in it. Recall that the horizontal axis for my acknowledgments concerns how good your compromise is for me. If I say, “You just offered me a much better deal,” which is exactly what happy signals, then something good just happened to me. That’s positive valence. If instead I say, “You just offered me a much worse deal”—that is, I signal unhappy—then that’s bad for me. That’s negative valence.
Figure 31. (a) James Russell’s “circumplex structure,” whose horizontal axis is valence (pleasant-unpleasant) and vertical axis is arousal (activation-deactivation). (b) Our acknowledgment space, which drives the overall structure of our combined diagram, also turns out to have these axes. Expressions within the same acknowledgment leaf bunch should be deemed to all have the same valence as the acknowledgment in the center.
The horizontal axis of our acknowledgment space therefore clearly maps nicely onto the horizontal valence axis of the circumplex space.1
How about the vertical axis, which is about how likely you are to start a fight? That is, my expression of surprise says, “You’re saying you’re more likely to give up on negotiation and just fight about it.” Internally I need to have an emotion of surprise, including a higher level of readiness to react to whatever you’re threatening to do. I need to have a higher level of arousal (or activation level) to react.
Acknowledgment space, then, maps perfectly onto circumplex space, the horizontal compromise axis lining up with valence, and the vertical tension axis lining up with arousal.
This wasn’t something we devised. Our two axes emanate, recall, from first principles concerning two parties’ beliefs about how much zucchini bread they should get (which, really, is two parties’ beliefs about how much zucchini bread they’d get if they fought about it).
Our horizontal axis didn’t start as a valence axis at all but as the dimension of disagreement the parties are arguing about (the compromise axis).
Our vertical axis began as each party’s degree of disbelief in any particular compromise being the truth (about what would happen in a fight), which related directly to how likely that party was to initiate a fight. And it ends up mapping so nicely onto arousal (or activation) because one needs to have a high level of arousal to correspond to a high probability of a fight.
Our acknowledgment space maps perfectly onto circumplex’s valence-arousal space; furthermore, our space isn’t a mere space to usefully place emotional expressions within, but an inevitable mathematical consequence of our theory, one having hosts of implications for negotiations between social animals. In this sense, one could view our theory as (among other things) a first-principles justification for using valence and arousal as dimensions on which to map emotions in the first place.
In this light, let’s look again at our emotion space, seen in Figure 31b but now relabeled to show how it relates to valence/arousal space. To a first approximation, then, Figure 31b is how our theory predicts that emotional expressions fit into valence/arousal space.
We say “to a first approximation” because in this way of organizing the expressions, all the expressions within the same leaf bunch are actually at the same position within valence/arousal space. For example, in Figure 31b, angry is shifted up and left compared to the unhappy expression it is clustered with because that’s the direction within negotiation space it pushes (for Mark, who is pushing leftward), but in regard to the valence and arousal of angry, that’s determined entirely by its unhappy component, and so its valence/arousal position is at the same spot as unhappy.
That said, that’s not quite perfectly true either. The vertical axis of acknowledgment space concerns my arousal, or readiness, level for reacting (somewhat defensively) to what you might do if you start a fight. But the vertical axis of response space also concerns arousal, though it applies to what my action would be if I start a fight (think offensive action, rather than defensive reaction to your offense). After all, in Russell’s circumplex valence/arousal space, it doesn’t mention anything about the level of arousal concerning how I’ll (offensively) act if there’s a fight or how I’ll (defensively) react. So, even within the leaf bunches, the vertical differences probably do correspond to vertical differences in general arousal. The horizontal differences between responses within a square, however, do not concern differences in valence. Valence concerns how good things are for me, and that depends entirely upon what you offered, not on what I subsequently merely say I want.
With these caveats in mind, though, Figure 31b nevertheless gives a pretty good representation of how the emotional expressions in our theory fit within valence/arousal space.
Because within our space we have six of the most famous emotions—those argued by researchers such as Paul Ekman to be “basic emotions” universal to humans, namely happy, surprise, angry, sad, fear, and disgust—it is of interest to see where they end up in valence/arousal space according to our theory, and then to see where researchers in the emotion literature actually measured them to be.
Figure 32a removes all the emotional expressions from the previous figure (Figure 31b) except for these six traditional basic emotions, and it re-clusters them with the caveats we just mentioned above: all four are deemed to have the same valence, but angry and fear have greater overall arousal than disdain and sad.
How do the positions of the six historically basic emotions within valence/arousal space predicted by our theory compare to their positions as measured by emotion researchers? Figure 32 shows their positions in our space (Figure 32a) adjacent to their locations as approximately typically measured (Figure 32b), and one can see considerable similarity.
The emotional expressions within our theory’s system that seem to best match the intuitive meanings of the traditional six basic emotions do end up in approximately the same positions within the space as others have found, serving as a kind of sanity check.
Goldilocks
You should understand that the space in our theory is four-dimensional, and it can sometimes be a little confusing. You might wonder why a simpler space, and a simpler theory, might not instead be right.
Figure 32 (a) The six “basic emotions” of Ekman are highlighted, and all the others are removed. The horizontal differences in Figure 31 within a leaf bunch do not indicate valence differences—valences only differ from one leaf bunch to another—and so angry and fear have been placed inside a single dashed ellipse to indicate they’re to be deemed to be at the same horizontal valence position. And the same for disgust and sad. The vertical axis in acknowledgment space concerns arousal, but the vertical axis in response space also concerns arousal. It’s just that the former concerns readiness to react to you (intuitively, defense), and the latter readiness for how I will act if there’s a fight (intuitively, offense). “Arousal” in the context of the circumplex valence/arousal space doesn’t distinguish between these distinct kinds of arousal, so we should nudge angry and fear higher, and disgust and sad lower, to show their difference in arousal. (b) The approximate typical positions of the basic emotions as measured within the emotion literature, which is close to what our theory suggests.
Our theory, however, is actually not very complicated. We’re not saying it doesn’t take some concentration to get through, but the beauty of it is that its rich tapestry of emotional expressions comes from the barest minimum of ingredients: a pinch of belief (certainties), a teaspoon of correcting each other (responses), confirmation receipts to taste (acknowledgments), and a loaf of precious zucchini bread (the resource being negotiated).
And it led to something we’re all very familiar with: negotiation. You may not have consciously realized that negotiation has the vertical “and this is my final offer” axis, but you intuitively knew it.
Our theory is simple and intuitive! Of course, we had to derive our theory from first principles to show you where the theory comes from and that takes some work. But what it leads to is simple and elegant.
Now what about this super gigantic clustery four-dimensional space we’re making you suffer through in Figures 29 and 30?
It can be difficult to know whether four is “bad” or “good.” Is four a lot of dimensions? Compared to what?
The circumplex complex space we discussed in the previous section has just two dimensions, not an unwieldy four!
While valence/arousal space is indeed a smaller space, and the traditional six basic emotions can be visualized within it, the true space for properly grasping the traditional six basic emotions would be . . . six-dimensional! That’s because, if one believes that those are the six independent basic emotional expressions out of which a suite of more complex combinations can be built, then to visualize the space of emotional expressions that these basic ones allow would require one dimension for each of the six.
Our theory has only four dimensions, not six: (1) happiness (happy-unhappy), (2) surprise (surprise-unsurprise), (3) pride (pride-humility), and (4) respect (respect-disdain). And, just as three dimensions is, in a sense, infinitely larger than two dimensions, a six-dimensional space is truly vast compared to a four-dimensional space.
So, that’s great! If you think our four dimensions make things problematic, six compounds (and compounds) things much further. Even if we were to focus just on the qualitatively distinct combinations that emanate from the six basic emotional expressions, then that would be 36 = 729 combinations.2 You may have thought that 81 (or 34) expressions was a lot, but we were able to make sense of those 81, and each had a distinct negotiation-related meaning we could grasp. Eighty-one emotions also seems more in the ballpark of reality than 729!
And, for those six dimensions—and the corresponding 729 qualitatively distinct emotional expressions—no one is close to possessing an underlying theory making rigorous sense of the axes and what they mean in terms of the use by social animals. So even if we could somehow visualize those six dimensions, it would have no explanatory benefit.
In our account, however, the six basic emotional expressions aren’t basic at all. They’re simply part of the entire repertoire of emotions.
They are, however, important parts, which is another sanity check. Happy (and its opponent, unhappy, or “negative happy”) and surprise (and its opponent, relaxed, or “negative surprise”) have privileged roles in our theory as well. They are the two axes of acknowledgment space and are primes (i.e., indivisible) in our theory’s view.
The other four (angry, sad, fear, disdain) are not primes in our theory, but are closely related to primes. Remember that our response space is pride-humility and respect-disdain. When combined with unhappy, we have argued that they respectively become angry-sad and fear-disgust. That is, these four are our theory’s response opponent pairs, but when colored with unhappy.
Four, then, ain’t so bad after all. One shouldn’t expect a grand unifying theory of our complicated emotional expression system to fit into too small a space! The reason our theory is four-dimensional in the first place ultimately comes down to the fact that there are two people, and each has an opinion about their two respective certainties.
Even in the absence of a theory, the fact that there are two people suggests the number of dimensions will end up being even. A simple Goldilocks argument: Two is certainly too small—that would lead to only (32) nine qualitatively distinct emotions. Six is too big—what are we going to possibly do with 729 qualitatively distinct emotions?!
But four is jusssst right.
Sword and Shield as Signals?
Emotional expressions are, in our view, best thought of as symbols—or signals. They’re like words. They just stand for some (negotiation-related) meaning, something that other animals of the same species come to somehow know. The signal for pride need not necessarily possess any intrinsic hint that it means pride, just as the spoken word “bath” possesses no hint as to its soapy-clean meaning.
But, while we made progress in understanding why emotional expressions are emotional thus far by considering internal emotions as preparatory states, we’ve avoided the obvious idea that internal emotions are by no means the only sort of preparatory states.
We also have externally visible preparatory states as well.
As Nigel angrily catches up to lunch-stealing Butch, Nigel’s incisors might have been more visible than usual. But this is not because Nigel was expressing anything to anyone; rather, it is simply because his teeth were thereby in a more ready-to-bite state. (We realize sharks probably don’t have incisors. Work with us, people!)
So, just as social animals might often have internal emotions serving as appropriate preparatory states for the fight that might occur given the state of the negotiation, social animals might sometimes get physically ready for it as well. And that might be something not internal—something visible to the other party.
In fact, our earlier little-dude drawings implicitly relied on this. We used external preparatory states as a way of representing the internal ones.
But, given all those salient differences in that little dude, the little dude might wonder, “Why don’t I just use my sword and shield preparatory state as my emotional expression itself?” Why not let the stimulus for an expression—i.e., what the expression looks and/or sounds like—just be the external preparatory state?
For example, if my species’ preparatory state for “I should get a better deal” is baring my sharp claws, then perhaps it is sensible for the baring of my sharp claws to be the signal itself. The fact that I’m baring my claws basically does inform you that I am claiming that “I should get a better deal,” so why bother with having anything else as a signal specifically for this?
There are, however, several reasons why it nevertheless might often make sense to have a separate signal, above and beyond any external preparatory state associated with the signal; i.e., why it might often make sense to have something else signal “I should get a better deal” besides claw baring.
First, social animals find themselves in a large variety of kinds of disagreements, and there are a lot of different kinds of fights they might find themselves in if they can’t come to a compromise. The preparatory states associated with signals will therefore have to vary quite a bit depending upon the kind of fight that would occur if someone chooses to end the discussion and fight. But whereas the preparatory states need to vary across all the different kinds of fights, the signals used to negotiate can be the same: one generic compromise signaling system to rule them all.
Second, perhaps there are kinds of fights where there are no external preparatory states needed at all. For the authors’ disagreement about zucchini bread, for example, whereas each of us might internally be planning on how to find the café owner’s phone number at her undisclosed location and what to say to her if we manage to get hold of her, there’s not really anything external needed.
Third, there may be situations where there’s some advantage to not visibly showing an external preparatory state. By doing that, maybe I get the other party wondering whether I really mean it, and perhaps that’s to my advantage (akin to the opposite of a standard bluff).
Fourth, preparatory states simply won’t tend to be good signals. Signals need to be perceived by the other party, and so they should be easy to see or hear and easy to distinguish from other signals. External preparatory states, on the other hand, are all about the action and don’t care whether they’re perceived by the other party. My bared claws, for example, tend to be inconspicuous, hidden within the dirt or grass.
Those are some of the reasons to expect that the expressions won’t usually simply be the external preparatory states. Nevertheless, there are a couple of reasons for believing that preparatory states themselves could be at least partially related to the signals themselves.
First, even though there may be a lot of different kinds of disagreements, for most animals (and even for humans for most of our biological history), much of the time the fight was probably one of tooth and claw. Violence is exceptionally effective at settling disagreements! It could therefore be that the expressions animals use sometimes have overlap with the preparatory states associated with them. For example, an angry facial expression might be, in addition to the signal that it is, partly a preparatory state for offense in a fight, where the teeth might be employed.
Second, even if signals are always “only” signals (like words), and not preparatory states, they at least shouldn’t interfere with the preparatory state. If my preparatory state associated with “I want a better deal” involves baring my claws, then let’s definitely not have unbared claws as the signal!
There are a lot of interesting directions one could pursue concerning what these compromise signals ought to look like, species by species, something our abstract theory doesn’t have much to say about, other than the sorts of considerations we just went through in this section. For our purposes, we largely treat them as word-like signals.
But they’re word-like signals that commit one to potentially having to act in a certain way if there’s a fight, and that will tend to imply that one will have the associated internal emotion at the time, because that’s the emotion that best prepares one for that possibility.
The Periodic Table of Little Dudes
In the previous chapter, and earlier in this chapter, we covered why it is that emotional expressions are emotional. They tend to associate with that particular internal emotion because that’s the internal state that prepares them to do what needs to be done in a fight, both offensively and defensively.
We have seen that response emotional expressions associate with offense-related emotions, and acknowledgment emotional expressions associate with defense-related emotions. Each of these had a horizontal dimension related to (offensively or defensively) fighting for more or less, and a vertical dimension related to how ready they are to act (offensively) or react (defensively).
By virtue of having these two two-dimensional spaces of internal emotions (as seen in Figures 21 and 23, each symbolized by a little dude with a sword or a shield), we can combine these two spaces into one massive space that has eighty-one qualitatively distinct internal emotions. Each concerns a distinct preparatory state and is associated with its corresponding emotional expression. Figure 33 shows all of these. And we’ll leave this chapter with a variant on that, Figure 34, which provides a more personal viewpoint of the “little dude with sword and shield,” rather than from a third-person perspective as in Figure 33.
Figure 33 Combining Figures 21 and 23 leads to this way of visualizing all eighty-one emotional expressions, helping to capture the entirety of the situation.
Figure 34 You can now see the full suite of eighty-one emotional expression cartoon faces, along with representations of the possibly externally visible preparatory state associated with each expression.
1But remember, as we have discussed earlier in the book, any pleasant or unpleasant feelings associated with these signals are, in our theory’s view, secondary to the expression. The point of the expression “You just offered me a better deal” is to acknowledge your previous response signal offering me a better deal; that is, to provide a confirmation receipt, so to speak. That’s the principal role of the happy expression.
2These little calculations have the number 3 in them because each dimension has just three qualitatively distinct values: positive, zero (or neutral), and negative. So, for example, for two dimensions, there are the following 32 = 9 possibilities: pos-pos, pos-neut, pos-neg, neut-pos, neut-neut, neut-neg, neg-pos, neg-neut, and neg-neg.