Strange Attractors

Like relationships between people, mathematical systems often evolve over time. But the evolution is always toward something, toward some final state. Human relationships can evolve into a strong friendship, into a committed relationship, into two strangers who no longer associate. So too can mathematical systems evolve, and the final state they move toward is known as an attractor.

The best example of this is a bowl. Drop a marble in a bowl and the marble will roll around a bit before finally settling on the bottom. That central point on the bottom is like an attractor, and the basin of attraction is the bowl itself, the area within which the attractor has influence (in this case, within a literal basin). If you were to remove the marble and set it beside the bowl on the table, the marble would no longer be in the basin of attraction and would no longer be drawn to the central bottom point of that bowl.

No matter how long that marble rolls and ricochets around the bowl, it eventually finds its way to that bowl’s “attractor”. The same is true of mathematical systems. For any dynamic system, the attractor is the end point. Of course, when I say point, I don’t mean a literal point. While some attractors are points, others are orbits, curves, and manifolds. The attractor is simply the final shape/set/what-have-you that the system settles to.

But not all systems have tidy attractors. Some systems have chaotic solutions. These systems possess strange attractors. Strange attractors are unique in that you never know where on the attractor an evolving system will be. Sometimes two points will be right next to each other, and the next time they’ll be arbitrarily far apart. The motion of systems never quite repeats and the attractor doesn’t close in on itself (thus the “chaotic” descriptor). For example, here’s the first strange attractor, the well-known Lorenz attractor:

As you can see, no solution ever exactly duplicates- they come close, but never quite. And while strange attractors can have definite figures like this, they remain chaotic. Never quite replicating what’s come before or what will come after, never quite settling into a firm shape- almost like it’s dancing around completion. Unpredictable except in short intervals, oscillating around each other without quite touching.

Like strange attractors, some human relationships never quite settle into something one might call concrete. They flow endlessly, never quite what they were, never quite what they could be. Like their timing is never right, something always pulling them apart, but throwing them back together at random moments. Unpredictable except in short bursts, even they don’t know where they will be in the future. There is no stability in their system, but there is a kind of poetry to the motions.

And I suppose that’s something.

And Now a Surprisingly Poignant Moment From “Red vs. Blue”

…what I’ve learned is that a great love is a lot like a good memory. When it’s there, and you know it’s there, but it’s just outta your reach, it can be all that you think about. And you can focus on it and try to force it, but the more you do, the more you seem to push it away. But if you’re patient, and you hold still, well maybe, just maybe, it’ll come to you.

This is Your Brain on Love

We all know that the emotion of love originates, not in the heart (or liver), but in the brain. The same is true of sexual desire (turns out, men are always thinking with just one head). But, strangely enough, no one has bothered to make a comprehensive map of exactly which areas of the brain activate for feelings of love and desire.

Until now, dear galleons.

In an international study involving scientists from both the United States and Switzerland, 20 separate studies that mapped love or lust in the brain using fMRIs (you know, monitoring brain activity while looking at sex-ay picture or pictures of significant others) were analyzed and compiled.

The result was the first complete map of love and desire, allowing us to actually follow how desire morphs into love within the brain. Despite the hideous phrase “making love,” sexual desire and love actually activate different (but related) areas of the brain. Ergo, we can still want to slam someone against a wall without wanting to walk down the aisle with them.

There are two primary areas in the brain that trace that path from wanton desire to actual affection- the striatum and the insular cortex (more commonly referred to as the insula). Now, the striatum is this funky bulbous structure inside the brain with a curling tail-like-bit (the purple structure in the following image):

The striatum is located deep within the brain, near the center (inside the forebrain). The insula, on the other hand, is located a little further out, folded between the temporal and frontal lobes. In the following frontal cross-section of the brain, you’ll notice the insula over on the right side of the image.

Now, you might not realize it, but the striatum is also evident on this image. Look for the caudate nucleus and lentiform nucleus– those are parts of the striatum. As you can see, the striatum and insula are located nearby one another.

That area, dear galleons, is the home of love and desire in the brain.

Now, some of you might be flaring your nostrils at me, sputtering about how the amygdala, widely known to be deeply involved in the processing of emotional events, wasn’t listed. Calm the fuck down. The limbic system (of which the amygdala is a part) actually works with the striatum, as does the cerebral cortex (which is where the insula comes in). Remember, the brain’s this complex, intricate system, and I’m just bastardizing it with my woefully inadequate words. Suffice to say, the striatum (the primary basal ganglia input center) is taking in information from places like the insula and the amygdala, okay?

So, love and desire actually activate very different sections of the striatum. See, the striatum is one of those big names in the reward system of the brain. It’s taking in information from the limbic system and cerebral cortex, information relating to pleasure and novelty. Now, when you’re feeling the need to ride someone until neither of you can walk, you’re using a section of the striatum that’s activated by things that are inherently pleasurable. Like food. And sex. But when your crazed rabbit humping starts to move into the realm of love, a different part of the striatum is activating. This is the part involved in behavioral conditioning and reward. Here, something (or someone) paired with one of those inherently pleasurable activities is given its own inherent value.

So yes, at first, it might just be about the sex. Or the conversation (What? Intellectual blokes are dead sexy). But eventually, if you are sexing up the same person again and again, or are spending night after night in exciting debates and conversations… well, then that person is going to develop their own inherent value. In your brain, they are now a source of pleasure.

And you, my galleons, find yourselves in love.

Because the striatum is so involved in the pleasure/reward system of the brain, it plays a strong role in drug addiction as well. As Jim Pfaus, co-author of the study, said, “Love is actually a habit that is formed from sexual desire as desire is rewarded. It works the same way in the brain as when people become addicted to drugs.”

Like it or not, it looks like Ke$ha had it right.

 

Foie Amour

Throughout the ages, the heart (though cartoonishly distorted) has been considered the seat of emotion in the body. A universal symbol of love, we gift our sweeties with paper hearts and candies nestled in heart-shaped boxes. In fact, the image of a cartoon heart has become so inextricably bound to the concept of love that it is used as a stand-in for the word itself, in everything from emoticons ( ) to classic/trite souvenir items.

However, it wasn’t always that way.

Back in the day, galleons (around 150 CE), there was a Greek physician by the name of Galen. Galen had a lot of ideas about the human body (due to his intense study of it during his numerous human dissections and vivisections- anything in the name of science, yo), and while many of them later proved inaccurate (like many early biological theories), they were interesting nonetheless. One such theory of his involved the liver. Namely, Galen believed blood originated in the liver before sloshing around the rest of the body. In Galen’s world, the liver became the emotional center of the human body, the origin of the vital fluid of blood.

From a scientific perspective, this is preposterous… but no more preposterous than the idea that the heart is the body’s emotional home. But because we’ve grown up with this strong, symbolic tie between heart and emotion (particularly love), it’s easier for us to accept the idea that our forebears might have seen the heart as the mystical center of love. But the liver? Say it isn’t so.

When you really think about it, though… is it all that strange? Personally, I think it makes more sense to equate the liver with love than it does the heart. After all, most people can’t even accurately pinpoint the emotion we call love and get it all mixed up with a funny feeling in the genitals directed toward another human being. And what facilitates crazy monkey sex… excuse me, crazy monkey love better than booze?

Perhaps we should be rethinking this whole heart = love thing…

Much better, don’t you agree? [I’ll leave it to you lot to think up an emoticon]

An Excerpt from Salman Rushdie’s “The Enchantress of Florence”

For the last time in his life he wondered if he had wasted his love on a woman who only gave her love until it was time to take it back. He set the thought aside. He had given his heart this once in his life and counted himself blessed to have had the chance to do so. The question of whether she was worthy of his love had no meaning.

His heart had answered that question long ago.

Amplexus

For all around these days
Can’t let my embrace go free
Into my arms and veins
It’s hard for time to see ~Feel.Love.Thinking.Of Faunts

In 2007, a pair of human skeletons were found in Valdaro, near the Italian city of Mantua. The skeletons are a man and a woman, between 18 and 20 years old, dating back to the Neolithic Period (5000-4000 BCE). What makes this double burial unique is that the two skeletons are positioned face to face, curled together with their limbs entwined, as if in an embrace.

Galleons, meet the Lovers of Valdaro:

While a Neolithic double burial isn’t unheard of, the positioning of these two is certainly unique. But little is known about the purported “lovers.” Even now, four years later, we’re no closer to unraveling the mystery of just who these two were.

The media latched onto the discovery of the Lovers, painting them with all the romantic tragedy of Shakespeare’s Romeo and Juliet (which is such a shit play- after knowing each other for a goddamn day, two dumbshit teenagers get married, bang, and then end up killing themselves because they are angsty, stupid prats). The sight of these 6000-year-old skeletons, entwined with one another, embracing through the ages… it stirred something in people. In the Lovers, people found that sweet, enduring, perfectly pure note of love that their little hearts longed for. Here it was. Love. For all the world to see.

“I’ve never been so moved,” said archaeologist Elena Maria Menotti, who led the excavation, “because this is the discovery of something special.”

I’m not going to lie- the squishy, girly portion of my heart is warmed by the image of the Lovers.

However, the bigger part of me is drawn to the Lovers for another reason. Four years. DNA testing. A 3-D laser scan. X rays. And what do we know about them? Hardly anything more than we did when we first found them. The Lovers don’t seem to have met a violent end, leading some to speculate that they really were a pair of young lovers, who died holding each other on a freezing night. And if you really need to believe in that almost poetic little love story, then go ahead. Because there’s no evidence that can actually dispute that.

And while it’s possible the Lovers really were lovers who died in one another’s arms, it’s more likely that they were positioned that way, buried together in a prehistoric cemetery. According to Menotti, “It’s possible that the man died first and then the woman was killed in sacrifice to accompany his soul.”

Another interesting thing about the burial is that it’s… wrong. Burials in the Neolithic Period were always East-West, possibly following the path of the sun across the sky. But the Lovers were buried the wrong way.

“They were buried North-South, and we don’t know why,” said archaeologist Daniela Castagna.

I like that we’ll probably never know the story behind the Lovers. That we have these tantalizing little snippets that will never get pieced into a whole picture. There’s more truth in life and love in the mystery than in the tidy little love story of the romantics. Life… love… they are haphazard things, pieced together from moments. There’s not necessarily narrative- they simply are.

Just like the Lovers.

And I like that they were removed from the earth together, completely intact (typically, skeletons are removed from excavation sites one bone at a time). Because of this, they can be displayed together just as they were found, wrapped around each other. And they were- two months ago, they were displayed in public for the first time at Mantua’s Archaeological Museum, and a local group is working to raise the money to give the Lovers a permanent exhibition space.

It would be nice to have these two on display for people to see. Whether you love the shroud of mystery or the saccharine, Shakespearean fantasy, we all need a little wonder in our lives. And if these Lovers can bring that to people, then they should be displayed for the public to admire, to stand before in awe.

The Lovers inspire. They inspire hope, joy, tenderness, wonder, curiosity… and, apparently, at least one pretty rockin’ tattoo:

Rubin’s Scales of Liking and Loving

In my intrepid internet wandering, dear galleons, I happened across an article that mentioned a social psychologist by the name of Zick Rubin. His primary field of study was love, an area much maligned, both by other psychologists and the public at large.

Something I find myself ardently admiring him for is his staunch defense of tax-funded (from the National Science Foundation) work in the area of love. Beset by harsh criticism from Wisconsin Senator William Proxmire, who claimed the Harvard love studies “a futile and wasteful attempt to explain the impossible,” Rubin retorted by stating Proxmire was “taking advantage of the fact that it is easy to trivialize and sensationalize such matters as these.”

Love is not some mystical force that defies explanation. Love is an emotion, a strategic release of certain chemicals in the brain at just the right time, a reaction that gives us our feelings of affection, trust, protection, adoration, desire. It is part of the human condition, something that bears as much scientific scrutiny as memory or congestive heart failure. Science, hard and soft alike, strives for knowledge. And we should not place boundaries on the pursuit of said knowledge simply because the area in question has been so thoroughly romanticized by artists and poets.

Anyway, Rubin’s research seemed to focus on two main areas. One was the study of eye contact. Basically, the more a couple in his study reported to love each other, the more eye contact they made. This information seems like common sense at this point, seeing as it comes at us from even the most mundane and ridiculous sources as Cosmo’s constantly recycled list of ways to make your man want you.

The more interesting facet of this research is that science actually doesn’t have a definitive answer as to why eye contact is linked to love- there is much speculation and some predominant theories (my personal favorite being that narcissism fuels love- we are affected most when someone takes enough of an interest to look at us), but no real answer.

However, it was the second part of Rubin’s research that really piqued my interest. First, Rubin differentiated between liking and loving, giving three elements that defined each, a differentiation that has been adopted by many other social psychologists. According to Rubin, liking is conceptualized as feelings of warmth, closeness, and admiration of another. Loving, on the other hand, is made up of caring, attachment, and intimacy.

Upon doing that, Rubin created scales by which to measure liking and loving by contrasting them with one another. Initially, he had a questionnaire of 80 questions designed to assess the attitudes a person holds about others, with the questions sorted in regards to whether they reflected liking or loving. From here, he narrowed it down to 13 questions for each- 13 questions he considered the most reliable measures of these two variables.

Curious as to what these questions are, dear galleons? I know I was. Have no fear- I will share them with you. Note that each question should be answered on a 9-point Likert scale, with 1 being “Not True” and 9 being “Definitely True.” The more points accrued on a scale, the stronger you like or love them.

Liking Scale

1. When I am with [friend], we are almost always in the same mood.
2. I think that [friend] is unusually well adjusted.
3. I would highly recommend [friend] for a responsible job.
4. In my opinion, [friend] is an exceptionally mature person.
5. I have great confidence in [friend]’s good judgment.
6. Most people would react very favorably to [friend] after a brief acquaintance.
7. I think that [friend] and I are quite similar to each other.
8. I would vote for [friend] in a class or group election.
9. I think that [friend] is one of those people who quickly wins respect.
10. I feel that [friend] is an extremely intelligent person.
11. [Friend] is one of the most likeable people I know.
12. [Friend] is the sort of person whom I myself would like to be.
13. It seems to me that it is very easy for [friend] to gain admiration.

Loving Scale

1. If [loved one] were feeling badly, my first duty would be to cheer him/her up.
2. I feel that I can confide in [loved one] about virtually everything.
3. I find it easy to ignore [loved one]’s faults.
4. I would do almost anything for [loved one].
5. I feel very possessive toward [loved one].
6. If I could never be with [loved one], I would feel miserable.
7. If I were lonely, my first thought would be to seek [loved one] out.
8. One of my primary concerns is [loved one]’s welfare.
9. I would forgive [loved one] for practically anything.
10. I feel responsible for [loved one]’s well being.
11. When I am with [loved one], I spend a good deal of time just looking at him/her.
12. I would greatly enjoy being confided in by [loved one].
13. It would be hard for me to get along without [loved one].

Doubtful that these actually differentiate between liking and loving? Test it out- fill them both out, once for a loved one (mate, partner, limerent object, crush, etc.) and once for a good friend. While your friend will score high on the liking scale, they shouldn’t score high on the loving scale.

…Unless you have some hitherto unaddressed feelings for them, I suppose.

Maybe this is the point where you are asking yourself a very important question:

Why do I give a shit?

The answer is that, while I find this all mildly interesting, I’m mostly drawn to the idea of someone measuring love. And this is for a silly, silly reason.

Once upon a time (5 years ago), I had this image in my head of a woman going into a scientist’s lab and having her remaining capacity for love measured. The end result of that was a rather crappy poem, but I’ve always had a fondness for the initial image and the idea that love was something that could be reduced to figures, to a percentage, to something tangible.

Which is why Rubin’s scales held my interest today- not because they are particularly revolutionary, not because they are mind-blowing… just because they made me remember that old idea and smile.

***

And now, to wrap this up:

FUN FACT

It seems that, while men love women, they don’t particularly like them. According to a Harvard study, while the two sexes love each other equally, women like men a hell of a lot more than men like women.

Really, can you blame them?