Seventh Grade Blues

the one

When I was in the seventh grade, one of the girls told me I looked like Keannu Reeves.

Was this some awfully cruel, sadistic joke little girls liked to play on unsuspecting boys?

When I was in the seventh grade, one of the girls told me I looked like Keannu Reeves. No, seriously.

I was hanging upside-down on the jungle gym, minding my own business, and she just walked over and blurted it out. Then she giggled like a moron and ran away. Girls can be so mean.

This became the highlight of my school year (my academic career, even), but you see, I was torn. On one hand, how could anyone confuse Keannu (black shades, gothic trench coat, infinite awesomeness) with me (pubescent, angst-ridden, gawky)? Was this all some awfully cruel, sadistic joke little girls liked to play on unsuspecting boys?

But on the other hand, maybe — maybe she was on to something. Maybe somewhere — somehow, behind all that bad acne and ruffled hair, I really did look like Neo. After all, who was I to disagree?

Today, however, I no longer have to wonder because, according to the latest advances in facial recognition, she was right.

Who in the Land is Fairest of All?

MyHeritage is an internet-based company that offers you the chance to see which celebrity you most resemble. Remember how in Snow White, the queen has a magical mirror which provides her with uninhibited flattery? This is the same, but like, tons better.

After a free signup, you upload a large-ish jpeg of your mug, then let the software crank away. Here were my results: Brad Pitt (71%), Keannu Reeves (63%), Luke Perry (63%), Matt Daemon (63%), and Jordana Brewster (60%).

Brad Pitt? Really? Matt Daemon? Really? Who wouldathunk? But y’know, as I gaze into the mirror…well…yes, I see it now. Definitely. We’re practically brothers!

How does it all work? Is this actual science or just deceptive flattery? To understand how facial recognition works, we’re going to have to delve into the mathematics behind the algorithm.

Recognizing Faces

Suppose we were given someone’s picture. How might we go about identifying that person from a large database of faces?

One way we can go about it is by identifying the characteristics of the subject – perhaps the person has small lips, or a pointed chin, or distinct eyes. From here, we then study the database, going from picture to picture, each time isolating the features of the faces and checking for a match.

But while this might work, it’s also a lot of work; algorithms would need to be defined to analyse each desired feature and a large number of faces to mix and match and could potentially take eons to compute.

A more efficient way to proceed would be to examine these faces as a statistical whole rather than as the sum of its parts. This is similar to the difference between identifying a city by its landmarks and identifying the same city by the density of its roads, the clusters and heights of its buildings, its downtown areas and rural areas, and so on.

A Picture is Worth a Thousand Digits

Snap! But what are pictures, really?

As stored in a computer, a picture is nothing more than a great big grid of dots (or pixels). If the picture is greyscale, each pixel is associated with a number from 0 to 255 representing its brightness, from pitch black (0) to pure white (255).

Now in the abstract theory of Linear Algebra, these grids of pixels are called ‘vectors’. You’ve probably encountered vectors before in Physics class and in fact, these ‘face vectors’ are quite similar.

Like vectors representing force or motion, these new ‘face vectors’ have a `magnitude’ (an overall brightness), as well as a ‘direction’ — the only difference is that they inhabit some higher-dimensional Face Space, rather than the two or three-dimensional physical world we live in.

Thus, faces found in the database are nothing more than vectors that, like other mathematical quantities, can be added, subtracted, multiplied, and generally manipulated as they roam about in the Face Space.

What’s Your Eigenface?

However, Face Spaces are complicated affairs — they’re high dimensional boxes stuffed with a large number of faces, each face containing thousands of pixels.

It would thus be foolish to try and compare each face pixel by pixel; instead we look to construct a small group of pictures representing the general facial patterns of the database. This small but crucial group is called the Eigenface Basis.

Think of how, when we analyse the motion of a ball flying through the air, we break the motion into its horizontal and vertical components. These horizontal and vertical components provide a fundamental basis for which all motion can be broken down into.

Similarly, once the eigenface basis is found using Linear Algebra, each face in the database can then be expressed using certain percentages of each eigenface. For example, we may say that a picture is composed of 10% of the first eigenface, 25% of the second, 4% of the third, and so on.

The beauty of this treatment is that even in a large database, each unique face can be expressed very simply using its eigenface decomposition. We no longer have to express each face using thousands of pixels; now, like a simple recipe in which the eigenfaces are the key ingredients, the entire database can be reconstructed as it was before.

A Problem of Distance

Now imagine each face in the database, represented in terms of its eigenface percentages, akin to coordinates lying in some higher-dimensional plane. Our test subject (which may or may not lie in the database) is then projected onto this plane by expressing it in terms of the eigenface components.

But now, the problem of recognising the subject becomes as simple as finding the shortest distance (or closest match) between our subject and each face in the database, a problem which is aided enormously by the fact each face is represented by only a handful of eigenface components.

The Future and You

But really, just how accurate are these eigenface algorithms?

In optimal conditions (with good lighting, a representative database, front-facing pictures, etc.), a simple eigenface routine might produce accurate readings of up to 90%.

Unfortunately, real life is never that simple, and in reality, one must contend with other ‘noisy’ factors. Factors like variance in pose (person facing at an angle), obstructions (sunglasses or other people), resolution and lighting, and so on. Despite this, however, the science of facial recognition has steadily improved to the point where today, it is becoming a standard for many military, security, and commercial applications.

Yeah, yeah. But now that you know how facial recognition works, go and try it on yourself.

What celebrity do you look like?

A Review

exponential asymptotics

Exponential Asymptotics then, is the bridge between God’s picture-perfect, but wholly unrealizable representations, and the Devil’s ambiguous, but entirely necessary evils.

Last time, we left off talking about asymptotic approximations. Nature — we explained — is often too complicated to describe exactly, and so we turn to these approximate methods for help. Unfortunately, such approximations are divergent and mathematically badly-behaved, even though they provide excellent results.

Now, we will see that there are indeed consequences to using these devilish and divergent approximations.

Dancing with the Devil

Maybe the best thing we can do is look at a concrete example.

For this, we’re going to imagine the flow of water with speed U over a step which is relatively well submerged. To solve this problem, we propose the following asymptotic expansion for the surface of the water:

In this case, the perturbation parameter, ε corresponds to a measure of the inertial and gravitational forces. The idealized state, or first approximation corresponds to the case that ε = 0, or the case for which the force of gravity is infinite.

What that means is that our first order asymptotic approximation tells us the free surface should look like this:

That’s right. Completely flat.

Sure, this does make some sense: Imagine the step as being infinitely deep. Then in this ideal case, free surface wouldn’t feel the bump at all. Hence it would lie completely flat.

Unfortunately, this isn’t quite what happens.

If we use a computer and calculate the solution, it gives us something like this:

Somewhere on that free surface, something is happening.

The asymptotic approximation we calculated does a wonderful job initially, but then out of nowhere, a light flickers on and Pop!.

Waves appear where there were none.

Into the Mist

Maybe the first person who documented the first “WTF?!” moment upon encountering this strange phenomenon was none other than George Gabriel Stokes, one of the greats of British applied maths. He described the phenomenon as a new term, entering into view from behind a mist:

How do we clear the mist?

The argument goes like this: First, we have an approximation that works on the far left. Now, somewhere, along the surface, a switch is turned on, and an exponential (or a sinusoidal, if you will) is turned on.

Thus, there must be something that’s going on the complexified free surface.

Whoa there, Missy! What the heck does that mean?

By complexified free surface, we’re referring to extending the water surface (a real number) to the complex (or `imaginary’) numbers. In other words, if x measures the distance along the water surface (say, 1 meter, 2 meters, etc.), then we allow x to be an imaginary number (say, 1 + i or 2 - 2i)

Physically (and philosophically), it’s pretty nonsensical. We picture it like this:

So we’ve extended the surface by adding an extra dimension.

This, while baffling to outsiders, is a well known trick by mathematicians. Maybe there’s an easier way to explain it.

The Imaginary Route to School

Let’s suppose that Billy walks from his house (x = -10) to school (x = 10) every day.

Monday, however, he wakes up and hears on the radio that due to faulty engineering and a freak division-by-zero accident, the bridge (x = 0) on the way to school has collapsed. What can Billy (determined and diligent student that he is) do?

The answer is that Billy needs to find another way to school. He needs to complexify his usual route, enter into another dimension, and find a new path.

Billy’s adventure is the essence behind the mathematician’s method: Often, we will have some sort of singularity between two points. To deal with it, we seek a new path. It turns out that useful paths can be taken in the ‘imaginary’ plane. So while this is definitely unphysical and unintuitive, take a lesson from Billy.

If he can warp his mind to change his usual route, so can you.

Singularities and Stokes Lines

Let’s return to our complexified water surface.

Well, it turns out that on this extended surface, there are singularities: points where our asymptotic approximation (remember that?) goes terribly awry. This is the reason why the asymptotic expansions diverge — because of these singularities.

With a lot of work and advanced maths, it can be proven that there exists lines (called Stokes Lines) emanating from these singularities, across which a small exponential term is switched on.

Like into the mist, remember?

And so following the above picture, you can see that the asymptotic approximation (the flat surface) works well at the start. But then it hits the edge of the Stokes Line, and at that point a teensy exponential is turned on.

So actually, we should have,

Exponential Asymptotics is the name we give to the branch of mathematics which studies these small exponentials which seem to fly under the radar of ordinary methods. It’s these hidden exponentials which emerge from the divergent tails of asymptotic expansions.

From Heaven to Hell

It’s time to wrap up.

In each previous part, I ended by asking a crucial question. They were:

Part I: Sometimes, as mere mortals with a capacity for only understanding the finite, we’re forced to cut corners and make approximations. Most of the time, it won’t matter. When will it matter?

Part II: In order to describe nature’s oceans and lakes, mathematicians have had to use divergent (badly-behaved) series approximations. Although these give superb results, we are nonetheless representing perfect phenomenons using a far-from perfect representations. “Inventions of the devil”, said Niels Abel. But this is a practical necessity. How else are we to describe God’s infinity with our finite minds? The real question is, what’s being lost in translation?

In this part, we showed that while divergence is bad, there’s no need to disregard it. By using certain mathematical tools, we can unravel the divergence, and reveal what details were lost using the approximations.

Exponential Asymptotics then, is the bridge between God’s picture-perfect, but wholly unrealizable representations, and the Devil’s ambiguous, but entirely necessary evils.

This bridge is where I stand and this bridge is what I study.

A Review

abel’s hell

“Divergent series are the invention of the devil and it is shameful to base on them any demonstration whatsoever.”

niels abel

Last time, we left off talking about Pi.

We talked about how one can imagine Mother Nature using Pi to all its infinite glory, but for mere mortals like you and I, we have to truncate the number — to its tenth decimal place, hundredth decimal place, or even millionth decimal place.

But however we do it, we still miss infinitely many digits (infinity minus a finite number is still infinity, don’t-cha-know).

This is simply an example of our inability to describe the Universe to its fullest.

For the most part, that’s perfectly fine. But in what circumstance does our inability to capture the true nature of a phenomenon become a problem?

A Hopeless Challenge

Let’s talk oceans.

There are few things more majestic than a ship in water. Captain Ahab knew it. Jack and Rose knew it (well, at least until the end). So should you.

Just imagine it. The sparkling blue waters. The expanse of never-ending ocean. The beautiful wedge-shaped pattern that flows behind every ship, like a streaming cape.

And near the ship: turbulent white-water splashes, jets, and ripples, forming in a million different places with a million different patterns, often too quick and too elaborate for the eye to capture.

The mathematical equations which govern the flow of water in an ocean were known as early back as the 18th century. But for the next century and a bit, scientists were absolutely confounded by the equations.

“What in the world,” they asked together, “Can we do with that?”

The equations, as they stand, are much too complex for a direct analysis. Even today, there is a million dollar prize for anyone who can answer even the most basic questions about these equations.

So with no possibility of exact solutions in sight, the mathematicians and physicists turned to developing methods for approximating solutions.

Asymptotic Approximations

One method, in particular, traces its roots back to the time of Henri Poincare (1854-1912) who developed it in order to solve a rather terrifying problem in celestial mechanics.

The idea is to break up our solution into more manageable chunks. The first chunk describes the system — the ocean, in this case — in some idealized state. To this, we add the second chunk, which includes some kind of perturbation to this initial state. To this, we add a third and even smaller perturbation. And on to infinity.

For example, suppose we were to express the height of the water waves in this fashion,

Here, the greek epsilon, ε represents a small perturbation. It can represent, for example, the Froude number, or the surface tension, or some other small effect.

These sums or series are called asymptotic approximations because they get better and better in the asymptotic limit that ε tends to zero. That’s the idealized state.

The amazing thing with these approximations is that they tend to be very good. So good, in fact, that calculating only one or two chunks provides an excellent approximation to reality in most cases.

This was great. People were happy. We’d at least established some kind of systematic way of approaching these intractable formulae and, with a moderate amount of sweat and tears, they seemed to give excellent results.

The Physicists were happy.

So were the Applied Mathematicians.

The Pure Maths chaps, on the other hand, were incensed.

The Puries and their Partypooper Tendencies

The problem, the Puries were quick to point out, is that these asymptotic approximations are usually divergent.

What that means is that the approximations get better and better as we include more and more terms…but only up to a point. After that point, all hell breaks loose, and the whole thing blows up (to infinity).

Thus in effect, we have taken a system of water waves, perfectly well behaved and all very pretty, and approximated it using an infinite series of terms which, when added up, gives us completely nonsense.

The Pure Mathematicians, in all their need for rules and regulations, just weren’t comfortable toying with a concept that was so ill-defined.

But everybody else was all, “Fuggetaboutit. Take a look at all these purty graphs, yo.”

Should We Worry?

By now you’ve hopefully grappled with issue.

Nature in all its magnificence is woefully complicated.

In many cases, it’s so horrendously complicated that its mathematical description needs to be approximated. One such method of approximation involves using a divergent series.

Why do we use them? We use them because they work so nicely.

So the question becomes, in using these divergent approximations, are we ignoring anything useful? In particular, what is the nature of this divergence? Why does our approximation work so well initially, but behave so badly later on?

What’s the price we pay for dancing with the devil?

Let’s face it. Some things in life are certainties. This is one of them:

Or so I thought.

“I don’t wanna die.”

See, when your plane is plummeting towards the Atlantic and dozens of oxygen masks are simultaneously popped from their compartments, that’s precisely what you’re supposed to be thinking.

That’s what most sane passengers on board Flight 888 were thinking, anyways, but not me; personally, I was content to stare at the gorgeous woman sitting by my side and wonder — amidst all the screaming — whether, she’d be the type to favour wit and humour over a Calvin-Klein physique.

Mind you, this was just the setup (it turned out to be a false alarm, anyways — “Due to horrendous weather conditions,” said the pilot), but I still wanted to give you an idea of the truly epic life-or-death scope of the story to come.

The real story, however, begins with her.

Even in the limited illumination of the cabin, her hair shone a rich, copper red. This framed not only a perfect curving face, but also two of the bluest eyes I’d ever seen. But this wasn’t all. The earlier theatrics had scared her and despite clear skies and smooth sailing, I could tell she was still on edge. But this was perfect, you see, because it gave me a chance to swoop in and sooth her poor, tortured soul (that’s how it’s supposed to work, anyways).

“Just a little turbulence,” I offered helpfully, “Nothing to be scared of — uh…” I trailed off, motioning expectantly towards her.

“Rhea.”

“Right. Rhea. It’s Jeff, by the way. There’s nothing to be scared of, Rhea,” I assured her again.

She was silent for a moment; then leaning over me, pointed a slender finger out the window. “Nothing?” she said, raising an eyebrow, “Yeah, nothing is what’s stopping us from plummeting, oh I dunno, twenty-thousand feet to the ground in a blazing tomb of shattering metal and death, right? …Jeff?”

So it was going to be harder than I thought.

Ten minutes had passed since my disastrous attempt to heroically intervene, and by now, she was already nervously fingering her way through a Cosmo magazine.

I needed to do something — something drastic — or I was going lose her to another one of those ghastly how-does-your-love-life-stack-up quizzes.

“You’re wrong,” I blurted out, loudly.

She turned and looked at me, bemused.

“About what?”

“What you said earlier. About how nothing is holding us up.”

I ran my fingers through my hair and backtracked. “Look, flying wasn’t invented overnight, right? Da Vinci, Cayley, Lanchester, Joukowski, …” I rattled off a few more impressive-sounding names, “Thousands of the greatest minds conspiring over hundreds of years with the sole purpose of reaching one of man’s greatest dreams…”

“So?”

“So…today — today, aerodynamics, all this –,” I gestured out the window, “All this — is grounded in solid, rigorous mathematics. It’s not nothingness that’s holding us up. It’s math.”

“Math,” she repeated disinterestedly, “I’m not very good at math.”

“You don’t have to be,” I replied softly.

She picked up the Cosmo magazine from her lap and froze for what seemed like ages. Then, seeming to have made a decision, she placed it in the pouch before her and leaned back in her seat, sighing.

“Okay,” she said, nodding, “Let’s talk.”

By now, we’d both finished our creations: three crisp paper airplanes assembled with the enthused precision only a 10-year-old could muster.

She threw hers and laughed as it flopped straight to the ground. Mine careened suicidally into a bulkhead and the stewardess, having witnessed all our shenanigans, scowled in our direction.

As I held up the last plane, I explained. “There are four aerodynamic forces we need to talk about: thrust, drag, lift, and gravity.” I said, gesturing in each of the four directions.

“As air flows over the plane, pressure is exerted on the surface of the plane. If there’s more pressure on the bottom than the top, lift is produced, and the plane stays aloft so long as the force is greater than gravity.”

“But this,” she said, waving at our surroundings, “is not made of paper.”

“Ah ha! Obtaining lift is easy — heck, even a barn door raised at an angle produces lift. The second problem is drag, and so flight is actually the problem of maximizing lift, while minimizing drag.”

“But how?” I asked excitedly, “What kind of aerofoil design do we need, Rhea?”

“Beats me,” she said, amused by my enthusiasm, “But I bet you’ll tell me all about it over dinner.”

It was like a date, really.

But with only two meal choices and really crappy wine.

“So…” Rhea said, prodding her chicken suspiciously, “When the Wright Brothers managed the first ever flight in nineteen-hundred-whatever, they didn’t actually know how the math worked?”

With a fork, I poked my own in-flight meal timidly. Half-expecting the chicken to wake up and start clucking hysterically, I wisely opted for the fruit cup instead.

“The Wright Brothers were at the forefront of experimental aerodynamics,” I corrected, “Using their own wind tunnel tests, they produced different aerofoils until they found one that worked. Most importantly, it had to be curved (or cambered) so air flows faster over the top; this reduces the pressure on the top and so produces more lift.”

“But surprisingly, there were almost no meaningful aerodynamic theories at the time. We had the right equations — but nobody knew what to do with them.”

“But this changed?”

I pushed my meal back with a grimace. “Oh, sure. Theoretical aerodynamics was rampant only a handful of years later. But, uh…I dunno,” I said, teasing her, “You sure you’re ready for this stuff?”

I leaned back and pretended to peer at her dubiously.

“I mean, it’s pretty wild.”

She just rolled her eyes and went back to eating.

The crew had turned off the lights and so most passengers were dozing quietly. Not us, though. We insisted on whispering softly, and with the lone reading light providing the only illumination, it had the eerie effect of making it seem like we were the only two passengers on board Flight 888.

“The three governing equations of fluid motion are known as the Navier Stokes Equations,” I explained while scribbling on napkins, “And together, they simply express three fundamental laws of nature in a mathematical form.”

“This one here,” I said pointing to the first equation, “Says that the total amount of fluid — or, in our case, air particles – has to remain constant. This is just conservation of mass. Stuff can’t disappear.”

“The second one here is Newton’s Second Law: Mass times acceleration, is equal to the total applied force. That’s just conservation of momentum.”

“And the last one here is conservation of energy — the total energy in the system must remain constant.”

She looked disdainfully at the row of napkins strewn before her and pointed a single, perfectly manicured finger at one of them. “What can we do with that?” she asked.

“It’s tough,” I conceded, “These equations are too hard to solve directly. And even for the two-dimensional problem (flow around a cross section of the aerofoil), it’s still too complicated because of the geometry.”

“So what we do is we consider a simpler geometry, say, the airflow around a flat plate; we solve the governing equations for this problem, then we construct a mathematical map that brings us back to the original, more difficult geometry.”

“It’s tough, I know. But the point is, the math is all there. It’s not a mystery anymore, like it was for da Vinci and the Wright Brothers.

And that — believe it or not — was the last time we’d talk about math.

She was relaxed now, and her head was gently propped against a pillow resting on my shoulder. But whether or not this Zen-like state of relaxation was because of newfound understanding (as opposed to sheer mental boredom)…well, I’ll let you decide.

In any case, it worked, and hell, she hadn’t touched that damn Cosmo since we both started talking.

“Are you asleep?” I asked.

She took her time answering. “Not yet”.

“Sooooo…”, I said, stretching out the vowel and grinning sheepishly, “Tell me, what do you do?”

At that suggestion, she whipped her head off the pillow and gave me such a look of pure, seething outrage that…well, I tell ya’, it would have immediately sent lesser mortals fleeing.

“Oooooh, I get it,” she squealed, “Good looking stranger corners you on an airplane for a three hour balls-to-wall math lecture, and then asks what you do. Typical,” she sniffed.

“Wha–?”, I said, feigning mock hurt, “But I got you dinner and everything.”

She gave me a mischievous grin, punched her pillow, and put her head back.

“Admit it Jeff,” she said, “You’ve been using me.”

I pushed the button on my armrest turning off the overhead lights and plunging the two of us into blissful darkness.

“Babe,” I said, “You’ve no idea.”

I am told that beautiful women are everywhere.

No. Really.

They’re literally everywhere. They’re in every nook and every cranny, every street and every corner. They have big blue eyes and small brown ones, long blonde hair and short raven hair. Legs that reach the skies. Soft, velvety skin. And they love to tease us with their skirty skirts.

You — you could very well be one of these beautiful women.

You probably are. Don’t lie.

But it doesn’t matter. It doesn’t matter because I can’t see them. I know it sounds crazy, but it’s true. I can’t see any of them.

It started a few years ago. That’s when the numbness started. But it’s worse, now. It’s so bad, I can’t feel anything.

Imagine this: I’m walking down the street with a friend, and a girls passes in the distance. So my friend’s all, “She’s pretty cute”, right?

“Hrmm…” I’d mumble, looking up for a second. “Yeah, she’s alright…”

That’s it. “She’s alright”. Not, “she’s spectacular,” or “she’s gorgeous”, and never ever is she “wow”. I can’t remember how long it’s been since I’ve had a ‘Wow’ moment. They just stopped happening.

These women — these women I pass on the streets or see at the University — they could be Venus and it wouldn’t matter. They could be Jennifer Connelly or Jessica Alba in the flesh. Even Audrey Hepburn, back from the dead. I wouldn’t have even raised an eyebrow.

Because I’m numb, you see.

The thing is, I do see them; I see that they’re pretty, I see that they’re slim and have a nice figure, and I see that they have great hair. But I don’t really see them, you know? It’s more like I’m a judge, rather than a spectator.

I’m impartial. Neutral and unaffected.

But this numbness, it doesn’t take the Crane brothers to figure out what brings it on. I actually know the cause.

My days are roughly the same, day in day out. I wake up in the morning and haul my ass to work. If I decide beforehand to bring a lunch and dinner to work, I’ll stay there until eight or nine in the evening. If I don’t bring a dinner, I’ll head home at six to cook myself one or, if I’m feeling particularly adventurous, I’ll head to dining hall for dinner. At ten, it’s gym-time, and by 11:30 PM, I’m back home.

Occasionally, I’ll play rugby with the college in the evenings, and that helps break up the monotony. But for the most part, it’s an easy cut-and-paste affair.

Do I mind that my life is structured like this? Maybe. But it’s what I do. That’s the best answer I can give to friends and family who criticize me about my lifestyle. It’s what I do. At least for now.

Besides, that’s not the real problem.

At night, I prepare for my slumber with an episode from a favoured television series or an interesting piece of cinema.

The choices are endless. And the women, well, the women are simply delightful.

Maybe I’ll watch an episode of House and wonder whether all doctors come with the looks of Allison Cameron (Jennifer Morrison) or the wit of “Thirteen” (Olivia Wilde). Reliving high school is as easy as popping in The O.C., where I can follow Melissa, Summer, and Taylor (Barton, Bilson, and Reeser) through their four years. And if I’m in the mood for sand and beaches, I can always spend some time with Kate (Evangeline Lilly) and Claire (Emilie de Ravin) on Lost island.

And then there are the movies.

I can spend time listening to the poetic ramblings of Juno (Ellen Page). I can fight despair and temptation alongside Jennifer Connelly in Requiem for a Dream. I can laugh at the deadpan humour of Zooey Deschanel in Almost Famous.

The list goes on.

The beauty of it is, not only are these women beautiful and gorgeous, but they’re funny, smart, and sassy. They wake up looking great, and they say and do things no real woman would.

Because, duh, they’re exactly that: not real.

But it doesn’t matter.

Because these women, they get me.

When the gorgeous Charlotte (Scarlett Johansson) in Lost in Translation lies next to Bob (Bill Murray) and asks, “Does it get any easier?” — that’s the kind of connection I want. That’s the kind of relationship I need. But of course, I can’t have it.

There isn’t really a 24 year old, lost and confused, beautiful Yalie philosophy graduate named Charlotte. And even if there was, it’s doubtful I’ll ever meet her on a trip to Tokyo.

But that doesn’t stop me from hoping.

Real women are hard. Even if they have the looks of Number Six (Tricia Helfer), the intellect of Temperance Brennan (Emily Deschanel), and the sardonic wit of Lorelei Gilmore (Lauren Graham), they won’t know you. They won’t really know you.

It’s just not the same.

And so I go to work, I come home, and I escape in the company of these lovely — albeit fictitious — women. It’s escapism at its best.

I realize it’s sad. It’s humiliating. Wrong, even.

But there’s nothing I can do.

I’m numb, you see.