Wednesday, 27 June 2012

Contempt with a Passion

George hated Picasso. He despised Picasso. He loathed him with a passion. I had never seen him so upset during any of our previous discussions. As overwhelmed as he appeared to be by the mere mention of Picasso's name, his life, his paintings and the new style he was said to have created, a style so liberally copied by many others who came later and some of whom are perceived to have then based cubism on, so overwhelmed was I by George's unusual, unexpected and intense emotional reaction. Whatever had Picasso done to him, I was wondering.

Pablo Picasso
Self-Portrait
When I thought we were objectively discussing one of the world's outstanding artists, he retorted that it wasn't possible to discuss anything objectively that itself wasn't objective to begin with, and generally art wasn't anyway, he insisted. He was adamant that Picasso's works were grossly overrated and that the man himself had been a self-satisfied pompous whippersnapper; yes, that was the word he used; whippersnapper.

So much so, George unyieldingly went on, that according to some Spanish ideal he was almost obsessed by his own eyes; eyes that may even be seen as coming out of his paintings, time and a gain, staring aggressively at the beholder; eyes with which the artist is supposed to have claimed he was capable of seducing any woman he wanted, although he'd always been terrified by the possibility of contracting a venereal disease. Syphilis was rife in the late nineteenth and the early twentieth centuries and couldn't be cured yet. But eventually that couldn't completely deter Picasso from entertaining various relationships.

George vehemently despised both the man and his paintings. The man, based on photos showing him as a young man during his days at Montmartre, Paris, because he considered him to overestimate himself to the point of insanity; and his paintings, mere rubbish to George, for the over-hyped oversimplification that only in the eyes of art critics could ever stand for something bigger just for the purpose of allowing those critics to justify their own professional existence.

Pablo Picasso
Self-Portrait
George denied the artist and his works any significance and attributed the fact that others tried to copy or emulate Picasso's style to no more than a simple and straight-forward commercial self-interest, not in the least any better than performers at the European Song Contest trying to copy the style of the previous year's winner, and be that by making use of violins or face masks, whichever seemed to have provided a brief edge. So, I wondered, wasn't it a compliment, rather, to Picasso that others tried to copy his style?

Picasso's works, lauded by some art critics as bringing man, humanity and nature in a supposedly genial way down to two-dimensional basics, for George were mere degrading simplifications of reality, or perceptions of it, primitive and crude ones at that, that could be produced in almost no time at all, and then left to the critics and self-proclaimed art lovers to be interpreted and over-interpreted, and interpreted to bits until they were made to stand out and convince museums and art fanatics with too much money on their hands and who would regularly gravitate to Christie's or Sotheby's and other auction houses.

Picasso, in fact, had never said much about his paintings. A fact that could be seen - or interpreted - as proving George's point - perhaps, but not incontestably so. Compared to real works of art, he maintained, that on top of being breathtaking and impressive (not referring to any particular style, but I knew that George had always admired the works of Salvador Dalí), Picasso's paintings were mere amateurish cartoons that could easily be improved by a host of professional cartoonists who could technically outperform Picasso with ease.

Weeping Woman
by Pablo Picasso
He ranted on and continued on his rampage, calling Picasso a maniac, an obsessive, compulsive scribbler, and the people impressed by his works a bunch of hysterical nincompoops. The inappropriate monetary value, way over the top, attributed to Picasso's paintings and achieved at auctions were to George signs of bubbles much like the first dot-com age or the investments in Dutch tulip bulbs in the 16th and 17th centuries that had driven many to financial ruins. (To recall to mind: By around 1600 the Netherlands were a vast centre of tulip cultivation.)

It was just a matter of time until this happened to buyers of Picasso's paintings, George claimed, and in a way he wasn't very wrong about investments of this kind in a more general sense, in particular when a painting turns out to be a fake or is claimed by a previous owner from whom it had once been stolen. Things like that have really happened but so far it hasn't to my knowledge occurred to a piece of art having lost substantially in monetary value, either gradually or in a sudden crash-like manner.

Therefore, George added, he wouldn't mind if all those investing in Picassos, for the sake of seeing them grow in value like precious metal or shares, ended up like investors in Dutch tulip bulbs that after the bubble had burst were left with nothing more than obscenely and impoverishingly expensive onions.

Though bored by stamp collections, George said that stamps might in the end be even more useful than Picasso's paintings. I was wondering if that also applied to stamps featuring Picassos on them, of which I'm sure there are some, and be that in Spain.

Pablo Picasso
Les Demoiselles d'Avignon
It is fascinating to note that George's reaction equalled if not surpassed in some respects the reactions of many contemporaries of Picasso's at the time when his painting "Les Demoiselles d'Avignon" was exhibited. Even some of Picasso's acquaintances had turned against him condemning this painting in particular as crude and vulgar.

I couldn't come to Picasso's rescue. Like George, I'd always admired Dalí, and both the man and his works are so strikingly different from Picasso and his works. In my admiration, I'm talking about Dalí's works of art, not about the artist personally.

I don't mean to say I was against Dalí's appearance in public in any way; I found him droll somehow, and at times I found him a little lost and at a disadvantage at an English-language talk show. Was he arrogant and pompous? Or did he disguise an ego problem? Did he even have an ego problem or was his ego simply big and boisterous to begin with? I'm not sure, and it doesn't matter much to me.

And would I want to defend Picasso at all? I could, instead, even deny having ever heard of the man the way he is said to have done with regard to African art that had influenced some of his works, including the Demoiselles, so distinctly, though his reaction was reported to have been "African art? What's that?"

One way or another, Picasso was certainly more than a simple two-dimensional scribbler. Looking at what he produced over many decades, one cannot help seeing him as a noteworthy multi-layered artist.

Friday, 15 June 2012

Moonset at Dawn

It was one of those amazing moments when the moon was nearing the horizon in the west, not too long before the sun was due to rise at the other end, that other horizon in the east, when I stood beside the window with two dumbbells in my hands just gazing at the moon.

(Microsoft Media)
Forgotten were the early-morning exercises I had planned to commit myself to, that early-morning workout meant to give me a good start into the day (the part brightened by sunshine, more or less, depending on circumstances). It was just too fascinating, and I was left somewhat spellbound seeing the moon over the neighbouring houses and trees; the sight was inescapably mesmerising.

I had to take a photo of it, I decided, immediately, before it could vanish behind those trees and houses, and before it could become too bright for it to have that enthralling effect. Off I dashed, only just thinking about putting the dumbbells carefully on the ground instead of simply dropping them, and into the direction of where I had last seen my mobile phone, which I hoped was equipped with a sufficiently detailed onboard camera.

Then I stood there again, at the window, with the moon appearing on the little display of my mobile and suddenly seeming so tiny that I was beginning to wonder what all the fuss was about. But I could still see it "in person" (and if it still has a personality then it would definitely have to be "he" and "him", that good old Moon, even today) through the window, just to make sure there was a good enough reason for the exhilaration. The mobile's screen couldn't bring out the dazzling scene and atmosphere.

I took a shot anyway. And when I looked at the result, the moon had become a glowing dot at the back of a tiny landscape. But maybe, once downloaded to the computer, I found myself hoping, it was going to turn out much better.

I touched the moon on the screen, pulled it into the centre and then tapped on it twice in order to make it double in size, at the expense of some of the scenery that got pushed aside and away over the edge of the screen, and what did I see? The moon was squeezed into a grid of strings making it look even sadder. I hadn't thought about the flyscreen.

I went to a fixed window, one that couldn't be opened and where a flyscreen wasn't needed, to take another shot. But the result still wasn't all too impressive, though I tried hard to imagine it on a computer screen later, where there was more space to look at the finer details; it might still leave a bit to be desired, though; it was surely going to be too blurred.

(Microsoft Media)
I thought about the digital camera and began trying to figure out where I had seen it last. I rummaged around in a cupboard or two. Things like that tend to happen when you rely on a smartphone for so many things that it can do reasonably well (apart from providing you with a wireless telephone connection) that you can easily end up forgetting about those special or specialised, unifunctional, monofuncitonal devices that can do one thing extremely well.

I eventually found it, pressed a button to get it to work, but nothing much happened. There were no batteries in it. I faintly remembered taking them out, a rather long time ago, so that nothing could happen to the camera in case the batteries became so old that they were likely to leak. But where on earth were they now, those batteries? At the same time, it was decidedly getting brighter outside and I imagined the impressive scenery at the back window becoming less and less remarkable, the moon disappearing behind the horizon.

Disappointment began to build when I spotted the batteries at the back of a drawer. Was it still worth the trouble? I grabbed them with some indecision, looking at them on my palm, wondering, thinking about the dumbbells; the batteries were in a see-through plastic bag. I'd almost thought of everything, yes, they could just as well leak at the back of the drawer, leaving a sticky mass that might be too hard and tough to ever completely come off again.

I hastily took them out of the bag while it was getting brighter outside. Then I began trying to open the battery compartment of the camera. It wouldn't work. I pushed a lever from left to right and then tried to push the lid open. It wouldn't open. I tried a couple of times. No improvement. It was getting brighter still outside.

A tired look, getting weary, at the lid revealed that I had to slide the lid open after pushing the lever. Slide, it said, slide, not pull. I tried. It worked. I put the batteries into the compartment. There were four tubelike sections in there and I assumed that the plus poles of the batteries had to be up where there was a little bump opposite on the lid, and the minus poles had to be covered by a flat surface.

It was too dark in the room, and why hadn't I turned on the light, for me to see the plus and minus signs in the compartment? Oh, yes, surely because of the moon. I was beginning to forget the purpose of all my busyness for all the trouble I was having just for the sake of taking a nice photo of the moon, a single nice photo; I certainly wasn't being immoderate in my expectations.

While the details of the entire situation were beginning to dawn on me, I was hoping it wasn't dawning all too much outside, because too much light inside or out would spoil the purpose of my bustle even further.

I closed the battery compartment and pressed the "on" button of the camera. Nothing was happening. My assumption had been wrong. At least I could open the compartment more quickly this time, while it was getting decidedly brighter outside.

I took the batteries out again tilting the camera upside-down. Naturally, since gravity is a natural thing, after all, three batteries fell down and ended up on the floor. Luckily I didn't drop the camera. I picked the batteries up again and put them in the compartment's sections the other way round, and this time it worked.

But the camera's objective didn't move. Why? I was convinced something was wrong because I hadn't used the camera for too long. Luckily, again, I spotted another little lever that could switch the camera's mode of operation from input to output.

The lever was currently set to output, which meant that stored images were shown on the little screen that doubled as a lid at the back of the camera. I hadn't opened that lid. I had been using the eyepiece, instead, and wasn't aware of the images on the little screen.

I needed the input mode for new photos, I thought. With the lever switched over and the lid swung open, the objective moved with a zoomy sound and telescoped out, and the moon appeared on the little screen.

It was now very close to a tree, that moon, well, virtually at least, and the background had become distinctly brighter than before, making the moon a little less discernible before the morning sky. Before the morning sky? Virtually.

(Microsoft Media)
Anyway, there was no time for stereoscopic thinking right then; I had to put that off until later. I took a few shots and then decided that this was enough and I could finally make breakfast ready, even without my usual early-morning exercises.

Later, in the afternoon, when I found some time to have a closer look at the photos, when I had finally downloaded them into my trusted computer, I found out I had taken them in the "small" setting which resulted in rather weak image quality, the picture files were barely 80 kilobytes in size; compare that to a megabyte, two or more of high-quality image files. Everything was small, and there was no point enlarging the photos since they would only have turned out coarse and gritty, without any worthy details.

It was a botched job. Whenever it was that I had used the camera last, for some reason I must have left it on "small" instead of "large" or "widescreen". I should have stuck with my morning exercises. They would have been far less frustrating.

Wednesday, 13 June 2012

Our Companion, the Moon

Since the moon always sets at dawn when it's a full moon, this one, that I was watching, definitely was a full moon on all accounts. The logic of full, half and new moons is actually pretty simple once you take some time to have a think about it; provided you have some time to spare for the moon. I have heard someone call moon-watching a mere Stone-Age pastime. There's some certainty, though, that watching the moon was more than a pastime for Stone-Age beholders with less than primary-school attendance.

(Microsoft Media)
Strange, though, to call it "a" full moon taken that it's always the same good old moon that it already was in the Stone Age and even earlier. And there's a lot that is earlier, a whole lot earlier, than just the Stone Age that might have been only yesterday in geological terms. I can already hear someone telling me that, oh no, yesterday were the dinosaurs. All right, I won't argue about these time scales. In particular since it was the same moon for the dinosaurs, too.

On top of that, if dawn means daybreak then naturally you'd assume that day breaks when it begins to become bright, and that is some time before the first bits of the sun show up on the horizon - opposite the full moon, provided it isn't overcast or cloudy.

Following Yahoo Dictionary, dawn is the "time each morning at which daylight first begins". So the moon really sets "at" dawn and not "before". The moon takes roughly four weeks - more or less which is probably why we keep having to adjust the length of our Earth year, the calendars (Roman, Julian, Gregorian) and try and avoid leap-year errors - around our home planet in the seeming opposite direction to the sun.

So, look at that. What do we have here? The full moon sets at dawn. The sun shows up at about that time and is opposite the moon. We don't need to be Sherlock Holmes to come to the conclusion that, in order to be full, the moon needs to be face to face with the sun from an Earth perspective to appear like a complete shiny disk in the sky. From other vantage points it may always be, or at different times.

After the sun has finally risen - and could, in theory, be gazed at for enjoyment or closer inspection, too, if it weren't so prohibitively glaring - the moon would have to be expected to not be visible any longer, because it would already have disappeared beyond and below the horizon if it still wanted to be called a full moon, though by that time seen from somewhere that it hasn't set yet.

You may be forgiven for saying that when it's a half-moon for us, an entire half, pardon the pun, of its surface would still be under the sun; it's just: we can't see that particular half completely from Earth. You'd be right; and it's exactly what is meant.

When we call it a half-moon, what we see is actually the seemingly two-dimensional half of one half of its three-dimensional surface. Yes, it really is a three-dimensional surface simply because the moon's is as little a flat plane as our Earth's was once thought to be with the sun hovering over it.

(Microsoft Media)
And if Mother Earth is in between and casts her shadow over the entire surface of the moon that's facing her, we've got a lunar eclipse. And if the beholder isn't even on the planet, which would call for the perspective to be somewhere between Earth and the sun, then it wouldn't just be the shadow preventing a closer inspection of the lunar surface - it would be Earth's full bulk.

In case you are wondering why the moon (or should it even be the Moon with a capital M) is a neuter "it" - in spite of all its influence on Mother Earth (as seen e.g. in the tide) and (more importantly for its, well, gender) its presence in ancient mythology, stories, fables, and tales - here's some lexicology:
   
In German, and therefore also in Old English, the moon is and was male (Mond and mona respectively are at least grammatically male), in French it is female (la lune), but this looks and sounds a little different orthographically, phonetically and anyway.

It would appear the story of the Man in the Moon isn't convincing enough any longer to justify the moon's maleness. The fact that the moon is less of a mythological entity these days - perhaps since mankind landed on it ("one small step for a man, one giant leap for mankind") - may account for it to be seen as nothing more than an Earth satellite, a piece of rock (even full of useful minerals and metals waiting to be mined), a planetoid at best.

In short: the moon's a thing much like an asteroid or the now degraded Pluto that's currently called a dwarf planet to spare it (!) the shame of being just a piece of rock, most likely having drifted off the asteroid belt at some stage.

(Microsoft Media)
In spite of its or his gender, of whether there is an elusive man on the moon who may keep escaping modern detection technology, or of whether the moon is just Earth's rocky satellite - or call it an attendant, a companion or even an accomplice, because that's the meaning of the Latin word "satelles" - spinning around Earth from west to east, the moon is always a bit further to the east from day to day (the 24-hour ones) when you look at it at the same time of day (the bright part) or night (the more or less dark part of the 24-hour day).

It might pay to have a separate word for either kind of day, like e.g. in the Scandinavian languages. We can, of course, tell them apart by saying "full day" and "daylight", or we might adopt yet another Greek word for it, tongue-twisting much like "ophthalmologist": nycthemeron, which simply means "night'n'day", "hemera" being the day part of this compound.

For all it's wandering around Earth (careful here, though, since the wandering could make it eligible for being a planet which is also Greek meaning "wanderer"), the moon cannot possibly stay full for too long. Seen from Earth, its position towards the sun changes as it moves around us. If you are confused now, let's recap:

The Earth spins west to east, too, like the moon which was most likely born out of Earth anyway, some time, long ago, due to an impact of sorts (with Mars perhaps, as one theory goes, very early on in the history of our solar system). This collision quarried out a huge terrestrial chunk that kept rotating like Mother Earth. The Moon is Earth's child, much like all the planets were born from what became our sun in due course.

Now, with both Earth spinning from west to east (taking, yes, it's true, 24 hours for one rotation) - which is why we see the sun seemingly rise on the eastern horizon while in fact we are every morning turning towards it - and the moon dashing over and past any given point on Earth in the same direction (taking, as we already know, about four weeks for one cycle, and meaning it is not geostationary like many of our artificial and highly technological satellites - and if that sounds Greek to you, then that's ok), the moon is less and less lit by the sun, seen from where we are, until it becomes a new moon turning its back on the sun while not necessarily standing in between us and the sun.

(Microsoft Media)
When it does block the sun completely or partially, it creates a full or partial solar eclipse, but that doesn't happen every month. And the moon, though being so tiny, can only achieve this feat of eclipsing the sun, that's so much bigger even than Earth, because it is so much closer to where we are. Coincidentally, the moon also rotates around itself, but that hasn't got any effect on eclipsing the sun or turning around Earth. And it does so in a way that makes the same spots on its surface always look at Earth.

And after being a new and invisible moon (invisible, that is, on most occasions other than during a solar eclipse when it's in front of the solar disk and should be treated with due caution in case you'd like to have a closer look at that eclipse), those parts of the surface of the moon facing us gradually become more and more lit on their way to the next full moon. Unless there's a solar eclipse on the moon with Earth standing in between.

This should pretty much sum up what we learnt, or should have learnt, at school. Though if our teacher had presented it in such a long-winded and at the same time concise way, there'd have been no surprise if we still hadn't been able to understand it after our school finals.

At the same time, and in fact all the time, our sun sits tight at the centre of our solar system - which is why it's called the solar system in the first place, nowadays that we know that Earth is neither flat nor at the centre of the universe - and it turns around itself, our sun does; just around itself, or herself, not around Earth, and yes, the sun shouldn't be "it" either.

In Old English, and therefore in German, it was, and is, female, sunne and Sonne respectively. And you might have guessed it, yes, in French it's male (le soleil). Talk about differences in outlook. At least when it comes to Mother Earth, she's a she in German (Erde), in Old English (eorðe), and even in French (la terre).

And if you miss the letters eth (ð) and thorn (þ) in today's English: they were done away with long ago by Norman-French monks who simply didn't like them. They simply chose "th" for either of them, whether voiced or not, much like the Romans had once transliterated Greek aspirated consonants, as opposed to non-aspirated ones, with two Latin letters, namely: kh, ph, rh and th; just think of rhapsody, philosophy, orthography and ophthalmology.

Let's quietly add, for the sake of completeness, that our sun - and all of us turning around it - is also spinning around the centre of our galaxy. So much for it or her being a fixed star.

Friday, 1 June 2012

Dimension or Auxiliary Factor?

Time has certainly been used extensively as a crucial factor for many a scientifically or practically oriented mathematical and statistical calculation, or for an approach to a solution or a deeper understanding of nature, from the infinitesimally small to the almost unimaginably big and far away.

In physics, depending on the section of the scientific community whose views one subscribes to or which one is a part of, it is either taken as fact or a well-established theory (at least one with a highly plausible outcome) that speed and gravity exert a certain influence on time.

The Persistence of Memory
by Salvador Dalí
There's that scene, well-known by now in one or the other staging form or variation, of a bunch of daring astronauts starting off on a journey to another star system, or even a distinct planet somewhat earlier discovered by means of a new array of radio telescopes (such as the Square Kilometre Array) or a powerful orbital telescope (such as the Hubble), which would see them arrive there - from the perspective of their fellow earthlings back on the home planet - after about twenty years.

Yet for them onboard their vessel - depending on how close to the speed of light they'd be able to dash to their destination in their flash new space craft propelled by one of those systems that are currently in their pre-infancy theoretical stages - only a year or two might have passed, though they would have experienced every second like a second, much like people back on Earth.

Objectively speaking, that is, and therefore measurably, these would be experiences inside people's respective environments - one might almost feel inclined to say "inside their respective universes" influenced by flexible factors that create stable and comparable circumstances inside their spheres of influence - which is the reason why we are dealing with different objectivities to begin with, and under the exclusion of emotions, moods and tempers that can subjectively influence the experience of the passage of time for, say, the astronauts.

(Microsoft Media)
Taken the growing distance between the spaceship and Earth, communication between the astronauts and their headquarters on Earth would either be adapted by their trusted computers, since, even at the speed of light, it could hardly be instantaneous - meaning: in real-time conditions. But what real time anyway, one might wonder. Whose time is the real one? They would both have to be, just differently so. There'd have to be a certain delay with which any given message would arrive.

Or there'd be the Mickey-Mouse effect for the astronauts when they have to digest an Earth minute in five to ten seconds as opposed to the drag effect for listeners back on Earth with words and voices drawling along in slow motion, stretching a minute's worth of onboard chitchat to about ten minutes. - Or is this imagery completely wrong to begin with? Could there be a natural adaptation en route? We haven't experienced it yet, if ever we will, so for now it's difficult to say.

But what if time is just the measurement of movement and no more? After all, we have precision atomic clocks now that take the time by the oscillations or energy-level jumps performed by electrons. We can even download "atomic clock sync utilities", or probably apps for mobile phones, to optimize how our computers and smart-phones receive updates from time-servers.

(Microsoft Media)
This makes a second equal to more than nine billion oscillations or spin cycles of the electron of, most likely, a caesium atom. More correctly, the microwave signal is being used for measurements, the signal namely that electrons in atoms emit when they change from one energy level to another - at a particular temperature, mind you, because not just molecules, further down and into the structures of their component parts, even electrons oscillate or spin or jump levels more or less rapidly depending on the surrounding temperature.

If that leaves you amazed, you're not alone. Much of our modern technology, including GPS, has come to depend on it. Simpler, and more traditional, chronometers are even calibrated according to atomic-clock output, taken that time measurements by atomic clocks can be expected to be absolutely reliable for thousands if not millions of years to come.

So what, therefore, if this analogy of electron movement compared with time elapsing is not an analogy at all, but instead all there is to time, or rather the perception of time? Meaning: there's no time at all but just movement and we use it much like a standardised scale of millimetres on a ruler to measure geographic distance, in those auxiliary units.

(Microsoft Media)
Certainly, if speed and gravity are intertwined and exert an effect on molecular movements - such as on electrons racing around the core of an atom (something much more divisible than its name of Greek origin would suggest) inside their cloud spaces - and all of this in turn has an effect on the general movement of things and people composed of and living inside spaces themselves composed of such slowed-down atoms forming molecules and bigger structures further up as we go from the microcosm into our world visible with our own naked eyes (i.e. without microscopes) and beyond (where we'd need telescopes), then there'd still be a difference between how we experience time, i.e. the movement of everything from subatomic particles upwards, inside the spaceship at the speed of light for one, and back on earth for another.

But time wouldn't be a dimension, then, or would it. And objectivity would seem to become astonishingly subjective by its nature.

This would ultimately mean, measuring change by means of what we call time in seconds, and nano-seconds for scientific purposes, that we are not tapping into a further dimension in its own right after all. Time would instead be no more than a ruler for measuring the distance on Earth between, say, two city centres or from the surface of any given point on Earth to the closest point on the surface of the moon.

The fourth dimension then wouldn't be time at all - not to mention further dimensions that come in so handy in some mathematical models and which would be another story altogether and not under scrutiny at this point... in time?

The fourth dimension may even be from where we could see three-dimensional quantum realities inside our 3D universe much like points on the surface of a sphere that we can observe and point at from any given position in our three-dimensional world.

(Microsoft Media)
For a being, human or otherwise, adapted to life in a four-dimensional world, we would be like the (theoretical) two-dimensional homunculus that Einstein had used to explain to us why we were having trouble imagining a three dimensional reality curved in the fourth dimension, much like a two-dimensional life form would be at pains on the surface of a sphere (a balloon in Einstein's example) to grasp the quantum leap up yet another dimension his flat world existed in... or on.

Would, at some stage, he (or she or it, who knows, we have some trouble, too, imagining 2D life forms, don't we) happen to see the shadow of the sphere on which he lived his two-dimensional life, the shadow would be just two-dimensional again anyway, but he'd have trouble understanding where the shadow came from. Is that when we spot something we cannot fully if at all understand but try to in the context of our three-dimensional world?

We might already have spotted something that exists in more dimensions than three but we were unable to make sense of it. Did we try to explain it as a UFO? Maybe, but we cannot be sure. Will we ever be able to probe into more dimensions than three other than by way of mathematical models? Do we really understand the implications of such models?

Or will we forever remain the two-dimensional homunculi trying to make sense of our world, curved in another dimension?