Ever since I saw the movie Interstellar, I have been curious about 4D geometry. Near the end of the movie, the dude finds himself trapped in a tesseract, which is a four-dimensional extension of a three-dimensional surface.

Thinking in four dimensions is very very tricky. We are three dimensional beings and our reality is bounded in three dimensions. Imagine a one-dimensional civilization that lives on a line and cannot see left or right or up or down. Only straight ahead and straight backwards. In other words, their reality is composed of points on that line. Now try explaining a square to these folks.

Similarly, a two-dimensional civilization that lives on a plane and cannot see up/down will be perfectly fine with squares, but will have a horrid time imagining a cube.

We humans, being more awesome than the 2D people, can see up/down. I am looking up right now, and...eeek...a spider...

Ahem...moving right along.

So we can see up and down. But that is where the awesomeness stops. Our perception is limited to three mutually perpendicular axes: X, Y, and Z. It is impossible to sketch a fourth axis that is mutually perpendicular to all three. Hint: don't even try.

To add to the confusion, some people will tell you that Time is the fourth dimension.

Four-dimensional objects have nothing at all to do with time. Here is how I try to visualize four-dimensional things. Like I said, this is very very tricky. I can barely get my mind around the idea.

Here is one way.

Take a square piece of paper. This is a two-dimesional object to you, for practical purposes. Now hold this piece of paper perfectly flat and parallel to the floor and near a wall. The shadow of this paper on the wall will be a line, if you are holding the paper perfectly flat. We can say that the projection of a two-dimensional object is a one-dimensional object. 'Cuz we fancy like dat.

Similarly, the projection of a three-dimensional object is a two-dimensional object. Like the shadow of a sphere on a floor, or the shadow of your head on a wall. See below.

Taking that further, a three-dimensional object is simply the shadow or projection of a four-dimensional object.

The implication of this line of thinking is profound. It means that every object around us is situated in four dimensions and what we are observing, touching, and interacting with are the three-dimensional shadows of these objects. That cellphone you are clutching is a shadow of the "real" cellphone in 4D space. Indeed we ourselves are shadows of our four-dimensional selves. If we ever encountered a more endowed civilization who can see in 4D, they would see us very, very, very differently from how we ourselves see us. And we would only see their shadows.

Also, why stop at four dimensions? There may be an infinite number of dimensions each projecting onto a lesser dimension. That four-dimensional cellphone that we cannot see in 4D space, but only touch the shadow of in 3D space, is itself a shadow of its five-dimensional self. Reality is a bloody hall of mirrors. Most of that hall...we are effectively blind to, except through mathematics and imagination. And even imagination fails us here. Or fails me at least. I can barely think about four dimensions. Thinking in five dimensions? Forget it.

This isn't pop science-fiction either. There is indeed real mathematics around this. Serious people have serious jobs working with this shit.

Bizarre, no?

Here is another way to visualize four dimensions that I find helpful.

Wait, come back.

Imagine a perfectly flat and square piece of paper. It has four edges. So four lines make up the four faces of a square; you can think of it like that. A cube has six square faces. Generalizing that, we may say that every N-dimensional object has a certain number of (N-1)-dimensional faces.

So it goes that a four-dimensional object has eight three-dimensional faces. Now imagine an object with eight cubic faces, and you have just imagined a four-dimensional object.

Unhelpful Note: In case you are inclined to think so, this is not as easy as imagining a cube with eight other cubes hanging off it like geometrically perfect tumors. That is not a four-dimensional object.

Laters.

You either die a hero or live long enough to see yourself become the villain.

So have I heard.

https://www.youtube.com/watch?v=23KHLW2dw_o

Places to put on the bucket list.

10 Amazing Places: https://www.youtube.com/watch?v=w7AFRg7-hrA

Walking on water. Not just for Jesus: https://www.youtube.com/watch?v=8WBqX7MSqWw

They say that you like someone because of who they are. And you love someone in spite of who they are.

Try this: Go ahead and pick the most important person in your life. And try to decide if you like that person or love that person. Or both.

You may be surprised at the answers you get.

I have a weight loss tip. Completely free. Ready?

Go to the moon.

Ha, ha.

Oh, you wanted a practical tip?

But really, so many people say they want to lose weight. I know, we are shallow. But there is a small physics lesson here. Technically speaking, what people really want to lose is mass. Mass and weight are different.

Your mass is the same everywhere you go. I am simplifying a bit and pissing off Einstein's ghost, but just roll with me here. Your mass is the same everywhere you go. And it is this mass that you pay your gym membership for.

What about your weight? It is decided by mother Earth. Yes, that planet you always trusted...

See, unlike your mass, your weight actually depends on where you are. Particularly, how big the planet you are standing on, is. Your weight is tied to your planet's size through a simple and elegant mathematical equation.

Whoda thunk it?

(Er...Newton, that's who.)

Every planet has a number that represents its gravity. Bigger the planet, larger the number. Earth's is 9.8.

9.8 what? Doesn't matter. You can think of it as 9.8 kilo-candles or 9.8 cow-patties. Nobody cares. Units are kinda arbitrary anyway. A "meter" exists because we say so. It is all convention. There is no such thing in reality. Don't believe me? Look up the definition of a "meter". Go ahead. I'll wait.

So the earth's number is 9.8.

The moon's number is 1.6, since it is so widdle.

And the sun's number is a whopping 274.

It is this number that you have to multiply your mass by to arrive at your weight. So once again, your mass is constant. For all practical purposes. But to find your weight, you have to multiply.

On the sun, Twiggy would weigh like a motherfucker. On the moon, you could be Elvis Presley sitting in a vat of peanut butter and not give a damn, as long as nobody handed you a mirror.

Since our muscles are uniquely adapted to earth's number, we can do some strange things when on the moon. Like jump about six or seven feet straight into the air. Our muscles are suddenly much stronger, having had to "fight" earth's number all our lives (every time we walk or so much as raise a finger, we are fighting earth's number). So we sneeze at the moon's number when visiting there.

If there were moon-people and if they ever got uppity with the earth people and started a war, they would be so weak compared to us, we could simply slap them to a bloody pulp.

So they better not start a war, wherever they are hiding.

Er...bye now.

---

Now for the boring bits. All this stuff above about mass and weight boils down to Newton's Second Law, one of the most important derivations in physics: Force = Mass x Acceleration (due to gravity)

Or, in short: F = ma

Your weight is a downward force acting on the planet. You arrive at it by multiplying your mass by the planet's gravity. The "downward" bit is important since force is a vector quantity, having the same direction as the acceleration due to gravity. Never, ever, mix up your scalars and vectors. Your physics will be all wrong and this will make the sun-people very very mad. And they are very very strong.

How fragile are we?

Very.

There is a very, very tiny corner of the Universe in which we humans can live in comfort. Or live at all, really.

So let's talk about the Universe a little bit. The Universe, my daughter, is a big place. Tremendous, stupefying, mind-numbing big. Just how big it is, is a topic for another time, but trust me that it is bigger than anything you've seen. It's bigger than that elephant we saw at the zoo, it's bigger than our house, it's bigger than Deeda's car, it's bigger than even Deeda. It was pretty close for a while, but then the Universe had a late growth spurt, and I didn't. [If we were to split hairs, that is actually quite true; at one point, the Universe wasn't just smaller than Deeda, it was smaller than even you...all compressed into an infinitely dense point that we, rather weakly I think, call a "singularity".]

But to get things rolling, here's a sense of scale. Look at the picture below.

That is a picture of Earth taken by the Voyager space probe from within our own solar system, just beyond the orbit of Pluto. There floating on a beam of sunlight, you see our home, the size of a pixel in that photograph. The radio signals that carried that photograph back to Earth traveled for five and a half hours at the speed of light to give us that perspective of our place in the cosmos.

One more picture.

See that blue glow around our planet? That is our atmosphere. That thin skin around our planet is what gives us life and protects us from deep space. And even within that layer, we cannot live comfortably everywhere. We need a very narrow range of temperature and pressure. Too much sunlight and radiation and we are...toast. We are like Goldilocks; things have to just right. Deserts and tall mountains won't cut it. Deep sea, nuh-uh. Too far to the right or left of California weather, and our numbers dwindle rapidly. You wouldn't think like that when cooling off by the A/C or soaking in the July sun, but when it comes to livable conditions, clemency is the exception. Hostility is the norm.

That is why I say we are so very fragile. And perhaps astronomically lucky to be here, walking around in that thin layer of breathable gases on a bit of space-dust that we call Earth. Surrounded literally everywhere by an incredibly inhospitable Universe. So remember that and try to be nice to everybody who shares this bit of luck with you.

So we are a bit of a wuss-out, for sure, when it comes to being a species. Who's tough? What animal on this planet do you think is better suited than us to tackle all this sucktitude the Universe is chucking at us?

Meet Mr. Tardigrade. Or more cutely known as the water bear. Believe me, this is the least scary picture I could find of him on the Internet.

That little guy--grows to about a millimeter--is tough. Super tough. If we were a tenth as tough as him, we would get our swag on and give the Universe the smackdown it so deserves. He is what is conversationally called an extremeophile ("loves extreme conditions"). Try using that in a conversation next time.

If you check out his eHarmony profile (or wikipedia entry), you would notice that he says:

1. Athletic build.
2. Agnostic.
3. Willing to live in almost absolute zero temperature to well above boiling point of water.
4. Can survive pressures six times higher than the deepest ocean trenches.
5. Can go for over 10 years without food or water (but loves a good mug of stout).
6. Can suck down hundreds time more radiation than would kill a human. (eat your heart out, Dr. Bruce Banner).
7. Smokes: Socially.

So there you have it. The original Quiet Man, the John Wayne of Nature. Beware his tiny fists.

And in the end on dreams we will depend

The Blue Angels is the US Navy's show-flying team. The video is incredible; what it takes to fly like that. The job has a 10% fatality rate. You have a better chance of surviving an average war.

I am teaching my five-year old to say "please" and "thank you". I don't want her being perceived as rude. The culture that surrounds her puts great stock in those words and we simply bend to the environment.

I grew up in a culture that did not say "please" or "thank you". There isn't a word for "please" in Bangla. The word for "thank you" is stiff and formal and I barely recall anyone using it in casual conversation. This doesn't mean that we were taught to be impolite or ungrateful. Politeness was expressed with tone and body language. Gratitude was implied and everybody understood this; nobody felt taken advantage of.

I remember hearing someone express this quite well, "When someone is very close to you, you consider that person to be a part of yourself. Do you thank yourself for doing something nice for yourself?"

This is also the case with the words "I love you." My parents had...have, the most wonderful and solid relationship I have ever seen. I have never heard my mother tell my father that she loved him because I guess she didn't have to. He knew.

Here's a little story. My mother was a ballsy woman who went against the wishes of her family to marry my father. This was not as easy it sounds, today. This was a different and unforgiving generation. She had to leave home, with no income, and trust that my father would do the right thing. Her family, including two brothers, were very traditional and put up every roadblock they could manage and she was but a wee young woman.

So one day, many many years later, my youngest sister was in a listening mood and asked my mother what that was like. "Tell me the gory details, Mom. What was it like? How did you manage it? Weren't you afraid?"

I will always remember my mother's reply. She said, "Yes, I was very afraid. But I loved your father more than I was scared of my father."

Ka-zing.

End of story.

Even very clever guys can be very wrong about things until hindsight catches up to them.

[Aside: This, by the way, is a great source of comfort to guys like me, who are not so clever. It allows us to go, "Nyah". Schadenfreude.]

Ptolemy was an ancient astronomer. And a geographer. And a mathematician. And a poet. He was smart. He was one of the smartest men of his time. Many who came later stood on his shoulders.

He also believed that the sun and the planets went around the earth.

Today we call this the geocentric theory and laugh at it. Those days, they simply called it the truth.

To those bearded astronomers of yore, Earth was the Kanye West of planets. Standing in the middle, refusing to give up the mike, while the others planets hovered.

But, like I said, hindsight catches up. The first glitch that had people scratching their heads is the retrograde motion of the planets that supposedly revolved around the earth.

What is retrograde motion? OK, so grab a friend. And ask her to start walking around you in a circle. Tell her it is for science. As long as she keeps walking, she will always appear (to you) to be going in the same direction.

The same thing should happen to, say, Jupiter, If Jupiter revolves around Earth, then Jupiter should always appear--to someone on earth--to move in one single direction. Like any well-behaved planet should. But strangely enough to the ancient astronomers, Jupiter sometimes seemed to back up suddenly and start moving in the opposite direction in the night sky. This is retrograde motion.

And they couldn't explain it. The theory didn't fit.

Did Jupiter, like, suddenly go, "Oh wait, I think I left the gas on." and start scooting backwards? Well, planets are pretty darn big and look like a determined lot who don't change their minds often. So there had to be another explanation.

So quick, grab your friend again. Explain to her that, yes, the medications are still working and this is still a science experiment, and then both you and her starting walking around the kitchen table in the same direction.

A few steps into the lap, look over at your friend. She will appear to be moving in the same direction as you, as agreed. Now let's say that you are slightly faster than your friend. Eventually, you will "lap" her. At the moment that you pass her, she will appear to be moving backwards. This is retrograde motion.

That kitchen table is, of course, the sun. And Earth and Jupiter both revolve around the sun. Earth goes around the sun quicker, because of the smaller orbit. Jupiter loses this "race" sometimes and gets lapped and appears to move backwards.

The heliocentric theory explained retrograde motion. The geocentric theory was ditched.

This is science. Clever men proposing clever ideas that other clever men overturn.

Fact: Ptolemy's geocentric theory was dominant for 1400 years. You read that right. One and a half centuries before it got a proper burial, when Nicolaus Copernicus proposed the heliocentric theory.

Tamaso ma Jyotir gamayo (From darkness, lead us to light)
Asad ma Sad gamayo (From ignorance, lead us to truth)

So let's say you have invented something wacky and wondrous. Obviously you have smarts. But what else do you need before the money and fame starts rolling in?

Not to discourage you, son (or daughter), but innovation is hard. I would say it requires: (a) patience, (b) unwavering self-belief, and, perhaps most importantly, (c) the willingness to tell everyone else that they are wrong. 

You may have heard in marketing circles that the customer is always right. If you've invented something truly disruptive, throw that sentiment out the window. Henry Ford said, "If I had asked my customers what they wanted, they would have said a faster horse."

Loads of talent She demonstrates what is possible with a single guitar and a sleek, sexy voice.

"You live until the last person who remembers you dies."

 

I came across that line a couple of days ago. I like that. It makes sense. That line makes people like Newton, Jenner, and Turing damn near immortal. If you have ever wondered what afterlife is, that sentence above sums it up neatly.

I plan to write something on this blog every week. Mostly, it will be some bit of knowledge I've picked up. I hope to make it interesting.

so you wanna dance

my daughter and I laying down the moves

There are lines that you carry with you from childhood to dotage. Matthew Arnold's Dover Beach fits that bill for me. There is beauty in that despair. And there is a ringing appeal to love, charity and humanity in that struggle. At least that is how I see it. Pretty much sums up the human condition.

Ah, love, let us be true

To one another! for the world, which seems

To lie before us like a land of dreams,

So various, so beautiful, so new,

Hath really neither joy, nor love, nor light,

Nor certitude, nor peace, nor help for pain;

And we are here as on a darkling plain

Swept with confused alarms of struggle and flight,

Where ignorant armies clash by night.

 

Every victory has a taste that's bittersweet

A three-chord symphony crashes into space
The moon is hanging upside down
I don't know why I'm still on the case
It's a ravenous town
And you still refuse to be traced
Seems to me such a waste
And every victory has a taste that's bittersweet
And it's your face I'm looking for, on every street.

On Every Street, Dire Straits

Wind by the Fireside - NWN

So as you shiver in the cold and the dark 
look into the fire and see in its spark - 
my eye 
watching over you. 

As you walk in the wind's whistling claws, 
listen past the howling of the wolf's 
jaws. 
my song 
comes to you. 

And when you're lost in the trackless snow, 
look up high where the eagles go. 
My star 
shines for you. 

In deep, dark mine or on crumbling peak 
hear the words of love I speak. 
My thoughts 
are with you. 

You are not forsaken. 
You are not forgotten. 
The North cannot swallow you. 
The snows cannot bury you. 
I will come for you. 
Faerun will grow warmer, 
and the gods will smile 
but oh, my love, guard yourself well - 
all this may not happen for a long, long 
while. 

They say that with time comes maturity.

Not very long ago, I used to get into these rousing Internet fights. I know, I know, I was a Macho Internet Guy. It would usually be someone attacking an idea I liked or someone attacking someone who liked an idea I liked and there I would go again--sound and fury would abound. And these would be long drawn out affairs, ending only when one party got tired of coming up with creative ideas to get intimate with the other party's mother.

Nowadays, when I see something that would have irked me no end in the past and started a prolonged flame war, I cluck to myself gently and move on.

They say that with time comes maturity.

Fuck that.

Just because you are older does not mean that the milk of human kindness is suddenly sloshing around inside of you; I am still the cunt I was.

Just because you are older does not mean that the number of other cunts that crawl the planet has dwindled in number. So what gives? Why this inner peace?

They say with time comes maturity. This is not true. That is not why you stop. You stop because with time comes the realization that you have less time.

Majestic.

Wonderful song. Turn the lights low, break out the icecream wine and wonder. Am I wrong?

Try to tell someone this once in your life before it's too late.

The link.

(Click on the link and play the video, jackass.)