In using something like a simple map, what becomes simple is that I only have a limited surface area to cover. So, if the spiral I use to traverse over the map has a very very tiny pitch, I can approximately pinpoint each point on the map. But that’s still not perfect.

So, to do the same, we can change two things: the nature of the surface on which the map is plotted; and the description of the line. I did the latter in the previous, figurative attempt, by making my “single dimension” along a (well defined spiral). I currently, cannot imagine how to do the former.

I thought of numerous possibilities for changing the nature of the single line I’m using. The best so far, seems to make it some sort of a fractal. That is applicably, second to creating a much more brilliant definition of a spiral, but also much far-sounding. But theoretically, it wouldn’t be as simple as a spiral.

The inspiration to choose them to be a fractal, comes from the fact that most space-filling curves, are fractals (apart from the fact that I love them, of course). And space filling curves do exactly what I want this construct of mine to do — cover all the points in 2 dimensions, using a single continuous 1-D curve.

All I want, is an equation which for a certain iteration, given one parameter, can give me back a unique value, and this equation for different parameters can cover all the points belonging to the above. That’s it. Easy, innit?

More for later..

Update: This question brings up a rather old doubt of mine — can I call an equal pitched spiral, a fractal? Or does it have too “simple a definition”?

Note: This post is a summary of all that I’ve read, and found to be related to this specific idea of mine — I don’t really know what I can do that would be counted as entirely ingenuous.

How the images above were made:

• • plots for the logarithmic spiral plotted, were obtained from Wolfram|Alpha, with a=0.5, and b=0.02 randomly put into the r=a*e^(b*theta)formula for a logarithmic spiral, so that the arms were relatively tight.
  • the “zoomed-in” Gnomonic projection of the globe, if from Wikipedia’s article on the same.
  • the “zoomed-out” one, below, is from this random … thinige’s site, taken and used without permission (though, with apparent, attribution).

I got the “inspiration”, from Escher’s Spiral Globe, the image of which, I first saw in The Infinite Book.

On a bit of looking around, I found out that that thing is called a Loxodrome, and it a logarithmic spiral projected onto a sphere. The cool thing, and why I want to use this map system, is that on a specific plot, I can use just one angle to specify where I am, as the distance from the centre, is only a function of the angle. It obviously reduces the fidelity two pieces of information provide, as in the case of a longitude and latitude angle, but I can add the piece of information about which longitude I am using as my X-axis, and then cover all locations.

What’s the benefit? By my cursory reading about this, the Rhumb line is similar to something called a Great Circle Route, (though this might be severely wrong, and just some sort of name confusion, because the wiki article about the Rhumb Line specifically talks about the severe difference between this Rhumb Line, and the Great Circle Route) which is the straightest point between two points, used by aircraft routes, and looks like a latitude  curve joining the two points. I don’t know how, yet, but somehow I could specify the translation of the origin, such that the source and destination lie on the same arm of the spiral, and again two angles would be adequate to specify along which course the plane should be navigating.

Understanding an azimuthal projection:

Rhumb Line Coolness:

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Or at least, so I believe. When Lockhart said,

In fact,  if  I  had  to  design  a mechanism  for  the  express purpose  of  destroying  a  child’s  natural curiosity and  love of  pattern-making, I couldn’t possibly do as good a  job as  is  currently being done.

I didn’t quite agree with him as the current system being that bad. After all, we had lost the thingie of using canes, and as the CBSE would like to believe as well, I thought we’ve come at least some way from where we’d started. When I heard my fellow classmates laughing at that joke (unfortunately, not at me), I realized we’ve come absolutely no way. For all the prefaces filled with curiosity and scientific nature, and the unanswered questions in the book, it is rare to find somebody who realizes that we need to learn to ask questions, rather than know answers. Every step  in the education system goes ahead to fill in this prejudice — it is wrong to not know answers, and absurd to ask questions without answers.

It is out duty to believe everything we are told is the gospel truth, juxtaposed with the fact that we don’t really care about it at all. Teachers bullshit us about how being educated is different from being literate. And the English teacher no less — somebody who chose to study language for maybe the reason that she had no idea what knowledge really was. We aren’t ever even hinted that there is something called being knowledgeable, which uncomparably superior to being educated. Being educated simply involves being a drone. Being knowledgeable, gives us some right to be human.

Similarly, there’s a joke which goes on the lines of, if the teacher asks you a question, you ask her the reason for asking — “Don’t you know the answer yourself?”

It remains as a joke, because any question discussed in any place like the school, is bound to have an answer, isn’t it? What would be the point of discussing some bizarre unsolved problem at all?

That’s why I hate exams. I feel sick that I actually used to practice all the questions from all possible reference books for Math way back in 9th. I actually believed it’ll be better if I knew the answers beforehand. Even I, effectively, treated Math like a subject worth rote memory (though not as terribly. Other wise I would’ve failed in it as badly as I did in Social Studies).

I hope I get freedom from this wonderful system of creating obedient robots called education, soon. Very soon.

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Trivially, we all begin by thinking how to circumvent the hardness of the concrete, or the weakness of the egg. We do not keep conscious of how much more essential the journey is, as compared to the end.

We would live our lives wanting to procure one or another thing, but, say, if Einstein had deduced the Unified Field Theory, or Beethoven had completed the “Unfinished” Symphony, either they would have found another objective to accomplish, or died as impoverished people; impoverished of a desire, of a target to achieve!

If any of us got everything we desired for –even if we unthoughtfully asked for immortality — we are sure to realize how pointless life would be beyond that point of time — when we achieved everything we dreamed of. We would be left with no reason to live; no motive to work towards.

Just as they say, thieves steal so that the police has someone to chase!

One might realize that an egg could be made to fall through four feet unharmed, simply by dropping it from a height of five feet, and catching it mid-air.

Also, as Ayn Rand wondered in ‘The Fountainhead’ — “His head thrown back, he felt the pull of his throat muscles and he wondered whether the peculiar solemnity of looking at the sky comes, not from what one contemplates, but from that uplift of one’s head.”

P.S: This essay and the previous one were practice essays for my SAT. In which, I eventually did terribly — even in the essay, which I thought wasn’t that bad.

When was the last time you were delighted to get something you were ‘supposed’ to? For instance, how many of us would actually delight in receiving breakfast? Not me!

What we do not struggle for, we take as granted — the most fundamental example being our own existence. Rarely would one find somebody so conscientious, he actually valued the mere presence of himself. Why? — because one did not have to struggle to be born.

Very unexpectedly, we attribute more value to something of such necessity, we anyways get it. Air to breathe, water to drink, are some more instances of existences having incalculable , and equally unperceived value as well.

Hence, we only value what we struggle for. As is again noticeable — how many memorable stories would we have read — of love, achievement, success, anything! — that did not involve a struggle, an effort? And that was the only factor which gave it the value it attained.

One would not measure the height of the fruit on the tree by a meter scale from the sea level — but by how hard one had to jump; or carefully one had to throw a stone, to get it!

Posted via web from The Mystic Ranger

Posted via web from The Mystic Ranger