Relativistic Doodles

This post explains how my illustration of general relativistic time dilation works. This is the parent post.

Here is an image of a simple classical timeline:

timeline_1

There are 2 observers: green and red. They have their own watches. The red observer shoots an arrow towards the green observer. The position of the arrow vs. the time recorded by the two observers looks like the picture above. If we take a trace of the trajectory of the arrow, we get:

timeline_2

If we were to take the trace of a 2 signals 1 second apart that travel at constant speed, and 2 signals 1 second apart and traveling instantaneously, we would get:

timeline_3

You will notice that the components of all 4 traces (like the ones drawn in grey) are parallel and perpendicular to the space-time axes. This is always the case. So even when I distort the edge of the red timeline a bit, I get:

timeline_4

So if I am standing with the red observer, and I see him sending out signals, I will not notice a difference even when the red timeline distorts, because to me, the components of the signals are still parallel and perpendicular to my space and time. In the same way, when an observer is falling into a gravity well (like that of a black hole) and sends out signals, the observer does not notice the relativistic effects of gravity on the signal. However, the observer who is standing far away from such distortions notices an altered signal. So even though the signal at t=8 was instantaneous according to the red observer, it reached the green observer at t=9.

If you understood this, then you will know what is wrong with this set of traces of signals that a red observer sends as she falls into a black hole:

time_dilation_gravity_WRONG

Planning for the Future

I was stumbling around the internet when I came across this series of pictures. If any one of you is interested in long term investments, high return savings, that sort of thing, this is a really good view of what the coming years will bring.

future

Investment Outlook for the really meticulous planners

Click here if animation doesn’t play.

But seriously, this image had a profound effect on me. A lot of people consider themselves lucky to be living in this age of innovation, on the pinnacle of existence. And believe me, I am not ungrateful. There is Naruto and Xbox and the Grand Unified Theory, and trips to the moon and probes to Mars; there is the internet, the standard bearer of the freedom of expression, and there is Game of Thrones and Harry Potter. And most important of all there is the asymptotic ideal of liberalism that, ever so faithfully, supports one’s occasional venture into the more “contestable” realms of morality, hiding behind the slippery paradox of the ownership of the intangible.

I am, of course, talking about The Pirate Bay.

Circumlocution at its Finest

Circumlocution at its Finest

I get excited when I write about things I like. Anyways: profound effect, ok. What I was trying to say is this: when you look at the larger picture of the universe, the largest picture that you can ever picture yourself in, you realize how insignificant of a speck you are. Despite living in an age of exponential progress, there is infinitely more that you have not yet beheld. The universe has so much yet to unveil. At every point in time, mankind has perceived itself as teetering on the pinnacle of progress, having reached the absolute limit of evolution. Every time, we have been proven wrong. Perhaps it is instinctive for us to identify with an unstable equilibrium, cautious creatures that we are. And it is this tendency of ours that forces us to ignore the broader realities of nature: that its progress is eventual, inevitable and perpetual.

I thought this picture is profound not because it is humbling, but because it showed me how much I will miss. I can’t fast-forward this show, I can’t torrent re-runs. I can only hope to experience the living daylights out of an infinitesimal period in the Universe’s life; a period that in all probability might be one of the more mundane parts of the universal timeline.

Just something to think about in times of inflated optimism.