Sun rise angle

                             On December 21st, at evening time, I was on our roof looking at the Sun. I wondered what would be the angle the Sun was at w.r.t. the East direction. As it was Dec 21st, it was winter solstice for us "Northern Hemispherers". So, the Sun was above Tropic of Capricorn.
                             We should first understand the direction of East. East is not the  point on the horizon where Sun rises as it keeps on changing throughout the year. It is the direction perpendicular to North-South towards rising Sun. So, it is parallel to our current latitude. If we take a tangent to the Earth at our current location parallel to our latitude, it shows the East-West direction.
                             

In this picture, green line is our current latitude, black line is Equator, pink line is Tropic of Capricorn, brown line is the direction of the rising Sun, dark red line corresponds to the Sun being above Tropic of Capricorn and lambda is the latitude angle of Tropic of Capricorn.

As Earth's radius is small compared to Earth Sun distance, the brown and red lines are parallel. Hence, angle between our East and rising Sun is lambda.

So, on any given day, the angle rising Sun makes with East is the latitude above which the Sun currently is.

To calculate the angle Sun makes at noon, we can easily see that at noon our perpendicular is along the radial line to our location.

In this above pic, light green line is the perpendicular at our position. Now again we can consider the blue and red lines to be parallel. Hence, at noon Sun angle will be lambda 0 + lambda T.

Hence, Sun doesn't always rise on the East and doesn't always reaches the Zenith at noon!

How far is the horizon?

Many times we go on our roof tops in the evenings and look at distant buildings and trees and get lost in our thoughts. When we go to a beach we like to look at the horizon to see sunset or some ship sailing by.

If we want to calculate how far the horizon is, we can do this way:
Imagine the earth to be a perfect sphere. Now, our viewing angle is a tangent to this sphere. If we consider in 2D it is a tangent to the circle.
Now, from the center imagine 2 radii one to our feet and another to the point of intersection of the tangent to the circle.

As we can see, we have a right triangle with hypotenuse R+h and one side R where R is the radius of the earth and h is our viewing height.

From pythagoras theorem, we have the remaining side as sq. rt (h^2 + 2Rh)

If we substitute R = 6400 km or 6400000 m and h = 1.8 m we get surprisingly not a very large value
which is just 4.8 km!

So, the horizon is just at 4.8 km!

Vuze problem

I started using Ubuntu again. Now I am in 11.10. I wanted to use a good bit torrent client hence installed Vuze. But it would somehow disappear. When I try to see it in system monitor, it wouldn't appear. If I try to start it from terminal, an error would appear.
After searching in the internet I finally found the issue. Ubuntu wouldn't allow system tray icons anymore. As Vuze's default preference is to be in system tray when minimized, this issue came.
This thread helped me solve the issue.
https://answers.launchpad.net/ubuntu/+source/azureus/+question/186616

All I need to do is kill java process using 'killall java' as Vuze runs as java.
Then start it again and disable system tray option from Tools->Options->Interface.
Then restart it again and everything works well!

Ignorance

What is truth? Why am I separated from it? These questions assume the existence of 'truth' and 'I'.
And everything that is said assumes the existence of logic/rationality.
      If we assume the existence of such a truth, we question why the truth is the way it is. Why not in some other way? E.g. Newton's law gravity. One level of understanding nature is to be able to see the existence of this law governing bodies with masses. The next question that comes is why this gravity? If it is explained by some other model like there being gravitons which are exchanged between masses, then there is always the next question why them?
       Why is our logical way of thinking able to extend questions like this and not be contended with what it already has? Is there a quantification to this logic like prepositional, predicate etc?
        Why anything? Or at least why this consciousness? If I were without consciousness, I wouldn't experience any of this. There still can be evolution and rational beings etc. but there won't be a consciousness to experience.
       What problems should I solve in life? What are the important problems? What are unimportant?
       Why can we understand things? When every definition is dependent on some other, why are we still be able to understand?
E.g. Force = mass * acceleration.
 Mass  is inertia. Inertia is difficulty in movement. Movement is change in position with time.
Time is change in position of something. Position is distance wrt some other position. Distance is measured in length. Length is wrt some other length.

But, still when I read this in 6th class, I could feel it. I know what force is, what mass is. Acceleration felt wierd as it is meters per second squared as against speed which is meters per second which can easily be understood.
              Why the uncertainty principle? Is this God's way of making the world imperfect to observation? Making us not able to understand everything that is there is? Or did He make the world itself imperfect making everything probabilistic? And why are the probabilities well-defined? Why aren't they themselves probabilities?

Pre- historic man asked the question who was above the mountains pouring rains and thunders. Got the answer as God.

He accepted as facts his existence, earth, trees, eating and God raining etc.

In the middle ages were questions asked as why the apple falls down?

Gravity came the answer. It's in the nature of things to attract that makes the apple fall down on earth.

Accepted as facts are existence, earth, apple, gravity, nature of things etc.

Today we ask what the fundamental particles are, what the fundamental forces are?

Quarks, gluons, weak force, strong force etc.

Accepted as facts are rationality, existence of forces, existence of laws etc.

Is it the case that with the increasing questioning capacity of our brains that answers come with increasing complexity of reasoning and insights but older facts merely being replaced by newer ones?

Mumbai