Understanding Infinity

Ambi was born on 13th October 1989, as per many of his certificates, which may be expressed as 13101989
There is a number in mathematics called pi, which has infinitely many digits, starting from 3.14159
Ambi was surprised to find that,

"the string 13101989 occurs at position 40,160,873 counting from the first digit after the decimal point."-according to Pi-Search

Screen capture of an MIT site.
As one might observe, the billionth digit has not yet been loaded into my computer.
The string 13101989 is highlighted. Click to enlarge.

 If there is a method of translating letters to digits, it is possible then, that:

• Full text of Merchants of Venice be found exactly.
• Full text of all of Shakespeare's works be found exactly.
• Full text of all of English literature till date be found exactly.
• All literature of all of the languages till date be found exactly, if there is a method of translating all human language to digits.
• All spoken, written, printed and displayed word till date be found.
• All spoken, written, printed and displayed word in the past and the future be found.
• Instructions to become a billionaire be found. Not those self-help-books-kind-of instructions, but computer-algorithms-kind-of instructions, with details like how many grams of toothpaste should one use today.
• This blog post be found.
• DNAs of all creatures be found.
• Co-ordinates of each electron in the universe at any time be found.
• Tomorrow's stock prices be found.
• First billion digits of pi be found a billion times.
• Answers to all unanswered questions be found.
• Every-thing be found, including no-thing.

Only God would not be surprised by all these. If one is not surprised, they better get a check up done. They might turn out to be God. Just kidding.

Holograms and Pi

Built a simple device today which can project three-dimensional images to space from a surface.

The device has shape of a truncated square pyramid with transparent faces.

Place it at the centre of a display and play a video made specially for it.

It gives the effect of a free-floating object.

A 3-D video of a jellyfish being played on the device from a flat display.

It can give four different views of the object, if looked from the sides of the pyramid. We could see front, back, left and right of an object. But not any other view. It lacks a continuous 3-D feel as we expect with real objects. That is, if one slightly changes her point of view, the image remains the same, it does not rotate.

If, instead of a four faced pyramid and four images to project on them, one could use a shape with infinitely many faces and enough images to reflect on those faces, one might create a real looking object inside it. That is what I think.

Such a shape might look like a sphere. And I have a strong feeling that we are sitting inside a giant sphere.

That makes more sense when I find pi, the irrational number, in the most unlikeliest of places!

As if God placed it there so that we do not forget where we are and get lost!

Good idea mate! Thank you.

Map or Place?

I am at a place.
I have a map of the place.
I take out the map and spread it on a table.
There is a one-to-one correspondence between points on the map and points on the place.
For example, I can find a point corresponding to north-east corner of the table on the map.
But these two points are distinct.
One is on the place and the other is on the map.

Photograph taken from Richard's Photostream. Thank you.

Question:
If I am marking a point on the map, am I marking a point on the place or a point on the map?
The map is a part of the place.
Or is the place a part of the map?

On e

The base of natural logarithm, e, continues to interest people with some knowledge in maths. This is an irrational number, which means we can never pin-point its location on the line of real numbers with no error. (Pi, the ratio of circumference to diameter of any circle, is another such elusive number.) Logarithm with base e is called natural logarithm because of a reason. It is, to me, like this:

Remember compound interest schemes banks speak about? You deposit some money at first and after say, quarter of an year, an interest on your deposit is calculated for this period with some rate of interest. This amount of interest is compounded to your initial deposit and for the next quarter, you derive interest for this compounded amount. This addition continues till the deposit is with the bank.

If we reduce this period of calculation of interest to smaller intervals, to months, to days, to seconds, we approach an exponential rate of growth. From nowhere, irrespective of rate of interest, the factor e comes into picture, when the period is infinitesimally small. The ratio of amounts in your account at times 2t and t is equal to e raised to the rate of interest.

When the rate of growth of something is equal, not just proportional, to the amount of the thing, e appears. That is how a colony of bacteria grows, with very small periods and with characteristics very close to e. That is how temperature of a hot small metallic ball drops. That is how a radioactive element decays. A lot of naturally occurring growths and decays closely follow the e- based exponential curve. The title of 'natural' came this way, probably.

It is still a mystery how this number walks into these situations with complete authority and exuding confidence.

The Complete Model

It all started with an attempt to predict the outcome of coin-tossing. A complex model was developed. Give air conditions, mood and geometry of hand of tosser, the model could predict whether it would be a head or a tail. Accuracy was improved as years passed.
Now someone came up with this: why don't we enlarge this model to cover all of the world? A model was developed. A big computer contained algorithms of the model. It was a preliminary model. It needed a large amount of data to begin the process and accuracy was not very impressive. But both of the problems were getting solved as more resource flew into the project. The computer was getting bigger. Initial data requirement was coming down. Accuracy was improving. Computer getting bigger was a problem. So compact machines were developed, with greater complexity.
As time passed, beauty of the model set fire to men's hearts. At one point of time the model became indistinguishable from the world it was created to predict. And people never bothered to go back.

The Common Place

.
One walnut and one supernova are hardly the same.
But, see the magic, zero walnut and zero supernova are exactly the same.

..

None has seen or achieved:

1. a state of zero pressure. Absolute vacuum.
2. absolute zero temperature. 0 kelvin.

It does not seem that these are two different states at all. There is only one zero.
...
It does not exist outside human mind.
If zero exists then it is a fallacy to refer it as zero!
Isn't it?