Footprints( or shoe prints) in time?

In his poem 'Psalm of Life', Longfellow talked about 'footprints in the sands of time'. Though it then falls into other topics later, this line struck me as very significant, and I stored it away for future use. And I was proved  right. So, today,  me and  me friends had a  hell of our time at the beach, and I went there and dug my leg in deep. Obviously, there was a footprint(or a shoe print). However, in like 10 seconds, a huge  wave came crashing and the beautiful footprint(or shoe print) was washed away. And the metaphor came to mind too. Makes sense, does it not? Our footprints in time, our deeds, our actions, our memory, how long  will it be till all is washed away too, and we are absolutely forgotten? How long till a huge wave comes crashing down, and the footprint(or shoe print) is washed away. Nice thing to occupy the night. :)

Lifes a race. :D

Life's a lot of fun,
Says the black clad nun
A waste of time
For those in white

Life's a gift
Says the spendthrift
For Shakespeare,
Life's a stage

But no matter the writings
Or what the fat lady sings
Always remember, despite the outrage
Life, Life's a fucking race.

Roman story 1: Iphis and Ianthe

In Crete, Ligdus had promised to pregnant Telethusa, that he would kill the child if it turned out to be a female. Telethusa grieved because she knew the child would be female. So she prayed and prayed, and nothing(?) happened. However, in the night, Isis came. Isis is the Goddess for a whole bunch of stuff, from simplicity, to sinners and artisans. She brought with her the jackal-headed God of mummification(:\) Anubis. Isis promised that no problem would happen. She told that the childs gender should be hidden from the King. (How???)

So, Iphis grew, really a girl, but shown as a boy. In eventuality, Iphis' marriage was declared, to a girl named Ianthe. Ianthe was really beautiful and after an extended courtship, fell in love with Iphis. Iphis reciprocated. However a little snag surfaced, gender snags. So followed another long period of prayer, after which (:D) nothing happened. Isis to the rescue, she came and changed the gender of Iphis. Iphis became a guy, and all other things were easily resolved. Alls well that ends well!!!

Vertically and crosswise: Vedic Math 1

All right, this is an interesting way of multiplication.

In this method, you create a new number system, based on a common number near to both the numbers we need to multiply.

1: So, for a multiplication of 103 * 102, I would take a base of 100.

103             +3

102             +2

105              06

103*102=10506.

The method is simplicity itself.  The base used here is 100, so write the distance from 100, i.e. +3 and +2 respectively. Once done, cross-add. Since the base is the same, the number, and the distance of the second number from hundred is the same. 103+2=102+3=105. So write 105 down. Then multiply the numbers of the right handed column, 3*2= 6. I write it as 06, so it corresponds to the number system. Behold!! The answer!!!

2: The interesting thing is that we can take any base we need. Still, it’s probably better if we take a good base, like a multiple of 10. Therefore 1003*998=

1003           +3

998             -2

1001           -006

1000            994      

1003*998= 1000994

Again it’s pretty simple. I write the base thing again. However, the slight twist here is my second part is negative. So, I add it to my base, (1000 in this case) and subtract one from the left hand side.

3: As I said before, its particularly better if we use a good base. That, however is unnecessary, since all numbers can be expressed as a multiple of 10. So 20= 10*2, 45=4.5*10, 3=0.3*10 and etc.

So 21*23

21                   +1

23                   +3         

24                   +3   

48                   +3        

21*23=483.

Simply assume that you would make a base of 10, but write the distance as from 20. At the end of it all, multiply your left-hand side with your multiple (in this case 2) and there you go!!!

4: 26*23

26                     +6     

23                     +3     

29                     18     

58                     18    

59                     8

It’s as simple as it can get. The twist is that the right hand side contains more digits than possible, so we use the carry on method, adding one to the left hand side to give us the answer.

23*29= 598.

5: The last one. 47*41

47                 +2                  

41                 -4            

43                 -8                

193.5             -8                 

192.5              2                 

192                 7       

47*41= 1927

This one is almost completely useless, since it is actually much faster to just use the normal way.  The base here could be taken as 40 or 50 even, to give a much easier solution. However, here, multiply by 4.5.  Subtract one to make the right hand side positive. The last step is just that you take the number in the decimal place and add it to your right hand side.

Notes: The whole way of solving has a mathematical solution to it. So if you know it, then please mail me the proof. However, experimentally this method seems to work on everything I have tried. Again, if you spot any mistake, then please mail.

I found this method in a Vedic math book, containing the heading of vertically and crosswise.

Vertically and crosswise has a whole bunch of applications from multiplication and division to finding equations of a line, valuation of logarithms, exponentials, trigonometrical functions and solutions of simultaneous, transcendental, polynomial and differential equations.   

Fractal's. Mandelbrot set in particular.

Mandelbrot set of fractals. They are quasi fractals, but very famous due to extended graphical technology.

Picture 1
A fractal is basically a geometric shape which can be divided(at least approximately) to a many parts which have the same geometric shape. Fractals, thus exhibit a property of self-similarity, and are bound by a mathematical equation, largely recursive in nature. This means that it is bound by a set of iterations. A fractal shows the following characteristics,

• Its geometric. Its made up of irregular straight lines(or points).
• It is too irregular to be easily described in traditional geometric language.
• It is self-similar (at least approximately or randomly).
• It has a simple and recursive definition.

Many naturally occurring objects are actually fractals(at least in part) like clouds and lightning bolts.

This is a Koch curve, supposed to be a complete fractal. Its actually made from an equilateral triangle.

 To Mandelbrot then. Mandelbrot set is a quasi-fractal set(i.e, shows many fractal properties, but is not exactly self-similar.)  It has a formula, z_n+1 = z_n² + c, where n is substituted by the number. The condition is, a complex number, c, is in the Mandelbrot set if, when starting with z₀ = 0 and applying the iteration repeatedly, the absolute value of z_n never exceeds a certain number (that number depends on c) however large n gets. i is one of the numbers in this set.
Its famous for the aesthetic value, and for the fact that its a relatively simple equation.
http://www.dailymotion.com/video/x3su4b_mandelbrot-fractal-zoom_creation

A poem: First They Came..

They came first for the Communists,
and I didn't speak up because I wasn't a Communist.

Then they came for the trade unionists,
and I didn't speak up because I wasn't a trade unionist.

Then they came for the Jews,
and I didn't speak up because I wasn't a Jew.

Then they came for me
and by that time no one was left to speak up.

Martin Niemöller

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo Buffalo

Strange as that may seem, the above is a perfectly valid English statement. Three different forms of buffalo are being used here, the town, the animal, and the bully. It translates to the following sentence: The Buffalo's from Buffalo, who are buffaloed by other buffaloes of Buffalo, also buffalo other buffaloes of Buffalo. check it out here :http://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo 
Insane right?? :D