Adonis Diaries

Archive for May 16th, 2022

“I am Israel”?

Jah militant posted on FB, and Written by Professor Norman Finkelstein.

May 9, 2022

Did I come to a land without a people for a people without a land?

Those people who happened to be here, had no right to be here, and my people showed them they had to leave or die, razing 400 Palestinian villages to the ground, erasing their history

.”I am Israel”.

Some of my people committed massacres and later became Prime Ministers to represent me.

In 1948, Menachem Begin was in charge of the unit that slaughtered the inhabitants of Deir Yassin, including 100 women and children.

In 1953, Ariel Sharon led the slaughter of the inhabitants of Qibya, and in 1982 arranged for our allies to butcher around 2,000 in the Palestinian refugee camps of Sabra and Shatila.

I am Israel.

Carved in 1948 out of 78% of the land of Palestine, dispossessing its inhabitants and replacing them with Jews from Europe and other parts of the world.

(Mind you that the first Palestinian Intifada in 1935 demanded from the British mandated power to arrange for municipal election and denied them this right on the ground that Jews represented barely 20% of the population)

While the natives whose families lived on this land for thousands of years are not allowed to return, Jews from all over the world are welcome to instant citizenship.

I am Israel.

In 1967, I swallowed the remaining lands of Palestine – East Jerusalem, the West Bank and Gaza – and placed their inhabitants under an oppressive military rule, controlling and humiliating every aspect of their daily lives.

Eventually, they should get the message that they are not welcome to stay, and join the millions of Palestinian refugees in the shanty camps of Lebanon, Jordan, Syria….

I am Israel.

I have the power to control American policy. My American Israel Public Affairs Committee can make or break any politician of its choosing, and as you see, they all compete to please me.

All the forces of the world are powerless against me, including the UN as I have the American veto to block any condemnation of my war crimes.

As Sharon so eloquently phrased it, “We control America”.

I am Israel.

I influence American mainstream media too, and you will always find the news tailored to my favor. I have invested millions of dollars into PR representation, and CNN, New York Times, and others have been doing an excellent job of promoting my propaganda.

Look at other international news sources and you will see the difference.

You Palestinians want to negotiate “peace!?”

But you are not as smart as me; I will negotiate, but will only let you have your municipalities while I control your borders, your water, your airspace and anything else of importance.

While we “negotiate,” I will swallow your hilltops and fill them with settlements, populated by the most extremist of my extremists, armed to the teeth.

These settlements will be connected with roads you cannot use, and you will be imprisoned in your little Bantustans between them, surrounded by checkpoints in every direction.

I am Israel.

I have the fourth strongest army in the world, possessing nuclear weapons. (From USA tax payers)

How dare your children confront my oppression with stones, don’t you know my soldiers won’t hesitate to blow their heads off? (Last week, Israeli sniper shot dead a Palestinian/American journalist, Shirine Abu Akli, for daring to cover the Jenine camp attack by Israeli army)

In 17 months, I have killed 900 of you and injured 17,000, mostly civilians, and have the mandate to continue since the international community remains silent.

Ignore, as I do, the hundreds of Israeli reserve officers who are now refusing to carry out my control over your lands and people; their voices of conscience will not protect you.

Iam Israel.

You want freedom? I have bullets, tanks, missiles, Apaches and F-16s to obliterate you.

I have placed your towns under siege, confiscated your lands, uprooted your trees, thousand of years Olive trees, demolished your homes, and you still demand freedom?

Don’t you get the message? You will never have peace or freedom, because I am Israel.’-

Written by Professor Norman Finkelstein.

Jah militant

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Ramanujan’s Nested Radical Problem.

Note: I have watched the movie on Ramanujan.
Ujjwal Singh

Aug 29, 2021

Left: Srinivasa Ramanujan. Right: The problem posed by Ramanujan in the Journal of the Indian Mathematical Society.

In 1911, the Indian mathematical genius Srinivasa Ramanujan posed the above problem in the Journal of the Indian Mathematical Society.

After waiting in vain for a few months, he himself provided a solution to the same journal

In this article, we go over Ramanujan’s solution (taking note of its spell-binding simplicity) along with exploring a calculus-based approach for the problem.

Disclaimer

But first, let us state us state a few important things explicitly.

  1. We will work on the assumption that the sequence given above converges. Strictly speaking, we should first prove the convergence of the sequence, and then go about finding its limit. However, for the sake of simplicity, we’d take the sequence’s convergence for granted, and just focus on finding the limit.
  2. The solution presented below is not the exact one provided by Ramanujan in the journal. Rather, it’s a simplified version, the intention being to capture the gist of Ramanujan’s solution.

Ramanujan’s Solution

Note that for any non-negative real number x, we have —

Now, (x + 2) can again be written as ((x + 1) + 1), to get —

Carrying on with the process and writing (x + 3) as ((x + 2) + 1), we get —

The pattern is pretty visible by now. It’s clear that if we carry on this process infinitely, we’d land at —

Now comes the magic! Plugging in x = 2, we get —

The solution to our problem turns out to be just !

It’s hard not to wonder at the remarkable stroke of genius at the heart of this solution. Who would have thought that representing a number as the square root of its square could lead to such a beautiful identity?

Also, the above serves as an excellent example of a broader category of problems — wherein the problem posed is a particular case of more general identity.

In such cases, we discover the general identity first and then plug in suitable values to get the desired result.

For example, we can now easily say that —

So, that was Ramanujan’s solution to the problem. Next, we move on to explore a calculus-based approach for the same!

A Calculus-Based Solution

Another disclaimer: We assume the existence of a differentiable real-valued function f, defined implicitly as 

Again, we have forsaken some mathematical rigor here, by assuming that such a function exists without actually proving the same. Now, our goal is — provided such a function exists, can we exploit it to solve our original problem?

Note that —

Carrying on, we arrive at —

As would be clearly visible by now, the solution to our problem is — f(2)! That is because,

Of course, the above is what inspired our function definition in the first place! Now, let’s try finding out the value of f(2).

Again,

Now, let’s see what the derivative of f(x) tells us!

Again, setting x = 0 in [3], we get —

We’re almost there! Getting back to the original equation —

There we have it! The value of f(2), and thereby the answer to our problem, is 3!

Concluding Remarks

To add some historical context, Ramanujan published this problem in 1911, while trying to establish himself within the national mathematical community.

A couple of years later, he’d get in contact with G.H. Hardy, move to Cambridge, and over the next five (during WW1) years the duo would go on to form one of the most productive mathematical partnerships ever.

Of course, Ramanujan is a name that needs no special introduction. His life and achievements have already been thoroughly documented. This article (as well as the problem posed by Ramanujan in the Journal of the Indian Mathematical Society) is merely a teaser from one of his favorite domains — nested radicals and continued fractions.

As was typical of him, Ramanujan possessed an all-absorbing interest in particular fields of mathematics, while remaining completely oblivious to the rest.

Who could have better understood this than Hardy himself! We end this article with a brilliant quote from him which aptly sums up Ramanujan—

The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems… to orders unheard of, whose mastery of continued fractions was… beyond that of any mathematician in the world;

And yet he had never heard of a doubly periodic function or of Cauchy’s theorem, and had indeed but the vaguest idea of what a function of a complex variable was

— G.H. Hardy


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