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Member since: Thu Sep 25, 2008, 03:38 PM
Number of posts: 3,169

Journal Archives

ERB: Nye vs. Newton

Given that integral(sec(x), dx) = ln( abs( sec(x) + tan(x) ) ) + C

One finds

integral(sec(x), dx, {0, Pi/6}) = ln( abs( sec(Pi/6) + tan(Pi/6) ) ) - ln( abs( sec(0) + tan(0) ) )

sec(0) = 1
tan(0) = 0

integral(sec(x), dx, {0, Pi/6}) = ln( abs( sec(Pi/6) + tan(Pi/6) ) ) - ln( abs( 1 + 0 ) )

abs( 1 + 0 ) = 1

integral(sec(x), dx, {0, Pi/6}) = ln( abs( sec(Pi/6) + tan(Pi/6) ) ) - ln( 1 )

ln( 1 ) = 0

integral(sec(x), dx, {0, Pi/6}) = ln( abs( sec(Pi/6) + tan(Pi/6) ) ) - 0

sec(Pi/6) = 1/( cos(Pi/6) ) = 2 /((3)^(1/2))
tan(Pi/6) = 1/((3)^(1/2))

integral(sec(x), dx, {0, Pi/6}) = ln( abs( sec(Pi/6) + tan(Pi/6) ) ) = ln( abs( (2/((3)^(1/2))) + (1/((3)^(1/2))) ) )

integral(sec(x), dx, {0, Pi/6}) = ln ( ((3)^(1/2)) ) = ln( (3)^(1/2) ) * 1

Since ln( (3)^(1/2) ) * 1 = ln( (3)^(1/2) ) * ((k)^64) implies 1 = k^64 or k^64 = 1, one must find the sixty-fourth roots of unity.

The sixty-fourth roots of unity are the elements of the set {e^((2*Pi*i*n)/64)} with n being an element of the set {0, 1, 2, 3, ..., 63}.

Euler's formula states that e^(i*m) = cos(m) + i*sin(m). If n = 16, (2*Pi*i*16)/64 = i*Pi/2 and m = Pi/2.

cos(Pi/2) = 0 and sin(Pi/2) = 1, so e^((2*Pi*i*16)/64) = 0 + i*1 = i.

Thus, the solution in the video corresponds to the 17th of the sixty-fourth roots of unity -i.e., the one that has the value n = 16.

Would anyone care to analyze the prism's refraction of light (i.e., the displayed order of colors) relative to the orientation of the prism? It is difficult to tell, but the intended refracted beam looks a lot like it is reflecting off one of the lateral faces or lateral edges of the prism.

This is a really neat video and a cool rap.

On Iraq, the TAZ Mission Accomplished Photo and the Content of the Subsequent Commentary....

Following this brief introduction is a rough translation of the first four paragraphs of the TAZ commentary that accompanied the altered picture of Bush's mission accomplished speech. That commentary's message is different than one that merely goes after President Bush. It is a piece regarding the practical realities of the current situation in Iraq - even though it followed a picture that damned Bush by highlighting his folly. The untranslated remainder (3 paragraphs) of the commentary focuses on the part of the title that is in italics and underlined:

June 12, 2014
ISIS Must Not (Be Allowed to) Achieve Victory
What is happening in Iraq is a catastrophe for the world community. New strategic partnerships must be considered.
by Ines Pohl

It is difficult to say which was the greater mistake: the American invasion of Iraq in 2003 or the withdrawal of 2011 - a withdrawal from a country whose government order appeared to lay in total disarray after, during and in spite of the eight-year American occupation?

In the final analysis, it is idle to argue whether President Bush is more responsible for the current situation than President Obama who ordered the final military withdrawal three years ago. What now counts - and what must be of the greatest concern - are the reports that reach us: hundreds of thousands of people are fleeing before the apparently inexorably advancing ISIS militias, a radical Islamic terrorist organization which is so brutal that even Al Qaeda declines to cooperate with it.

One city after the other take the terrorists in without any noteworthy resistance from the Iraqi army. On the contrary, it (the Iraqi army) surrenders and leaves behind the most modern undamaged American weapons of war: this further strengthens the mob's (ISIS's) military striking power.

What is happening here is not only a catastrophe for the people of the region but a catastrophe for all people who believe in democracy (original word: Demokraten) - indeed, the world community. This catastrophe is also the result of western military interventions that simply do not lead to the transfer of freedom and democracy, but instead to the disintegration of countries.



Here is the altered mission accomplished photograph:

The Guardian: A eulogy to the NHS...

Here is an article that describes access to healthcare before the creation of and after the creation of the NHS in the UK - the article goes on to speak of some current changes in healthcare in the UK:

A eulogy to the NHS: What happened to the world my generation built?
In 1926, Harry Leslie Smith's sister died of TB in a workhouse infirmary, too poor for proper medical care. In 1948, the creation of the NHS put a stop to all that. In an extract from his new book, Harry's Last Stand, he describes his despair at the coalition's dismantling of the welfare state

Harry Leslie Smith
The Guardian, Wednesday 4 June 2014 14.03 EDT


As I convalesced, I was gobsmacked at the great consequences of free health care and the potential it offered to improve our society. It was a transformational shift in how we as a country viewed our fellow citizens. The creation of the NHS made us understand that we were in truth our brother's keeper, and that taxation benefits everyone through maintaining not just our roads and sewers but the health of our children, workers and elderly.

To me, the introduction of free health care was the first brick laid on the road to the social welfare state. So it has always been difficult for me to listen to politicians, proud possessors of health insurance and shares in private health care companies, when they talk about how the health service that we fought so hard to build must change. The coalition government's Health and Social Care Act will create a two-tier health care system. This act will see the NHS stripped down like a derelict house is by criminals for copper wiring.

Ukip has even proposed that A&E patients should have the right to buy their way to the front of the queue, while in Merseyside a private for-profit cancer clinic has set up shop under the NHS umbrella. Where will all of this end? What will be given the greatest priority in a new health care system that sends every service, from blood work to chemotherapy, out to the lowest bid tender?

It ends where I began my life in a Britain that believed health care depended on your social status. So if you were rich and insured you received timely medical treatment, while the rest of the country got the drippings. One-fifth of the lords who voted in the controversial act which provides a gateway to privatise our health care system were found to have connections to private health care companies. If that doesn't make you angry, nothing will.



Ernst Wins Iowa Republican Primary for US Senate

Source: Associated Press

Joni Ernst, an Iowa state legislator whose ads about guns and hog castration helped her shore up support among conservatives, won the GOP nomination for U.S. Senate Tuesday to set up a fall matchup that Republicans are eyeing as a prime opportunity to pick up a seat.

Once a long shot when better-known party leaders passed on the race, the state senator and Iraq War veteran received enough votes to avoid a nominating convention in the five-way race. Most of the voting in the primary came ahead of severe storms, which curbed turnout and forced some precincts to suspend voting temporarily.

Ernst moves on to face Democratic U.S. Rep. Bruce Braley in a race expected to play a key role in the battle for Senate control.

Five-term Democratic U.S. Sen. Tom Harkin announced last year that he would forego another term, leaving a Senate seat open in Iowa for the first time in 40 years. Republicans have made the traditional swing state one of their top targets.

Read more: http://abcnews.go.com/Politics/wireStory/ernst-wins-iowa-republican-primary-us-senate-23983684
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