A Test of the Numerical Integration Speediness of Six Calculators
Jenab6
jenab6
The six calculators are:

1. The TI-36X Pro (scientific calculator)
2. The Casio fx-115ES Plus (scientific calculator)
3. The Casio fx-991EX ClassWiz (scientific calculator)
4. The Casio fx-9860gii SD (graphing calculator)
5. The Casio fx-9750gii (graphing calculator)
6. The TI Nspire CX CAS (graphing calculator)

The problem used for test:

B = 1.3271244e+20
C = 6.957e+08
D = 1.495978707e+11
Evaluate:
∫ (C, 0.999999D) 1 / √(2B(1/x − 1/D)) dx

This integral returns the amount of time, in seconds, for an object to fall to the sun's photosphere (one solar radius = C) starting from a distance of 1 astronomical unit (D), assuming that the sun and the object are initially at rest with respect to each other and are acted upon by no forces other than their mutual gravitational attraction. The variable B is the solar gravitational parameter.

TI-36X Pro
Answer: 5570898.581
Time to Solve: 90.4 sec

Casio fx-115ES Plus
Answer: 5570898.583
Time to Solve: 76.6 sec

Casio fx-991EX ClassWiz
Answer: 5570898.583
Time to Solve: 17.3 sec

Casio fx-9860gii
Answer: 5570898.583
Time to Solve: 7.1 sec

Casio fx-9750gii
Answer: 5570898.583
Time to Solve: 4.9 sec

TI Nspire CX CAS
Answer: 5570898.58274
Time to Solve: 0.5 sec

As you can see, the TI-36X Pro is a slow-poke. The TI-36X Pro costs anywhere from $19 to $30 on Amazon.

The Casio fx-991EX ClassWiz is the official (and substantial) Casio upgrade to the earlier Casio fx-115ES Plus. For moderately complicated numerical integration chores, the Casio fx-991EX is more than four times faster than its predecessor model. Furthermore, the Casio fx-991EX is more than five times faster than its ostensible competitor from Texas Instruments, the TI-36X Pro. The Casio fx-991EX sells at prices ranging from $14 to $36 on Amazon.

But the Casio fx-9750gii is more than three times faster than the Casio fx-991EX ClassWiz and is about 18 times faster than the TI-36X Pro. Reasonable prices on Amazon go from $30 to $37, but there are some sellers (that should be ignored) who are trying to gouge for more.

The TI Nspire tops the list for speediness, however, being about ten times faster than even the Casio fx-9750gii, and it is 180 times faster than the slow-pokey TI-36X Pro.

I have solved the indefinite integral analytically. Omitting the intermediate steps,

∫ 1 / √(2B(1/x − 1/D)) dx
= √[D/(2B)] { √(XD−X²) + D arctan[√(D/X−1)] }

When I used the calculators to solve the integral numerically, I had to avoid entering D itself for x, since that would cause an overflow error. But in the analytical solution, when X=C, the answer is 5578001.670517. When X=0.999999D, the answer is 7103.088517. So the precise answer from the analytical solution, used twice to evaluate the integral from X=C to X=0.999999D, is 5570898.582. There is no appreciable error in the numerical results from any of the calculators.


A Second Test of the Speediness of these six calculators, using a different numerical integration.

The definite integral to be solved:
∫(0,6) exp(x³) dx

Casio fx-115ES Plus
Answer: 5.963938092e+91
Time to Solve: 120 sec

TI-36X Pro
Answer: 5.963938091e+91
Time to Solve: 81.5 sec

Casio fx-991EX ClassWiz
Answer: 5.963938092e+91
Time to Solve: 24.5 sec

Casio fx-9860gii:
Answer: 5.963938092e+91
Time to Solve: 6.5 sec

Casio fx-9750gii
Answer: 5.963938092e+91
Time to Solve: 5.8 sec

TI Nspire CX CAS
Answer: 5.9639380919e+91
Time to Solve: 0.7 sec


A Third Test of the Speediness of these six calculators, using a different numerical integration.

The definite integral to be solved:
∫(−5,99) ln(x²) dx

Casio fx-115ES Plus
Answer: 717.9281095
Time to Solve: 174 sec

TI-36X Pro
Answer: 717.9281268
Time to Solve: 61.5 sec

Casio fx-991EX ClassWiz
Answer: 717.9281095
Time to Solve: 35.0 sec

Casio fx-9860gii:
Answer: 717.9281095
Time to Solve: 8.2 sec

Casio fx-9750gii
Answer: 717.9281095
Time to Solve: 6.7 sec

TI Nspire CX CAS
Answer: 198 ln(99) + 10 ln(5) − 208
Answer equals: 717.9281095
Time to Solve: instant

Pulsars: Beam angular size and the probability of detection.
Jenab6
jenab6
The angular radius of a beam coming out of a pulsar is estimated as

θ = 4.8° [1 + (0.22 m⁻¹)λ] P⁻⁰·⁵

Where λ is the wavelength of the light in meters and P is the pulsar period in seconds.

(Adapted from "Revisiting the Shape of Pulsar Beams," D. Mitra and A.A. Deshpande, Equation 7, _Astronomy and Astrophysics,_ 1999.)

Younger, faster-spinning pulsars have thicker beams than older, slower-spinning pulsars do. The beams thin out as the pulsar ages and slows down.

The longer the wavelength of electromagnetic radiation is being observed, the thicker the beams is at that wavelength. Radio gets spread out more than visible light does.

The probability of our being able to see a random pulsar is equal to the ratio of the solid angle swept out by the rotational cones of the beams (there should be one spinning around either pole of the rotational axis) and 4π steradians.

if α≥θ, then
probability = cos(α−θ)−cos(α+θ)

If 0≤α<θ, then
probability = 1 − cos(α+θ)

Where α is the angle between the rotational axis and the magnetic pole axis, assuming that these angles are the same in both hemispheres of the pulsar. If α=30° and θ=5°, then the probability of being observed is about 8.7%.

Tommy Robinson has acted as a knight of the realm ought
Jenab6
jenab6
Tommy Robinson has defended the weak at his own peril. He has confronted evil repeatedly, at personal cost. He has rescued children and damsels in distress by his courageous activism, when the bureaucracy was too corrupt and the police were too cowardly to do their jobs. His state has put him in prison for his exertions. His Queen can't be bothered to pardon him, let alone give him the knighthood for which his actions have qualified him. May God sweep all of this dirtiness out of Britain, and may all of the white people in the world be His broom.



(The above JPG image should work as a Facebook cover image. Copyright waived. These words are hereby given into the public domain. Post freely.)

The government and the media in the United Kingdom have been trying to advance a narrative about the arrest and imprisonment of Tommy Robinson that is false or deceptive in several ways.

First, the UK Establishment is trying to convince the public that Tommy was a threat to due process in regard to the trial of the Muslim pedophile gang rapists. No, he was not. Even Snopes.com spreads this particular misinformation. Tommy showed up on a sidewalk across the street from the courthouse in Leeds, England, only after the jury verdict had been issued, meaning that Tommy's Facebook livestreaming was never a threat to the due process rights of those Muslims. By that time, they had already been convicted and were going into the court for their sentencing.

Second, the UK Establishment is trying to convince the public that Tommy was treated according to the same laws that apply to everyone else. No, he was not. There were other citizen reporters present near the courthouse in Leeds at the same time that Tommy was there, and they were videoing the same Muslims and saying the same things about them. In particular, there was a Sikh gentleman (Bhai Mohan Singh) who reported on the trial before, while, and after Tommy was present. The police didn't arrest the Sikh gentleman. They only arrested Tommy. It is obvious, then, that police didn't arrest Tommy because of what he was doing. The police arrested Tommy Robinson because he was Tommy Robinson, against whom the authorities have a political grudge.

Third, the UK Establishment is trying to convince the public that the press restrictions against reporting on Tommy Robinson's arrest were lifted when they were no longer necessary. That isn't true. Those restrictions were lifted because they hadn't worked. Word of Tommy's arrest became international news, getting back to the British public via the foreign press. It became politically expedient for the UK Establishment to drop the gag order and hire public relations firms to spin lies about the whys and wherefores, to put as good a face on things as they could.

The authorities in the United Kingdom are, for the most part, corrupt. They are low-down, dirty, rotten and despicably high-handed elitists who should be in prison themselves.

Even Queen Elizabeth has much to answer for. She has knighted at least three PEDOPHILES: Jimmy Savile, Peter Hayman, and Cyril Smith. And there are probably more in this Sir Molester category.

Homework problems for high school science teachers to give to smart-alecs
Jenab6
jenab6
.

1. Two masses, M₁ and M₂, are initially at rest and separated by a distance d. They are in vacuum and are acted upon by no forces other than their mutual gravitational attraction. How much time elapses, beginning at the instant the separation is d/2 and ending at the instant the separation is d/3?


2. Given...

An observer in orbit around an exoplanet in its equatorial plane

The angular equatorial diameter of the exoplanet at the observer's periapsis
Dₑ₀ = 16.3060482°

The angular equatorial diameter of the exoplanet at the observer's apoapsis
Dₑ₁ = 12.0634564°

The angular polar diameter of the exoplanet at the observer's periapsis
Dᵨ₀ = 16.2567986°

The angular polar diameter of the exoplanet at the observer's apoapsis
Dᵨ₁ = 12.0271323°

The sidereal period of the observer's orbit around the exoplanet
P = 108000 sec

The observer's altitude above the exoplanet's surface at the periapsis of the observer's orbit
h₀ = 52568218 meters

Find...

The exoplanet's mass.

Leftist Theologians Pervert Biblical Statements that Condemn Homosexuality
Jenab6
jenab6
Leftists are exercising their talent for obscurantism again, in this case with regard to the writings of the Apostle Paul about the wickedness of homosexuality.

REFERENCE: Paul, Romans and Homosexuality

QUOTE: "To most readers, the first chapter of Paul’s letter to the Romans contains the Bible’s clearest condemnation of same-sex relations—both male and female. Recent scholarship, though, reads the same text and finds just the opposite—that homosexuality is innate and therefore normal, moral, and biblical."

That "recent scholarship" is hogwash, of course. It's a thin attempt to put a convenient and politically correct veneer over Paul's message, despite the clear meaning of the apostle's words.

"For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature. And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompense of their error which was meet." —Romans 1:26-27.

"Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God." —1 Corinthians 6:9-10.

Paul said that there is no place in Heaven for homosexuals. That being the case, then, Paul implies that all homosexuals are damned to hell, unless they repent of their sins and stop being homosexuals.

Supporting Paul's case are two verses from Leviticus, specifically 18:22, which refers to homosexuality as an "abomination," and 20:13, which describes homosexuality as such an egregious sin that homosexuals should be killed.

QUOTE: "In Romans, Paul seems to use homosexuality as indicative of man’s deep seated rebellion against God and God’s proper condemnation of man. New interpretations cast a different light on the passage."

Again, those "new interpretations" are hogwash. The leftists are trying to introduce an obfuscation regarding Paul's writing, as if it were scholarship, when their "interpretation" is merely a political expedient based on falsehood.

QUOTE: "Paul, the religious Jew, is looking across the Mediterranean at life in the capital of Graeco-Roman culture. Homosexuality in itself is not the focus of condemnation. Rather, Paul’s opprobrium falls upon paganism’s refusal to acknowledge the true God."

Wrong. Homosexuality, itself, is indeed the focus of condemnation. Certainly, Paul included the Graeco-Roman culture, but he wasn't speaking of them especially. He meant any homosexuals: any at all, regardless of which culture they were found in.

Nor was this particular part of Paul's writings aimed at Paganism's refusal to acknowledge Paul's God. Paul might have made such criticisms elsewhere, but this passage [Romans 1:26-27] specifically addresses homosexuality.

QUOTE: "It’s also possible Paul did not understand the physiological basis of genuine homosexuality. John Boswell, professor of history at Yale, is among those who differ with the classical interpretation. In Christianity, Social Tolerance, and Homosexuality he writes:

[SUBQUOTE] " 'The persons Paul condemns are manifestly not homosexual: what he derogates are homosexual acts committed by apparently heterosexual persons....It is not clear that Paul distinguished in his thoughts or writings between gay persons (in the sense of permanent sexual preference) and heterosexuals who simply engaged in periodic homosexual behavior. It is in fact unlikely that many Jews of his day recognized such a distinction, but it is quite apparent that—whether or not he was aware of their existence—Paul did not discuss gay persons but only homosexual acts committed by heterosexual persons.' "

Wrong. Paul was discussing anyone who commits homosexual acts, without regard to how much they prefer the perversion to normal sex. He meant both casual abusers of the sexual function as well as those we refer to as "gays."

You can see what the leftists are doing. They're trying to wedge an excuse for homosexuals into the Bible so that homosexuals who regard themselves as Christians can feel good. Feel righteous. Feel safe from hell's fiery pit.

Good government vs evil government, in Europe
Jenab6
jenab6

The weak ontology of physical laws
Jenab6
jenab6
The ontological principles of physical laws are:

(1) It is not possible for nothing to be.

(2) Hence the initiation of being is inevitable.

(3) What can happen once can happen multiply, including the initiation of being. Existence isn't a unique instance, but many instances.

(4) Some sort of pattern will exist in the behavior of what does exist in each instance, which can be described by some set of physical laws.

At the lowest level that I can imagine, you find these principles in the transient existence of vacuum fluctuations, and the virtual particles they sometimes produce. At the highest level that I can imagine, you find them in the universes of the multiverse.

Indeed, I wonder whether vacuum fluctuations and universes might be the same thing, with ourselves between high and low levels of these goings-on. A metaphysical ceiling. A metaphysical floor.

Is there a "higher" realm of existence for which our multiverse is their vacuum fluctuations? Likewise, is there a "lower" realm of existence for which our vacuum fluctuations are their multiverse?

There are many ways for the multiverse to be "multi-." An inflaton field can have an infinity of non-inflating universes. There can an infinity of inflaton fields. And each inflaton field can be a part of an infinite stack of virtual-particle-to-multiverse layers, in the sense described in the previous paragraph's questions.

Israel still trying to round up and deport blacks, just not directly to US/Europe
Jenab6
jenab6
Do you remember the racist Israeli decision to round up all the blacks and deport them? At first, they were going to be deported to Uganda, regardless of which country they'd come from. Later, the Jews changed their minds; instead of deporting the black immigrants to Africa, they'd dump them on white countries: America and Europe.

Then Benjamin Netanyahu changed the plan. For now, anyway. The effort to deport all the blacks from Israel to — somewhere else — is on hold. Not for any humanitarian reason, of course. Someone in the Likud party, of which Netanyahu is chairman, pointed out that rewarding African blacks with free passage into white countries would encourage more blacks to attempt to come to Israel, in the hope of being shipped thereafter into a white country where they can get free everything at the expense of white taxpayers.

While the Jews do want to saturate white countries with non-whites, they prefer that Israel not be a part of the pipeline. So, although you can bet that the Israeli government still plans to rid their country of blacks eventually, the execution of the policy is currently in abeyance.

By the way, it might be of interest that Benjamin Netanyahu referred to blacks in Israel as "infiltrators." Not migrants. Not immigrants. But infiltrators.

EDIT: My most recent information indicates that the latest Israeli plan is similar to the original plan: round up all the blacks in Israel and pack them off to Rwanda, regardless of which African country each of the blacks calls home. Rwanda withdrew from a previous agreement with Israel to absorb blacks who were forcibly deported from Israel. Benjamin Netanyahu is trying to negotiate a new deal with Rwanda so that the forced deportation of blacks from Israel can continue.


The Israeli Minister of Culture and Sports is Miri Regev, who once infamously referred to the migrants as a "cancer." Regev said while accompanying Netanyahu that "the [Jewish] residents of south Tel Aviv are the ones who became refugees in their own country."

Sound familiar? I'm sure that it does to whites who are still living in Oslo, Stockholm, London, Berlin... Atlanta, Baltimore, Chicago, or Detroit.

A difference between Jews and whites is that Jews are hypocrites about their racism. That is, Jews have the attitude that it isn't racism when they do it. So without the slightest fear of penalty being imposed by some overlord, official or nebulous, Netanyahu and the rest of the Jewish cabal running Israel freely make racist comments about blacks and openly present their plans for getting rid of blacks.


Here's more information from The Jewish Press.


Why do white liberals speak for black people?

Because the liberal whites are better-spoken, meaning they have superior language skills, as compared with the blacks themselves. And the liberal whites are cleverer liars than the blacks are. That’s not to say that blacks aren’t frequently liars. But blacks aren’t especially skilled in making their deceptions convincing.

Blacks make mistakes when they lie, and then they have to resort to intimidation, violence, and dogged persistence and repetition (chanting in large numbers) while pretending that their views aren’t internally contradictory, when, indeed, they are.

White liberals, full of sympathy toward blacks' ineptitude in creating their own falsehoods, are often willing to lend them a hand by offering them, and by telling on their behalf, a wonderfully well-crafted set of monumental lies sure to win the hearts of dishonest media pundits and corrupt judges.

Of course, some blacks might consider this unasked-for aid to be patronizing, and I can certainly understand their point of view. But liberals are liberals, and treating their inferiors with hypocritical condescension while at the same time falsely assuring them that they are “just as good as anybody else” is what liberals do.

Once again: governmental corruption in Charlottesville sends another white man to prison
Jenab6
jenab6
Alex Michael Ramos and Jacob Scott Goodwin were defending and/or avenging Howard Ray Crews, after Corey Long and Deandre Harris combined to assault him and try to steal/damage his flag.

Corey Long approached Howard Crews from behind, grabbed the flag pole with his left hand, and held it pinned against his left hip. Howard Crews did not have control over the top end of the flag pole. At no time was the flag pole poking into Corey Long's torso.

Deandre Harris was close enough to the two who were struggling for possession of the flag to see that the top end of the flag pole was being held in Long's left hand alongside Long's hip and was not a threat to Long. Deandre Harris was not running to Corey Long's defense; he was joining Long's attack on Howard Crews.

When Deandre Harris swung his heavy black flashlight, he was aiming for Howard Crews' head. He was not aiming for the flag pole, as he claims. You can see, in one of the frames in the video, an arc of reflected sunlight from the Maglite lamp end. Follow the curve, and you find Crews' head in its path. The flag pole, on the other hand, was about two feet out of reach of Harris' flashlight.

Deandre Harris' lawyer told several lies about what happened, including a lie about Harris aiming for the flag pole and another lie about Howard Crews' wound on his left cheek being the result of another blow at a different time. It is true that Howard Crews was again attacked by a white AntiFa member who hit him on the back of his head with a club, but this isn't the blow that caused the wound on Crews' left cheek — that injury was put there by Deandre Harris.

We are watching, in the courts of Charlottesville, a continuation of governmental malfeasance, motivated by leftist racial politics. Judges must be presumed careful observers of evidence videos. Therefore, it isn't likely that Judge Robert H. Downer's false description of what the video shows is the result of careless examination, but instead is the result of an intentional abuse of his office.

In Downer's court, we have seen a train of biased decisions: the decision to reduce Harris' assault on Crews from a felony to a misdemeanor, and then Downer's subsequent acquittal of Harris on that misdemeanor charge, followed by the felony convictions of two white men who came to the defense of the embattled Howard Crews. In Ramos' case, undue importance was given to the fact that Ramos was not the first to react to Harris, but arrived a few seconds behind Howard Crews' quicker defenders.

Jacob Scott Goodwin wrongly convicted; Deandre Harris wrongly acquitted.
Jenab6
jenab6
Racial politics. Judicial corruption.

Video evidence from the Charlottesville incident has proved that

1. Corey Long and Deandre Harris assaulted Howard Ray Crews. It wasn't the other way around.

2. Jacob Scott Goodwin was defending (or avenging) Howard Ray Crews from an attack by Corey Long and Deandre Harris.

The videos show that Corey Long approached Howard Crews from behind and grabbed Crews' flag pole.

The videos show that Crews never used the flag pole to threaten Long, but merely tried to recover possession of his property.

The videos show that the end of the flag pole is never pointed at Long's torso, as alleged by Deandre Harris' lawyer, but is held by Long's left hand alongside Long's left hip.

The videos show that Corey Long hauled Howard Crews toward Deandre Harris by pulling on the flag pole.

The videos make it clear, by the arc of reflected sunlight from the flashlight swung by Deandre Harris, that the flashlight did hit Howard Crews on his left cheek. The flashlight did not hit the flag pole, which was far out of Harris' reach.

The lawyer for Deandre Harris told a bunch of lies to the court, and he got away with it. The jury in Jacob Scott Goodwin's trial either did not examine the video evidence, or they did and then disregarded what they saw. Lies won the day, both times.

The best summary opinion regarding Jacob Scott Goodwin's wrongful conviction and Deandre Harris' wrongful acquittal can be found at Occidental Dissent. Social justice is frequently in conflict with plain old justice. Charlottesville's public institutions are, evidently, rotten with leftist political corruption, just like the mainstream media.

Deandre Harris is a thug who is indeed guilty, in the sense that he actually did commit the act of which he was accused. Jacob Scott Goodwin is a political prisoner, incarcerated for defending an old white man who came under attack because some blacks didn't like the color of the flag he was holding.

What the malicious liars in the mainstream media failed to do to George Zimmerman in 2012, they succeeded in doing to Jacob Scott Goodwin in 2018.

References.

DeAndre Harris Admits Charlottesville Assault As Reported In August By @NYTimes

Conclusive evidence that DeAndre Harris ATTACKED protesters

Deandre Harris, the Flashlight, and GoFundMe Refunds?

Warrant for black male beaten in C'ville

Deandre Harris charged

?

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