Spare Me Your Pseudo-Moral Outrage, Ted Olson!

I had to laugh heartily when I spotted former Solicitor General Ted Olson's polemic ('A Disgraceful Process') in the latest issue of TIME Oct. 1, p. 27).  First it helps to jog readers' memories on just who this asshole is, in case they forgot.   He was the chief lawyer for the Dumbya side in the now historic case of Bush v. Gore in 2000.   This was yet another case of the archaic Electoral College playing a major role in grabbing a presidency for a Repuke - in this case George Bush Jr.  But maybe the bigger picture - as spelled out by Vince Bugliosi in his book, 'The Betrayal of America'-  was how the then Supreme Court basically chose the president.

As Bugliosi writes (p. 41,  Chapter: 'None Dare Call It Treason'):

"In the December 12 ruling by the Supreme Court handing the election to George Bush, the Court committed the unpardonable sin of being a knowing surrogate for the Republican Party instead of being an impartial arbiter of the law."

As an accomplice to this perfidy we find one Ted Olson, taking the side for BushCo.  Now this villain of the piece (an accomplice to "treason" by Bugliosi's reckoning), wants us to get all worked up over the terrible deed being perpetrated on Brett Kavanaugh. Olson writes to start:

"HOW LOW WE HAVE SUNK. the DEMOCRATS have demanded an FBI investigation into an alleged drunken assault from 36 years ago, between teenagers, at a party in a private home."

How low have we sunk? Before you go into that, you'd do well to ask that question of Sen. Mitch McConnell who happily kept Obama's SC pick (Merrick Garland)  on ice for the better part of a year, to deny ANY process. And now Olson has the nerve to insist on Kumbaya - and Kavanaugh confirmed with zero impediments?  Note also Olson's parlance: "an alleged drunken assault ....between teenagers"  thereby cynically conflating victim (Dr. Ford) with alleged perp (Kavanaugh)..

And then, predictably, Olson trots out the usual canned attacks perfected by the Reepos:

"The accuser doesn't remember exactly when the offense took place or exactly how she got to the house. And she allowed her name to be publicly associated with the accusation only after the completion of a two month investigation into its subject, Judge Brett Kavanaugh, by the U.S. Sente Judiciary Committee and two days of questioning by 18 senators."

Ok, back up here a bit. The "investigations" were bogus because they were partisan and that is why Dr. Ford called for the FBI investigation (something done as a matter of course, especially if new information comes to light).  It was clear Christine Ford didn't trust the bullies and buffoons of the Senate GOP to do any proper investigation, and by the end of the two months that was obvious. Hell, the pair of  elderly GOP Senate Judiciary Bozos  - Chuck Grassley and Orrin Hatch- didn't even pick up on Kavanaugh's assorted lies.  So why the hell would Dr. Ford feel any confidence in the process up that point?   Yes, Olson mentions the FBI did its own investigation too, but now he disallows a further one that new information from Dr. Ford has some to light.

As for as the bit about not being clear on details, anyone who's taken a Psychology 101 course knows this is standard for a sexual trauma survivor.  Nearly all specific details are lost in a protective "limbo" (the victim is protected by her mind's own impaired memory from re-living them, as my newly minted Ph.D. (in Psychology) niece Shayl has made clear.).  As Dr. Shayl also added: "It's incredible to me Olson wouldn't know that as he appears not to be a stupid man. And yet he writes with full -on steroids stupidity"

He also whines a lot, emulating other Reepo whiny bitches, e.g.

"Today's confirmation proceedings are characterized by acrimony, political grandstanding, nasty charges, protests, mischaracterizations and quite possibly defamatory innuendo."


So what did you expect? That for a guy specially selected by the nation's number one admitted pussy grabber, things would be all sweetness, light and decorum? Hardly! Given the polarization of the nation and a budding tyrant and traitor left with no checks on his own behavior we have already entered the era of constitutional crisis and political warfare. Only a rank imbecile or naive fool would fail to see that, and Michael Moore's new film makes that clear. (See my review two posts earlier).

The beginning of the last paragraph of Olson's petulant screed is almost laughable given how he summarily dismisses the fact the same Dr. Ford has been mercilessly bombarded by hate emails, death threats, and hacking (impersonating her online) from deranged Trump cultists.  This has forced her and her family from their home and even forced them to hire security.  WHY,  Mr. Olson, would any woman bring that upon herself and her family just for a lark, or made up story?

Anyway, Olson scribbles:

"It is surprising that anyone of the character, integrity and standing required of our highest court would allow their names to be submitted for such deplorable treatment."

Yeah well, maybe - like Kavanaugh - they believed they could get away with their crimes and attempted rapes. Want me to believe your boy is all in the clear and the model of morality being portrayed? Then let him take a lie detector test like Christine Ford did, and also allow and actively encourage the further FBI investigation.

Unless, of course, he has something to hide!  We now know, for example, that Kavanaugh's sexual misconduct continued beyond high school to Yale where a Colorado woman - Deborah Ramirez - has now accused Trump's fellow pussy grabber of gross, indecent exposure.  E.g.

Senate Democrats Investigate a New Allegation of Sexual Misconduct ...

Then, there's also been the titanic response (720,000 tweets on  #WhyIDidn'tReport) to Dotard's tone deaf questioning of Dr. Christine Ford, i.e. in not reporting Kavanaugh's attempted sexual assault earlier.

Let's get it clear that the deprivation of Kavanaugh’s life or liberty is not at stake, but rather the privilege to hold one of the most important positions in the nation, for which good character and fair treatment of others is necessary.   We may be able to excuse the fact this guy was nominated by the nation's number one serial sexual assaulter, but we cannot have his confirmation if there's even a whiff of  extreme sexual impropriety, as there appears to be.

It's time that Ted Olson and his fellow moralizing  hypocrites wake up, and stop treating the victims of Kavanaugh's assaults and misconduct as the perps wreaking "disgrace" on the SC confirmation process.


See also

http://smirkingchimp.com/thread/john-grant/81230/awesome-uncontrollable-male-passion-meets-its-match

And:

Alex Henderson

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Republicans

These 5 Far-Right Republicans Just Proved They Don’t Take Sexual Assault Seriously

Selected Questions- Answers From All Experts Astronomy Forum (Design of the Celestial Sphere)

Question: I've been learning  about the celestial sphere lately and wonder how it was originally designed? What exact considerations led to the form it has including the coordinates of Right Ascension and declination? - Curious in Michigan

Answer:  The celestial sphere, probably since antiquity, has been perceived as a sphere of infinite radius, only half of which we can see at any one time.  (The other half on the opposite side of Earth). Using it to fix on the distant stars, it also appears to be rotating in an east-west direction.  Basically, it is a result of projecting the Earth's own latitude and longitude lines - as well as the Earth's north and south poles - onto the sky,  thereby yielding a corresponding sphere in the sky which has its own coordinate system. This can then be used to locate sky objects presumed to be on its interior surface.


The projected coordinates corresponding to latitude circles are called declination, and those corresponding to longitude are called Right Ascension.  Given this, the "celestial equator"  would simply be the Earth's own equator (latitude 0 degrees) projected onto the sky sphere, while the North Celestial Pole is the projection of the Earth's north pole and the South Celestial Pole is the projection of the south pole.   These projections are shown on the accompanying diagram.

In effect, the "design" of the celestial sphere is such that if one were travel to one of the Earth's geographical poles, the corresponding celestial pole would be directly overhead (at the zenith).  If one were to travel to Earth's equator, the celestial equator would pass directly through your zenith.

Declination circles, like latitude circles, run in the east-west direction parallel to the celestial equator, starting at 0 degrees and increasing to +90 degrees (North celestial pole or NCP). Also decreasing in the opposite direction to (-90) degrees, or the South celestial pole. When one superimposes these lines one would envisage this more complete celestial coordinate system:



The other celestial sphere coordinate, Right Ascension,  corresponds to Earth longitude. Both longitude and Right Ascension circles run from pole to pole.   However, the 'prime meridians' are different. For Earth, the prime meridian of longitude is the same as the Greenwich meridian defined as 0 degrees. All longitude circles to the west, e.g. Barbados at 60 degrees W., are designated such that times are earlier than a calibrated clock reads at Greenwich.  All longitude circles to the east are designated as having later times than at Greenwich.

By contrast, for Right Ascension we need to use a specific abstract point in the sky, called the Vernal Equinox, to mark the meridian of origin.  This is the point at which the Sun - on its journey north (seen as a projection via the ecliptic on the celestial sphere) crosses the celestial equator. This is visible in the second diagram, where you will see the reddish line for the ecliptic (which is the projection of the Sun's apparent path onto the celestial sphere).  Bear in mind here, the Sun is not really moving across the sky.  It is only the appearance of such because the Earth is really doing the moving, i.e. orbiting about the Sun.  Hence, in a real sense, the ecliptic is the projection of Earth's own orbital motion onto the celestial sphere, but which is embodied in the Sun's apparent path.

The point called the Vernal Equinox -  as can be seen in the diagram - occurs on or about March 21 each year.  Now, the celestial circle of longitude which passes through the Vernal Equinox is defined as 0 hours Right Ascension.    Note here that Right Ascension is measured in hours and minutes (60 minutes being  equal to one hour), and increases numerically eastwards from the Vernal Equinox This would be continuously (unlike Earth longitude - which divides into E. and W. ) from 0h through 24 h.

Using the design conventions given here any astronomical object, planet, star, star cluster, etc. can be pinpointed by coordinates in the night sky.

FAHRENHEIT 11/9 - A Film Every (sentient) Citizen Needs To See

Let me say I was glad to read John Anderson's bogus, distorted WSJ review of Michael Moore's new film  'Fahrenheit 11/9' before going to see it with wifey earlier today.  Reading Anderson's claptrap before  actually seeing the movie on the big screen showed me in retrospect the WSJ clown didn't know WTF he was talking about. Indeed, I was led to conclude the author didn't actually see it but instead resorted to canned fishwrap the WSJ likely had on hand for previous Moore films - with a few tweaks and updates added.

But both Janice and I agreed, that contrary to Anderson's balderdash, i.e. that Moore "hasn't made an honest film since 'Bowling for Columbine (2002)'", this latest effort rings  with veracity in every scene, every segment.   To first set the stage here, the title derives from the fact Trump was appointed president at 2:29 a.m. on November 9, 2016.  Hence, "11/9"  The opening scenes show (in juxtaposition) the Hillary party in Philly - expectantly awaiting the confirmation of history (first female president) counterpoised with the initially dour atmosphere at the Trump camp - accompanied to the opening music from the 1976  film  'The Omen'.

As November 8th transits into the wee hours of November 9th, the real horror story begins  This is as first Ohio, then Florida fall to Trump, followed by Pennsylvania, Wisconsin and Michigan -  and we see the scenes from Hillary's would be victory party now looking like a wake. Oh, and all her supporters' stricken faces appearing as if Satan himself had incarnated in their midst, as we behold in the reactions:  sobbing, convulsions, screaming...it's all there. For Janice, this was the most difficult part to watch.

The story then burrows into the particulars of the assorted horrors to which we've now been exposed, especially leading up to Trump's coronation.   From the unholy depiction of infamous Michigan criminal governor Rick Snyder (a Trump wannabe billionaire) - who brought on a "slow rolling ethnic cleansing" of Flint, MI -  e.g. by cutting off its water supply to Lake Huron and replacing it with the toxic Flint River (leading to thousands of cases of lead poisoning), to Obama himself actually showing up in Flint to sip its toxic water in a PR gag . That actually provided cover for Snyder, and left a hall full of African -American Flint citizens appalled.  That faux pas also tamped down any 2016 election response from Flint's minority voters - likely helping to toss the industrial Midwest state to Dotard.

Then there were the scenes of Flint subjected to a live fire exercise, with the Dept. of Defense using abandoned ramshackle bldgs. (in minority neighborhoods)  to unleash  bombs and mortars to practice "urban warfare".   A sad and sorry decision sanctioned by good ol' President Obama.  The scenes at the Dem Convention were also enraging as well as illuminating as we beheld each state, VT, RI, WVa, etc, respond to the delegate roll calls by shouting out false delegate totals, i.e. for Hillary, when Bernie actually took the states. Wonder why so many Bernie supporters never bothered to show up to vote, there you have it after that charade.

Moore also features segment after segment showing NY Times headlines pumping and humping for centrist or capitalist positions, including inveighing against "socialists".  None of the Times clips Moore interjects were fake or touched up.   Yes, The Times has been more out in the open with its criticisms of Trump now, but not always. (And they even botched it up again with a half -baked story misrepresenting a Rod Rosenstein sarcastic jab -  to Andy McCabe of the FBI -   re: putting on a wire, i.e. to get Trump using the 25th amendment.  All the Times butthead reporters did is provide ammo for Mueller's enemies and give Dotard a bogus excuse to fire Rosenstein.  Press like that we don't need, if they can't discriminate the sarcastic from the real!  N.B. The Times reporters who broke this malarkey also admitted tonight the sources they relied on weren't even in the meeting where Rosenstein reportedly made that remark.)

That is the other underpinning theme of Moore's film, the degree to which the corporate media - especially the electronic voices of CNN, NBC,  ABC, CBS had all been in bed with Trump from day one.  All the outlets saw a classic   way to keep viewers' eyeballs glued to their broadcasts while they're ratings soared and they raked in money. As former CBS head Les Moonves was heard saying: "This may not be good for the country but it's great for CBS!"  Yeppers,  profits over country.

The effect, as Moore shows, was to give Trump a gazillion hours of free advertising and air time, that helped his campaign immensely. How could it not?  At one point in the film, perhaps one of the more disgusting in the media segment, we see the gathered network lapdogs and cameras all surrounding an empty stage set for a Trump appearance, salivating with bated breath while Dotard keeps them waiting for more than a half hour.  The people's voices and protective "fourth estate"? More like trained dogs, so when Trump barks 'Jump!' they asked 'How high?'

Of course, as with other Michael Moore films, some levity was interjected at specific points, usually when the viewer is almost too distressed with Trump World's antics. One such example is after Moore tries to make a citizen's arrest of Michigan's governor Rick Snyder - but ultimately has to be satisfied with spraying his property using Flint river water,


Now, let's look at some of John Anderson's complaints.

- "One of the chief plaints of 11/  9  - in which he trashes Barack Obama, Hillary Clinton, The New York Times.  the entire Democratic establishment - is about the media's slavish attention to Mr. Trump in a movie devoted to Mr. Trump"

But see, the movie was not "devoted to Trump" but rather foursquare devoted to exposing all the ways our system broke down to pave the way for his bogus selection (by the Electoral college, see     .e. g.

• Had The Electoral College Done Its Job The "Anonym...

So, from Obama's Flint MI hijinks, fake drinking its river water, and ordering a live fire exercise on Flint abandoned buildings, to HRC keeping a low profile in key Midwest states (WI, MI), to the D-establishment rigging the game against Bernie using the superdelegate system (and even more recently Dem centrist Steny Hoyer telling a young Colorado candidate from the 6th congressional district to get with the program) we see none of Anderson's "plaints" have a leg to stand on.

The last complaint about the media's slavish attention to Trump when Moore's film is about him is particularly enraging, given it conflates two separate elements: The media's genuinely giving Trump millions of hours of free air time during the 2016 election, vs. Moore making a single 125 minute film - of which maybe 20 mins. at most treats Trump's antics - but in a negative way, to inspire citizen response. That is why I refer to the film as an anthem to action, for progressives to get off of their butts and VOTE November 6th.  Moore's basic message  is simple: Don't "hope" for Mueller, or the press or (name your hero) to save us amidst the Trump nightmare. Get off your butts and do your part going to the polls this  November!)

- "There's more than a little bait and switch going on in Fahrenheit 11/9 and it raises the question of exactly what Mr. Moore is, other than a propagandist. He's not a journalist except of the aggregator variety."

But aggregators are critically important because they deliver point of view and a needed perspective. In this case of how our country is being adversely affected in multifold ways  The aggregator then in many ways is like the scientific researcher, say in solar physics preparing a paper on solar flare formation-  who first provides an array of  historical background snippets and examples.  These then pave the way to showing the value of the current work,  say offering a flare model based on current sheets, while also delivering an overall perspective of the flare phenomenon.

In the same way, Moore's collection of scenes - from the Snyder "emergency plan"  takeover of the Michigan cities of Pontiac. Detroit, Flint  and Benton Harbor, to the Flint water debacle itself, to the media's slavish treatment and use of Trump for ratings, to the striking teachers of West Virginia, and the Parkland school tragedy and kids response- all weave toward a coherent whole, a point of view that helps us understand what's going on in this country. 

If one looks at similar other efforts by aggregators, e.g. Josh Fox's 'Gasland II',   e.g.

Brane Space: Gasland II - Fracking is Worse Than You Think

One sees that the same method applies. To save time, and not have a 1,000 hour documentary, one selects the most meaningful examples and stitches them together in a coherent whole to forge a viewpoint.   The name for such a person who does this sort of thing then, whether Josh Fox or Michael Moore, is a documentarian.

- "Almost the entire movie is lifted from other sources, and then edited in a way that makes his enemies look as foolish as possible."

This complaint is really, truly imbecilic, because what he describes - at least in terms of using other sources- is exactly what the aggregator Documentary maker does!   It's what Josh Fox did too in 'Gasland' and 'Gasland II'.   So one wonders what planet Anderson inhabits.  As for the editing, there isn't a damned thing wrong with it, having myself seen many of the same scenes, e.g. of the lead catastrophe and brown water in Flint, on the nightly news.  Did Moore have the prescience to put the scenes together in a cogent way? Yes, of course! So what?  That is what he's there to do in order to underscore the account and provide a coherent theme for the movie, i.e. that we are in fire alarm mode with Trump's residency.  Besides, as Anderson then finally admits: "It's not as if Moore has no leg to stand on. ..his was the most prominent liberal voice warning of Mr. Trump's appeal to Midwest voters."

Jeez, on behalf of Mike, thanks for small favors, you blockhead!

And as if to support my contention he's a blockhead:

"And if Moore is going to castigate Mrs. Clinton for her various electoral missteps - shouldn't he mention that despite losing the Electoral College she won the popular vote."

He DID mention it, you fucking dolt! In fact,  he devoted a whole 6 minute segment to it.   This featured the "baby coffins" full of the states' electoral votes being carted in for final verification and counting with Moore's voice over noting "and that should be the end of this"  and "the one who gets the most votes  (Hillary) should be the one elected president"  - as is done in every other democratic nation, He also points out that the EC is a carryover from the "slave master" days.  He leaves little doubt that because of this asinine anachronism the Dems have seen presidential hopes crushed at east twice (including in the Bush v. Gore farce in FLA in 2000).

The most sensational  (and powerful)  tour de force is near the end showing Hitler in one of his many rants but mouthing Trump's own words, directed to his idiot base.  There is also a segment of the last days of the Weimar Republic before Hitler brought it down,  alternating with images of what's happening today, i.e. in separating the children of immigrants.  We also see Hitler using many of the same mass mind appeal techniques Trump is employing now   Pay special attention to the interview with Ben Ferencz - a Chief Prosecutor for the Nuremberg Trials- and the fears raised now, especially in the Trump separation of children from immigrant parents which holds eerie similarities to how the Nazis did the same in their concentration camps.

Anderson - providing more evidence he never actually saw the film (or at least the whole film) also kvetches about the "casual reduction of Trumpites to Nazis."   But  Moore does no such thing. What he does is use a graphic showing the progression (regression?)  of putative democracy to despotism and how Trump hits every marker on it just as Hitler did, beginning with the lack of respect for minorities and outgroups like Muslims.  (The presentation features interspersed clips of assorted white Americans attacking black people in different venues, such as on golf courses and on buses) Also extending to vilification of the press and reporters as well as attacking the judiciary.  The very sort of things Hitler did leading to the Reich laws.   So the analogizing of Trump to Hitler is not off the mark at all.

Incredibly, Anderson also bitches about Moore's choice of a film poster,  e.g. "the poster for the film is a highly unflattering shot of the president's rear end, midswing at  golf course."  So WTF?  You want Moore to be dishonest and touch it up or photo shop it, fake news style? If you have a beef with the poster tell Fatty Arbuckle Jr. to lose a few pounds. (Oh, and maybe spend less time golfing at his properties!)

The most idiotic comment of Anderson's I saved for last, writing of Michael Moore:

"Some might even say he's the left's version of Donald Trump."

No, see uh... Michael Moore has a functioning brain!

The very fact a paid hack like John Anderson couldn't handle this film is reason enough to see it.  But in terms of content and insights (some of which not even Janice was aware of) any citizen who misses it will regret it, especially in the run up to the midterms.

Yes, The GOP And Trump Want To Give Even Bigger Tax Cuts To The Already Rich

It seems clear with every move they make the GOOPs are determined to toss this country into history's dumpster, certainly financially - as well as in their protection of Traitor Trump. But it is the first that concerns us here.  Namely the news,
House Republicans Move to Extend Individuals' Tax Cuts - WSJ

The feckless GOP plans are now to extend the existing Trump tax cuts, despite massively growing  deficits .  Clearly these poltroons believe that at least making a show for an extension will win them the hearts and minds of their GOP base- who will then turn out in greater numbers for the midterms. But I have news for them: that base doesn't care one way or other, they are already complacent with the crumbs they've received and will not turn out like the Dems.

Meanwhile we learn (ibid.):

"On top of last year's $1.5 trillion tax cut, the new proposal would reduce federal revenue by $613 billion over the next decade, according to the nonpartisan Joint Committee on Taxation. Most of that cost is packed into the end of the  next decade and the cost beyond that would be much higher."

And bear in mind, that means your kids and grand kids will be paying the freight - mainly to support the lifestyles of the rich, the famous and the corporate - since they will reap the greatest rewards by the extension as they have the 2017 cuts. (Politifact has found that median income families received only about 6.6 percent of the $1.5 trillion tax cut, while 93.4% went to the corporations and top earners.)

In the words of Lloyd Bloggett, a Texas Dem quoted in the above piece:

"We have something that is truly disastrous headed our way and it's not just a hurricane."

What is it?  How bad? In a separate piece in the same issue ('Deficit Widens On More Spending'), we learn:

"The U.S.  federal deficit nearly doubled in August from a year ago, as government spending swelled and revenues decline".

And again, let us make note here the GOP's planned tax cut extension will starve revenues even more.

We also learn:

"The government ran a $214 billion deficit last month, compared with a $107.7 billion budget gap in August, 2017... the Treasury Department said Thursday."

So, even as the great jobs and growth narrative is spreading, we are being undermined by massive deficits, debt.    The biggest revenue -starving culprit?  The ill-advised cut in corporate income taxes.


As we further note (ibid.):

"Corporate income taxes in particular have dropped off. The Treasury said Thursday
gross corporate taxes have fallen 20 percent so far this fiscal year, while indiviudal
tax receipts are up 1 percent"

The loss in corporate tax revenue might  - in a stretch - be worth it - if the bastards paid decent wages to their workers, but as per my previous post, we know this isn't the case.  Worse, because the Congressional Budget Office now projects a total deficit of $793 billion for fiscal year 2018.

The "big picture" of U.S. debt isn't any better, as the CBO notes. As per a WSJ op-ed reveal (Sept. 15-16, p. A15):

"The U.S. owes $21.5 trillion of Treasury debt, the majority of which is scheduled to be refinanced in the next eight years. - disregarding the additional $1 trillion required by the 2017 tax reform and an estimated $100 trillion of unfunded entitlement spending ahead."

Incredibly, three days ago there we beheld one of the biggest tax cuts propagandists (Stephen Moore,  'The Corporate Tax Cut Is Paying For Itself', WSJ, p. A13) scribbling:

"Thanks to the magic of compounding the corporate tax cuts will yield more than $6 trillion in additional GDP over the next decade..."

But seems unable to reckon in that additional GDP growth doesn't translate to revenue growth, i. e. to pare back growing deficits as the CBO forecasts, though he does add:

"Perversely, because the economy is bigger now than expected, the CBO has revised upward  its estimated cost of the tax cut..."

Well, duh, of course they've revised it upward given - as pointed out above - corporate tax revenue has fallen off 20 percent this year, and will continue to fall off each year it's in effect.  In other words, never mind the GDP growth, it will not overtake the loss in revenue growth (including from individual income tax cuts).  But this is the sort of fantasy land we now inhabit where 'up' is down, and 'down is 'up'. Blame a lot of it on the lying landscape imparted by Trump and his pack of maggots,

Folks, let's not  accept bullshit or pretend: we are not swimming in a literal sea of red ink. In this environment the proposal of an extension of tax cuts borders on the derelict and criminal, and those pushing it need to have both their sanity and patriotism questioned.

See also:

Another Tax Scam for the Rich

Special Relativity Revisited (1)

In the popular mind, at least, the word "relativity" usually conjures up visions of space travelers returning youthful to Earth after journeys of many decades (measured on Earth). Of course, there is much more to relativity than this. 

As a matter of fact many aspects of relativity as in the case of motions, aren't new at all. Basically, it merely entails the assertion that the laws of physics appear to be the same in given reference frames or coordinate systems. This is made more accurate in Einstein's special relativity by referring motion to inertial reference frames. That is, non-accelerating frames for which -  if one has a net force. F(net) = 0, one will also have a = 0.

Though Henri Poincare came close to discovering the principles of relativity, it was Albert Einstein first and foremost who ruthlessly and relentlessly pursued the basic principles to their utterly logical conclusions, including that lengths shrink as velocities tend toward the speed of light, c, and time slows or "dilates".  

Like Ernst Mach before him, Einstein adopted the view that in considering two objects in relative motion, it is futile and meaningless to attempt to decide which object is "really" in motion and which is at rest. If you are in a Jumbo jet traveling at a speed of 900 km/hr relative to the Earth, it makes no difference whether someone says you are moving at that speed, or the Earth is moving at that speed. In either case, the operation of the laws of physics in your jet and on the Earth will be the same. Balls will still drop, and you will still fall off your chair if not careful. There exist no absolute frame of reference to contradict you.

The Special Theory of Relativity, interestingly, may be said to have had its origins in the null result of an experiment the primary aim of which was to detect relative motion. This experiment was first carried out by the American physicist Albert A. Michelson in 1881, and subsequently repeated in 1887, with the help of Edward W. Morley. The experiment has thus come to be known as the Michelson-Morely Experiment. 

The basic idea was to time the transits of light in two distinct directions: perpendicular to the Earth's orbital motion, and parallel to the orbital motion. This was to be accomplished by using an arrangement of mirrors and light beams such as depicted in the first  intro frame of the preceding link (hyperlink to name of exp.) A difference in light velocities (transit distance/ time) would reveal itself by a delicate interference pattern formed by two separate beams after rejoining each other. 

The implication of a difference in velocities would mean the confirmation of a remarkable entity called "the Ether". In effect, if light represents waves propagating through the Ether, the velocity of light as recorded by instruments on Earth's surface must be distorted by the motion of the Earth through space. An analogous principle is that a swift river must retard a swimmer's combined upstream and downstream speeds more than his cross-current speed. Similarly, a large difference in light velocities (along the two different paths) should show Earth is moving rapidly through the Ether, while a small difference would show it's moving slowly. 

A difference in time D t was found equivalent to a path difference:  c (D t)/ l (d)

where d = the width of one fringe and  l  is the wavelength of the light (taken to be 6 x 10 ^-7 m). 

From this, the time difference between the two beams could be computed from:

D t = t1 - t2

= 2L/c{ 1/ (1 - v²/c²) - 1/ (1 - v²/c²)^½}

This equation can be approximately expressed as:

D t »  L/c (v²/c²)

Astonishingly, on each occasion the experiment was conducted the result was virtually negative. There was no evidence of any time difference indicating an ether flowing past the Earth in any direction. Any minor deviations fell within the purview of the experimental errors.  

In a last ditch effort to satisfactorily explain the riddle of the null result a fantastic idea was put forward by George F. Fitzgerald in 1890. Using the analogy of a rubber ball which is deformed upon striking a wall, Fitzgerald conceived that the ether would distort matter.

This distortion would take the form of a contraction of length in the direction of the motion through the ether. Such a contraction would explain the null result of the Michelson -Morley experiment. That is, the arm L, of the apparatus, moving against the ether would be shortened by "ether pressure" just enough to compensate for the slowing down of light by the ether wind.

A similar but more mathematical theory was worked out by the physicist Hendrik A. Lorentz, who expressed the length contraction in the direction of motion by:

L' = L[1 - v²/c²]^½

This famous equation became known as the "Lorentz-Fitzgerald contraction".

Understandably, the hypothesis of Lorentz and Fitzgerald gradually gained general acceptance, except for a Swiss Patent clerk, who refused to be deluded by such a contrived idea (based as it was on absolute motion). The clerk's name was Albert Einstein, born in Ulm, Bavaria, in 1879.

Einstein had graduated as a physics major, but he managed to produce such a poor impression as a teacher that he was dismissed from three teaching jobs in succession. Having been reduced to a 'hand-to-mouth' existence, he was lucky to find a job processing patent applications in Bern, Switzerland. Fortunately, he also has a leisurely schedule that permitted him to while away a good many hours contemplating space, time and energy. (A good thing his time was nearly a century ago, otherwise - today- he'd be accused of "gold bricking"!)

After much thought, Einstein was forced to conclude that motion is never observable as motion with respect to space and that there is no basis for the introduction of "absolute motion". In Einstein's mind, the only kind of motion was relative rest perceived from different viewpoints (e.g. "reference frames"). Einstein called this insight the Principle of Relativity. According to Einstein's Principle of Relativity: "All the laws of physics are the same in all inertial reference frames."

It's instructive at this point to commence a quantitative approach to see exactly how Einstein reasoned. This necessitates we first get accustomed to the idea of a coordinate system. Basically, the purpose of any coordinate system is to enable us to identify a particular point in space. The standard procedure (for 3-dimensional space) is to take three mutually perpendicular axes with coordinates in x, y and z, representing distanced to where the axes meet at the origin, or 0. In special relativity such coordinate systems are typically designated: S, S', S" etc. or alternatively, S1, S2, S3.

In Fig. 1 we have two coordinate systems, S and S', with S having coordinate x, y and S' having coordinates x', y'. (We confine the systems to 2 dimensions here for initial simplicity.) Thus, S' has its origin at 0' and S at 0. In the figure, S' is shown moving with constant velocity v in the x - x' direction (which obviously coincide for S and S').

Keep in mind though we arbitrarily assigned S' as moving this depends on which coordinate system is taken to be at rest. An observer attached to system S may very well consider himself moving and S' stationary. This would resemble the well-known example of a passenger in a stationary train observing a train parallel to his through his window and deducing he is moving, though it is actually the train parallel to his. The key point is that the systems S and S' have a constant relative velocity. Such coordinate systems occupy a special place in relativity and are called "inertial reference frames" or "inertial coordinate systems". Their primary feature is that they lack and acceleration of one to the other.

Now, think about this carefully: if the origins O and O' coincide at time t = 0, and we are observers in S', then we will see 0' move along OX with velocity v. Then the two sets of coordinates, representing the same point (in S and S') are related by:

x' = x - vt and y' = y

If we chose we could append a 3rd axes (z) i.e. coming out of the page, and have also:

z' = z

The preceding equations describe the "Galilean transformation". From these it is very easy to obtain velocities, and we need only differentiate with respect to t:

E.g.

dx'/dt = dx/dt = v

dy'/dt = dy/dt

dz'/dt = dz/dt

(Note here that never once did we write t' = t since the notion of an absolute, universal time was the very cornerstone of Newtonian theory!)

We now start with the preceding transformations and see how Einstein reasoned. Reference may be made to Fig. 2 which displays a three-dimensional perspective of the relative motion and hence is a bit more complicated. Our aim in using it is to find an alternative to the Galilean transformations - which obviously can't be correct for all situations.

For example, according to the Galilean transformations, a pulse o flight sent out from S' would move with the velocity c, the speed of light, as measured from S', but with the velocity (c + v) measured from S. But this directly contradicts the demopnstrated fact (Michelson-Morley) that the speed of light is always constant when computed from one reference frame relative to another.

Einstein thus began afresh by using not only the Principle of Relativity (just stated, i.e. the laws of physics are the same in all inertial reference frames)) but also:

The speed of light is always found to have the same value no matter what the motion for the source or the observer.

From these two postulates, Einstein deduced a number of surprising results which would have been totally unacceptable to a more conservative mind.

Start then with the two systems depicted in Fig. 2 which are coincident in space at at the instant a flash bulb (say) is set off when the origins coincide. The observer S sees S' moving in the x-direction with the velocity v and observer S' sees S moving with the same velocity in the opposite (-x) direction.

Both observers see the flash of light travel away from the origin with the same velocity c. The distance the light travels in the S system during time t, is ct. This must be true in any direction. If the light spreads out equally in all directions, then by the end of time t it has extended to fill a sphere whose radius is r, and we can write:

(1) r² = x² + y² + z² =  c² t²

The exact same equation holds in the S' system since the flash was set off when O coincided with O. Thus, while the 2 systems are separating from each other, the observer in S' also sees the light fill a spherical shell in his own system, so writes (for r'):

(2) r’² = x’² + y’² + z’² = c² t’²

Note the velocity of light is the only thing that's the same in both systems. The two preceding equations thus describe a point lying on the spherical shell. Even though they describe the same point in space, the observer in S sees the point at position (x, y,z, t) and the observer S' at position (x', y', z', t').


Subtracting equation (2) from equation (1) and transposing terms:

x² + y² + z² -  c² t²  = x’² + y’² + z’² - c² t’²

We now look for a transformation similar to the Galilean transformation, but which will allow c to be the same in both S and S'. Since the y and z coordinates of the position are not affected by the motion in the x-direction we can say y' = y and z' = z. For the x-coordinate, we try a transformation of the form: x = a(x' + vt') and x = a(x - vt), where a is an invariant determined by the two fundamental postulates (i.e. the same quantity is used in going from x to x' as from x' to x).

Further, we expect a to depend on the velocity v in such a way that it becomes equal to 1 when v becomes very small compared with the speed of light. When this happens, the x and x' transformations become the same as the ordinary Galilean transformations.

So we begin by using x = a(x' + vt') to solve for t' and obtain:

(3) t' = 1/v (x/a - x')

For x' above, we now insert the value for x' (e.g. x' = a(x- vt)):

(4) t' = 1/v(x/a - ax - avt) = at - x²(a² -1)/ va 

Similarly, we find for t:

(5) t = -at' + x'(a² - 1)/ va 


If we now substitute x' = a(x - vt) and equation (4) into the right hand side of equation (2), we obtain:

(6) x² + y² + z² -  c² t²  = a²(x - vt)² + y² + z²

=   c²[at - x/v (a² - 1)²/a] 

Now, re-arrange terms and cancel the z and y terms, which are the same on both sides of the equation, to get:

(7) x² -  c² t²  = [a² - (a² - 1)c²/ a²v²]x²

+  2[(a² - 1)c²/v² - a²] xvt - (c² - v²)a²t² 

If the preceding is to hold true for any value of x and t, each term on the left side must equal each term on the right. Since there are no terms with the combination xt on the left, the xt term on the right must be zero. This means:

(8) (a² - 1)c²/ v² - a² = 0 

Solving for a:

(9) a² = 1/ (1 - v²/c²) and a = [1/ (1 - v²/c²)]^½

Finally:


(10) (a² - 1)/a = v²/c²/ [1/ (1 - v²/c²)]^½

Substituting the preceding into our x, x' transformation equations and equation (3), we arrive at the following transformations to replace the Galilean:

(11) 

x = x' + vt'/(1 - v²/c²)]^½
and


x' = x - vt/  (1 - v²/c²)]^½


(12) y = y' and y' = y

(13) z = z' and z' = z


(14) t = t' + x’v/c²/[(1 - v²/c²)]^½  

and


t' = t - xv/c²/[(1 - v²/c²)]^½  

Equations (11)- (14) are known as the Lorentz transformation or the Lorentz-Einstein transformation.

Note the important feature is that the time must be given as well as the position, because the respective clocks in S and S' will cease to read identical times after they have parted from one another. This is the significance of (14) in the above set. Also, the fact that time is given the same importance as space (i.e. as another dimension) shows there's nothing special or mystical about "the fourth dimension".

Comprehension Problems:

1- Given that x' = 1/a (x - vt) and t' = 1/a (t - vx/c²), derive similar equations for x and t in terms of x' and t'.  (Recall: 1/a = (1 - v²/c²)^½)

2- An event in space-time occurs at x' = 60 m, t = 8 x 10^-8 s, in a frame S' (y' = 0, z' = 0). The frame S' has a velocity of 0.6c along the x-direction with respect to a frame S. The origins O and O' coincide at time t = t' = 0. Find the space-time coordinates of the event in S.

3- Suppose an astronaut is traveling at 0.9c in a space ship with respect to the Earth. How long a time interval will his clock indicate when the Earth has revolved once around the Sun? (Take the duration of one standard revolution of Earth around the Sun to be 365 ¼ days.)

 (A book prize goes to the first person who can solve all three correctly - submitting the solutions via the comment section. Good luck!)

Curvature, Arc Length and Parametric Representations of Curves

One of the more important areas of higher mathematics involves finding the arc length of a curve, as well as the curvature.   A number of instructive examples are given in this post for doing so.  A logical place to begin is with the arc length formula (derivations can be found in any good Calculus textbook.  For example,  an element ds (du) of arc on a curve is:

But in derivation terms - treating dx (du1) and dy (du2) as 'legs' of a right triangle:
we can treat ds as the differential of arc length such that.

ds² =  dx² + dy ²

Or:   ds   =   Ö (dx² + dy ² )  =    dx Ö [ 1  +  (dy/dx) ² ]

This can then be integrated (between appropriate limits, say x1 and x2) to give the total length of a curve..   Thence the arc length  is given by:

where the function f(x) defines the curve for which the arc length is evaluated between the points x1 and x2.   For which we have:  f(x)   = y =    [(x)]^½

Consider then finding the arc length between x1 = 2 and x2 = 8, i.e. for the segment of the parabola shown:

 

Then evaluating the integral as shown, one obtains: s =   8.886

A more difficult problem involves a polar curve, i.e. a curve in polar coordinates such as:

This curve has the function:  r(q)  =  q  - sin (q)

And we wish to find its length between q = -p   and q = p .  

The relevant integral for the arc length for this example is:


Performing the integration one then obtains: L  = 8.764

Which interested and energized readers are invited to check!

Parametric Representations:

In advanced treatments of curvature including determining the curvature of a complex curve, parametric representations are the norm. This usually entails taking the tangent T  to the curve at a point.  From this the curvature  k  of the arc can also be computed.  For example, one can give the parametric representation of a specific type of curve using:

x =  6 sin 2 t,  y = 6 cos 2 t, z = 5t

For which the tangent to the curve at a point is given by:

T = dR/ ds =  i(dx/ds) + j(dy/ds) + k(dz/ds)

=

i (dx/dt) (dt/ds) +   j (dy/dt)(dt/ds) + k (dz/dt) (dt/ds)

Then:

dx/dt=  12 cost 2t, dy/dt = -12 sin 2t,  dz/dt = 5

Therefore, the tangent unit vector is:

| T |  =  1 = (dt/ds)² [(12 cost 2t)² + (-12 sin 2t)² + 5²]

|T |  =  1 = (dt/ds)² [(144 + 25)] =   (dt/ds)²  (169)

So that: (dt/ds)   = 1/ 13 

And:  T   = 1/ 13   [12 cost 2t) i + (-12 sin 2t) j + 5 k ] dt/ds

The curvature can then be obtained from: k = | dT/ ds | 

Thus, any curve can be given by a parametric representation:   u1 = u1(t)  and u2=  u2(t)

For such a curve, consider now the distance between two infinitely near points on the surface, i.e. the distance or interval ds between two specified points.

Example problem:

A curve is given in spherical coordinates xⁱ by:

x¹ = t,   x² = arcsin 1/t,    x³ =  (t2 – 1) ^1/2

Compute the length of the arc between t = 1 and t = 2  

Solution:

(ds/ dt)² =    (dx¹/ dt) ²  +  (x¹ ) ²  (dx²/ dt) ²    +   (x¹  sin x  ²) ² (dx³/ dt) ² 

And:

(dx¹/ dt) ²  =   1

(dx²/ dt) ²   = [ -1/  t²   / Ö {1 – (  1/  t²  )} = 1/ t²  (t²  -   1)

  (dx³/ dt) ²    = 2t/ Ö2(t²  -   1) =  t² / (t²  -   1)

Whence:

(ds/ dt)² =     

1 +  t²   · 1/ t²  (t²  -   1) + (t ·  1/  t ) ²   ·  t² / (t²  -   1)

=   2 t² / (t²  -   1)

Then the length of the curve is:

L = ò ₁ ²   Ö2 t/ (t²  -   1)^1/2  dt = Ö2(t²  -   1) ] ₁²      =  Ö6

Problem for Math Mavens:

 For the parametric example with:

 T   = 1/ 13   [12 cost 2t) i + (-12 sin 2t) j + 5 k ] dt/ds,

 Find the curvature and the length of the curve from t = 0 to t = p.