Tuesday, December 31, 2019

Newsflash! 2020 Is NOT The Start Of A "New Decade"

Let's accept as a proposition there are some claims, especially to do with the calendar and astronomy, which are facts and beyond contention, or "polarization".  I bring this up because once again the bugbear over when a decade commences has come into focus with the new year tomorrow. Is the first day of the new year then also the first day of the new decade?  No, it is not, hence you will not catch me saying "Happy New Decade".   But you can be sure the media's scatterbrains will in unison be hailing the "start of a new decade" on the a.m. shows tomorrow. If not before, i.e. at the Big Apple's New Year's eve celebration - broadcast on ABC, NBC..

So it was hilarious when I spotted an NPR  story to the effect "this country is so polarized that people can't even agree on when the next decade begins."  Which is not true, because the issue is not one that is subjective (requiring any opining)  or which can be "polarizing".  Either then one goes by the logic of our calendar or one goes off on an irrational tangent.

The central fact pertinent to the issue is our accepted calendar has no year 'zero'.    The absence of any year '0' means that the only consistent way to measure decades (or centuries, or millennia) is to start or index them in years ending in '1'.   Thus, for reference, the new century did not commence on January 1, 2000 but on January 1, 2001. Similarly the new millenium did not begin on Jan. 1, 2000 but on Jan. 1, 2001.  In like manner, the new decade will not commence until January 1, 2021.  Can you dig it?

A decade then is defined as a ten year interval, with the terminal year ending in '0'.. We can extrapolate the above to bracket the assorted decades of the 20th century. Some examples:

The 1920s spanned from 1921 to 1930.  Ten years, count 'em off on your fingers if you must.

The last date of the 1920s decades then, was December 31, 1930.

Likewise, the 1930s spanned from 1931 to 1940.

The 1950s from 1951 to 1960.

The 1960s from 1961 to 1970.

And so on, so the 2000 -oughts went from 2001 to 2010.

The 2010s from 2011 to 2020.

An analogous case is made by Alan Mcintire  on Quora, focusing on the transition from B.C. (or B.C.E.) to  A.D.  (or C.E.):

"Based on our current calendar, the day after December 31, 1 BC was January 1, 1 AD.  There was no year zero.  Zero was just the point at midnight between 1 BC and 1 AD,

One year AD did not go by until midnight of December 31, 1 AD/Jaauary 1, 2 AD.  Carrying that reasoning forward, 20 centuries AD did not go by until the calendar reached midnight, December 31, 2000 AD/January 1, 2001 AD.  Based on that system, 202 decades will have passed after the BC/AD point at midnight, December 31, 2020/January 1, 2021"

I wrote my own exhaustive skewering of this calendrical counting nonsense in a Baltimore Sun letter, before we left Charm City  for Colorado Springs in December, 2000.  It read as follows:

"It is mind-boggling that in the most technologically advanced nation on Earth people are too innumerate to figure out that the 'new millennium' will not occur until January 1, 2001. All the premature hubbub of the past year has merely been fed to a naive public in order to bolster an impatient media hype and sell newspapers, magazines and other special  'pictorials of the past century' .

Indeed, any first grader able to count on two hands would be able to deduce that ninety-nine times one (year) yields 99 years, not 100. And certainly not a 'century' and not - in context-  a turnover to the 'new millennium'! Since there's no year 'zero',  years commenced with 1. 

That means 1-100 is one (first) century elapsed, and  1901-2000 is the most recent.

All this is apart from historical speculations and specious arguments to do with the year of Christ's birth (which some of us -atheists- do not believe occurred anyway.)  Point is, you either adhere to the existing standard or throw everything out and say 'anything goes'.  In which case we (older folk) can even resort to giving our age in 'Martian years' thereby cutting them in half.

Have we somehow become more stupid and innumerate than our predecessors? Recall they  recognized  that the year 1900 was the last year of the nineteenth century- not the first year of the twentieth? (Cf. The Baltimore  Sun, Editorial, Jan. 1, 1900) :

'The year 1900 enjoys special attention because it is the last year of the nineteenth century.'

 Is this  the extent to which our brains have been hijacked?  That we can no longer even tell what a century is?   When it begins and when it ends? No, I think it is more a case of the power of 'PR' and marketing to convert even basic facts into gibberish . Which reaches a nadir when a breathless network news anchor (like Katie Couric)  sputters this a.m. about twins likely to be born minutes apart over New Year's "being born 'millennia apart'.  So wait, one twin is going to be  a thousand years older than the other?

Where is the truth in  advertising? Where is the truth, period? Or accountability? What will it be next? If some media wonk asserts 2 + 2 = 5, is that going to be adopted? If it is asserted that henceforth all centuries will be measured as 99 years - as seems the case now, is this to be blithely accepted without question?  Is a millennium henceforth going to be reckoned as 999 years, not 1000?   We could as well toss out the whole school curriculum- especially math, and teach kids 'PR' instead. Or  that 'PR always trumps mathematical truths'.

The bottom line is that the whole baloney about 2000 being the first year of the 'new millennium' arises from a counting error that should be evident to a bright kindergartner. For some reason, at the cusp of this particular new century, etc. reason (and numeracy) seem to have been tossed to the four winds. It's so bad that every manjack - just about, now believes this year is the new millennium. And most newspapers, journalists, instead of setting their public right, merely jump on the bandwagon of ignorance.. 

Finally, don't even think of describing anyone who corrects this nonsense as a 'pedant'.  Demanding simple accuracy in math is not the same as pedantry."

I stand by everything I wrote then, in terms now of defining when a new decade begins. It does not begin at midnight but one year from then.

Monday, December 30, 2019

Contour Integrals Revisited

Contour integrals are integrals of complex functions f(z), i.e. of the complex variable z = x + iy. Such integrals are defined in terms of the values of f(z) along a given contour C extending from a point z = z1 to a point,  say, z = z2 in the complex plane.  It is therefore a line integral. This can be written as:

òC  f(z) dz

It may alternatively be written with limits, say from z1 to z2, usually when the value of the integral is independent of the choice of contour taken between the two end points.

Illustration: Suppose that the equation:  z = z(t)  such that (a <  t  < b)  represents a contour C extending from some point z1 = z(a) to a point z2 = z(b). let the function f(z) be piecewise continuous on C. That is, f(z(t))  is piecewise continuous on the interval a <  t  < b. We define the line integral or contour integral of f along C as:

ò f(z) dz   =  ò a b  f[z(t)] z’(t) dz 

Since C is a contour then z’(t), i.e. dz/dt is piecewise continuous on the interval  a <  t  < b so the existence of the integral is assured.

Example (1)

This is by reference to the contour shown on  left side below:
Image result for brane space, Contour integrals

Here C is the right hand half of the circle  êz ê  = 3.8 from z = -3.8i to z = 3.8i. Hence we want to find the integral of:

I = ò C  z z* dz

For which z = 3.8 exp (i q)  (- p/2 <   q  p/2)

Then:    I=  ò p/2 -p/2  (3.8 exp(i q)) (3.8 exp(- i q))  dq 

=  14.44i  
ò p/2 -p/2   dq

= 14.44 (p/2  - (-p/2)) = 14.44i   (p)  =  14.44 pi

Note that for such a point z on the circle êz ê  = 3.8, it follows that zz* = 14.44 or z* = 14.44/z. So that the result  14.44 pi can also be written: I = ò C  dz/ z =  pi

The reference contour is shown in the graphic to the right in preceding diagram, along the path OAB. So  the integral can be solved as follows:

ò C  f(z) dz  =   ò OA  f(z) dz  +    ò AB  f(z) dz  

Where f(z) =  y – x   -i3x2   (z = x + iy)

The segment OA can be represented parametrically as:  

z = 0 + iy (0 < y < 1)

Since x = 0 at all points on that segment the values of f there vary with the parameter y according to the equation: f(z) = y(0 < y < 1)


ò OA  f(z) dz   =     ò 0 1   y idy = i ò 0  y dy = i/2

Meanwhile, on the segment AB, z = x + i(0 < x < 1) so that:

ò AB  f(z) dz   =    =     ò 0 1   (1 – x –i3x2) 1 dx =

ò 0 1   (1 – x)dx  –  3i ò 0 1    x2dx = ½ - i

Based on the original contour definition  (adding the integrals for the segments OA and AB):

ò C1  f(z) dz  =   1 – i/2

If C2 denotes the segment OB of the line y = x then we have:
 z = x + ix (0 < x < 1)

And we can write:

ò C2  f(z) dz  =    ò 0 1   -i3x2( 1 +i) dx =

 3(1-i)  ò 0 1    x2dx = 1 – i
We can see from this that the integrals of  f(z) have different values though the two paths C1 and C2 have the same initial and starting points. It follows from this that the integral of f(z) over the simple closed contour OABO or C1 – C2 is:

ò C1  f(z) dz   - ò C2  f(z) dz    = [½ - i] – (1 – i ) =    -1 +i / 2

Problem For Math Mavens:

Redo Example (1) except change the limits of the contour to have z = -2i to z = 2i.

Friday, December 27, 2019

"Opacity Events" - When Ash (Or Other Toxins) Falls Onto An Unsuspecting Colorado Town - For The 75th Time

A drilling rig operates in Erie in 2015.Josh Fox from Gasland II, and fracking in Colorado where more and more "opacity events" are being reported, with citizens, kids having to shelter in place.  

There is growing concerns over the ...Suncor refinery in May this year.

When the ash began falling in Commerce  City on December 11th, no one who saw it covering their cars and the ground had a clue what it was.  But very soon, residents related to each other how it was like trying to breathe in air laced with grit.  This was not surprising given that, subsequently,  car wash attendants, e.g. Vidal Rodriguez, reported having to clean windshields "caked in yellowish white scum".  Well, imagine trying to breath in that crap before it caked?

As reported by Denver news stations on the evening of Dec. 11 there was trouble at the Suncor Energy oil refinery north of Denver.  The Wednesday morning incident triggered a “vapor release alarm,” prompting operators to place one of their units into “safe mode” and announce they’ll launch a full investigation as soon as possible.

Suncor officials called it “an opacity event” in a statement emailed to local officials and posted on the company’s Facebook page. They said the company’s tests showed air quality in surrounding neighborhoods “is within acceptable levels.”

Just before 11 a.m. Wednesday, South Adams County Fire Department got a call to investigate a strange odor at Adams City Middle School. People were also reporting they were seeing ash falling from the sky.  The kids at the middle school were told to shelter in place and not come outside.  Meanwhile, photos were being shared by residents all over Commerce City of cars covered by ash, e.g.

No photo description available.
Finally, late in the afternoon Suncor Energy admitted the ash was coming from their facility.   What the hell was it? Suncor's PR release - from its Facebook page- is shown below:
Image may contain: text

One is entitled to ask what this bejabber really means and at least one Denver TV station went to the Colorado Dept. of Public Health (CDPH) to learn more.  The questions and answers  (from CDPH) are given below from the 9 News web page:

We wanted to better explain to people what an operational upset is? 

"Operational upset" is a term used by Suncor - companies usually define it to mean that equipment failed to operate in a normal and expected manner. We do know there was unusual activity, and that's why we are investigating the incident and will be reviewing the activity logs. We will also require Suncor to give us any data they have."

What was in the ash that fell on people's car?

"Suncor has stated that the material is catalyst from one of the units at the refinery. We are conducting an investigation to confirm the details and verify Suncor's statements, but based on the information we have now, it was likely clay-like particulate matter.  We control emissions of particulates like these to protect health and visibility. Excess emission are not acceptable."

Was that dangerous for them to be near? 

"Particulate matter is a pollutant, and it can cause health problems at high levels. Based on the state's best air monitoring data in that area, the particulate matter was not at levels that exceeded the national ambient air quality standards, which are set to protect public health."

Is Suncor working with the state to remedy the problem? 

"The state has ordered Suncor to provide information and data as part of the investigation. So far, Suncor is complying and has been providing updates on the status of the refinery. Right now, the company is keeping the state informed of their activities around this event. Suncor will be held accountable if it violated any laws or regulations. We are requiring a full accounting of what occurred and will pursue appropriate action."

Has this happened before? 

"There have been other incidents and violations at the Commerce City facility, and the Air Pollution Control has fined Suncor before. We are already in he midst of our investigation and enforcement for prior events and violations.."

Just because a fracking-energy company "complies" - let us note- doesn't mean there aren't scores of repeat violations -  many of which are detrimental to human health.  (In 2019 alone, Suncor’s two operations accrued 75 separate permit “upsets,” according to the Colorado Department of Public Health and Environment.)  

The history of the fracking industry thus far is an appalling indictment of local and state governments across the country and how little they care about their citizens' health - even in an era of exploding medical costs.  The main fracking chemicals list alone constitutes an eye-opening list of horrors, e.g.

Benzene: a powerful bone-marrow poison (aplastic anemia) associated with leukemia, breast and uterine cancer

- Styrene, which may cause eye and mucous membrane irritation, neurotoxic effects in the central and peripheral nervous systems.

- Toluene, which may cause muscular incoordination, tremors, hearing loss, dizziness, vertigo, emotional instability and delusions, liver and kidney damage, and anemia.

- Xylene, with cancer-causing (mainly in the kidneys, liver) and neurotoxic effects, as well as reproductive abnormalities.

- Methylene chloride, which may cause cancer, liver and kidney damage, central nervous system disorders and COPD.

It was Prof.Tony  Ingraffea  - in Josh Fox's amazing documentary 'Gasland II' who explained in detail the cement failure phenomenon in frack wells.  He emphasized that such failure is a "very well known and at least as long as we've been drilling wells and casing them".  He also took pains to point out  that amongst the thousands of gas wells (including those offshore), there is a probability of 1 in 20 that a given well will immediately show a failure (opening between the well casing and rock), and that means methane migration. It also means anything else stored in the rock, including salts, heavy metals, other deleterious things now have a pathway for escape.

Voila! Enter the particulates vented in the "opacity event" spawned by Suncor in Commerce City.   It is clear many of these are likely  PM  2,  5   which I described in an earlier post, e.g.

A New Pollutant Category Appears ( PM_2,5) And L...

Denver Post investigations into the decline of front range air quality ties the degradation almost entirely to the enhanced presence of  PM  2,  5    triggered by coal fire plant emissions, and fracking operations (releasing "organic volatiles").  Meanwhile, the national scale of destruction of our water, soil, air and human bodies continues as revealed in the excellent monograph, 'The Real Cost of Fracking', by Michelle Bamberger and Robert Oswald. 

 Among their primary findings (summarized below):

- The irresponsible behavior of the drilling companies and the state environmental regulatory agencies in handling problems occurring after the onset of oil and gas drilling.

-The same human and animal health problems occurred irrespective of the method of drilling, i.e. shallow, or deep vertical drilling with low-volume hydraulic fracturing.)

- Adverse health events had the potential to spread far beyond the immediate drilling-related events. For example, farmers faced with livestock (cattle) losses "felt pressed to send the exposed animals to slaughter".   Thus, the meat, eggs and dairy products produced from such livestock would also be affected, "making it likely these chemicals could appear in food products" made from these animals. 

- For nearly all the cases investigated, "children and animals became like the canaries in the coal mine" - as to revealing toxic effects of the fracking before they befell adults. The reason is that children, being smaller, eat, drink and breathe more air relative to their body weights- so are more affected by any kind of degraded environment. 

And: "While children are sentinels, animals are even more so, for many reasons. When families leave for work the animals are left either in the house, barn or yard, increasing exposure times dramatically."

For many good reasons, then, the "opacity event" that occurred in Commerce City nearly three weeks ago ought to concern us all.