Saturday, December 31, 2011

One Sure Prediction: Even More Climate Catastrophes in 2012!

As we wind down one of the worst years for global climate catastrophes, including heat wave records broken over 800 times for many U.S. municiplaities, we're now on the cusp of yet another year of tumultuous climate change, havoc and vast destruction. Will people begin paying attention, force their reps to act in the long term interests of humanity, or continue the status quo? The answer to questions such as this hold our lives and those of future generations in the balance.

As Physicist Michio Kaku observed on a recent MSNBC documentary: "For the first time in history, humans have the potential to alter the destiny of a whole planet."

On the same documentary ('The Last Days of Planet Earth') astrophysicist Neil Degresse Tyson put it another way:

"Imagine the irony of our species having the intellect to stop an asteroid impact, but lacking the intellect to moderate the worst effects of global warming. It boggles the mind!"

Indeed, because it's inexcusable! Further, I go so far as one British climatologist who opined in the same documentary that so-called "climate mavericks" and their skeptic pals who are holding back bold changes, are no different from Holocaust deniers. (Who in a number of countries, such as Austria and Germany can be jailed for making public pronouncements).

Is this an incursion of liberty or "free speech"? Well another question: If a fire breaks out in a crowded theater and several 'maverick' voices yell 'There is no fire, stay put!' and all the people perish, what is their accountability (hint: they sneak out after yelling the injunction to stay put)? Should they not face lengthy prison terms? The same situation applies to the global warming deniers whose defective PR has postponed necessary, timely action, which will make the difference between a moderately-warmed, tolerable planet and an intolerable one in the maw of the runaway greenhouse effect.

In this light, the failure of the recent climate conference in Durban to accomplish anything significant or durable is an ominous portent. According to The Economist (December 17, p. 138):

"Its terms - even assuming they are acted upon - are unlikely to prevent a global temperature rise of of more than 2 C, which was the stated aim of the whole UN climate 'process'. Indeed, they might easily allow a 4C rise"

The latter would be catastrophic and on top of the existing (hitherto) 1.2 C increase, bring us to the precipice of the runaway greenhouse. Carl Sagan noted in an interview (with Ted Turner) ca. 1989 (still have it on tape) that the limits for catastrophic climate change- we're talking species exterminating magnitude with a runaway greenhouse - are not as high as many think. In fact, he cited the tolerance increment of six degrees Celsius.

This position was reinforced in Sagan's essay: 'Ambush - the Warming of the World', p. 98, in his last popular book, Billions and Billions, Random House, 1997.

Is this all "scare mongering"? That is what the flat Earth, Denier cultists want you to believe, so they can wreck the world on the basis of pure economics with no thought of the morrow or how our children and grand children will forever curse us for putting our comforts and stock profits over their welfare.

In a blog two years ago, I warned about the impending signs of ice sheet breakup and melting in Greenland in connection with the phenomenon known as "Jokulhlaup" (cf. ‘Jokulhlaup Observed in Greenland ice sheet’, appearing in Eos: Transactions of the American Geophysical Union (Vol. 89, No. 35, 26 Aug. 2008, p. 221). The cited paper specifically noted an increased frequency in occurrence of “jokalhlaups”or sudden glacial bursts of melting runoff from glaciers. It was this phenomena that also played a role in the “unusual cracks" that set off the separation of a “chunk of ice the size of Manhattan” (19 sq. miles)from Ellesmere Island in Canada’s northern Arctic.

Since then, many more drastic break-ups of glaciers have been observed and documented and now readers can access this material directly at the following link:

Anyone watching this documented evidence who isn't terrified, has lost most of his or her brain neurons.

We also know that this process provides one of the nonlinear drivers toward catastrophic climate change. Melting of ice caps and glaciers (already occurring) results in diminished albedo (fraction of solar radiation reflected back into space), a darker Earth surface - with more infrared radiation (e.g. HEAT) being absorbed - reinforcing and enhancing global warming. As more ice melts from the polar regions, the positive feedback from lowering albedo proceeds faster. The overall (mean) ocean temperatures continue to rise - ultimately becoming too hot for any marine life- and reaching equilibrium temperature somewhere in the next 500 years. All ocean currents, circulation systems will, of course, eventually cease. With atmospheric circulation soon following (as on Venus) , all solar energy going into heating the oceans until their specific heat capacity is reached. We then will have vaporization.

Even now, before the runaway has set in, we know the acidity of sea water has increased nearly 30% since the Industrial Revolution. Given that sea life, including corals, fish, and the critical phyto-plankton (which provide most of our planet's oxygen) can only exist within very narrow pH levels this may be most disturbing. It means that there is the potential for humanity to suffer devastating famines and loss of life long before the Runaway Greenhouse charges up.

Given all this, 2012 looks to be an even more devastating year, climate-wise, than 2011. Look for many more F4-F5 twisters pummelling the South and central plains from late March or even earlier and also torrential rains in many other areas. Expect heat waves that rival or exceed those seen last summer in Texas and Oklahoma and especially enhanced record breaking night time temperatures - the prima facie signature for global warming. Lastly, drought will continue its grip over much of the southwest and even the midwest. Mexico, which had to slaughter 1.7 million starving or thirsty cattle last year, will see even worse this next year.

Can all this be halted? Unlikely. But there's still a chance to stop the worst of it, though I fear this next year will be the last opportunity we have. If so, look for the full runaway to commence sometime in 2045 if not before.

Friday, December 30, 2011

Be Careful What You Wish for....Fellow Citizens!

In an interesting and intriguing interlude on ABC Evening News two weeks ago, a parade of citizens in Youtube offerings was seen all saying the same thing: "Please, congress! Stop playing games and pass the payroll tax cut! We need that money!" This was during the time a couple weeks ago when Repugs had done their typical end of year grandstanding and threatening to take down a deal to pass these cuts along with a 59-week unemployment benefits extension and a prevention of the proposed 27% cut to Medicare physicians.

In retrospect, one wonders if these people really appreciated and grasped what exactly they were asking for, and that in the end.....they have been pleading for a small increase in their yearly income which over the long term guts their retirement prospects.

This was brought into focus today with a report out of The Washington Post noting that for the first time in history, politicos are using Social Security's funding as a poker chip in their high stakes games. The danger? A mechanism which has assured Social Security's integrity since its inception, is now being gutted which may well pave the way for either the program's collapse or its conversion to a welfare program. This at a time when nearly 1.7 million a year are desperately trying to get Social Security disability after months or years of unemployment, and nearly 40 million seniors over 65 depend on their Social Security benefits for most of their income.

The prospect of lawmakers and politicos continuing to use the payroll taxes and specifically cuts to provide economic stimulus during a quasi-recession has disturbed many experts, especially Social Security's two public trustees. They both worry that if this tactic becomes entrenched Social Security will lose its status as a protected benefit due every American based on what they paid in - via payroll taxes- and instead becomes another welfare program, or a program subject to appropriations approvals.

In the first case, we might see either it being cut outright, or possibly converted into a "work to welfare" format such as transpired with the 1996 Welfare Reform Act. Picture then 88-year old tottering grannies barely managing to stand up as Walmart greeters in return for the $800/month checks. In the second case, we'd see the Congressional Budget Office declare social Security no longer sustainable so that yearly budget appropriations must pass through the House. If its GOP-controlled most able-brained folks can predict how that will work out.

One of the trustees, Charles Blahous, quoted in the article, said:

"It's a grave step for Social Security. It just seems to me the program both financially and politically will be on a lot rocker footing".

Blahous added:

"We've never monkeyed around with Social Security before. Until now it was understood the payroll tax was supposed to do on thing. It wasn't supposed to be a stimulus mechanism. Now the payroll tax is this variable thing that goes up and down according to other economic conditions. That is a real transformation of what the money was supposed to do."

Not only that, but if the payment support is variable then logically it means the whole program is variable and can become welfare, or subject to appropriations bills. Well, I had warned about this in previous blogs, e.g.

Meanwhile, Robert Reischauer, the other trustee, acknowledged that extending this cut during a period of high unemployment could be justified, but "if it continues for a substantial period of time it could undermine one of the foundational arguments that makes the Social Security program inviolate"

Well, that undermining is already underway, as noted in the last of the two blog links above. You can bet your sweet bippy it will swing into high gear if the GOP takes over both legislative houses as well as the Presidency. And as other skeptics have noted, the problem is when one plays this game one can become hostage to it, or maybe addicted is a better word. We've already seen how the Zombie Bush tax cuts - which ought to have been finally expired last year- rose to life again and we're barely two votes away from them becoming permanent zombies - forcing vast cuts to all benefits later.

Nancy Altman, co-Director of Social Security Works, makes a more salient point:

"All of a sudden Social Security will have to compete with every oter program, whereas before it had its own dedicated revenue. It's breaking the kind of firewall that has always existed between the trust fund and the operating fund. The biggest concern is that this was done without any hearings, without any apparent regard for the impact on Social Security."

Which, of course, introduces the question of WHY, especially under a Democratic regime. This year, Social Security is projected to pay out $46 billion more in benefits than it takes in- meanwhile, Social Security disability is projected to be broke by 2017. It is claimed (in the article) that the first shortfall is being made up for by "redeeeming Treasury bonds bought in years when there were cash surpluses". But that isn't the critical factor here. The critical factor is what will the yields of those Treasurys be? One thing we do know, this sort of strategy is unsustainable when the Federal Reserve is already on a bond-buying spree driving down the yields of even 30-year Treasurys to barely above 3.09% (according to a WSJ piece from 4 days ago).

Meanwhile, the chief actuary of the Social Security Trust fund has claimed that the payroll tax cut "will not put a dent in the $2..6 trillion fund". But how long do you supposed that argument will hold up when politicos are still playing both ends against the middle and using Trust Fund monies to pay for things general revenue ought to cover, like the pullout from Iraq (estimated cost $300b) and the Afghanistan supplemental budgets.

The saddest fact in all this is that, bereft of arguments to defend higher taxes in the face of the Repuke tax cutters, Demos caved and "borrowed from the Republican playbook" arguing now that reverting to the old (payroll tax) rate of 6.2% would be a tax hike. Well, they may have outsmarted themselves! Now, their words will commit them to doing this ad infinitum, even as they likely sustain the Bush tax cuts to be consistent. This, despite the fact that actual computations disclose that payroll tax cuts do next to nada for the economy, just as the Bush tax cuts do next to nothing. Again, see The Financial Times' report on those ten years of Bush tax cuts (FT, Sept. 15, 2010).

A much more powerful economic stimulus would be delivered by extending unemployment benefits indefinitely, or at least another 99 weeks. The unemployed will spend that money immediately on food, rent, mortgage, school supplies....whatever. That is what will keep jobs from being sliced.

In the meantime, Sen. Bernie Sanders has rightly warned that Americans should be more cognizant of what they are yearning for here. Is it really worth it to put maybe $900 extra in your pocket then later in your elder years, when you REALLY need money - to have to live on peanuts after Social Security cuts. Or, be forced to work as street sweeper on a "Social welfare to work" program?

Blahous one more time:

"Whether you're on the left or the right you should really dislike this. It has been somewhat mystifying, the determination to do this. I just think it's short sightedness."

Actually, not mystifying at all. Merely reinforcing once more how crass, calculated and cynical political gamesmanship can fool enough of the people enough of the time -when times are somewhat tough - to make them grab for an instant sop while forgetting their long term welfare. No one can say they weren't forewarned when the shit finally hits the fan.

Linear Algebra: Solutions

The last set of problems and their solutions:

1) Recall t^A, found in Ex. 1 and let B =

a) Find AB and thence: t^(AB)


AB =

(2...1) (-1....1)
(3...1) (1.....0)



Then: t^(AB) =


b) Verify that: t^AB = t^B t^A


From Ex. (1) in previous linear algebra blog we found t^A=


Given the matrix for B in part (a) then, t^B =


then: t^B t^A =

(1.....0) (1....1)



2) Find the trace of: R3(Θ) =

(-sin (Θ)......cos(Θ)...........0)
(0 ..................0..................1)


Irrespective of dimension the trace Tr is the sum of the diagonal elements. Then, Tr(R3(Θ)) =

cos(Θ) + cos(Θ) + 1 = 2cos(Θ) + 1

3) Let A =

(cos Θ .....cos φ)
(cos φ .....sin Θ)

And let B = t^A

Find: AB

From this, t^A =

(cos Θ....cos φ)
(cos φ......sin Θ)

Then AB=

(cos Θ .....cos φ)(cos Θ....cos φ)
(cos φ .....sin Θ)(cos φ......sin Θ)

(cos^2 Θ + cos^2 φ...............cos Θcos φ + cos φ sin Θ)
(cos φ cos Θ + sin Θcos φ .............cos^2 φ + sin ^2Θ)

4) Find the traces of the following 3 x 3 matrices:

a) M1 =



tr(M1) = -i - 7 + 4 = -3 - i

b) M2 =

(-7.......-3......-3i )


tr (M2) = 3 + (-4) + (-3i) = -1 - 3i

c) A =


tr(A) = 1 + 4 + 1 = 6

d) B =


tr(B) = 3 + 1 + 1 = 5

5) For the last two parts (c and d) of (4), show: tr(AB) = tr(BA)

This requires multiplying two 3 x 3 matrices:

Then AB =

(1.....-1......1) (3.....1.......2)



tr(AB) = 1 + 8 + 7 = 16

BA =




tr(BA) = 11 + 3 + 2 = 16

Then: tr(AB) = tr(BA)

Thursday, December 29, 2011

Of Calendars, God-Men and the Date of Christmas (Part 2)

The Roman Sol Invictus image bearing the inscription: "The most holy and sacred Sun"

We now continue with the complaints of one disgruntled fundamentalist blogger:

"The chapter then turns to what Mr. Muncaster did with this information. It shows that after studying the Greek word translated “believe” in John 3:16 and learning that it had a deeper meaning than to simply intellectually acknowledge a fact, but that it carried the sense of “to put one’s trust in,” he came to the conclusion that he needed to do more than simply know the truth; he needed a close relationship with Jesus—he needed to place his trust completely in Him. "

But, of course, if Jesus existed in no real historical place (at least as determined by the historians of the time, or even the OT) then this amounts to pure question begging. In effect, if Nazareth didn't exist as a true historical place it likely means no events associated with it ever existed, and then we have a whole cloth fabrication, as many have already shown (e.g. Geza Vermes, Bart D. Ehrman, John Dominic Crossan etc.) Thus, whether John 3:16 says anything in Greek, or Latin or even Hindu is irrelevant. If basic historical markers aren't met, then one must suspect the whole thing as fabricated. Indeed, no less than one of the historians of the Catholic Church, The Rev. Thomas Bokenkotter, in his monograph ‘A Concise History of the Catholic Church’, notes (page 17):

The Gospels were not meant to be a historical or biographical account of Jesus. They were written to convert unbelievers to faith in Jesus as the Messiah, or God.”

This is a shattering admission indeed, and from a historian of Christendom’s largest Church. It is a de facto admission that no historical support exists for any of the accounts in the New Testament. Indeed, if they ‘were not meant to be historical’ (or accurate), then we cannot be sure if any are! Quite possibly, none of the accounts should be taken seriously.

Whatever one may think of his religion, at least Bokenkotter is honest! The illustration of the Nazareth site as a late 4th century confection also illustrates the point.

Nonethless our impetuous blogger waxes on:

"He realized that the study he had engaged in had changed his mind completely, that now he knew that the Bible and Christianity were based on facts—lots of facts and evidence that could be verified. It was not based on blind faith."

And yet that is exactly what Muncaster's conclusions are based upon: blind faith. Muncaster already knew what it was he wanted to find and then simply excavated it from the assorted nether regions of his brain's OAA (Orientation activation area). Presto magicko! I have found truth, facts and .....statistical certainty! Except never once did he compute a single solitary statistical probability as I illustrated in my last blog (graphic). Our only conclusion to make is that Muncaster is a fraud, a tool, and a willing obscurantist, in his own way no different from Jason Lisle and his "young Sun" bollocks.

The only "facts and evidence" are what he himself conjures up, simply dismissing the much vaster scholarly bona fides of those who have spent many more years on these issues - like John Allegro and John Dominic Crossan. But why be surprised? The True Believers will always find what they want to find, if it suits their fancies! They are congenital perpetrators of the logical fallacy known as "affirming the consequent' and most don't even know it!

Our fundie moves on:

"All that being said , the unbelievers now point to the fact that December 25th was NOT the date of Jesus' birth. And you know what? I , AGREE WITH THEM! But here again , that's a red herring."

This is interesting in that he agrees with me, but decides it's a "red herring". But, it can only be a red herring if it is not relevant! Let's see what he says next:

"One atheist blogger had wasted much time on this subject , writing how Christians should not celebrate Christ's birth because Dec. 25th was not His actual birth date. He goes on to write how Christmas had its origin in pagan religious customs. And here again , I AGREE with him! "

Now, this is very interesting, because...first, I never said or wrote "Christians should not celebrate Christ's birth". What I did was ask, at the very end, DO Christians KNOW what they are celebrating when they DO celebrate the occasion of Dec. 25th as a putative "Savior's" birth date? In other words, do they know which savior that is? This is a different thing from how the blogger has phrased it. Second, I never insisted December 25th was not his "actual birth date" only that this date is suspicious because it had been the original winter solstice and was celebrated as the birth date (from antiquity) of the Roman Sun god, Sol Invictus. Thus, I intimated it to be a coincidence of the highest order to have two saviors' birth dates exactly the same! (And again, I remind readers, that Sol Invictus' came before Jesus. And up to 354 A.D. no firm date was known for the latter's birth).

In addition, I dispute it is a "waste of time". I warrant MOST people are not aware of the many changes in the calendar, including that 10 days were simply lopped off between October 4 and 15, 1582. If most people don't know these things, then bringing them to their attention is emphatically not a "waste of time".

One wonders then what all the kerfuffle is about when he agrees with me, but he moves on:

"He then goes on ( wasting more time and space ) , explaining the various "calendar types" ( e.g., The Roman Republican Calendar , Alterations in the Julian Calendar , and The Gregorian Calendar ). BUT....he leaves out the Philoclian Calendar. Speculation as to the time of Jesus’ birth dates back to the 3rd century, when Hyppolytus (ca. 170-236) claimed that Jesus was born on December 25. The earliest mention of some sort of observance on that date is in the Philoclian Calendar, representing Roman practice, of the year 336."

Actually, in this passage he confirms my point that the details of the altered calendars were NOT a "waste of time"!

First, it isn't the "Philoclian Calendar" but the Philocalian Calendar. In fact, I didn't "leave it out" I just didn't call it by name. But I did refer to the earliest versions of the Roman Republican Calendar, of which the Philocalian was one version. Thus, the first certain record associating December 25 with the birthday of Sol Invictus is the ROMAN Chronography of AD 354 where, in the part known as the Philocalian Calendar, VIII Kal. Jan. is identified as N INVICTI CM XXX (Natalis Invicti; CM abbreviates circenses missus or circus races)

"Natalis Invictii" refers to the birth of Sol Invictus, NOT Christ. (See graphic attached of a Roman rendering of Sol Invictus). The celebratory factor in the inscription is punctuated by the fact XXX (30) races were to be scheduled in the Roman Circus. This would NEVER be done to commemorate the exclusive birth of a Jewish Messiah! Even given that the Edict of Milan was formalized some 40 years earlier. But Christians still trudged on shaky ground and many Romans exhibited suspicion or outright hostility.

Coincidentally, this is also the earliest reference to December 25 as the birthday of Jesus. In a commemoration of Christian martyrs, the notation for VIII Kal. Jan. is natus Christus in Betleem Judeae ("Christ was born in Bethlehem of Judea"). Because the Depositio Martyrum was completed in AD 336, the first celebration of Christmas can be dated to that year as well. In the list of consuls, there also is the note: "Dominus Iesus Christus natus est VIII kal. Ian".

Note the first celebration can be dated to the year 336, but it was not formalized! As I noted in my last blog, it wasn't until 29 years after the Council of Nicaea, in 354 A.D. that the newly liberated Christians formally claimed December 25th - the designated original birth date of the Sun god Mithra- as their own nativity for Christ. This exactly parallels the timing already cited for the Chronography of AD 354 where, in the part known as the Philocalian Calendar the date first emerges in a written record.

Given he misses all this information, it was obviously not only a good thing I "wasted my time" on the original blog, but the last two as well!

Again, the more salient points I made are all fully validated! Thus, neither Mark nor Paul made any reference whatever to when Jesus was born, and Matthew and Luke do not mention the date. When Clement of Alexander (d. ca. AD 215) does refer to the day of Jesus' birth, December 25 is not included among the possibilities. The church did not agree upon December 25 as the Nativity of Jesus until the fifth century. Even then, the winter solstice, which coincided with the Christian festival, still was recognized.

Which, again, bears out my earlier point to do with the suspicious coincidence of the Christian "Savior's" birth date with the much earlier one for Sol Invictus.

He then continues, in a most intriguing remark:

"The church thereby offered people a Christian alternative to the pagan festivities and eventually reinterpreted many of their symbols and actions in ways acceptable to Christian faith and practice"

This is interesting because he essentially admits the Christians stole the Roman celebrations and date to "reinterpret" and recast them to make them "acceptable"! Well, this is certainly one way of looking at what happened. But another equally legitimate, if not more legitimate take is what I wrote in my Dec. 25th blog, "There are many speculations as to why Christians appropriated this particular date when the eastern orthodox and other variants stuck with January 6th. The most plausible one is probably because the conflation allowed Christian Rome to pay homage to the earlier Emperor Constantine who had expedited their liberation".

Bear in mind the climate at the time! Think about it! You had been scum of the Earth, worms of pity and even persecution for hundred of years. Tossed to lions for the cheering of Coliseum spectators and roasted on spits. Then Voila! One day you are decreed by Emperor Constantine to be fellow citizens able to go about your business unimpeded. Why would you not express gratitude? The ultimate gratitude would be to make your most sacred date, for your Savior's birth, identical to that of the Emperor's god, Sol Invictus!

Indeed, the fundie blogger basically agrees with me in a follow up remark:

"Was He born on December 25th? Probably not - that's a date chosen by the early Roman church (Catholicism ) , to correspond to a preexistent Winter solstice festival. "

My only complaint here is he again conveniently isolates the "Catholic" church when at that time, it was the ONLY church, and hence THE Christian Church - neither Protestants nor evangelicals emerging for at least another 1300 years. Thus, instead of accepting the miscues of the original CHRISTIAN religion, he selectively blames the Catholics. But this isn't cricket. It could only be cricket if both evangelicals and Catholics existed at the same time. They didn't. Thus, the history of the Catholic church is the history of the Christian church at least until Martin Luther's reformation.

Finally he remarks:

"Oh yeah , this atheist blogger ( in a recent post ) , also likes to quote Buddhist philosopher Alan Watts. Now , both Matthew and Luke were willing to lay their lives on the line to authenticate the credibility of their messages about the birth of Christ. Now , consider the data relative to the alleged “miraculous” birth of “the Buddha” — one of the supposed parallels, to which appeal is commonly made"

Which, of course, is totally irrelevant to the issues at hand: 1) the meaning and signficance of December 25th in antiquity, and 2) whether in fact Jesus was really a "god man" or savior. All the evidence points to the answer for (1) being that December 25th has always been a pagan commemoration, marking the birth of the Sun god, or Sol Invictus. Meanwhile, for (2) I do agree that a Jesus was born but not that he was a divine entity. There is no evidence for that, and all the 'miracles" etc. attributed to him were all confections that can be easily explained.

Consider the claim of a miracle: Jesus “walking on water”. Prof. Hugh Schonfeld has a simple explanation for this: a mistranslation of the Hebrew word “al” which can mean “by” or “on”. So, when a scribe really wrote “walking by the water” it was retranslated to “walking on the water”.

Next apply David Hume "miracle" test that reads: "No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish."

Let us then apply the Hume test: Is the Schonfeld claim of mistranslation MORE or LESS miraculous than a man actually violating the law of gravity and walking on water? It doesn’t require a lot of thought or effort to see that the mistranslation of a passage of the New Testament is LESS miraculous (or if you prefer, less improbable) than that a man actually, literally walked on water.

As for the Buddha, there is vastly more information and knowledge of his activities over the major portions of his life, than for Christ. Interested readers can find more here:

Of Calendars, God-Men and The Date of Christmas (Part 1)

It seems a Christian fundamentalist blogger is seeing problems with my earlier (Christmas Day) blog on the date of Christmas. Since his misperceptions may be wider than just a few people, I will not examined his complaints in more detail.

He writes, referring to blogs like mine, e.g.

"Sadly , they do not hold other books to the same standard that they hold the Bible to. One book I would recommend that they ( as well as anyone ) , should read is A Skeptic's Search for God by Ralph O. Muncaster.

But the Xtian blogger misses the point! If standards are to be met, they must be of the highest academic standards, not based on prejudice or because a book dovetails with one's pet belief system. The problem with Mancaster's book is it simply doesn't meet this academic standard, as it's replete with hundreds of scientific inaccuracies, omissions, and selectivly slanted misrepresentations of current scientific knowledge. For example, vast swatches of current evolutionary theory are deliberately ignored, in particular the import of biochemical cybernetics in micro-evolution and the genetics underlying it. Thus, there's NO mention of the enormous microscopic chemical activity maintained by a certain class of proteins – the enzymes- playing the role of specific catalysts.

For example, there is the Krebs cycle for aerobic metabolism, whose pathway is:

CH2 COOH-coenzyme A + 2 H2O -> 2 CO2 +8 (e- + H+) + coenzyme

possessing a self-catalytic feature in that intermediate products necessary for the cycle to occur are generated by the cycle itself. In this case, Oxalo-acetic acid combines with acetic acid to begin the cycle and is regenerated from malic acid at the end of the cycle. This in turn paves the way for ancillary reaction which lend themselves to the functional coherence of what are - in effect, complex chemical machines, which are autonomous as well. I don't believe this "skeptic" goes into any of this, because: 1) he doesn't know enough about it to critique or examine it in depth, and 2) if he did it would annihilate any basis for his Xtian beliefs.

On the other hand, in preparing my blog on the putative dates for Xmas (above link) I used many standard academic astronomy and astrometric texts, including: 'Spherical and Practical Astronomy Applied to Geodesy' by Ivan Mueller and Eichhorn von Wurmb (chapter on the def. of the tropical year and its relation to Julian year etc.), Spherical Astronomy by W. Smart, on the role of precession in altering calendrical computations, and 'Exploring the Universe', by G.O. Abell, referencing his Ch. 4 on the changes initiated by the Gregorian Calendar.

Thus, the basis of a proper approach is not selection of "books" per se, or "which books" but rather those which reach the highest academic standards such that their results have already been vetted, substantiated in many previous works, and also peer -reviewed journals! Mancaster's book fails miserably in this, and indeed, I wouldn't even recommend it for a high school class in critical thinking, far less one at the university level.

The Xtian blogger then recycles the typical errors in Mancaster's book, i.

(1) life could not possibly have come about by random chance (naturalism), and since the only choices for the origin of life are random chance and creation, therefore God must exist—and by definitions, God=Creator;

But as biochemist Jacques Monod has shown (e.g. 'Chance and Necessity'), this is false. Also, Richard Dawkins has repeatedly shown how these creationists confuse randomness and chance and hardly ever get the difference correct, or how each applies to evolution. Dawkins once referred to this as “the single most unfortunate misunderstanding of Darwinism – that it’s a theory of chance”.

I suspect the misconception arises because one input for natural selection is mutation, and it is largely governed by random chance. (I.e. Up to 60% or more of mutations may be caused by external factors such as cosmic rays interacting with DNA. But who can say when or at what frequency these interactions occur?)

However, natural selection itself is anything but random.

We can see this simply by doing simple experiments, as with fruit flies, and examining the emergence of specific traits over generations – governed by gene frequency. It can be seen that over time there is a genetic "favoritism", as it were, for certain traits or characteristics to be passed on or selected out of a group of competing traits in the gene pool. Thus, what natural selection does is to consolidate particular random mutations into a more stable, adaptive adjustment – governed by deterministic factors and inputs. It is at the stage of this determinism that "random chance" ceases! With the gene frequencies in place evolution is then set.

But do these critics ever process things correctly? Hardly! It's always the same errors repeated over and over.

And the other major error:

and (2) a planet so precisely suited to man could not have come into existence by random chance, therefore, God must exist, and by extension, He must be all-powerful.

Again, a false argument! Out of hundreds of billions of sun-like stars in the cosmos, and we've located nearly a thousand already in our own galaxy alone, it stands to reason that plain ordinary probability would allow that at least ONCE (and likely many more times) a planet emerges at "the right" distance from its central star, and hence that the temperature conditions are favorable for evolution. Hanging the existence of a deity on this is therefore one sure way to lose one's deity! It also devastates the "all powerful" . For example, a much more devastating counter argument would be:

"If there truly is this Being that must exist, and is 'all powerful', then why didn't It also allow for life to evolve on Mars? If indeed 'all powerful' why not use that planet's own features to "create life"? Yet all the evidence from all our Mars probes discloses no life exists there! Of course the stock answer from bible bangers will be some "biblical" gibberish such as that it is "decreed in the Bible that life only be created on earth".

Neat and convenient escape hatch, but it doesn't work on real skeptics!

And more gibberish:

"He had statistical evidence that if any holy book has many significant prophecies that are 100-percent correct—with a statistical probability of their coming true randomly of less than the scientific standard of 1 chance in 10 to the 50th power—that book must be supernatural, which essentially proves the existence of God. Valid prophecy in the Old Testament (the Jewish Bible) far exceeded that standard. "

Of course, this is bollocks because no such "statistical probability" is shown (computed), and indeed the author confuses normal probability (such as proposed by the models of Richard von Mises) with Bayesian models. Readers can see in the example I have included, meanwhile, how one would actually compute the probability of number between 1-100 divisible by 6 OR 10, and the probability of the numbers divided by 6 and 10. Unlike me, neither Mancaster or his fundie apologist shows one line of how they comptue ANY probability from the Bible!

The truth is there are no real prophecies because all are gamed in terms of ambiguous language that can be read any number of ways. We've already been through this in earlier blogs.

For example, Barbadian Xtian cultist Roger Marshall who once invoked Isaiah 40:22a which he claimed "predicted the host of heaven cannot be numbered long before Astronomy realized it"

True or not?

Hardly! In fact this so-called "prediction" is is simply common sense that anyone who peers into the night sky (especially with a powerful telescope) can see for himself. Even the earliest Sumerian and Babylonian astronomers would have accepted it! (Given there are about 6,000 stars visible to the naked eye, but no one would have seriously tried to count them in an era before the constellation boundaries were defined - to prevent counting errors - by the International Astronomical Union and others.

Another one claimed by Marshall: "Biblical authors knew of the Earth's sphericity long before anyone else". (cf, Isaiah 40:22 )

But again, nonsense! Indeed, the ancients knew about the sphericity of Earth since the time of Aristotle, Eudoxus and Eratosthenes, hundreds of years before the birth of Christ. Thus, any references made in the Bible were likely already in the Zeitgeist of the learned folk of the time, and would naturally have been included- if the scriptural author (or more likely, later transcriptionist-translator) had any awareness at all.

Roundness (circularity) and sphericity are two different properties. One (circularity) applies to a simple two dimensional surface or geometry. Indeed, the property of circles was investigated by Sumerian and Egyptian mathematicians long before any of the biblical authors emerged from their caves. As I pointed out also in an earlier blogs, the particular property of sphericity can only be determined by the use of mathematics. Without mathematics, people would believe the Earth is a round, flat space. How so? If one looks across a vast, flat horizon – either from the middle of a desert or the ocean- the perspective one obtains is that of a vast FLAT expanse with a circular boundary at the far periphery. Thus, the impression created in an ancient mind – without use of discriminating mathematics- would be that he or she inhabits the center of an enormous flat circle!

How did the ancient Greek astronomers (e.g. Eratosthenes) break out of this and arrive at sphericity? In Eratosthenes’ case, around 240 B.C., he had to first decide what exactly he had to measure to assess sphericity as opposed to circularity. This is where a key assumption entered: that the Earth was spherical and the Sun distant enough that its rays at Earth were essentially parallel.

Thus the next statement that:

"This indicated that God is real. "

Is a non-sequitur. What it really indicates is that few people today can properly interpret biblical language or "prophecies" in terms that make real practical sense, and moreover, can be used for further future predictions.

Another example is when he writes:

"Furthermore, the many valid prophecies of the Messiah that Jesus fulfilled were verified in the New Testament.

But the truth is much more cruel for biblical fantasists. Forget for the moment that the name borne by the earliest followers of Yeshua was “Nazoreans’ - NOT “Christians” – And Yeshua was known as “the Nazorean”. This is a sectarian term of which the Hebrew is ‘Notsrim’ and is NOT connected directly with a place called “Nazareth” or with the messianic “Nezer” branch from the roots of Jesse.

Nazoreans’ members proclaimed themselves the “preservers of the true faith of Israel”- but this claim was also made by the Samaritans, inhabiting Samaria (Shomron) who represented themselves as the ‘Shamerine’ – the custodians or keepers of the original ISRAELITE religion, as opposed to the Judeans (Jews)

In his article ‘Where Jesus Never Walked’. (American Atheist, Winter 1996-97, p. 34) Frank Zindler notes “Nazareth” is not mentioned once in the entire Old Testament, nor do any ancient historians or geographers mention it before the beginning of the 4th century. As Zindler points out:

"The Talmud, though it names 63 Galilean towns, knows nothing of Nazareth. Josephus, who wrote extensively about Galilee (a region roughly the size of Rhode Island) ….mentions Nazareth not even once – although he does mention by name 45 other cities and villages of Galilee. This is even more telling when one discovers that Josephus does mention Japha, a village which is just over a mile from present-day Nazareth!


Although the New Testament tells us very little about our mythical municipality, it does tell us enough to allow us to conclude that present day Nazareth couldn’t be the biblical city referred to say, in the fourth chapter of Luke

Like the White Queen whom Alice met in ‘Through the Looking Glass’, Christian pilgrims have always been able to believe six or more mutually contradictory, impossible propositions every morning before breakfast. Unlike the White Queen, however, the Christians have been able to maintain such belief after breakfast as well

In other words, all the alleged NT "prophecies" don't even make use of an actual historical place that was supposed to have existed at the time! If this is so, why would anyone logically accept a figure purported to exist in this make believe place would be real?

Thus the claim by the fundie blogger:

"This also had a statistical probability that far exceeded the standard—which indicated Jesus’ Deity."·

is more accurately read as:

"this exhibits a statistical probability of near zero, since even the claim of the town (Nazareth) where he was purported to live, isn't supported by historians of the time"

More to come!

Wednesday, December 28, 2011

The Power of Bal- ONE- y!

The problem with mainstream magazines that purport to adopt scientific standards, but in popular form, is that the neophyte can easily be suckered in to accept that any pronouncements or claims therein have equal validity to findings in a refereed journal article. Note first, that the latter aren't simply accepted even if a paper appears to show some 'proof' or correlation. It doesn't enter the realm of approximate validity until and unless it is confirmed by independent researchers.

Thus, the recent offering in Psychology Today (Jan./Feb/ 2012), 'The Power of One', claiming that a 1 -point difference in IQ can make a "difference" must be reckoned as mostly babble without foundation, especially statistical. Before going into the assorted claims of the article, let's back up and understand several things about IQ tests.

First, there are different tests, i.e. Stanford -Binet, Wechsler (or Wechsler Adult Intelligence Scale, WAIS etc.) and they each offer different IQ measures. Thus, a 130 in the Stanford -Binet will not in general mean the same as 130 IQ in the WAIS, or the Wechsler for children. So the 1 point IQ difference amounts to gibberish unless the specific test is specified. (If one is referring to a specific individual's score in relation to a sibling's and performance characteristic issuing therefrom).

Second, IQ is not a precise number to identify one's abilities, nor is IQ-testing an exact science. Scores from tests are really estimates based on test performance on a particular day. There is always a margin of error (variance). The "actual" score could be higher or it could be a little lower within the margin of error). Thus one might give the Stanford -Binet IQ as 130 +/- 5. In effect, a 1-point IQ difference is literally "swallowed up" by the variance associated with any given test result as well as any aggregate of such. While the latter will remove some of the variation it can't be used as a basis to make major generalizations apart from what standard deviations allow, say on the Bell curve.

Recall in previous blogs I noted the bell-shaped curve which defines what we call the normal distribution, which presupposes a tabulation or assembly of results randomly selected. In the case of IQ (after normalization with all the various tests) the score of 100 will fall at the exact center or where the Gaussian peak occurs. The standard deviation used in many tests, including the Weschsler IQ test, is 15. The majority of test scores (about 70%) fall somewhere between one standard deviation below and one standard deviation above 100. That means most scores are somewhere between 85 and 115. Those scores are considered the "average" or normal intelligence range.

What one has in defining a category of IQ test takers is therefore a spread not definition enabling a precision to 1-point difference in IQ! The farther a score is from 100, the fewer people we will find with that score. If we move one additional standard deviation below and one additional standard deviation above 100, we will find about 25% of the scores falling within those ranges. In other words, people with IQs between 70 and 85 and between 115 and 130 make up about 25% of the population. That leaves only about 5% of the population who will have scores somewhere beyond those first two standard deviations away from the norm.

Because of the nature of the spreads created by the standard deviations (which again, are peculiar to the nature of the statistical distribution we call a Gaussian or Bell curve - see attached graphic with x-underbar the norm) we obtain categories of giftedness from the IQ test scores. In general, these can be assessed as follows:

- Mildly Gifted: 115 to 129
-Moderately Gifted: 130 to 144
- Highly Gifted : 145 to 159
- Exceptionally Gifted: 160 to 179

Again, it is ludicrous to believe one can make a clear distinction between any of the above groups based on a 1 -point difference. (Even if one did appear, say between 129 and 130 or between mildly and moderately gifted, one still has to factor in the margin of error or variance. Then again, what if the person took the test on another day when he or she didn't feel as well? This difference could putatively be negated!)

Lastly, there is the matter of correlation, which in very crude sciences such as psychology has become overdone, though I admit they do come up with fancier forms all the time. The point is that even for a very high Pearson product -moment correlation coefficient, e.g. r = 0.80, that doesn't signify causation! Correlation is not causation so it's dangerous to infer the latter even if one actually were to obtain r = 1.0.

What then of the claims made by the PT article? They are as follows:

- Every additional IQ point in a group results in a 1 percent increase in the likelihood of cooperative choice.

- For each additional point in the national IQ of their country of origin immigrants to the U.S. earn 1% more per year.

- By age 35 every additional IQ point you have - say over siblings - means an extra $810 earned per year.

- Each additional point in their country's IQ meant a foreign diplomat had 6.2% fewer unpair parking tickets

- Every 1 point enhancement in the average IQ of the smartest 5% correlates with an extra $468 in per capita GDP.

Note first, that there is a conflation between single IQ point differences in the examples. We see the alleged benefit of a sibling over his fellows in terms of assumed earning power, then also see what is referred to as a "national IQ". But we are talking chalk and cheese here! Even if one could nominally extract a 1 -point difference for an individual (which as I showed is statistically impossible given the standard deviations lead to spreads and IQ testing isn't an exact science) that doesn't translate into anything like a "national IQ".

What does the "national IQ of a country" mean anyway? What if a country is small, like Barbados, but has a vast number of foreign workers, expatriates who are very talented? How does one isolate their contrbutions? How does one measure national IQ at all? It is a common error of statistics to simply lump all IQ test scores of all citizens and take an average then call it the 'national IQ'. In reality, there is no such thing.

The nonsense example of fewer parking tickets paid based on a national IQ for a diplomat is even more absurd. This reminds me of one 1977 study which found a 0.9 correlation between an increase in the sighting of unidentified flying objects and the oppositions of Mars. The unwary or careless were tempted to take this to mean that on Mars' closest approaches (at opposition) the probability of alien visitors in space craft was greatest. Hardly! It merely disclosed a correlation between two disparate sets of data, which otherwise bear no relation to each other. The same between unpaid parking tickets and diplomats' "national IQs".

The last example of a $468 bump in GDP may be the funniest howler of them all, given that GDP is also a very poor economic indicator, as pointed out by University of Maryland economist Herman Daly. Let's leave out the fact that it's dubious (based on what I showed already with the spreads based on standard deviations) that one can actually obtain the "average IQ of the smartest 5% of a nation", and that even if one could - the standard error would likely be so large as to make the number meaningless.

But let's look at what this meaningless number is alleged to be correlated against: the GDP. In his lecture 'Uneconomic Growth: in Theory and in Fact', at Trinity College in Ireland, Prof. Daly noted the GDP is supposed to measure the total production and consumption of goods and services in the United States. But the numbers that make up the Gross Domestic Product by and large only capture the monetary transactions we can put a dollar value on. Almost everything else is left out.

Thus, 40 million -odd people, putatively possessing as high an IQ as their commodities trader and investment bank brethren, are now currently caring for one or more ill or disabled relatives. Their total monetary contribution has been estimated by the AARP as over $400 billion. But not one cent of that is factored into the GDP. Then what does GDP mean? Well, a confected number for a certain cabal of economists to try and push policy decisions that follow their own agenda.

The bottom line is that pop-science or pop psychology are very shaky foundations on which to base claims or findings. Is there "power" in 1 IQ point difference? Maybe! But then there's also power in one slice of baloney too! It just depends on when you eat it!

Tuesday, December 27, 2011

Linear Algebra: Matrix Operations

In a blog last year, we looked closely at matrix operations:

In particular, we saw the simple operation of matrix multiplication such that, given a matrix A:

(a11 a12)
(a21 a22)

and a matrix B:

(b11 b12)
(b21 b22)

then A X B =

(a11 a12) (b11 b12)
(a21 a22) (b21 b22)

= [{(a11b11) + (a12b21)} --{(a11 b12)+ (a12 b22)} ]
[(a21b11) + (a22b21) } --{((a21 b12) + (a22 b22)}]

For example, let A=

(1 2)
(1 2)

and B =

(1 3)
(2 2)

then A x B=

(5 7)
(5 7)

Readers should be able to work this out using the format shown. We now want to extend this to further operations with matrices, and we will confine attention to 2 x 2 matrices as subset of R^2.

1) Not all matrices multiply commutatively.

For example, with regular numbers it is a given that (2 x 3) = (3 X 2) = 6

Thus, in symbolic form: a x b = b x a

and we say the multiplication is commutative. But this need not be so with matrices and matrix multiplication.

For example, let: A =

(1 2)
(3 -1)

and B =

(2 0)
(1 1)

We find: A X B =

(4 2)
(5 -1)

But: B X A =

(2 4)
(4 1)

so that: A B NOT = BA and matrix multiplication doesn't give the same result both ways.

Another application is to obtain the transpose of a matrix and repeat such multiplication. The transpose of a matrix M, call it t^M, is obtained by the following procedure:

Let M =


Then t^M is obtained by switching the elements such that for the transposed matrix:

m11 = m11,

m12 = m21

m21 = m12

and : m22 = m22

Exercis (1): Let A =


Find: t^A:

Using the procedure shown above for the elements, we have t^A =


Lastly, we come to the trace of a matrix. This is simply the addition of its diagonal elements. Thus, for any matrix M such as dentoed above:

Tr(M) = m11 + m22

The beauty of this is that it can easily be extended for any dimension matrix, say 3 x 3, or 4 x 4 or whatever. You simply add the diagonal elements:

Exercise (2): Find the trace of M1 =


We easily see the diagonal elements and thence add them:

Tr(M1) = (-1) + (-1) + 1 = -2 + 1 = -1


1) Recall t^A, found in Ex. 1 and let B =


a) Find AB and thence: t^(AB)

b) Verify that: t^AB = t^B t^A

2) Find the trace of: R3(Θ) =

(-sin (Θ)......cos(Θ)...........0)
(0 ..................0..................1)

3) Let A =

(cos Θ .....cos φ)
(cos φ .....sin Θ)

And let B = t^A

Find: AB

4) Find the traces of the following 3 x 3 matrices:

a) M1 =


b) M2 =

(-7.......-3......-3i )

c) A =


d) B =


5) For the last two parts (c and d) of (4), show:

tr(AB) = tr(BA)

Monday, December 26, 2011

Catholic College Evangelists Need a Reality Check!

Curtis Martin - kneeling at center- during a noon mass at the offices of FOCUS, The Fellowship of Catholic University Students.

Buddhist philosopher Alan Watts in his magnificent monograph, The Wisdom of Insecurity , noted that the path for peace on Earth is paved by cultivation of benign passivity as opposed to neurotic, paranoid hyper-reactivity and seeing "evil" in that which is different or apart from one's own field of righteous vision. In the first, the attitude of "live and let live" is cultivated, and not deviated from unless one is directly attacked. One never acts merely upon speculations or even "possible threats", far less on vacuous religious beliefs and contentions concerning what is "good' and what is "evil".

As noted in an earlier blog ('On The Origin and Definition of Evil') what people refer to as “evil” is easily explainable in terms of brain evolution. Thus, Homo Sapiens is fundamentally an animal species with a host of animal/primitive instincts residing in its ancient brain or paleocortex. Meanwhile, the paleocortex sits evolutionarily beneath the more evolved mesocortex and neocortex, the latter of which crafts concepts and language. This tri-partite brain structure has been compared to a car design welding a Lamborghini to a Model T Ford chassis, with a 1957 Chevy engine to power the Lamborghini. If an automotive engineer can conceive of such a hybrid beast, I'd be interested to know exactly how he thinks it would run.

The behavior resulting from this hybrid brain is bound to be morally mixed, reflecting the fact that we literally have three “brains” contending for emergence in one cranium. Behavior will therefore range from the most selfless acts (not to mention creative masterpieces) to savagery, carnal lust run amuck and addictions that paralyze purpose.

The mistake of the religionist is to associate the first mode of behavior with being “human” and not the latter. In effect, disowning most of the possible behaviors of which humans are capable.- and hence nine tenths of what makes us what we are. Worse, not only disowning these behaviors – but ascribing them to some antagonistic dark or negative force (“Satan”) thereby making them into a religious abstraction or external alien force.

The neocortex then goes into over-drive, propelled by its ability to craft words for which no correspondents may exist in reality. Suddenly, our “souls” are at risk of being “lost” to “Satan” who will then fry us in “Hell”. In effect, the religionist’s higher brain centers divide reality into forces of darkness and light, just like the ancient Manicheans. As the divide grows and persists, certain behaviorally idealistic expectations come to the fore, and a mass of negative or primitive actions is relegated to “evil”. Humans tuned in to this Zeitgeist, which is soon circulated everywhere, being to suppress all behaviors that they regard as defective or “sinful”. They don’t realize or appreciate that humans are risen apes, and not “fallen angels”.

Buddhist Watts had two salient points to make in this respect:

The first (p. 111) is that "Your goodness must have an edge to it"

In other words, there is never perfect or absolute goodness. Goodness has bounds and limits inherently factored in, on account of humans' possessing a defective brain. This means the person who strives to be absolutely good will be exposed sooner or later as a pretender and plaster saint, with feet of clay. We need look no further than those numerous evangelicals - such as Jimmy Swaggart, Tammy and Jim Baker etc. in the 80s, who put on a public goody two shoes facade that was later ripped off.. We have also seen it with self-righteous politicos - many of whom often ranted against sex or gays, and then were themselves found in compromising positions.

Never try to be too good, or your brain's "edge" will find you bitten on the ass!

Watts goes further than merely accepting the edge of goodness by noting (ibid.):

"For all the qualities which we admire or loathe in the world around us are reflections from within...Our feelings about the crawling world of the wasps' nests and the snake pit are feelings about hidden aspects of our own bodies and brains, and all of their potentialities for unfamiliar creeps and shivers- for unsightly diseases and unimaginable pains."

In other words, we are beings already enfolded in those biological and neurogical limits and patterns that portend "evil" and it is as impossible to escape from them as to escape one's own shadow. (Another way to put this, first posed by Philosopher N. M. Wildiers, is that "an evolving world and a perfect world are mutually exclusive propositions.")

But the Catholic College Evangelicals don't see it that way. According to today's Denver Post a new breed of Catholic Evangelicals, as represented by one Curtis Martin, are out to change that antiquated religion's dynamic by mounting an evangelical mission to recover "lost souls" who have strayed from Holy Mama Church. According to the article (p. 1A, today) Martin saw "a hunger and an openness among young people to learn about Catholicism."

Obviously, this would be prevalent among young people, including of college age, who haven't yet done their own thinking or wide reading. This is especially so of those attending Catholic Universities, which already places them inside a kind of cocoon. By contrast, at Loyola University in the 1960s, the Jesuits invited all manner of outside guests to lecture and expose students to a wide variety of ideas. The purpose was to incite critical thinking. My good fortune was to encounter Existentialist Jean Paul-Sartre which set me on the road to atheism.

The conclusion then is that this "hunger" singled out by Martin is a pseudo-hunger. It is the product of not knowing enough, not living enough and not encountering all the ways humans are fallible, including their popes. (Which is why the papal infallibility doctrine is among the most specious as well as pernicious).

Martin goes on:

"Their parents are scandalized. But young people look at the saints, not the sinners. They know you can find sinners everywhere."

Martin here, like most latter day Catholic apologists with blinkers, believes their parents (mainly baby boomers) were simply "scandalized" by the priest pedophile crisis and incidents, and that is true. But it goes much deeper than that. It extends to the fact that the Church's own malignant doctrines spawned the very moral contradictions embodied in the pedophile incidents. Thus it was that on the one hand they could hector couples against practicing artificial contraception and youths against masturbation while the priest themselves engaged in the most hideous acts imaginable. And yet the latter were dismissed - more or less- as the foibles of a few and in no way connected to the Church's magisterium or teaching office. Virtually, no one, other than we atheists and hardened former Catholic skeptics, saw that all were of the same piece: the actions of the pedophile priests was bound up with the Church's own moral limits, failings and malignant doctrines.

Here then Martin is too clever by half because the issue isn't that one "can find sinners everywhere" but rather that those who purport to uphold a perfect moral or ethical standard, e.g. to "lead sinners", i.e. to "goodness", "salvation" or "God" lack the innate, inherent moral compass in themselves or their fabricated dogmas, doctrines, structures to do so! This fundamental deficiency is therefore what outsiders beheld, but that ostriches like Martin and his FOCUS (Fellowship of Catholic University Students) associates and apologists have not processed.

Evidently, Martin left the Church once then came back, and like most of the re-converted, displays the peculiar holier-than-thou attitude of the true believer. He claims:

"I was morally, spiritually dead. And I knew it. I spent all my time pursuing fun because I believed the lie that fun leads to happiness. God tells us that goodness leads to happiness."

But since I already noted, from Alan Watts, that all human "goodness" is limited and has "an edge" than it follows that the pursuit of blind goodness in itself, as an abstraction, can never bring happiness, only disillusionment. Indeed, the other point of Watts is that since human conceptions of goodness and founded on limited brain structures and evolve in different cultures, then goodness must be relative.

One need only consider the case of the Catholic nun dismissed from her hospital in Arizona by her Bishop some months ago, because she saved a mother's life, which cost the life of her stillborn child. By the Church's abysmal and misguided teachings, the nun had no right to interfere to choose one to live. Both ought to have died, because that would have been the ineluctable "natural" outcome of not "playing God". The nun, by contrast, believed in her own conscience that one life saved was preferable to none saved, and so acted on the mother's behalf.

Is there absolute goodness here? Of course not! It's totally relative to the situation. The goodness has an "EDGE (limit) . This is why Alan Watts' statement of goodness having an edge must be taken seriously. And if it has an edge, it can't be pursued single-mindedly! In the same manner, happiness can't accrue singly from it. When the edge of the goodness emerges, as it must in human choices, then happiness itself must be contained or limited by degrees - since no perfect choice for the 'good' exists or is feasible.

One would have thought these Catholic missionary upstarts would have learned these basics, but evidently not. Indeed, they still appear to operate in the world or realm of delusion fueled by the part of the brain known as the OAA or the orientation association area disclosed by the research of by Andrew Newberg, M.D. and his associate Eugene Daquill M.D. ('Why God Won’t Go Away: Brain Science and the Biology of Belief’.) Recall here that once the OAA processes a religious idea, image or idiom and focuses on it, then that entity monopolized brain function to the extent of creating self-reinforcing feedback loops.

In this light, the article notes:

"FOCUS personnel spend at least an hour a day, "the holy hour," they call it, in prayer and contemplation. 'They spend seven hours a day talking to young people about God and at least an hour a day talking to God about young people' according to Martin".

It would be interesting to ask Martin here, if he's aware of which portion of his brain "talked to God" and whether he received any intelligible answers at all.

Linear Algebra - Solutions

We now look at the previous set of linear algebra problems and their solutions:


1) Let V = R^2 and let W be the subspace (2,1). Let U be the subspace generated by (0, 1). Show that V is the direct sum of W and U.


We have: U = (u1, u2) = (0, 1) and W = (w1, w2) = (2,1)

By Th. (4): If: U + W = V and if U/\W = {0} then V is the direct sum of U and W.

We see: U/\W = (u1 + w1) - (u2 + w2) = 2 - 2 = {0}

Then: V = U + W = (u1, u2) + (w1, w2) = (0, 1) + (2, 1) = (2, 2)

2) Prove theorems (1) - (4)

Theorem (1): Given V is a vector space and one basis has m elements and another basis has n, then m = n.

Proof: Let w1, w2......wn be elements of V, and assume n > m. Then w1, w2......wn are linearly independent. If we let {v1, v2.......vm} be a basis of V over the field F then there exist elements a1, C F such that:

w1 = a1v1 + a2 w2 + wm

By assumption we know w not = 0, hence some ai not = 0. Now, say a1 not = 0 without loss of generality then solve for v1:

a1 v1 = w1 - a2 v2 - vm

v1 = w1/ a1 - a2 v2/ a1 - ...............-am vm/ a1

Thus the subspace of V generated by w1, v2..........vm contains v1 and thus must span all of V since v1, v2......vm generate V. This implies both n > m and m > n are impossible, hence m must equal n.

Theorem (2): Let V be a vector space and {v1, v2, } be a maximal set of linearly independent elements of V, then {v1, v2, } is a basis of V.

Proof: We need to show every element of V can be expressed as a linear combination of v1, Let v be an element of V. Then the elements w, v1, of V must be linearly dependent by hypothesis, hence there exist numbers xo, x1, x n not all zero such that:

xo w + x1 v1 +.........................xn vn = 0

We can't have xo = 0 because if that were so, we'd obtain linear dependence among v1, Then, solve for w in terms of v1, v2 etc.

w = - (x1/xo) v1 - (x2/xo)v2 -.............- (x n/xo) vn

Proving that w is a linear combination of v1, and hence that {v1,} is a basis.

Theorem (3): Let V be a vector space consisting of n elements. Let W be a subspace which does not consist of zero alone. Then W has a basis and the dimension of W is less than or equal to n.

Proof: Let w1 be a non-zero element of W. If {w1} is not a maximal set of linearly independent elements of W, we can find an element w2 of W such that w1, w2 are linearly independent. Proceeding one element at a time there must be an element m < or = n such that we can find linearly independent elements w1, w2........wn such that:

{w1, w2............wn}

is a maximal set of linearly independent elements of W. (See, e.g. the proof for Th. 1 and note the number of such elements is at most n).

Now, use Theorem (2) and we can conclude that {w1, w2......wn} is a basis for W. Again, note the number of such elements is at most n, so the dimension is n.

Theorem (4): Let V be a vector space over the field F and let U,W be subspaces. If: U + W = V and if U/\W = {0} then V is the direct sum of U and W. (Note: /\ denotes intersection)

Proof: Given v is a member of V- by the first assumption- there exist elements u in U and w in W such that v = u + w. Thus, V is the sum of U and W. To prove it is the direct sum, we need to show that these elements u, 2 are uniquely determined. Suppose there exists u' belonging to U and w' belonging to W such that: v = u' + w'. Then:

u = w = u' + w'

Then: u - u' = w' - w

But u' - u belongs to U, and w' - w belongs to W. By the 2nd assumption, we conclude that u - u' = 0 and w' - w = 0, whence u = u' and w = w' (Q.E.D.)

3) What is the dimension of the space of 2 x 2 matrices? Give a basis for this space.

We posit the space of 2 x 2 matrices belongs to the vector space V. If V is a vector space thenany two bases for V contain the same number of vectors. The number of vectors in a basis for a vector space V is called the dimension of V.

For a member matrix of R^2 we have the most generic bases (forming each column):

(1) (0)
(0) (1)

Thus one basis would be:


and thus dim(R^2) = 2

4) What is the dimension of the space of m x n matrices? Give a basis for this space.

By Theorem (1) both n > m and m > n are impossible, hence m must equal n. Thus, the dimension of the space of m x n matrices is n. A basis for this space is:


Another would be:

(a m1)

By use of the most generalized matrix written as (a ij) with i = 1,......m, and j = 1.....n. the reader should be abel to verify the preceding.

Sunday, December 25, 2011

Chester B. Smith’s “Thoughts concerning the Universe”

It's always welcome when newbies express their personal thoughts and speculations regarding the cosmos, but they need to keep in mind: a) their level of knowledge compared to others who've put in many more hours or YEARS, and b) that if and when they attack astronomers and physicists in whatever way, they leave themselves open for takedowns. Such is the case with a recent article in the Intertel Journal Integra - by Chester B. Smith entitled 'Thoughts concerning the Universe'.

I could skewer all of Mr. Smith’s pet fantasies about how he perceives the universe, but just want to examine more closely a few where he oversteps the bounds of scholarly proprietary by taking pot shots at physicists’ logical or thinking capacities.

In his first paragraph, for example he wonders if physicists “share a common hallucinatory drug” in respect of how they ascertain the age of the universe by measuring its red shift. Like many neophytes, he conflates the distance determinations with ages, say of galaxies, and hence wonders “how a distant galaxy was formed at the beginning of the universe rather than 6 billion years later”.

However, pure distances alone don’t translate into ages. One must be aware of parameters beyond that. The most critical of these is the Hubble constant. One can think of it as setting the “’slope” or gradient for the relationship that links the velocity of recession of a cosmological object to its distance. Hence, it is more fundamental than just the single distance to a given object – since the cosmos is expanding in all directions and there is no one defined center of origin! (I.e. we cannot geometrically pinpoint the location of the Big Bang because it was an instantaneous inflation of both space and time)

Then, the age of the universe (in seconds) is: t = 1/ H_o

where H_o is the Hubble constant.

The beauty of this computation is that it renders redundant all distractive issues and questions such as "what distances are we rewinding back to", which truly aren't much use! Currently, we estimate H _o~ 70 km/ sec/Mpc, where Mpc denotes ‘megaparsec’ – and each parsec has 3.26 light years.

The above is little use, however, without changing a lot of units and ensuring their consistency. The key initial step is to obtain the megaparsec equivalent for kilometers:

MPC(km) = (c) (86400)(365.25)(3.26)x 10^6

where c = 300,000 km/sec, the velocity of light

Then: MPC(km) = 3.08 x 10^19 km/Mpc

Now, what is usually colloquially called the "Hubble constant" is in reality the Hubble scale factor (a = 70 km/ sec/Mpc). The REAL Hubble constant (H_o) is the scale factor divided by MPC(km):

H_o = a/ MPC(km) = 2.26 x 10^-18 s^-1

then, t_o = 1/ H_o = 1/ {2.26 x 10^-18 /s} = 4.4 x 10^17 s

Which, when converted, is about 1.3 x 10^10 yrs. or 13 billion years in age.

Smith’s next point of bafflement concerns gravity and “how it could change in a star unless it’s imposed from outside”.

But think of a star like a gigantic onion with multiple layers. The layers at the top or near the surface are lighter, because they have lighter gases which aren’t so compressed. But as one piles additional layer upon layer the weight of those layers presses down more on the layers toward the center of the star. Thus, the gravity is greatest near the stellar core and this helps to compress the gases in the core to their maximum pressure. Hence, it is precisely within the star’s core we expect the nuclear fusion reactions which provide its energy to occur.

A star, Main sequence – like the Sun – remains in balance and stability (what we call “hydrostatic equilibrium”) because each layer’s weight acting downwards is balanced by the radiation pressure (from the outward flowing radiation) acting outwards. I believe this is what Smith means when he argues against stars “balancing themselves against themselves”. Except they don’t: two distinct forces are balanced at each layer against each other.

Smith also appears to have problems grasping how “space dust” can agglomerate into a stable mass and then “combust” as a new star. Perhaps one of the best books he could get (as well as anyone else mystified by the process) is Isaac Asimov’s ‘The Collapsing Universe’. Using basic physics principles Asimov shows (Chapter 3, ‘Compressed Matter: Stars’ p. 55) exactly how the accumulation of dust and gas unfold – under the influence of gravitational attraction – for form a new star.

Another paragraph of mystification becomes clear once basic principles are learned:

Smith writes:

I believe the purpose for the change from pure energy into the various forms of matter is to achieve balancing or stabilization in order to prevent collapse back to the original point”. But pure energy isn’t needed for this. . We know that the cosmological density parameter is crucial, viz.

OMEGA = rho / rho_ c

where rho is the observed cosmic density, and rho_ c is some critical value or threshold such that only if:

rho > rho_ c

the cosmic density reverses the expansion and forces a new cycle, starting with Big Bang. But current data, e.g. from Boomerang and other satellite detectors (See, e.g. 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003,) shows that W » 0.3 or that: r = 0.3 (rho_c) I.e. that rho (less than) rho_c so there is no danger of the cosmos decelerating, and hence re-collapse. Hence, it is the residual mass of the cosmos (mostly in dark matter, such as black holes, intergalactic matter etc,) which inhibits any collapse, not “pure energy”.

Another mystifying comment from Smith is:

Why assume the laws of physics are abandoned once you look into outer space?”

But who says they are, other than Smith? In fact, the laws of physics attain their state of maximal potency and application in space, and again – we have measurements to back up whatever claims are made. There is no “mystery” other than one deliberately confecting such, as Smith does. For example, he appears to question the rational basis of the Big Bang, and yet we have the evidence for the isotropic 2.7 K relic radiation – first observed by Penzias and Wilson at Bell Labs in 1965 and for which they won a Nobel Prize twenty-odd years later – which shows a cosmic fireball had to have originated some 13 billion years ago. That he (or others) may not be able to wrap their brains around that doesn’t make it less so, or counterfactual.

Like many other hobby- hunchers I see (those who come up with oddball conjectures to try to supplant accepted physics) Smith also displays an ambiguity in his terminology which conflates differing aspects of the physical world without a proper description or definition. For example, at the bottom of p. 18 he advances formation of an “energy field”. But there is no such thing. What we have are electrostatic fields, electro-magnetic fields, strong and weak nuclear fields, and gravitational fields. There is no …generic…”energy field” and none has been observed or measured. Neither is there such a thing as a “universe field” (p. 19 top). You can't simply make up entities like "fields" in your head and confer reality on them by fiat!

Smith rambles on that "we love mystery at the expense of logic” (ibid.) but this is codswallop. The thing most physicists hate above all is leaving any “mystery” out there so that assorted obscurantists, crackpots, cranks and others can parlay it into mumbo-jumbo….say like Michael Talbot’s alleged holographic “miracle” fields popularized in his Holographic Universe.

The truth is that physicists are ruthless in their logic applied to the cosmos, but this logic is always framed in its most concise and precise form – the language of mathematics. Physicists understand that without mathematics, such as tensor calculus, differential equations, non-commutative geometry and the like, we’d only really be able to theorize about one one thousandth of what we have. Mathematics makes the transfer from verbal conjecture to hypothesis to testing concrete.

Thus, it’s odd when Smith blurts that “math is likewise inefficient’. Perhaps only because he doesn’t know enough, and maybe never even took an advanced (e.g. college algebra) course, far less calculus or differential equations.

He appears to arrive at this nonsense by referring to a “pre-telescope European astronomer who proved mathematically that the sun and planets revolved around the earth..he accomplished this by adding loops in the orbits”

He is referring, of course, to the astrologer Claudius Ptolemy who generated a complex model (published in his Almagest) using “epicycles” (the added loops of which Smith writes) to explain the planetary motions, especially the retrograde motion of Mars (when it appears to be moving backward relative to the fixed stars)..

The problem, of course, is that the Ptolemaic system of epicycles is mythical and not based on the actual heliocentric system which follows from Newtonian principles of gravitation. It is here that the use of mathematics such as the differential equations of celestial mechanics, proves far more efficient and powerful than endlessly adding cycles that have no physical basis.

Thus it is that the over-complicated system of epicycles is rendered redundant once one understands and appreciates the planets move in elliptical orbits, not in circular ones. Ptolemy’s error was in trying to squeeze planetary motions into a “perfect” circular mold. Once this change to the actual physical orbits is made, then the appropriate equations, such as Kepler’s, e.g.

n(t – T) = E – e sin E

where n is the mean motion (in degrees per day or per second), t the referenced time, T the time of perihelion passage (e.g. closest point to the Sun), e is the eccentricity and E is the eccentric anomaly.

This can then be used in conjunction with others to arrive at the orbital elements for all the planets. These include: the eccentricity of the orbit, e (e.g. how elliptical it is or the deviation from circularity), the semi-major axis, a, or the mean distance to the Sun, the inclination (i) of the orbit – or the tilt of its plane with respect to the reference plane, and others.

Once these are known, I can then use the relevant equations, as I have done – whether in university projects or my own research – to accurately forecast the position of any planet well into the future – say the position of Jupiter in the sky on Feb. 1, 2100.

This is something Ptolemy and his epicycles could never do, and certainly not to the accuracy I can attain – an accuracy, by the way, that enables us to land complex Rovers on Mars, and mount close flybys of other worlds.

This alone skewers Smith’s claim that “mathematics is more of a copy machine than a discovery tool”

For his info, without the mathematics of tensors, general relativity would have remained a wild speculation and never attained theory stage. Without the basis of complex analysis neither plasma physics or quantum mechanics would have attained the maturity they have.

What Smith’s foray into the universe shows, if nothing else, is that a little knowledge is a dangerous thing – if it leads one to accept a perception of the cosmos totally fabricated from vague hunches, professed “common sense” and a mish mash of whacky ideas and terms …picked up from who knows where.

A final suggestion to Smith: there are terrific online courses in astronomy and physics available at the Yale University Open Course site:

See, e.g. the Astrophysics course at the top and Fundamentals of physics I,II lower down.

Even if you’re not mathematically adept, exposure to even some of these principles, concepts and illustrations will dispel at least some of your misconceptions about the cosmos! The question for you to address is: Do you wish to persist in these pet, subjective misconceptions ….or do you want to remove the blinders?

Saturday, December 24, 2011

WHAT Event Does Dec. 25th REALLY Celebrate?

This is a fair question: what exact event is the date December 25th to commemorate? The answer is not staightforward, and unless one delves into the past - and especially the assorted manipulations of our calendar, one cannot claim to know very much! There are in fact two serious ways in which the deviations of any given prescribed date can occur: i) via a year or years error (which is major) and a date error.

The error of type (i) throws out presumptive times for any given event. For example, if we know that Abe Lincoln was assassinated on April 15, 1865, we would have serious issues if the real date were actually 4 years earlier or later. The reason is that it would throw the timeline for all other events off as well. The error of type (ii) is perhaps not as serious at first glance, unless the date is intended to be specially commemorative of some major event, like a birth or death. In the case of our calendar both types of error have transpired.

1. The Roman Republican Calendar:

The earliest form of this calendar probably had 10 months but a later improved version, but this evolved to a later 12-month form based on the Moon's synodic period (e.g. the time from the same phase to the same phase, say full Moon to next full Moon). Because it was lunar synodic, where the Moon's period is 29.5 days, it meant that 12 months were set out with alternate durations of 29 and 30 days. That meant a total: (6 months x 30 days/month) + (6 months x 29 days per month) = 180 days + 174 days = 354 days.

Simple arithmetic shows that given this - relative to our own calendar (and the assigned length of the year being 365 ¼ days), one would find a whole month's (30 days) difference would accrue after about 3 years (e.g. 3 year x 11 days/yr = 33 days).

A more enhanced version of the Roman Calendar in use from 70 B.C. made small adjustments to the individual months such that the assigned days became (for each month):

Ianuarius (29)

Februarius (28)

Martius (31)

Aprilis (29)

Maius (31)

Iunius (29)

Quintilis (31)

Sextilis (29)

September (29)

October (31)

November (29)

December (29)

For a total of 355 days. So again, as before a whole month deficit accumulated after every 3 years. Since the original version was formed around 2 B.C. this meant a lot of time elapsed before the Julian calendar reform of 46 B.C. (In this reform, driven by the advice of the Alexandrian astronomer Sosigenes, the lunar synodic month was abandoned and the resulting calendar based on the tropical year - determined then to be 365 ¼ days.

For a total of 44 years elapsed this meant a total period displaced:

(44 years x 10 days/ yr.) = 440 days or about 1.3 years on average when other small errors are averaged including odd intercalations of the calendar, i.e. declaring as full years those periods (which may have been only 9 months) when the intercalator's friends were holding public office.

Thus, by the time of the Julius Caesar's redo the calendar was already out of whack by over a year. This meant the putative date for Christ's birth was not 0 A.D., but had to be earlier than 1 B.C. (This, of course, may have been one reason why the antiquated forms of 'B.C.' and 'A.D.' were eventually dropped for C.E. (common era) and B.C.E. (before common era).

2. Alterations in the Julian Calendar:

The main change in devising this calendar, as noted previously, is that a 365 ¼ day year was adopted, which meant tallying 365 days normally, then 366 days every fourth year, which would be a "leap year'.

Another alteration was needed to re-adjust the date of the vernal equinox which had fallen badly out of place under the Roman Republican (lunar) calendar. Of particular import was the vernal equinox or first day of spring, which was originally March 25th, but had devolved to March 22. In addition, since March 25th was the vernal equinox it meant that December 25th was similarly the winter solstice.

This held special import on account of the tie in of the solstice - when days begin to grow longer, with the birth of the Sun, and hence the Roman Sun god. Thus, near midnight of the 24th of December the followers of Mithra would be heading to their special temple on the Vatican (Vatican hill) and declare joy at midnight for the birth of their Sun savior - born in a cave (like so many Sun gods) and to free men from sin, or save them. As noted by author and historian Joseph McCabe (The American Atheist, Nov.-Dec., 2007, p. 9):

"The Savior Mithra had been in possession for ages of December 25th for his birthday. He was the real 'unconquered Sun': a sun god transformed into a spritual god with light as his emblem and purity his supreme command."

In effect, an intercalation by Caesar of the Julian calendar would preserve not only March 25th as the vernal equinox but December 25th as the original birth of Mithra the Sun god. To do this, Caesar intercalated 3 extra months in the year 46 B.C. bringing its length to 445 days. For this reason, 46 B.C. became known as the "year of confusion". (After Caesar's death in 44 B.C. the month Quintilis was named in his honor, hence, July).

3. The Christian Emergence and Further Changes

The Edict of Milan, formalized in 313 A.D. returned confiscated property to Christians (hitherto under persecution) and more importantly, allowed religious toleration so that Christians could gather without fear of interference or challenge. This directly set the stage, along with other steps, to unite the Christian church with Sun god religion of Constantine. Calendrical alterations directly preceded this 'takeover' of one god by another.

The first alteration in the wake of the Edict was the Council of Nicaea which, in 325 A.D. defined the dates of Easter and certain other religious holidays. In particular, March 21 was re-specified as the date of the vernal equinox while Easter was defined to occur on the first Sunday after the 14 day of the Moon (e.g. days after the full Moon). It ought to be noted here that the Christians at Nicaea didn't willy- nilly just change the date of the vernal equinox from March 25 back to March 21. No, what happened is that between 45 B.C. and 325 A.D. that date had slipped back from March 25th to March 21st. The reason is based on simple math: Because the Julian year (Sec. 2) was defined with an average of 365 ¼ days and is 11 mins. 14 secs longer than the tropical year of 365 days 5 h 48 min 46 ec then the slight difference had accumulated to 3 days in those 4 centuries.

Of course, in the same interval, the original winter solstice of December 25th had also regressed to the earlier date of Dec. 21-22 (depending on the year).

"Christmas Day"

It wasn't until 29 years after the Council of Nicaea, in 354 A.D. that the newly liberated Christians claimed December 25th - the designated original birth date of the Sun god Mithra- as their own nativity for Christ. There are many speculations as to why Christians appropriated this particular date when the eastern orthodox and other variants stuck with January 6th. The most plausible one is probably because the conflation allowed Christian Rome to pay homage to the earlier Emperor Constantine who had expedited their liberation. By allowing the key dates for the Sol Invictus cult and their own deity to coincide, the emerging Christian church not only gained further credibility for their own god (while pacifying many skeptical Romans) but also timed their celebrations to coincide with the Roman "Saturnalia" - which emphasized good will to all men and "peace on Earth" (so no wars could commence)

4. The Gregorian Calendar.

By 1582, that tiny deviation between Julian and Tropical year of 11 mins and 14 seconds had grown to another 10 days so that the first day of spring was occurring on March 11. If this regressive trend were allowed to continue, Easter would eventually fall in the middle of winter. (Bear in mind again, Nicaea assigned Easter not by date of year but by days after the first full Moon after the vernal equinox. If the latter date was earlier, then Easter had to be as well because its timing was bound to the equinox date).

The correction or Julian calendar reform was instituted by Pope Gregory and became known as the "Gregorian Calendar".

The reform here proceeded in two steps:

1) Ten days were dropped off the existing calendar to bring it back to March 21 - where it was at the time of Nicaea. This was undertaken on October 4, 1582 when the next day was proclaimed as October 15, 1582. (Some idiots at the time actually complained that the pope had "taken 10 days out of our lives".)

2) The rule for the leap year was changed so that the average length of the year would closely aprpoximate the tropical year. The rule then applied was that only century years divisible by 400 would be leap years. Thus, 1700, 1800 and 1900 - all leap years under the Julian calendar were not under the Gregorian, while 1600 and 2000 were.

Meanwhile, the average length of the Gregorian calendar, at 365.2425 days, was correct to within 1 day every 3300 years.

Now, WHO says math isn't important?

The upshot of all this is very strange but needs to be stated.

1) Up until 354 A.D. Christians had no remote idea of when their Savior was born. As noted by McCabe (ibid.):

"Early Christendom found itself in the peculiar position of telling the world of the most tremendous birth there ever was...but being unable to say when it happened."

2) The current assigned month, date and year cannot possibly be correct, but must be a confection. As we saw, the designated year is off, and in addition, December 25th marked the original winter solstice and birth of the Roman Sun god, Mithra.

So tomorrow, when people are saying they're celebrating the birth of a "Savior" are they truly aware of which one that is?

Inquiring minds want to know!