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The Author is actually a fictional character created by Washington Irving. His name is Dietrich Knickerbocker, and he is a historian. The last name most probably came from the traditional Dutch community where Irving resided in and ulitimately made fun of. Irving and other writers of the same period were called Knickerbocker writers.
http://www.bibliomania.com/Reference/Simonds/SHAL/p1-chap3.html
http://www.hudsonvalley.org/education/Background/abt_irving/abt_irving.html
This collection of descriptions are taken from actual 'creation' myths. One example being the sky held up by the four pillars which is from Egypt. The sky is actually the roof of the earth and the four pillars, placed at certain points around the globe, supported it. Knickerbocker, by mentioning these myths in rapid succession without giving them a source, is actually doing precisely what he says he won't do towards the middle of the passage, confusing and obscuring the intent of his words with extra, needless information.
http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node25.html
Anaxagoras (500-428 BCE.) He was a very well known philosopher in Ancient Greece. He was banished from Athens after his philosophies outraged the local citizens. Some apparently thought he was calling for aethism or monotheism. Anaxagoras was actually trying to establish the idea of the 'seed' or the basic element of everything. He had come to the theory that everything is comprised of 'seeds': fire, air, etc. Depending on what the item was, they would have more of one seed than another.
http://www.utm.edu/research/iep/a/anaxagor.htm
Heraclitus (535-475 BCE.) Another Greek philosopher, he indeed had the name 'the Weeping Philosopher' for his pessimistice outlook on life. When Knickerbocker refers to the sun going out, under the approval of Heraclitus, it is a twisting of one of Heraclitus' theories. He claimed that fire, eternal fire, was a constant process of give and take. What the fire took away as it burned would give back as it extinguished.
http://www.utm.edu/research/iep/h/heraclit.htm
Herschel's full name was William Herschel, though he had a son named James Herschel, the elderly one fits the time frame better. He built powerful telescopes and increased, with his research, people's understanding of the universe, or more specifically the nebulae. Hence the attention Knickerbocker gives in describing the area around the sun as "certain empyreal, luminous or phosphoric clouds"
http://windows.ivv.nasa.gov/cgi-bin/tour.cgi?link=/people/enlightenment/herschel.html&f
This is where one of the contradictions come in. Knickerbocker has just spent most, if not all, the intro in the naming and listing of all possible theories of creation and stars which he could come up with. Irving, by having Knickerbocker state that he will have nothing to do with them, is simply drawing the reader's attention to the universe and clueing them in that what he will speak of, perhaps if not in this chapter, than in later chapters -will- have something to do with the theories of the stars and nebulae.
A collection of pictures of New York from 1883. The link leads to a page outside this one and is a series of pictures. Though the pictures are approxmiately 75 years later from when Irving wrote this passage, it is still worth a look.
http://www.preserve.org
Here again is a contradiction or an irony depending on who's point of view one is looking through. From Knickerbocker's statement here and then a few paragraphs earlier where he tells the reader to disregard everything he's said because it is inapplicable - it provides the opposite effect. If Irving has gone to so much trouble to provide the background information, then has Knickerbocker tells the reader to discard it - it is something to pay attention to. If Knickerbocker than says to pay the utmost attention to what he says because it is all relevant from here on, the reader can expect the following paragraphs to be of no use. And as it turns out - the following few paragraphs are useless, quite literally. The philosphers and scientists with their theories are disgruntled that the sun and earth refuse to run according to their theories. They learn that it is useless to direct the course of the sun, being capricious like a woman, and change their theories instead.
Another contradiction. As proved by his extensive use of footnotes early on, Knickerbocker is precisely one of those philosophers/historians who write, not for the edification of others, but to impress his peers. Why else would he have written earlier on, " I must here intreat my unlearned readers not to be discouraged when they encounter a passage above their comprehension." if he plans on writing fully comprehensible theories for everone. Irving, once again, through Knickerbocker is mocking the academic crowd.
For his knowledge standeth so upon the abstract and general, that happy is that man who may understand him, and more happy that can apply what he doth understand--Phillip Sidney, on philosophers, An Apology for Poetry
An understatement here. Making full use of ironic statement, Irving sets up the reader for another esoteric explanation involving long, complicated explanations which go nowhere. Instead they are treated to Knickerbocker's grave and meticulous description of a professor who swing a bucket full of water over his head as a teaching tool.
This is less a footnote than an idle comment. Though I was unable to find a link or a reference, I vaguely remember Puddinghead being a character from a children's book or a nursery rhyme.
Another point of absurdity. Philosophers, so intent upon their theories and formulas, fail to exercise common sense. That they have worked out and so expect the earth to fall into the sun is ridiculous. This is much like Knickerbocker himself who can not see how absurd his thoroughly detailed descriptions of such experiments and teachings are. Another example at how Irving works, through Knickerbocker's words and his own expectancy for the reader to see through his placid and condescending tones.
A university in Norway, they discovered how to use the Leyden jars, which are named after them. These jars were developed to contain electric currents.