Wednesday, April 16, 2014

Astro picture for the day/ quote/thought extras

Credit & Copyright: T. Rector (U. Alaska Anchorage) & H. Schweiker (WIYN, NOAO, AURA, NSF)

Quote for the day,

"The moving finger wrights and having writ moves on. Nor all your piety nor whit can cancel half a line.  Nor all your tear wash out  a word of it." - Omar Khayyam

In episode 30 of the Mechanical Univese(Potential and Capacitance), David L. Goodstein mentions how come lightning rods have round nobs on them instead of a sharp point as Benjamin Franklin thought. The reason is because of King George(of the British/American revolutionary war fame) thought they should be round instead of a sharp point. These are the types of connections that James Burke seems to be most in to. But, he makes some other connections.  I make some connections between these other connections and Jacob Bronowski's understanding of the nature of mathematics here,

Mathematics is the real connections. It's the underlying structural connections found by questioning assumptions - like the way questioning the assumptions of the flat Earth because that's what it looks like on first appearance.

Mathematics is an abstraction.  Abstraction is a common form that many other structures have.  For instance, two apples and two oranges both have the similar structure of the number two. Or the way differencial equations can be used to describe chemical, mechanical, electrical phenomenon. Yet, James Burke is proudly quoted as saying,

“Learners may study either history or physics, or perhaps only Renaissance history and astrophysics. People tend to become experts in highly specialized fields, learning more and more about less and less.” –James Burke

It happens(James Burke connections like) that legitimate things are done for illegitimate reasons.  For instance, Brahmagupta comes up with the general form solution of the linear Diophantine equation(Diophantus doesn't solve this in his collection of 'Diopantine equations.') to fix the stats of planetary motions collected by generations of Indian(India indian) astronomers. James Burke shows that the major historical events of Western civilization at least can be mapped out and clarified by the history of science and technology.  But, as the quote above indicates, he doesn't understand the connections of mathematics(the fundamental knowledge) to everything else.

Wednesday, April 9, 2014

astro picture for the day/ Quote for the day/thought for the day . . . Greek Philosophy

Image Processing: Oliver Czernetz - Data: Digitized Sky Survey (POSS-II)

Quote for the day,

"Concepts without precepts are empty. but precepts without concepts are blind." - Immanuel Kant

Thought for the day . . . Aegean collapse and Greek philosophy,

My initial exporation of the Greek period focused more on Greek mathematics; i've recenlty learned some of the value of their philosophy.

The word Renaissance makes most people today(21st century through the past to the Renaissance) think of the European 1500s Renaissance.  Before then, there's what the Renaissance people called 'the dark ages.' But, another dark ages has become the greatest archaeological mystery of the last hundred years or so. This dark ages led to the Greek renaissance from 600 B.C. to the Athens golden age.  The Athenian high point really only lasted a generation or two before the Spartans ganged up with the Persians, other Greek city-states that didn't like being taxed to put up the Parthenon.  And then, the Macedonians of Alexander the Great led to the beginning of the Hellenistic Roman period which really made Athens just a city in the Hellenistic mediterraenean.

Before this dark ages before the Greeks and the Israelites, there was the world of the Egyptians, Hittites, and Minoans(also Babylonians). A recent book about the Aegean collapse is getting a little popular. Eric Cline's "1177 B.C.: The Year Civilization Collapsed."  I'm not going to explain what the conclusion is; really, the conclusion is complex and inconclusive.  I'll say that their world became to big to administer.  One could say much the same happened with the Romans.  I've of course argued for a certain religious anti-science that took over.  I don't think this happened with the late bronze age. But, I do think that because they didn't spend their time and wealth(whether you want to call it money back then or not) on science and technology to make everything from agricultural to dealing with pirates, they collapsed.

Because of the collapse of these hugh empires, more people were able to learn on their own and what they wanted to learn.  As everyone notes, the Greeks before the Athenian period were a bunch of city-states. These city states evolved in a diversity of ways.  The contrast between the Spartans and Athenians is particularly striking. But, the fact is the Greeks diversity allowed a certain amount of questioning of various assumptions/beliefs. The video below talks about some interesting Greek philosophy.  Rebecca Goldstein mentions the Greek tragedies argued for doing science/art to make life worth living.

Some more Greek philosophy that I've learned about recently, through Peter Pesic's "Abel's Proof"(chapter one), is Plato, Socretes, and Thaetateous{who made certain generalisations of irrational numbers beyond the Pythagorean proof of the irrationality of the square root of 2; There's infinit series, and with different proportionalities like arithmetic, geometry(addition and multiplicative respectively); Thaetateous made this connection and defined different types of irrationality.  Eudoxus then was able to calculate the precise number angles of the Platonic solids . . .)} is how doing mathematics stings you're assumptions.  Kind of like how learning the Earth is round and not flat which is what your initial perception is.  The Greeks valued this sting as what should happen.  Religion tries to prevent this sting.

astro picture for the day

Credit: ESO(European southern Observatory)

This is a supernova remnant with a chance alignment with a star.

astro picture for the day

ESA/NASA Hubble Space Telescope image

Tuesday, April 1, 2014

astro picture for the day/ Throught for the day - 3102 B.C!

Image credit ESO/MUSE consortium/R. Bacon

This astronomy picture of the Orion nebula is from the ESO's new 'Muse' 3d spectrograph.  They're pretty excited about it.  I must say it's pretty close and maybe better than the Hubble Space Telescope image.  There may be details that my eye anyways, can't see.

- Thought for the day,

3102 B.C.

I don't want to get into too much large numbers and technicalities, but the Indians divided up time into cycles of various thousands and millions of years. The fundamental return of all planets is called Mahayuga which is 4,320,000 years long. It is divided into 4 quarteryugas of equal duration, and the last quarteryuga is Kaliyuga which starts according to the Indians around Friday, Febuary 18, 3102 B.C!

There was a sunrise and midnight system, they tried to calculate the number of revolutions. Aryabhata, around 510 A.D. The mean(average) motions motions of the sunrise and midnight calculations did not agree. Brahmagupta tried to make corrections of these. He did so by making the general solution to linear Diophantine equations.

Kind of like there's a quadratic equation that allows you to solve all second degree equations just by plugging in, there's were efforts to solve number theory, and make a closed form solution. The linear Diophantine general form equation was arrived at first, as far as I can tell, by Brahmagupta. He used Euclid's algorithm. There's actually two forms of it. One is a subtraction form(real easy, just subtract the smaller of two numbers of a number couple . . . repeatedly till you can't calculate anymore), and a division version; the division form is expressed as a=bx+r, r is the remainder. After the first division of a by b, you divide b by r. This is a slight change from regular division. You can repeat this and solve say G.C.D problems. Most people learn how to calculate G.C.D. by prime factor trees today. That's a later more sophisticated way. Euclid's algorithms turns out to still be interesting and valuable for number theory purposes that most people never see, like the linear Diophantine equation. There's a few more things to arrive at the linear Diophantine equation though. One performs the Euclidean algorithm till you get to 1. Then you rearrage one of the Euclidean algorithms to get 1 on one side. Then you rearrange another to get a remainder term that is analogous to the previous algorithm calculation, and then substitute. Do some simplifiying, and one gets the linear Diophantine equation. I'm just describing it.

Brahmagupta didn't correct Aryabhata empiracly. He did so assuming the date of 3102 B.C.

But, here's the kicker, a Kaliyuga is one tenth a Mahayuga, or 432,000 which equals 2x60^3. 60 is a common number of Babylonian mathematics. This number occurs in some Berossos, a Babylonian astrologer who moved to Greece to found a school of astrology around 300 B.C.

Berossos tells of a conflagration will take place at conjuctions in cancer, and a deluge when they come together in Capricorn. In Persian sources, a deluge is said to take place whenever the planets come together in the space between Pisces and Aries; the last time this happened was on Febuary, 3102 B.C.!(at least according to astrology, not scientific fact; this is a date long enough ago, that they could just say there was a conjunction back then).

We don't know whether Berossos got his 3102 from the Indians or the other way around, but in some quotes mentioned by Van Der Waerden in his "Geometry and Algebra of Ancient Civilizations", he suggests the end of the world predicted by astrological means was a common idea. He mentions one quote from the "Laws of Manu."

----------------- more astronomy for the day

Spitzer infrared space telescope 360 degree panorama of our entire Milky Way galaxy!

Monday, March 24, 2014

Astro picture for the day

ESA/NASA Hubble Space Telescope image

Note for the day: I've more or less updated or fixed the mechanical universe links.  Instead of embedding, I just put in links.  For some reason, I couldn't find the videos when searching for them through the blogger youtube search engine. I could have sworn I posted almost all the Mechanical Universe videos, only in order.  The Mechanical Universe videos are not exactly in order of how science discovered things.  For instance circles is episode 9.  Circles should have been number one!  Then the Mechanical Universe producers made two episodes about the fundamental forces; these should have been last!  These are episodes 10 and 11 respectively.  I'll go ahead and post those here just to make this a bit more of a thought for the day.

Mechanical Universe 10: Fundamental Forces  and Mechanical Universe 11: Gravity, Electricity, & Magnetism

- Quote for the day extra,

""Let us come to Chaldean manifestations. In discussing them Plato's pupil, Eudoxus, whom the best scholars consider easily the first in astronomy, has left the following opinion in writing: 'No reliance whatever is to be placed in Chaldean p471astrologers when they profess to forecast a man's future from the position of the stars on the day of his birth." - Eudoxus, through Cicero, De Divinatione, book 2, 87

Thursday, March 20, 2014

astro picture for the day/Evolution of Human thought for the day

Image Credit & Copyright: Fred Vanderhaven

The April, 2014 issue of Scientific American has an article about Human evolution that summarizes some of the major discoveries in physical anthropology over the last few years.  These discoveries seem to me to make an arguement for how we went from another animal to being able to think about the universe.  I'm sure brain and genetics discoveries await, and more fossils and insights abound.  Well,  I still find this article to bridge the gaps.

The puzzle has always been, "how did we survive in a land with much more athletic cats, animal(and Australopithacus) killing/eating eagles?" One insight I recall and included in this Scientific American article was running.  Sure, we still could never compete with any four legged animal  . . . in short range; but, over long distances, even the mightiest and fastest predators would get tired.  And this only with in a mile or so, most of these stronger faster animals would get gased.  Of course, how could we get these athletic beasts to run away from us?  We could throw heavy stones(Homo Erecuts at least was probably stronger than you'd think, and stronger than most humans grow up today), and gang up on them. Endurance running appears to have evolved along our line two million years ago.

Because of this running, we developed sweat glans - a cooling mechanism.  This evolved about 1.6 million years ago. Around this time, we started to loose our fur.  We'd soon need to cover up every now and then with clothes.

Another insight over the last couple of years ago is our ability to throw.  Studies of anatomy that allows us to throw so much better than say chimpanzees shows we developed this ability around the time of the Australopithacines. The ability to throw made it harder for us to be good at climbing trees.  They made decisions to evolve in different ways; it was almost impossible for our species to turn back technologically almost two million years ago.

The shift to a meat diet from being able to hunt down a source of food not previously available to them meant less deprived diet, and the brain was able to grow more than ever before. From two million years to two hundred thousand years, the brain went from 600 cubic centimets to 1,300 cubic centimeters.

Homo Erectus may have also developed a division of labor long before the coming agricultural revolution(generally speaking, a division of labor is noted as a feature of the agricultural revolution). Males generally went and hunted, while females foraged and cooked and maybe did much more, like government.  This female leadership may have lasted all the way down to the famous Venus figurines found all over Europe of pre-Egypt/Mesopotamian cultures.  Cultures like Stonehence and the Malta ruins builders.

-  I'd like to note another insight not mentioned in the article.  Chimpanzies don't know how to swim. When a fellow chimpanzee falls into a water too deep to stand up in, the others are helpless and just watch the guy go straight down to the bottom and drown.  Humans learned how to swin hundreds of thousands of years ago. There's some evidence of boats back in Homo Erectus days.

This is Turkana boy, one of the most complete skeletal fossils ever discovered.  It goes back to 1.6 million years.