Sunday, March 20, 2016

astro picture for the day/ Quote for the day - Galileo and Venice


ESA/NASA Hubble Space Telescope image

"Now, the cowardice(if we may be permitted to use this term) of ordinary minds has gone to such lengths that not only do they blindly make a gift-nay, a tribute-of their own assent to everything they find written by those authors who were lauded by their teachers in the first infancy of their studies, but they refuse even to listen to, let alone examine, any new proposition or problem, even when it not only has been refuted by their authorities, but not so much as examined or considered." - Galileo Galilei


The above is a video documentary about Venice. As the video itself explains, Venice evolved out of the dark ages, to escape the Germanic barbarians. It was called the crown jewel of the middle ages. People will often deny that the European dark ages ever happened.  Venice is one place they'd point out.  Other places would be the Byzantine empire, and maybe even the Arab Spain of Andalucia. One thing to note quickly, is that Venice was partly protected/paid for by the Byzantines.

  Also, much of the wealthy architecture came after the European crucades from the 1000 to 1400s.  Those are interesting dates, because the dark ages are really divided into early and later dark ages.  These are defined by the Europeans discovery of the Arab mathematics/science texts in Arab Spain/Andalucia.  These turned out to be Arab translations of Greek mathematics. Then, the end of the 1400s was the end of the dark ages and the beginning of the Italian Renaissance. The Venice was partly built on blood money. This is some of what's not mentioned in the Venice documentary above.

I've mentioned some of Venice before when mentioning some remarkable things found by explorers of the Americas.  Previous explorers had traded Venice products with the Native Americans. Venice was put in it's place by the explorers of the Americas(English/French/Spanish/Portuguese). Venice had conquered the late middle ages, but after the Explorations/Exploitation of Native American wealth, Venice became a relic of a glorious past, and a pleasure capital of the world(something Europe kind of it today; it's the vacation capital of the wold right now). One major last thing not mentioned in the video documentary above is that much of the drama of Galileo took place in Venice!

--> Galileo wiki link . I read Galileo's "Two New Sciences" many years ago.  The book is amazing for all the mathematical proofs and mathematical ideas like the equivalent infinities of the even numbers to the natural numbers.  I don't remember it all, when writing this. But, I did just finish reading Galileo's "Dialogue concerning the Two Chief World Systems".  I also recall through just seeing Jacob Bronowski's "Ascent of Man" videos that Galileo had created scientific instruments other than a telescope. The wiki link above mentions those.

I mean most people here that Galileo rolled balls down inclined plains, and so what?  Maybe they see the connection between that and different mass bodies falling at the same rate in a vacuum.  This is remarkable enough; but few realize the amount of other science and mathematics he did.  Not to mention that Galileo represents the end of the Greek Aristotelian and Ptolemaic physics. Isaac Newton physics, which came just after Galileo's death goes way beyond Galilean physics, but 1) Newtonian physics is built on the foundation of Galileo's work, and 2) Galileo as indicated above did so much already.

I find it often stated that Galileo didn't know the calculus.  This is for the most part true; but, he did know average speed in his "Two New Sciences" book, and he knew one half of the fundamental theorem of the Calculus. The fundamental theorem of the Calculus relates, indeed equates the differential calculus of instant velocity on one side, with the integral/sums calculation of smooth surfaces on the other side. He knew that distance is the area of velocity, with respect to time.  Fermat, in France around the same time as Galileo came up with the tangent method to find instantaeneous velocity; this would be the other half, and both insights found there way to England just a generation later for Isaac Newton to put them together.

Some of what's noted in Galileo's "Dialogue Concerning the Two Chief World Systems" is the Americas . . . he argues for the sphericity of the moon based on its brightness! He considered brightness reflectivity on smooth and rough surfaces to deduce that the moon is spherical . . . when he talks about how in a pendulum, the time of the swings are the same whether the swing is long or short in terms of a ball moving in a vacuum hole through the Earth . . . Galileo constantly finds wonder and the excitement of discovery in logic and scientific facts throughout his books. . . . he points out that an infinit circle has equivalence to a straight line . . .

He makes simple geometric proofs of some physics that the Greeks could have done, but just didn't(not even Archimedes). He shows how smaller motions would take greater energy to keep an equivalent mass attached than the bigger circular motion(one can think of smaller and larger wheels, or even planets in motion around the sun here); this he does by showing the secants pointing towards the central point shared by the two larger wheels are of different lengths; for the smaller wheel, the secant is greater than for the larger wheel.  Let me put it this way, if you have tangent lines to a curve, one can see the curve moving away from the tangent line; in the smaller curve, this moving away from the tangent line is greater than for the larguer circle.

. . . he gives the mathematics of parallax, and argues that the two new stars(we would call them supernova today) as seen by Kepler and Tycho Brahe in their lifetimes(he mentions Tycho Brahe's great experimental work) must be very far away . . .

  He also shows frustration in a couple of pages towards the end that would land him in trouble.

His arguing for Copernicus puts him in a bad standing as it is.  But with the need for cannons, the church had to relent enough as it was.  Galileo didn't need to spout off like he does in a few places in his Dialogue book. . . . on page 380(of my copy anyways), he uses the word "imbeciles; he says people are too stupid to even acknowledge that they are stupid . . . on page 380 he uses the word simpletons, and a main character of his dialogue is "simplicio"; "Indeed, the simpler they are, the more nearly impossible it will be to convince them of their own shortcomings."  He argues that the problem is philosphers(which he's suggesting or linking with pseudoscientists here) is they don't know enough mathematics.

But, Galileo was not perfect.  He tries to solve the tides in the last day of his Dialogue book, and as the wiki article points out, he argued in an earlier book, the Assayer, that comets are just figments of your imagination!  Well, he corrects this in his Dialogue book.

It's been suggested, in Koestler's Sleepwalkers, that Galileo's biggest mistake was leaving the safe confines of Venice for Flourence, from where the catholic church caught him, and turned him in to the inquisition.

Wednesday, March 16, 2016

Astro picture for the day/ Quote for the day


NASA, ESA, CXC, NRAO/AUI/NSF, STScI, and R. van Weeren (Harvard-Smithsonian Center for Astrophysics)
Acknowledgment: NASA, ESA, and J. Lotz (STScI), and the HFF team

"Philosophy is questions that may never be answered. Religion is answers that may never be questioned." - Daniel Dennet

Thursday, March 3, 2016

astro picture for the day/ "In Search of . . ." as a window onto the mythmaking mind


Credit:
ESA/Hubble & NASA
Acknowledgement: Judy Schmidt

astro picture for the day/ "In Search of . . ." as a window onto the mythmaking mind

Mankind is defined and distinguished by the other life on Earth by it's dependence on science and technology. I've tried to show the growth of knowledge and mankind's exploration of knowledge.

There was mathematical knowledge early on, but progress towards more mathematics was slow.  After one learns of a few numbers, maybe some arithmetic, there doesn't seem to be much left to do . . . but make mythology. I'm suggesting here that mythologizing religions partly comes out boredom.  There was simply no other way to excersize the imagination back then. Some didn't know any mathematics at all.

It seems that mythologizing stopped far back in the past, after Christianity was created.  But, there's the case of Islam which was created six hundred years later. But, also, in the twentieth century and really back to Kepler. 

As soon as Copernicus was confirmed by Kepler and Galileo, some, in this case Kepler himself, started mythologizing.  Kepler wrote of going to the moon in a dream.

A famous example is War of the Worlds, published in 1897. Almost exactly after that, UFO mania started. Well, the U.F.O. wiki, finds the first use of unidentified flying objects to 1878.  The person says a remarkably fast flying balloon.  Well, as I was going to say, U.F.O's started when space rockets were starting to be known.  Here, we have a case of people reporting U.F.O.'s around the time when flying balloons were common. Either way, we have people being fantastical and mythologizing.  This mythologizing would push very far.

Rod Sterling, famous for the twighlight zone, and Star Trek stars William Shatner and Leonard Nimoy helped narrate a great window on the religious and mythmaking minds - the "In Search of . . ." series and William Shatner later with MYSTERIES OF THE GODS (1977).


The first video that documented these ideas(I've yet to address them), Rod Sterling's "In Search of Ancient Astronauts"


The first interesting part of these videos is the blending of science and mythology(in this case - U.F.O.s). They go to astronomical telescope observatories, including radio telescopes. Rod Sterling's "In Search of Ancient Astronauts" interviews Werner Von Brawn, who explains to them "Fermi's paradox."  "Fermi's Paradox" involves the Big Bang cosmology.  Fermi actually comes up with this in the 1950s, before the cosmic background radiation discovery/confirmation of the Big Bang cosmology over the steady state cosmology in the 1960s. So, Fermi's paradox is doubly remarkable.  Fermi notes that the Big Bang cosmology suggests the universe is between ten to twenty billion years old(Hubble Space telescope has narrowed this down to like 13.82 Billion years old.  It's now measured down to some decimal points . . .), and Fermi notes that the recent radioactive dating of the geologic history of the Earth makes the Earth 4.5 billion years old. Taking just the Earth's life history, and the Big Bang cosmology, and the abundance of stars in our galaxy alone, suggest, that Extraterrestrial Civilizations should be billions of years older, and should have gone spacefaring all over the galaxy for billions of years. They should have visted the Earth . . . a long time ago.  Well, the U.F.O's mythology in the videos above go far beyond that.

They go to all the great ruins of the past - the Egyptian Pyramids, the Mayan Pyramids, and Easter Island.  And they say, humans couldn't possibly have made these, ancient Aliens must have come down and made them and/or taught humans how to make them. Just making a quick disproof; why didn't they build them out of daimondoid materials(diamond, the hardest material in the universe, by physics), or some more exotic material?

One big point I'd like to make of what these U.F.O believers are doing is saying, "we don't know"; therefore, U.F.O's exist and must have visited the Earth a long time ago.  Similarly, god believers often say, "we don't know how the universe works, how the brain works", or "our theories are imperfect"; therefore, God exists - submit your souls and believe in "my church and god."

In rewatching Rod Sterling's "In Search of Ancient Astronauts", they show video of a hunter/gatheror tribe who made a straw airplane as a god, because they saw one come over them.  It was the first airplane they had ever seen; they never thought that such a thing could ever exist, so they idolized it, made it a statue god. So, this is valuable video of the mythologizing/religious mind in more than one way!

These videos make for great viewing of the great accomplishment of mankinds past - both Egyptian and Mayan temples.

astro picture for the day/ Grothendieck quote


Image credit: APEX, the Atacama Pathfinder EXperiment telescope

Quote for the day,

"I prefer to accent “unity” rather than “generality.” But for me these are two aspects of one quest. Unity represents the profound aspect , and generality the superÔ¨Ācial." - Alexander Grothendieck

link --> How Grothendieck simplified Algebraic Geometry

As Velleman points out in his "How to do Proofs", proofs starting from conclusion are by means of reexpression(I'm not sure who first came upon this proof technique/insight actually) . . . here, we see Algebraic Geometry being reformulated many times; this cuts through and unifies much mathematical history from the 1800s up to . . . Alexander Grothendieck.