Monday, March 25, 2013

astro picture for the day/ Glass Giant of Palomar

Credit: ESA / NASA / JPL-Caltech / STScI

The above image is an infrared image of the Large Magellanic Cloud(a dwarf irregular satellite galaxy to our own galaxy).  It comes from the Herschel space telescope as well(located at one of the lagrange points; an utterly remarkable technological achievement to be eclipsed shortly by the James Webb telescope).

Astronomical telescopes have the remarkable historical tradition of clocks(clocks, gears and the industrial technological existence more or less enjoyed by humanity today is described by James Burke's "connections" and "the day the universe changed" and I've posted those throughout this blog).  To observe an astronomical object, the telescope has to be kept precisely on that astronomical object for a certain amount of time; otherwise, the Earth's rotation makes the given astronomical object drift out of the field of view.  The bigger the telescope, the more remarkable the fact that telescopes are kind of giant clock.

Telescopes involve more historical/intellectual traditions.  That of the conic sections.  Trying to draw a circle by hand is next to impossible.  While everyone knows the simple trick to make a perfect circle, few ponder significance of doing so.  No other lifeform has created a perfect circle. Nobody is sure which came first; the mathematical discovery of the circle, or the discovery of the wheel; but, the earliest today's archaeology(and this is an archaeological fact that hasn't changed for hundreds of years!) suggests the Sumerians around 3500 B.C.  That's a really long time ago; longer than the building of the Egyptian pyramids.  I've pointed out the difference between the Egyptian accomplishments and that of the Malta ruins - mathematical.  The Sumerians had the circle and the wheel long before the Malta people created their admittedly great temples.  If you look at their temples, they lacked an ability to make a perfect circle. The conceiving and making of a conic section like a parabola(say for an astronomical mirror) is even harder.  Only the Greeks ever conceived of a ellipse of a parabola, or a hyperbola.  They did so because of trying to solve the three Delian problems - the trisection of an angle, the duplication of the cube, and the squaring of the circle.  The Greeks discovery of the conic sections is just one more piece of evidence for Jacob Bronowski's ideas about the nature and origin of mathematics(see the second to last post of this blog).

Sumerian/Babylonian art showing the use(and hence discovery) of the wheel and circle.  Remarkably, the Native Americans all the way up to when the Europeans found the Americas around 1500 never discovered/invented the circle or the wheel.

The Greeks studied optics, but they never hit on the idea of making a telescope.  Had they done so, maybe the scientific revolution of the 1600s would have come sooner.  Aristarchus had infered the sun-centered solar system, but nobody took it seriously.  Archimedes practicaly laughed him off the stage(see Archimedes introduction to his "Sand Reckoner").  But, the anti-science supernatural religious had to have their day; so, we tried it their way for five hundred years till the translations of Arab texts in Arab Spain; these Arab texts turned out to be tranlations of even more ancient Greek mathematics.  Even then, it took Europeans awhile through wars and fighting the new knowledge before optics advanced enough to make telescopes.  In the end, the idea for a telescope wasn't concieved of by those who made the optics advanced enough to do so.  Galileo learned of this optics and knew what to do more than the optics guys.  Just comes to show that technical skill is one thing; insight is another.

While Galileo's little telescope is humorous to lookers today, his was actually an advance over Hans Lippershey's optics.  Descartes made a hyperbolic lens.  Huygens made refractors a hundred feet long. Then Isaac Newton made two great experimental science discoveries - one, the spectrum(but, he never thought to find spectral lines), and the reflector.  Even since Newton's reflector idea, the refractor and reflector telescopes competed back and forth for which is better.  William Herschel made a reflector in the 1700s.  He went on to discover Uranus; the first planet discovered since the Greeks noticed a few stars moved. William Herschel also discovered infrared light, but didn't know it; he noticed using a prism that something was still heating a thermometer even though the thermometer was moved outside of the visible spectral colors generated by the prism. Spectral lines were discovered by Thomas Young.

I don't believe that nobody made telescopes between William Herschel and the Lick and Yerkes observatories; but, generally, those were the great astronomical telescopes of their times.  In between those intervening years, much science and technological advance was going on(this is the 1800s). I found this youtube of the Lick observatories still going strong!  The Lick refractor went into service around 1880 - the Yerkes around 1890.  The Mount Wilson 100 inch reflector that was used to discover the Big Bang of the universe went into service around 1916.  But, I'm getting a little ahead of myself.

I'm sure there's plenty of discoveries about spectroscopes and other things; but, I'll try to give as many highlights as I can before getting back to the battle between the refractors and the reflectors.

Helium was discovered in the sun before it was discovered on Earth by Lockyer around 1868. Freidrich Bessel first measured the parallax of a star in 1838(hence somebody must have made a telescope and used it in between Herschel and the Lick telescopes).  I'm not putting these in historical order!  Foucault invented a way of testing how perfect a parabolic mirror was.  Steinheil first silvered a mirror.  Daguerre invented photography which of course revolutionised astronomy.  By late 1800s, the Yerkes had measured the parallax of thousands of stars(Tycho Brahe had thought of parallax back in the 1500s with influence from reading Aristarchus). 

The great telescopes, pre-Palomar 200 inch was made from herculean efforts of individuals.  The Clark and Richey's.  I don't remember reading an account of grinding and polishing the glasses for the refractors, but the description for the sixty and then the hundred inch Mount Wilson reflectors of very early 1900s is stunning.  It took them months to grind away, and years to polish.  Richey washed down the whole laboratory after the months of grinding, left the floor wet to hold down the dust as he polished.  Richey of course used the Foucault method to determine how perfect the parabolic mirror. The room would be made pitch black dark.  He'd put a knife to the edge of the surface and shine a light so that the light would reflect off the distant walls; in this way, the irregularities of the surface would show up.  This reminds me of how Cavendish weight the Earth.  He had weights on a horizontal beam, and another beam that was given a certain tension to prevent it from settling on the set beam.  He'd detect the gravity of the weights of torsion beam with the static beam by seeing the light reflected off the walls in a darkened room.  Well, you can do it that way.

Relating the scientific method(as I explain in my "origin of mathematical knowledge article") and daming up nature, experience with the refractors, they built the sixty and hundred inch Mount Wilson reflectors on concrete domes to dampen out the heat of the Earth's surface.

Nobody knows when George Hale first started championing the creation of the two hundred inch Palomar telescope, but with the way Geoge and his intellectual group was able to raise money and progress the technology of the telescope, you know they wanted to see what they could do.  Before I get into the Palomar telescope, I should say a few things about George Hale.  George Hale coined the word "astrophysics."  He was very into the idea that the sun is our own star and studying it gives us a astrophysics laboratory in our own backyard(it would be Arthur Eddington who first thought of nuclear fusion as the process that powered the stars).  George Hale apparenly made the suggestion of testing Albert Einstein's General theory of Relavitity by means of a solar eclipse(it was Arthur Eddington who carried it out succesfully; actually, some modern scientists detect Arthur Eddington biased 'some' of the data; or, the data was a little fuzzyer than initially thought).  George Hale also practically created Caltech which became the scientific and technological factory for much of the technology for the Palomar telescope. I'm sure George Hale knew tons of stellar facts; but, his major contributions appear to be solar astronomy(and the organising of large projects).

A solar observatory is a bit odd looking.  George Hale is responsible for a good amount of it!  He determined the height of the rolling heat waves due to the ground; and so, the solar observatory is structured to the pattern of nature.  The Solar telescope uses a system of mirrors to focus and reflect the image to the bottom of the observatory.

Getting back to the Palomar telescope.  The Palomar telescope required a whole community to build than the herculean efforts of one or two people.  In this sense, the Palomar telescope was a lot more of a cathedral or Egyptian pyramid.   Those projects outlived some of their creators.  The creators had to pass along the plans for the construction of the project. People were practically born to create the cathedrals and the well maybe not the pyramids. A few people died before the Palomar telescope was completed - George Hale among them. The Palomar telescope was a great accomplishment for its time(1930s); but, due to the intervention of world war 2, its contribution and shelf life was considerably shortened.  If it had gone into operation in the 1930s, the amount of time between its operational lifetime and the next great telescopes(the twin keck and the Hubble) would have been very great indeed. 

The Palomar telescope shares with the Egyptian pyramids and the Cathedrals the requirement for innovation due to shear size. As a project gets too big and impractical to build, new methods are needed to construct it.  The arch has historically been the example of this. The crossbeam can only be built so big before it's impossible to make buildings in which you can move around in. The arch allows people to build higher and give more space and room to walk around in.  One thing seemed certain in constructing the Palomar telescope, the two hundred inch glass needs to be made out of some other material.

The story here is pretty long.  Originaly, they tried to make it out of quartz.  Quartz compared to glass has almost no warpage due to thermodynamics.  They successfully made small eight inch quartz reflectors; but, they found that as they made bigger and bigger quartz disks(blanks not yet ground into parabolic shapes), the more heat and equipment it took to make it; the coefficient of difficulty appeared to be on an exponential curve.  They got close to a hundred inch and failed.  They spent millions of dollars in failing; making a two hundred inch appeared to be so expensive, that they quickly looked into another direction.  They choose pyrex.

Pyrex is actually somewhat related to quartz; it has a percentage of quartz; but, it's not a pure quartz.  Now, the problem with trying to make a astronomical mirror out of heat resistant material is you have to heat the material up to make it molten and poor it in the desired shape! So, the Pyrex was a compromise material to make the two hundred inch Palomar telescope. They failed on a first attempt which was attended by a bunch of bored rich folk who never got past calculus or did much manual labor to get all their money.  They just barely made the second disk blank. But, then WW2 intervened, and the grinding and polishing had to await after the war in 1945.

I forgot to mention the 200 inch disk had to be annealed.  Annealing is a kind controlled cooling down.  This process takes out imperfections and strains which can double the stress problems due to thermodynamics. The corning company who made the pyrex disk tested the annealing by means of a polariscope.  It consisted of two prisms on the two ends of a beam.  They'd shine a light through; if there was any warpage, the light wouldn't align.  The disk took ten months to go through the annealing process.  Also, after the war, when they ground it into shape and polished it, they didn't have the same problems had in shaping the 100 inch due to the Pyrex's superior thermodynamics.  Richey  had to wait for the glass disk to cool down after shaving off a bit here and there.  He'd use the Foucault method to find an irregularity, and then he'd grind; but, then, after doing a certain amount of grinding, he had to let the disk cool down again before he could get back to work.  This process of course took him years to complete!

The polishing and grinding was done by a process of starting with courser grains and then finer grains.  And of course, the grains of various materials would get ground down in the use. The grinders were a team of like six people.  I know they did something to keep the dust down.  Any little dust could have set them back in the process of going from rougher to finer grinding materials.

 One of the major innovations was the bearings that would link the support structure with the gearing.  The weight of the telescope would crush any ball bearings.  They settled on a oil slip bearing.  There was some skeptism even this would work.  But, as it turned out they didn't need very powerfull pumps and motors to keep the oil flowing.

There's apparently some worm gears to drive the movement of the telescope.  I feel like the description I have isn't that detailed. But, I am under the impression that the machining here is as precise as the grinding/shaping and polishing the lens itself.  I've been to the Palomar telescope, and I've not seen these gears.  Maybe next time, I'll ask somebody about them.  You need these massive hundred ton gears to be as precise as possible to be able to position the telescope on a given region precisely; so, yes, I would imagine since they've obviously been able to successfully do astronomical research that these gears are a machinists nightmare or pride depending on who you talking to. Readers might have noted the remarkable ease that car doors shut, or maybe even experienced some heavy military steel doors that can be moved by humans.  They been engineered with some leverage principles to allow such affects.  Similarly, the Palomar telescope is driven by a less than one horsepower motor.

The Palomar telescope mirror was made reflective with a new aluminizing process over the Steinheil silvering(the silvered Mount Wilson mirror had to be resilvered quite often; sometime every day; almost every day, workers had to take the disk off, move the disk to the underground facilities and resilver and then put it back on the telescope above).  The process involved aluminizing a tungsten wire.  In a vacuum, they electricute the tungsten wire, the the aluminum would vaporize off onto the mirror surface below.  This was revolutionary for the day.  The aluminum mirror was far more reflective than the silver coated mirrors of yesteryear.

For perhaps my favorite the not last thing to describe(and I probably havn't found everything that can be said about the technology of the original Palomar 200 inch) is the positioning system.  The astronomers want to be able to type in the coordinates and have the computer program tell the whole 14 foot gearing system and the less than one horsepower moter position and keep the telescope positioned at any desired point in the sky.  Before the Palomar telescope, some MIT people had created electromechanical positioning systems for the military(the guns on ships and so on).  There's analog computers and theres digital.  There's also mechanical and electronic.  These electromechanical systems combine the two.  This electomechanical computer used quartz vibration timing circuits.  The designers had already taken into acount that the weight of the structure from the lower 200 inch mirror to the top secondary mirror would bend.  Well this electromechanial analog/digital positioning system actually corrected even the errors that couldn'be machine tooled out.  What's more, it took into account the refraction of the atmospher due to temperature and density.

From the exotic material mirro(although a compromise) to everything described so far, the Palomar telescope was a scientific cathedral/Egyptian pyramid for its day.  It doesn't look like much.  But, there it is.  There's so much more to describe though!

The science of optics showed that a short focal length leads to faster astronomical picture taking. So, the Palomar telescope is engineered to a scientific principle much as George Hale's solar telescope is structured to the pattern of nature itself.

George Hale and his fellow astronomers gained experience in different seeing conditions when building the Yerkes and the Mount Wilson telescopes.  They found remarkably at times the bigger telescopes would get blurred out while a small two inch refractor could see Jupiter just fine(I've experienced this; i've viewed through my fathers six inch reflector and his three inch refractor.  I viewed the 1990's cometary impacts of Jupiter throug the Refractor).  As it turns out, a large telescope has a termodynamic 'tremer error.'  They soon took little telescopes around that they could get this tremer error disk and went around various mountain, flats and so on to test seeing conditions.  Mount Palomar was a bit of a compromise between good seeing conditions and accessability.

They even considered the geology.  They studied the earthquakes of California and determined the mount Palomar only experiences moderate, and by building on a mountain, the mountain generally damps out the earthquakes. 

There's innovations in the dome, but I kind of read through it quickly and didn't jot down notes.

George Hale's founding of Caltech led to numerous support technologies.  They improved spectroscopy; they found that most spectroscopes only use five percent of the light coming; they improved it to ninety percent.  A W.B. Rayton created a lens of aperture f:0.59.  This was unheard of back then.  Without it, the Mount Wilson 100inch could not have done the work to discover the expansion of the universe.  There was all kinds of things like this that went into the telescope or contributed to the science that went on.

The Palomar telescope was finaly outdone by the Twin keck's at Hawaii.  They are an optical interferometer.  The radio telescope guys innovated interferometry.  Well, I suppose interferometry went back to the Michelson experiment to detect the ether in the late 1800s.  But, for the longest time, astronomers didn't think interferometry could be done at visible wavelengths.  Interferometry was exclusivelly a radio telescope luxery.  Mathematical innovations made it possible(and of course technological developments there after).  So, right there, the twin kecks should have been an astronomical revolution.  Unfortunately, the Hawaii people said astronomy is interfering with their religion, and the interfermetric extra units outside of the Twin keck were not built.  Back in the making of the Mount Palomar telescope, there were various supernatural religious people who said "maybe mankind is not meant to learn natures secrets."  All this shows clearly why people believe in religions(supernatural and not rational philosophy).  And, all this justifies my efforts on this blog.

Astronomical telescope technologies continued to advance.  Quantum optics guys soon advanced enough to calculate just how reflective a given material is.  The Hubble space telescope was suppose to be coated with almost 100 percent reflective material.  But, unfortunately, time constraints prevented the technological develpment to catch up with the theoretical developments; the Hubble mirrors are a compromise.  Later on, this quantum optics developments made their way onto the Palomar telescope mirror.  The laying of the reflective surface has also advanced past the tungsten wire. I'm not sure if even this is the latest.  But, I've seen the use of plasma to lay down atomic layers.

I remember the CCD revolution reported in my Sky and Telescope magazines back in the 1980s.  The CCD's are continueing to advance. The spectrographs continue to advance. I can't even say I know the latest developments. But, as nanotechnologies advance, so do the spectrographs and the CCD's.

The Herschel Space Telescope  is infrared and requires cooling.  What's remarkable about it it's located at a Lagrange point.  A gravitational stable point between the Earth/Moon system.  It's millions of miles out there.  Astronomers of course can't wait to make an optical and even radio and other wavelength telescopes on the dark side of the moon.  The seeing is of course pitch black.  But, one could imagine making a comparable interferometer at one of the lagrange points, and even making a hugh interferometer between the moon telescopes and the lagrange point!  With the coming nanotechnology revolutions, I'd expect this to be possible before the twenty first century is out!

And perhaps to finish off this latest blog, I could mention some of the latest I'm hearing about dna-nanomanufacturing.  Since all the great breakthroughs months ago, there hasn't been much reported - till a week or so ago. I did see some of the major dna-nanomanufacturing teams suggest their latest plans for scalable dna-nanomanufacturing and the ability to bootstrap to a more robust nanomanufacturing system.

Wednesday, March 6, 2013

astro picture for the day

Image Credit & Copyright: Terry Hancock

Quote for the day,

"By studying Eloquence we cultivate reason itself." - Rector Rosted

One observation of mine from reading all kinds of history of mathematics is that most were language masters at a young age; i like to joke that mathematicians are the ones who got bored with language and philosophising and went on to mathematics.

There's also the famous Einstein quote that "elegance is for tailors." This was Einstein's criticism of mathematians; on the other hand, Einstein's getting help from mathematians is a famous historical issue. Before Einstein did his special relativity, Henri Poincare had thought of the shift in space and time dimensions(but not spacetime; that was done by a Grossman If i'm recalling correctly; another mathematician; also, I'm forgetting the name of another who thought about shifts in space and time before Einstein).  And when Einstein went to work on General Relativity, David Hilbert did much of the mathematics at the same time.  Some say David Hilbert did the mathematics but gave Einstein the credit anyways just for thinking of the idea.  There's more to be said.  Point is despite Einstein's not to shabby mathematical ability, he never had a feel for mathematics and never solved mathematical problems.  I point this out because to be a mathematician takes a lot of different elements to come together.  For instance, in the mathematical physics of the discovery of the solar system by Tycho Brahe and Johannes Kepler, you had two guys doing two different stages of the development; one did the experiments/observations mathematically(Tycho Brahe had a gold nose from a duel over "who's the better mathematician"; don't know who shot off his nose, but Tycho clearly went on to do better things), and the other did the theory to make sense of the data - Kepler. Tycho Brahe was actually jealous of the mathematical ability of Kepler(as was Galileo). The problems of why people(humans who are technologically dependent and hence scientifically dependent) don't learn to become mathematicians and to hate it and turn to some make belief god comes from how multifaceted mathematics is, and the fact that mankind has evolved from ignorance; people have often not wanted to embrace learning because of some taboo or another; or fear of loosing their fear and anti-learning friends.  Rector Rosted came from a society that was struggling with all these social issues of reason vs faith/social upbringing back in the early 1800s.

I got this quote from Arild Stubhaug's "Niels Nenrik Abel".  The book is well written, but short on mathematics(it seems to be picking up . . . two hundred pages after tons of social political issues; he even proves the infinitude of primes; i'm hoping for more;).  It's been more interesting from the standpoint of a society struggling with reason vs faith.  Norway was battling with whether to combine with Sweden and Denmark or not(as was Denmark and Sweden).  The Scandenevians know full well that they are all related, but they're fighting each other for who's going to rule the world anyways(Denmark had already lost to the English after Denmark was starting to rule the seas and trade in a mighty sea battle).  Niel's Henrik Abel turns out to have family going back to royalty of Norway.  But, due to Niel's father's effort to make a rational enlightenment period christianity, his family was disgraced.  But, Niel's family had already done enough to make a university and bring in enough mathematical classics for Niel to learn from. One more historical note is that Niel goes to school right after the Normans decided that beating children to death is not the best way to teach people anything.  Before Niels entered school, a kid had been beaten to death.  This news maybe didn't make the Normans look to good to the cultured French south of them.  And the French culture makes this whole story of the Nordik society and Niels Abel even more interesting.

I had noted before that the French seem to be the more successfull intellectual society; they've been able to crank out the most mathematians consistently for the longest time at least since the Renaissance.  But, their intellecual tradition goes back at least to the eleven and twelve hundreds A.D. with the building of the great Cathedrals.  The French took to intellectualism and rationality(and struggled with rationality versus faith issues) perhaps earlier than just about anyone.  This was due to the translations of Arab texts of Greek mathematics back in Arab Spain around 1000 A.D.

The French tried to make a similar revolution that the Americans did, but went into a Reign of terro instead.  It's an interesting social phenomenon that I'm not sure anybody understands yet.  But, the French culture and revolution had a powerfull affect on Nordik culture.  They likewise wanted to be cultured; and likewise, they also struggled with whether to be rational or somehow fudgefactor rationality and faith.  The Abel family went from royalty to poor because of this.  Niels Abel's father was torn to bits because he combined rationalty with christianity.  But, Niels Abel got enough of the mathematical spirit to become one of the greats of all time.

Niels Abel proved the binomial theorm in general as oppossed to just negative numbers,  or just fractions.  This is something Newton and Leonard Euler failed to do.  Niels also did some work in real analyses and even integral equations(as oppossed to differential equations).  Niels also proved the impossibility of solving algebraically the fifth degree equation.  Most people have probably seen the quadratic formula.  This is the general solution to the second degree equation.  There's a similar general closed form solution to the third and fourth degree equations(solved in the early 1500s by a Cardano and Ferrari respectivelly).  But, the fifth degree resisted solution all the way to the 1800s where it was proven first by Niels and then Galois to be in general not solvable. Niels Abels' proof just proves their's no quadractic formula like solution to the fifth degree.  Galois practically invented abstract algebra(groups and fields; rings come form number theory) to disprove the fifth degree equation.  Niel's Abel before his death around 27 years old started to hint at a calculus solution to the fifth degree(Galois likewise died at an even younger age in a duel over politics; it's been noted that the natural successors to Frederick Gauss died before their twenties). In the calculus, there's derivatives and anti-derivatives; as it turns out, you can't always find the anti-derivatives by elementary functions.  Niels Abel showed how to come up with inverted elliptic integrals or elliptic functions.  He went on to generalise to Abelian integrals.  Mathematicians soon took these hints and related them to algebraic geometry; they solved Galois theory and number theory problems with elliptic functions just like the Newtonican/Liebniz calculus unified and solved algebra, geometry and trigonometry problems that were hard before the calculus.  The whole relationships between calculus(elliptic and abelian functions) and algebra, number theory, and algebraic geometry was the core pattern of mathematics from Niels Abels initial hint through the twenty first century.  Some would say that with the solving of the Poincare conjecture recently, we're entereing into a new level of mathematics; we're just now moving past the Abelian stage of mathematics.

There's more to higher mathematics that most people don't know about - Lie theory.  I recently bought Arild Stubhaug's histories of Niels Abel and Sophus Lie because I noticed I could get them for twenty dollars each.  I had bought a great book on the history and mathematics of Emmy Noether back around 1996-7 or thereabouts.  I bought it in Port Townsend, Seatle area.  It was a nice little used book store. I looked it up on amazon and noticed this great book was going for five hundred dollars!  I'm so glad I bought that book when I did!  So, when I noticed these two books about these two highly influencial mathematicians, I just had to buy them!  So, I'm wasting time(sort of; it's always good to read!) trying to knock these two books out(again putting off finishing some real mathematics books;).  Well, the philosophising is somewhat worth it; i think!

------------------------------------------science/technology extra?

There's of course all kinds of quantum computing breakthroughs.  I'm hearing there could be a big announcement from Ting about dark matter; they hinted at it a week ago, and said in two weeks or so, there could be a big dark matter breakthrough.

But, in nanomanufacturing, there's been more hints at when the real nanorevolution could happen.  It's been realized for awhile now that untill the process of picking up an individual atom and another and bringing them together mechanically is settled, one shouldn't worry to much about making small nano-manipulators.  Once it's done, then one can design around the principles.  Well, recently, I saw a little remark that they could around three to six years be able to make nanocomputers with trillions of transistors made out of dna and the ability to preciselly place individual atoms in various dna nanobricks to make them stronger and perform their functions precisely.  I really can't say who I think could do this.  

Sunday, March 3, 2013

astro video for the day/Sibudu cave

Video Credit: Solar Dynamics Observatory, SVS, GSFC, NASA;

I recall mentioning this before; that archaeologists recently pushed back the dates of the flowering of art and technology from around thirty thousand to a hundred thousand years ago.  What they mean is a significant increase of art and technology above stone flakes for technology.  For more than a decade, physical anthropologists and archaeologists(they kind of meld together as the archaeologists push back further and further into time) has observed that each significant Bipedal primate that evolved towards Homo Sapiens started in Africa first and then spread out; first, it was Homo Erectus and then of course Homo Sapiens who started spreading out around two hundred thousand years ago. In this light, the latest archaeological findings of a cultural flowering a hundred thousand years ago also started in Africa - in fact in South Africa/Sibudu cave.

This now archaeological site found a number of significant technological advances - the use of fire to make a glue to hold spear tips and perhaps more amazing of all, mosquito repellant mats. Nothing more needs to be said about how amazing that is.

Archaeologists and physical anthropologists can't resist trying to say what clues this Sibudu culture has for when and how come Homo Sapiens became so much more technological than other life on earth. This idea seems pretty interesting.  The suggestion is that with a higher population, you have more people experiencing more things.  In the Sibudu cave, this is what they found; they found a culture that had a population increase.  Further study shows that the cave painters of thirty thousand years in Europe also experienced a significant population increase.  The fact that we have two cultures that experienced increase in technological ability but had to happen again around thirty thousand years ago can be explained by the ice ages.  The ice ages could have caused a little bit of a dark ages.

This correspondence between population size and the creation and combination of every more complex ideas is interesting from a mathematical viewpoint. People tend to grow up in a given culture and take on that culture; hence, an increase of population can increase the different cultural or technological ability of a given society. Life in general can be viewed as a technology; a technology to swim; a technology to fly, and technology to exist in hot or cold environments.  Also some life/technologies are to forage; others are to hunt.   Some life/technologies take in the suns rays and make oxygen; others take in that oxygen and put out carbon dioxide. Well, this idea of correspondence between population size and creation of new ideas is on a population of Homo Sapiens level.  Marvin Minsky is famous for his "Society of Mind" idea; that our brains are a collection of ideas(technologies) that influence and even compete with one another.  The archaeologists championing this idea are saying that well, its not how smart you are, it's who you know.  I'd say it's both; but, maybe back then, when most people didn't have time to do all the experiments in the world, it was more who you knew. Mathematics would come in from the society of mind in a given individual(and with taking in knowledge from previous people; one could argue that language was invented to preserve and communicate this wealth of new ideas).

Let me just say that, in general, a given technology solves a particular problem.  A given key unlocks a given lock.  All the life/technologies for billions of years generaly only existed to solve one problem; after they accomplish their work, they often die by some other technologies/life who's purpose was to solve the problem of keeping that other life in check; this is called an ecosystem. But, Homo Sapiens became the general lifeform; the key that could unlock more than one lock.  Mathematics is ultimately the main technology that unlocks any lock in general.