The above picture is of course the Greek Parthenon. Soldiers used it around 1600s as a gunpowder storehouse. Their enemies rolled in a cannon fire; and well, the gun-powder went up in smoke and left the Parthenon in its current state. It's well known the Parthenon's columns curve so that those viewing it from below see straight lines.- The video I give is Carl Sagan's account of Greek science and mathematics. Decades have past by and nobody has made a better video account of this Greek era. Likewise, actors make hundreds of films, but, there' still only a handfull of decent and interesting sci-fi. Enough of that. Most history courses focus on the Parthenon and Athenian era Greeks. Carl Sagan shows as do most mathematicians who have worked to give an account of how and why Greek mathematical science came about. But, lets connect between what happened with the Sea people's I more or less finished off with my previous 'thought for the day.'(the youtube's of Carl Sagan's Cosmos and most documentaries were usually divided up into ten minute pieces. As of me sitting down to write about this era, somebody has put up the pertinant Carl Sagan episode for my post here in one hour long piece! The part of the show I want you to see starts at nine minutes; )- Not that the human species is a gracefull beautiful one, but generally speaking the better looking humans(whether male or female) don't go into science and mathematics. Why? Because they've realized they're good looking, and decide to ride it. Likewise, why do most people in say a generally predominant christain country decide to take on christianity? Why do most people in a muslim country decide to be muslim? Why do most people in oriental countries decide to be whatever oriental religion/philosophy(same thing in my opinion) is predominant in that country? Because by 'incrowding', they get their money and sex and social acceptance. Why do I bring these things up? Because the ancient world of Troy and Minoa Crete, Karnak and Abu Simbal Egypt and the Hittites were locked into their ways; and then, the Sea Peoples came and caused a kind of social vacuum(a social damming up of nature). Because of this social vacuum, knew social ideas were allowed to spring up. Archaeologists generaly give the Phoenicians the credit for starting the alphabetical language innovation. Before then, natural language was pictographic(an outgrowth of the cave painters tens of thousands of years ago). This is significant because this allows language to distinguish between verb and noun ideas. Sentences are formed far more clearly now. Mathematics and Mythology are both analogies. Mythology is poetry; poetry is simily and metaphor- analogy. A major part of the nature of mathematics is that it is all an abstraction. An abstraction is a common form of different structures. A structure is composed of a relation or a verb like in a natural language sentence. This relation is completed by nouns that either make sense or in the case of poetry don't make sense. A given relation can take on many different noun elements to make sense. When you define this general form apart from all its concrete instances, you have an abstraction. This is a major part of all mathematical concepts. The Phoenician innovation allows these structural relations to be expressed far better than ever before. Two peoples took up this Phoenician innovation - the Greeks and the Hebrews(these two peoples sprang up because of the social vacuum created by the sea peoples whoever they were). They were to use this innovation in wildly different ways.I've already given more of a hint of the relations between the Greeks and Hebrews in my "Gospel of Truth." I want to stress the fact that both Mathematics and Mythology are both analogies a bit more here. The fact that they are both analogies I hope I've made clear enough already.- The point is, unless you believe the universe is static, that we evolved from a state of ignorance. Back then, mythology was science. The universe was unknowable because nobody could point to knowledge(or at least not much knowledge). And, there was the whole class structure of society started by agriculturalism; some people got educated(to some degree); others didn't. Or, they got educated differently. But, the bottom line is generalization is a part of thinking no matter who they are in this agricultural civilization. They grow up in specialized ways and they generalize from there. Not only that, but they grow up picking up ideas from the past; ideas from a state of ignorance. They generalize from there. Societies get locked into what works. Untill, something happens, a shift of the weather to cause a people to pick up there stuff and leave their cities(hence the reason why we get ruins like the Anasazi in Chaco canyon, New Mexico(in current united states; i'm counting on this blog surviving into the future - whatever futuer that is!), or competition from militant other communities, new ideas are not considered for socio-political reasons.-The sea peoples once again disrupted the world of Troy, the Minoans, the Hittites; they did so for their own reasons. But, what they did was open the human mind to new possibilities. It's almost as if a dark ages needs to happen before a new Renaissance starts. And, I find the happenings of the Hebrews and the Greeks a Renaissance just like what happened around 1400-1500 in Europe.
- Around this time of the dark ages brought about by these sea peoples, two cultures thought up the universe in different ways. These two cultures differenct ways of figuring out the universe using this new language ability is not a precise division. One culture was the Greeks; the other was the Hebrews. The Greeks certainly took to the mathematics a lot more. The Hebrews tried coming up with a single god(they were not the first; the Zorastrian Persians were first). They viewed this God as beyond number, "Job 36:26 Behold, God is great, and we know him not, neither
can the number of his years be searched out." I can't find this one passage in my notes(they're so much I can't find this passage; the passage I just found will have to do!). There's the mathematical constructive analogy and there's the poetic vague analogy. The Hebrews were trying to do the poetic. Once again, this division between the Greeks and Hebrews is not precise. But, considering the mathematics that was done by the Greeks versus the zero done by the Hebrews, I find this striking.
- This is not meant to disparage the Jews then or now. Before the Greeks were
I've gone ahead and posted as far as I got before the computer started doing all this reloading . . . and each time combining paragraphs . . . i've designated paragraphs by means of hyphens because of this . . . and then, after the reloadings, each time I press the space bar or anything else, the computer just sends me to the top; so, I just decided to post it and write up and post the rest as replies. Apologies ahead for anybody who cares.
Now, that I've explained why the post stops with an explanation of the greeks and hebrews, I'm going to continue this. I want to say that I'm trying to show mathematics coming from the vague ignorance that we evolved from. And well, as you should be able to see if your being objective, the Hebrews end up being what gets talked about. If you read my "Gospel of Truth" you might learn the real reasons why the Jews were hated then and some idea of what happened in Nazi Germany. The Jews believed in one god, and they banned believing in multi-gods; if you don't see or understand any of this; you havn't read or undestand anything about the Old testament! Most peoples around that time would just mix and match each others gods; the Hebrews were intolerant! Sorry! What further happened around the supposed life of Jesus Christ was the Jews were waiting for a messiah to wipe away all these evil multi-god 'seekers after smooth things(greek mathematics; this is in the dead sea scrolls)" cultures; it didn't happen. They said there was delay; there's a delay of paroisia in christian tradition; christians don't think twice about it. The Jews said the savier didn't come; the sungod religions all over the med wanted it to happend; so, they said it did; so, the Jews were called for over 1900 years "christ killers." The Germans picked up on Christianity just like the Native americans did in the 1500s and the Africans were then and now; christtian missionaries told them so; sometimes by torture. I think I've said enough. I'm moving on to Greek mathematics.
The Hebrews went through much before the Greeks were much more than a bunch of quareling barelly townspeople. I've already explained this in my "Gospel of Truth" actually. As I've remarked before, most people think of athens when they think of Greeks. But, much Greek mathematics happened long before the Parthenon and Athens and the Delian league and a lot of that stuff. We seem to know who the first Greek mathematician was - Thales. Thales was running around Mesopotamia and Egypt much at the same time of the Jewish exile to Babylon; so, much of the events of the Torah had come and gone. The Israelites had built temples and cities that the Greeks were no where near building for hundreds more years. Once again, I point out essentials of this in my "Gospel of Truth." Carl Sagan mentions Thales; but, then he moves on. I'm thinking about just posting my review of Van Der Waerden's "Science Awakening" now. But, maybe I should point out a few things mentioned in Carl Sagan's account of "Science Awakening" in his "Cosmos" video. Carl Sagan points out this shower device. Here's one more proof of what I'm getting at in my "origin and nature of mathematical knowledge" article. Empedicles thought of air because he dammed up nature with this shower device.
Carl Sagan goes through a tunnel built on the Island Samas. This tunnel was built later after the life of Pythagoras and the Pythagoreans were dispersed by Greeks who feared this mathematical knowledge that the Pythagoreans were creating! The Greeks were not all rational curious people! I thought I'd describe this tunnel. Van Der Waerden notes the striking contrast between a tunnel built by a Judea king(orderd by him). The Judahites(Judahites by now; the Israelites were taken away by the Assyrians by now and never heard from again; see my "Gospel of Truth") tunnel is a zigzag because the way they kept track of the tunnel diggers was by means of cutting shafts from the top down so they can see if the tunnel diggers are on the right path or not. The result is the tunnel is a zigzag pattern! The tunnel at samos is straight for a mile long. How did they do it? I'm somewhat limited on this blog(blogs are not good for mathematics!); i can't show the geometric figures. But, I'll try to give a rough description. Herodotus happens to mention that Eupalinus was the engineer who made this happen. Eupalinus started by determining where to start drilling into the mountain. Then, starting with one designated point, he drew straight lines that would go around to the other side. He's start by going straight out for a little bit; then, make a right angle to start moving around the mountain; he'd go the rest of the radius of the mountain he's trying to pierce. Then again a right angle(always a right angle as he'd make his way around to the other side of the mountain). Then, once he got say past the other designated point of the mountain to start drilling, he'd once again make a right angle to that point. Now, he'd like to make another right angle into the mountain; but, that takes digging; but, he could use the right angles he's already made to make a right angle into the mountain to be usefull to him. He'd split up the line segments into those that are horizontal and those that are vertical; he'd use both to determine what the distances into the mountain at right angles into the mountain that he doesn't want to dig. He'd end up with two lenghts at right angles to each other. Then, he'd draw a straight line, the hypotenuse(you should know what hypotenuse means if you know the pythagorean theorem); this hypothenus is the line from one designtated point to the other through the mountain; Eupalinus would then instruct the slaves to start digging. Eupalinus may have also had a little mechanical device called a Dioptra; it's a horizontal bar with two sights; they'd make sure that they are digging along those sights. As Carl Sagan says, the tunnel is a kilometer long and almost perfectly straight. From here, I think I'm just going to post my review of Van Der Waerden's "Science Awakening." I certainly don't feel like rewriting all that right now!
I've gone ahead and posted as far as I got before the computer started doing all this reloading . . . and each time combining paragraphs . . . i've designated paragraphs by means of hyphens because of this . . . and then, after the reloadings, each time I press the space bar or anything else, the computer just sends me to the top; so, I just decided to post it and write up and post the rest as replies. Apologies ahead for anybody who cares.
ReplyDeleteNow, that I've explained why the post stops with an explanation of the greeks and hebrews, I'm going to continue this.
ReplyDeleteI want to say that I'm trying to show mathematics coming from the vague ignorance that we evolved from. And well, as you should be able to see if your being objective, the Hebrews end up being what gets talked about. If you read my "Gospel of Truth" you might learn the real reasons why the Jews were hated then and some idea of what happened in Nazi Germany. The Jews believed in one god, and they banned believing in multi-gods; if you don't see or understand any of this; you havn't read or undestand anything about the Old testament! Most peoples around that time would just mix and match each others gods; the Hebrews were intolerant! Sorry! What further happened around the supposed life of Jesus Christ was the Jews were waiting for a messiah to wipe away all these evil multi-god 'seekers after smooth things(greek mathematics; this is in the dead sea scrolls)" cultures; it didn't happen. They said there was delay; there's a delay of paroisia in christian tradition; christians don't think twice about it. The Jews said the savier didn't come; the sungod religions all over the med wanted it to happend; so, they said it did; so, the Jews were called for over 1900 years "christ killers." The Germans picked up on Christianity just like the Native americans did in the 1500s and the Africans were then and now; christtian missionaries told them so; sometimes by torture. I think I've said enough. I'm moving on to Greek mathematics.
The Hebrews went through much before the Greeks were much more than a bunch of quareling barelly townspeople. I've already explained this in my "Gospel of Truth" actually.
As I've remarked before, most people think of athens when they think of Greeks. But, much Greek mathematics happened long before the Parthenon and Athens and the Delian league and a lot of that stuff.
We seem to know who the first Greek mathematician was - Thales. Thales was running around Mesopotamia and Egypt much at the same time of the Jewish exile to Babylon; so, much of the events of the Torah had come and gone. The Israelites had built temples and cities that the Greeks were no where near building for hundreds more years. Once again, I point out essentials of this in my "Gospel of Truth."
Carl Sagan mentions Thales; but, then he moves on. I'm thinking about just posting my review of Van Der Waerden's "Science Awakening" now. But, maybe I should point out a few things mentioned in Carl Sagan's account of "Science Awakening" in his "Cosmos" video.
Carl Sagan points out this shower device. Here's one more proof of what I'm getting at in my "origin and nature of mathematical knowledge" article. Empedicles thought of air because he dammed up nature with this shower device.
Carl Sagan goes through a tunnel built on the Island Samas. This tunnel was built later after the life of Pythagoras and the Pythagoreans were dispersed by Greeks who feared this mathematical knowledge that the Pythagoreans were creating! The Greeks were not all rational curious people! I thought I'd describe this tunnel.
ReplyDeleteVan Der Waerden notes the striking contrast between a tunnel built by a Judea king(orderd by him). The Judahites(Judahites by now; the Israelites were taken away by the Assyrians by now and never heard from again; see my "Gospel of Truth") tunnel is a zigzag because the way they kept track of the tunnel diggers was by means of cutting shafts from the top down so they can see if the tunnel diggers are on the right path or not. The result is the tunnel is a zigzag pattern! The tunnel at samos is straight for a mile long. How did they do it?
I'm somewhat limited on this blog(blogs are not good for mathematics!); i can't show the geometric figures. But, I'll try to give a rough description. Herodotus happens to mention that Eupalinus was the engineer who made this happen. Eupalinus started by determining where to start drilling into the mountain. Then, starting with one designated point, he drew straight lines that would go around to the other side. He's start by going straight out for a little bit; then, make a right angle to start moving around the mountain; he'd go the rest of the radius of the mountain he's trying to pierce. Then again a right angle(always a right angle as he'd make his way around to the other side of the mountain). Then, once he got say past the other designated point of the mountain to start drilling, he'd once again make a right angle to that point. Now, he'd like to make another right angle into the mountain; but, that takes digging; but, he could use the right angles he's already made to make a right angle into the mountain to be usefull to him. He'd split up the line segments into those that are horizontal and those that are vertical; he'd use both to determine what the distances into the mountain at right angles into the mountain that he doesn't want to dig. He'd end up with two lenghts at right angles to each other. Then, he'd draw a straight line, the hypotenuse(you should know what hypotenuse means if you know the pythagorean theorem); this hypothenus is the line from one designtated point to the other through the mountain; Eupalinus would then instruct the slaves to start digging. Eupalinus may have also had a little mechanical device called a Dioptra; it's a horizontal bar with two sights; they'd make sure that they are digging along those sights.
As Carl Sagan says, the tunnel is a kilometer long and almost perfectly straight.
From here, I think I'm just going to post my review of Van Der Waerden's "Science Awakening." I certainly don't feel like rewriting all that right now!