It doesn't make them the same; radix point shift is a particular case of multiplication/division. They satisfy definition of multiplication/division. Check any suitable math book. Or Wikipedia
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Sorry about being somewhat on the tangent; are there any respected theories on why Europeans didn't colonize America in 11th century? It seemed like they could, but never really put effort in it. And what has changed by 16th century that made it a race for colonies?
A large part of this was necessity. Eastern Europe (or perhaps it's better to say the Eastern Mediterranean) had been the economic center of Europe for quite a while. However, population and wealth in Western Europe been continually expanding. At the same time, the Mongols and Byzantines were in decline, which meant access to age old trade routes was closing as the more hostile Muslims gained control over them. States like Venice and Genoa largely monopolized the remaining wealth in that area. States like Portugal and France wanted to avoid Italian competition and Muslim interference. This is where you get a much stronger drive to explore and set up colonies (which often start as trade ports).
Basically what Dafool wrote. Remember that Columbus did not intend to go to America, or even know about America - he wanted to find the Western sea route to Asia. After the Ottomans had conquered Constantinople in 1453 and it became clear that the land trade routes to India would be much more difficult to use for the Europeans, finding the Western sea route to Asia became a priority.
Ironically, one of the reasons Columbus attempted his expedition was that it was based on wrong calculations. Not only did Columbus believe that the circumference of the Earth is smaller than it really is, he also believed that Asia was much bigger than it really is. Both were common misconceptions in the geography of the time. So, basically, he assumed that the Western sea route from Europe to Asia would be much shorter. Had he known the real distance, he would probably not have attempted his expedition, because no European ship of the time could have carried enough provisions to go all the way west from Europe to Asia without landfall.
As for your point about the 11th century: I don't believe that the Europeans could have colonised the Americas in the 11th century even if they had had an incentive to sail west. The caravel and carrack ship types, which Columbus used for his expedition, were only developed in the 15th century. The Vikings who reached the northern parts of North America with their longboats during previous centuries, on the other hand, did not have the political and economic infrastructure to mount an actual colonisation program. They could establish tiny coastal colonies like the one that was discovered in Newfoundland, but they would not have been capable of a large-scale, Cortes-style expedition that goes inland.
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It doesn't make them the same; radix point shift is a particular case of multiplication/division. They satisfy definition of multiplication/division. Check any suitable math book. Or Wikipedia
By the same reasoning, "hitch-hiking" and "flying on a plane" are totally the same thing, since I can use both to go to Beijing (one just takes a few months, the other 12 hours or so). Sorry, but you're simply wrong. Two different methods are two different methods, even if they arrive at the same destination.
While viking technology was good enough to start a colony in North America, it wasn't good enough to sustain it. Colonies in their early stages depend a lot on contact with their mother countries for supplies that aren't available locally (eg timber, iron, people...) or help if things are going badly. "vinland" was supplied from Greenland (of all places), which itself depended on supplies from Norway. They also antagonised the natives (vikings are like that). In any event, it was abandoned after about 10 years and 5 probably single ship voyages (which can compare with the fleets Spain sent to the Caribbean post-discovery). In any event Norway-> Greenland-> coast of NA is a smaller distance than across the middle of the Atlantic. Later climate change (among a few other factors) also made that route more difficult.
A fair amount of the viking colonization efforts were also against the background of growing state power in Scandanavia. (Greenland and Vinland were both set up by nobles with an unfortunate propensity for killing people and had consequently had to leave Norway in some haste), as that process completed, the capability for such adventures diminished.
A fair amount of the viking colonization efforts were also against the background of growing state power in Scandanavia. (Greenland and Vinland were both set up by nobles with an unfortunate propensity for killing people and had consequently had to leave Norway in some haste), as that process completed, the capability for such adventures diminished.
Vinland failed because Greenland was only a colony itself and couldn't support it.
But he knew there was a landmass somewhere in what is now America. He just thought (did he?) that it was Asia.
There is some evidence that suggests he knew of Vinland which made him think Asia was way bigger than we now know.
Not only that, he studied currents in Madeira, and I remember I read he encountered debris and from his calculations there must have been land in that place.
Not quite. Columbus was still pretty much set in the ancient model that split the world into Asia, Africa, and Europe. He didn't expect to find anything in between Europe and Asia when sailing west, because there was supposed to be one giant world ocean surrounding the continents. However, based on older and not particularly outstanding geography, he expected to find Japan somewhere out in the Pacific. From there he would go to India. When Islands in the Atlantic were discovered, such as the Azores, it only reinforced this view that land could be found if one sailed far enough. The fact that Japan would have sat roughly near the Caribbean only reinforced Columbus's view that he had discovered a westward route to Asia.
I also believe he did it on faulty data. I heard once that around this time the Portuguese had "rediscovered" (if you will) the proper circumference of the Earth. But Columbus had a different answer (one more suitable to sailing from Europe to Asia in a westward direction. When he went to the Portuguese for sponsorship, they turned him down because his numbers were wrong. But the Spanish were more than happy to help. Apocryphal? Probably. Interesting to consider? Definitely.
Like I said, he knew there was a land mass there, he only thought (did he?) it was something else.
The did he? part is a reference to the proposition that Columbus worked as a spy to the Portuguese king to divert Spanish attention from the Indies. There are several discrepancies pointing in that direction, but as everything else in Columbus life, it is a bit hazy.
The Norwegians were able to colonize Iceland.
The Icelanders were able to colonize Greenland.
I think the Norse did not manage to colonize North America because of the Native Americans. As far as we know the Norse, maybe apart from a few Irish monks, were the first people to settle in Iceland. When Greenland was colonized no people lived there (although people had lived there before, and another group of people would arrive later). North America however had a large population. Without a depopulation due to disease it may have been hard to set up a colony there. And maybe they did not know enough about America to consider it worth it to settle there.
@ Laskaris.
I've seen you take the stance of the rest of the world being ahead of Native Americans in technology with the possible exception of sub sahara africa. I ask you then what you rank technology as. I'm of the opinion that their troops being only 1/2 as good as European troops is enough to show military tech being behind Europeans. Making their tech research speed 10% of Europeans is pretty unrealistic too. The Meso-American/Andean Natives were at least on par with Europeans in engineering, medicine, astronomy, and organization. Sure they were behind because they didn't have steel and did not have as complex an economic system (unless you think the Inca quasi communist system is advanced). This shouldn't be represented as a 10% tech speed though having their soldiers be 1/2 as effective and no cavalry is surely enough to show weapon technology disadvantages.
I've seen you take the stance of the rest of the world being ahead of Native Americans in technology with the possible exception of sub sahara africa. I ask you then what you rank technology as. I'm of the opinion that their troops being only 1/2 as good as European troops is enough to show military tech being behind Europeans. Making their tech research speed 10% of Europeans is pretty unrealistic too. The Meso-American/Andean Natives were at least on par with Europeans in engineering, medicine, astronomy, and organization. Sure they were behind because they didn't have steel and did not have as complex an economic system (unless you think the Inca quasi communist system is advanced). This shouldn't be represented as a 10% tech speed though having their soldiers be 1/2 as effective and no cavalry is surely enough to show weapon technology disadvantages.
AFAIK Greenland had native population with whom the Vikings fought and traded. But without Greenland supporting Vinland was not possible.
Greenland did not have a native population (or at least the area settled by the Norse) when the Norse settled in Greenland. The previous population was gone and the modern Greenlanders came into contact with the Norse much later. The Norse colonization of Greenland began in 986, but the Inuits reached Vestribyggð in 1350. They had reached Diskobay by 1150, they for some reason stayed around the Diskobay for 200 years (according to a book I have they went south after it got colder). The Inuits then reached Eystribyggð around 1400.
Edit: I read a little bit more about Greenland and according to what I read (this bit comes from Wikipedia) parts of Northern Greenland were populated by the Late Dorset culture when the Norse colonized parts of south-eastern Greeland.
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Greenland had no native population (or at least no native population in the area the Norse settled), at the time the colonies started, the Inuit only arriving (in the area) later, which given subsequent relations undoubtedly helped the initial success of the colony.
While the colonists came from Iceland, most of Greenland's subsequent trade was ultimately with Norway, in part because neither Iceland or Greenland had much timber for shipping, and in part because they largely demanded the same things. Its not clear if ships destined for Greenland tended to stop at Iceland on the way, but a few references seem to suggest that a fair number didn't.
Regarding Vinland, well its probably informative that it was abandoned after 10 years, while the Norse persevered with Greenland.
@olverki. A rather large problem with your thinking is that the population and resources of Norway, Iceland and Greenland were not equal to each other. You probably should take the time to consider that the last was desperately poor and ultimately failed. Neither Iceland nor Greenland were self-sufficient and depended on trade with Norway for some essentials notably timber (in the case of Iceland after a fun experiment in deforestation) and iron (by the end of the Greenland colonies' existence iron is near-nonexistant so no iron weapons etc).
While the colonists came from Iceland, most of Greenland's subsequent trade was ultimately with Norway, in part because neither Iceland or Greenland had much timber for shipping, and in part because they largely demanded the same things. Its not clear if ships destined for Greenland tended to stop at Iceland on the way, but a few references seem to suggest that a fair number didn't.
Regarding Vinland, well its probably informative that it was abandoned after 10 years, while the Norse persevered with Greenland.
@olverki. A rather large problem with your thinking is that the population and resources of Norway, Iceland and Greenland were not equal to each other. You probably should take the time to consider that the last was desperately poor and ultimately failed. Neither Iceland nor Greenland were self-sufficient and depended on trade with Norway for some essentials notably timber (in the case of Iceland after a fun experiment in deforestation) and iron (by the end of the Greenland colonies' existence iron is near-nonexistant so no iron weapons etc).
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Mathematics deal with formal terms. If you define an operation and it meets definition of division then it is a division. It leaves no room for word-wiggling.