The sons of Noah
Now the sons of Noah were three, Shem, Japhet (Japheth), and Ham, born one hundred years before the Deluge. These first of all descended from the mountains into the plains, and fixed their habitation there; and persuaded others who were greatly afraid of the lower grounds on account of the flood, and so were very loath to come down from the higher places, to venture to follow their examples. Now the plain in which they first dwelt was called Shinar.
God also commanded them to send colonies abroad, for the thorough peopling of the earth, that they might not raise seditions among themselves, but might cultivate a great part of the earth, and enjoy its fruits after a plentiful manner.
But they were so ill instructed that they did not obey God; for which reason they fell into calamities, and were made sensible, by experience, of what sin they had been guilty. For when they flourished with a numerous youth, God admonished them again to send out colonies; but they, imagining the prosperity they enjoyed was not derived from the favor of God, but supposing that their own power was the proper cause of the plentiful condition they were in, did not obey him.
Nay, they added to this their disobedience to the Divine will, the suspicion that they were therefore ordered to send out separate colonies, that, being divided asunder, they might the more easily be oppressed.
Nimrod tempts God
Now it was Nimrod who excited them to such an affront and contempt of God. He was the grandson of Ham, the son of Noah, a bold man, and of great strength of hand. He persuaded them not to ascribe it to God, as if it was through his means they were happy, but to believe that it was their own courage which procured that happiness. He also gradually changed the government into tyranny, seeing no other way of turning men from the fear of God, but to bring them into a constant dependence on his power.
Nimrod also said he would be revenged on God, if he should have a mind to drown the world again; for that he would build a tower too high for the waters to be able to reach and that he would avenge himself on God for destroying their forefathers!
Rise and fall of the tower
Now the multitude were very ready to follow the determination of Nimrod, and to esteem it a piece of cowardice to submit to God; and they built a tower, neither sparing any pains, nor being in any degree negligent about the work. By reason of the multitude of hands employed in it (the tower of Babel), it grew very high, sooner than any one could expect; but the thickness of it was so great, and it was so strongly built, that thereby its great height seemed, upon the view, to be less than it really was.
It was built of burnt brick, cemented together with mortar, made of bitumen, that it might not be liable to admit water. When God saw that they acted so madly, he did not resolve to destroy them utterly, since they were not grown wiser by the destruction of the former sinners. He, however, caused a tumult among them, by producing in them divers languages, and causing that, through the multitude of those languages, they should not be able to understand one another.
The place wherein they built the tower is now called Babylon (Babel), because of the confusion of that language which they readily understood before; for the Hebrews mean by the word Babel, confusion (Strong's #H894).
The Sibyl also makes mention of this tower (of Babel), and of the confusion of the language, when she says the following.
"When all men were of one language, some of them built a high tower, as if they would thereby ascend up to heaven; but the gods sent storms of wind and overthrew the tower, and gave every one his peculiar language; and for this reason it was that the city was called Babylon."
But as to the plan of Shinar, in the country of Babylonia, Hestiaeus mentions it, when he says the following.
"Such of the priests as were saved, took the sacred vessels of Jupiter Enyalius, and came to Shinar of Babylonia."
The Biblically recorded reason for building the tower of Babel was, "And let us establish a name for ourselves, lest we be scattered upon the face of the whole earth" (Genesis 11:4). This act was in direct defiance of God who wanted man to disperse and populate the whole planet (Genesis 9:1, 7).
Biblestudy.org's research places Noah's birth in 2913 B.C. and the great flood taking place in 2313 when he is 600 years old (Genesis 7:6). Because he lived 350 years after the flood (Genesis 9:28), Noah almost certainly lived to see great-grandson Nimrod born and supervise the tower of Babel (Genesis 11:1 - 9).
Japheth (Josephus spells it "Japhet"), Noah's firstborn son, was one hundred years old at the time of the flood (Genesis 5:32). Shem, the second oldest, was ninety-eight years old when the flood took place (see Genesis 11:10). Ham, the youngest, was almost certainly in his 90s when he entered Noah's ark (based on Genesis 5:32), meaning he was likely born between 2410 and 2403 B.C.
Although it is difficult to pin down the exact year the tower of Babel was built, it was likely erected around 2233 B.C.