Bereishit 11:4
וְנַעֲשֶׂה-לָּנוּ שֵׁם
vena'aseh-lanu shem
so that we can make a name for ourselves.
According to the peshat (plain meaning) of the text, all these people wanted was to settle in one single location on earth in order to stay together. However, they did not find a location other thant he valley of Shinor in which to do this. This is why they wanted to build a city and a tower which could accommondate all of them. The purpose of the tower was to serve as a beacon so thaat people all over the earth would be able to see it and to orient themselves by means of it. They themselves would all live in a single city. This is the reason the Torah quoted them as saying "lest we will scatter. This is why G-d punished them by scattering them to teach them that they had contravened His commandment to fill the earth with their presence (v9:1). Yeshayahu 45:18 pointed out that G-d had made the earth in order for it to be settled by mankind.
From an homiletical point of view the operative clause in the verse are the words "let us make a name for 'ourselves.'" This is an oblique reference to idolatry. The word שם (shem) "name here and the same word in Shemot 23:13 "and you must not mention the name (שם) of any other deity," mean the same thing. We also have a Midraschic comment in Midrash Tehillim 1, that the word הבה (havah), introduces an evil thought, an evil intention as it does in Shoftim 20:7 "come up with a plan here and now!" Furthermore, we have a tradition that the word עיר "city" is reference to a deity as we find in Dani'el 4:10 that the words עיר וקדיש (ir vekadish) refer to a destructive angel (ha-satan or similar). According to one Midrash on the Ten Commandments, these people proposed to take spades planning to invade heaven to flood it and drain it in order to ensure that another deluge could not originate from that source. They wanted to take large chunks of heaven and to engage in war with the King of the heavens. The Tower had seventy steps in an easterly direction and seventhy steps in a westerly direction on its opposite side. G-d descended those seventy steps accompanied by seventy angels and He confused their language and their dialects. Thus far that Midrash.
In Bereishit Rabbah 38:6 it writes that these people said, "we do not agree that G-d should have exlusive right to heaven whereas we have only been assigned earth. Let us make war against Him."
Looking at this story from a rational point of view, the words "and let us make a name for ourselves," must be understood as follows: The people of that generation were very advanced in matters of philosophy and even technology. However, they used their intelligence in a sinful manner. They constructed the city and Tower to protect themselves against a deluge of fire (seeing tht G-d had promosed not to again bring a deluge of water). This is what the word "war" in the Midrash refers to. They prepared to contend with the heavenly forces, such as angels, against the will of HASHEM. They tried to isolate and tame the power of fire in order to neutralise its deadly effect so that it could not engulf their city.
There was another reason which motivated them. They had been witness to the fact that G-d had decreed death on Adam, while they perceived themseles as physically powerful and enjoying a much longer life span than the 120 years G-d appeared to have decreed. They thought that they were all powerful (G-d Himself in v6 questioned whether their power should not be curtailed). They planned to scale heaven wie alive and well in order to overcome the impediment to this imposed pon them by their mortality. Their principal aim was to overcome the decree issued against Adam which made all of them mortal also. all of their planning in building the Tower was designed to achieve immmortality. The reaon G-d had to scatter them was because they planned to nullify His world order. The Torah has worded its report in such a way that it did not spell out these people's evil intent in detail. Whereas the Torah revealed the sin of the generation of the deluge, it did not spell out the sin of the generation of the Tower.
The Torah did want us to know that basically, their sin was of the same category as that of the first man. This is why the Torah refers to the people in this paragraph as בני האדם (ben ha'Adam) "Adam's sons", to hint that what they did paralleled what Adam had done. The extra letter ה (heh) before the word אדם (adam) stresses that they behaved not like ordinary human beings but like the first human being, Adam (as opposed to 5:1 where the Torah describes "this is the Book of the generations of man," without the letter ה in front of the word אדם.
The words "ben ha'Adam" are a hint that these people were like the first human being and the Torah had indicated that the people of the deluge had sinned by denying that there is something higher than the emanation "Keter", which had led to their destruction in the "lower universe." The word שם (shem - name) in this instance is reference to the highest emanation "Keter". They were under the mistaken impression that that emanation is the absolute highest level of heaven, i.e. celestial force which exists. The Attribute of Justice, even when in a dominant role, is always accompanied by some aspect of the Attribute of Mercy as represented by שם the Ineffable Name YKVK. In the case of the deluge, the principle of midah keneged midah (measure for measure) operated in such a away that as punishment for that generation's refusal to recognize anything beyond the emanation שם=כתר, they experienced the full impact of the unrelieved Attribute of Justice so that even the earth they had lived on was destroyed. The earth had been the creation of the Attribute of Justice, i.e. אלוקים (ELOKIM). The Attribute of Mercy, i.e. השם (HASHEM), had been "co-opted" only at the time when the Torah reported the creation of Adam (2:4) as a functioning human being.
Basically, man had tried to separate the role of the Attribute of אלוקים from the role of the Attribute of שם, or YKVK. G-d demonstrated to them that such an attempt if successful spells disaster both for them and for the earth they lived on. They had wanted only "nature," as represented by the Attribute of אלוקים.
It is quite possible that prior to the deluge such considerations had not had a philosophical basis, had been mostly based on an emotional resentment of authority from an extra-terrestrial force. At this time, it had been developed to a philosophy by highly intelligent people, people who had already learned of the value of co-operation, unity, working towards a common goal. This was why their newly developed approach was so dangerous.
G-d scattered them, i.e. separated them from their unity all over the globe as retaliation for their attempt to "scatter," i.e. separate His Attributes from one another. They had calculated the precise number of steps needed to ascend to heaven - 70. According to Pirke de Rabbi Eliezer, the number reflects 70 miles, a mile per step. The number may also allude to the 70 representatives of the 70 nations in the celestial spheres. According to tradition, Nevuchadnetzar, who was also from Bavel (though it was renamed Babylon) introduced the golden image of Baal into the remnants of the Holy Temple to symbolize that this philosophy had triumphed. In Yirmeyahu 51:44 the prophet predicts the eventual humiliation of that idol and that of the people who worshiped it. Dani'el 3:1 speaks of a huge gold image Nevuchadnetzar had put up in the valley of Dura in the land of Babylon. this valley may be identical with the valley described here in this chapter where the Torah described these people as וימצאו בקעה (vayimtzeu vik'ah), "they found a valley." All of this is part of the aforementioned hints the Torah provided concerning the sins of that generation.
May HASHEM protect us from committing similar errors.
The confusing of their languages was an example of the principle of the punishment fitting the crime, midah keneged midah (measure for measure). Their sin consisted of the words they spoke, i.e. "they said, 'Let us build a city for ourselves...'" Seeing they had put the power of speech to improper use, their power of speech now became impaired so that they no longer could understand each other.
The descendants of Noach who had numbered seventy at that time, were now divided into seventy nations, each with a distinctive language.
★ There are seventy "princes," i.e. representatives in the celestial spheres who represent these seventy nations before the throne of G-d. They correspond to the respective kings or heads of these nations here on earth. Each one of these seventy celestial "princes" is a part of the nation he represents, unlike Yaakov (Yirmeyahu 10:16) of whom the prophet said "unlike these is the portion of Yaakov, for it is He Who forms all things." Just as the Jewish people do not need intermediaries before G-d but have direct access to Him, so the Hebrew tongue is superior to all the other languages in the world. It is G-d's own language and as such it is as superior to other languages as is G-d Himself to any of the agents He has appointed in this world to do His bidding. It is the duty of Jews to draw the help from celestial sources by means of the Holy Tongue, Hebrew. Unless they are capable of praying in Hebrew their prayer loses in effectiveness.
May HASHEM continue to enlighten us with the Light of His Torah.
-Bachya; Chazal