This post is addressed to those who believe in the Bible, including believing that the
biblical book called "Daniel" was written by a prophet named Daniel in the 6th century BCE. It is not directed to my fellow atheists, though some of them might appreciate the post.
The OXFORD STUDY BIBLE: Revised English Bible with the Apocrypha (copyright 1992) and The New English Bible with the Apocrypha: Oxford Study Edition (copyright 1976) in their introduction to "The Book Of Daniel" say the following (except that the Oxford Study Edition says "B.C." instead of "B.C.E.").
"The reports about Daniel in this book may contain elements about an older figure, or figures, with the same name .... in chs. 7-12 the author builds on elements from the Book of the Prophet Ezekiel to fashion the most fully developed example of apocalyptic literature in the Old Testament ....
The stories and visions are set in the Babylonian and Persian periods (sixth-fourth centuries B.C.E.), but they reflect a later time, primarily that of successors to Alexander the Great. Antiochus IV Epiphanes (175-163 B.C.E) and his wars with the Egyptians (see 7.8 n.) are especially in view. In chs. 7-12, Antiochus though anonymous as befits apocalyptic literature, emerges in more and more detail as the oppressor of the Jews."
Both study Bibles say the following regarding Daniel 2:37-40.
"The four kingdoms are usually taken to be the Babylonian, the Median, the Persian, and the Macedonian Greek; compare 8.20-21. There is no confirming evidence for the opinion (9.1), found in Jer. 51.11,28 as well, that the Medes existed as a world power quite separate from the Persians."
Regarding Daniel 4:33 the annotation/commentary in the two study Bible editions say the following. "A temporary lapse in the reign of Nebuchadnezzar is unknown, but does fit the last Babylonian king, Nabonidus, who (inexplicably) spent part of his reign at the north Arabian oasis of Talma."
The above is further evidence that the book called "Book of Daniel" (or simply named "Daniel") was written in about the year 164 B.C.E. The above is also further evidence that the 'Book of Daniel" has at least one incorrect view about the period prior to 164 B.C.E. (such as regarding the Medes), and some incorrect predictions of what was to happen soon after the year 164 B.C.E. (such as the establishment of God's kingdom over the whole planet Earth and hence the end of all gentile governments).