Why did the Eastern Orthodox Church not have a Middle Ages like the Catholic Church d

Why did the Eastern Orthodox Church not have a Middle Ages like the Catholic Church did?

It broke off from the Catholic Church. It essentially was the Catholic Church.

Because the Dark Ages (middle ages) are what the reign of the Holy Roman Empire is called. The HRE did not control the East. The HRE made illegal much science and other knowledge, which is why they are called the dark ages.

Are you giving a prize to the 1st person to work out what you are talking about?

Because the Eastern Orthodox Church was not under papal restrictions on education, science and having dealings with the non-Christian world.

In western Europe, just about everybody was illiterate except for church and government officials.

Another way of looking at it is that when Emperor Constantine converted and became a Christian, he took his court east and created a new capital city named after himself: Constantinople. That part of the Empire left behind mostly withered on the vine.

The Patriarch of Rome (later to become the Pope) still ran the western church, but the government was behind the Eastern Church in Constantinople.

While the west entered into the dark ages, there were all sorts of intrigues in the east due to the fact that there was no separation of church and state.

The dark ages in the west are primarily due to the fact that the government decided to leave Rome and move elsewhere. The Byzantine Empire flourished while the Roman Empire died a slow death.

It did. The Middle Ages was a time, not a religious movement.
When the Western, Catholic, part of Europe was "having the Middle Ages" to Orthodox World was, mostly, still under Byzantine (Roman) rule.

In the waning years of the Roman Empire, it became impossible to govern the entire Empire from one local (Rome). Therefore, it was decided to split the Empire in two and have two Emperors - an emperor governing the Western Roman Empire from Rome and an emperor governing the Eastern (Byzantine) Roman Empire from Constantinople (Istanbul).

It just so happens that the Western Roman Empire collapsed into the Dark Ages while it remained "business as usual" in the Eastern Roman Empire for centuries later.