SENTENCE 3: So them reformist guys set about modernizing Japan, borrowing Western knowledge, technology, and everything else appropriate they could borrow (including the nasty art of colonization), and they built railroads and set up formal government institutions and universities.

Why MEIDAI?
Now someone who pays attention to titles is screaming: "You haven't answered the 'Why Meidai' question, stupid".

Oh, actually, I knew all along I was evading the question, since answering it would require that we delve into the intricacies of the Japanese writing system. Now I tells ya, you donta wanna know what this writing system is all about. It's just about the craziest and most inacessible writing system in the whole darned solar system. But since I brought up the topic I am bound to explain it, and worry not, gentle reader, for I am not only good at complaining, I also specialize in summarizing (as in, for example, "My whole 21 years can be zipped as moments spent angsting myself sick and throwing up all over two-footed creatures.").

So, Why Meidai? Here goes (just 5 sentences, buddy):

SENTENCE 1: The Japanese writing system consists of three alphabets (four if you include Roman letters) and these are:
Kanji- Chinese characters, around 2000 for daily use;
Hiragana- curly characters, less than 50;
Katakana- not-so-curly characters (actually, they look like robot scratches, or hiragana written with a rusty elbow), less than 50.

SENTENCE 2: A Kanji usually has two readings, called:
Kun-yomi- original Japanese way of reading; and
On-yomi- Chinese way of reading,
and reading depends on where the character is placed in the ordered scheme of the universe... make that in the highly inconsistent scheme of Japanese writing. Usually (but definitely not always), when Kanji are placed side by side, you take the Chinese readings; On the other hand, when a Kanji is put alongside hiragana, then usually it's the Japanese reading at work. You can never be sure of which, however (This much I can guarantee).

[ OK, so let's skip this boring portion and get on with the Meidai thing:]

SENTENCE 3: Nagoya University in Japanese is

"nagoya-daigaku"

which, when broken up further, becomes

NA-GO-YA-DAI-GAKU

written with 5 kanji. The reading "nagoya" is the Japanese reading, and the word for uni, "daigaku", is the Chinese reading.

SENTENCE 4: Still, the Japs like to shorten names and phrases, etc, so they take the first Kanji of Nagoya,

"nagoya"- NA

and the first Kanji of university,

"daigaku"- DAI

and put them together, as in

NA + DAI

But to make things consistent (in this case), the powers that be decided that the readings for these two Kanji should all become Chinese, so the kanji NA becomes MEI (the character's Chinese reading), and add DAI (already read in the Chinese way, as said earlier, if you aren't lost yet).

By this time you are probably face-down into your key board, snoring boredom. Now, gentle reader, I suggest that you take your face off the keyboard as soon as possible, unless you want squarish pockmarks all over your lovely face.