Using kanji, many ideas can be expressed using just a few characters. For example, here’s how we write the 12 months in various ways:

Kanji 
Hiragana 
Roomaji 
English 
Indonesian 

一月 
いちがつ 
ichigatsu 
January 
Januari 

二月 
にがつ 
nigatsu 
February 
Februari 

三月 
さんがつ 
sangatsu 
March 
Maret 

四月 
しがつ 
shigatsu 
April 
April 

五月 
ごがつ 
gogatsu 
May 
Mei 

六月 
ろくがつ 
rokugatsu 
June 
Juni 

七月 
しちがつ 
shichigatsu 
July 
Juli 

八月 
はちがつ 
hachigatsu 
August 
Agustus 

九月 
くがつ 
kugatsu 
September 
September 

十月 
じゅうがつ 
juugatsu 
October 
Oktober 

十一月 
じゅういちがつ 
juuichigatsu 
November 
November 

十二月 
じゅうにがつ 
juunigatsu 
December 
Desember 
Average character 
2.17 
4.17 
8.83 
6.17 
6.25 
Note that the average character count drops from roomaji to hiragana. That is expected, since each hiragana symbol expresses the idea of mora which for this discussion can be regarded as a syllable. If we use roomaji, most syllables must be written using two or more characters. Therefore hiragana can be thought to compress roomaji. As a character, hiragana is more high level than roomaji.
The average character count drops again when we go from hiragana to kanji. Kanji is even more high level than hiragana. Each kanji expresses a certain idea. Because most kanji expands to more than one character when written using hiragana, kanji can be thought to compress hiragana.
I’ve heard people say, “kanji is sooo ancient. They should abolish it and replace it with something simpler and modern like the latin alphabet.” It eventually boils down to the unwillingness to memorize lots of high level symbols.
However, kanji is a form of pictogram. What they don’t realize is they also use some pictograms. Ever saw 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? Great, let’s abolish them. Then we can all have fun writing “sixty five thousand five hundred thirty six” or “enam puluh lima ribu lima ratus tiga puluh enam”.
Anyway, it is natural to ask, “can we define even more higher level elements?”. I don’t see that happening in natural language, but there is one language in which simpler concepts (encoded in symbols) are used to consecutively build more complex ones: mathematics.
In modern mathematics, everything starts with the set theory. There we see symbols like “{“, “}”, “,”, and “⊆”. From sets, we can define things such as the natural number, and naturally (no pun intended) new symbols like “1” and “0” appear.
Going even higher level, there is calculus in which symbols like “∫” appears. Calculus is very high level so that using vector calculus, all electromagnetic phenomena can be written in only four equations (the socalled “Maxwell’s Equations“).
I think it is astonishing that using the more highlevel symbols in Clifford Algebra, the Maxwell’s Equations can be written in only one equation.