Other answers have mentioned Chinese. I'd like to point out the modern standard pin yin Romanization that's commonly used for typing, too. Everyone here on this English board can read "Beijing", but typing those same letters in the IME produces north capital: "北京".
Now my mother-in-law can’t type on a computer because she never learned pin yin, and her accent doesn’t match the people who came up with the transcription. She learned an earlier form of phonetic instruction (I suppose it would be this one) which is not roman-based. It’s fair to say that most Mandarin speaking people younger than 60 would find this unintelligible.
An example in History is Linear B script.
Imagine the surprise of the scholors figuring it out when the language turned out to be Greek!
The point to remember is that a writing system is not the same thing as a language.
Rather than simply different ways to draw a letter (making them hard to recognise), you have real differences between an idiographic or syllable based script and a phonetic script.
Another thing is moving from an "artistic" scheme such as Myan script to something more familiar to us. Myan "letters" are not written in a row but are combined into squares.
Furthermore they make a point of not writing the same letter the same way twice, which confused those who tried to read it later. In the above illustration the same word is shown 3 times!
There are certain graphic features that determine which meaning it has, but you have artistic freedom to represent the needed features in some drawing, and each block becomes a unique work of art.
So, a culture with a rich history of this kind of system may switch to a plain pedestrian system of letters that are minimal icons of the needed features (not a picture containing them), always the same, and set in neat rows, perhaps in conjunction with the advent of movable-type printing.
Even with the words and "letters" being the same, it would take quite a different mindset to read the old stuff.
Here's some concrete examples of what you might use. This is far from simply different ways to write the same characters.
The historical writing system is more like Myan than anything we use today. Glyph-patterns are made from design elements, not specific renderings. E.g.
- 5 outward pointing points symmetrically arranged, like a star.
- a large round shape on the left and two smaller rounds stacked vertically to the right
- a wedge shape (open triangle) with small things inside
A scribe/artist would draw an artistic rendering incorporating the features, in a mini-mural where the order of finding the features is led through lines of composition and the context of the scene. For example, a pictorial of a river going through the kingdom will look like a sketch, but actually encode specific details of the story, which concerns the kingdom along the river.
What started as a clever way of including phonetic information in pictorial art to "speak the picture" evolved into a writing system that looks like Myan. A "character" is never drawn the same way twice, but you can find the meaning based on whether it's pointy or round, symmetry or lack of, number of elements, etc.
Larger scale order and arrangement act as modifiers for tense, imperitive vs question, etc.
Over time, a large collection of syllables were pared down to a phonetic system, but it was still drawn with "elements" not glyphs. Merchants and accountants have their own ideas and made stale writing for journals and ledgers.
A 5-pointed star became the glyph, etc. With simple essential line drawings used as a prototype for the pattern, each drawn in isolation. When it came to inventing printing and mass literacy, they moved to letters written in a neat row etc. like we understand.
Just as people study Shakespeare and calligraphy, well-cultured people in some subcultures learn the old idea of elements and apply the current alphabet and language, but draw them creatively in blocks, or as a form of poetry/art incorporate them into pictorial drawings.
Someone who didn't know that would be completely baffled at not even seeing writing (in the pictorial) or think the block form was an unrelated language.