Knowledge From Experience in Chinese / Japanese...

體會 is a Chinese word that basically means “knowledge [comes from] experience,” or “to learn through experience.”

This can also mean realizing or gaining understanding from your experiences.

吃一塹長一智 is a Chinese proverb that means “Fall into a moat, and you will gain wisdom from the experience.”

It really suggests that the failures, troubles, frustrations, and setbacks that you encounter in your life are actually helping you to find wisdom. Some would also translate this proverb as “Learn from your mistakes” or “Learn from your experience.”

If you are studying Chinese, you will recognize the first character as “eat,” but in this case, it means to “experience” (as used in this proverb, it is suggesting that you have fallen into a moat and/or had a hard time crossing it).
Translated character by character, this whole proverb is, “Experience one moat, gain one wisdom/knowledge.”

Note: This can be pronounced in Korean, but it's not a commonly used phrase.

不經一事 means “You can't gain knowledge without practical experience.”

This is the short form (first half) of a longer Chinese proverb. These 4 characters remind you that wisdom only comes from experience.

You can translate this 不经一事不长一智 Chinese proverb in a couple of ways.
The first is: You cannot gain knowledge without practice.
The second, and perhaps more popular way is: Wisdom comes from experience.

It literally means if you are inattentive to your affairs or situations you encounter, you will not gain or grow any wisdom or intellect.

溫故知新 is a proverb from Confucius that is used in Chinese, Japanese, and Korean cultures.

It can be translated in several ways:
Coming up with new ideas based on things learned in the past.
Examine things of the past, and obtain new knowledge.
Developing new ideas based on the study of the past.
Gain new insights through restudying old issues.
Understand the present by reviewing the past.
Learning from the past.
Review the old and know the new.
Taking a lesson from the past.
Taking a lesson from the wisdom of the ancients.
Follow the old ways.

The direct translation would be, “By asking old things, know new things.”
The Character meanings breakdown this way:
溫故 = ask old
知新 = know new

Explained: To learn new things that are outside of your experience, you can learn from old things of the past. You can find wisdom in history.

VS.

Note: Japanese use a variant of the first Kanji in modern times.
Therefore if you order this from a Japanese calligrapher, expect the first Kanji to look like 温 instead of 溫.

In addition to 温故知新 as mentioned above, this is sometimes written as 温古知新 in Japan.