Not Thinking in Chinese / Japanese...

Hishiryō (非思量) literally means not-thinking.

Hishiryo can be described as a state of mind beyond thinking and non-thinking during the practice of Zazen.

Shiryō (思量) means “thinking,” and hi (非) is a prefix for negation and opposition.

Therefore, hishiryo amounts to “unthink” or “not the matter of thinking.” The word hishiryo appears in Dogen Zenji’s Fukanzazengi, Shobogenzo Zazengi, Shobogenzo Zazenshin, and Keizan Zenji’s Zazen Yojinki. It is one of the most important words used to describe zazen. Hishiryo in these writings comes from a dialogue between Yakusan Igen (745-828) and an unnamed monk, which is described in Keitoku, Dentoroku, and other Zen texts.

The above is an abridged except from School of Shodo: Hishiryo
I suggest you visit that page for a full explanation.

理念/理唸 means idea, notion, concept, principle, theory, philosophy*, or doctrine in Chinese, Japanese Kanji, and old Korean Hanja.

This word is OK for a wall scroll, although it's more commonly used as an oral/informal word in Asia.

* This is not the title for philosophy but rather is about having a certain philosophy or approach to something.

不拘一格 is a Chinese proverb that speaks of exploring different styles and not being stuck in conventional thinking.

It can also be translated as “not sticking to one pattern” or “not limited to one type (or style).” The most simple translation is “being creative” or “unbridled creativity.” Some may also say this means “not being stuck in a rut,” in the context of a designer or artist.

If you translate this, the first two characters mean “not stick to” or “not confine oneself to.”
The second two characters mean “one mode,” “one pattern,” “one form,” “one style,” or “one rule.”

動物王國 is literally what it says.

There is even a TV show in China that is similar to Wild Kingdom or what you would currently see on the Discovery Channel that has this same title.

For your information: In the Chinese way of thinking, the Tiger is the king of the animal kingdom (lions are not native to China, so the tiger took the role that we have given to the lion in our western way of thinking).

The modern Japanese version has a slight variation on the last character (国 instead of 國). Let me know if you want the modern Japanese version (國 would be considered the old or traditional version).

獅子王 is the Chinese title for “The Lion King” (also associated with the Disney movie).

This has the “Lion King” meaning in Japanese however, not associated with the movie you are thinking of. 獅子王 is also a Japanese surname that romanizes as Shishiou.

無我 is a more common way to say selflessness in Japanese. This literally means “no self,” or a better translation might be “not thinking of oneself.” 無我 is also understood in Chinese and Korean. 無我 is a very old word in CJK languages.

無我 is the word a Buddhist would use to express the idea of selflessness or unselfishness. For Korean Buddhists, it can mean self-renunciation.

See Also:  Altruism

刻舟求劍 is an originally-Chinese proverb that serves as a warning to people that things are always in a state of change.

Thus, you must consider that and not depend on the old ways or a way that may have worked in the past but is no longer valid.

This idiom/proverb comes from the following story:
A man was traveling in a ferry boat across a river. With him, he carried a treasured sword. Along the way, the man became overwhelmed and intoxicated by the beautiful view and accidentally dropped his prized sword into the river. Thinking quickly, he pulled out a knife and marked on the rail of the boat where exactly he had lost his sword.

When the boat arrived on the other side of the river, the man jumped out of the boat and searched for his sword right under where he'd made the mark. Of course, the boat had moved a great distance since he made the mark, and thus, he could not find the sword.

While this man may seem foolhardy, we must take a great lesson from this parable: Circumstances change, so one should use methods to handle the change. In modern China, this is used in business to mean that one should not depend on old business models for a changing market.

This proverb dates back to the Spring and Autumn period (770–476 BC) of the territory now known as China. It has spread and is somewhat known in Japan and Korea.

大公無私 is a Chinese proverb that comes from an old story from some time before 476 BC. About a man named Qi Huangyang, who was commissioned by the king to select the best person for a certain job in the Imperial Court.

Qi Huangyang selected his enemy for the job. The king was very confused by the selection, but Qi Huangyang explained that he was asked to find the best person for the job, not necessarily someone that he liked or had a friendship with.

Later, Confucius commented on how unselfish and impartial Qi Huangyang was by saying, “Da Gong Wu Si” which, if you look it up in a Chinese dictionary, is generally translated as “Unselfish” or “Just and Fair.”

If you translate each character, you'd have something like

“Big/Deep Justice Without Self.”

Direct translations like this leave out a lot of what the Chinese characters really say. Use your imagination, and suddenly you realize that “without self” means “without thinking about yourself in the decision” - together, these two words mean “unselfish.” The first two characters serve to drive the point home that we are talking about a concept that is similar to “blind justice.”

One of my Chinese-English dictionaries translates this simply as “just and fair.” So that is the short and simple version.

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

See Also:  Selflessness | Work Unselfishly for the Common Good | Altruism

In Japanese, 無心 means innocent or without knowledge of good and evil. It literally means “without mind.”

無心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: “No mind, a mind without ego. A mind like a mirror which reflects and dos not judge.” The original term was “mushin no shin,” meaning “mind of no mind.” It is a state of mind without fear, anger, or anxiety. Mushin is often described by the phrase “Mizu no Kokoro,” which means “mind like water.” The phrase is a metaphor describing the pond that clearly reflects its surroundings when calm but whose images are obscured once a pebble is dropped into its waters.

This has a good meaning in conjunction with Chan / Zen Buddhism in Japan. However, out of that context, it means mindlessness or absent-mindedness. To non-Buddhists in China, this is associated with doing something without thinking.
In Korean, this usually means indifference.

Use caution and know your audience before ordering this selection.

More info: Wikipedia: Mushin