Three main stems exist in all major ikebana schools. They maybe named differently. In Sogetsu school, we call them "shin (真)", "soe (副)", and "hikae (控)". In Ikenobo school, they are called "shin", "soe", and "tai".
From time to time, people who studied ikebana from other schools may ask me that if I teach ikebana in a way to emphasize "heaven, earth, and human." They want to relate their ikebana practice in a more spiritual way. But in Sogetsu school, we never talked about the spiritual meaning. The founder of the Sogetsu, Sofu Teshigahara, advanced the ikebana from ritual, rigid practice to an art form. Even though "shin", "soe", and "hikae" from time to time can relate to "heaven, earth, and human", we never feel we have to. It only can limit our creativity to a formality. It won't add to our free expression.
But what is "heaven" and "earth" in ikebana? If the stem pointing to the sky represents "heaven", the stem pointing downward is "earth", I think "heaven" and "earth" in this way are too limited. Let's give them a more broad meaning.
"Heaven" is the sky, the freedom. In order to fully express "heaven" in our ikebana, we need to be free. This is aligned well with creativity and imagination. In other words, heavenly quality is about freedom, creativity, and imagination.
"Earth" is the ground, the disciplines and the rules. Without disciplines and rules, things will fall apart. "Heaven" and "earth" are indeed "Yin" and "Yang", they cannot exist alone. Sometimes when you see an arrangement, all you can say is "Oh, it's very creative." But in reality, it's groundless, messy, and pointless. Other times, you would say "Oh, it's cute." Everything is tight, compressed, and sometimes depressed. It's lack of breathing room. Both are too extreme. The first one has too much "heaven" quality. Without "earthy" rules, it doesn't work. The second one is the opposite. It has too much "earthy" quality, lack of freedom. We "human" are in the middle. Our job is to bring "heaven" and "earth" in perfect harmony. It's not an easy task, but that's what we keep studying for.
Heaven and earth are not the branches pointing up or down.
Heaven is the creativity.
Earth is the discipline.
Human is the balance between heaven and earth.