When Zen Master Dogen was a teenager ("teenage Dogen" - now there's an interesting concept), he visited Onjoji Monastery and asked the abbot a question he had while studying Buddhism on Mt. Hiei. According to Dogen's biography, the abbot suggested that Dogen go visit Rinzai Master Eisai to resolve his question and to practice Zen, thus setting in motion the chain of events that resulted in Dogen's eventually trip to Great Song China.
That abbot of Onjoji Monastery, Sojo Koin, had once said, "Bodhi-mind is studying the dharma teaching of 'the three thousand worlds in a single moment of thought' and keeping them in one's mind."
Nagarjuna once said that bodhi-mind is the mind that solely sees the impermanence of this world of constant appearance and disappearance. Koin said that bodhi-mind is the three thousand worlds in a single moment of thought. "The three thousand worlds in a single moment of thought" is an essential doctrine of the Tendai school, which holds that the whole universe, with its 3,000 realms of existence, is contained in a practitioner's single thought. The 3,000 figure is not an arbitrary number, but is arrived at based on classical Buddhist mythology.
It is said that there are ten states of existence. Some teachings limit the number of states to six, and others have them is slightly different order, but to arrive at the 3,000 figure, we need to assume 10 states: hell, hungry ghosts, animals, asuras (fighting spirits), human beings, heavenly beings, arhats (saint-like disciples), pratyekabuddhas (self-realized or private buddhas), bodhisattvas, and buddhas (fully awakened ones).
The lower realms, below human existence, include hell, hungry ghosts, animals and asuras. In the hell realm, sometimes referred to as the insect realm, life is short, nasty and brutal. Like insects, those in the hell realm are said to be hacked into pieces, devoured by birds with iron beaks, and cut up by the razor-sharp leaves of the hell trees. Existence in the hell realm is not infinite, however, and rebirth into higher realms is possible after karma has been worked off.
The next highest realm, the realm of the hungry ghosts, is only slightly better: hungry ghosts are beings with enormous, unfilled bellies but tiny mouths no larger than the eye of a needle, through which they cannot possibly pass enough food to satisfy their craving. It is a life of constant hunger and starvation.
The next highest realm is the dog-eat-dog, survival-of-the fittest realm of animals.
And finally, the fighting spirits (asuras) are enemies of the gods, caught up in unfulfilled sensual desire. The state of an asura reflects the mental state of a human being obsessed with force and violence, always looking for an excuse to get into a fight, angry with everyone and unable to maintain calm or solve problems peacefully. The term is sometimes translated as "titans," and in some schools of Buddhism, the asuras constitute a higher realm than human beings and are considered lesser gods who live on the lower slopes of the world mountain Sumeru or in castles in the air. I like to think of them as poltergeists, although the closest analogy in European traditions may be the Nordic jötnar, who range from the semi-divine to the monstrous, and are sometimes at war with the gods and sometimes married to them.
The higher realms of existence above humans include the heavenly beings or gods, arhats, pratyekabuddhas, bodhisattvas, and finally, the realm of the buddhas. The heavenly beings live on the summit of the world mountain Sumeru and unlike humans do not know suffering. As a result, further spiritual advancement is not possible and rebirth into higher realms does not occur. It is sort of like in a board game where landing in a space very close to but not quite at the final goal sends you back several spaces.
Arhats are those who have completely purged themselves of desire, greed and hatred. An arhat has extinguished all passions and defilement and is certain that they will not return, but is still subject to some certain delusions. A saint-like arhat, unlike the heavenly beings, can go on to become a bodhisattva and perhaps ultimately a buddha, and skip over the next highest realm, that of the pratyekabuddha. (Perhaps the 10 realms would make a good board game - you advance based on the karmic roll of the dice, and if you land in the heavenly beings realm you go back a number of spaces based on a roll and if you land on the bodhisattva space you get to roll again.)
Pratyekabuddhas are those who have come to enlightenment by their own means and do not pass their wisdom on to others. They are those buddhas off in their own private Idaho. This can be thought of as a theoretical possibility - if a hermit attained enlightenment and then died in the forest, how would anybody know? - or as an explanation for those poets, artists, recluses and mystics who seem to have attained a degree of enlightenment but whose understanding had never been verified by a master. Contemporary Zen Master John Daido Loori has cited Walt Whitman as an example of a possible pratyekabuddha.
Those who forgo their own nirvana until all other beings have entered first are called bodhisattvas. This is the ideal in the Mahayana Buddhist tradition and bodhisattvas occupy a higher realm than pratyekabuddhas despite their not yet having achieved enlightenment because they pass the dharma on to others. Zen practitioners take the bodhisattva vow to first liberate the numberless beings in all realms ("However innumerable all beings are, I vow to free them").
And, finally, buddhas are the fully awakened ones in the highest possible realm of existence.
So, all together, including human beings, that makes ten realms of existence. Within each of these ten realms lies the potential for all of the ten realms, thus making 100 realms of potential existence. There are also 10 aspects to all existence, such as appearance, nature, etc., so there are in all 1,000 aspects of potential existence. Finally, there are three forms of mind: the mind of the insentient (such as the mind of trees and grasses), sentience, and ego-awareness. As each of the 1,000 aspects of potential existence can have these three forms, there are altogether 3,000 forms of existence.
Sorry for all of that doctrine, and I hope that you weren't turned off by the implicit cosmology, but I wanted to clarify what Sojo Koin meant when he said, "Bodhi-mind is studying the dharma teaching of 'the three thousand worlds in a single moment of thought' and keeping them in one's mind." In that single moment of thought is contained the three minds of all 10 aspects of all 100 existences and potential existences. Sojo Koin taught that the mind that continually encompassed these 3,000 realms was bodhi-mind.
Later, the adult Dogen said, "Some say that bodhi-mind is the mind that contemplates the three-thousand-realms in the space of a single thought. These people do not understand bodhi-mind, moreover they recklessly slander it. They are awfully far from the Buddha-Way" (Gakudo-Yojinshu [Points to Watch in Practicing the Way], Chapter 1, The Necessity of Arousing Bodhi-mind).
Was Dogen contradicting Koin? If you understand, you won't tell anyone.