Buddhas have three modes of existence, called “kayas.” These are the nirmanakaya, sambhogakaya, and dharmakaya.

- A nirmanakaya Buddha is one who exists physically. For example, Nyingmapas generally would say that Dudjom Rinpoche (who lived from 1904 to 1987 and taught extensively in the West) was a nirmanakaya Buddha.
- Sambhogakaya Buddhas exist in the realm of visionary energy.
- The dharmakaya is undifferentiated enlightened potential. It is the essential nature of luminous emptiness.

There is a vast amount to say about the kayas, and I am vastly unqualified to say it. However, I would like to talk a little about the sambhogakaya. That is because of its role in visionary history. On the last page, I talked about the relationship between visionary and objective history. On the next one, I will discuss the fact that many human figures from Tibetan history probably did not exist as nirmanakaya—but certainly did as sambhogakaya.

So what does it mean to exist as sambhogakaya? It is possible to explain only by analogy. There are many traditional analogies. For example, it is said that the dharmakaya is like invisible water vapor, the sambhogakaya like clouds, and the nirmanakaya like rain. As with all analogies, this is imperfect. Water vapor, clouds, and rain are all physical phenomena; the dharmakaya and sambhogakaya are not.

Here I will give an unusual analogy. It is not an analogy from the Aro tradition. It is just mine, so it should not be taken seriously. It may be useful in understanding the compatibility of visionary and objective truth.

Sambhogakaya existence is similar in some ways to the mode of existence of numbers.

Numbers are neither physically real, nor fictional. They have no location, no substance, no mass. Yet their meaning is undeniable. The sambhogakaya is like that.

Numbers are neither a human creation, nor separately existent. Numbers cannot be invented or manufactured. Yet without humans to know them, they would not appear. The sambhogakaya is like that.

You cannot make numbers do what you want. They do what they like. You cannot say “I have made up a new number called Wallace. Wallace is smaller than six and bigger than seven. When you multiply Wallace times an even number, you get a positive number, and when you multiply Wallace times an odd number, you get a negative number.” That won’t work. It is not that mathematicians are stuffy and they won’t let you. Six and seven won’t let you. Wallace will not function as a number.

#### Tiffany will not function as a yidam

The sambhogakaya is like that. You cannot say “I have made up a new yidam called Tiffany. She has four hands, holding a Valium tablet, a credit card, a makeup compact, and an Uzi. They symbolize the four Buddha karmas of pacifying, enriching, magnetizing, and destroying.” That won’t work. It is not that Tibetans are stuffy and they won’t let you. The sambhogakaya will not let you. Tiffany will not function as a yidam.

From time to time, new numbers are discovered. (In fact,
new *types* of numbers are discovered.) But, this takes the form of
discovery, not invention. It seems to proceed from the insubstantial realm of mathematical
objects, not from the conceptual minds of mathematicians.

The sambhogakaya is like that. From time to time, new yidams are revealed. But, this takes the form of discovery, not invention. It seems to proceed from the insubstantial realm of enlightened mind, not from the conceptual minds of tertons.

### More than you wanted to know

The discovery of each new type of number has been accompanied by religious horror and wonderment.

In ancient Greece, Pythagoras founded a mystical religion, Pythagoreanism, that has had immense influence on subsequent Western thought. (It also has striking similarities to early Buddhist thought, and I bet that is not a coincidence.) Central to the religion was certainty that all numbers were “rational,” which meant that they were either “whole numbers,” such as 7, or fractions, such as 2/3. From this, the fundamental nature of the universe follows.

Then his student Hippasus discovered the first “irrational” number, which was neither whole nor a fraction. With the fundamental nature of the universe at stake, it was obvious what had to be done . . . The other Pythagoreans drowned him.

The names of later types of newly-discovered numbers demonstrate the shock and awe of their discovery. There are negative, imaginary, transcendental, surreal, hyperreal, subtle, ineffable, and transfinite numbers.

The smallest transfinite number is what we usually call “infinity.” The observable universe is really, really big. It contains billions of galaxies, each containing billions of stars, each trillions of miles from the next. Yet it is not infinite; it is infinitesimally tiny in comparison with infinity.

#### colossal, gob-smacking, fantastic, hypergimundous

The second-smallest transfinite number is mind-bogglingly, inconceivably, shockingly larger than infinity. You could pile up all the superlatives in every language in the universe—colossal, gob-smacking, fantastic, hypergimundous—and you would not faintly approach how much bigger than infinity the next-to-smallest transfinite is.

Needless to say, the third transfinite is considerably
larger. And how many transfinites are there? A whole lot more than infinitely
many. A whole lot more than the second-transfinite-number many. A whole lot more
than *any *transfinite number many.

Pretty nearly everyone who studies transfinite numbers finds it a major religious experience. It is often said that the transfinites provide a direct view into the Mind of God. Perhaps, in Dzogchen’s atheist terms, this is a glimpse of Longchen—the “Vast Expanse” of unconditioned primordial space/awareness.

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