Sooner or later, we will have to change this way of presenting science. We might begin by looking more closely at the common ground that science shares with all disciplines, particularly with the humanities and with social and behavioral science. For there is indeed such a common ground. It is called bewilderment. There are more than seven times seven types of ambiguity in science, all awaiting analysis. The poetry of Wallace Stevens is crystal clear alongside the genetic code.

One of the complaints about science is that it tends to flatten everything. In its deeply reductionist way, it is said, science removes one mystery after another, leaving nothing in the place of mystery but data. I have even heard this claim as explanation for the drift of things in modern art and modern music: Nothing is left to contemplate except randomness and senselessness; God is nothing but a pair of dice, loaded at that. Science is linked somehow to the despair of the 20th-century mind. There is almost nothing unknown and surely nothing unknowable. Blame science.

I prefer to turn things around in order to make precisely the opposite case. Science, especially 20th-century science, has provided us with a glimpse of something we never really knew before, the revelation of human ignorance. We have been accustomed to the belief, from one century to another, that except for one or two mysteries we more or less comprehend everything on earth. Every age, not just the 18th century, regarded itself as the Age of Reason, and we have never lacked for explanations of the world and its ways. Now, we are being brought up short. We do not understand much of anything, from the episode we rather dismissively (and, I think, defensively) choose to call the ''big bang,'' all the way down to the particles in the atoms of a bacterial cell. We have a wilderness of mystery to make our way through in the centuries ahead. We will need science for this but not science alone. In its own time, science will produce the data and some of the meaning in the data, but never the full meaning. For perceiving real significance when significance is at hand, we will need all sorts of brains outside the fields of science.

It is primarily because of this need that I would press for changes in the way science is taught. Although there is a perennial need to teach the young people who will be doing the science themselves, this will always be a small minority. Even more important, we must teach science to those who will be needed for thinking about it, and that means pretty nearly everyone else - most of all, the poets, but also artists, musicians, philosophers, historians and writers. A few of these people, at least, will be able to imagine new levels of meaning which may be lost on the rest of us.

In addition, it is time to develop a new group of professional thinkers, perhaps a somewhat larger group than the working scientists and the working poets, who can create a discipline of scientific criticism. We have had good luck so far in the emergence of a few people ranking as philosophers of science and historians and journalists of science, and I hope more of these will be coming along. But we have not yet seen specialists in the fields of scientific criticism who are of the caliber of the English literary and social critics F.R. Leavis and John Ruskin or the American literary critic Edmund Wilson. Science needs critics of this sort, but the public at large needs them more urgently.

I suggest that the introductory courses in science, at all levels from grade school through college, be radically revised. Leave the fundamentals, the so-called basics, aside for a while, and concentrate the attention of all students on the things that are not known. You cannot possibly teach quantum mechanics without mathematics, to be sure, but you can describe the strangeness of the world opened up by quantum theory. Let it be known, early on, that there are deep mysteries and profound paradoxes revealed in distant outline by modern physics. Explain that these can be approached more closely and puzzled over, once the language of mathematics has been sufficiently mastered.

At the outset, before any of the fundamentals, teach the still imponderable puzzles of cosmology. Describe as clearly as possible, for the youngest minds, that there are some things going on in the universe that lie still beyond comprehension, and make it plain how little is known.