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You go into the family room, sit down, and remark on the lovely day. "Isn't it?" she answers. "Come sunbathe with me."

The sunny patio gives excuse for bare skin by anyone's standards; thankfully she throws off the robe and stretches out on a couch. You hesitate a moment. After all, she is your own grandchild, so why not? You undress quickly, since you left your outer wrap and shoes at the door (only barbarians wear street shoes in a house) and what remains is easily discarded. Your grandparents had to get used to a mid - century beach. It was no easier for them.

On the other hand, their bodies were wrinkled and old, whereas yours is not. The triumphs of endocrinology, of cosmetics, of plastic surgery, of figure control in every way are such that a woman need not change markedly from maturity until old age. A woman can keep her body as firm and slender as she wishes - and most of them so wish. This has produced a paradox: the United States has the highest percentage of old people in all its two and a quarter centuries, yet it seems to have a larger proportion of handsome young women than ever before.

(Don't whistle, son! That's your grandmother - )

This garden is half sunbathing patio, complete with shrubs and flowers, lawn and couches, and half swimming pool. The day, though sunny, is quite cold - but not in the garden, and the pool is not chilly. The garden appears to be outdoors, but is not; it is covered by a bubble of transparent plastic, blown and cured on the spot. You are inside the bubble; the sun is outside; you cannot see the plastic.

She invites you to lunch; you protest. "Nonsense!" she answers, "I like to cook." Into the house she goes. You think of following, but it is deliciously warm in the March sunshine and you are feeling relaxed to be away from the city. You locate a switch on the side of the couch, set it for gentle massage, and let the couch knead your troubles away. The couch notes your heart rate and breathing; as they slow, so does it. As you fall asleep it stops.

Meanwhile your hostess has been "slaving away over a hot stove." To be precise, she has allowed a menu selector to pick out an 800 - calorie, 4 - ration - point luncheon. It is a random - choice gadget, somewhat like a slot machine, which has in it the running inventory of her larder and which will keep hunting until it turns up a balanced meal. Some housewives claim that it takes the art out of cookery, but our hostess is one of many who have accepted it thankfully as an endless source of new menus. Its choice is limited today as it has been three months since she has done grocery shopping. She rejects several menus; the selector continues patiently to turn up combinations until she finally accepts one based around fish disguised as lamb chops.

Your hostess takes the selected items from shelves or the freezer. All are prepared; some are pre - cooked. Those still to be cooked she puts into her - well, her "processing equipment," though she calls it a "stove." Part of it traces its ancestry to diathermy equipment; another feature is derived from metal enameling processes. She sets up cycles, punches buttons, and must wait two or three minutes for the meal to cook. She spends the time checking her ration accounts.

Despite her complicated kitchen, she doesn't eat as well as her great grandmother did - too many people and too few acres.

Never mind; the tray she carries out to the patio is well laden and beautiful. You are both willing to nap again when it is empty. You wake to find that she has burned the dishes and is recovering from her "exertion" in her refresher. Feeling hot and sweaty from your nap you decide to use it when she comes out. There is a wide choice offered by the 'fresher, but you limit yourself to a warm shower growing gradually cooler, followed by warm air drying, a short massage, spraying with scent, and dusting with powder. Such a simple routine is an insult to a talented machine.

Your host arrives home as you come out; he has taken a holiday from his engineering job and has had the two boys down at the beach. He kisses his wife, shouts, "Hi, Duchess!" at you, and turns to the video, setting it to hunt and sample the newscasts it has stored that day. His wife sends the boys in to 'fresh themselves then says, "Have a nice day, dear?"

He answers, "The traffic was terrible. Had to make the last hundred miles on automatic. Anything on the phone for me?"

"Weren't you on relay?"

"Didn't set it. Didn't want to be bothered." He steps to the house phone, plays back his calls, finds nothing he cares to bother with - but the machine goes ahead and prints one message; he pulls it out and tears it off.

"What is it?" his wife asks.

"Telestat from Luna City - from Aunt Jane."

"What does she say?"

"Nothing much. According to her, the Moon is a great place and she wants us to come visit her."

"Not likely!" his wife answers. "Imagine being shut up in an air - conditioned cave."

"When you are Aunt Jane's age, my honey lamb, and as frail as she is, with a bad heart thrown in, you'll go to the Moon and like it. Low gravity is not to be sneezed at - Auntie will probably live to be a hundred and twenty, heart trouble and all."

"Would you go to the Moon?" she asks.

"If I needed to and could afford it." He turns to you. "Right?"

You consider your answer. Life still looks good to you - and stairways are beginning to be difficult. Low gravity is attractive even though it means living out your days at the Geriatrics Foundation on the Moon. "It might be fun to visit," you answer. "One wouldn't have to stay."

Hospitals for old people on the Moon? Let's not be silly - Or is it silly? Might it not be a logical and necessary outcome of our world today?

Space travel we will have, not fifty years from now, but much sooner. It's breathing down our necks. As for geriatrics on the Moon, for most of us no price is too high and no amount of trouble is too great to extend the years of our lives. It is possible that low gravity (one sixth, on the Moon) may not lengthen lives; nevertheless it may - we don't know yet - and it will most certainly add greatly to comfort on reaching that inevitable age when the burden of dragging around one's body is almost too much, or when we would otherwise resort to an oxygen tent to lessen the work of a worn - out heart.

By the rules of prophecy, such a prediction is probable, rather than impossible.

But the items and gadgets suggested above are examples of timid prophecy.

What are the rules of prophecy, if any?

Look at the graph shown here. The solid curve is what has been going on this past century. It represents many things - use of power, speed of transport, numbers of scientific and technical workers, advances in communication, average miles traveled per person per year, advances in mathematics, the rising curve of knowledge. Call it the curve of human achievement.

What is the correct way to project this curve into the future? Despite everything, there is a stubborn "common sense" tendency to project it along dotted line number one - like the patent office official of a hundred years back who quit his job "because everything had already been invented." Even those who don't expect a slowing up at once tend to expect us to reach a point of diminishing returns (dotted line number two).

Very daring minds are willing to predict that we will continue our present rate of progress (dotted line number three - a tangent).

But the proper way to project the curve is dotted line number four - for there is no reason, mathematical, scientific, or historical, to expect that curve to flatten out, or to reach a point of diminishing returns, or simply to go on as a tangent. The correct projection, by all facts known today, is for the curve to go on up indefinitely with increasing steepness.