AS A FIRM BELIEVER in family loyalty, I was heartened to read this letter to The Economist from Samuel Engle Burr Jr., president general of the Aaron Burr Association:

"Sir -- We deeply resent certain parts of your review of the book: 'Aaron Burr: The Years from Princeton to Vice President,' by Milton Lomask. Evidently, your review has been indoctrinated and brainwashed with anti-Burr falsehoods, misstatements, half truths, and innuendos.

"Colonel Burr . . . did not kill his opponent in the duel -- Hamilton was mortally wounded. . . ."

You must have read about the Navy sex scandal. Seven women on the U.S.S. Norton Sound have been accused of lesbianism and threatened with discharge. Who cares whether they are lesbians or not? I suspect the prime cause of the investigation is the men who have been doing the investigating. Next time you go to a paperback bookstore, notice who picks up the lesbian novels -- nine times out of 10 it will be a male. I can hear the prosecuting officer unctuously saying, "And tell me, my dear, just what happened next?"

With our armed services in such desperate need of capable people, it is outrageous to reject female or male homosexuals. If the fear underlying this policy is that the homosexuals will molest the straights, I have a solution: The Verbal Standard. Anyone may proposition anyone else so long as force or the threat of force is not used. That way, no one would be harmed, the recruiting base would be broadened, and social discourse in the services would, I suspect, be considerably enlivened.

Stop wasting your money sending little Algernon to Camp Shawnee. Sure he has a lot of fun swimming and hiking, but what do you get out of it? Nothing, right? Next summer send him to the Youth Business Camp, which offers to teach children 10 to 18 "how to read and play the stock market." Tell the kid you'll stake him in return for a share of the profits. If he turns out to have a hot hand, you can retire. If he doesn't, just send him back to Camp Shawnee.

We should congratulate Washington Consumer's Checkbook, a local publication that, in rating the area hospitals, did something you can bet your boots the medical accrediting societies have never done. It asked the nurses of the Washington area to choose the hospital they would prefer to be patients in. The winner was Georgetown University Hospital. But the real significance of the study was that it asked the right people the right questions. Every patient knows what happens to him, but he doesn't know whether his case is typical or not. Doctors are usually defensive. The nurse is the one person who sees the interaction of physician and patient and sees enough to be able to generalize.

As a former patient at Georgetown, I must say that I suspect there is at least one non-medical explanation for the hospital's record of effective care, namely the food. It is dreadful. In my case, at least, it provided a powerful incentive to get well fast.

The army has finally produced the new helmet it has been promising for 20 years. The old helmet was metal and had a removable lining and therefore was useful for cooking and shaving. The new helmet, according to a report in Defense Week, is made out of Kevelar plastic fiber and has the padding permanently fixed to the inside. It weighs the same as the old helmet, but, according to Dr. Joseph Yang, the army's deputy assistant secretary for research and development, it has "greatly improved aerodynamic properties." This will give the infantryman something to be thankful for as he scrounges about the battlefield looking for something to cook and shave with: If he moves very fast he may cut a hundredth of a second off the time of the search.

Did you read about Mrs. Sam Church drawing unemployment while Mr. Church is being paid $61,000 a year by the United Mine Workers? And did you also read that the National Commission on Unemployment Compensation proposes that we raise benefits from the current $25 billion to $35 billion next year? And of course you know Social Security payments are going up, as are the pensions of federal employes. According to the National Taxpayer's Union, the unfunded pension liability of the federal government now exceeds $5 trillion. Yet no politician wants to face the problem. They remember what happened to Barry Goldwater when he mentioned the possibility of changing the Social Security system during the 1964 campaign.

The problem is that recipients of various income maintenance programs tend to panic whenever reform is mentioned because they fear the loss of a particular benefit they receive. In health care, for example, physicians panic at the first mention of any reform that might appear to threaten their income and prerogatives.

When reform does happen, it tends to come in a form calculated to offend no single group. As a result, the basic problem that reform is supposed to attack usually goes unsolved. An example was Medicaid, which was made unthreatening to doctors at the price of adding to the inflationary bias of the health care system -- which was and remains the basic problem of American medicine. Another example is the synfuels bill that Carter and Congress have given us as an answer to the energy "crisis." It does not have one paragraph that could panic any interest group. It threatens no one, and will merely exacerbate our present problems, producing, at tremendous expense, a pittance of overpriced oil.

It is for this reason that the country needs a president who is a teacher -- who will try to explain the nature of the country's long-range problems in a realistic but non-threatening way that says, "There's something we've got to do something about, not immediately, but in the next few years."

Carter is not a teaching president, and Reagan does not offer the faintest possibility of becoming one. The rest of us are going to have to do something about filling this need. In particular, we must change secondary school and college curricula so that, in reasonable part, they focus on main problems facing the country, both in the domestic sphere and in our defense and foreign affairs. We must encourage the television networks and newspapers and magazines to forget about the Billygates and the Abbie Hoffmans and to do a better -- radically better -- job of reporting basic national issues in a way that not only lays out the essential facts but analyzes possible solutions.

How dull, you must be thinking. But it doesn't have to be -- think about how the "60 Minutes" episode on Marva Collins began to revolutionize many people's thinking about the public school bureaucracy. And remember the highly entertaining "60 Minutes" segment on unemployment compensation, which showed some beneficiaries splashing around Florida beaches. The point was made that a lot of people were getting unemployment compensation who, just like Mrs. Sam Church, didn't need it, and the viewer could begin to think that if he doesn't want the national bankruptcy that our current income maintenance programs promise in the next decade or so, we might just have to tell Mrs. Church that she can't have her unemployment compensation. And if we take time to educate -- to explain why -- maybe she won't even be mad.