The bigness of institutions -- government and business -- is a major characteristic of our society. And as all of us have learned the hard way, bigness and arrogance are not strangers. In some runarounds we have come to feel that we are aiming small epistles at huge monolithic enterprises with little chance of penetration or are trying to talk sense with a closed-circuit computer.

We need an intermediary, someone to run interference. Or, as it sometimes turns out, we need a relief valve, someone to sound off to in this giant of an operation -- someone willing to listen.

In the media, ombudsmen are still a strange and rare species. Now the federal government has appointed ombudsmen to help taxpayers deal with the Internal Revenue Service and to help small businessmen seeking help in dealing with federal agencies.

The IRS Mr. Fixit began in 1979 as a result of a study on how to make the tax collection process more responsive to taxpayer problems -- such teeth- gritting situations as tax bills continuing to arrive for taxes already paid, for example. In 1976 four of the nation's 63 IRS districts were selected to try out a problem-resolution program to deal with cases where the system had broken down.

In each district a problem-resolution officer was appointed from the in- house staff to deal with snafus. It worked out so well that now each district and each of the 10 service centers has one.

At the top is the ombudsman, now George A. O'Hanlon, a 24-year IRS accountant, who has held assignments in Albany, Hartford and Cincinnati. In August 1983 he was appointed ombudsman in Washington by IRS Commissioner Roscoe Egger and serves at his pleasure.

The district problem-resolution officers, all career civil servants, are appointed and report to the heads of their offices. Mr. O'Hanlon helps run training seminars and advises the local officials. "Very few cases come to Washington," Mr. O'Hanlon said, so most of the work is done throughout the country. In the fiscal year that ended Sept. 30, there were 306,395 "problem cases" -- situations "where the system wasn't taking care of them."

Sounds like a lot, but there were 95 million individual returns processed in the same 12 months, Mr. O'Hanlon pointed out. Why did .003 percent of them go sour? "Some were very complicated, some simply fell through the cracks, but we resolved 76 percent in the first 30 days and did 97 percent or better in 60 days," he explained. The remaining 3 percent ran into "difficulty in getting old records or involved working with another agency."

Sometimes the problem is the taxpayer. He or she uses an incorrect Social Security number or fails to include all the appropriate schedules or forgets to sign the return. These are the relativey easy ones and help the problem-resolvers maintain a 21-day average time-resolution record.

Mr. O'Hanlon also serves as principal adviser to the commissioner on taxpayer problems and on the IRS tax forms committee.

At the Small Business Administration Frank S. Swain, chief counsel for advocacy, also serves as ombudsman for the agency, but unlike his IRS counterpart, his principal concern is representing small businessmen in their dealings with other federal agencies, rather than in their business with SBA.

Mr. Swain, who was appointed by President Reagan in 1981 and serves at the pleasure of the president, thinks that it is a "red-tape snipping relation to other agencies" that he provides. In addition he testifies before Congress on broad policy matters affecting small businessmen, such as changes in government contracting, taxes or paperwork requirements. But emphatically, he does not deal with requests for loans that hve been turned down by local SBA offices. His volume is a lot smaller than IRS, about "several dozen a year."

A number of states have also established the post of ombudsman to help residents deal with the state government -- Hawaii was first, then Oregon, Iowa, Nebraska and South Carolina followed. Several foreign countries have appointed ombudsmen to investigate citizen complaints against the government -- Sweden, Finland, Denmark, New Zealand and Norway were among the first.

Among newspapers the Organization of News Ombudsmen has recorded 35 thus far.