A controversy is beginning to take shape here as Canadians realize that, despite government pledges to the contrary, information on almost every aspect of their lives is being computerized under a single identity number.

The social insurance number, the equivalent of the U.S. social security number, was initially issued to employes here a decade ago in order to keep track of their retirement and disability pensions.

The government promised that it would not become the sole means of identification for citizens, but would be limited to monitoring social benefits and might serve to minimize abuses of welfare, tax and unemployment compensation programs.

But Canadians have been perceiving gradually that the number is being used in a vast variety of ways that intrude into their privacy. So far, however, the government has turned a deaf ear to complaints, and it seems likely that growing protests may escalate into a major campaign.

However, the social insurance number has pervaded public and private institutions here so profoundly that it may be impossible to reverse the trend.

For example, the social insurance system is totally unrelated to the banking structure. Yet a person seeking to redeem a government savings bond must furnish the bank with a social insurance number.

The social insurance number has replaced the old dogtag number for members of the Canadian armed forces. Mail sent to servicemen overseas is required to bear the number in the address.

The new gun control registration law, which goes into effect this year, is based on the social insurance numbering system. The number also appears on government paychecks.

Canadians who balk at using the identity number find themselves entangled in bureaucratic red tape, not only in dealing with the government but also with private enterprises. Many banks now insist, for instance, that social insurance numbers by provided in opening accounts.

The first awakening to the threats inherent in the system came a couple of years ago, when probes into the shadier activities of the Royal Canadian Mounted Police disclosed that its officials had been using supposedly confidential information compiled by the social insurance department.

In short, the identity number gave the police the income, employment, health and other private data on individuals, thus expanding their authority enormously. For the single number is the key by which computers can produce a mass of information on people - without their knowledge.

The power of the number is all the more frightening because it can, through computer networks, link a number of data banks and consequently furnish public and private agencies with classified information on individuals.

Canadians are therefore starting to display concern about the brave new world of the computer. And the question being asked with increased frequency here, as elsewhere, is whether technology can be kept under human control - or whether it will control humans.