"I don't see that there is a big discrepancy between being concerned for the world's children and concerned with nuclear arms," said Dr. Benjamin Spock, explaining his 20-year sponsorship of SANE, a citizens' group for nuclear disarmament, last night at its new national headquarters.

Spock, the antiwar, antinuke activist and author of a best-selling book on child raising, was the guest of honor last night at the dedication of the Ben Spock Center for Peace.

"During the Vietnam war, I was a very popular speaker for the undergrads," said Spock, wearing a tie decorated with peace signs and looking at home among the many balloons and children of SANE supporters and staffers. "But as soon as American troops withdrew, the speaking engagements went way down. Now, as a result of Reagan's belligerent policies, that has changed."

The turnaround in national interest and support for nuclear disarmament was the topic of much of last night's discussion. Those present gave testimony to the movement's recent success. Many of them were longtime supporters of SANE: Hilda Mason, city councilwoman and SANE board member; Chad Dobson, an organizer of last weekend's nuclear protest in New York where 800,000 people showed up; Rep. Ted Weiss (D-N.Y.), SANE board member; George Kourpias, representing William Winpisinger, the president of the International Association of Machinists; and Dr. Herbert Scoville Jr., president of the Arms Control Association and author of "MX: Prescription for Disaster."

"The membership has more than doubled since President Reagan came to office," said the organization's executive director, Dave Cortright. "People are scared by his warlike rhetoric and his policies for a large military buildup. That has mobilized the people."

"It's just an amazing phenomenon," said Scoville. "A year ago it was hard to find politicians to support arms control. Now even people who don't believe in arms control are calling for a nuclear freeze."

"I think that for the first time there is hope," said volunteer Sheila Rotner, who has spent the past three weeks lobbying for the nuclear freeze campaign. "I was 12 years old when the bomb was dropped on Hiroshima and I was horrified. Maybe we have finally learned something."

"We have clout," said Cortright, discussing the mass of supporters who came out for the New York demonstration. "Politicians are realizing that they have to support nuclear disarmament to ge re-elected."

Nevertheless, Sen. Edward Kennedy (D-Mass.), one of the scheduled speakers at last night's dedication, failed to show up. The ceremony proceeded about an hour late.

"Ben Spock has been and continues to be a center for peace," said Weiss, unveiling a plaque over the center's door which read "The Ben Spock Center for Peace."

Yet despite the prevailing optimism for the movement, many were far from optimistic about the June 29 conference in Geneva and the policies of world leaders.

"They say that only the roaches will survive a nuclear war," said Robert Schwartz, a vice president of American Express and a SANE board member. "And that's not a pretty picture."