The USSR was never actually catching up. With access to more accurate historical data we now know that much of their reported economic development was based on falsified official statistics.
They might have falsified the statistics in order to boost people's morale, but they were also very serious about actually progressing.
Bulgaria was under USSR's wing when I was a kid, and I have first-hand experience about that.
There was this thing called "kruzhoks", (a Russian word, diminutive of "circle", like in "circle of friends"), which were after-school interest-based clubs, mainly about technical stuff.
Every other kid was a member of some kind of kruzhok.
Back then I didn't realize that, but the state must have had some sort of "master plan" to prepare as many kids as possible for technical careers when they grow up.
I also distinctly remember the exceptional quality of the textbooks (math, mechanics, electronics).
The content was presented in a pedagogical order, with increasing difficulty, and carefully selected exercises that helped the concepts sink in. I used Russian textbooks from the 60's and 70's up until I graduated the university in 2005. (I'm a mechanical engineer, physics hasn't changed much since then, heh.)
The typography was also excellent. When I first saw LaTeX output, the first thing that came to mind was Russian textbooks. I don't know how they did it back then.
That's not entirely accurate. Between 1930-1970s (with some hiccups) the USSR was indeed "catching up", but this was because they were industrializing from almost nothing, plus rebuilding after the war.
It was the stagnation in the 1970s where the centrally planned economy couldn't adapt to consumer goods, light industry, and technology where they fell further and further behind. Various incentive problems exasperated things. Things would have been much worse in the 70s if high oil prices didn't mask these underlying problems, allowing the USSR to obtain hard currency to import goods.
Don't get me wrong, communism was bad. However, there were periods where it appeared to look superior. The quality of life in North Korea was "superior" to the south until the late 70s (much of this was backed by soviet subsidies, etc), but the optics still existed. There was a similar, though much more brief, period where east Germany had a faster growing economy than the west. There is a reason the Berlin wall was built in the 60s and not earlier.
In industrial societies, we re-invested about 20% of our GDP into production capital; under Stalin, that percentage was closer to 40%. That diminished after he died, to improve people's quality of life, but at the expense of overall productivity improvement.
