“There’s always a mathematical solution to anything.” That driving principle comes not from a renowned scientist but from prolific director Allan Dwan, whose career grew with the very birth of cinema. The problem-solving that made his name during the silent era and beyond is evident even in trifling 1945 comedy Getting Gertie’s Garter. Who knew that math was so entertaining?

Dwan was as much electrical engineer (his training) as artist; although at this late stage in the art it seems impossible to imagine that a single person invented the crane shot, that’s what Dwan did, and it was just one of his technical achievements, which along with the math quote was related at length to Peter Bogdanovich in the essential collection of interviews Who the Devil Made It. Yet Dwan came into the industry with an eye to efficient business, not art; fortunately, the impulses came together more often than not. Dwan’s prominence came and went with the silent era, yet he continued to work his mathematical magic into the sound era, making silk purses out of a sow’s ear nearly every time he took charge of a production.

One such unlikely success was Getting Gertie’s Garter. From the title alone—which producer Edward Small had to get past the raised eyebrows of the Hays Office—it seems like the most inconsequential fluff. And indeed, the end product plays much like a sit-com well before the form’s peak. But with a good deal of math—and just as important, chemistry—the comedy’s complex equations came together in an elegant solution.

An anecdote from Dwan’s early career is enlightening. Working on an early Western, he was scouting locations when he found a cliff that looked like a good place for the leading man to hurl a villain to his death. Dwan then shot the ending of his movie first, and, as he explained to Bogdanovich, “I had to go backward and try to figure out why this all happened.”

Based on a play and already adapted into a 1927 feature, Getting Gertie’s Garter was obviously not reverse-engineered. But it’s useful to examine from its end point backwards. As the 1945 movie concludes, all is calm; as a series of couples who had spent the previous acts at odds finally retreat to private quarters, and behind closed doors…well it’s the end and a beginning as well. But what leads up to that harmony is 75 minutes of screwball madness.

After a brief establishing shot, Dwan introduces his protagonist, promising young scientist Dr. Kenneth B. Ford (Dennis O’Keeffe). It’s telling that when we meet Ken, he’s adjusting his glasses to see what a colleague is concocting with a beaker; this should be a common sight for Dr. Ford, but as O’Keeffe plays him, the scientist seems to struggle with the most ordinary tasks, which makes the ensuing hijinks that much more difficult.

The plot is set in motion when, owing to a legal dispute, the happily married Ford is forced to acknowledge an expensive gift (the pivotal garter) he once gave to an old girlfriend who is herself soon to be married. As a problem-solver, Ford‘s approach is the opposite of Dwan’s; instead of coming clean, Ford begins to conspire with Gertie (Marie McDonald) to retrieve the shining memento. But of course, Ford’s attempts quickly arouse the suspicions of his wife (Binnie Barnes) and his best friend (Barry Sullivan), who happens to be engaged to Gertie.

The complicated farce sows the seeds for countless sit-com misunderstandings to come and bears the fruit of centuries of comedy before it. But part of what makes Getting Gertie’s Garter so clever is that, despite the bawdy title, nobody’s getting any action to speak of. The plot has its roots in the bedroom farce of 17th century Restoration comedy, but where works such as Love in a Tub and The Country Wife made hay on the back of insatiable Lotharios, Gertie inverts the trope of the busy rake; everybody *thinks* everyone else is getting it on, but, until the happy ending, nobody is.

And it drives everybody batty. Dwan was fond of elaborate spatial set-ups, as in the trapdoors and secret passages that overwhelm the 1939 horror comedy The Gorilla. But here, Dwan’s pace and timing is pitch perfect as he sends his absent-minded scientist and all of his friends and loved ones on a jagged adventure tailor-made for white mice; except instead of examining furry charges running a lab maze, humans run futile escape routes through doorways and haylofts, windows and rooftops, all in pursuit of the elusive garter and truth.

Superficially, this may come off as secondhand, with the plot and O’Keefe often seeming like an imperfect cast molded from deteriorated 16mm prints of Bringing Up Baby. Yet that very near-familiarity adds to the sense that Getting Gertie’s Garter is a grand masquerade, taking place in an asylum, headed by a man who was there at the beginning of the movies, and always knew how to leave ‘em wanting more. You can watch it on YouTube, and marvel at how far visual efficiency has fallen.

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