*not a serious theory, but it was fun to think about*
S.W. Erdnase. Is it a reversal? An illusion? An anthropomorphic nose?
Well, here it is... S.W. clearly stands for Sherlock and Watson. S.W. Erdnase was Sir Arthur Conan Doyle.
Why did he do it? And why hide his identity? I surmise that Doyle was, in reality, a prankster. Similar to the things that Andy Warhol did and claimed in earnest not to know anything of chicanery involved in. Houdini was, as you know, obsessed with card magic- once billing himself as the "King of Cards." Doyle, with a hint of the hyperfocus that his most famous character had, must have then dedicated himself to mastering the art. He created a system to master it. As a doctor, he had an inherent manual dexterity, sensitivity, and analytical mind. Then for a time he kept it to himself. A private joke when lavishing praise on Houdini's talent- "Oh, you're soooo magical, it must totally be ghosts, bro..." Remembering that Doyle was definitely Jack the Ripper, this satisfaction was similar to his notes to the constabulary regarding those crimes.
But a funny thing happened on the way to Reichenberg...
He had no anonymous notes in varied handwriting this time. He needed to somehow share his latent cleverness without exposing the ploy. So he wrote the book. Anonymously. He created a new class of magicians that maddened the long-suffering Houdini. He created Dai Vernon- who flattened Houdini with a card trick after mastering Art the Ripper's system. And what of the name "Erdnase?" As has been pointed out- it could translate as "Earth nose." Dirt on the nose, the opposite of "keeping your nose clean." Through teaching a gambling system he encouraged others to enter a criminal underworld. To not keep their noses clean.
And there you have it- the perfect Erdnase theory.