The Fun House of Wonderland went by several names, depending upon the time. In the earliest reports it was called The House of Mirth or The House of Follies or The Foolish House. The latter is the name that appears on the 1906 Sanborn Map and on one sketch, but on no photographs that I have seen:
“Foolish Ho.” is the abbreviation for “Foolish House”
“Foolish House” appears on a drawing by Rollin Lynde Hartt from his book The People at Play.
But most images show the building with the name The Third Degree written on it. This may be because there was a fun house franchise called The Third Degree, and the Wonderland management might have thought it more convenient to leave the running of it bto someone else, even if it required a name change.
The design of a funhouse with an entrance between the legs of a monstrous idiot figure occurs in other amusement parks of the period. The face of the figure is very nearly the classic “imbecile” face found in drawings and advertisements from the time. He has a broad face with jughandle ears and a missing tooth. If this makes him resemble the Mad magazine icon, Alfred E. Newman, it’s because it’s a familiar resemblance — they’re both based on the same early 20th century model. This figure also has goggle eyes, unlike Alfred.
He also is dressed in a burlesque of fine clothes — he sports a monocle, a top hat, and an outrageously large boutonniere. Each of his hands is grasped by a well-dressed lady with a bouquet. The scene suggests that he’s there for his own wedding, but that he’s being claimed by two different women.
For the 1908 season, the title was changed again, to The House that Jack Built. The well-dressed ladies with the bouquets were removed, and now the imbecile figure holds tools in each hand — evidently he’s Jack, and the tools are what he’s using to build the funhouse. Presumably the interior remained much the same. The name change might have been due to dropping the services of the Keystone company, which ran the Third Degree franchise.