all right, here was the write up i did for the WHJ scholarship...pardon the info dump, i was taking a very "throw everything at the wall and hope the wall doesn't fucking break" approach...
Professor Why
In the same way Start Trekkin' borrows tropes and takes place in the sci-fi world of Star Trek, Professor Why emulates and exists alongside the longest running science fiction franchise in history, Doctor Who!
Of course, just as Start Trekkin' doesn't take place on the Enterprise or feature James Tiberius Kirk, our adventures take place on a different TARDIS with a different (but vaguely similar) Time Lord called the Professor. Perhaps they're two different generations of Gallifreyan, running around space and time avoiding each other. Maybe they're parallel dimension wavelength variant entities, alternate versions of one another. Who cares? You can explain anything away with science-y jargon if you say it fast enough!
Among its many instruments and gauges, our TARDIS has a wheel with four settings: Past, Present, Future, Space (what? if Time is the fourth dimension of space, why can't Space be the fourth dimension of time?). The Professor spins the wheel. Where it lands prompts the suggestion he asks for from the audience...
What historical figure would you like to meet? (why, we can travel in time and do just that!)
What monster do you fear the most? (odd, there are reports of similar creatures...but they can't be true! we should investigate!)
What's a made up planet's name? (by strange coincidence, it turns out that planet exists and we can go there!)
How will the world end? (i'm getting readings that that very threat is looming in the 300th century. perhaps we can avert it!)
Et cetera. (Latin? i LOVE Latin! let's visit the New New New Roman Empire on Tiberian V in the year 52165 repeating!)
Once the suggestion is gotten, the Professor reenters the TARDIS with his faithful (and most likely quite attractive) Companion and...they're off! The lights swirl as we dive through the Vortex, that classic theme music swelling in the background!
From here, of course, it's a completely made up Doctor Who story dressed up in "please don't sue us" clothing. Whatever time or planet they've traveled to holds incredible wonders...and dangerous threats (which, inevitably, are revealed to be alien in origin). Beyond that, it all lies entirely in the imagination of the performers (and their knowledge of the show). Things don't need to make perfect sense because there's always some sci-fi gobbledy gook to explain it away. Causality and paradox are just play things that can be used or ignored at will. An undefeatable threat always has some hidden weakness to be exploited at the last second. Incidental characters can die left and right, but the Professor and his Companion will always conveniently be kept alive or survive for the flimsiest of reasons ("Don't shoot him! His mind may be of use!" "Of course! Lavender oil infused with a tachyon energy flux at the right frequency can regenerate entire limbs! EVERYONE knows that!"). Sonic screwdrivers always have the perfect setting except when they don't and psychic paper always works except when it doesn't. Deus ex machina is par for the course and any established rule can be thrown out the window the second it proves inconvenient ("...of course, that was a one time trick. If i ever tried that again it'd split the universe in two. Unless...!"). The only things that matter are high energy, high stakes, mad ideas, melodramatic speeches, good guys win the day, lots of running...and always, always FUN! Remember, Doctor Who started out as a kid show, so if you're taking this TOO seriously, you're missing the point!
Sets, costumes and such should emulate the original. Bits of TARDIS bridge that can be moved on and off. A door to a differently colored police box, perhaps. Everything should feel simultaneously retro kitsch and deliriously post-modern. A 30th century idea of how the 1960s would view the future. This is anything-goes sci-fi...and in improv, that can be quite literal!
Rubber masks and cheap CGI might not be an option, but the aliens can look just as cheesy via random costume elements (how many Klingons have been represented in Start Trekkin' by a shirtless guy in a rock star wig and a seat belt strapped across his chest?). And you can always have a cheap homemade Dalek on stand by for a visit from old enemies as well as new.
Each performance could be self contained...but in a run of shows, you could also build a loose continuity or growing story arc, with a constant Companion and the rest of the cast rotating in each week as a newly regenerated (and differently attired) Professor, embracing the unique challenge of playing a slightly different but fundamentally the same iteration on the same character throughout.
All of time and space is your playground. The tools of genre and narrative are your toys. The only question is...where do you want to go?
Sweetness Prevails.
-the Reverend