Robin Ince will see your carol service and raise you chaos theory, ironing board cuisine, Darwin folk songs and a laser harp. The acclaimed comedian and science enthusiast responded to an accusation from Christian Voice's Stephen Green that he wanted to "ban Christmas" with an annual variety show, now in its sixth and final year. Rationalism can be positive, rather than negative: rather than standing in opposition to one thing, Ince embraces a million things, from philosophy and cartography to comedy and music.

A stellar line-up performs over 10 nights, some across the run, others dropping in for a show. One constant is Steve Pretty and the Origin of the Pieces, who put a groovy jazz spin on traditional carols in between acts and conduct a live experiment, measuring audience reaction to an improv game involving, among other things, playing their instruments with no hands. They're typical of the evening's wonderful combination of skill, knowledge and willingness to play in order to engage every single viewer.

A staggering 14 acts maintain this generosity of spirit, until even the most unpromising concept becomes involving. Subjects many of us would change channels to avoid (as someone who studied only humanities from AS level onwards, that's most of the maths and science for me) opened out into engrossing ideas like free will, social injustice and the exhilaration of stepping out into the unknown. "In physics, 'dark matter' basically means 'Dunno'" admitted physics teacher-turned "Geekpop" pioneer Jonny Berlinner, and the genius of this show is making such ignorance feel like a liberation.

Berlinner celebrated Alfred Russel Wallace, whose natural selection hypothesis prompted Darwin to finally publish On the Origin of Species, through the medium of a Tom Waits-esque song, while folk singer Gavin Osborn lauded theoretical physicist Richard Feynman's courage: "Not knowing things – it doesn't frighten me." Fellow folk artist Grace Petrie looked at the emotional cost of such courage in the poignant "Our One Life", addressing the fear of Darwin's wife that his ideas meant they could never be reunited in the afterlife.

Both musicians and speakers found emotional resonance and a sense of wonder in intellectual exploration, rather than confronting us with a series of equations. Charismatic bubble physicist Helen Czerski teased a link between popcorn, a hot air balloon and an internal combustion engine, marvelled at bat-hunting snakes with infra-red capabilities and gave us experiments to try at home. I, for one, will be livening up Christmas Day by dropping raisins in lemonade, holding my nose while eating a jelly bean and drizzling red cabbage water on everything in sight.

Quantum physicist Jim Al-Khalili questioned whether the future is pre-ordained, or just unpredictable, while economist Tim Harford eloquently warned about the danger of altering the world to fit our sense of order, and of making assumptions rather than seeking the truth. Mathematician Steve Mould used John Conway's Game of Life (a grid showing behaviour of cells, rather than the board game) to both communicate the joy of discovery – "Look at it go! Wheeee!" – and reveal we'd just witnessed the process of evolution, surely the scientific equivalent of the badass mic drop.

In each case, the examples made a wider point and illustrated that a complex subject can be rendered comprehensible when teacher and student find a way to communicate. If only that happened more in our school system – I remember no joy of discovery in science, but a lot of leaf cells and carboniferous limestone.

Comedians leavened the evening (something else we should try in schools?), with Josie Long sharing maths punchlines in a slightly meandering set, Richard Herring relating his imagined feud with Chortle over the matter of puns based on his demise, and John Lloyd preaching Ignosticism and cheerfully plugging his book Afterliff.

Hot Brew (Anthony Elvin and Sightseers' Alice Lowe) was perhaps better suited to the five-ciders-deep festival crowd, but John Luke Roberts stole the show with a similarly idiosyncratic idea: coolly mannered aphorisms delivered while wittily heckling the band in an Alain de Botton parody via Tim Keys. Most innovative act has to go to George Egg, who whipped up an ironing board meal while sagely comparing the pressure-sensitive hotel minibar to Raiders of the Lost Ark. Even this had a philosophical message: "Think beyond your perceived boundaries."

All of this was managed with great aplomb by Ince, jocular master of ceremonies. Whether praising the piglet squid ("That's evolution, baby!") or Peter Higgs, his genuine passion shone through. "It's a great time to be human", he proclaimed, and after that experience, I'm inclined to agree.

Nine Lessons and Carols for Godless People, at Bloomsbury Theatre

Nine Lessons and Carols for Godless People at the Bloomsbury Theatre provides an alternative take on seasonal entertainment with a jam-packed, humorous and hugely inspirational feast of ideas.