Colin Kapp has written a few stories which have some good, hard SF mixed up with highly tongue-in-cheek, believable flights of fancy. The present story is set on the single planet, Getawehi, of a rogue star, Geta, a million light years from the nearest galaxy. The gravitational field on Getawehi fluctuates in unpredictable manner, causing a number of odd effects (there's a hilarious scene of a drunken, walking rocket-ship and a novel mode of transport across the planet). A project to investigate the possibility of "borrowing entropy levels from other parts of the universe" is a complete failure due to the odd geometry which appears to prevail on the planet. The planet appears to radiate large amounts of radio energy with no apparent source. A landing team stuck on the surface does not have much of a way of communicating with the mothership. And when the rescue party comprising of the Unorthodox Engineers does manage to land on the planet, they run into physical manifestations of changed laws of mathematics. When two pieces of a cut girder are brought back together, they don't fit and their total length is quite a bit less than the original. None of the instruments manufactured to high tolerance levels can be reassembled on Getawehi because of the severe distortions in geometry. All seems lost...till they win and explain everything.

Well, not everything. The mathematical distortions are never explained. The author should really have assigned that part to the distortions in space-time, given the ultimate explanation, instead of actual deviations in mathematical logic. But his attempt at articulating the anomaly was really beautiful (reminded me of Greg Egan's writing). Some part of it shown below. All in all, a fabulous story.

"In all my books, twice one is two - and it's never before been in dispute" "But your books were written on Terra, not Getawehi. On Getawehi, they don't apply" "But that's insane!". Mathematics is merely a system for expressing the properties and relationships of quantities. It's universal, not a local phenomenon. Once one is one, twice one is two...."

"Not on Getawehi. It seems to be different here. Once one is one but twice one is only a bit over one and a half. One point five seven zero eight, to be more exact. And three times one is about two point three six."

[...]

"It's long been suspected that our mathematics may not be universal. Dimensionless numbers, for example, although have an accepted value in the part of the universe where we customarily use them, are more likely to be local coincidences than physical absolutes. But on Getawehi, we seem to have hit on something even more fundamental [...] It has something to do with unity." "Unity?"

"Yes. Unity...one...a whole. I'm no mathematician but it seems to me there's a darn great hole in our idea of the structure of numbers. We've explored number structure up to infinity and several orders beyond - but something we've always taken for granted is the constant mathematical value of unity."

"But it has to have a constant mathematical value!. Once one is one...it can't be otherwise by its very definition."

"So we've always assumed. But what if we happened to be wrong? What if there is a difference between the value of one as representing a whole thing and the value of one as a mathematical factor? They both seem to be the same in our corner of the universe but one used as a factor on Getawhei is demonstrably only 0.5785 of what it was on Terra"

Great fun!