So imagine people were the size of house cats, and the world's land masses were scaled down accordingly (in volume). In comparison to the original size of the landmass, how big would England be? And how would the scaling down change the climate of England?
An image example would be nice for visualization, or an equation would be helpful, but is not required.
There are a lot of answers that describe size if humans were cats, but from what I can tell, you want humans to be the same size as cats.
If we assume the average human is 6 feet tall, and the average cat is about 18 inches, that means a cat is about a quarter the size of a human, at the longest length, not counting the cats' tail. England (or rather, the island of Great Briton) is 300 miles across, and 600 miles long. Reducing by a quarter for the new human proportions, that would make the Island 75 miles across and 150 miles tall, reducing its area from 80,823 square miles to a mere 5,051.4 square miles.
Assuming this new England were in roughly the same location, and the rest of the world remained roughly the same, the weather would be somewhat as if you took the first hundred miles of coastal area and threw away the middle bits. Scotland would be barely above sea level; any storms that came through would be much, much worse!
Size by mass is not the same as size by 2d footprint
There is a cat here. She weighs about 5 lbs. I weigh 200 lbs, rounding to nearest 100. Cat is 1/40th my size. A sack the size of me could hold 40 cats, tightly packed by someone besides me.
England is 50,000 square miles. Divided by 40 is 1250 square miles. Long Island in the US is 1401 square miles. So you might have an England the size of Long Island.
That said, one could also look at 2d footprint. The cat and I occupy a similar amount of space on the ground; I just stick further up into the air. Feral cats have ranges on the order of 1-2 square miles.; a human hunter might range over a similar area. In this comparison of space occupied by a cat as compared to a human, you might want an England-sized England for your cat sized people.
People are already cat sized. There are machines that People have bred to provide food for People... those machines are called “humans” (in the machines’ own tongue). The scale of England need not change because the People are already its rulers.
Cats are imperialists, they purr and lull you into a defenseless state. They put up with us because we feed them. Given a choice, cats will take England just the way it is and humans can have that other place you want to give them. Go stuff the humans there, but leave the cushions and food.
This means England stays the same size and the weather may improve, as cats now own it and they have connections.
Roughly 50,000 square miles.
Did you know that the length of a 'foot' differed quite a bit - ranging everywhere between 9 and 16 inches. But ultimately, it was a measurement that was designed based off a person's size-of-foot.
Did you know that the mile has been defined both by "number of paces" and "number of feet"? It gets its name from the Roman 'Mille Passus' - or '1,000 paces', but is currently defined by 5,280 feet.
All of this is to say: if human being were the size of cats? And the land masses were shrunk down similarly? Then it'd all still be the same number of square feet and the same number of square miles! Because those measurements are based on the scale of a human. Which means the answer is simple: it's the same 50k square miles it is now.
For what it's worth, this attribute of universal standardization (uniform across all hypothetical human sizes) is why scientists have generally abandoned the metric system and have gone imperial. :-)
This is an excellent and sophisticated question. There would be many, many ways to think about this, such as conservation of energy, material science (you can not just slim down materials abstractly, issues of tensile strength, laminar flow etc, become critical), farming and food production, and so on.
Just one interesting issue which would need to be examined is the extremely highly variable ratio of cat groundspace in different postures, compared to humans who are generally upright except when sleeping.
The best calculation would be to compare the size of a typical cat house to a typical human house.
If you think of quaint London terrace houses, I just googled the typical width of the street frontage is about 6 meters.
Now, picture an imaginary cat house, such as in the film The Cat Returns where our heroine shrinks down to a world of cute little cat-size houses,
Cat fanciers will be able to answer the question, about how wide would a cute little cat-house be?
Let's say one meter across.
(It could be more like 1.5 .. I don't know. The worldbuilder, or some cat fanciers, would decide this.)
Let's use a calculator to divide 6 by 1, it turns out
In fact, Britain is conveniently 1000 km long and 500 km across.
So the actual answer to the question is
So that's it.
Note that issues of volume, weight etc are totally irrelevant.
UKCat would have cat-cars, cat-skyscrapers, cat-trains, cat-roads, cat-Tescos, cat-Brexit and so on.
You simply have to decide on how wide a cat-terrace-house would be compared to a normal-terrace-house - I've said "one sixth" - and you have your answer.
A typical cat - Felis silvestris cattus (Fsc) - is often compared but not necessacily a derivate of felis silvestris (Fs) - the european wild cat. Both demand territories. Territories for domestic Fsc range from 0.07 to 0.28 km², those for Fs range from 1 to 8.7 km². Let's take the middle as an average. That gives 0.17 km² for Fsc and 4.85 for Fs. Ferral Fsc demands territories similar to Fs.
24% of the UK human adults are adopted by a cat, for about 10.9 million house cats. Add 0.9 million ferral cats that chose not to adopt a human or lost theirs and 2000 Fs, mainly in Scotland, that hold up ancient tradition to never adopt humans. That's the general cat population, so we can assume this will be the population of people, or otherwise we'd need to house 66.44 million people. Each of the people shall get their proper territory as it would be natural:
That's not all the cats in the UK though! Let's look into the zoos what other cats get their share of the UK... for example if we take just the ZSL report we have to also accomodate for these inhabitants of the London and Whipsnade Zoo:
Add to that that in all, England had in 2018 the following big cats in private homes "13 leopards, three cheetahs, nine lions and nine tigers" -
We need to allocate extra territories for 2 Lion Prides (20 to 400 km²), 9 loner lions (600 km²+), 3 cheetahs (40-80 km²), 13 leopards (10-500 km²) and 16 tiger (60-100 km²). Taking the upper as food in england is not abundant but somewhat scarse, these few bigcats get a share of 1.754 million km² (or 7 times GB), but that's only England's statistics, so we double them for Scotland, Wales and North Ireland.
So, all in all, our people demad 6,247,280 km². But Great Britain only supplies 242,495 km², so we have to increase Great Britain's size by a factor of close to 26 to house all people comfortably.
If we however just turn all the 66.44 million people into housecats, we'd need 11637000 km², or 48 times Great Britain, if their former housecats vanish, or 13534500 km² if those stay but the other cats are expelled. 55.8 times GB.
Hm going by rough length I would go from wikipedia - a "mid-sized" cat to have shoulder height of 0.3 m , a "mid-sized" man around 1.8 m .. so divide length by 6 - and squares by 36 .. Going from Great Britain (island)'s area of 219.331 km² .. gives ~6100 km².
If I assume the same length "translation" to your fantasy planet, gives a roughly 2200km diameter planet (earth ~12750 km) and your fantasy "little britain" around 950 km from the equator (instead of ~5890 km on earth).
If such a planet could exist in orbit at earths position it wouldn't change the climate since your fantasy planet would have a steeper temperature gradient between equator and poles ...
