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Let's start with how necromancy works in this setting. A magic-user grabs a corpse, shoves magical energy inside, and gets to boss it around until the magic runs out.

The efficiency that a corpse varies depending on its condition or how the magic-user has prepared it before animating it. Unless given very specific direction to do otherwise, magic follows the path of least resistance to reach the task the magic-user has given it. The resistance in this case is against the laws of reality (our physics). As the locals like to say, "Magic is lazy, and clever about it."

The fallout of this rule when applied to necromancy is that a corpse in perfect working condition is not the ideal target for necromancy. When commanded to make the corpse move, magic will do just that, wasting most of its energy kickstarting biological subsystems that the necromancer almost certainly doesn't care about and are not necessary for the newborn zombie to pick up heavy thing or chase away annoying adventurer. A damaged corpse is even worse, with magic trying to animate the whole meat-bag only to find out there's a hole and then waste even more magic keeping the corpse from falling apart through said hole. We will ignore that case for now.

The magical energy needed to animate a zombie is equal to the energy usage of a living human body minus the energy used by the brain, as this specific necromancy does not interact with the physical mind.

Zombies are highly inefficient, so the preferred target of necromancy is a clean skeleton. Magic is smart enough to skip trying to hotwire any nonexistent biological systems, so when commanded to animate a skeleton it instead focuses its energy on simply keeping the parts all in the right places and moving in a way that looks like how a human moves.

The magical energy needed to animate a skeleton is only the energy needed to hold the individual bones in place (there are no muscles or ligaments) against gravity, and the energy needed to physically move itself and whatever it needs to carry.

The third type of undead, a ghost, is simply the inverse of a zombie. Only the mind is reanimated, usually used by necromancers to ask the dead questions or just hang out in graveyards without feeling lonely.

The magical energy needed to animate a ghost is equal to the energy usage of a living human brain, plus a small overhead of creating sound vibrations in the air if the necromancer feels the need to verbally converse with the dead, but we can ignore that.

Now to get into the apocalyptic scenario proposed by the title of this question. One particular necromancer thought himself very clever when he came up with a spell that outsourced the cost of animating a corpse. Instead of requiring a payment of magical energy from the magic-user to get the corpse moving and doing useful work, it would absorb energy from its surroundings.

Problem 1: This completely removes the dependency the animated corpse has on the magic-user once the initial spell is cast. If corpse isn't going to run out of energy any time soon, there was never a hard rule in necromancy that the corpse had to stop moving as soon as it finished its initial job.

Problem 2: This setting has nothing along the lines of "ambient magical power." Magical power is simply another form of energy, and Magic, again being lazy, when instructed to just suck up any nearby energy to make a corpse move around, decided that the most readily available energy to use was thermal energy. So these new undead are able to continue to exist simply by lowering the temperature of their immediate surroundings. The Earthly belief in ghosts causing cold spots has officially become a reality for this particular world.

So the situation this world now finds itself in is a growing population of zombies, skeletons, and ghosts that are continuously sucking up heat to move around and continue to un-live. Assuming that all of these undead are simply walking at a casual human walking speed and not exerting themselves, my question is:

If this undead horde consisted of entirely zombies or skeletons or ghosts, how many would there have to be to plunge the world into a global ice age?

Some things I've been mulling over that might complicate what I initially imagined could be solved by a simple (or not so simple) math equation is if factors such as location or distribution affect the end result, such as if having such a large undead heat sink near the equator would alter wind patterns in a different way than if the horde was place near the already-chilly North or South poles.

I have found a similar question (as far as calculating the energy needs of a skeleton), with potentially useful numbers in some of the answers provided.

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    $\begingroup$ Your question might be unanswerable. $\endgroup$
    – Rhymehouse
    Dec 15, 2023 at 0:44
  • $\begingroup$ Can you specify a time period for achieving this? The more the quicker. ....but as Rhymehouse states, it may still be tricky to give anything more than a range of guesses. $\endgroup$ Dec 15, 2023 at 1:31
  • $\begingroup$ I was imagining "eventually" as the timetable, since the undead are just going to grow in number over time. My simplistic thinking, likely ignoring a whole host of factors, is that at some point the heat being absorbed by the undead would outweigh the heat hitting the planet from the sun, and on the way to the heat death of a planet there would probably be an ice age along the way. $\endgroup$
    – IVIX
    Dec 15, 2023 at 2:04
  • $\begingroup$ Hmm. Then there's the issue of what happens when they freeze solid (circa <0 Celsius)? Do they keep absorbing heat? $\endgroup$ Dec 15, 2023 at 2:30
  • $\begingroup$ Keep in mind that lowering the local temperature actually creates a source of human/machine usable energy, by creating a temperature differential (and violating the laws of thermodynamics). It can also be used for refrigeration with zero ongoing costs, and that's the most likely use case rather than being a stupid automaton or inferior combatant. (If it needs to use up energy to "create cold" then create a bar fridge that follows you around, like a less militant version of the Luggage in Sir Terry's books.) $\endgroup$ Dec 15, 2023 at 3:14

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You'll Run Out of Bodies First

Using the logic expressed here and rounding up, a human uses about 100W of power when just kind of being a human. All of that winds up radiating out one way or another, so ten million humans produce a gigawatt of energy.

If humans in your setting are about as efficient, and have been around for about as long as we have (in terms of species), you could potentially have a hundred billion corpses (though most have decayed away to dust, which might make the necromancers' job harder). That's ten terawatts of energy. Quite a bit, one might think.

The sun continuously delivers 173 000 terawatts to Earth..

Normal solar maxima/minima can vary the sun's radiative output by as much as 0.1% over an 11-year cycle. So normal solar variability has an effect about twenty times greater than animating every human to have ever lived as a zombie.

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    $\begingroup$ It's worth noting that you have to be quite close to another human being to perceive the heat they're radiating. A big group of people in a cold setting can make the area around them perceptibly warmer, but still have no effect climatologically. $\endgroup$
    – jdunlop
    Dec 16, 2023 at 2:04
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    $\begingroup$ Applying the 4th power law for power radiation vs temperature, you could expect a global drop of about 0.000433 degrees C if the 100 billion zombies could just make the energy vanish. Localized cooling in high density zombie zones might reach 0.1 degrees or even 1 degree in extreme cases. 2,843 zombies provide about 100 tons of refrigeration. The Houston Astrodome has about 6000 tons of refrigeration or 170,600 zombies. The Astrodome capacity is 70K, so 70K zombies to offset the human heat load, and another 100K zombies for everything else including reserve capacity. At least it was. $\endgroup$ Dec 16, 2023 at 8:49

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