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As part of a series of questions that I've been doing about microscopic humanoids ...

In my world , there are a race of microscopic humanoid organisms ( 0.2 mm - 0.22 mm ) . They live in a variety of biomes , such as leaf litter , stone , and on plants and trees. My questions is -

Would weapons such as axes and spears be useful when scaled down to such sizes , especially against small arthropods such as ants and Pseudoscorpions?

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  • $\begingroup$ Note that, square cube law aside, mechanical properties of materials are very different at small scales. Air drag is also higher, so you won't be able to throw things efficiently. $\endgroup$ – Davidmh Mar 8 '16 at 12:25
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    $\begingroup$ @Davidmh how can that be so when their is proportionally less air per unit? $\endgroup$ – user15036 Mar 8 '16 at 13:10
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    $\begingroup$ Think about it like this: why can an artillery shell fly further than a bullet, even though their basic shape is pretty much the same? The momentum of the projectile increases faster than the amount of momentum lost to air drag. Drag is a bit complex, but it roughly grows with surface area in an aerodynamic projectile - on the other hand, momentum grows with mass, which grows with volume. It's just another application of the square-cube law :) $\endgroup$ – Luaan Mar 8 '16 at 13:28
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    $\begingroup$ @TheoclesofSaturn fluid dynamics is complicated, but the gist is that smaller fluids become more viscous. Look at dust: small pieces can float on the air for long periods of time, but as soon as they clump up, they fall to the floor and hide whenever you can't clean them away. $\endgroup$ – Davidmh Mar 8 '16 at 16:34
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No, your humans are too small.

A 0.2mm tall human is about 9000 times shorter than a 1.8m human, but its volume, and thus its mass, drops by 90003 or 729,000,000,000. A typical 70kg human becomes just 0.00009mg. Let's look at your expected opponent.

A typical black garden ant is about 4mm long, or 20 times longer than your humans are tall. A Brontosaurus, at 20m long, is only 10 times longer than a human is tall. Black ants weigh 1.5mg or 16,000 times more than your humans. By comparison an African Elephant only weighs 150 times a normal human.

Here is what that would look like.

Ant versus tiny human

Here is a human and an elephant for comparison.

enter image description here

Your humans simply would not have enough mass to affect an ant. Nor would they have enough height to do anything but poke at its legs.

Trying to scale humans down has myriad problems. This video on What Would Happen If You Were Shrunk? by VSauce3 scratches the surface.

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    $\begingroup$ An interesting, although sceptical analysis. What about strategy? If nothing else ants can swarm a larger enemy (and in some cases kill), so why can the mini-humans not do the same? A couple hundred mini-humans swarm the ant - climb it's legs, over it's back and start hacking with mini-axes at it's various joint or something. I admit it's not a good strategy - it would send the ant berserk trying to shake / brush the mini-humans off - killing all (or, at the very least, most) of the mini-humans. Perhaps a trap that ties the ant down long enough for the mini-humans to cut at the joints? $\endgroup$ – Richard Parnaby-King Mar 8 '16 at 10:33
  • $\begingroup$ @RichardParnaby-King To put that to scale, do you think a swarm of 4 gram beings with tiny little axes could take you down? 4 grams is a bit less than the weight of a US quarter coin. I've added a picture for scale. $\endgroup$ – Schwern Mar 8 '16 at 17:48
  • $\begingroup$ Again - strategy. Mini-humans dropping onto the back of the ant and taking off the head. Or make giant masks with water in them to drop over the ant's head and drown the sucker. Find some sort of poisonous mushroom, tip the spears in poison and stab the ants in the joints. Gulliver's Travels - tie the giant down and start carving up for dinner for winter! In summary - one on one there is no way a mini-human will win against an ant; many on one (with a fair whack of strategy) and there's a chance of success. $\endgroup$ – Richard Parnaby-King Mar 8 '16 at 17:59
  • $\begingroup$ All this is moot, though. Kill off one ant and it's friends will come looking for it. Won't be long till you have 5+ ants in your little village eating up the people. $\endgroup$ – Richard Parnaby-King Mar 8 '16 at 18:00
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    $\begingroup$ @RichardParnaby-King Taking off the head with a teeny-weeny little axe? Look at a coin. Now imagine that coin with a tiny axe trying to chop your neck off. I think you still don't understand the scale. Let's go the other way and scale the ant up. It's now 40 feet tall and weighs 1 million kg, or about 15 M1 tanks. You'll drop onto the back of a moving, thrashing 40 foot tall monster? And from where? Tie it down? Put a mask on it? It weighs 1 million kg! $\endgroup$ – Schwern Mar 8 '16 at 18:10
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What humans are good at is throwing rocks. That should be sufficiently primitive.

Here, like in many other cases, the cube-square law causes problems. A stone is 8000 times smaller, thus it has an area that is $6.4*10^7$. Its volume, however, is $5.12*10^{11}$ times smaller. Having the impact concentrated on a small area is how spears work, and the rock's impact is now much less concentrated. But it gets worse, small creatures can not throw a rock as fast as large creatures. All in all, rock throwing is much less dangerous. Sure, they might push the target a little, but nor brake bones or cause wounds.

Same for a spear, but there, the cube-square effect is cancelled but the fact that it is 8000 times sharper. It is however moving much slower, so no weapons based on hitting the enemy is very efficient.

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  • $\begingroup$ A spear is equally affected by the square-cube law. You penetrate because you can put force (roughly proportional to its mass) into a very small area (ie, sharp point, quadratic). $\endgroup$ – Davidmh Mar 8 '16 at 12:24
  • $\begingroup$ @Davidmh The square-cube law applies, but there exist two other effects there, and they cancel each other. In the end, the square-square cube law is standing alone. $\endgroup$ – Hohmannfan Mar 8 '16 at 13:16
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Basically, what Schwerm has stated. No, you cannot use these weapons effectively against those threats. At 0.2 mm (max limit), your people would be able to wield a spear hardly more than 0.3 mm. By comparison, even a juvenile ant is around 3mm and has 6 legs AND a pair of powerful denticles. An ant bite can send pain waves even in a grown up 6 feet tall human being. How do your people can fare against such a threat when being 1/30 of its length?

To help you think in perspective, would you be able to fight an ant that is double the size of a T-rex? It doesn't need to bite you at all (which would instantaneously clip you in two). Just a stomp by that monster ant would be enough to painfully end your life.

Also keep in mind that arthropods have exoskeletons, so that your weapons would hit the harder parts of the body first, which further implies that you will not be able to punch a hole through your arthropod adversaries (in perspective, a 6 foot person would have to punch a hole in 2 feet thick bone before his spear could hit the softer tissue inside).

So all in all, no. The weapons would be as useless against such adversaries as you trying to bring down a T-Rex with a spear.

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    $\begingroup$ Why do you think it would be imposible to bring down a T. Rex with spears? Is there some reason why you'd expect it to be harder than hunting, say, mammoths? Also note that all else equal, human muscles, bones etc. are much stronger than an ants - if you scale a human down to ant size, it would be much tougher and stronger than the ant. Well, and it would freeze to death almost instantly, I guess. And while ants do have an exoskeleton, they still have plenty of weak spots an intelligent opponent would target - assuming the skeleton was able to deflect their weapons in the first place. $\endgroup$ – Luaan Mar 8 '16 at 13:25
  • $\begingroup$ One simple reason is that the ants are 10 or more times larger in length alone. Compounded with width and height differences the total (volume) difference would be horribly great. I haven't done the math myself, but I'm quoting Schwerm that the overall (volume) difference would be in thousands, as compared to humans and large mammalian alive today, which does not even approach the scale of 500. If you require 5 people with spears to take down an African Bush Elephant (200 times larger) how many would you require to take down an ant around 2000 times larger than you? $\endgroup$ – Youstay Igo Mar 8 '16 at 13:34
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While attacking the traditional way will not work, your humans are small enough that they can crawl in through the joints and other openings on your ant. When inside, they are still large enough that they might survive the immune system for some time. Risky business, but such is life for any creature that small.

Inside, the small spears and knives could do significant damage. Maybe the humans could even accomplish rudimentary control of the ants, like some parasites do in the real world.

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What weapon? Intelligence.

I'm looking at Schwern's illustration when contemplating it, BTW. Diagrams like this ought to be part of the OP's posts. Now that he understands the scale that should be presented goin in rather than needing to be a major part of the answers, for subsequent questions in his series.

Anyway, poison comes to mind. As does a rope covered with sticky stuff that the ant can't break free of, to get tangled up in or at least get teathered with!

More intelligent then sticks and stones would be to use chemical pheromones. Make the ant do what you want, go where you want, including in a pen or cage. Make it hold still while you attachnthe reins, make it refuse to perceive any alarm even as you dismember it.

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