What issues as a result of square-cube law would a human scaled to the size of an ant face?

Question

Stories with shrinking never seen to take into account the Square-Cube law. I'm trying to consider what it would take to do a story like this that actually fully addresses the square cube law. I know most of the advantages humans would gain, such as:

1) being proportionally stronger, able to lift far more then 50 times their weight and survive drops from, quite possibly, any height thanks to terminal velocity

2) being much stronger then any insects or bugs of the same size they run into, thanks to having a body designed to have far more muscle and strength then creatures adapted to take advantage of the square-cube law.

However, I'm wondering what disadvantages they would face. For instance, I assume they would be quite cold, perhaps even dangerously so, since they can't rely on producing enough internal body heat? What similar down sides, even lethal ones, would someone face being scaled down to that size? For that matter what other advantages or otherwise odd effects would they experience?

To be clear I'm only interested in effects caused by the square-cube law. I can anticipate all the standard threats that come from being afraid of being stepped on etc (then again, would we be in danger of being stepped on? we may be able to survive that...)

Answer 1

As mentioned, they will quickly freeze to death due to inability to regulate body temperature (which is the reason why small homeotherms such as the shrew and hummingbird need to consume massive amounts of food relative to body mass).

Additionally, problems such as molecular size will come into play. Since the DNA/proteins of an organism are already molecular in size, shrinking a human wholesale would require shrinking of the molecules as well. This will make the enzymes used in digestion unable to break down any normal food, as their active sites are too small for the normal-sized food molecules such as starches and proteins.

The same will occur for respiration, where oxygen/food molecules will no longer be able to diffuse across cell membranes due to their large size with respect to the membranes.

Therefore, this results in Required Secondary Powers for the shrunk human to have a "shrinking field" maintained around himself/herself to shrink and enlarge molecules passing through that field, otherwise no molecular exchange can occur with the environment.

Answer 2

The smallest mammal is a shrew and the adults are about 2 inches long and weigh less than a dime. The Bee hummingbird is about 2 inches and 1.6 grams in weight.

These are tiny animals and yet they are still significantly larger than (most) ants. So the next question is what size ant are you looking to compare to? The largest ants are over (Bullet Ant) can grow up to 1.2 inches, and the Queen ant of some species can be a full 2 inches in size.

So assuming you are talking about an average sized ant in an American back yard (5mm?), I would say the 2 primary reasons for the shrew's and hummingbird's minimum size are:

1. body temperature: REALLY hard to keep it high. In the fall hummingbirds can die of starvation/hypothermia if they didn't get enough to eat during the day.
2. competition: everything else that size is already armored and has vicious weapons.

Answer 3

If you shrink the size and characteristics of the fundamental particles (protons, electrons, etc.), which requires changing some fundamental constants of the universe, then you won't be able to take in any oxygen (as pointed out in DS9's One Little Ship). Simply put, the haemoglobin in your blood accepts O₂ of a certain size, and if that size changes than it won't. Actually the oxygen probably won't even make it to the haemoglobin because being so large it will have problems diffusing through any membranes or into liquid.

If you try remove "extra" molecules (e.g. trying to scale down a Lego model by just replicating everything in proportion), other biophysical problems will occur:

• Your nervous system will immediately stop working as it will be overcome with noise. The connections between neurons (axons) has evolved to be about as thin as they can be (200-300 nm), and if they get much smaller (<75 nm, or about a 4x reduction in size), randomness in the opening/closing of some of the voltage-sensitive proteins is sufficient to cause the entire cell to fire. See Faisal, et. al. (2005) Ion-Channel Noise Places Limits on the Miniaturization of the Brain’s Wiring, Current Biology

  • Actually, if you get much smaller (20x reduction in size), the lipid bilayer will take up all the space in the axons, leaving no room for anything else. At that point there will be no structural integrity and the axons will disintegrate.

• While cells seem 'huge' compared to molecules, things on a cellular scale are curious in that they bridge the realm of countable (individually enumerating molecules) and uncountable (measuring things with molar concentration). As March pointed out, you can't stoichiometrically reduce the amount of chromosomes in your cells because you already have one, and subdividing that would be a Very Bad Thing™. It doesn't stop there, however. Many proteins (orders of magnitude smaller in size than the DNA) and especially mRNAs are actually present at a very low concentration or "copy number", some even on the order of 1-2. Significantly changing the size of the cell while keeping some of these individual proteins around will wildly alter the concentration and kinetics which will cause massive misregulation. (Couldn't find as good of a paper for this...this one is a decent overview, this one is paywalled, talks about counting individual proteins)

Outside my area of expertise, I'm not sure if it's theoretically possible, or what would even happen if you were to, "compress" space locally around a shrunken person. This is to say, matter crossing some threshold was magically shrunk (or appeared to shrink) to an outside observer. It would be like some tightly regulated black hole. It seems like you'd just have problems with insufficient (but breathable) air, which would actually be good from the thermal point-of-view as you won't heat up or cool off as quickly. I think you'd still need some sort of pressure suit and supplementary air though (or method to pressurize what little is there).

Answer 4

They're also going to be unable to see, since their eyes are sized and designed for more wave input. There's a reason insects have compound eyes. I could look up the math / physics... but the gist is, that the pupil needs to be a certain size to let thru wavelengths (iirc).

Edit:

Squeaky voice, at very low volume: Their speaking pitch will be 3,400 cycles a second (vs. 200 cycles a second) - (300x reduction in size roughly - square root == 17). And they'll only able to generate 1/17th (or less, not sure of the math - diaphragm is basically flat) of the volume of compressed air from smaller lungs.

Hearing reduction: eardrum reduction, means the lowest frequency they can hear is 340 cycles a second (vs 20 cycles a second) -ie: can't hear a normal human speak. The eardrum is unable to respond linearly to density variations near the source of sound, and the ability to distinguish differing sounds is degraded.

Blurry vision: 650-400 nm for visible light. Normal humans in normal light == 5mm in diameter (or a 10Kx larger hole). Divide by 300, pupil is now only 30x larger than the light waves. Scattering off the edges results in interference pattern, called diffraction - which is most noticeable when the dimensions of the object scattering the wave are comparable to the wavelength. Which is why insects have lousy vision, and different types of eyes (which adjust for diffraction effects). Or; No Ho, there would be noticeable diffraction ;)