Effect Sizes & Direct Scaling Problems

A Zentradi soldier sporting light combat armor...

A Zentradi soldier sporting light combat armor next to a common human soldier. (Photo credit: Wikipedia)

It’s common, among proponents of free-energy machines, advocates of the paranormal, and claims of quantum mechanics as magic, to point to the tiny effect sizes in their machines, psi-studies, and known quantum-scale effects, and claim that these will necessarily scale up to useful levels.

Never mind that these tiny effect sizes tend not to increase with newer machines or better studies when replication is attempted. Never mind that quantum mechanical phenomena in even tiny macroscopic objects occurs only under very rare and fragile conditions (there’s that nasty decoherence getting in the way…). In fact, as errors in the study, or flaws in the machine are accounted for, the effect sizes tend to shrink ever closer to zero.

But don’t take my word for it. Instead, refer to the extensive scientific and skeptical literature published by those far more studied than I in these areas, the experts who do this sort of research for their day-jobs.

As an example, If there is one thing that most obviously doesn’t scale up, it is the human form.

During the 1980s and through much of the 90s, I was a huge fan of anime SF, particularly the Macross series. My favorite alien species, with which I annoyed a great many more worthy than myself, were the giant Zentradi.

Soon afterward, reality snuck in, and I found out about the square/cube law, the principle of squaring the cross-sectional area and cubing the volume and thus mass when increasing the size and conserving physical proportions.

And these get very much out of step with each other the bigger or smaller you make something. It’s one of the reasons that modern arthropods are their current size, and why if you try to scale a mouse to elephant size, you get an elephant, not a giant mouse.

How does this relate?

I realized that, as portrayed, with human or almost human proportions and a height five times that of a human (I’m going by the Japanese version, not the American remake, Robotech.), it would be nearly impossible for the giants to support their own mass without a great deal of trouble in anything like normal gravity.

And yes, they did have normal gravity on their warships, judging by the ability of normal sized humans to move about in them without trouble in the anime.

Let’s do the math on this:

Let’s assume an adult human height ranging between 1.5 and 2 meters, giving our hypothetical enlarged human the upper end of this range to reduce size discrepancy with our giant and thus keep the numbers manageable.

Assume also a mass of about 100 kilograms and the musculo-skeletal development of a healthy, mature adult.

Finally assume that the anatomy and biochemistry, and the proportions of baseline humans are conserved in the giant, as usually assumed by many sources on the Zentradi.

What we have then, applying the square/cube law, is a human form with only 25 times the cross-sectional area of a human for its load-bearing members, and 125 times the mass, as mass depends on volume, not area. Our giant literally masses five times more than what it may support in normal gravity, at about 12,500 kg.

To move and operate normally, our Zentradi would have to be subject to the gravity of say, slightly more than that of the Moon or less, at about 0.20 Gs or lower.

Either this, or we must disregard our assumptions of the giant being physiologically human in all essentials save size.

But what if we reduce the size of a roughly 2 meter tall human by a factor of 5?

Things get strange, and the relationships of structural strength and mass reverse, helping to explain the unusual proportional strength of beings like insects and other arthropods:

Reducing our 2 meter tall human’s size by a factor of 5, to 40 cm, assuming what we did when enlarging it by 5 times (no infants or toddlers here), we divide the cross-sectional area by 25, and the mass by 125, or if we wish to complicate things, multiply by the square root of 5 and the cube-root of 5 respectively. Either way, the results are the same.

What??

Well, this means that the load-bearing ability of our miniaturized adult has proportionally increased by a factor of five relative to its volume, and so its mass. It can now support five times its mass under normal gravity, or its own mass at five times normal gravity.

This is why, if you want to build humans for heavy-gravity environments, you want to make them smaller, not bigger.

Of course, the actual strength compared to that of a full-sized human is reduced, but we’re concerned with proportional strength, which reduces as we increase in size and all else is conserved.

This makes physiologically human superheroes with the proportional strength of say, spiders, very unlikely indeed. We would have to violate our baseline human assumptions, and assume a different anatomy, biochemistry, or both, significantly departing from the human to make it possible.

Sorry, Marvel comics.

It’s why insects have their proportional strength,quite a few being able to carry many more times their own weight, and this same feature of scaling things up and then down drastically changes what we are scaling.

It’s just one thing out of many, the math readily accessible, that many things don’t scale up or down quite as we wish them too. Many things don’t scale up at all, and many experimental effect sizes shrink to the vanishing point with a closer look…

…much less scaling up usefully enough to revolutionize the world and our ways of thinking as often as claimed.

But wouldn’t it be wonderful if they did?

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