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This site boasts hundreds of questions about the size of particular creatures and the effect the square-cube law has on them. However these questions usually focus solely on the skeleton and are often answered with examples of Gigantism, which is a growth problem where the body limbs grow disproportionally compared to the organs that try to support it.

As we scale up an insect for example, we know that at some point their method of breathing becomes insufficient and their skeleton will grow too heavy. So we have to use another solution to solve these issues: lungs and endoskeletons. Then as we grow an insectoid creature bigger we know that other problems arise in a set progression, such as the method of leg articulation requiring different methods. The question I'm having is: what does this progression look like when we start scaling from a humanoid size upwards?

As an example for the answer I'm looking for here's a hypothetical answer:

The first thing that needs a solution is the skeleton to support the weight, focussed mainly on the legs and hips. The next thing that gives out are the muscles, which simply cannot create enough surface area on their cross-section to efficiently support its own weight and add more strength to the overall creature. Then bloodpressure becomes a problem... then neurological problems to steer it... then the surface area of lung tissue, intestine length, liver position, kidneys etc.

The goal is to give people with questions a simple guideline to what size does to a creature, and where approximately on the scale of size their creature is going to be and the changes necessary to make it a reality.

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When talking about size and weights one should keep in mind that there are some "cheating" mechanisms. For example, why dinos where bigger than mammals in general? They were cheating! For eaxample: holow tube bones - lighter and more solid, "double breath" - many of this hollows were used as air bags, small brain - more resources for muscles, less heat production and etc.

This means that this list is highly specific for the type of animal we are speaking about. For humans first critical point is hip fracture, for hipo and elephant it is knees, for fish it is metabolism (it can't eat fast enough), for dinos it were heat managing, for insects it is breathing.

You just can not have universal "cheat-table" for all creatures.

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  • $\begingroup$ You can have a universal cheat sheet. Dino's used hollow bones because of their size, a human of that scale would require similar hollow bones as the Dino's (and earlier due to bipedal). The exact placement of a problem like hip or knee is less important than the solution: both are caused by the same type of excessive weight and would require a similar solutions. Insect breathing is a problem because their size, at that moment, stops allowing that type of breathing mechanism. So basically you just gave a few examples of problems but not where they would happen in the scale cheatsheet. $\endgroup$
    – Demigan
    Commented Jun 17, 2020 at 11:17
  • $\begingroup$ @Demigan, all my examples are first in cheatsheet for each type of animal. For mammals - first comes structural stability and this is not just hollow bones - it is the whole complex from the first paragraph. But for dinos it all the other story - they already had it ( and for other reasons, than size increasing) $\endgroup$
    – ksbes
    Commented Jun 17, 2020 at 11:46
  • $\begingroup$ When you increase a mammal in size it will have to pass certain milestones. As they keep growing in size their shape and the solutions to the increase in size will become more and more similar to the Dino's that didnt collapse under their own weight specifically because of the solutions they had. Similarily scaling a Dino down would result in the exact same cheatsheet in reverse, with more and more options becoming possible and making the dino more efficient, until it is basically a mammal, and going further it would basically turn into an insect. $\endgroup$
    – Demigan
    Commented Jun 17, 2020 at 11:55
  • $\begingroup$ @Demigan, your are quite wrong.Hummingbird is a dino smaller than some insects but it has nothing common with them. As I said earler - all dino features were developed not for size control but for different reasons (mostly for speed and thermo-control). Elephant is similar size and weight as many allosaurus, but they have very little in common. Same goes for all same-size fish/mammals/dinos/insects - each of them chooses it's own strategy to fight with cubic-square even when they have similar look (like large water predators). $\endgroup$
    – ksbes
    Commented Jun 17, 2020 at 12:19
  • $\begingroup$ Thank you for trying to ruin a perfectly good question. This isnt about evolution, it is about the necessary changes at various sizes. A bird requires modifications much earlier due to the fact that it needs to fly, but for the exact same final reason: they wouldnt be able to support their own weight. The cheatsheet would still be mostly be the same with a few exceptions like intestine length and bloodpressure. $\endgroup$
    – Demigan
    Commented Jun 17, 2020 at 13:15
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The best way to beat the tyranny of the square-cube law is to invest in fractal-based organs, distribution systems, and structures. A high degree of fractality(known as the fractal dimension) can essentially make a 1D, 2D, or 3D system behave as if it were of a higher dimension than it actually is. An example of such a system is your lungs. They depend on surface area to diffuse oxygen, yet they scale as if they were somewhere between 2 - 3 dimensions.

If your creature developed perfectly fractal surfaces and volumes, they could perhaps scale indefinitely, no longer bound by the tyranny of the square cube. If perfectly fractal, the surface area of your creature's lungs, capillaries, skin, and more would all scale cubically, preserving the surface area to volume ratios needed for different organisms.

I should note, such a fractal pattern would almost certainly be practically impossible in any living organism, but it is theoretically possible. Unfortunately, I can't see a way for things that rely on the cross-sectional area to benefit in the same way from being highly fractal. At the very least, you don't have to worry about surface areas while scaling if you assume they're highly fractal.

Fractals are one of the reasons a lot of the equations below increase by 1.75 instead of 2. That's what I call evolutionary efficiency!

Some useful equations and concepts to keep in mind as animals scale:

  • N = number of times mass is doubled.

  • Heart rate decreases by 1.25^N.

  • Lifespan increases by 1.25^N.

  • Calories required increases by 1.75^N.

  • Brain size increases 1.75^N.

  • Aorta cross-section increases 1.75^N.

  • Cellular mitochondrial densities decrease by 1.25^N.

  • Total # of Heart Beats in a lifetime remains constant.

  • Mass to cross-sectional area ratio increases by 2^N.

  • *implies bones must double in relative size every time a creature's size is doubled

  • *doesn't explicitly apply to circulatory and respiratory systems in most animals, as they are significantly fractal, and so scale by 1.75^N

  • Average cell size remains constant

  • Blood pressure and velocity remain constant

  • Many of these numbers come from the fantastically written book Scale, which, as the name implies, is a fantastic read about the effect size differences have on life, and the patterns inherent in life of all sizes.

On a final note, there are a lot more factors that affect scaling, but those are some of the key ones and hopefully, they can guide your thinking.

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