BMR=M^(3/4)
What this equation says is that the base metabolic rate (BMR) does not scale linearly with mass (M). This is a measure of an organism's capacity to both intake and expend energy.
A way of understanding the derivation of this is a popular tool used in engineering: assume everything is a sphere. For a sphere, we know that surface area is 4πR^2, cross sectional area is πR^2, and volume is 4/3πR^3. If we double the volume of a sphere, what we find is both the cross sectional area and the surface area increase not by a factor of 2, but by 2^(2/3) or ~1.5. Assuming a constant density and assuming power output from a spherical organism is proportional to the increase in cross sectional area, like with fasciculated muscle fibers, we can arrive at the formula where power or BMR=M^(2/3).
However, animals are obviously not spheres nor are they uniformly dense. What biologists found is the exponent is empirically closer to 3/4. We can spot assess the validity of this equation by looking at say, Olympic weightlifting records:
https://en.wikipedia.org/wiki/List_of_world_records_in_Olympic_weightlifting
If we take the ratio of men's total Snatch, Clean & Jerk of 294kg in the 55kg class to 435kg in the 109kg class, we find the power ratios scales almost exactly to the mass ratios raised to the 3/4:
(109/55)^(3/4) ≈ 435/294
What does this mean for animals of different masses?
This equation can explain why monster sized ants wouldn't even be able to hold their heads up if they were linearly scaled up to human size by mass despite their ability to lift up to ten times their weight at their natural size.
Not only would the atmospheric oxygen demand of their metabolic rate through their spiracles likely not be met, but their exoskeleton/joints wouldn't be able to support their weight. Their body geometry would render them too weak to hold themselves up. It's likely their legs would simply buckle under the weight of their own thorax/abdomen/head, and why movies such as this one will never come to be, at least on this planet. Secondly, because their metabolic rate would be incredibly high for their mass, it's likely they would quickly overheat with limited surface area to vent their internal waste heat.
In the Honey I Blew Up the Kid, the same logic would apply to the giant toddler. Upon enlargement, he likely would have immediately collapsed to the ground struggling just to breathe under the weight of his own chest. His muscles wouldn't have been strong enough to expand his massive rib cage and might have suffocated. He also likely would have been sweating profusely struggling to maintain his body temperature. Going the other way, in Honey I Shrunk the Kids, those kids likely would have had super human strength for their relative scale. They would have been able to leap through the air like fleas and bound back home in no time. However, again because of the law, they would have quickly gotten ravenously hungry and may have passed out from depleting their stored energy after one jump. They would have also felt freezing cold even at tepid temperatures and might have starved within a day, like an insect.
Conversely, millions of ants at natural size totaling the weight of the average human could overwhelm a person. This is why animals will typically flee from ants in large numbers. It is also why they say "strength in numbers".
How does all this this relate to the sexes and how does it explain our differences?
By the pound, according to this equation, women would be energetically "stronger" than men, in a sense. Their BMR per mass is higher. This would make them higher expenders of energy, and consumers of energy. Simply because they weigh less. Men, because of their increased mass, would be the opposite. They are energetically "weaker" by the pound and smaller consumers and expenders of energy.
So what gives? Why are men considered the stronger sex in most of the physical metrics we can think of in today's society and why in the world would our species have evolved this arrangement? Why would the sex that has a lower capacity for production per pound evolve to be the primary long distance hunter and the other the short distance gatherer? If we were to allocate biomass between genders, wouldn't it make more sense for the gender that can exert the most energy per mass be the better hunters? Why haven't we evolved with a higher female to male sex ratio to favor large packs of female hunters? Why aren't the men the ones who conceive and bear children?
The answer lies in leveraging our environment, body composition, and just plain population dynamics. And more simply, bigger is better (for certain tasks). When it comes to an environment with more elusive, massive, and diffusive resources, it is favorable to gather as much sustenance as you can while expending the least amount of energy. So, when long distance hunting or gathering, because of their size, men were able to travel longer, farther, and carry more resources to bring back for consumption. They were "stronger" in their efficiency of acquiring resources via leverage. Nature does not yield to humans so easily, we need to be able to apply the right amount of leverage to extract said resources. You can try whacking a tree more times with a hatchet with shorter, lighter arms (lower penetration per swing and higher BMR/mass); or you can grab a long handled axe maul with longer, massive arms to build up larger amounts of momentum to really chop into it fewer times (larger penetration per swing and lower BMR/mass). Because of their size, men were also more suited for bringing down larger and faster prey.
They also evolved to be natural risk takers, which is why their mortality rates were higher in acquiring resources. This also meant a higher tolerance for acute pain and injuries to cope with their higher occurrence rates. They were also primary participants in war. Conquering neighboring tribes was a quick and easy way of plundering resources.
But that is merely half the story. Women, with their elevated metabolic rates, evolved to be more sensitive and meticulous. This made them well suited for smaller, energy intensive tasks. Their short distance gathering made them excellent discerners of plants and other fruits that were vital to both gender's diet. This paired well with their risk averse nature in identifying and avoiding potentially toxic food sources while focusing on gathering more nutritious ones.
Their elevated senses made them more efficient extractors of smaller amounts of resources, sometimes for medicinal use. Their heightened senses also made them better caretakers of men, the infirmed, elderly, children, and other women. Because gestation is an energy intensive process requiring lots of nuturing, the gender with the higher energy intake rate and smaller stature would be well suited for inputting the required energy to quickly develop new life, shortening the gestation period. Were men to conceive, it’s possible the infants would be much, much larger upon delivery and require longer gestation periods. Again, because of strength in numbers, it makes sense why we as altricial animals would value a woman's life more than a man's given the disparity in mortality rates. It can also explain why men were evolved to be virile and women fertile.
Body composition also plays into this. Women tend to have a higher fat %. Which would help insulate them and reduce their BMR by exchanging muscle for fat. Despite the added insulation, women still tend to feel "cold" a lot of the time with their BMR and larger surface area per mass. Thus, their desire for a large, warm body to cuddle up to at night when temperatures dropped. So, not all pounds are created equal, as many dieters are acutely aware.
What about intelligence?
On IQ, Kleiber's law does not seem to strongly correlate when it comes to “smarts”. Men may have larger brains, but it appears most of the extra mass goes towards controlling motor functions of extra body mass. One could go so far as to say the dense, compact nature of women’s brain power explains their preference for densely organized information like reading. Whereas men’s more rarefied brainpower could explain them preferring loosely organized spatial information such as objects in wide open areas.
Neither gender comes out ahead on the WHOLE average, as in the areas under the respective curves are equal. However, the shape of the curves tell a different story in day to day living. It plays out that if you lie the the left of the curve, the average woman is smarter than the average guy. If you lie on the right of the curve, the average man is smarter than the average woman. These curves also suggest that men and women are wired differently. Men are on a wider distribution band, a larger standard deviation, which makes them the dumbest and smartest gender simultaneously. This translates to a higher degree of intragender variance. Women have a tighter band, smaller standard deviation, where more of them tend to share similar levels of intelligence.
One could argue this distribution is necessary for women to be able to exert more psychological "control" over the majority of less bright men. <-Guys don't be butt hurt about this, and it’s not like many of you will be aware of it anyway. Trying to outwit a smarter woman who is designed to be your better half will likely land you in hot water. Reading this myTake likely won’t give you any type of informational advantage because they know it too.
This can also explain the nature of each gender’s mentality about the opposite sex with women having a complex mindset being more cautiously attracted to creatures who can cause them harm, while men with a more simplistic mindset are more easy going being attracted to creatures less physically dangerous to them.
What's also interesting about this curve is at the tail extremes, the number of genius and retarded men and women alike converge on the same number. Marilyn vos Savant (serendipitous name) has the highest last recorded IQ at 228 in the Guinness book of records born right here in St. Louis. She gained notoriety for figuring out the best strategy for the Monty Hall Problem or similar to Let's Make a Deal. She also stood her ground on her findings despite widespread criticism, in fact you can test this strategy for yourself at home with three cups and a ball.
So, neither gender was, or even is, explicitly "better" than the other. They're complementary. They both have their strengths and weaknesses. Men desired a smaller framed, yet high BMR/mass woman to provide his voluminous excess resources to while receiving her smaller, essential ones. Women desired a massive larger framed, yet lower BMR/mass man to receive his voluminous resources while providing him with other much needed resources. The exchange came to an equilibrium for both their well-beings. It was a partnership, to increase odds of survival.
It's worth noting that these roles were not literally set in stone. When faced with survival, anyone could take on any role as needed by the community. Women have been discovered to be hunters for smaller game. Men were also discovered to help with duties closer to their encampments. But the traditional model that played to our biological strengths likely yielded a tribe's best chance for survival.
So what's up with modern society?
Well, industrialization, mechanization, automation, and fossil fuels preceded by “ages”: agrarian, bronze, iron, neolithic, sail, discovery, etc. The “hunt” has moved to where we work, the acquired resource is now money, neighborhoods are now our our communities, and stores are where we now do our “gathering”. And what do we see genders doing? Men still traditionally move into more dangerous vocations working longer hours, commuting farther, and still taking more risks. Women tend to move into caretaking being around people in some form working shorter hours and spending more time at home and taking fewer risks.
Modern life has almost removed all environmental pressures our ancestors faced. On a 2,000 Cal diet, the average American consumes ~20 times that in external energy sources, and we're not even the worst, that prize goes to Russians by a wide margin. It's also had an unintended side effect in some industrialized nations, they've increased in mass.
The weight of the average American woman is at 170lbs and the average American man at 195lbs. It's mostly fat gain. A majority of Americans are considered overweight or obese. It's like they're preparing for a winter that they won’t actually suffer through. Simply because their expended BMR is lower than their resource intake. Resource concentration, ie. refinement, is a major factor in this. Our rations are the biggest, and most nutritious this world has ever seen and we don't have to take a single step to consume any of it if we don't want to. Hell, with a blender and a long enough straw, you don't have to even move and just mainline it straight into your mouth without chewing.
Modern society and the removal of environmental pressures also explains why feminism has come as far as it has and why we are seeing so many traditional roles being challenged. Our biological programming and physical differences have been rendered redundant when we are flush with black gold (oil). However, this won't last forever. It's also worth noting that science, technology, and ingenuity have done far more to bridge equality between the sexes than all the politicians in history ever could.
In Conclusion
There are far more differences that I haven't covered. But if you're ever confused or frustrated with understanding either sex, perhaps you can recall this and remember we are all dealing with hard wiring in an environment we’ve only had a few centuries to evolve in. We aren't enemies, we're just different. We evolved along side one another, not in opposition. We were meant to help each other survive.
Not only do these biological differences exist, we evolved to enjoy some of them. So while we may have removed some of stressors that trigger basic needs, we have not yet evolved out of many of our desires. In fact, these desires in high dosages can sometimes become the source of our stressors. They still makes us feel good, even if machines are doing most of the work, most humans still feel they more or less need each other. And there is nothing inherently wrong with that.
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