# Order of magnitude estimation for some intriguing questions

The physics TA showed us a few examples in which one can estimate many things from first principles, sound logic, and scaling arguments. This led usually to understanding of why some numbers have the values they do.

I asked myself a few questions and after struggling with them, I could not get a clear answer:

1. Why is our body temperature is about 30 C? Is there a way to understand where that number comes from?

2. Why is the pregnancy period in humans is about a year, not 10 years, not a month?

3. Why is our life time about 100 years, not 1000, not a year?

Any help will be really appreciated.

The problem is that humans are complex systems, and one of the characteristics of complex systems is that they show emergent behaviour. By this I mean that the behaviour is not simply related to fundamental properties of the system.

People have noticed various trends, for example it has been observed that many mammals live for about the same number of heartbeats. This sort of makes sense if you consider that if aging is the result of cumulative damage by metabolic byproducts then animals should live to be roughly the same metabolic age. Still, I doubt you'd be able to link this to any simple mechanism.

• Agreed, but these are good questions that can be addressed by order-of-magnitude arguments. Admittedly, the arguments are likely to have more of the character of hand-waving than we like to see in physics. Speculating: perhaps body temp can be deduced by identifying the most important biochemical processes, and the relative rates needed to be a viable human. Aside: G. Taylor famously used dimensional analysis to estimate the yield of the Trinity nuclear blast, using photos published in Life magazine. – garyp Mar 14 '14 at 12:41
• Also note, humans tend to break away from the model of average heartbeats per lifetime in mammals, we tend to live much longer. This suggests the opposite of a single explanation, but rather a factor of environmental stress, hygiene, nutrition, modern medicine, ect. which allow humans to accumulate less damage to the heart. And in fact, it is not the heart that usually wears out in a vacuum, but a combination of factors that contribute to mortality. – kleineg Mar 8 '16 at 20:13

I think the latter two questions may lend themselves to order of magnitude estimation approaches, but I don't think the first one does.

## Q1: Why is our body temperature around 30 °C?

The first clue is in the original definition of the Celsius scale: 0 °C the freezing point of water and 100 °C the boiling point.

Life as we know it relies on chemistry and a solvent allows chemistry to happen on a reasonable time frame, as molecules can dissolve, diffuse, react. The solvent that makes life possible on Earth is liquid water, and at the pressure that Earth's atmosphere ended up with, it is liquid between 0 - 100 °C. As we're 70% water and we'd like to keep it from freezing/boiling in our bodies, that gives a general range for where our body temperature would be. Note it's just a general range-- there are plenty of animals with different body temperatures, including some fish with antifreeze proteins which allows them to go a bit below 0 °C.

## Q2: How can you estimate human pregnancy period & lifespan from order of magnitude estimation?

The more information you know the more accurate your estimation. For example, say you know cell division in humans takes 24 hours. Then pregnancy probably wouldn't take thousands of years and would certainly not be shorter than 24 hours. Depending on what kind of information you have access to, you can improve the bounds.

Estimating human lifetime is a bit stickier because there is no genuine answer to "how long does a human live"... some humans only survive a few days or less and it's not entirely clear that future humans won't live thousands of years.

I recommend looking up Fermi problems. Seeing a number of examples can help you understand this way of thinking and where it is appropriate.