# Proteins

Protein deficiency will kill you; as will protein excess. Same is true of any nutrient. As you increase the intake of a nutrient, its utility first increases, then reaches a plateau, and eventually starts to decrease. Once it’s in the negative, it has potential to kill you.

The ideal amount of protein to consume per day is somewhere between 200 calories to 600 calories (~50 to ~150 gms).

Interestingly, proteins help in both losing weight and gaining muscle mass. Proteins have a satiating effect; so people consuming low amounts of proteins feel more hungry and eat more food, thus consuming more calories. This effect plateaus around 15% protein intake.

Proteins also signal to the body that there’s enough food in it and so it can focus on muscle growth. This is why higher protein intake helps grow muscles. Note, however, that muscle growth is mostly supported by a high calorie intake. As long as you are near the higher end of the 200-600 calorie spectrum, increasing protein intake will not help grow muscles. But increasing calorie intake helps, no matter what the composition of the calories.

# Taste

One of the main implications of the theory of evolution is that if a trait is prevalant among the majority of the human population now, it means individuals that possessed the trait during our evolutionary history enjoyed some advantage, in the process of survival and replication, over those who didn’t. This arguably obvious conclusion leads to some very non-obvious insights once we expand the definition of a “trait” to its full potential.

A commonly cited trait is the existence of opposable thumbs whose evolutionary advantages have been well explored in the past. Things become interesting once we start looking at behavioral traits instead of merely the physiological ones. For example, feeling hungry when starved is a behavioral trait found in almost every human being and its evolutionary advantages are clear. Sexual attraction is another easily explained universal trait.

We can also get into the specifics of hunger and explore exactly what kinds of food are coveted the most. In most cultures around the world, the foods most sought-after happen to be either sweet or deep-fried, i.e., high-calorie, high-sugar food. This seems to suggest that individuals that enjoyed high-calorie high-sugar foods in the past had a certain advantage over those who didn’t. And yet, a person in the modern world who survives on a diet of donuts, fried chicken, and pepsi doesn’t survive very long. So what’s going on?

The paleo-diet hypothesis is that fast-food companies have hacked into the hunger-controlling part of our brain in order to maximize their revenues. Evolution has hardwired into us a program that goes: “If host is lacking in macronutrient X, make him want to eat food rich in macronutrient X. Otherwise, feel satisfied about the food situation.” How does the brain judge if something is rich in a certain macronutrient? From its taste and the smell.

If you wanted to make food that would motivate this hunger-controlling program to give you anything in exchange of it, the kind of food you would make would taste and smell exactly like the food the program desired without actually being like that food in terms of the macronutrients it contained. As a result, the body would eat and eat, but never be satisfied. This is exactly the kind of food produced by the fast food companies.

What does all of this mean? It means that fast food is bad because it does not contain the amounts of macronutrients our body desires. But everyone knew that. What it also means is that fast food smells and tastes like food that was supposed to be healthy for us. So if we could somehow ensure that the food we ate was not deceptive, i.e., it contained exactly the kinds of things it made our brain believe it contained through its taste and smell, then healthy food would taste as good as the modern unhealthy fast food. Or, in other words, if we only eat non-deceptive food, then healthy food is the same as tasty food.

# The ideal macronutrient ratio

There are reasons to believe that the diet ideal for the long-term health of an average human should consist of: 20 to 35 percent carbohydrates, 50 to 65 percent fats, and about 15 percent proteins (the percentages are by calorie).

Reason #1: That’s what all mammals consume.

Not exactly. Different mammals consume different proportions of macronutrients. However, the differences arise from differences in their digestive systems. Some have a bigger colon and some have a different set of gut bacteria. The difference results in different capabilities to convert one nutrient into another. However what remains constant is the ratio of macronutrients left once the food has gone through all the interconversion. So if some species seems to eat a lot of carbohydrates, it’s because its digestive tract has a more developed carbs-to-fats conversion mechanism. And what’s the ratio of macronutrients left after this preprocessing? 20 to 35 percent carbohydrates, 50 to 65 percent fats, and about 15 percent proteins.

But why should we assume that just because all mammals consume this ratio, this is the right ratio for us? Why should we believe that they have figured out the optimal diet for them when humans, a much more intelligent species, have not?

We do not need to attribute excellent optimization skills to the non-human mammals to conclude that they are doing things right. We only need to attribute the optimization skills to evolution. Any non-domesticated species has consumed pretty much the same kind of diet for the last several millions of years. This means evolution has optimized their body to respond well to the diet. That is, the mammals have not optimized their diet to suit their bodies; evolution has optimized the body to suit the diet! Once we transfer the burden of optimization to natural selection, the argument starts to make sense.

Humans also lived on a similar diet for millions of years in the paleolithic time, but things changed drastically once they invented agriculture.

Reason #2: That’s what the human body is composed of.

The human body (and the bodies of all mammals) consists of 20 to 35 percent carbohydrates, 50 to 65 percent fats, and about 15 percent proteins (see Perfect Health Diet) for details. Why does that mean this is the correct ratio for our diets as well?

Because throughout most of evolution, our diet mostly consisted of our own cells. We spent a lot of time fasting because food was not so readily available. And the only food our body consumed during the fasts was our own cells.

Reason #3: Human breast milk has a similar composition.

Again, not exactly. Breast milk is supposed to be for babies and babies have slightly different nutritional requirements than adults because of the accelerated growth of the brain during the early years of one’s life.

The human brain feeds on less fat than the rest of the body. Fats can be used by pathogens and viruses as carriers and thus if the brain fuelled itself with fat, it would be more susceptible to infection. This has led the brain to evolve means of fuelling itself with glucose and ketones. If we adjust for this difference, the breast milk composition is almost 20 to 35 percent carbohydrates, 50 to 65 percent fats, and about 15 percent proteins.

But why does the composition of breast milk have anything meaningful to say about the ideal composition of an adult diet? Because breast milk has been optimized by evolution to be the ideal diet, at least for babies. Adjust for the differences in the nutritional requirements of babies and adults, and you get a reasonable formula for an ideal adult diet.

# The Paleo Diet

The paleo idea is that we should eat what our ancestors ate before the invention of agriculture. It’s based on sound evolutionary reasoning and fair bit of empirical evidence.

The evolutionary argument is that we lived for millions of years on a paleolithic diet and only 10,000 years on an agriculture-based diet. Keep any evolving species in one specific environment for millions of years and it will optimize itself to survive in it. This means our body is optimized to survive in an environment that feeds it a paleolithic diet. It hasn’t had enough time to adapt to the modern diet.

The empirical evidence comes in several forms. First, the fossilized skeletons show that pre-agriculture humans had healthier skeletons than the post-agriculture ones.

The tall stature and strong bones of Paleolithic skeletons indicate that Paleolithic humans were in remarkably good health. Paleolithic humans were tall and slender; cavities and signs of malnutrition or stress in bones were rare; muscle attachments were strong, and there was an absence of skeletal evidence of infections or malignancy.

(From Perfect Health Diet.)

Then, there is stuff we know about animals. For example, elephants that are exposed to a diet resembling the paleolithic era—i.e., wild elephants—live longer than elephants exposed to a modern diet—i.e., zoo elephants. The rate of obesity among pet cats and dogs is much higher than that among wild wolves and tigers. One might be tempted to attribute this to the fact that wild animals are more likely to be malnourished because of the difficulty associated with obtaining food. However, feral rats that live in cities and eat food discarded by humans are obese too.

# Notes on Peter Thiel’s “Zero to One”

I just finished reading Peter Thiel’s new book “Zero to One” and I want to write something that can neither be called a book summary nor a book review. I just want to discuss a few ideas from the book that I liked, interspersed with my own commentaries, without meticulously stating which one is what. So I am just going to call it “notes” and accept an adversarial reader who assumes all good ideas to be the author’s and all bad ideas to be mine.

Monopolies are good. Competition is bad.

This was new to me since I always thought of competition as a sign of a healthy economy. Peter Thiel argues that in any sector with high competition, profits are low and all progress is incremental: sign of a stunted economy. The conventional argument against monopolies is the lack of a force that drives progress. If there’s no competition, then the monopoly may be able to do whatever it pleases, which includes not doing anything at all and still mooching money off the public. However, this argument is flawed since there does exist a progress-driving force: profit.

Deciding what to do is way more important than doing it well.

This is not new to me since I have come to this realization myself through experience. In the world of venture capital, a portfolio usually follows a power law: one company in any VC’s portfolio outperforms every other company in the portfolio combined. So if your strategy is to half-blindly diversify hoping to hit the good ones just based on probabilities, you are mostly going to miss the superstar companies. The only strategy that works in the VC world is to meticulously screen for only those companies that have a high chance of outperforming everyone else combined.

Peter Thiel takes this argument to the next level: the options available to you in any decision follow a power law. Thus doing many things just in order to increase the probability of hitting the good ones is never a good strategy. One needs to meticulously fish for the superstar options and devote all resources to them.

Solving the really big problems requires sales skills.

Barring the problems that can be solved by a PhD student in at most a few months, most problems can be solved more efficiently by a strategic allocation of human capital to it. Once a problem becomes big enough, a strategic allocation of human capital is the only way to solve it. And motivating the humans to work on the problem requires sales skills.

# Wealth is not money

Money is just a kind of wealth. It is not wealth itself. Realizing this leads to some interesting insight.

Arbitrage

If you know that a stock is definitely going to cost \$50 more one month from now than it is now, you will buy tonnes of it now, sell it a month later, and make a definite profit. But remember that wealth is not money. Thus if you know that a stock and an apple cost the same right now but are definitely going to cost different in future, you can once again make a definite profit. So if the stock is going to cost double in future, you sell an apple today and buy a stock. A month from now, you sell the stock and buy two apples. You have just converted one apple to two apples in a month.

Import-export

A country’s total import is always equal to its total export. Why?

If a person decides to, he can of course keep on buying things without ever selling anything. So if a person can do this, why can’t a country?

This one is a more subtle application of the wealth is not money principle. The point is to treat money as just another kind of wealth, i.e., to realize that every trade is a barter trade. When you are buying an apple for a dollar, you are selling a dollar for an apple. So there you go, even a person cannot buy without selling.

So since everything one can own is some form of wealth, how does one grow it? There are two ways of doing it:

1. Own more things.
2. Somehow make people want the things you already own.

Similarly, there are two ways of losing wealth:

1. Give away stuff you own.
2. Make people hate the things you own.

The second point above restricted to money is called inflation. If you own a currency that people start disliking, you have been a victim of inflation.

This also means that being wealthy is a dynamic state and not a static one. Most people’s formula for being wealthy is to own a lot of money and stash it into a bank account. While this may work to a certain degree, it does not reflect reality. Being wealthy is really about owning lots of things that other people want. This is specially difficult since what other people want is a variable that changes constantly with time. Thus to really be wealthy, you need to constantly look out for people’s changing preferences and perform strategic trades to maintain a valuable portfolio.

# Collecting coupons

Every time you buy a pizza from Pizza Hut, they give you a coupon selected at random from a set of ${n}$ different coupons. How many pizzas do you need to buy on average in order to collect all possible coupons? We know from kindergarten that the answer is ${\Omega(n\log n)}$. Here’s an intuitive explanation why.

First, let’s look at a cool trick.

Suppose a biased coin with probability of showing heads to be ${p}$ is being tossed repeatedly. How many times, on average, does it need to be tossed to get a heads for the first time? I promise this is related, and the relation will be clear soon.

Anyway, this is a standard geometric distribution and thus we can plug things into known formulas and get the value ${1/p}$ for our answer. Intuitively, it does look like that should be the answer, since if we rolled a die with ${1/p}$ faces repeatedly, we would expect to see face #1 after an average of ${1/p}$ rolls. We can also derive the formula ourselves by writing down an infinite series and using standard summation tricks. But here’s a nice trick that can be used to get to the result immediately.

Let ${E}$ be the expected number of tosses need. Then if the first toss shows a heads, we know that ${E}$ is 1, and if the first toss shows a tails, we know that ${E}$ is ${1+E}$. Writing this “in math” we get ${E = p + (1-p)\cdot E}$, which solves to ${E = p}$.

Anyway, back to coupon collection. Suppose we already have ${x}$ coupons. What’s the probability that if we buy a pizza, we get a coupon that we do not already have? Clearly, ${\frac{n-x}{n}}$. Thus the expected number of pizzas needed to get one new coupon, from the previous calculations, is ${\frac{n}{n-x}}$. This means the expected number of pizzas required to collect all coupons can just be written as a the sum ${\sum_{x=1}^{n-1} \frac{n}{n-x}}$, which solves to ${\Omega(n\log n)}$ after using the well-known approximation for the Harmonic number.