# A mathematical model for beard growth and awesomeness

It's a general rule that the longer you grow your beard, the more awesome you become. Does beard growth really lead to increased awesomeness? As a scientist by training, it is my scientific duty to poke and prod at so-called "rules of thumb" to ascertain the true reality. Do beards really grow half an inch per month? Do you actually get more awesome? How much more awesome do you get? Today, I'm going to present to you a mathematical model for beard growth and its correlation with personal awesomeness. This is some pretty serious stuff. Furthermore, since this is Beards & Money, I'm going to show you the parallels to net-worth growth and *feelings *of awesomeness.

## Beard growth is science

My job as a practicing scientist is to observe nature, hypothesize about why nature behaves as it does, and to test those hypotheses. We start the whole scientific process by studying nature through what we call observation experiments. This is really just us observing what actually happens in reality with no pre-existing hypothesis about why it happens. From these observations, we can develop models that *explain *the observations. Once we have a theoretical explanatory model, we conduct what is called a "testing" experiment of that model. From years of bearding and observing the bearding process of my bearded brethren, I am now prepared to present to you a mathematical, explanatory model for beard growth and personal awesomeness as a function of beard growth.

The Beard Coach starts this conversation with his mathematical beard theory. He starts off with a pretty good model for beard growth and awesomeness, but I'm going to take it one step further. (Yes, I totally rant on the entire concept of "beard coaching," but The Beard Coach is about motivation and his email list is free. I yell and scream about spending too much money on stupid shit. However, beards are awesome, and motivation for growing a beard is free with The Beard Coach.)

First, I know what some of you are thinking. Why am I wasting my time on this when I could be focusing my time on earning more money to make that net worth grow? Why am I spending intellectual resources on something so stup ... Let me stop you there, because if you haven't noticed, this is a silly little site about *beards*and money. So, you know, beards. It's right there in the damn title. Next, as I explain in my article about the lack of ads on this site, my motivation for this site is partially as a means to grease the groove with my for-reals paid writing. I actually do and write about this kind of mathematical modeling as a full-time job. Right now, I'm working on a paper that utilizes the same mathematical thinking, where I have to explain the same types of data trends as I'm going to do here for you today. Writing about real stuff is hard, specifically at the start. So here I am on this silly little site where I don't have to worry about crappyness, crapping out crap to get the wheels turning.

## A Mathematical Model for Beard Growth

In general, beards grow at roughly the same rate as the hair on your head. That turns out to be about 0.5 inches per month. A simple mathematical expression for this is as follows:

`L(t) = 0.5 t`

where t* *is measured in months. There is a problem immediately with this model for beard growth. Although growth is roughly linear within the first 12 months or more, your beard will not grow forever and ever, amen. You will reach a **terminal length of beard** dictated by your genetics. Beard hairs stop growing, and then fall out just like the hairs on your head. They are replaced by other hairs that are growing, then stop, then fall out, so it looks like the hair in total is growing rather uniformly.

Growth is actually governed by a fairly complex rate equation that requires a differential equation to model. I'll spare you the details, but real beard growth follows more closely to the following:

`L(t) = L_T / {1 + e^[-(3)/(L_T)(t - L_T)]}`

where t* *is once again measured in months, and L_T is the terminal length of your beard.

Let's say you're beard is genetically predetermined to only grow a maximum of 6 inches. This would result in a terminal beard in approximately 1 year. Your yeard *is *your terminal beard. This is a plot of what the growth model would predict for you:

Fancy. This model shows a slightly slower growth right at the beginning, but it tracks with about 0.5 inches per month until it approaches terminal length at about 12 months. If your terminal beard length is a solid 2 feet (24 inches), then it will take you a solid 4 friggin' years to hit terminal beard, with growth averaging around half an inch per month, starting a little slower, and slowing down as you approach month 40. It looks like this:

This is a much more accurate model for beard growth. If beards kept growing linearly with time, then you could expect every bearder to be have the ability to grow a beard all the way down to their toes. It just doesn't work that way, though.

## Awesomeness with Beard Growth

The Beard Coach models Awesomeness (A) on a growth factor of about 1.25, which results in a mathematical expression as follows:

`A(t) = 1.25^t`

where t is once again measured in months. This also *only *applies if you are actively growing a beard. This is a pretty good approximation, because we all know that awesomeness is not *linearly *proportional to length. It also depends on how long you have been rocking those glorious whiskers. So we shouldn't expect asymptotic behavior like we see with beard growth. Personal awesomeness can keep growing forever so long as you keep bearding with your bearded badass self.

Let me show you a slightly different model. Now, awesomeness is a little tougher. I'm using what is called a phenomenological model here, where I just look at the data and fit the data to a function that best describes the data. It turns out, for awesomeness, the actual relationship between A and t is better expressed as a 3rd degree polynomial having the following form:

`A(t) = at^3 + bt^2 + ct + d`

The constant *a, b, c, *and *d *are just fitting parameters and could be positive or negative. Below, I overlay a graph of awesomeness with the plot of beard growth above.

The red line in the graph is a measure of personal awesomeness in arbitrary units. As you can see, you're awesomeness grows in concert with your beard length. But then, something happens. You reach a point called the "awkward stage" in your beard journey. This is the point were your beard is doing weird stuff.

When you start a beard journey, once you get past the itchiness, everything is awesome. You're cruising along and everyone is totally admiring your beard. But, once it starts to creep past the shorter, well kept business beard, that thing can get straight up weird. It's longer than "average" but not quite long enough to lay down and play nice. You get hairs pointing off in all kinds of directions, and it can be tough to make those glorious whiskers look "professional." This is the awkward stage.

Fear not! As you can see from the graph, even during the awkward stage, your personal awesomeness is still growing, even if it doesn't feel like it. And if you beard it out, then you'll start seeing your awesomeness rate increase once again, and you're well on your way to badassity.

## Net Worth and Happiness - is it similar to beard growth and awesomeness?

If you're doing it right, your net worth growth might look like beard growth. The factor is a little different, though, because net worth growth is much less linear than beard growth due to compounding interest. It starts off slower and then blows up quickly as you get closer to seven figures. If you decide to retire when your investments start covering your expenses, then just like beard growth your net worth will level off.

Unlike personal awesomeness due to beard growth, you *will* reach an asymptope for personal happiness as your net-worth grows. You're feelings of personal awesomeness are a little more difficult. You see, money only buys a certain level of happiness. At a certain level of net worth or income, you really just don't feel any happier by adding more money. There's science behind this, too.

Your day-to-day mood is not effect by money once you pass a certain threshold. It turns out to be, on average, about $75,000 per year of income. If you're a Mustachian like me, then you need a LOT less than that to meet your basic needs and not need to worry about money. At that point, you're happy, and no more real amount of money will significantly increase your happiness.

Now, this is not to say you can't get even happier! You can always increase happiness through other means than money. For example, since you are getting awesomer and awesomer through the power of Beard Magic, you can get happier and happier about that fact.

This also doesn't mean you can't be happy without money. Hell yes you can. So if your net worth straight up sucks, that doesn't mean you have to suck. Net worth is a shitty name, since how much money you have doesn't equate to your "worth" at all. It's just money. You can get happy just on the prospect of growing your monetary net worth, and doing the things that will make you beard awesome and money awesome. That's what this blog is about.

So in summary, keep growing that beard and growing that stack of cash. Stop shaving, and stop spending too much and you'll be on your way to supreme badassity and peak monetary bliss.