In a standard corporation, the shareholders can sue if the company does not maximize profit. For example, if a company wanted to promote employee well-being by paying more than market wages to its lesser-skilled workers, the shareholders could sue. If that Inc was instead a Pbc, the requirement to maximize shareholder value at all costs is relaxed. The company could give its workers a raise, arguing as Henry Ford did, that employees who can afford to own the products they produce, are better for the world and better for the company. Even if, on paper, short-term profits took a hit, increasing public benefit is not considered a violation of the shareholders’ rights in the PBC.

This profit-maximization restriction is a large part of the reason corporations are bad citizens. If a company can increase shareholder value by making the world a worse place in which to live, they must do so. Economists might argue that shareholders do live in the world and thus would not invest in a company that would harm it. People by and large, however, think in the short term. If I have more money, I can afford to have air conditioning when global temperature rises, right? If I have more money, I can afford to live in a gated community when the 99% have to steal to eat. If I don’t take the profit, someone else will, and that someone else will live in the gated community while I scrounge for food.

We are taught to not hate the player, but rather to hate the game. When the rules of the game require bad behavior, the winners will be those who behaved badly! Unfortunately since the C corp option still exists, potential investors will likely be wary of the PBC. To really fix this issue, the definition of C corp needs to change. Any existing companies would need to be grandfathered, but if all new companies were granted PBC protection, investors wouldn’t be able to discriminate against them. Hopefully some brave pioneers will adopt the PBC model anyway and demonstrate the public good of this kind of incorporation, making it politically viable to make the change across the board.

HB 13-1138 on Colorado Public Benefit Corporations

Public Benefit Corporations Look Like a Go: leafferlaw.com

Colorado Public Benefit Corporations Part 2: leafferlaw.com

Colorado Public Benefit Corporations Part 3: leafferlaw.com

Colorado Public Benefit Corporations Part 4: leafferlaw.com

I wanted to talk about hyperspaces. Often, the more I learn, the more I realize that I don’t know. Other times, the curtain is lifted and things at which I used to marvel, are revealed to be rather pedestrian. You may have heard of a figure called a hypercube. Below is a 3d representation of what is supposedly a 5-d object. Stuff like this used to blow my mind. I still wouldn’t be able to make a video like this – project a n-dimensional figure on 3 dimensions – but it is displays like this that totally miss the point of n-dimensions, and prompt popular media to draw wild conclusions.

Hypercube in Hypercolor!

Here is what a scientist means when (s)he says “multiple dimensions”.

- One dimension. Popularly known as “numbers”. In one dimension the coordinates are valued like and . The distance between points and is . This is a space often referred to as or just . It includes any number you can think of, as well as all of those that you can not.
- Two dimensions. Often called the x,y plane. You use 2-dimensional math when you analyze a graph. Points in 2-space are often denoted by ordered pairs like and . The first number refers to dimension 1 and the second to dimension 2. The distance between and gets slightly more complicated, but many of you know the Pythagorean formula . Many may also know that the distance between two 2-space points is where a is the distance between two points on the x axis and b is the distance between two points on the y axis. (On a side note, here’s a nifty visual explanation of how the Pythagorean identity works.
- Three dimensions. Now, it gets a little more interesting, but it’s more of the same. We now add a z-axis, and points become and . We can still visualize a meaningful concept of “distance” in 3-space. If we have two points, and we label their coordinates and , then the distance between the two .
- Now, let’s skip to n-dimensions. With n-space we usually drop the x, y, z (we don’t want to be limited to 26 dimensions) and label points like so, point and point . Once we’re above three dimensions, distance has no real non-mathematical meaning. We do, however extend Pythagoras’ formula into n-space in order to give a measure of magnitude which we call “distance”, . (The double bars are a way to denote magnitude.)

Now, let’s do some n-dimensional math! Suppose I want to go to the grocery store. I have $100 to spend. Lettuce costs $2, (b)read 3$, bolo(g)na 1$, (m)ayo $2, m(u)stard $2, and (c)heese $3. I can choose how many of each to buy, as long as the total is no more than $100. The set of all of my possible mix of goods lies in 5-space. There, I’ve gone into five dimensional space and I didn’t even need my special time shorts! This “space” would be a purely mathematical construct, the set of all points such that . Isn’t that boring?

So the next time you see an article trying to explain to you how String Theory predicts 10 dimensions, you can scoff. “Hah, I’ve got more than 15 or 20 just in my shopping cart!”

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