Cost of an MBA

Here’s an infographic on the cost of an MBA.

And steep tuition is continuing to climb further while salaries stay stagnant.

That applies even if it’s just a normal degree.

Less people are hiring MBAs

Really? It might have something to do with being overqualified.

Of all US Presidents, only 1 has an MBA: George W. Bush

That’s interesting. Maybe a political career takes too much out of a candidate for him/her to take up studies.

What’s an MBA?

MBA stands for Master of Business Administration. I don’t have one, so I’m going to make a general assumption. You study how to administer a business, right? Accounting, finance and whatnot.

I don’t know the actual course curriculum. Does it focus mostly on administering a medium to large sized company? Does that appeal to you? Will what you learn benefit you as a startup founder?

I would even go so far as to say you’d be learning to administer other people’s money. You’d have bar charts and pie charts and business matrices to support your argument to your superiors that they should go about their business this way, or handle their finances that way, or streamline their product lines in such-and-such way.

But it’s not your money. It’s not your money on the line. You’re not worried. If your proposition fails? The worst that can happen is you get a pay cut. Possibly even get fired.

I’m all for getting a degree (but start a business on the side too). But an MBA seems like an overkill.

After over 2 years of running my own business, I’d say nothing gets you up to speed on how to administer your finances than having your own money on the line. And it cost me less than my degree, let alone an MBA.

Get an MBA if you feel it’s worth your time and money. Just don’t get one because everyone’s getting one (or telling you to get one). Make your own decisions.

Thanks to Tony Shin for telling me about this.

Does the point lie on the Bezier curve?

Someone recently asked me how to tell if a point lies on a Bezier curve.

For the purposes of discussion, it’s a quadratic Bezier curve and all 3 control points are known (or the start and end points and the 1 control point if you prefer). You can read more about the reverse process of finding the control points here, which is the reference point of that person’s question.

The answer is actually straightforward. Substitute everything into the Bezier curve equation and solve for t. Here’s the quadratic Bezier equation:
B(t) = (1-t)^2 * p0 + 2(1-t)t * p1 + t^2 * p2

Let’s say p0 is [1,1] and p1 is [1.5,4.5] and p2 is [2,3]. We’ll keep the points in 2 dimensions to keep the maths working less cumbersome. And let’s say the point you want to check is [1.8,3.4]. We substitute all the points into the equation, and we get this:

[1.8,3.4] = (1-t)^2 * [1,1] + 2(1-t)t * [1.5,4.5] + t^2 * [2,3]

I know, it doesn’t look pretty. But hey, we’re doing this by hand. If you’re writing code to generalise the solution, the code will probably look just a little uglier, but the solution will come out faster. Like probably instantly given the current modern processors.

Because we’re dealing with 2 dimensional points, that equation splits into 2 separate equations (with scalars instead of vectors as coefficients), like so:
1.8 = (1-t)^2 * 1 + 2(1-t)t * 1.5 + t^2 * 2
3.4 = (1-t)^2 * 1 + 2(1-t)t * 4.5 + t^2 * 3

If you have 3 dimensional points, you’d have 3 equations. Note that even then, the degree of your equations remains as 2. The degree of the Bezier curve is independent of the number of dimensions you’re working with.

If you simplify
1.8 = (1-t)^2 * 1 + 2(1-t)t * 1.5 + t^2 * 2

You get t = 0.8. It so happens that in this case, there’s only one solution.

If you simplify
3.4 = (1-t)^2 * 1 + 2(1-t)t * 4.5 + t^2 * 3

You get
5*t^2 – 7*t + 2.4 = 0

and after solving for that, you get t = 0.6 or t = 0.8 (you’re a smart person, you know how to solve a quadratic equation, right?)

Now, the solution t=0.8 appears in the solution sets of both equations. Therefore, the point [1.8,3.4] lies on the Bezier curve. In fact, t=0.8 is the t value.

Multiple solutions

What if you get multiple t values appearing in multiple solution sets of equations?

Consider the case where p0 is [1,1], p1 is [2,3], and p2 is [1,1]. Notice that the start and end points are the same point. Let’s say you want to know if the point [1,1] lies on the curve (yes I know it’s the same point). Substituting all the points, we get:

[1,1] = (1-t)^2 * [1,1] + 2(1-t)t * [2,3] + t^2 * [1,1]

This gives us the 2 equations:
1 = 1 – 2*t + t^2 + 4*t – 4*t^2 + t^2
1 = 1 – 2*t + t^2 + 6*t – 6*t^2 + t^2

They simplify to:
2*t^2 – 2*t = 0
4*t^2 – 4*t = 0

Hey presto! The solution set is t=0 or t=1 for both equations. Therefore, the point [1,1] lies on the curve. In fact, it lies on the curve where t=0 or t=1. And t=0 and t=1 happens to coincide with the start and end points respectively.

The whole point (haha!) is that, as long as you have at least one value of t that appears in the solution sets of all the equations, then said point you’re checking lies on the curve.

Higher degree Bezier curves

This is a toughie. If you have a cubic Bezier curve, then you’re solving a degree 3 polynomial (of t). If you have a Bezier curve of degree N, then you’re solving a degree N polynomial.

There are algorithms to solve generic degree polynomials, but they are out of scope here. Assuming the highest degree of Bezier curves you’ll ever work with is 3 (cubic), then this Wikipedia article on cubic functions will help. Remember, cubic Bezier curve equations are still cubic equations.

Higher dimensionality

The number of dimensions you’re working with determines the number of equations you need to solve. If you’re working with 5 dimensional points, then you need to solve for 5 equations.

For example, if you’re working with cubic Bezier curves and using 5 dimensional points, then you need to solve 5 cubic functions. You will have possibly 3 (unique) t values for each equation. Let’s say your solution sets are as follows:
t = -1, 3, 5
t = 0, 1, 3
t = -2, 2, 3
t = 3, 3, 4 (yay repeated values!)
t = 3, 6, 8

The value t=3 appears in all 5 sets of solutions, therefore your point lies on the curve.

Keep it real

In the process of solving your equations, there’s a possibility that you might get imaginary solutions. You know, those involving the square root of -1. Dismiss them.

Your Bezier curve is in the real world. The point you’re checking must therefore also lie in the real world.

Unless you’re working with some abstract imaginary Bezier curves on an advanced maths paper. Then good luck to you! The logic above for solving still applies.

Actual applications

When applying the above, you don’t usually get nice numbers like [1.8,3.4] lying on the curve with t=0.8. You get numbers with lots of numbers behind the decimal point that seems to continue forever. You don’t get exact values.

What if you get a t=0.798 for one equation, and t=0.802 for another equation?

Use your common sense. Set an error margin for what is acceptable.

My suggestion is to NOT use the values of t to check for the margin. Substitute the values of t into the equation, and then check the points if they’re within the error margin.

This means you don’t check the difference between t=0.798 and t=0.802, which is 0.04. Is 0.04 within your error margin? Maybe. But you’re not checking for this.

You substitute t=0.798 and t=0.802 into the equation, and you get 2 points: [1.798,3.40198] and [1.802,3.39798]

Then you say, “Are these points close enough that I consider them to be the same point?” Use whatever you think is appropriate. I think the Euclidean distance norm works fine. Then check if that “close enough” criteria is within your error margin.

If you’re checking for [1.8,3.4], then ask yourself, “Is [1.8,3.4] close enough to [1.798,3.40198]? And is [1.8,3.4] close enough to [1.802,3.39798]?”

Obviously, doing this by hand sucks big time. Good thing you’re a programmer.

Students don’t graduate because…

… because they’ve lost hope.

They’ve lost hope that:

  • they can fulfill degree requirements (some subjects are tough!)
  • they can actually graduate
  • (more importantly) they can graduate in a shorter time so they pay less tuition fees
  • they can get a good job with that degree

And so they give up. They’ve lost hope. They don’t believe anymore.

A degree can still be useful. But the current educational and economic outlook doesn’t exactly inspire a lot of confidence in the immediate use of a degree.

Educational institutes mostly teach students towards knowledge that’s known. I mean, your professor won’t set a question that he can’t answer, right? The world we now live in rewards those who solve the unknown, possibly even seeking questions that weren’t ever asked.

Teachers need to start teaching students to face the unknowable. They need to instill hope in the next generation.

University degrees and debt

Make the time and money you spend while studying in university count. The value of a degree doesn’t fluctuate much, year to year. But if you take just one year longer to obtain that degree, it means you’ve wasted one year of your life and another few thousands of dollars in tuition fees. Which means it takes that much longer for you to repay the tuition fee loan (if you took out one).

University/college tips from Bryarly

University/college tips from Emily

Business or degree

Degrees as general intelligence shortcut

Today I went to the library. Never mind the reason. Suffice to say, I decided the best use of my morning was to go to the library.

While I was browsing the shelves, I found this book Spent, by Geoffrey Miller. He’s an evolutionary psychologist, and it happens that his writing is a little… dry at times. Whole blocks of text with few bolds, italics and headings to break the flow.

Degrees and sexual evolution

I persevered and managed to skim through some of the chapters. Basically, his premise of modern consumerism and marketing is affected by sexual evolution. You buy stuff to show you’re a better mate. You buy expensive (but deemed as socially coveted) goods to show off. You buy stuff that’s seemingly a waste to show you can waste resources.

He also pointed out the 2 extremes: the people supporting consumerism (despite the credit card debts and other financial disasters), and the people opposing pure consumerism. He also said both are dangerous, which I agree.

Anyway, he said something about education. I’m paraphrasing here, but he said university degrees are used as a shortcut to determine a person’s general intelligence. He also used the term IQ as well.

He said the people who scoff at the idea of using IQ to determine a person’s intelligence are usually already clever, and hang around people of their intelligence level. “Anyone with average intelligence can understand string theory!”, ignoring the fact that they’re surrounded by janitors and other school staff.

Schools require stringent tests to determine if you’re intelligent enough to attend at their establishment. The most prominent of these tests is the SAT. But the idea of an IQ test to determine intelligence threatens these schools. Because anyone can easily take a short IQ test to determine their intelligence.

If it’s easy to obtain, it’s harder to use it as a screen or charge for it. Thus, the academia typically scoff at the usefulness of an IQ test, ignoring the SAT they used for admission.

If it’s easy to fake, or is almost indistinguishable from the original, then the original loses value. The example used here is cubic zirconia, directly competing with diamonds.

Our ancestors might have developed humour, creativity and kindness to compete for quality mates. Those are alternative traits to body musculature, body symmetry and other physical properties. In time, those “inferior” traits won. There are women who prefer a guy with humour, creativity and kindness to other human beings.

Social status (or showing off)

What I’m getting at (and what I believe Geoffrey was suggesting), is that a degree is a social status object, just like any other social status object. Having a degree shows other people that you had the time and money to pursue a degree, and the discipline to actually fulfill the requirements to get a degree. It’s a shortcut. Having a degree doesn’t necessarily mean you’re intelligent because there are some graduates who are frightfully stupid.

I will admit right here that I’ve never actually applied anything I learned for my degree in my jobs. Maybe that I learnt C and Unix shell scripts and commands.

My only regret is that I didn’t try to do more during my university days. Maybe learning about how businesses actually work. Did you know an employee typically costs a company 3 times his salary to employ him? This means an employee has to do work that generate a revenue amount 3 times his own salary just to justify his existence in company payroll. Where does the money go? The lights, the cleaning, the pantry, the security, the stationery. How can a company survive then? Because there are sales people that generate revenue amounts equal to 10 times their salary. That’s why sales people can be highly paid.

What was I talking about? Oh yes, degrees.

To increase the value of the original, you can increase the precision of getting the original and/or decrease the credibility of the competition. For example, the judgement of diamond quality and the emphasis that cubic zirconia rings aren’t rare (thus not as “valuable”).

The crux of the matter is that educational institutes are afraid their degrees will lose value. Just read the backgrounds of those who fervently support the obtaining of degrees, and those with a “meh” attitude towards degrees. Are they academics? Do they hold a job? Are they entrepreneurs? Are they open to new ideas? Are they ambivalent? Do they propose alternatives?

I suggest you get a degree if you can. But start a business while you’re there. A degree is still a valuable social status object. But don’t kill yourself trying to get one.

Consider what you want out of your life. I would hate to think you would waste 4 years of your life and tons of money to just scrape by and get a degree. Do something useful while you’re there! Make it more than just a piece of paper!

Did you know that because cubic zirconia is cheap to produce, the processes can be refined to the point where they’re less flawed than diamonds? Imagine, “fake” diamonds that are “purer” than real diamonds!