## 18 General Lessons I Learned in University

Some of these may seem obvious; keeping their importance in mind is not so obvious.

Through my experience as an undergraduate, I’ve found that the following lessons are useful to be aware of. Hopefully, they will help you and those you love to avoid unnecessary suffering. Some of these lessons overlap and they are not in order of priority.

I recently received the Thiel fellowship, and wrote a seperate post on additional lessons I’ve learned.

### 0. Putting as many hours as you can into doing what you love pays off.

The best programmers I know started programming as a hobby first.
The best researchers I know started researching as a hobby first.
The best mathematicians I know started playing with math as a hobby first.
The trend continues and transcends disciplines of study.

It’s better to say “I don’t know.” People respect honesty and pure intellectual pursuit/curiosity more than your pride. Plus, you learn more that way!

### 2. Don’t cut corners.

Build up your knowledge base from understanding.
Put effort into doing (even tedious or arduous work) as well as you can. By doing this you may discover passions you wouldn’t expect!

### 3. Fix your procrastination habit.

Don’t know how to fix it? Read this.

### 4. You can do anything but you can’t do everything.

Don’t start an entirely different project each day.
Good quality work is done by working through the tedium inevitable in the details of a complex project, and thinking of each step as a new project.
Sort out your priorities and keep them in mind.
Good food, exercise, and sleep are foundational to long-term functionality.

### 5. Create your own motivation.

Do things in chunks, reach the “mindset”, if you hit a wall, come back to it, you will ponder it unconsciously.
You have to assign your own meaning to life – no one will do it for you. The rules and meaning I live by are an improved version of Neil DeGrasse Tyson’s philosophy:
1. Stay healthy.
2. Learn [and make] something new every day.
3. Lessen the suffering of others.

Keep these in mind; these simple rules changed my life for the better.

### 6. Being a Jack of All Trades is itself a talent.

Limiting yourself to the current ideas of one discipline makes original research unnecessarily difficult. I find original research is really just connecting past ideas into a new idea that is more than the sum of its parts.

My friend Adam Munich wrote this lovely post detailing the dangers of overspecializing. I highly recommend it!

### 7. Be aware that friendly curiosity occasionally comes off as interrogation.

I’ve recently begun briefing myself with: “I’m an incredibly curious person, feel free to stop me if I’m asking too many questions.”

### 8. Don’t fear failure.

Giving up before you begin is far worse than failing.
Don’t waste opportunities due to fear of failure and cling to the theoretical hope offered by the past possibility of success.

### 9. You can’t please everyone.

You will quickly exhaust yourself trying to conform to the needs of all.
If you are motivated, honest, kind, and aware of (and abide by most) social norms, fearing the opinions of others is largely unnecessary. Many things that work for others may not work for you and vice versa.
Don’t feel obligated to help everyone that requests your help.

### 10. Have a workspace.

Make yourself a workspace that you can retreat to and feel at home in.
I have some friends who prefer to work on different task types in different places, and others that enjoy using one workspace for most if not all of their work. Find your preference.

### 11. Accept compliments.

Compliments are mostly beneficial to those who give them.
“Thank you, that’s very kind of you to say” is my favored response, for it is truthful.

### 12. There is a difference between nice and kind.

In my opinion, the difference lies in your motivation.
Being kind is honestly (and gently if possible) doing what is best for the other person.
Being nice is saying what they want to hear.

### 13. Communicating your ideas is an important skill.

Keeping the audience interested during public speaking is is of equal if not more importance to the content of your speech.

### 14. Credit your collaborators and prior art.

Don’t claim the work of others as your own.
Keep a log of your contributions to a project to avoid IP disputes.

This applies to homework as well: Making use of the internet to research a problem is to be encouraged as there could be hidden treasures of mathematics to be discovered beneath the surface of many of these problems. However, there is a fine line between researching ideas and using the answer you found on another website. If you photocopy a crossword solution then what have you achieved?

### 15. Stuck? Explain it to someone.

If you are stuck on a problem, explain the problem, then brainstorm or bounce your ideas off of a friend.
Can’t find a friend who will listen? Explain it to yourself out loud or free write.

### 16. Write it down.

Although possible to keep all of your project plans and todos in mind, a purely mental method is an unnecessary burden. Writing things down significantly lowers my stress level.

### 17. If you don’t immediately find your passion, fear not.

I switched my major from:
Philosophy/Physics
$$\rightarrow$$ Psychology/Studio Art
$$\rightarrow$$ Anthropology/Studio Art
$$\rightarrow$$ Math
$$\rightarrow$$ Math/Computer Science
$$\rightarrow$$ Math/Physics
$$\rightarrow$$ Electrical Engineering
$$\rightarrow$$ Computational Physics.
Playing in these disciplines I’ve discovered that what makes me happy is implementing my passion for STEM to enable the disabled. I wonder what you will discover!

## Megan’s Present

I visited my friend, Megan Brusnahan, before I left for CA. She had a picture I’d drawn her in middle school (2009) mounted on her wall in a frame. I’d forgotten that I’d drawn this picture! It’s done entirely in black sharpie.

## Natural Transformation

This quick post assumes a basic knowledge of categories and functors, which can be gained from a previous video post.

A natural transformation is defined for two functors $$F,G: X\rightarrow Y$$ when for each object $$x \in X$$ there is an arrow $$\psi(x): F(x) \rightarrow G(x)$$ in $$Y$$, AND we have the property that $$\forall f: a \rightarrow b$$ the equality is true: $$\psi(a) \circ G(f) = F(f) \circ \psi(b)$$.

I assume the name “natural” refers to the consistency found in these functor interactions (actions on arrows). Dat consistency!

Get Weather on the Unity top panel in Ubuntu! Worry not, this tutorial doesn’t assume any term aliases.

sudo add-apt-repository ppa:weather-indicator-team/ppa
sudo apt-get update
sudo apt-get install indicator-weather

If you’d like the indicator to launch upon startup, hit the super key and search for Startup Applications. Click on the icon, click Add, pick an arbitrary name, and enter indicator-weather as the command.

Sidenote:
I personally prefer to use Celsius. If you were raised with the Imperial system, then I suggest using the following poem to transition.

30’s hot,
20’s nice,
10’s cold,
0’s ice.

Happy hacking!

## JDX

My old laptop decal peeled away.

The phrase “JDX” is a motivator I write on everything from my notebooks to my bathroom mirror.

Grade 2 Braille for “just do it” translated into Grade 1 Braille is “j d x”. This is because “j”, “d”, and “x” are full word contractions in G2 when they are used outside of a word.

## What is Bra-ket Notation?

Bra-ket notation is concise and useful.

A wavefunction is represented by a ket $$|\psi\rangle$$.

The complex conjugate of wave function is written as a bra $$\langle\psi|$$.

The complex conjugate of a variable is found by swapping the sign of the imaginary part of said variable’s complex number, in other words: reflecting z across the real axis. For example,
\$$z = x + iy\$$
\$$z^* = x – iy\$$

A bra on the left and a ket on the right implies integration over dt.
\$$\langle\psi|\psi\rangle \equiv \int\psi^*\psi dt\$$

Similarly
\$$\langle\psi|\hat{X}|\psi\rangle \equiv \int\psi^*\hat{X}\psi dt\$$

My brief tutorial covered the basic usages of bra-ket notation in a quantum mechanical context; bra-ket notation is also used elsewhere.