But hey, indecision is a tool for procrastination. Anybody have any advice? In the meanwhile, we’ve adopted a new little boy, and he’s keeping me quite busy - happy to say. At the same time, I’m still excited about getting this new circuits tutorial out. I think it will be really cool.

Listening to these folks, it’s clear that they don’t do it for the money. The cash is nice, but it’s not the driver. For them, the fascination, focus, and total obsession is with the idea, a tiny seed of abstract thought that can potentially grow into practical “must have” contraptions of astronomical scale. And herein lies the practical utility of abstract thinking. The abstract spawns the practical. We must have an idea to start. No idea, no practical result. And these guys will tell you that the initial idea is usually pretty crappy; it’s the constant stretch thinking and refining that transforms the starter idea from worthless to superstar. The entrepreneur has to mature his idea in the abstract before developing and executing in the practical.

The abstract stage is critical since it determines where risks will be taken as well as where all resources will be spent - essentially the farm bet. This stage determines the success or failure of the venture. Certainly, the the execution phase is also critically important, but even flawless execution is irrelevant if the seed concept is underdeveloped.

So take every opportunity you can to build your abstract muscle. We have plenty of time for practical experience; our world is filled with practical tasks. It’s the abstract thinking muscles that really atrophy if we don’t push them - and they have the biggest potential to contribute game changing discoveries.

For the math teachers out there, I found a blog of another teacher who is very focused on bringing out the practical side of math. This blog entry is filled with tips for the classroom:

Higher Abstraction Equals More Power

Here at picomonster we specialize in transforming one of the most abstract concepts, the imaginary number, into a very concrete and physical interpretation. It’s brain candy and great exercise for the synapses if you’re game - you’ll actually feel them firing away. You can try it at our Applications of Imaginary Numbers in the Real World page. Have fun!

Some common threads of advice from these speakers:

1. Win big or fail big. There is no crime in failure itself, only in failure from lack of boldness.

2. Harness brainpower and energy from others. Be a good listener and others will help to mature your idea into big opportunities.

3. Only you really understand your vision.  Don’t let the nay sayers discourage you.  Keep your eye on your passion and develop your plan to make it real.

4. Market first, technology second. Startups are tough; do them in a great market.

5. It’s not all about the idea.  You need a great team and a great market for the really big wins.

6. Total focus.  Develop your vision, create your strategy, then execute with intense laser focus.

7. In startups, speed is everything.  Beat the big fish with agility.  By comparison, they have bottomless resources, but they are slow.  Use your speed to win.

Help us get started by by sharing your experiences with us. Or you can also make suggestions for material on this site. We’d love to hear from you. If you have not yet played with our interactive imaginary number tutorial, give it a whirl at our HOME page. It’s candy for your brain!

1. Imaginary numbers provide only an intermediate and conceptual mathematical result but have no physical significance in engineering and physics applications. Circle True or False.

2. A complex number is most often used in real world applications to quantify what kind of physical variable:

3. In a vibration system with an oscillating input motion and an oscillating output motion, the imaginary part of a complex output can best be described as:

4. In a vibration system with an oscillating input motion and an oscillating output motion, the real part of a complex output can best be described as:

And another variation on the test above:

1. Imaginary numbers are far more than a mathematical abstraction; they often represent physical characteristics in engineering and physics applications. Circle True or False.

2. A complex number is most often used in real world applications to quantify what kind of physical variable:

3. In a vibration system with an oscillating input motion and an oscillating output motion, the imaginary part of a complex output can best be described as:

4. In a vibration system with an oscillating input motion and an oscillating output motion, the real part of a complex output can best be described as: