1. Understanding the Problem.
First you have to understand the problem.
- What is the unknown? What are the data? What is the condition?
- Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
- Draw a figure. Introduce suitable notation.
- Separate the various parts of the condition. Can you write them down?
2. Devising a Plan.
Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
- Have you seen it before? Or have you seen the same problem in a slightly different form?
- Do you know a related problem? Do you know a theorem that could be useful?
- Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
- Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?
- Could you restate the problem? Could you restate it still differently?
- Go back to the definitions.
- If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Can you solve a part of the problem.? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or the data, or both if necessary, so that the new unknown and the new data are nearer to each other?
- Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?
3. Carrying out the Plan.
Carry out your plan.
- Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?
4. Looking back.
Examine the solution obtained.
- Can you check the result? Can you check the argument?
- Can you derive the result differently? Can you see it at a glance?
- Can you use the result, or the method, for some other problem?
Here’s a pretty easy and straightforward tutorial showing you how to make the rainbow cake that when sliced, looks freaking awesome and so damn delicious that I wouldn’t mind sitting on my ass for an entire afternoon with a fork in one hand and a glass of milk in the other and devouring the whole damn thing like the glutton that I can be.
Even if you’re not a genius, you can use the same strategies as Aristotle and Einstein to harness the power of your creative mind and better manage your future.”
The following strategies encourage you to think productively, rather than reproductively, in order to arrive at solutions to problems. “These strategies are common to the thinking styles of creative geniuses in science, art, and industry throughout history.”
Look at problems in many different ways.
Find new perspectives that no one else has taken (or no one else has publicized!)
Leonardo da Vinci believed that, to gain knowledge about the form of a problem, you begin by learning how to restructure it in many different ways. He felt that the first way he looked at a problem was too biased. Often, the problem itself is reconstructed and becomes a new one.
When Einstein thought through a problem, he always found it necessary to formulate his subject in as many different ways as possible, including using diagrams. He visualized solutions, and believed that words and numbers as such did not play a significant role in his thinking process.
A distinguishing characteristic of genius is productivity.
Thomas Edison held 1,093 patents. He guaranteed productivity by giving himself and his assistants idea quotas. In a study of 2,036 scientists throughout history, Dean Keith Simonton of the University of California at Davis found that the most respected scientists produced not only great works, but also many “bad” ones. They weren’t afraid to fail, or to produce mediocre in order to arrive at excellence.
Make novel combinations.
Combine, and recombine, ideas, images, and thoughts into different combinations no matter how incongruent or unusual.
The Austrian monk Grego Mendel combined mathematics and biology
to create a new science of heredity. The modern science of genetics is based upon his model.
Make connections between dissimilar subjects.
Da Vinci forced a relationship between the sound of a bell and a stone hitting water. This enabled him to make the connection that sound travels in waves. Samuel Morse invented relay stations for telegraphic signals when observing relay stations for horses.
Think in opposites.
Physicist Niels Bohr believed that if you held opposites together, then you suspend your thought, and your mind moves to a new level. His ability to imagine light as both a particle and a wave led to his conception of the principle of complementarity. Suspending thought (logic) may allow your mind to create a new form.
Aristotle considered metaphor a sign of genius, and believed that the individual who had the capacity to perceive resemblances between two separate areas of existence and link them together was a person of special gifts.
Prepare yourself for chance.
Whenever we attempt to do something and fail, we end up doing something else. That is the first principle of creative accident. Failure can be productive only if we do not focus on it as an unproductive result. Instead: analyze the process, its components, and how you can change them, to arrive at other results. Do not ask the question “Why have I failed?”, but rather “What have I done?”
Paul Cézanne (1839 – 1906) is recognized as one of the 19th century’s greatest painters, and is often called the father of modern art, an avant garde bridge between the impressionists and the cubists. During his life he only had a few exhibitions though his influence on subsequent artists was great as an innovator with shape and form. His genius, however, was not evident until late in life. He was refused admission to the Ecole des Beaux-Arts at age 22 and his first solo exhibition was at age 56. His genius was the product of many years’ practice and experimental innovation.
And low and behold, I found this two part video on Youtube…damn I should hit up Vegas with this luck. Anyways, here’s a two part video of cinema surrealist, David Lynch taking us through the necessary steps to get our Quinoa on, the grain that keeps on giving. If you seen any of David Lynch’s movies, then you know that this is the most straightfoward video shot by him. Not symbolism, no methapors, no creepy alien hiding behind the trash bins, no psychotic, ether breathing maniac, just the facts folks.
Go to auto parts store and write a check for $50.00 for oil, filter, kitty litter, hand cleaner, and a scented tree. Discover that the used oil container is full. Instead of taking it back to O’Reilly to recycle, dump in hole in back yard. Open a beer and drink it.
Jack car up. Spend 30 minutes looking for jack stands. Find jack stands under kid’s pedal car. In frustration, open another beer and drink it.
Place drain pan under engine. Look for 9/16 box end wrench. Give up and use crescent wrench. Unscrew drain plug. Drop drain plug in pan of hot oil: get hot oil on you in process. Clean up mess. Have another beer while watching oil drain.
Look for oil filter wrench. Give up; poke oil filter with screwdriver and twist off.
Buddy shows up; finish case of beer with him. Finish oil change tomorrow.
Next day, drag pan full of old oil out from underneath car. Throw kitty litter on oil spilled during step 18. Beer. No, drank it all yesterday.
Walk to 7-11; buy beer.
In The Event That An Nuclear Apocalypse Wipes Out All Our Electronic Devices, You’ll Need This Instructional Video On How To Use An Abacus
This video goes out to all those few ‘lucky’ survivors of the nuclear apoclaypse who need to do complex mathematical equations when an EMP wave has wiped out all electricity in their general area. Although I think these mathematical equations should take a back seat to the fact that an extra limb has started to grow out of the side of their heads.