In any field of endeavor, improving your thinking skills is helpful. You can learn how to think. Become smarter. Scientific thinking uses a formalism called the scientific method. For an excellent discussion of this technique, see Neil deGrasse Tyson’s Masterclass lecture series at https://www.masterclass.com. This app contains many lectures by renowned teachers on a wide variety of subjects: business,science and technology,film,

writing, art, education,cooking,etc. It is worth the investment. For a free discussion on the subject, download the Khan Academy app, select science, high school biology, and scientific method.

The trained mind frequently uses a type of reasoning known as boolean logic. For an introduction to classical logic, see a free lecture series on you tube at https://youtu.be/K4ChzesrWKI.

There are three

types of classical logic; abductive,deductive and inductive.

Science is mostly inductive; mathematics is deductive, since it even proves its inductive statements deductively.Abductive reasoning postulates the most probable conclusion from limited data.You walk into a room with a desk an open window and papers on the floor. You conclude that the wind blew papers off the desk. That conclusion is the most probable. But a robber could have searched the desk. If you knew that there was no wind that night and thefts were reported by other neighbors, you might change your conclusion.Abductive and inductive reasoning are similar; abductive focuses on cause and effect while induction seeks a general rule. For training and practice in critical thinking, download the Khan Academy app, go to browse, choose Partner Content, choose Wireless Philosophy, then Critical Thinking.

Boolean logic is only a type of reasoning. It is deductive. In it, beliefs are either true or false, black and white. Current digital computers using logical 1 or 0 bits reason this way. Under development today at D-Wave, Google and IBM is a new type of computer called a quantum computer. This computer requires it’s own brand of logic. It does not obey the rules of boolean logic;it uses qubits, which can exist as a logical 1 (true), 0 (false), or both 1 and 0 simultaneously! This is not even comprehensible with human intuition. It is a consequence of a scientific theory called quantum mechanics. This is the story of how the very small behaves: atoms, molecules, and their constituents. Its’ weirdness is a consequence of the fact that the act of measurement itself can disturb what is being measured.

This action can be made negligible in our large world.

For a discussion on intuition versus logic, see http://www.collegiatetimes.com/opinion/the-importance-of-going-with-your-intuition-trumps/article_ee6e442c-2ddf-11e7-b03a-3fd63198affb.html.

Our intuition can be trained to be consistent with logic. Ones gut can be programmed with experience.

Caution! Our world does not always fit into the black and white nature of boolean logic. Life is not black and white. There are no winners and losers. We sometimes condemn black and white reasoning as too stereotypical and even plain wrong. Boolean logic may describe the weather as hot or cold; in actuality, it may be a mild 70 degrees Fahrenheit. The temperature has a value within a range. It is said to be analog in nature. In statements words like some or most or a few can be used but be careful about the words all and never.

Mathematicians developed an algebra around boolean logic; this math is called boolean algebra. It has its’ own operators and laws. The basic operators are: AND (*), OR (+), & NOT (○). See https://youtu.be/bCAULDuMcso

for an explanation of how to use these operators in search engine libraries like Google. Boolean algebra is used in engineering to design hardwired digital logic circuits.

The laws of boolean algebra require a brief introduction. A boolean variable X can have a value of logical 1 (true in positive logic) or 0 (false in positive logic). It can represent the condition of a premise or conclusion. Premise X is true implies X = 1. X is false yields X=0. (This is arbitrary convention.)

Consider 1+1=Y. A true (1) premise OR (+) another true premise (1) implies the conclusion Y. Examining the above shows us that Y is therefore true. Therefore Y=1. A law of boolean algebra is therefore 1+1=1! Boolean variables by convention can only take on logical values from the domain {0,1}. The operator AND is multiplication, OR addition, NOT negation. NOT X is an X with a bar over it. Now view the following lecture:

In other words, for example, a true belief AND a false belief produce a false conclusion. 1*0=0. Most cows give milk (1) AND milk is green (0) so most cows give green milk (0). As an exercise, do some of the other laws. An examination of the above table shows that the OR and AND operators commute, i.e., X + Y= Y+ X and X*Y=Y*X. For example, if two premises are true, their outcome is true, regardless of the order of determination. Classically, the determination itself has no effect on their truth value.This is consistent with our common sense.

What is different about quantum logic?A sub-atomic particle may have a property known as spin. Think of it spinning on an axis like the earth. If the spin revolves around a north-south axis,it can be said to have a value of physical 1 if pointing north. The truth value is said to be true also. Then it has a value of -1 if you point the measuring apparatus south. Truth value can be said to be false (0) by definition here. Under either condition, classically it would have a physical value of 0 from an east or west point of view. Suppose we prepare the classical particle in the n-s direction so that it has the value of its spin +1 while pointed north. Classically, if we measured the east component, we would get 0. Qubits are different. Their spin can only be a physical +or-1.Statistically, many measurements of the eastern component after preparing the northern value as one yield an average physical value of 0 from a series of +1 -1 +1 -1 etc. B=+1or 0. A+B = 1. If we go back and measure the north component, we classically would get +1. Qubits are different. They have been disturbed by the measurement of B. We get A = physical +1or-1. There is a one quarter probability that A=0 and B=0 That is one outcome of the four possibilities:{1,1} {1,0} {0,1}{0,0}. Therefore there is a 1/4 chance that B+A=0 and therefore A+B does not always equal B+A. These two components of spin do not commute. The seemingly obvious commutation of the classical bit doesnt hold true with a qubit for those components of spin.

See the formulas page to learn the laws of ordinary algebra and see them at work. In boolean algebra, the associative and distributive laws are also true.

Let’s discuss an example of wrongheaded or fallacious thinking in classical (boolean) logic. Consider: when it rains, the uncovered grass is wet.

The assertion above is true. However, if the grass is wet, it may not be raining! You could have watered the lawn or the rain had stopped already. In other words, if A implies B, B does not necessarily imply A. However, if the uncovered grass is not wet, it is not raining! In other terms, if A implies B, then NOT B implies NOT A. This latter relation is known as the contrapositive. It is true if the original belief is true. Both watering the grass or letting it get rained on is SUFFICIENT for wetting the grass. A NECESSARY condition is the grass not be covered. All necessary conditions to the truth of conclusion Q must be met for Q to be true.Only one sufficient premise P is required to imply Q.

Another very important type of human thinking is the imagination. Ask your mind for ways to do something. Visualize. For a good discussion on the imagination. see

Think intuitively. imaginatively. and critically.

Be careful about abductive reasoning.Be thorough; the more data you include, the better you’re conclusion. Test your reality.Keep it simple.Abduction,induction,deduction,boolean logic,analog,quantum logic,and intuition and imagination are tools in your toolbox. Use them wisely.