Logical markers: the most intuitive and misunderstood memory construct

Logical markers do not require special learning, as we already learned them in schools for more than a decade.  If you are not using them to remember things, it is a psychological barrier. Once you try, they will feel more natural and intuitive than any other memory construct.

My favorite logical marker

There is only one logical marker which I will quote always and use at every opportunity. Happiness = pleasure + purpose. Beyond the philosophical and psychological meaning, we can analyze its structure. This is an equation. Not a real or physical one as we do not really measure and conduct experiments. We use mathematical language to express a deeper understanding. And if we realize more, we can add that to the equation. Mathematically it is nonsense, but on a deeper intuitive level, it makes sense.  The equation is qualitative, not quantitative. It is a language, not a calculation.

Not really math

Many of my friends go around talking about how broken formal education is. More of my friends are actual professors in formal education. And I will be honest, these guys get along really well. Math can be hard to use properly, but it is really fun to misuse.

I will be honest. Even though my Ph.D. deals with complex mathematical ideas, sometimes I also hate math. Not all math. Just some overly abstract overly complex areas of math which I do not get. Like certain parts of the mathematical topology or sneaky subjects in number theory that make my head hurt. Seriously, Fermat’s Last Theorem or summing of three cubes can be diabolically complex. Fortunately, the engineering problems I deal with do not require that particular kind of math. I might use some linear algebra, statistics, and partial differential equations which are much easier to comprehend. Most people do not need even that.

If a person can calculate percentages, probabilities, and boolean logic – that person can do almost anything. At least mathematics will not be the limiting factor. Probably 99% of what we learn we will not use anyway. We can use math not as a tool for setting progressively more complex riddles and puzzles, but as a language to describe our needs.

Math as a language

From the first grade in school, we learn to use math as a language. Some scientists may immediately think of math as symbolic logic, using definitions provided by Bertrand Rissel. 1+1=2 is easy to write, harder to prove. The proof takes about a thousand pages. Yet even a small child uses that kind of math intuitively correctly.

We do not need to have a good mathematical understanding or even correct math formulation to use the language of math. The language of addition, multiplication, and equivalence come to us naturally after the first years in every school. If anything, proper math can make things much more complex and harder to understand.

F=m*a is a simple law in physics.  However, if we take real objects and try to integrate the stress along their shapes, we immediately get something very complex. You push a ball with your finger, and in addition to lateral motion, it starts to rotate. The motion gets weirder if the center of mass is offset. This is really a distraction from the main idea.

Focus… Simplify… Use the language to describe what you want.

Why is mathematical language so good?

Why should we use the mathematical language at all? Apparently, it provides very simple symbols to describe complex and abstract relationships. Simple mathematical signs like +, -, *, ->,= are pretty hard to visualize other than using these signs. It is pretty hard to visualize physical concepts – especially constants like pi or e, but pretty easy to visualize the relevant letters.

Even numbers are hard to visualize without numerical math. Our innate ability to count is not very good. If we see anything above 7 objects, we usually need to group the objects into chunks to assess their number. How do I visualize 49? Like a square of 7×7. Clearly, I could use more specific memory techniques, but why bother?

Why do the mnemonists use a decimal system of numbers, and not hexadecimal? In many ways the hexadecimal system is superior, but the testing in competitions uses decimal representation. The way we use and perceive math as a language is defined by the situations where we use math.

Conditions

You are not in the first grade anymore. Beautiful mathematical equations work very well in elementary school. At least if you are a good student. Then they start to fail. You put two hamsters in a cage. 1+1. How many hamsters will there be in a cage the next day? Will they die, multiply or persevere? Depends.

Typically our math holds only under some assumptions. It is only reasonable to add if/else clauses to our logical markers. Write down “if-else math notation” in google image search, and you will see a number of ways to represent the idea. Typically we can use the set symbols {, the causation symbol -> or the given symbol |. Visualizing the two or four letters keywords is also easy. If, then, else, ow (for otherwise), with, wo (for without)… There is freedom of choice: you can mix and match the logical representations, keywords, and symbols.

Brevity

The reason mathematicians use their language is brevity. If you want to say the same thing a thousand times, it is best to have a very simple symbol for it, made of one or two lines if possible. Mathematical notation is a shorthand for very complex ideas. In a similar way, logical markers present simple shorthand for very abstract and complex understandings. Sometimes they are already the language used. Physics or chemistry relies on math to describe complex natural phenomena. The equation or formula itself is the logical marker for more complex phenomena. If you learn physics or chemistry: your equations are your logical markers.

If you feel that the entire discussion did not teach you anything, go ahead a learn some math symbols. Find a way to use them in your visualizations.

Math symbols

 

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