Clarity of thought is all about being exact. To say that it comes with practice falls short of exactness. The desire for precision is what makes you pursue exactness. In Mathematics exactness can never be compromised as precision is the demand of Mathematical thinking. In the early stages of evolution primitive man did not go strictly by precision. Rather, he went by shadows and the visible sun light. He would tell time not numerically but by the nature and impact of sunlight that he perceived. He was more of an observer. As civilization evolved these observations were reduced to metrics and you have the clock which we now take for granted on account of it being present always. We measure reality through metrics. Therefore it is of paramount importance to seek precision in what we do. We have grown to be dependent on metrics as a result of the demand of criticality that we face. In schools and colleges we seek precision to procure our ends only, which could mean getting higher grades. If the motivation is to get higher grades only, we do not seek precision but buckle under the pressure of the need to be precise. If this is the case then we are removed from the criticality of our reality. As a result it is important for the tutor to explain the need for quantifying our observations of the universe. Although Mathematics is studied in a vacuum by many students the goal of Mathematics and Science is to describe our universe with its natural laws accurately. Unless this fact percolates we would not internalize what we are studying without which we tend to forget our lessons, after we find that it is of little use to us beyond examinations. What separates a Scientist from Science is the fact that he/she is a student of the natural laws that sustain him/her. To be a student is to be an observer, who seeks to understand the complex environment around him/her. This determination can make you a Scientist who looks at Science beyond personal ends. The moment you understand this aspect, you begin to appreciate the importance of precision. Without precision, Mathematical thinking cannot have impact. Tutors would do well to mention this point. In the era of cyber space, precision is what one needs, whether it is a question of getting reliable information or procuring accurate metrics of critical value. Cultivate the trait of precision, which in Mathematics and Science is a precious virtue.
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