By: Megan Prats

01/07/2015

Critical thinking is the gateway to the infinite realm of knowledge. Thus, one way to decipher whether or not the student is using her critical thinking skills is to see where problem-solving takes her. In short, thinking that leads to infinity is critical thinking.

Now, in order to assess if the student has reached the infinite realm of knowledge, it is imperative that you recognize the destination. Because Geometry has simply and elegantly drawn the different manifestations that infinity can form, I will use geometric figures to illustrate the many faces of the infinite realm of knowledge.

• Line Segment  ——-

The line segment represents the infinite realm of knowledge within confines because there are an infinite amount of points between the two endpoints of a line segment, but the line segment doesn’t encompass all points in space. Answers that lie in a line segment face of the infinite realm of knowledge would be, for instance, communicating in one language. The possibilities for communication in one language are endless however if the student steps out of the confines of that language (i.e. from English to Mandarin), the student enters the “wrong” place. It’s not to say that the line between English and Mandarin is clearly defined as fundamental language principles that are utilized in Mandarin can be applied to English; however, if the student begins writing English with Mandarin characters which have no meaning in English, the student has exited the confines of the line segment in which she should operate. But, if via the student’s thinking, she produces answers that show that she understands the confines in which she operates and also that the possibilities are endless within those confines, the student has arrived to the line segment manifestation of the infinite realm of knowledge.

• Ray —–>

The ray represents a way of thinking that leads to infinity from a starting point. For example, the other day my student and I were working on brainstorming in English. My student, because of his solid understanding of brainstorming, was able to allow his creative mind to take him to far off places from his starting point. Thus, he started with describing the beach, and then he followed his chain of thoughts to Italian and Spanish settlers of South America. If he continued on this path, he would never reach the end. Thus, because his thinking started at a fixed place and then led him to infinity, he was thinking critically.

• Line  <——>

The line represents the infinite expansion of the infinite realm of knowledge. Thus, there is no beginning nor end, just more thoughts, ideas, and learning. A student who thinks critically and lands up in the line face of the infinite realm of knowledge is most likely involved in Creativity in the Moment as Creativity in the Moment, if executed well, requires for the student to surrender herself to the infinite realm of knowledge and allow for the infinite realm of knowledge to make decisions on her behalf. Thus, many musicians, for instance, have stated that while being creative in the moment on stage they experience an out of body sensation and it is like their thoughts and execution of those thoughts are coming from elsewhere. Once connected with the infinite realm of knowledge on such an intimate and non-obstructive level, the mind knows no confines (unlike with the line segment or the ray). Creativity in the Moment taps into the deeper, more subconscious, part of the mind which the conscious mind cannot regulate. Therefore, thinking in this space can lead to answers that live beyond time, space, logic and reason, etc; in short, answers that live anywhere on a line.

The infinite realm of knowledge can manifest itself as a line segment, a ray, or a line because those geometric figures represent infinity as a destination. However, the circle, even though it represents infinity as infinite repetition, is not a shape of the infinite realm of knowledge as infinite repetition contradicts the infinite possibilities that lie within the infinite realm of knowledge. A circular way of thinking would materialize in the lessons as a repeated problem-solving process. For instance, the student wants to rewrite a sentence in her foreign language in five different ways. Thus, she starts with the noun in the sentence, looks in the Thesaurus, and produces five different sentences replacing the nouns with five synonyms that she found in the Thesaurus. Even though the results are different, her thinking keeps going round and round like a circle. Once she runs out of synonyms from the Thesaurus, she will seize to produce results thus her thinking hasn’t led her to infinite possibilities. Hence, even though the circle represents infinity in Geometry, the circle is not a face of the infinite realm of knowledge.

Finally, an obvious geometric entity that doesn’t represent the infinite realm of knowledge is a point. A point, by itself, is really the antithesis of the infinite realm of knowledge as it represents one which, is a far cry from infinity. A student who has a “pointed” way of thinking is one that continues to regurgitate the same answer. Like a broken record, the student cannot free herself from the one spot in which she resides. This, obviously, is not critical thinking as critical thinking would not lead the student to just one.

The infinite realm of knowledge is one of the most beautiful things that the student can experience because it represents freedom in its truest sense. But in order to take the student to this magical place, you need to understand the destination. Thus, the infinite realm of knowledge can manifest itself in line segment, ray, and/or line answers.

© Megan Prats 2015