The Plague of Misidentification

Causality Part 14

In today's TPOM, we are continuing forward with our studies of analogies. I will select slightly more complex examples that will offer us the opportunity to hone our analogical abilities to the next level. I am excited to take this adventure alongside you. May we all prosper. 

Analogies

XX : (a. L, b. C, c. CC, d. D) :: C : D

Just for clarity, let's take a look at the analogical form:

X1 : Y1 :: X2 : Y2 or X1 : X2 :: Y1 : Y2

We can decide which is functioning when we have enough data. Also, given that these are variables, it is not critical that we use either set. What matters is that they represent the correct underlying form and that we understand that form precisely. For now, don't fret about the introduction of the new set. We will learn to use it in time. 

First Things

When we encounter variables or letters that represent something that is potentially non-standard, we need to look for patterns. The first thing and second things I notice happen nearly immediately. First, I notice that XX : _____ :: C : D has the potential to be a distance analogy, which means a certain number of letters into the alphabet and a certain number of letters away from the end of the alphabet. Second, I notice that each of these letters is also a known Roman numeral. 

Let's start with the first thought and test to see if it fits. When we look at the portion of the analogy with both components present, i.e., C : D., we can see that C is the third letter of the alphabet and D is the fourth letter. If there is a pattern present, we would need to see that present itself symmetrically on the other side of the alphabet. It is clear that X is the third from the last letter of the alphabet. So far, so good. If there is a pattern, we would want to see W show up as an answer so that we can have the fourth from the last letter of the alphabet. Is there an answer option for W? No. Not great for that theory. 

We also need to note that there are two X's. One might infer if there is an answer with two letters of the same type, then that is our answer since that would create a pattern. It is important to remember that we are not looking just for patterns but for patterns of significance. When looking at the analogy from this context, I don't see this answer as being a logical fit. I think we should move on to another context. 

Let's move to my second thought, which was that these are Roman numerals and that they represent numbers. If this is the case, then we will actually have a number analogy on our hands. The next step is to write out the analogy with the number substituted in the place of the Roman numerals. 

X = 10 & XX = 20, C = 100 ,D = 500

20 : (a. 50, b, 100, c. 200, d. 500) :: 100 : 500

Before we go too much further, let's investigate to see if there are any immediate patterns of significance. The answer is a resounding yes. When we think in ratios, we can immediately see that 20 is 1/5 of 100 and 100 is 1/5 of 500. Put another way, if we multiply 20 * 5 = 100 and multiply 100 * 5 = 500. Are these options available to us in our answers set? Yes, answer (b. 100 is a viable option. I think this has the strongest logic of any of the other answers. What do you think? Before you move on, decide if you agree with this assessment. 

I select answer (b. 100. 

Is this the correct answer? Yes, it is.

Difficulty

Was the above actually more challenging than some of the other examples from prior installments of TPOM? That depends on your personal knowledge base to some degree. That said, if you jump to the doubled letters as a pattern and select heuristically, you would not have gotten the correct answer. Nor would you have reached the correct answer if you inferred an illogical distance-based methodology. 

Even in the most complex tier of analogies, sometimes you will just get it when others are struggling, so there is a component of subjectivism present. That said, it follows that it depends upon your knowledge base as much as the form if you judge the increasing complexity from that standpoint. However, if you look at form respectively, there is a slight jump forward in that we had to cover a few different or new types of materials to get to this answer. I say all of this to focus your attention on both the subjectivity of the complexity and the formal change or objective design that is slightly more complex. At the least, this will become inarguable in later questions. For now, I bring out this distinction when it can be argued both ways to drive you into the land of the critical distinctions needed to grasp the elements. 

Analogy No. 2

Top : Bottom :: Soup : (a. kettle, b. base, c. nuts, d. spoon)

Let's do a quick movement to think of form just in case it can help us. 

X1 : X2 :: Y1 : Y2 or X1 : Y1 :: X2 : Y2

First Things 

Do I see any direct correlates that have a logically significant pattern? No.

Next, what is the completed portion stating, and what does it attend to or relate to? I happen to know this one, but I will move forward as if I don't and see if we can get to the answer without prior knowledge. I can tell you that this will be difficult, but this type of thing is critical in understanding how to deal with analogies of this type and know them immediately. 

Top : Bottom deals with the concepts of orientation in space. This also attends to things like being able to orient, which in many instances regards gravity. The concepts of top and bottom also attend human perspective along with taking perspective, which has a sense of projective analytical functioning present. In short, there could be relativistic components present, or rather, there likely are relativistic components present.

Next, we look at that other part of the analogy. Soup : _____. Let's fill in the blank with some of the answers and see how they fit. 

Soup : (a. kettle

In what way is soup (to) kettle like top (is to) bottom? Soup is made in a kettle. Does that fit? No. In some sense, top and bottom have an abstract component to them in that they are relative concepts. Is there a way that this could fit then? Yes, if the other portion had an abstract concept that paralleled the first, that would complete the pattern. Do I see that here? No. We should move on and keep that piece of data top of mind. 

Soup : (b. base

In what way is soup (to) base like top (is to) bottom? I do not see any direct correlation. Once again, we would have to go into abstraction to make this work, and I have no knowledge of anything that fits. Suppose you are wondering what an abstraction might look like in this situation. In that case, it could be something like a figure of speech, an old wives tale, or something from a piece of art that one would have to have prior exposure to know. It could also be a form of code or other complex relationship that should be discernable but only by people with the know-how to search out such things. 

Soup : (c. nuts

In what way is soup (to) nuts like top (is to) bottom? One thing I neglected to mention above is that there is a relationship between the number of letters in the words soup and base in that they each have four letters. If other words did not have that relationship and if the other words in the analogy had that relationship present, that very well might be the correct answer, provided you could not find a stronger relationship. Meaning that if the other words in the answers set all had other than four letters, and the analogy portion that is complete had a word number pattern that fits, then it is likely that it would yield your answer. In this instance, we do not have such a pattern, and we should move on, taking care to look for other patterns. 

On the abstracted front, there is a match in that these both happen to be two sayings that deal with covering a thing in its completeness. I am sure many of you have heard the saying, "I went over it from top to bottom." This is a widespread saying, and that would be all of the clues needed to get us on the right track. Where the problem lies is that we need to know the other saying to properly get the correct answer. I will proceed as if we have all heard of the first saying but that many of us have not heard of the second saying. 

We do have a place to hang our hats in that we do not yet have any other significant correlations that yield highly significant answers. We should be thorough and test out the last answer to see if it fits any better or has any other logical component that we may have overlooked initially. 

Soup : (d. spoon

In what way is soup (to) spoon like top (is to) bottom? We use a spoon to eat soup. Does this correlate in any meaningful way? No. Soup and spoon have a relational aspect to them in that they are often used together. In other words, one is attached to the other through usage and a form of necessity, though culturally, that is arguable. This, in one sense, appears to be a better answer than the others because there is some form of relationship present. 

Crossroads

Now, we are at a crossroads, and we have to make a decision as to whether we are going to go with (c. nuts or (d. spoon. We know that top (is to) bottom is incorporated in a well-known saying, and we know that soup and spoon are correlated via a working relationship of a sort. We need to ask ourselves whether this working relationship correlates to top and bottom. No. The reason is that the formal or formative aspects of the association are different. This adds an issue for me in selecting this as an answer even though I already know the answer. We need the logic to flow, and it does not flow very well if we select (d. spoon. That leaves us with (a. kettle, (b. base, and (c. nuts). 

I think the reasons we passed by options (a and (b are well noted above, and that logic still stands in light of the known saying. At this point, I would select (c. nuts, even if I did not know the saying for the following reasons: 

Soup : kettle is out as it does not correlate even though it is a known saying.

Soup : base is not a known saying, nor does it correlate. 

Soup : nuts is a known saying, and it correlates in that it means what "from top to bottom" means. If we don't already know this, no problem; it is still in the running. 

Soup : spoon is also a saying, but it does not have the same meaning as "from top to bottom." 

By process of deduction, we are left with one answer, and that is answer (c. nuts. This would be the answer I would choose if I did not know the saying, which I do. 

Frustrations & Test Making

It is precisely these types of questions that upset people when dealing with the MAT or other analogies tests. I want to point out that we were able to arrive at the correct answer through devotion to our logical process even though we did not know the saying. It is for this reason that the test makers continue to use these types of questions as they test for higher logical processing. Though we would not leave this question on a test with 100% assuredness, we would undoubtedly leave feeling like the probability and the logic were on our side with the above answer. 

The point of stating the above is to let you know that though some questions on the MAT seem unanswerable if you don't know the prior data, you can often use logic to increase your odds of getting correct answers. 

In an ideal world, this type of test design would always have a purely logical analytic way to grasp and get to the proper analogy, and I suspect the test makers are doing a great job at moving in this direction. That said, analogies themselves have components that make the execution of the perfect analogy test nearly impossible. It can be done, but when the test has to test the entire populace and do a great job across the board, the test makers have an extraordinary task set out before them. 

Why Care

We care about analogies because they are one of the primary ways that humans think. We constantly think in analogies, and especially if we don't know all of what we are trying to learn, we often use analogies to test to see if we are correct. Think of how many times you have asked a friend in a discussion, "Is it like X?" You are attempting to analogize to help yourself understand whatever X stands for at the time. 

A Profound Thinking Error

This type of thinking also leads to one of the more serious thinking errors that I deal with in my work. When one encounters a concept or idea that is beyond their current grasp, they immediately move to analogy to try to understand that concept or idea. This is often done in place of a much better idea in most cases, which is the idea of reasoning logically from first things until you can reach the level of thought upon which that idea lives and has its fullness of being. 

When my students immediately attempt to take a robust, complex, high-level concept and bring it down to them at that moment, I always caution them that it is much more preferable to rise up to that idea rather than to destroy it by bringing it down to a level at which it does not have its fullness of being. This often frustrates them because they feel that they will never get it, or they resent that they will have to work to understand the idea altogether. 

Encouragement

It is a fact that many of the most incredible things a person can know and understand about this wonderous universe take great effort to grasp fully. If I could teach you one thing today that you would never forget, it would be the following: 

If you engage with all that is around you from love with curiosity, wonder, and excitement, along with intellectual honesty, rigor, and the ability to sustain yourself in intense focus and hard work, while always being careful to continue down the path that these traits, coupled with your intuition and your inquisitiveness, will lead you down, you will not be sorry for your efforts, and great things will come.

We will continue. 

B.S.R.