The Plague of Misidentification

Causality Part 13

In today's TPOM, more analogies plus a few more things on analogies with some analogies nested at various points in the analogies.

Math!

1/3 : 5/6 :: 6 : (a. 10, b. 12, c. 15, d. 20)

The math analogies can range from utterly simple to highly complex, requiring a vast amount of mathematical knowledge even to approach some of the higher-level analogy problems. 

We need to think about first things here and what this could all be about. Let's write this out in another way to see if we can get started by looking into the deeper structures present. 

x/y (is to) w/z (as) Q (is to) S where S represents the options (a-d) or (a. 10, b. 12, c. 15, d. 20). 

What can we tell so far? We are likely dealing with ratios since the first section is expressed in fractions and the second in whole numbers. Why do I take this path first? The given form of the question indicates there is to be a comparison. How would we compare such things? One of the first ways is in ratio expressions because this would allow the fractions and the whole numbers to have an analogous expressed relationship that is verifiable and, when proven, would make a logical analogy. Thus, I move forward with this as my first conclusion regarding how to proceed. 

Let's simplify the following:

1/3 : 5/6

We need to write this as a single fraction like this:

We can now understand that the ratio we are looking to see repeated with the whole number 6 is the ratio of: (2 to 5). If we are correct in our assessment of the analogy, we should then have a whole number that has the ratio of (2 to 5) in relation to the whole number 6.

Is there a number in our answer options that has this ratio to 6? Yes, clearly. The number 3 has multiples that accommodate this perfectly. Let’s look at the following:

3 * 2 = 6 and 3 * 5 = 15. This gives us the exact ratio we are looking for, which is the 2 to 5 ratio. I think we can now conclude that the answer is (c. 15).

Is this correct? Yes, it is, in fact, the correct answer. The hard ones are much more involved.

A note for future mathematical analogy questions: they often deal with prime numbers in all kinds of tricky ways. It will help us if we investigate primes and their implications, outcroppings, & usages as much as possible. More will come regarding all of this in future installments of TPOM.

Geography & Regional Things

Here is an analogy that deals with geography and things regional. Let's take a look and see if we can decipher what it is all about. 

Norway: _______ (a. Denmark, b. Scotland, c. Finland, d. Wales) :: Lutefisk : Haggis

Let's start with the complete portion of our analogy. Lutefisk (is to) Haggis. First things, how is Lutefisk to Haggis in any way? 

"Lutefisk is dried whitefish. It is made from aged stockfish, or dried and salted cod, pickled in lye. It is gelatinous in texture after being rehydrated for days prior to eating. Lutefisk is prepared as a seafood dish of several Nordic countries. It is traditionally part of the Christmas feast; Norwegian julebord and Swedish julbord, as well as the similar Finnish joulupöytä." Wikipedia. 

"Haggis is a savory pudding containing sheep's pluck, minced with onion, oatmeal, suet, spices, and salt, mixed with stock, and cooked while traditionally encased in the animal's stomach, though now an artificial casing is often used instead." "Haggis is an associated national cuisine of Scotland." Wikipedia.

We can see that Lutefisk is a cuisine of Norway & Sweden, which are both Nordic countries in Northern Europe. Haggis is a cuisine of Scotland. It seems we have our connection. We have Lutefisk being connected with Norway and Sweden. My current hypothesis is that the analogy is: 

(Y1 : Y2 - Norway (is to) Lutefisk)) (as) (X1 : X2 - Scotland (is to) Haggis)).

If we are correct, then we should see one of the answers be Scotland. We can see that (b. Scotland) is, in fact, one of the answers. I see no reason currently to suspect any other option. As I survey the other options, none of them are as sound logically as the completed analogy of:

Norway : Scotland :: Lutefisk : Haggis

I, therefore, conclude we are finished with this analogy and that the answer is (b. Scotland). 

Is this the correct answer? Yes, it is correct. They are both the national dishes of each country respectively. 

The Point

We can see that if we don't have somewhat of a broad knowledge of many subjects, we can be out in the cold concerning the analogies tests. While this is true, it is not always the case or the point. The real point of these types of questions should not be whether or not one has a vast knowledge of many subjects except where that is important. The point, in this case, would be that the person understands that analogies need to have a point-for-point form to be excellent analogies. This ability to analogize at a high level helps one to better understand the world and all that is the case. In short, it will help one to better understand reality if applied well. 

Tougher

Let's take a look at one that is slightly tougher, at least for some people (myself and others).

Strap : Spool :: ____ (a. part, b. reel, c. trap, d. tars) : Loop

We should start with the part of the analogy that is complete. We have: Strap : Spool. Now, we need to understand this analogy thoroughly. First, we must start with what each constituent part is and how they link. 

What is a strap? A strap is a narrow piece of leather or other material that is often used for securing, holding together, or wrapping. A strap can make a loop. 

What is a spool? A spool is a cylindrical device onto which a material is wound. It has a ridge at both ends and an axial hole to fit a spindle or pin. 

We can now see that we have an object that can make a loop and that could be wound onto a spool. This means that strap is a thing that binds or secures other things, and it can be wound onto a spool. Thus the spool is the tool that takes onto itself the strap. 

Let's take a look at the form and see if it will help us complete the analogy. 

(Y1 : Y2 - Strap (is to) ______ )) (as) (X1 : X2 - Spool (is to ) Loop)).

Spools and loops are circular. A strap is a narrow, straight material that could be formed into a loop but is still, when stretched out, "straight." This is just an observation, and I am not attached to the hypothesis yet. 

Let's look for an analog to a strap. 

(a. part

What is a part? It is something that relates to a portion or division of the whole. 

(b. reel

What is a reel? A device onto which yarn or thread is wound during production or processing and from which it may easily be wound off.

(c. trap

What is a trap? In keeping with the thread and weaving potentials, let's look at this definition: Weaving. A break in the threads of a warp; a faulty place resulting from this in woven cloth. Also, A contrivance set for catching game or noxious animals; a gin, snare, pitfall.

(d. tars

What is a tars? It is a Latin word that can be an abbreviation for the tarsus bones in the foot. They are a collection of 7 small bones and are collectively referred to as the tarsus. 

I am having a hard time finishing this one, as none of them seem to complete the analogy. It is time to look in other places. One of the places I look first when I encounter something of this ilk is toward trickery or cleverness. These often result in "right in front of your face" types of analogies. There are many non-standard types of analogies that require looking at things in a different way—number cleverness, word scrambles, archaic word usages, etc. 

Check this out:

Spool = Loops. Straps = Parts. Not perfect, but there is a pattern. Let's go further. 

X1 translates to X2 by spelling backward and taking away the last letter, e.g., Spools (X1) - Loop (X2). We should apply this pattern to the Y series. If we have a match, I will certainly go with this one as the answer.  

Y1 translates to Y2 by spelling backward and taking away the last letter, e.g., strap (Y1) - part (Y2). We have a perfect match, and we should go with this as the answer. 

The answer is (a. part

Are we correct? Yes, this one is correct. 

These types of analogies are more difficult for me than ones that follow a more traditional form, but if I don't get what I want from the traditional forms I have shown you so far, I immediately look for the more tricky options, and in this case, it paid off. 

One trick I have learned is to look for words that have clear mirror imaging going on, like "parts - strap." Some people call these palindromes, but they are absolutely not palindromes. A palindrome is a word, phrase, sentence, number, etc., that is spelled the same frontward and backward.

What we are dealing with is called an anadrome. Anadromes form a different word (or phrase) when spelled backward. Anadromes are also called volvograms, reversgrams, heteropalindromes, and mynoretehs. 

Further Knowledge Regarding Form

In going a little deeper into our understanding of form, we should look at a few types of semantic forms we will encounter. They are as follows:

Antonyms/Contrasts

This type deals with opposing words or concepts. They have opposite meanings or indicate dissimilar concepts, unlike each other in one or many ways. Consider:

• dorsal & ventral 

• rostral & caudal 

• macro & micro

• front & back

Degree/Intensity

This type deals with when one term expresses the same concept to a great or lesser magnitude. Consider:

• miserable & unhappy

• frugal & miserly

• assault & murder

• speeding & reckless endangerment or reckless driving

Meaning/Definitions

This type deals with when one term explains what the other term means. Consider:

• nosh & eat

• slumber & sleep

• sup & drink

• bequeath & donate

Synonyms

This type deals with words that have the same or similar meaning. Consider:

• surface & appear

• define & illustrate

• bad & atrocious

• preferable & superior

Of these categories, I find them all to be challenging depending upon the degree to which the relationships are stretched or the degree to which the concepts are abstracted. 

One of the most important things to understand here is that all of these concepts will be played with by the test maker in an effort to impose the various levels of questions that are required in order to set the test up so that there will be a proper distribution range from below average to average to gifted to high-gifted. What this means is that there must be a wide range of levels of difficulty of the questions placed within any one test. The good news is that there will be many that are easy to intermediate level questions. The bad news is that there will be quite a few difficult to extremely difficult questions as well. 

For our purposes, we need lots of questions to sharpen our analogy claws, and the more we do it, the better and sharper they get. This type of training helps one in many endeavors in life. The ability to properly analogize is an essential skill to develop to the highest level possible, as it helps and informs many other areas of thinking and reasoning. 

Coming Next

In the next TPOM, we will go a bit further in our ever-blossoming work on causality and analogies as a means to a more profound understanding of the reality in which we live. 

We will continue. 

B.S.R.