The Apple Lesson  Making the familiar unfamiliar
I had just begun to tell the following story.
“Sometimes it is a useful endeavor to look at familiar objects or ideas in unfamiliar ways. Moreover, the reverse is also true. That is, it is sometimes helpful to look at unfamiliar objects or ideas in familiar ways. Today we will analyze an apple in new ways, and then discuss the undressing of an apple. Before we undress our hypothetical apple, let’s talk about its components. The first thing we notice is that our apple has an outer component that we call the skin. The skin encloses the interior, or inside, of the apple. As the apple matures and grows the skin expands mostly in surface area. The increase in the amount of skin over a period of time is an accumulation of matter and the effect of this accumulation is similar what we call addition in mathematics.
At the same time, we find the pulp underneath the skin in volume as the apple matures. The natural growth cycle of the pulp is similar to a layering effect. Consequently, the expansion in volume is also an accumulative process. It is then possible for one to view the repeated layering as equivalent to repeated addition, and if repeated addition is equivalent to multiplication then repeated layering is the same as multiplication.. The symbolic depiction below represents our apple equation.
Apple = pulp x core + skin.
Now, let us undress the apple in a physical sense and see how the process can be paralleled by manipulating the symbolic form.

Pulp (t = 2)=pulp (t = 1) x layer
skin (t = 2) = skin (t = 1) + add’tl skin
core(t = 2) = core (t =1)
As we evaluate our apple and apple equation, we notice that what remains is pulp and core on both sides. Our next step is to remove the pulp. One physical method is placing ones thumbs on top of the apple where the stem is located and the fingers around the bottom of the apple, one then applies pressure with the thumbs and pulls the apple a part. The motion is similar to an inverting. The mathematical equivalent to turning something upside down is referred to as the reciprocal, or inverse. If we agree to let pulp/1 represent the symbolic form of pulp, then the reciprocal of pulp/ 1 is 1/pulp.
To remove the pulp from the actual apple means to separate the portions that have been designated as pulp from the core. Any method one uses to remove the pulp form the core must preserve the core. Therefore, all methods used would be similar because the pulp would be removed by a “taking away” gesture which separated small portions of the pulp from the core. If the removal of the pulp is done by a repeated “taking away”, and repeated taking away is equivalent to the mathematical operations of repeated subtraction, then to remove the pulp from the symbolic apple one divides both sides by M/1 or multiply both sides by 1/M. Where 1/M refers to the portions used to remove the entire pulp.
1/ pulp x pulp /1 x core = Apple  skin x 1/ pulp
or
pulp x core/ pulp = Apple  skin/ pulp
core = Apple  skin/pulp
Now let’s use the above process to a specific apple equation.
12_{Apple} = 5_{pulp} x Core + 2_{skin}
We first remove the skin from both sides.
12_{Apple}  2_{skin} = 5_{pulp} x Core + 2_{skin}  2_{skin}
We are left with the following apple equation.
10_{Apple  skin} = 5_{pulp} x Core
To remove the pulp we divide both sides by the pulp.
10_{Apple  skin}/ 5_{pulp} = 5_{pulp} x Core /5_{pulp}
2_{Apple  skin/ pulp} = Core
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