The Stone Tool - The PjProblemStrings Sequences
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Expressions Of Pj Problems
The Stone Tool - The PjProblemStrings

The Stone Tool

The group of Hominids (humanlike creatures) called Homo Habilis (able man) lived in East Africa about 2 million years ago. They invented the stone tools, the first multipurpose tools. There were no formal education systems at that time, yet these Homo Habilis were able to pose and solve (albeit minimally) perhaps the most important mathematical problem of humankind (the making of tools). In order words, unbeknownst to them, they were mathematicians posing and solving Pj Problems (see wrong views of mathematics).
(a) What Pj Problem was on the minds of Homo Habilis that led them to conceptualize the stone tool?
(b) Assume stone containership and identity to be given and the stones are laid out to be toolified. Sequence the PjProblemStrings from this point to the toolification of the stone.
(c) How much difference exist between the PjProblemStrings Sequence involved in the making of the ancient stone tool and a modern tool like the automobile?

The Stone Tool

Prerequisite Reading - Thinking With Numbers
The strings: Pj Problems S7P3A32 (force - push) and S7P3A31 (force - pull) are of interest.

(a) A tool to exert force (P3A32 and P3A31) was on their minds. Homo Habilis though able were initially poor hunters because they were tooless. They ate plants fruits, roots and carcasses. They conceptualized digging up the roots and chopping the plants. These were the first functions of the stone tool when they invented it. They later used the stone tool to scoop out the meat of dead animals and to crape open bones for their marrow. Eventually, they weaponized these stone tools against animals and against themselves. Thus began the arms race.

(b) Containerships and Identities are assumed known. Pj Problems of interest reduce to the Pj Problems representing fetch, chip and store. Equilibrium implied in each stage.
Fetch: source of fetch, the space where stones are laid out. Destination, the palms of the Homo Habilis.
So, fetch Pj Problems: 3141 (force-pull causing linear motion).
Chip: Stones in each Homo Habilis palm, he begins to chip by balancing one stone and using the other to chip. This process involves both linear and rotary motion (to shape stone).
So, chip Pj Problems: 3241 (force-push causing linear chipping) and 3242 (force-push causing rotary chipping).
Store: the destination of fetch becomes the source of store. The destination of store does not have to be the source of fetch
So, Store Pj Problems: 3241 (store)
So, desired Pj ProblemString Sequence: 3141324132423241. Recall numbers are read as ordered pairs.

(c)The ancient stone tool and the modern automobile are fundamentally similar in the sense that they are both man-made tools. However, the fundamental Pj Problem posed by Homo Habilis that created the ancient stone tool is different from the fundamental Pj Problem posed by the modern humans who invented the automobile. The Homo Habilis were interested in a force tool while the inventors of the automobile were interested in a motion tool for passengers. Consequently, their PjProblemString Sequences differ. Particularly as to complexities. Nonetheless, given the same assumptions, the sequence for the toolification of the automobile is a multiple of the sequence of the toolification of the ancient stone tool. In other words, the latter is contained in the former many times as a result of the many containerships and identities involved in the former.


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