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The Jigsaw Puzzle


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I grew up working on jigsaw puzzles periodically. It was a tradition at family gatherings for Thanksgiving and Christmas. A card table in the corner of the room had a new puzzle, the pieces were simply dumped out of the box onto the table. As life has progressed, I've found out that we were not "purists" when it came to this activity. You see, we committed the "sin" of leaving the box top there to be looked at by anyone working on the puzzle or not.

There are jigsaw puzzles applications now. One doesn't have to flip the pieces so that they are all face up. The particular application I use, the pieces all happen to be oriented so they cannot be rotated. When two pieces are aligned that do go together, they are joined together with a audio "click".

The audible "click" does not come in the traditional boxed puzzles. Interlocking pieces offer various visual clues, but even these can be overlooked early in the puzzle, only to be straightened out when it is discovered that they do not fit with the progression of the puzzle overall. Such pieces fit together, and if the portion of the two visual parts do not align while the edges do, you can either leave them together for the time being, or take them back apart, knowing you'll have to do it later if you do not. This isn't as obvious if the pieces are part of an expanse of blue sky, or perhaps a calm lake reflecting a blue sky. With these, it is only when you discover that the pieces actually go in two different locations. Usually, in these cases, only two or three pieces fit together, which simply won't connect into any other part of the puzzle as grouped together.

All of the puzzles I've ever encountered resolve into the equivalent of a perceptual, first level concept. They are the equivalent of a photograph of only things which can be photographed, applied to a cardboard (or equivalent) backing, and then cut up by one of the finite number of dies that render them into the final product. The 3-d puzzles are a variation on this theme.

The following was brought up about fitting information about reality together. On disk 18, track 3 of Objectivism Through Induction starting at 7:45:

"A better analogy is solving a jigsaw puzzle. Suppose that among the pieces of your puzzle, someone has added a few pieces from a different puzzle. As you go about solving the puzzle, the extra pieces will make the process more difficult, but they won't ultimately stop you from reaching a solution. Nor will the addition of outside pieces lead to a false solution of the puzzle that incorporates these pieces because the outside pieces just won't fit. This analogy illustrates the process of induction is one of classification and integration, not of computation (eluding to an earlier analogy in the letter) or deduction."

Read from a letter by Paul Blair(sp?) who thought this analogy may have come from Harry Binswanger.

The ultimate puzzle. The conceptual puzzle. Pieces that looks as if they fit. Some of them can even create rather large sections that fit together so well as to give the impression that the group of pieces have to fit into the ultimate solution.

Still, I am not a purist, not in the sense that the box top must be set out of sight, and not referenced during the course of solving the puzzle. The "box top" is all around us. The challenge becomes fitting the pieces together without the benefit of the audible click of a set of speakers hooked into a computer which has been programmed to generate such a sound when two pieces have been assembled correctly.

 

I eliminated television from my life in 1985. I purchased a widescreen monitor in 2010. I bought the TV Series "Columbo" I recall seeing the first few episodes and was disappointed in the fact that the crime was the opening of the show. Still, I found myself enjoying the show. Columbo would just keep playing his part, asking questions about the things which did not make sense to him. One show, that stands out in my mind is when he used "subliminal messages" embedded in a film to solve the crime. The notion was putting a frame into the picture that would flash for 1/30th of a second. The unanswered question to me remains that is it a long enough duration to register on the mind, otherwise, how can it have any impact?

Receiving the series "Bones" for Christmas, it is the reverse of "Columbo". Usually a set of remains are discovered, and all of the requisite evidence is sifted out from various observations of the team on the case to narrow down and identify the perpetrator of the crime (some of them leave open the question if a crime was even committed). The show is too fast paced, and the claims made that serve as evidence would have to be looked up to see if they correlate with actual forensic data. For now, I've relegated the show to entertainment, not placing much stock in the science presented as matters of fact.

 

The shows, themselves, represent sub-sections of the ultimate puzzle. As a work of art, they communicate the artist's metaphysical/epistemological values judgements. These get intertwined with one's own metaphysical/epistemological value judgements.  Reading Atlas Shrugged again, I find that there are many details I have not noticed in prior readings. I've found this in the sensuality of finer distinctions, as well as general overviews of wider themes dispersed strategically throughout the book. It is as if the puzzle pieces themselves are comprised of puzzle pieces, which may or may not have been assembled correctly.

 

A systematic approach to solving a puzzle can be reduced to taking one piece and trying to fit it with the other 999 pieces in a 1000 piece puzzle. If the edge pieces a produced with an interlocking side (instead of the obvious straight edge), this can amount to 3996 combinations to be tried, yielding several combinations which may seem correct. For larger puzzles, this amounts to the total number of pieces less one times contrasted against the total number of sides of the pieces times the number of sides of the piece being fitted.

The recursive aspect of this approach is considering the relationship of conclusions to their propositions, with those propositions as potentially being conclusions to other propositions, which ultimate reside in the concepts that make up a proposition's validity residing on the referents giving rise to the validity of the concepts being used in the proposition. The recursive nature of this process ultimately terminating at the source of all knowledge: existence, identity, and consciousness.

Hopefully, this hasn't been too puzzling.

Edited by dream_weaver
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When sitting down to a puzzle, the pieces poured out on a table, you are faced with a sea of pieces, some of which display the grayish belly of the cardboard to which the picture is affixed, others providing a small cut-out shape with a small portion of the picture on the box-top. One of the first tasks toward solving is flipping all of the pieces over to reveal the small portions of the picture.

During this process, and one I still practice to this day is separating the edge pieces from the rest, by the readily identifiable edge pieces possessing a flat side. On a puzzle which is oval or round, this would be an edge which contains neither an "innie" or an outie" — the distinctive rounded slot/tab that fit together in such a way as to interlock the two parts.

Again, not all puzzles are created this way. I've encountered puzzles where internal pieces have flat edges that fit together, held in place by the "innie"/"outie" configurations of the pieces surrounding them. There have even been puzzles comprised of triangular or irregular shaped pieces that get fit together strictly by the arrangement of the parts to piece together the "photograph". To this, all I can conjecture at this point is that the fundamental task consists of identifying the logical approach used to ultimately integrate the pieces. This correlates with what Miss Rand wrote in ITOE as " the fundamental concept of method, the one on which all the others depend, is logic.

If a puzzle company decided to generate a puzzle which could not be put together, where the pieces could not be integrated into a whole, how long would it last? Part of the "fun" of assembling a jigsaw puzzle is seeing the "payoff" of experiencing the completed result. If a puzzle consisted of just two pieces, and the second piece would not fit in any way with the first to form an expected result, such a puzzle would not fit into the concept of puzzle and would be rejected by those expecting the pieces to fit together ultimately.

 

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The analogy of a jigsaw puzzle is imprecise, yet some of its parallels are compelling. An art critic can encounter a work of art and point out things that are missing or present that another patron of the arts may not have noticed.

Regarding a puzzle, the completed solution can be resting on a table, where an observer can see that the puzzle is complete, that there are no left over puzzle pieces, that the completed whole is in accordance with the scene on the box top. True, the observer may not have put the puzzle together, true the individual that did put the puzzle together may say that unless you have put the puzzle together yourself, you have not put the puzzle together yourself. 

True, you can go thru the process of putting the puzzle together yourself, but what if you have stood by and watched the puzzle being pieced together?  You see the pieces being poured on the table. You watch as puzzle aficionados assemble the various parts of the puzzle time after time.

Rand indicated that accepting her on her word amounted to an equivalence of accepting her on faith. Given the number of puzzle pieces that have to fit together in order to form the completed picture, True, you have to be able to show that the parts go together a certain way for someone else to see it in the same form—does that mean you cannot recognize when the pieces are being miss-assembled, although you cannot point out why?

I don't think I am arguing Kelly's 'unbounded tolerance' here. In an interlocking puzzle the parts can seem to go together in a multiple of different ways. If someone is wedded to their particular arrangement of pieces, (including how Miss Rand presented them), understanding how they fit together can amount to each trying to fit their round peg into the other square hole. 

If at an impasse, how do the pieces ultimately get separated and then re-segregated in order to complete the puzzle?

Are we back to epistemology, anyone?

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