And more pieces that don’t make sense unless you’ve read everything up to this point.
Having said my piece I wish to discuss not only official strategies used but personal methods even more than any firmly fixed approaches and answers, lateral and vertical thinking to approach problems. I mention that what is here is commentary on problem solving and in the majority personal and informal approaches more than textbook ones. They are alternative ways to view problems, approach solutions, ways of thinking. Emphasis on that. And not only to address problem-solving related questions they may have, but also that whoever reads this to carry a piece of all these years of theory-making, in the most theoretical sense, with them. With this I begin this piece.
Involving Strategy, Problem Solving, and other Theoretical Game boards
A conflict. A solution. Two or more players. A problem. That is the set up of which we continually discuss as the design comes back to the idea of a problem presented to two or more parties and the prospect of its solving it. Let us discuss the word “problem.” What is a problem and how does it originate? A problem is an impasse, an issue, a difficulty, a sort of dilemma which presents a situation for those involved. A problem that can be straightforwardly solved, a complex problem with no easy solution, a problem by which neither player will be easily satisfied with the others’ solution. Or a problem without apparent solution. The word problem itself embraces the idea of “discrepancy”.
One might be prone to think the word problem is more overstated than it ought to, but I assure you than it isn’t. Unless we were to exist in a stagnant world conflict would not exist, however, that not being the case, problems arise every passing minute and second somewhere from ordinary disagreements to colossal dilemmas. The conflict between two neighbors, the conflict between co-workers, the conflict between two sport teams, the conflict of survival between the hawk that hunts for food and the rabbit who disagrees with the hawk’s prospect, the clash between empires, among many others. One does not have to look far to find conflict in a myriad of ways. Everyone encounters problems and everyone has to deal with them.
Everyone deals with problems everyday from the most basic ones such as waking up early to go to work or to attend an educational institution to working on difficult projects. See, a person is in constant need to be capable of solving all sorts of problems he or she encounters. Problem solving is a fundamental part of existing. We are inherently masters of every day problem solving due to our ability to reason that allows us to breeze through all types of encounters, however, we don’t think of us that way because how swiftly we handle them like they are second nature to us.
Problems vary yet we all without a doubt go through and undertake all levels of problems which we manage to solve daily with great efficiency. Difficulties and dilemma are in its most fundamental structure, without stating their precise complexity, certainly they are problems.
So before getting into problem solving we talk a bit about the sort of categories there are. We begin with the simplest problems which pose no difficulty. These can be referred to as “mechanical problems” because they are solved without a second thought. Opening a carton of juice is no problem as the process of getting it opened is automatic. So is turning on the faucet, a light bulb, or knowing that to reach a higher location one requires a ladder or any object to stand on. There is no real thinking involved so we don’t think of them as “problems” since they pose no difficulty to us. In one word, they are like reflexes.
Then there are problems “solvable by practice”. Problems that are neither as complex as getting the solution of an intricate predicament nor as plain as mechanical problems. We can think of them as problems which one may find them to be, initially, to some extent challenging. For instance, there several abilities one doesn’t know until he has mastered them such swimming or learning to drive. Psychical labor for example requires certain processes to be followed to be done correctly. When we have already successfully conducted these actions the next time we encounter them they are not as difficult as the first time. Eventually the process, the problem in question, becomes easier to solve each time until a problem stops being one.
“Constant problems” are issues which despite being previously solved prove to be challenging no matter how many times they are solved. Think of them as problems that have changeable or too many variables to consider. A type of problem which goes beyond one’s own capabilities and grasps, one that isn’t easily solved. Not necessarily for lack of skill but indeed a problem that in spite of oneself is inherently challenging no matter what. To provide examples, from real life occurrences to nature to even a person who one always have difficulty with. A problem is constant (note. not unsolvable) because it might be easily solved at one time then it might not be solved as easily or at all the next time – reason being variables that change each time.
“Inconsistent problems” are problems that have no easy solutions. Problems that emphatically go beyond a person’s control. Problems which the solution may not be a good one for everyone, creating complex dilemmas. An insoluble problem with an unreachable solution even. A problem whose solution no one agrees on. We call them inconsistent because the solution is not absolute or evident from the start or at any phase. The idea that the solution is never explicit and the disagreement in which it ought to be approached provides the reason why a problem is inconsistent.
These are the most frequent types of problems I established by myself regarding standard predicaments arranged by difficulty. Are they enough? Not nearly but they are sufficient enough to cover a part of the basics of the concept of “problems” which we address. Note they are vital. They are not rigidly connected to problem and solutions field which concerns solutions and results but one focused on the process and requirements required to solve a problem. With first list and with this piece my intent is to expand how one perceives problems and similarly to illustrate how often one encounters them in all forms and levels. As you can guess, this whole piece is dedicated to problem solving.
* Exercises in Observation
Imagine then the following scenarios which none of them are pure problems but instead observations. Say the first thought that comes to mind as you go over them.
– You see a dented car parked on the street.
Another car was not necessarily responsible. Isn’t it possible that an angry neighbor hit it with a blunt object? Isn’t it possible something else other than another car caused it?
– Someone opens the fridge, takes out an orange juice carton, drinks only a bit and returns it to its original position after making a displeasure expression. What is the reason?
There is still juice left. It hasn’t gone bad either nor is the problem that she dislikes oranges. Isn’t it possible she has just brushed her teeth a minute before hence the reaction?
– You see a person walking down the street with a visible bad haircut.
That he went to a bad barber, that a family member wishing to become one needed someone to practice? Why not imagine he lost a bet the other day?
None of them are conventional answers but they are quite possible for those scenarios as it is possible to be answers to solutions one hasn’t come up with. There could a scenario where any of these results actually happens.
Sometimes the obvious answer is indeed the obvious answer such in the case of a person taking out a book and putting on glasses means he is going to read. Or a person taking a pen out means he is going to write or draw with it. And asking the time is exactly, asking what time it is in actuality. On the other hand, we also must be aware that not all problems have the same solutions, hence not all common answers fit all the possible questions.
Indeed it surprises us. When the answer is different than what one imagines. One is naturally surprised, amazed, even sometimes shocked because the result is unexpected. Because we know a premise doesn’t necessarily mean the result will be the same as the one we imagined based on what was assumed. We assumed what the premise was. We assume the end result based on that. This is not always the case.
Those are natural “counters” encountered in everyday life where the answer varies. Occurrences and problems of other possible solutions than those expected and assumed. Problems where it is possible to theorize multiple possible solutions from a sole problem. In other words, what the mind does habitually and crafts as it encounters indefinite occurrences which we refer to them as problems. In one word – a theory.
Concerning Reasons why to Solve to Problems
By now your interest grows as we approach deeper to the field of problems and its applications. You are ecstatic, bored, or even lethargic. If you feel as if your interest grows then you are like me then you find problem solving and its implications to be mysterious formulas. If not, then you, who are not inherently interested in it, solemnly ask – “why”?
Perhaps based on the examples above you already have the answer. By having followed this far into this matter I think you dear reader are most interested in such speculative matters that have been so extensively written about before and currently. I strongly believe there is a degree of interest in the field or in its implications that piques your interest, other than my meager colloquial writing on other matters.
After that I say, “if you are reading this it means for some reason or another you find such long tedious discourses entertaining”, which I wish them to be considered thought-provoking nonetheless. With that I confess that that is probably something I thought I’d say sooner or later as it is a line that I considered in more than one occasion.
I’d like to think the theorist in you is interested more than simply a good story and wishes to read these type of discourses and is deeply passionate to read the train of process of another theorist similar to yourself. There is something fascinating about problem solving. Thinking of the variables to consider, thinking of multiple solutions, thinking of the prospect of solving that which was believed to be “challenging”. The concentration needed, the solution as it is found, the swirling in the stomach and the stimulation to brain as an entire self tries to reach solutions.
– That is probably what many would think I would say. And they might be close to it.
The emotions and the ritual from solving problems are best understood for those who fancy those theoretical problems and those who search for solutions rather than expecting to be given answers. For they rather look for the solution themselves because /it is better that way/. That is who the reader is dealing with.
Let’s lightly address common scenarios where thinking gets complicated, where possible mistakes happen and what to keep in mind.
Common Scenarios and Whether Isolated Events are Related
[A] or [B]
It is rarely that a problem is so straightforward as to have one or three main problems. It is more common and interesting for the problem to have multiple parts. The more complex the problem, the more parts it has after all. This would be what a yes or no, an A or B problem would look like if the possible answer would be one or the other.
Problem A ,Problem B, Problem C
\ | /
A common scenario is one where multiple events happen and the problem solver wonders if the events are related in actuality. It’s the standard dilemma of whether a) they are or b) aren’t. The question is simple enough but the solution isn’t always. Suppose multiple events happen. Let’s suppose that an important item was stolen from a study room. We’ll refer to this event as “Event [X]”. We don’t know the reasons behind it, we don’t know who did it, and we only know that the item was removed from where it previously was. Additionally three other important events happen very close to it which we’ll refer to as problems A B and C. How does Event [X] fit into these variables?
The problem is that one does not know how related *this* Event [x] is to the other problems. If the stolen item has to do with Problem A then the problem solver is all set in case that’s the correct path. On the other hand, if we attribute the Event [X] to any of the other two Problems (B and C) we’d be off base. It’s as if we are adding to a number we shouldn’t instead of the correct one. To follow that analogy, applying the amount (though correct) to the wrong number will inevitably give incorrect conclusions as they are not indeed related. Suppose a rather suspicious person is seen leaving the room in question. Said person could be related to the incident or not. Assuming he’s not (in fact it’s related to another event, say B) if we attribute this event to the wrong piece of information it will give us the wrong idea of what happened.
/ / | \ \
[A] [B] [C] [D] [E]
Event [X], Event [Y], Event [Z], Event [etc]
Of course, this is all to give a better idea of what we mean because actual problems aren’t so straightforward. There isn’t only one event. There are many events and those events have be attributed to the right variables for the rest to make sense. It would look something like what is above but more complex and other variables. It’d look like a large string of letter and events and smaller categories where they are connected.
Equivocations, other Red-herrings, and the Dilemma of Extra Pieces
Mentioned briefly concerning events or clues and we expand on that concept. Naturally, in the same way one can make the correct decisions one can also make incorrect ones. If one wouldn’t then there would never be mistakes and that is simply unimaginable no matter how masterful the problem solver is. If so, one inevitably encounters the recurring possibility of attributing the right clues to the wrong problems. That is always a possibility, after all.
This is very important. Always keep in mind that :
“Not because A happened means that B necessarily occurred”
For instance, a loud sound is made and one finds a closed door that was previously wide opened. It doesn’t necessarily means it was the sound of the door being closed. Not necessarily because something can’t be found within the first minutes means it is gone, as it could be very nearby. And even rare as it seems not because an individual takes out an umbrella means rain is coming that day.
It is this powerful and proven concept grand magicians and illusionists abuse to fool the senses into believing an action or event has occurred while in reality it hasn’t. This “association” one makes when two events take place closely to one another that makes one assume they are related. They are masterful tricks that fool the senses, which in a way they are like red-herrings that turns one’s attention away from what actually transpires.
It is commonly here that one makes “blunders in reasoning” while solving a problem that leads to incorrect conclusions by assuming “because A happened B occurred as result.”
Solution to a Problem
/ / | \ \
[A] [B] [C] [D] [E]
[Extra pieces] , Event [X]
We refer to “extra pieces” as pieces that are not part of the Puzzle.
This is an interesting concept that I’ve noticed – the idea of additional pieces of information and how one deals with them. I’m more used to referring to them as “extra pieces” rather than “red-herrings” as I was initially familiar with this concept rather than the formal term used in mysteries but I found that the same concept applies, reason being they both follow similar principles. A red-herring is a piece meant to distract the reader and momentarily hide the real solution of the problem. To illustrate, imagine a jigsaw puzzle. One only needs a certain amount of pieces to complete a jigsaw puzzle, correct? That is to say, any piece that isn’t part of the puzzle isn’t needed and would only confuse the individual.
In summary, there are pieces that fit right away, others that don’t seem to fit, and lastly those who don’t fit anywhere. If they don’t fit in any space on the board then it is quite possible the pieces do not belong to the puzzle. A problem occurs when the puzzle solver assumes that *this* (or these) extra piece /does/ go somewhere when in actuality, it doesn’t. It’s important to remember that even if a puzzle is made of multiple pieces it does not always mean that all pieces presented /are part/ of the main puzzle.
If the metaphor seems unusual then imagine an scenario where pieces of another puzzle have accidentally meshed with the one we are working on. Naturally, all the pieces we need will fit the main puzzle and all the extra pieces won’t because they don’t belong to the main puzzle.
Similarities between puzzles and mysteries are striking and I’ll have anyone know as both of them are in essence problems to be solved. Though I’ll mention this similarity is on a more metaphorical level concerning multiple scattered pieces, the act of putting the pieces together, and reaching solutions. Why not, also solve the problem.
Indeed, there are differences between puzzles and mysteries aside from the traditional clue searching and all that it entails. In an actual puzzle there are no actual “main events” like in mysteries, for example. There are /only/ pieces and more pieces. If there were something similar to that concept it would be the “images” the puzzle is composed of that give away the “theme” of the piece. A puzzle is the complete image of a figure that initially makes little sense and that it only starts to make sense once the pieces are put together. Once most of the pieces are put together the puzzle goes from nonsensical to logical providing a more concrete view. Once all the pieces are put in place the puzzle is complete. It makes perfect sense. Then I ask, are puzzles and mysteries so different after all?
If there is one thing I wish to stress in this section, and with this example, is to not exclusively look at a problem based on its definition, nature, or genre, as it limits one’s perception, instead to look at the /idea/ behind them. On that point, the intention here is to show that the concept of “problem” and “pieces” (ergo a puzzle) are both closely related to reaching a solution.
If an actual puzzle is a set of scattered pieces that belong to a board and form an image then a mystery contains pieces of information concerning a theoretical problem that only when placed in place makes sense and reveals a solution. A general problem is a sort of dilemma of unknown difficulty that requires a solution, reached by thoroughly analyzing all possibilities.
Tools of Trade and Lateral thinking. Impossibilities and Mystery Showdowns with the Masters And other Supplemental Mental exercises
And if so in the thinking process one requires tools to assists oneself to tackle these intricate and multiple problems. For that one requires a creative mind in every sense of the word. We require an open mind that can think of various alternatives for the same problem. This thinking will help us to remind us that we can continue reasoning even a problem appears difficult or be over. Be mindful that the methods to reach a solution are not one but often many. Not all problems are straightforward to have one single solution, for that we ought to always consider alternatives in our thinking in addition that it tremendously improves our conclusions and thinking.
It is not necessarily that because a certain premise is assumed the outcome is evident as a result, what we presumed it was. Note that there are naturally straightforward occurrences but often we forget that there are also those which do not follow any assumed premise. Here is where the possibility of jumping to conclusions of both ordinary and elaborate occurrences takes place.
So there no footprints in the snow near the corpse. The windows were locked from the inside. There was no way anyone could have entered the room. The victim dies in front of everyone yet the culprit is unknown. According to evidence no suspect could have traveled that distance in so little time. Witnesses are sure no one passed by or entered the building. How could any of these be possible?
Yes, impossible. Inexplicable events which appear impossible are made possible.
* A man is threatened by a rural town’s popular figure called the magician of crime after he makes a fool of him in public. The man holes up inside a tower just in case. It becomes a huge incident in the town and policemen keep watch outside the tower so no one enters it, making it a locked-room. Of course throughout the piece all policemen assure us no one suspicious entered the tower. They were correct.
Of course, the man is found dead up in his room upstairs sitting in a chair as he was reading a book. But before that the victim calls the detective’s friend telling a cryptic message before he dies. When they visit the scene of the crime the police deduces the cause of death is arsenic poisoning. The only remaining soul in the whole tall locked tower is a house cat.
It was afternoon that I picked up “The Night of the Wolf” and proceeded to mechanically solve the mysteries it contained the following days. Rest of the details are left out for the sake of time, however, one can theorize how any of them might have happened without having any names of the suspects or motives. It’s not mandatory to obtain all the pieces to make relevant conjectures. This much is plenty to create a theory. This much is enough present a viable solution.
* If it is a real locked-room then it was impossible for any man to enter or leave the tower so poising the man directly is impossible. Because it was impossible for the culprit to escape due to the police surrounding the tower before and after the crime was committed it reinforces the idea that no man entered the tower. Therefore, no man went inside it (or left it), the victim included. We could focus or ignore the main suspect, the magician of crime, who is the person who had threatened the victim but it doesn’t do anything for us unless we know how he did it. Finally, and most importantly, there is the matter of how the victim died – he died of arsenic poisoning but if it had been arsenic poisoning he would have died immediately unable to call for help. This is a contradiction.
Meaning? It happened very slowly. Meaning he took small doses of it -> meaning he naturally wasn’t aware it was poison -> Meaning he used the phone before he died as he realized his mistake -> meaning it was unintentional. Of course he wouldn’t drink anything suspicious -> meaning naturally the way the poison was poured in was not liquid or was unfamiliar to the victim. Meaning?
Meaning the following conditions: 1) the poison was cleverly disguised in an object the victim would not consider suspicious. 2) The poison was distributed in small doses. 3) And it was not a drink. One final question one asks: why did it work then? Because the culprit knew this was a certain way to kill the victim. What does this tell us? Reason being the culprit knew the victim well so much the culprit didn’t have to personally go inside the tower for murder the victim – as it was possible to accomplish it without setting a foot in the place.
You see, the how and who are connected so by learning one can deduce the other one. It’s much like Sudoku telling you what number you can use for the adjacent blocks. Up to this point, you have 3 suspects, which are actually two. The magician of crime, the doctor who used to be friends with the victim (and the magician), and the detective’s friend. The rest of the characters are culprit-wise immaterial since they are not the culprits. Finally, when you reach the final pages, the mystery reveals its final clues so the puzzle can be put together. By the time the mystery emphasizes the victim’s “cat” and a “book” delivered to the tower, the same book the victim was holding. By this time you only need this information to confirm your main theory rather than provide you with information. You now know how the culprit did it and who did it.
Then the mystery is solved before you flip the page to read the official detective’s solution.
”What Does This Tell Us? “
Nothing exists out of nothing for everything consists of other pieces and attributes. Whatever one can imagine can be broken down into prime elements. This applies for solid and abstract elements for they are made of other materials and ideas. A building is constructed from wood, steel or cement and supported by other materials which in turn these materials are supported by small ones. A story is divided into intro, middle, and its ending. Water is consisted by other elements. A laptop is made of several components that make it work. Without these elements they wouldn’t be it. They wouldn’t be what they are. Like one’s personality and peculiarities are part of oneself, when all these pieces are put together they become you.
For reference one can hypothesize with moderate high success the “state of [X]”, the matter or subject in question, depending on its present components.
*At the moment of shaking hands both individuals facing each other will extend their respective right hands unless there is a reason why they can’t. Depending on the amount of books one imagines an individual has an interest in that field. Unopened letters that haven’t been collected hints there hasn’t been anyone in the past days or weeks. Pet food indicates someone in the apartment own a pet.
No magic, no tricks, only accurate reactions and sound deductions based on what one sees. This is what it is, and what it has been all about – classic common sense.
We speculate what type of person lives in an apartment by paying attention to surroundings; the style of the apartment whether modern or classic may reveal the person’s taste and age; the number of plates, glasses, and chairs around the table may indicate the number of inhabitants; clipped coupons mean the person is wise with money. Whether the person has an artistic nature or not can be deduced from the paintings and decorations kept around the place. The gender may be reasoned from the paint colors around the house as well as the feel of the place and other subtler clues. The number of appliances, furniture, electronics (or lack thereof) and the quality shed light on the person’s finances. Moreover, the number of commodities and luxuries emphasizes his or her financial position. Having good wealth raises the chances the person having traveled abroad. Similarly, but not exclusively, the bathroom’s mirror cabinet would tell you that person’s health condition. Lastly, the contents of a fridge would give clues as to the person’s life style. Do you see where I am going with this?
“That is rather outrageous?”, one retorts.
But is it? Are these conjectures not accurate? Not likely on the mark? They would off if they were based on random guessing but they are based facts, on what’s there, educated guesses. The reason why they are close to reality is because as mentioned before everything is made of parts, made of small fragments that make up what they are. In the same way so is often one’s actions. One lives according to his or her means, preferences, and own style. One buys the brand one likes, one affords the car one can afford, otherwise it’ll show around the place anyway. One buys orange juice because one likes the flavor and vitamins. One’s wardrobe indicates the person one is showing the world. Fundamentally, what one does, doesn’t, has, and don’t have, are parts of who one is.
It is in this point that I wish to highlight that the main key to deduction. It is here that one emphatically remind us that /there are details all around us./ Details that one can observe, inquire, and thus conclude. While it is to be noted that the numerous factors that make up an element can be vast, vast enough to one can’t t figure them out all, and the more intricate the element is the more challenging it is, the most prominent factors tend to remain reasonably available.
And one can induce tremendously from the simplest details. One can know plenty from details without even meeting this theoretical person in the example presented. It’s all a matter of paying attention. What one calls deduction is directing our attention to the already existing clues. Back to the principle that “nothing comes from nothing”, we, everything, is made of multiple pieces. And so who we are, is presented in everything around and within ourselves. Metaphorically, walking books. Then if they are present, we can make use of our power of observation and deduction.
But doesn’t everything come to down to observation when you think about it?
One should neither underestimate one’s accumulated knowledge nor be too complacent with what one has. Because one can do plenty with what one has already learned and because there are always more fields to master. For the informal theorist, is not rare to find they already knew a method or term long before realizing there was already formal equivalent. Realizing that one already carries that knowledge in a different way but hasn’t explored that idea enough. Realizing that what famous bestseller authors tell us is common (yet very important) knowledge and that in nutshell what appeared to be completely new information was information we already knew in some way.
The difference is that seldom such information is viewed in new ways, rarely applied to other scenarios, and most importantly put into practice. This must encourage the thinker as it is a positive sign of a thinking creative and boundless mind – for not necessarily the older, heavier, and wordier a book is indicates quality and value.
One can learn from anything since even in simple occurrences and plain problems there are lessons to be learned. These are simple observations based on what’s there.
I am convinced you, reader, possess information that I don’t for sure. This is not an assumption but a certainty. Based on experiences, teachings, skills, background, and knowledge we all amass great number of information all our lives. That’s what our minds do. We receive and transmit information consciously and unconsciously 24/7, 365 days of the year. We are practically walking libraries of information. We start out with only a few books, quickly it becomes a stand then a whole section, soon we have to organize our books by alphabet letters. The next thing we know we end up with our personal libraries that embodies one’s accumulated knowledge consequently being part of who the individual is.
So you ought to go back to what you already know and see how that you can apply that knowledge to a problem. There you’ll find that there is certainly curious information in your archives that can help you tackle any new complex problem.
This informal or formal act of deduction that a certain genre has claimed as if it were its own? In mysteries the readers are supposed to carefully read the story and pick up clues while they read until based on all the clue presented and /found/ (because one doesn’t necessarily catch them all) then presents the best theory to the other player (who is no one else than the author) – who the reader has imagined the culprit is.
In many occasions it pays off, while in other one misses some subtle clues regarding the culprit. Still one learns plenty. In my opinion, mysteries are a great game of observation, imagination, deduction and wits. These concepts catch my interest.
Having written this much about deduction and problem solving, a respect and fascination for the detective figure is inevitable. I must admit that I find the idea that “the detective must not miss any clues”, as if the idea he embodies is the culmination of observational skills, fascinating. But the detective is fascinating. Not as flesh but as a figure. Here is an individual who will surely find and know the importance (sooner or later) of the necessary clues and without fail solve a problem.
And so this ritual also has two players playing the same game looking for the same end result. On the other side of the board there is the audience who are told the clues and who compete with the detective to solve the same theoretical problem. It’s a profound battle of wits like no other, against time, and also oneself. Page by page hard intellectual action, if you will. To solve puzzles, to solve problems. If this is not a fascinating experience for the mind then what is.
At some point, I did proclaim that alibis were not as important. Was the claim outrageous? Do I still believe it? The theorist ought to not be inflexible as granite but his mind ought to be nimble and creative. Instead it ought to mold and adapt to other ideas and concepts. Same as the theorist ought to also hold a neutral mind that questions ideas rather than denies what the problem solver comes across. And so I speak for myself, concerning alibis, when I mention that in the past I proclaimed that alibis were not as imperative. But this is because they are not final.
I’ll say that I prefer my personal problem solving methods when it comes to putting pieces together. There are occasions when alibis can be optional factors despite being exceptionally crucial to the investigation. Recall that in spite of it the culprit could still be someone with a strong alibi, I’m certain you’ll agree after being presented with this common scenario. Let’s put it this way. In some cases despite existing strong alibis a group of suspects are still suspects. Similarly, not just because someone lacks an alibi implies culpability. Do you see what I mean?
The more chaotic a game becomes the less relevant alibis become when they can be easily fabricated or when they can’t be properly corroborated by anyone. Here is where my take on it lies. Alibis are a sturdy tool but they alone won’t necessarily provide a culprit’s identify. For that, other clues are required and our thinking to consider all other hints and mechanisms behind it.
* So there no footprints in the snow near the corpse. The windows were locked from the inside. There was no way anyone could have entered the room. The victim dies in front of everyone yet the culprit is unknown.
According to evidence the suspect could not have traveled that distance in so little time. Witnesses are sure no one passed by or entered the building. How could any of these be. Perhaps that can’t be know right away, however, what is real is that something happened and that there are clues everywhere that can be picked up to arrive at a solution. One just have to look for them.
We need end this section with addressing perhaps the most popular field of solution making that is game theory and also a reminder that the theoretical is still theoretical. That even if the field is fascinating and a more formal technical approach to problem solving. The field is not almighty though as one can imagine. Game theory also has its limitations due to the mighty impossibly it tries to accomplish, that is, solve a problem, solve multiple games, and solve a game with multiple players.
Consider then knowing five out of a player’s moves but being short two. These last ones could be moves you /hadn’t considered/. These two could also be moves you /didn’t know they existed in the first place/. Yet you assumed there were only five moves while in reality there were two more. This is not uncommon, on the contrary, it is standard.
Same as one could only know what one is aware of, all of the other moves one doesn’t consider them. Therefore, the reasoning is never flawless. That is right. There is no way a system or a player could know – all – the moves the other players can make under normal circumstances unless the game in question and the players in question are so straightforward. These hardly being the case in real situations, the games are impossibly complex.
And so, one as ever, rational to a fault, creates a game and a system that takes only the most rational course of action as its foundation. So we base our moves on logical and strictly mathematical approach to obtain the closest theoretical answer to a real problem. So we create a field that attempts to solve actual problems “based on theory.”
Where it errs is when it assumes all players behave rationally, which one realizes that is not always the case. It limits the players’ moves to only a few. It assumes all players will make their best moves at all times. It tries its best to calculate a result based on what it assumes only to exist. Don’t think that Game theory is oblivious to this flaw. The field is perfectly aware of it but it also realizes that in order to theorize they must reduce the number of variables, inconsistencies and instead create an organized equation, turned an originally unworkable problem into a solvable problem, which they can realistically solve.
In conclusion, even then we are still only theorizing. Reality is not as simplified as that. Reality is much more complicated than a conventional theorem of equations playing fair by mathematical rules. Being realistic about it reality is full of constant problems and less gracious then ones presented in theory then why not think of ways of solving them while one is at it. Be actual ones or even theoretical in nature, one of them may eventually lead to more solutions.
One problem at a time.