How to Theorize and Solve Problems
You're sure you have a theory for just about everything perhaps. There's a right way and a wrong way to go about theorizing and testing your theories on solving actual problems. In this article, learn a good way to construct a theory.
Steps
- 1Investigate the existing theories; gain knowledge of how people think about the thing or problem already -- it can only help.
- 2Decide whether your theory contains a hypothesis. If there are no existing theories. Because, if it does, the Scientific Method was designed to handle very, very many hypotheses.
- 3Learn all you can about the Scientific Method of Investigation, because, done properly, it comes up with practically irrefutable theories!
- 4Ask yourself if your theory is widely applicable, by which it is meant that are there are many members in its set of potential users, and are there many members of the set your theory pertains to?
- 5Be ready to be disproved by scientists, lawyers, accountants, economists, ecologists, et al, because these people hold themselves out to be professional experts in some discipline or a rather thin slice of some discipline. They may criticize you with bothersome facts you had not previously considered, given their (at least partially applicable) knowledge and practical experience.
- 6Laugh at yourself, be ready also to be very surprised when it turns out your first guess leads to a better one, and so on, until you have it damn well perfect!
- 7Go back and do the previous steps again, just to be sure.
- 8You must be ready to become fully informed on your area of expertise. You now have a Working Theory on the face of it but what if someone comes up with quarrelsome facts? Be ready to refute those facts with claims that they are contingent on rare circumstances, next to impossible to achieve or ever occur again, or are based on bad science which you can disprove.
- 9Gather all the facts you need to prove your theory and disprove the theories of others.
- 10Test your theory against all the facts you can think of, which pertain under both normal and abnormal circumstances. Be wary of cosmic rays hitting people's DNA and causing them to mutate into entirely unknown entities, with all sorts of strange powers. Why? Because the comic books are full of super heroes and villains with highly desirable special powers, and people just might find a way to obtain same, or a very reasonable and possibly dangerous facsimile.
- 11Work the math out for your theory whenever applicable and be thorough. Math has a way of boiling situations and problems down to their simple elegant essence, so take advantage of the beauty of simplicity and Keep It Simple, Stupid! That's called the KISS principle. Don't try to solve too many problems with your theory, just take on something irksome to people, or about which they know very little, or is not risky or very risky, etc.
- 12Remember you'll want to publicize and spread your new truth, so it helps if it doesn't entail a lengthy explanation to justify it.
- 13Try this test: There are two competing theories, T1 and T2.
- Set up this equation: T1 - T2 = T1/ T2
- Proceed to subtract Theory #1 from both sides: T1-T1 - T2 = T1/T2 - T1
- Simplify the left and factor out T1 on the right: -T2 = T1(1/T2 - 1)
- Divide both sides by (1/T2 - 1): -T2/(1/T2 - 1) = T1*(1/T2 - 1)/(1/T2 - 1) = T1
- Put in the expected number of adherents or facts that represent T2: Let's say 100, because it could also represent 100%.
- Substituting in 100 for T2, you should get -100/(1/100 - 1) = T1
- Work out the math and get first -100/(-99/100) = T1
- Work that by flipping the denominator and multiplying by it, to get -100(-100/99) = T1.
- Arrive at the answer that 101.01010101 ... = T1. Better than 100%, in a way ...
- Put back the numbers for T1 and T2 in the original equation to make sure it is correct: Originally, T1 - T2 = T1/ T2, so you get 101.0101 - 100 = 101.0101/100.
- Solve the problem. Make sure the left side equals 1.01010101... and the right side, given you have a calculator or computer handy, you should get 1.01010101... also on the right! They're equal, the left and right sides of the equation. That is, the difference between the two theories is small, just 1.01010101 ..., and their ratio T1/T2 is also very close to Unity. Which means that these two theories are stating almost the same truth!!! There's a slight difference, yes, an advantage to T1 if being larger is advantageous (it's not, always).
- Notice T1 is 101.01010101...% correct. Why? Because he's checked all those decimal 1 tiny possibilities is why!! He's forever testing against smaller and smaller problems and bothersome facts, because the number repeats forever!
- You can further solve problems and you can use any number, except 1. The reason you cannot use 1, is because the equation has a step, -T2/(1/T2 - 1) = T1, where if T2=1, you get 0 in the denominator, which is undefined, or infinite, depending upon your own theory about division by zero. Let it be that the slope y/x of the x axis = the tangent of 0^{º} (i.e. when y=0) = 0. Call that m1. And the slope of 90^{º}, that is when y goes up forever in value and x approaches 0 infinitely closer and closer = Infinity or Undefined. Call that slope m2. Now recall your algebra and Cartesian Graph and remember that perpendicular lines, like the axes of x and y, must have their slopes multiply to equal -1. And since you can't multiply anything by "Undefined", and Infinity is not strictly speaking a number on the number line (depending on whose theory you believe), then the best we might say is that m1*m2=-1, so 0*INFINITY = -1, else those two axes are not perfectly perpendicular.
- Learn that, in that case, -T2/(1/T2 - 1) = T1 become -1/0 = Infinity, which is exactly what the Cartesian Plane submits is the fact. And happily, not only is Theory #1 correct in terms of tiny details, but it's also infinitely correct! Everywhere in Space-Time on at least 1 plane, of infinitely many such planes, it is correct.
- Make sure that your theory matters. Because we're all made up of very small particles, whizzing while spinning, and spinning while their whizzing, around. That's what matters, and don't let anyone tell you different.
- 14Set subtraction equal to division, which is one person's theory, called the "Theory of Operator Neutrality, or Neutral Operations". It works just fine with 100, even if 100 does not really mean 100%, 1.01010101 ... is extremely close to 100%. In Accounting, and Auditing, in most circumstances, for an account to be off by 3-5% with a 99% Confidence Level, makes for an immaterial discrepancy, and the firm will still have a pass on their audit, though there may be some specifics about the discrepancy way far down in the Notes to the Financial Statements, which nowadays are as important to read as the statements themselves, if you're thinking of investing that is, or divesting, as the case may be.
- 15Find that the theory of neutral operations is useful in other ways as well. Make your theory useful, because it matters.
- 16Let Truth + Beauty = Truth * Beauty = Omniscience, let's say.
- Let T+B-B = TB-B
- Let T = B*(T-1), where the 1 stands for something 100% Beautiful.
- Let T/(T-1) = B, by dividing both sides by (T-1), and simplifying. We now have Beauty isolated and defined in terms of Truth and 1.
- Let T= any number except 1, else Beauty is Infinite, with no room left for Truth?
- Let T = 12, like 12 jurors in a trial. Then, substitute 12 for T and get:
- Let 12/(12-1) = B. And 12/11 = 1.09090909....
- Test the original hypothesis: T+B = T*B = Omniscience (at least for 12 jurors, that is, the triers of fact.
- Find out if 12+ 12/11 = 12* 12/11?
- Proceed to find out that 132/11+ 12/11 = 144/11, which = 13.09090909.... or 12 and 12/11. In this case, the Jury is so beautiful in their relative omniscience, that they, by setting the sum of Truth and Beauty equal to the product of Truth and Beauty, have added a fact worth 12/11 to the Truth (=12). That's why people say "Facts are beautiful things".
- 17Make sure the Truth is on your side and then add Beauty to it, just enough so that it's sum and product with Truth are equal. "That's a rather beautiful theory you've got there" is what you'd like to hear, of course! Who wouldn't? ;)
- 18You can do it! Just add in the proper measure, test it, taste it, feel that it's right and good when it's there and when it's gone, and you will have developed the proper way(s) to theorize, about most anything you care to acquire the facts about.
- 19Be teased if you like, by other people's great lil theories! As mentioned before, check them all out before you just start off willy-nilly, okay? It's alright if some people call you "ridiculous" -- it just means you've planted your flag on the Moon, when everyone said it couldn't be done! And it matters, it matters a great deal, things like that.
- 20Don't forget: in the statement of fact, T+B = T*B, both operators are subject to the Law of Commutation. Therefore, one might as well have started out by subtracting Truth, instead of Beauty. In that case, it works out that B/(B-1) = T, just as T/(T-1) = B, because of Commutation. It's very symmetrical, which is a hot topic now in Higher Math. It also means that T^2/(T-1) = B^2/(B-1) = Omniscience, but the two 1's mean something different in each case. With the T's, the 1 was a B before, and with B^2/(B-1), the 1 was Truth previously, when they were factored. Their graphs being entirely similar, they are two lines or curves occupying the same course in the plane, simultaneously. They're twins, as it were, or a very strong Devotee and Master. See it with your two eyes and hear it with your two ears, males and females, for 'tis Truth, and Beautiful. Above is a picture of some "schizopairs" in a "rare state of attraction" like a + b, or T*B, in an image created via Neutral Operations in Excel:
- 21Be aware that there's another theory of interest, possibly. Listen carefully, because like String Theory, which is a very Strong Theory of vibrational consonance and harmony, this theory deals with extremely minute quantities. It's called the "Base 1 Theory" and like the base 2, it has two members, 0 and 1, but the 0's are all arbitrary and being arbitrary, are not exactly a defined number; the number of zeroes is both not important and very important, if you understand such paradoxes, because 0.00000000000000... is arbitrarily as close to a definition of 0 as one could want. In a way, this is both the Base 1 and the Base 0 theory, combined -- it practically doesn't count at all, except that it's an approximation (or direct statement and definition) of the smallest entity in the Cosmos, as theorized by humans. If 1/3 = .333333333...., then 3/3 = either 1 or .99999999999999.... The base 1 is simply the 1 that allows a person to convert the discrepancy between .999999999999... and 1 into an equality, and is simply 1^-n power, as n approaches Infinity. That is, by adding .01 or .0000000000000000001, somewhere arbitrarily in all those 9's, 1 is created, depending upon how large or tiny one needs the 1 to be. That's why it's the n^{th} power in the formula. If one asks, "but what about all the 9's to the right of where one puts 1^-n? They are infinitely close to 0, so they are of practically no consequence. It is just what is needed to solve all those "rounding errors" and discrepancies that are arbitrary in math today. That's the theory anyway ... the theory of the arbitrary 1, Base 1. It's arguable, of course, but may be just the trick Science needs to decide where they will cut off inquiry at its tiniest, for now ... it's right next to the proposal to have commas to the right of the decimal point too, like this: .00,000,000,000,000,..n. It matters very little, or quite a lot, as a teaching aid to students of the minute. I freely admit it's not as convenient as Exponential Notation, but it might help some people grasp how relatively tiny the subject matter is.
- 22You might ask a question about the Proof that 1 = .99999999....; if one performs that operation, 1 arrives at a version of the Base 1, which is repetitive in cycles, depending upon how many 9's were chosen to perform the division. For example, 1/.999 = 1.001001001001 actually, not 1 exactly. Some of those magnitudes of cyclical 1's would be fantastically large compared to a neutron's size, for example. That is a Cyclical Small Base, which is a little different than a simple Arbitrary Base, and awaits better definition ... because if one takes pi and subtracts or adds all the digits which make it equal 3, or 4, or a number arbitrarily rounded off in pi, so that pi becomes actually useful at tiny distances and amounts, one is really speaking of another arbitrary process which this author believe utilizes the Base 1, or not -- it's arbitrary. One could use this Cyclical Small Base to talk about a possible recurrence or non-recurrence of (some) physical laws at various levels of reality perhaps, because certain physical constants may fail to exist at those levels. As =1/0.9990999 = 1.00090091090991, once can dream up an infinite number of bases to count by, depending on their applicability in the realm concerned, with a given (tiny) Confidence Level, or series of them. Something exists at the practically Infinitely Small, we just have very little confidence assuring anyone that it's known or knowable.
- 23Note that the generalized Continued Fraction Expansion for the decimal portion of pi is different than it is for π itself, of course. Are we talking about the 3 made up of Phi? In that case, we have a situation where we're subtracting the most irrational number from one whose generalized forms of CFE (Continued Fraction Expansion) are very regular, if infinite. It's like finding the CFE for the reciprocal of the largest prime one multiplies by to obtain 1. It's there but increasingly difficult to find I imagine -- I don't know that for a FACT. Perhaps it's easily obtained, due to the process of establishing the largest prime. Maybe not. It's probably had by a fairly simple algorithm in fact. It may be a piece of work that's very piecework. Hypothetically speaking, it may very well be do-able.
Resources and Citations
- SchizoPairs - The Beauty of Neutrality by Chris Garthwaite, is a small book always still in production but available now, unfinished. It has yet to be published or copyrighted, and the author is not sure he ever will.. You can get it via emailing cathectio@sbcglobal.net. It's gone through many different titles. Here's a picture of one version's cover.
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