The Watson “i/j” Theory Part 2: “Pattern”, Absolute Determinism, Dimensionality Reduction, Assorted Mathematical Peculiarity and An Observational Rant From DTO™

**Disclaimer: In this second part of the Watson “i/j” Theory presentation, I’ll be going in detail about use of deterministic math and how it’s associated with this theory; I’ll touch a little bit (nh) on dimensionality reduction (more in-depth in the third of this series); assorted peculiarity on the math; and I go berserk in the end….rant-style, playa.**

Mathematical peculiarity comes in handy, especially when you’ve been confronted with a dire situation that doesn’t necessarily make it self-apparent. The employment of the Watson “i/j” Theory is based on the use of (-1 and 9) as the implied values of the letters’ corresponding diacritic dots (or marks). To familiarize yourself with its intended simplicity, let’s run across a random name, for example, “Donnie Wilkinson”. As you can see, the name “Donnie Wilkinson” contains three instances of the letter i in it. I’ll simplify this example by employing use of -1 as the implied value for the diacritic dot above the letter i; therefore, the i in “Donnie” has an implied value of -1, in addition to the letter i being the ninth letter in the American English alphabet, and the name “Donnie” is comprised of six letters, that leaves the name “Donnie” with a derived value of 14.

Donnie = -1 + 9 + 6
Donnie = 8 + 6
Donnie = 14

Take the surname, “Wilkinson” (with -1 as the implied value for the diacritic dot over i):

Wilkinson = (-1 + 9) + (-1 + 9) + 9
Wilkinson = 8 + 8 + 9
Wilkinson = 25

The derived value of “Wilkinson” is 25 [when you add]. From here, we could add the two derived values from the first name (“Donnie”) and the last [surname] (“Wilkinson”) and have 39 as the derivative, but how would you go about registering 39, and under what category would that derivative go? You may ask why did I not subtract the two derived values if I did not want such a large derivative? Thing is, I would have subtracted the two derived values from one another if either of the two derived values were negative. The Watson “i/j” Theory stipulates that “if both derived values are positive, then it is preferred for them to be added”. With the letter i being the ninth letter in the American English alphabet, the derived value will almost always be positive, using -1 as the implied value for the diacritic dot over i, and you can see how this is evident when you employ addition. Subtraction of the derived values of 14 and 25 leaves you with -11 [with the direct opposite of that derivative being (positive) 11]. Needless to say, the principle of subtraction is that subtraction “cancels out”, especially in this case in which the numerical 11 (and -11) rule each other out when they’re added together. With the Watson “i/j” Theory, subtraction would render the derivative as imaginary since -1 is being used as the implied value for the diacritic dot over i, and with i as the ninth letter in the American English alphabet, the letter will always hold the position of [positive] nine (9), in which you’ll always see this statement:

-1 + 9

…which always equals a [positive] eight (8) [in accordance to *theory*]. What we’re seeing is the beginning of a pattern. With -1 being the implied value for the diacritic dot over the letter i (imperatively lowercase), it substantiates a pattern–a numerical pattern. Patterned as it is, this establishes the existence of what the Watson “i/j” Theory calls the minimum. Decrement the numerical pattern down to its base, the [lowest] minimum is 10 when you implement the implied value of -1. The following example exemplifies the hypothesis and reveals yet another principle.

Using the name “Isis”, you’ll see that this particular name has both an uppercase I and a lowercase i but according to the Watson “i/j” Theory, the principle of applying the implied value of either -1 or 9 can only be applied to either a lowercase i or a lowercase j. Therefore, there aren’t any diacritic dots over an uppercase I nor can we imagine that one (or more) exists over an uppercase I. So, with -1 as the implied value, we see:

Isis = -1 + 9 + 4
Isis = 8 + 4
Isis = 12

Understand that the minimum, down to its base, is dependent upon the number of letters in the person’s name. If you’ll notice, the name “Isis” is comprised of four letters while the name “Donnie” is comprised of six; the derived value of “Donnie” (after utilizing the implied value of -1 for the diacritic dot over lowercase i) was 14, while the derived value for “Isis” (once again, with the implied value of -1) was 12. For a name that only has two letters, with one of them being the letter i], you’d be able to apply use of the implied value of -1, the derived value would be 10, the base….the minimum, according to the Watson “i/j” Theory.

So what about a “maximum”? A maximum is predicated on the instance of an incremental derived value; there is no absolute maximum. To say that there exist “the last number” would be disingenuous and would showcase intellectual dishonesty. For the Watson “i/j” Theory, an example of a maximum would “…entail the addition of one or more letters in an individual’s name and the alphanumerical position of each corresponding letter”.

{I_{(9)}} {s_{(19)}} {i_{(9)}} {s_{(19)}} = 9 + 19 + 8 + 19 + 4
{I_{(9)}} {s_{(19)}} {i_{(9)}} {s_{(19)}} = 55 + 4
{I_{(9)}} {s_{(19)}} {i_{(9)}} {s_{(19)}} = 59

59 is the plausible maximum for “Isis”, in theory–my theory. Keep in mind that 9 represents the alphanumerical position of the letter i in the American English alphabet and 19 represents the alphanumerical position of the letter s in the American English alphabet. My theory stipulates that for “…the rule of determining the maximum derived value of an individual’s name, implied values cannot be applied towards an uppercase i or an uppercase j” and you can see that the implied value of -1 was not applied to the first I in the name “Isis”. Instead of taking -1 as an implied value for the diacritic dot over the letter i, you simply add 9 (as the alphanumerical position of the letter i) to the next alphanumerical value which is 19, the alphanumerical value of the letter s. The only letter that an implied value of -1 (or 9, as either of the two applicably implied values, -1 or 9) can be applied towards is the lowercase i in the name “Isis”, and its derived value is 8. You’re seeing a pattern; the pattern starts with the implied value of -1 being added to 9 since 9 stands for the alphanumerical position of the letter i. The pattern continues whenever the alphanumerical position of i (9) is added/multiplied/divided by the implied value of -1–or 9 (as an implied value, once again, not to be confused with the alphanumerical position of the letter i). Let’s go back to an example from the first part of this series, “Susie”:

Susie = -1 + 9 + 5
Susie = 8 + 5
Susie = 13

As you all can clearly see, the derived value only went up by one from the previous example of “Isis”, therefore, you can see that therein lies a pattern. The problem that we’ll inevitably run into is a disruption in the pattern. An example of such a disruption would be there being more than one application of implied values with just one name. Let’s take a more in-depth look at the name “Willis”, once again using -1 as the implied value for the diacritic dot over i:

Willis = (-1 + 9) + (-1 + 9) + 6
Willis = 8 + 8 + 6
Willis = 22

…or, if you want to go the “maximum” route….

{W_{(23)}} {i_{(9)}} {l_{(12)}} {l_{(12)}} {i_{(9)}} {s_{(19)}} = 23 + 8 + 12 + 12 + 8 + 19 + 6
{W_{(23)}} {i_{(9)}} {l_{(12)}} {l_{(12)}} {i_{(9)}} {s_{(19)}} = 88

Now, let’s take a look at the same name [“Willis”], only this time using [positive] 9 as the implied value for the diacritic dot over the letter i:

Willis = 9 + 10 + 9 + 10 + 6
Willis = 19 + 19 + 6
Willis = 44

…and, once again, for those intrigued by the “maximum”

{W_{(23)}} {i_{(9)}} {l_{(12)}} {l_{(12)}} {i_{(9)}} {s_{(19)}} = 23 + 18 + 12 + 12 + 18 + 19 + 6
{W_{(23)}} {i_{(9)}} {l_{(12)}} {l_{(12)}} {i_{(9)}} {s_{(19)}} = 102 + 6
{W_{(23)}} {i_{(9)}} {l_{(12)}} {l_{(12)}} {i_{(9)}} {s_{(19)}} = 108

We can see that the first derived value [22] from using the implied value of -1, for the name “Willis” gets doubled to 44 as the derived value from using the implied value of [positive] 9 for the name “Willis”, however, it ain’t hard to tell that the disruption in the pattern occurs when use of the implied value (9) is in conjunction with the alphanumerical positions of the letters comprising the name “Willis” since the derived value of 88 did not double, it only incremented by thirty to a derived value of 108. From this simplistic observation, you can see the advantage that the implied value of -1 has over [positive] 9 when it’s utilized as the implied value of the diacritic dot over both the letters i and j. Keep in mind, that for use of [positive] 9, the derived value has now established a separate pattern; needless to say, the difference between -1 and 9 is 8, and that will be by how much the derived value will increment when utilizing 9 as the implied value of the diacritic dot over i and/or j. With that said, the “maximum” is not observed as the derived value but the increment, which is 8.

\text{ The plausible maximum is 8}\

With the Watson “i/j” Theory, lots of things are possible, or plausible. That’s why you have to do observations.

Folks, in the first part of this series, I established that the diacritic dot that sits above both the lowercase form of the letters, i and j, can be quantified by either of the two implied values (-1, 9) when you take a name that contains either the letter i or j, and, according to their position within their respective alphabets, corresponds with either 9 (since the letter i is the ninth letter in the American English alphabet) or 10 (since the letter j is the tenth letter in the American English alphabet). This entails the involvement of a mathematical statement comprised of the implied value being added to the alphanumerical position of i or j being added to the number of letters of an individual’s name. Obviously, a sum substantiates an incremental “growth” in the derived values; this creates a pattern. A pattern, in the context of the Watson “i/j” Theory, is defined as “the result of two or more principles compromised into a relationship that repeats itself”.

This theory, to me, represents a good format of practice, especially when it comes to experimenting with numerous ways of deriving numerical constructs and come up with numbers that match those experiments. For example, taking a set of principles and then you learn enough to mathematically figure out the consequences of those principles. One aspect that you all can take away from this second part of the Watson “i/j” Theory is how important it is to teach people how to critically evaluate information (i.e., the difference in determining the minimum and a plausible maximum in derived values). The research itself is extensive (multiplication and division have been saved for the third and fourth part of this series); if I were able to contribute a minimum of sixty hours a week towards my theory, these posts would be displayed sooner. Unfortunately, it doesn’t work out that way.

Sometimes, I just want to try and figure out what to do next. —Desmond

The quantifying of randomness–people, that’s what you’re seeing here. Entropy is probably the best and most useful way of quantifying randomness; maximum entropy on all orders means that there’s no advantage you have for any past information at all since a maximum value on all orders (independent, first-order conditionals, second-order conditionals, etc.) would imply that the analysis of all past values (i.e., implied and derived), with respect to each other, would not yield to you an advantage of any sort. The thing about entropy though is that you need to consider not only just non-conditional entropy but conditional entropy as well (the Watson “i/j” Theory is an example of conditional entropy). Imagine that you have a process corresponding to an infinite periodic sequence where one period consists of {0,1,2,3,4,5} in that order and repeats forever.

\text { Calculate}\ P(X = a) \text { for a}\ = {0,1,2,3,4,5} \text { which is maximal entropy}\

For this process we can see that, reflected in the following joint distribution…

P(X_n + 1 = a | X_n = a - 1) \text {MOD 6)}\ = 1

…because of the periodicity. The entropy of this joint distribution is 0 which is an implication of absolute determinism. Me telling you all that…

-1 + 9 = 8

…is an example of absolute determinism because no one who sees and understands that mathematical statement is going to say, “No, it doesn’t…”.

Back to the joint distribution, although the non-conditional entropy is maximal, the joint distributions are the direct opposite and through this we can establish a complete order that has been exhausted (meaning that it repeats itself), making the process deterministic. In a classical way of analysis, this is not only completely foreign in terms of our intuitive understanding and experience, it can become a lot harder to deal with mathematically. However, I choose to confront this from a mathematical viewpoint and not from one considered by physicists. In the first part of this series, I had expressed my reason for choosing the implied values of -1 and 9 as strictly random and voluntary; yet, as a general rule, order is found when entropy is greatly minimized. Let’s say you were to call time as only one kind of order. Depending on the system, most likely there are going to be many kinds of order. Classical physics teaches us that time has a very good order to it in a way that the conditional entropies have been highly minimized that the models give us something that is extremely predictable, which is a result of a very low conditional entropy in the context of a system comprised of conditional measures. There is no problem with finding orders but take into consideration that there might be other orders either from the system itself or from a transformed variant that gives insight that cannot be seen from the existing order either chosen or subsequently discovered. This leads to a discussion on dimensionality reduction and how it relates to the Watson “i/j” Theory.

Over the past few years, evidence has begun to accumulate suggesting that spacetime may undergo a ‘spontaneous dimensional reduction’ to two dimensions near the Planck scale. I review some of this evidence, and discuss the (still very speculative) proposal that the underlying mechanism may be related to short-distance focusing of light rays of quantum fluctuations.–S. Carlip

Dimensionality reduction is about the constraint of a physical action to the point where a context for the action no longer seems visible. You’re left with nothing but a lonely vector “floating” about in the vagueness. The model would have collapsed the other dimensions that would have served as a means of distinguishing the vector as a third direction, so all you would have left is just an image of raw actions and no background space in which they would be embedded. The thing is, with the Watson “i/j” Theory, the numbers (both implied values and derived values) are energy. I made mention of Noether’s Theorem in the first part of this series; the idea is that you have a set of rules with a symmetry, there will be a number that stays the same. Is this not exhibited in the Watson “i/j” Theory, in which an implied value is attributed to the diacritic dot over the letters i and j and the derived values are exemplified as substantiating a pattern? Before we get into equations that involve both the implied values and derived values, according to the principles of the Watson “i/j” Theory, I must stress that you all realize that some things that seem hard have easy math, such as implying -1 for the value of the diacritic dot over i and j, and that there some things that seem easy yet have hard math. If you were to take the equations for the whole universe, it would seem quite an easy feat to accomplish since you would be banking on an assumption, on the average, that parts of the universe are the same. Therefore, the calculation to do the whole universe would be no more than five lines and the reason for it being “easy” is that you would be calculating one number and how that one number changes over time. Light a match; blow out the fire and look at the smoke as it ascends–that would be quite a painfully difficult equation to figure out and solve.

As a mathematician, it’s my responsibility to make things as abstract as possible and my “i/j” theory helps out with this task. As a theoretician, I can either establish that either there is fine-tuning that can be administered to the theory or there are multiple deals that can be derived from the theory. Those “multiple deals” are the number of possibilities from application of the theory. Once you’ve narrowed those number of possibilities down to just two, you will then be able to figure out the consequences of those two. “Those two”, for the sake of simplicity, we’ll keep the implied values (-1 and 9) in close reach. One other thing, think of the diacritic dot that resides over the letters i and j as “…existing in their own respective environments, separate from body of the letter”. You have to consider, as an example, calculating the behavior of an electron, what you can do is assume that there are an infinite amount of electrons, each of them in their own universe and then sum up the results. That’s what you’re doing with the derived values; you’re summing (adding) them together. In order to have a well-posed scientific hypothesis you need to have something that is specific enough to make specific predictions. The main idea behind the Watson “i/j” Theory is that I came up with a specific theory that makes specific predictions. Once you have specific predictions, this reduces the number of logically possible premises and describes the situation without having to favor one premise over another. If a concise mathematical interpretation happens to not fit observations, then I have a problem. You have to understand that you just simply cannot force a theory to make the predictions that you want to make. Math is what keeps physics from rationalizing things; it’s the math the forces you to make some conclusions.

The lifeblood of the Watson “i/j” Theory is curiosity. Sometimes, I just want to try and figure out what to do next. In the third part of this series, I will be going deeply in detail in regards to dimensionality reduction, the inclusion of the implied values of [-1 and 9] as averaged squared projections and the equations, expressly abstract algebraic equations, not the bad-weird intellectual masochistic maniacal tutelage your standard Ivy League professor puts you through (mainly to gratify his/her jollies).

Which brings me to this point that I believe I need to make (though it has very little to do with my “i/j” theory): I’m going to contradict myself and head back to school to finish my degree in applied mathematics and pursue after my Ph.D. in applied mathematics and possibly pick up my Master’s in either economics or international affairs en route of the Ph.D. I do not wish to focus all that much on physics, academically speaking, due to the foreseeable fact that the market for physics Ph.Ds will become overly saturated on part of the currently ongoing popularization of science and that popularization is heavily leaning on physics–all facets of physics–from the astronomical all the way down to the bone of the theoretical, playa. Ask around if you don’t want to take heed to what I say: about 96% of the people who have graduated with a degree in physics wish they could live happier lives had they not done anything that has to do with physics. They’re now students for life. Now, if you’re obsessed with physics, then nothing I’m telling you is going to convince you otherwise; nothing I say is going to persuade you down another path since a good number of people have convinced themselves to pursue after that “dream job”. Admittedly, right now, in 2013, it ain’t all that hard for a physics Ph.D. to find a job on Wall Street with a starting salary of $150K. But there are only a few thousand of those jobs and if the market for physics Ph.Ds on Wall Street becomes suddenly overly saturated with 15,000 people with physics Ph.Ds [instead of just 1,000] applying for those jobs, that would overload the system [yes, an actual system]; salaries would plateau and the number of jobs would diminish (not increase in spite of demand (obviously not employer demand)).

The next generation should also take into consideration of exactly whom they choose to lend an ear towards: the general public that themselves have already crashed headfirst into a brick wall and can’t offer sound advice; the “scientific” community that have also hit a dead end; or individuals that have chosen to share their knowledge with whomsoever that will take the time to listen and take heed. The “scientific” community, on its face, is dead, playa. The conferences/meetings, where scientists, engineers, half-ass mathematicians who couldn’t come up with their own theories if their lives depended on it and the assortments of “fans” have all made their decision, while simultaneously falling on their own swords, to pursue blatant stupidity and continue to outright disregard the virtue of real science–and mathematics. Instead of getting their “fans” overly anxious about trekking to Mars, the “scientific” community would greatly benefit, they could be spending that energy telling them that figuring out how things are the way they are would be especially useful since the lot of them really don’t like the way things are in this day and age. Here’s a good reason why I despise the popularization of science: back in 1968, Stanley Kubrick made a movie, 2001: A Space Odyssey, in which people would be traveling to Jupiter. If the world had turned out that way, I’d be trying to make sense out of David Bowman’s last words in that flick and would probably be the lead scientist on a research team en route to Jupiter. But it’s not like that in the real world, and like the majority of people that would rather dream about the stars, quasars, pulsars and the whole nine, they’ll just end up with a Ph.D. and a dead-end job–and more time to dilly-dally about going to Mars, Jupiter or elsewhere.

I’m heading back to finish my degree not because of President Obama’s random firebrand speechifying about making promises to the next generation. I don’t do education on the shaky foundation of a premature assumption that there’s a pot of gold at the other end of the rainbow. Playa, school is just part of your education. Thinking that a degree is your meal ticket is wrong. That’s not how this education-thing works and it’s crucial for people to know this–especially those of us who reside here in the United States. People here in the U.S., that are honestly seeking employment, cannot compete globally due to the wage disparity, and yes, this is a global economy. I’ve already disclosed about the overt fascination of a college degree’s worth here in the U.S. in comparison with other countries but the point of a college education is to give you enough of a background so that you can figure out what to do next. This is where the critical thinking skills should kick in. Perhaps, this is where having a Ph.D. comes in handy because as the “jobs are heading overseas”, having a Ph.D. will put you at the head of the queue for those seeking to switch countries. I hope you’re all aware of the declining relative U.S. power. If there’s a committee full of Americans, you can appeal to “patriotism” to keep jobs here in the States but if it turns out that those who are running the committee aren’t American then appeals to “patriotism” are about naught. Just take a look at multinational companies; if you want to make a decision as to whether or not you should move a plant from the U.S. to Beijing, that decision will be economically-based. Ford can’t sell a car made here in the U.S. that’s “worth” $24,000 to those in India but Ford can sell a $3,000 car to Indians that was built in India. So Ford will the economical-sound decision to close a plant here in the U.S., move that plant [meaning, the jobs] overseas, set up shop in Mumbai, build cars for Indians who are employed and can only afford to pay $3,000 and maintain a profit. That equation always yields a positive–a profitable positive.

Can you really blame Ford for doing this? Answer: No. This is what’s happening now. Imagine this on the scale of researcher jobs, here in the U.S.–leaving the U.S…..

-Desmond (DTO™)


Title: “Spontaneous Dimensional Reduction?”
Author: Steven Carlip
Date: July 18, 2012

Title: “Probabilistic Math vs. Deterministic Math”
Author: S. Soleymani
Date: Last Modified April 27, 2013