**DISCLAIMER: I haven’t been blogging much, especially last month (April) since I spent the entire month working with a trial version of MATLAB. But anyways, in this blog post I’ll be introducing an unorthodox approach to a mathematical theory that I’ve been working on for the past ten years. It’s based on the values of -1 and 9; one number that’s below the “positive” threshold; and one that’s a derivative of the “positive” threshold. This theory ties the inclusion of alpha-numeric conditions, especially with the letters i and j, seeing how either -1 or 9 places that transitions the numerical values of such letters as i and j from simple to complex. Please, do not allow yourselves to get carried away with this; it’s only a theory that’s loosely based on the method of characteristics which, in itself, is debatable–even to me. This theory stipulates that one cannot formulate an unorthodox approach to forming a comprehension of the “i/j” theory without knowing exactly how the human brain “sees” and distinguishes between the simplistic and complex definitions of numbers, letters and the correlations of their characteristics. Specifically to wit, the numerical derivatives.**
Since early 2003, I have devised an idea about rethinking the value of -1 and how that value can be applied to certain letters such as i or j, and I wanted the direct opposite (the “positive” threshold) to hold a “higher” value (I’ll explain later why the word higher is in quotation marks); so I chose the number 9. So, what exactly do the numbers -1 and 9 represent? They represent the value of the diacritic point, e.g., the “dot” that sits above both a lowercase i and a lowercase j. Earlier this month (May), I had “tweeted” about the difference between how a mathematician [your more intuitively “hardcore” manipulator of complex numbers] and a physicist utilize mathematics. Physicists tend to cling to your more basic approach of math to science, which is understandable. It would be better to look at the difference through the lens of academia vs. industry. Most Ph.Ds do not go into academia and unless the Earth is threatened by malevolent space aliens, the course is not likely to change over the next twenty years. Math, in its essence, gives you precise answers which you can put to the test. If a theory states that I should measure 6+/-1 and I end up measuring 10, then the theory is wrong. Now, you can see where I’m going with this theory of mine. If a person comes up with a theory, and they do the math, and the math states that they should arrive at an answer of 5 but that person does the measurements and they end up with 500, don’t cry, because the end result is a good thing–and it’s a good thing because the answer of 500 proves that person’s theory wrong. Now, am I a theorist (in the sense of postulating the determining values of diacritic points in words, phrases, etc., that contain letters i or j)? Answer: Yeah, man. See, one mistake that people make about theorists is what exactly do theorists do. The “i/j” theory isn’t about trying to figure out the universe. The job of a theorist is to come up with new ideas about how the universe works and to come up with predictions in regards to the consequences of those ideas. If this is done and the numbers don’t work out, then you’ve accomplished something since you’ve now have shown that the universe cannot work in a certain way. Another consequence, that’s quite obvious about this theory of mine, is how silly some people can go with this. For example, taking every i or j, throwing in the values of either -1 or 9 and coming up with crazy values–to no end. Therefore, it’s imperative to devise a pattern and establish a boundary or a barrier or a box [if you will], in which people can think within the parameters of the characteristics which define the theory and not think outside of said boundary or barrier or box. The only plausible option they would have would be to create another box in which they can think freely or without worry of retribution from those that will critique the theory after putting the theory at hand to the test.
Has anyone ever wondered why theoretical physicists like GR (general relativity)? It’s because GR is mathematically simple. Whether or not GR is good-weird or bad-weird, that’s up to individuals (that can comprehend GR, from a mathematical standpoint) to determine. Is the completeness of a theory necessary before testing to see if the theory is applicable or not? Answer: No. A theory could be wrong because it’s just wrong. Life goes on. Let’s take gravity, for example. What we do know is that the true theory of gravity carries a similarity to general relativity. We know this because of the experiments that have been done to confirm this postulation. We take the numbers that general relativity says we get and then take a gander at the actual [real] numbers and they turn out to be relatively close enough so we posit that general relativity could be correct, or it could be wrong and the real theory is something that’s more close than what was initially postulated [i.e., the hypothesis]. You see, I’m no longer speaking from the perspective of a theorist, I’m conferring from the perspective of theoretical physicist. The responsibility of a theoretical physicist is often tasked with working out the consequences of an idea. Let’s say that someone else comes along with an alternative theory to gravity or what have you. Great. Now explain close that alternative theory to gravity is in comparison to general relativity. And exactly how long will that take? Months, perhaps? It’s important to understand that some theories impose philosophical proclivities more so than a confluence of mathematical elements of thoughts and/or propositioning and you’ll have to realize that different people will interpret philosophical queries differently. If a question is answered by “No!”, does that substantiate a consensus from anyone else that would attempt to provide an answer or, at the very least, address the question? If that question were to be addressed by all the right answers, then by definition the theory is correct since the definition of the word “correctness” is getting all the right answers. Can you tell me what’s the big problem in quantum mechanics? Take a look at objective realism, for a moment. Objective realism says that you’ll run into problems trying to figure out what happens when the observation that’s being made changes the very thing that you are observing. That is a big problem in quantum mechanics. This is why there are several different interpretations of quantum mechanics.
The “psychology” of getting through physics is just as important, if not more important, than getting the equations right or the right answer. Earlier this week on Twitter (the week of May 6th-10th, 2013), I had “tweeted” about the importance of adapting the habit of tying an equation with an emotion. Remember how nervous you were when you began your Introductory to Calculus class? If you haven’t experienced Introductory to Calculus, that’s a good thing because now I can prepare you for it and the best way that I can prepare you for it is to tell you to remember the feeling that will overwhelm you when that day comes (if it hasn’t already). Do know that a feeling is evident of how physical brain functions operate. This is standard physiology. When talking about the brain, the sensory thalamus is what receives emotional stimuli. The sensory thalamus sends neurotransmitters to the amygdala, which is responsible for producing an emotional response. Note that the amygdala is a part of the primitive brain and it governs the fight/freeze/flight response.At the same time that this is occurring in the sensory thalamus and amygdala, neurotransmitters are moving to the sensory cortex which controls higher functions. In a normal brain, the neurotransmitters that were sent to the sensory cortex will also be sent to the hippocampus by the sensory cortex and both the hippocampus and sensory cortex will promptly send neurotransmitters to the amygdala to shut it down [in the case of preventing the “wrong decision” from being made]. Case in point, if a person experiences a car accident in which a brain injury is incurred, an alteration has come about and the brain will no longer function in such a manner. The neurotransmitters that were tasked with shutting down the amygdala do not function, partly because synapses were destroyed in the accident by the brain injury and also partly due to the amount of new synapses that were created by the flood of chemicals during the event [car accident causing the brain injury]. Emotional stimuli hails from sound, sight, smell, taste or touch. A person’s reaction to that stimuli is based on learned responses. Essentially speaking, your emotions are nothing more than electrochemical reactions to outside stimuli. It is the chemicals that produce the emotions since those chemicals activate the relevant synapses where information is stored. This, in turn, tells you how to respond in certain situations. To some, the sight of partial differential equations, as an example, might set some people off (i.e., physicists–some of them at least) but others, say mathematicians, might find them oddly pleasant.
Some would see my “i/j” theory as somewhat “stepping off” past research on the correlation between the Arabic alphabet and its corresponding morphology. Others would say that my research on the “i/j” theory was influenced by the prior research conducted by Beesley and Karttunen (2003). The latter would be more correct. From their white paper, Explorations on Positionwise Flag Diacritics in Finite-Space Morphology:
Abstract: A novel technique of adding positionwise flags to one-level finite space lexicons is presented. The proposed flags are kinds of morphophonemic markers and they constitute a flexible method for describing morphophonological processes with a formalism that is tightly coupled with lexical entries and rule-like regular expressions. The formalism is inspired by the techniques used in two-level rule compilation and it practically compiles all the rules in parallel, but in an efficient way. The technique handles morphophonological processes without a separate morphophonemic representation. The occurrences of the allomorphophonemes in latent phonological strings are tracked through a dynamic data structure into which the most prominent (i.e., the best ranked) flags are collected. The application of the technique is suspected to give advantages when describing the morphology of Bantu languages and dialects.
I’m no linguist and “positionwise” seems to denote the position of the diacritic dots (in my research). However, the research conducted by Beesley and Karttunen do not include a numerical value of the diacritic dots [-1 and 9]. With that said, it’s obvious that my research and the research that’s been done by both Beesley and Karttunen are diametrically opposed to one another.
To simplify the “i/j” theory for everyone, I’m going to lay examples before you using energy as the variable for both the lowercase i and lowercase j. Where does energy come from? Answer: Energy comes from math. Ever heard of Noether’s Theorem? In respect to energy conversation, let’s say you have a set of rules that has a symmetry. The idea is that there will be a number that stays the same. It turns out that the rules of physics are time-invariant. Do the experiment and then do the same experiment tomorrow, the day after tomorrow and so forth, you’ll end up with the same exact results. Once this has been established, if then will follow that there will be a number that will stay the same. That number is energy. This is just another example of how mathematics plays an important role in theory (rather, the creation of a theory). Mathematicians live in a world that is very strongly supported by the basis of proofs; physicists, on the other hand, pretty much don’t care for proofs. If you were to take a physicist and compare his/her mathematics skills to someone from the general population, that physicist’s grasp on fundamental mathematics would be much better than the average layperson. But one thing that you’ll quickly come to terms with is the fact that if you go into physics, you’ll be coming in contact with other people whose mathematics skills are blindingly better than anything the aforementioned person may have. However, you mustn’t let your troubles with comprehending math get in the way of your research. Researchers have been able to get from one step to the next with theories that are mathematically bad. QFT (quantum field theory) is one of them. It is mathematically inconsistent but it’s inconsistent in ways that can be worked around–at specific energies, so to speak. This is why it is necessary to develop new math. Intelligence can be defined in form; and that form of taking risks of necessity. If you are digging for new treasure it would make sense to start digging where no one else has dug before. One thing about math is that there are numerous assortments of mathematical techniques that are useful in analysis with humongous numbers of degrees of freedom but unlike mathematicians, physicists get little-to-no training with those techniques. Often, if you were to increase those degrees of freedom it vastly simplifies the problem. A high-performance computing system, with an extremely large number of degrees of freedom, will go into equilibrium once that system reaches a fixed point. A lot of physics [think in terms of computational physics] involves use of systems with extremely high degrees of freedom. These systems can be modeled. The first thing that you do is try to reduce the number of high degrees of freedom by figuring out what processes are the important ones and which processes aren’t important.
The “i/j” theory can be applied by doing math with infinities. You have to understand that even with physics, as it is, it’s impossible to determine the state of a quantum system with a measurement. For the “i/j” theory, if I were to set up the equations as non-linear, that would mean that you can have a solution for one scenario and a solution for another scenario but if you were to mix the two solutions, you would end up with a behavior that is completely different from either scenario–and since the equation are non-linear you would not be able to break up the equations. On paper, in a computer simulation, this is cool but you have to take into consideration that there will be situations in which you’ll have no real physical intuition. To give you an example, if you were to try to use intuition to figure out how electrons behave based on events that happen in your daily life, you’d be wrong. Instead of intuition, it’d be best to utilize a feeling–a gut feeling, at that. The equations I’ve used in the “i/j” theory, I have stared at them for so long over the years I’ve developed a seemingly gut feeling for how those equations behave within the parameters of the theory itself. In this case, a gut feeling comes more in handy than the anticipation of utilizing a physical intuition. If it were possible to play with electrons, hand-in-hand, intuition would be the utmost beneficial. So, in regards to energy [represented as a number], why do I use -1 as one of the plausible values of the diacritic dot above either a lowercase i or a lowercase j? Why not zero? If you want, you can set the zero point wherever you want it to be, plain and simple. For an object that’s gravitational, the zero level consists of the gravitational field at an extremely distant location. Setting the level at zero, you’ll find that you’re getting closer and closer to this gravitational object (planet) and consequently the kinetic energy will increase and, in exchange, the potential energy will decrease which means that the energy relative to zero is negative. I’ll simplify it for you: the customary choice for potential energy in planetary or cosmic application is at “infinity” and since the potential energy due to the gravitational field increases with distance from the planet, therefore, you can see that by choosing zero (0) at “infinity” means that the value at any finite distance (meaning, closer to the planet) will be less than zero, or negative.
There is a heuristic that the universe is logical and natural. That heuristic is a valid assumption in the aspect of theoretical physics. There is no way to experimentally exclude the possibility that the laws of physics will change all of sudden next week, next month or whenever for no reason since experiments are about what happened in the past rather that the future. For future statements to be made, one would have to include a sort of logical and natural essence in their assumption. For one to state that a theory that is testable and predictable is a “better theory than one that isn’t” would need to realize that it’s different from saying that a theory that is untestable and unpredictable is outside the bounds of science. What makes a theory “good”? What makes a theory “bad”? Bad and good are not absolutes, therefore, they shouldn’t be considered as conditionals by which a theory gets judged. With that said, a theory that does not currently make testable predictions is not outside the bounds of science. As a theorist, you are to remove assumptions and see what happens but how do you do this without ending up with a model that isn’t inconsistent with itself? Answer: Make the math easier. “Easy math” is important. Essentially, it is the driving force of a model since any model that you cannot utilize in respect to making calculations from, is utterly useless. Factor in consistency with other physical principles as well. Models have to have constraints. See, some people have a problem with comprehending the fact that a lot of science involves heuristics (guessing), so no one should be surprised when they run across any sort of weird coincidence. Instead of just staring at a weird coincidence, spend your time wisely trying to figure out how that weird coincidence transpired. On another note, theorists often do not come up with the testing of their ideas, that’s for other people to figure out how to do and those processes can take decades to devise. Just because it took me ten years to develop the “i/j” theory, doesn’t mean that it’s necessary for a scientist to immediately come up with a way of falsifying the idea. You can falsify an idea with theoretical constraints. It’s often not all too obvious what is testable and not testable and what is falsifiable and not falsifiable. Much of the point in being a theorist is to figure out what is testable and what’s not testable and that can take some time. So, is the “i/j” theory a claim? Answer: Not yet. Do know that there’s a difference between stating a claim and believing a claim. At times, appeals to naturalness works; sometimes they don’t. When you have little-to-no idea of what to do, logic and naturalness aid you in creating theories, and if you don’t come up with theories (whether they’re “wrong” or “right”) then you had best believe that scientific progress has begun to stagnate. Nevertheless, just because I believe something to be true doesn’t mean that I don’t think it shouldn’t be tested. Do you think that I’m afraid of being wrong? Nah, playa. You need to realize that one thing that makes science diametrically opposed to religion is that science will admit that it is fallible, yet science is self-correcting. Religion is not.
Should a theorist wait on the experiments to justify the expectations? Answer: No. You have to make decisions based on current data, not the information that’ll be gathered afterwards. But before that, you have to make decisions on what experiments to make. What’s part and parcel of the job of a theorist is to give the observers an idea of what to look for; without some sort of an expectation as to what will or should be discovered, you wouldn’t even know how to set up the experiments. Now, will this present itself as a problem to the general masses? Answer: Yes, and the reason why is because the general masses not only lack a basic understanding of scientific principles but their minds are cluttered with impressions of what “science is to them”. You see, a lot of people get their impressions about what researchers, mathematicians, scientists and theorists are working on from the popular press rather than from professional literature. Much of the filth in the popular press are “Hey, aren’t theories just so damn COOL?! Teeheeheeeee!!”. In order to do something that’s real and actually beneficial, you have to make long and incredibly technical arguments that the overall majority of people who are deeply devoted to popularized “scientific” nonsense will fall asleep reading. Professional literature, on the other hand, is about trying to figure out what can be said and what can’t be said for the sake of argumentation. I mean, people don’t see a problem with Lawrence Krauss and Stephen Hawking spouting off before things are “confirmed”? I do, since that’s how science is popularized. From that point on, it’s no longer a science issue, it’s an issue of popularity. If Sofia Vergara were to make the statement, “I’ve discovered the secrets of the universe!”, it would garner more press coverage than if that same statement were made by a physicist. But, I digress. Is it that task of every scientist to be fervently skeptical of every theory that comes about? Answer: Absolutely not. Krauss-adherents need to take note. Let’s say someone argues that they’ve discovered zero curvature of the universe, you had best believe that I’m going to ask for a lot of evidence to suffice the claim. See, it’s a bad idea to pretend that scientists are less prone to belief than other people. It’s not a bad thing to interpret data without preconception, matter of fact, it’s damn near impossible to interpret data without preconception. How would you like it if the preconceptions [the scientists that utilize preconceptions in interpretation of data] all of sudden went underground (i.e., independent research)? Ever heard of “uneven skepticism”? If I were to assert something someone else agrees with, that person would let it pass, whereas if I were to assert something someone else disagrees with that person would argue the issue until it’s dead while demanding evidence that isn’t readily available. Some people in the scientific community are adamant subscribers to the school of thought that if a theory isn’t “onto something crucially important” then it ought to be scrapped. I do not subscribe to that school of thought. I’ve yet to run across a theory that matched data in its entirety and I would much rather that the “i/j” theory be a theory that’s “known to be inaccurate” rather than be something with uncertain predictions. Am I at all concerned with the possibility that my “i/j” theory will be seen as “bad” by other scientists? Answer: No. A bad theory can, at times, be good. If the “i/j” theory were to figure out the solution is X but in order to get X the “i/j” theory eliminates A, B, C, and D, how can that not be good?
There are times in which a theory is good even if it doesn’t predict something that’s “new”. Turn something into a small set of parameters and it’s a good thing even if it doesn’t predict anything. Sometimes, you have to go with the reality that you may not have that much data–or, any data, for that matter. You’ll just have to do the best with what you have. I mean, just getting to the point where you’ll have to come up with a model that fits the data is hard work in and of itself.
So, how would people know that science is being done (in regards to the “i/j” theory)? If someone were doing science they would either:
- …state categorically that any theory involving a model leads to unprovable and untestable conclusions and then that claim would be backed up by a chain of logic, or
- …come up with a model of their own that can be discussed.
So, again, someone will ask me: “Why are you using -1 in place as a predetermined (implied) value for the diacritic dot above a lowercase i or a lowercase j?”. I’ll respond with a question of my own, a basic question in mathematical form, and that question is:
The answer to that question is a number. To the mathematical eye, that’s a number greater than zero and less than or equal to one. So, where does -1 come into the picture? I reason -1 for the simple notion that the number, in question, would render a wild universe no matter if it’s a large number or a very small number. -1 is on a scale of implied values ranging from -1 to 9. Also, I personally chose these values because I wish for no double digits (i.e., 10, 11, etc.) as either of the two implied values. I had experimented with an example of utilizing the implied value of -1 for the diacritic dot over the letter i for the name “Susie”. Taking that name, you can see that the letter i is used once yet “Susie” is a five-letter name, so
…the value of the letter i, in this example, is 8. The letter i is the ninth letter in the American English alphabet, therefore, in this example, we derive the value of 8 from adding 9 (since the letter i is the ninth letter in the American English alphabet) to –1. It’s as simple as that. Theoretical? Yes, but still simplistic. You see, the goal of a theorist is not to be right. The goal of a theorist is to come up with something that is testable. One thing that makes a good theorist isn’t to come up with true theories. The job of a theorist is to come up with theories and then have those that make observations shoot them down. Try Bayesian analysis. If I have a fair coin and you flip it fifty times, and it always comes out heads, then the odds of the next flip coming out heads is 50:50. Trouble being is that if you have even the slightest reason to suspect that the coin is unfair then it changes things considerably. The element of creativity and luck is very real when it comes to developing a theory. One thing that is interesting is that some of your more creative theorists also have a somewhat stubborn character about themselves (Einstein, for example). There’s no shame in “doing theory”. As I’ve stated before, the point of a theorist isn’t to be right, it’s to be interesting. Pure thought alone cannot guarantee if you’ll be right or wrong. Being interesting often involves figuring out non-trivial consequences of having ideas. So, how do I do theory? Answer: A lot of it involves playing around with ideas. You have to be willing to create ideas and thrown them at each other. If you don’t, someone else will.
Experimental data distinguishes between a supposed theory and a hypothesis. Without any experimental data, you have a hypothesis. Experimental data is used to put tolerance to value, and, at the same time, the point of a theory is to go beyond current knowledge. A scientist comes up with random models without a clue if they’ll work or not–and that’s fine. As a result, observations are made to cross models off the list. In physics, there are current theories stating that all electrons carry the same charge and that particles and anti-particles have the exact same mass. What this means is that you will have models that are testable and that can result as being falsifiable. Another thing to know is that it’s always best to not harbor too many opinions about what is true or about what isn’t true. Personally, I would much rather have theories that “observationalists” try to shoot down. The point of a theory is to figure out the consequences of assumptions [or having assumptions]. How this relates to what I stated earlier about how the human brain work is that there are tricks that people use to deal with as far as psychology and cognitive bias aspects, especially when it comes to doing science. Bayesian analysis is one of those tricks; flip a coin, have one person advocate an idea and then someone else tears it down, then you blow a whistle and have people switch places. Another trick is to make heavy use of mathematics to make unambiguous predictions. You can disagree as to what the implied values for the diacritic dots in both a lowercase i and a lowercase j are for the “i/j” theory but a mathematical model can be made from the implied values of –1 and 9 so it’s not possible to conclude whether they lead to conclusion X or not.
Some would see this theory of mine as me just playing around with numbers and nothing more. That’s not true at all. How would you define mathematical statements? A mathematical statement is scientifically unverifiable. 2 + 2 = 4 is a mathematical assertion that cannot be scientifically verified. Unclear definitions can be changed at will. As far as the math behind the “i/j” theory goes, everything is simple until you find out that everything becomes hard (nh). The implied values of -1 and 9 and how they’re manipulated in corresponding fashion to the order of the letter i and the letter j (meaning that i is the ninth letter in the American English alphabet and the letter j being the tenth letter in the American English alphabet) shows to prove that in order to exemplify what happens, you have to do the math.
This is just the first part of the introduction to this theory. In later parts, I’ll be speaking on the minimums and maximums and how they correlate with the “i/j” theory and implied diacritic (combined diaeresis) values above other characters and their derivatives in comparison to the values derived from i and j. This series will get more and more mathematically intensive, therefore, it would be best for those who are curiously interested in where I’ll be going with the “i/j” theory to have a pen and plenty of paper on hand.
Title: Explorations on Positionwise Flag Diacritics in Finite-Space Morphology
Date: May 5, 2011
Authors: Yli-Jyrä, Anssi Mikael
Citation: Yli-Jyrä , A M 2011 , ‘ Explorations on Positionwise Flag Diacritics in Finite-State Morphology ‘ , in Proceedings of the 18th Nordic Conference of Computational Linguistics NODALIDA 2011 , pp. 262-269 NEALT Proceedings Series , vol. 11 (2011)