Notepad
A collection of thoughts, problems, solutions
Update12/13/2018 As you might have noticed, it has been about six months since my last post. The reason for this is that there will soon be a shift in how I share things online.
Firstly, my first semester at UVM has been an interesting and fruitful change. I have many ideas that I know will be paper worthy and I am excited about these prospects. In physics, many of my interests were not conventional - making it impossible to find a way to find an adviser. I mean, what academic would hire someone who was not interested in contributing to their topic of research? However, now I realize that my interests - what keeps me going - is exactly that which will establish me as a productive scientist. The first and most important ingredient for a productive scientific career has now been satisfied. Given this change, I will aim to turn each of my thoughts into a paper - which is exactly what I have been working on. While this means that I will most likely not post as much on my notebook page, this does mean that what I do share will be of high-quality. Thank you for understanding the thoughts of a developing scientist (although, I still like to think I can remain, operationally, as a physicist).
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Intuitionem5/7/2018 With full understanding of a topic comes an intuition. You don't need to understand a whole text to get at least some intuition - some parts are self-contained. What remains true, whatever the amount of information, is that once you understand - truly understand - the material becomes an entity, a friend you have an intimate connection with. You can finish its thoughts, you know what it likes and what it hates - if it were a real-live being, that is. What I mean to say is that you are confident about how that body of knowledge will relate to any other body of knowledge (for the most part), disregarding certain special scenarios which challenge the core of the idea itself. This is what I call intuition.
Sometimes people have an innate intuition that guides them in various tasks; cooking may be one example. However, in all cases it is generally accepted that this intuition can be taught and often requires refining for those who possess at least some measure of it. For myself, I have always relied on my intuition to guide me through my thoughts - sometimes at the expense of ignoring or discounting a more efficient or rigorous means to get to a particular outcome. This is the reason why I decided to study physics - "...to train my wandering wit" (Francis Bacon). Unfortunately, I am still quite the entitled brat. I demand to have an intuitive framework as I am learning formality. To clarify, I first expect that any logical step should be transparent to me given a particular presentation in a book. If I cannot get this intuition immediately, I look at another resource. I don't stop until I can explain the mathematics on an intuitive level, even if this means I must stop at every equation that the text demands `must simply be'. In my opinion, the writing of many technical books follow the bizarre practice of removing the very conceptual scaffolding needed to understand the 'beautifully terse' ideal that is published. Now, this does not mean every step should be worked out, but it means that there should always be a well-established universe in which each mathematical (logical) statement lives that allows one's intuition to coexist, so that past knowledge can be connected with that which is newly acquired. Should I put such a burden on the author? This is a tricky question that is more of a matter of taste than correctness. Suffice it to say that as a person who is guided by intuition, I have always been at odds with academe while often finding a home in it. A sort of love-hate relationship, if you will. So, do you need to actually understand something to get high marks? I think this necessarily must not be true at the graduate level. For many faculty have claimed that they really didn't understand material until they had to teach it. Understanding is not a black-white matter. However, sometimes I suspect that some pedagogical practices slows this process down. it seems to me that there are outdated methods that retard the development of such real understanding. Ye Olde and Wise Mathematician5/4/2018 Leibniz: Free will, Morality, and the Limits of Determinism When people argue about free will, or the need for morality or a "spiritual" mindset i.e., one that reveres something much greater than humanity or self, I am reminded of what Leibniz had to say about these topics. His view seems to have a balance and wisdom that is often lacking in modern discourse. 1. The Art of Questioning: Someone once said that the right answers reveal themselves only to the right questions. But the right questions are also powerful ways to direct thoughts. Well-phrased questions may be more effective than commands because the answer that the student must give is necessarily their own. The result of a command is impersonal; the result following from a question is personal. The art of skillful questioning in teaching is an active effort by the instructor to understand and guide students to their own understanding. The awareness and skill required to perform at this level of instruction is truly awe-inspiring! 2. Types of Questions: Note that the points to consider when formulating questions are, for the most part, not topical (low-level memory based). The underlying goals which frame the questions are often about developing the foundational skills. For a physics course, this underlying foundation or skill necessarily involves the method of scientific inquiry (or scientific process). Raising the “cognitive emphasis” of questions is critical. However, a balance of low-to-high level questions should also be considered. 3. Divergent Questions: The use of divergent questioning in the technical fields are just as useful as the convergent questioning. Too often, teachers forget that engineering or science is much more than just “right” or “wrong”. Everything must be evaluated in terms of what is already understood. One could even say that the process of doing science is a never ending quest to verify what we know. 4. Time: Instructors must wait at least five seconds after asking a question. A very good rule! 5. Purpose: Questions are to invite and stimulate discussion within the classroom, not to probe an individual student! I myself have experienced multiple uncomfortable moments when the lecturer asks a question and waits for a response. Someone with a temperament similar to my own will undoubtedly be afraid of answering any question in a classroom setting. In fact, I often break out in a sweat! To alleviate this stress in some students, instructors should craft their questions to stimulate and invite rather than assess. This small difference is the difference between dreading a course of study and being inspired by it for many pupils (including myself). Notes on Mean Field Theory2/13/2018 Just wanted to share a powerpoint I made some time ago to summarize chapters 4-5 of the classic text by Bruus. Theorems on existence1/12/2018 About seven years ago, I was itching to come up with a theoretical framework that could describe differences and commonalities between objects. A general philosophy emerged a few years later when I was bored out of my mind and felt an inspiration to write. Over the course of my undergraduate education, I have revisited these ideas, connecting them to my newfound training in physics. Eager to make my ramblings relevant and providing an excuse to learn LaTeX, the document below represents a lifelong quest to fully appreciate and understand existence, consciousness, and their mathematization. Having revisited it again, I am beginning to see how mimetic theory, quantum mechanics, and category theory could all be utilized together to construct a theory on consciousness. Maybe I am crazy...but, I think I know and value the difference between my own hopes and ideas and a well-established theory. The little training I have received taught me to avoid vague philosophies and pursue rigor. Lecture Footage6/24/2017 I have captured session 3 in the set of lessons I have developed for the OLLI program at UA. Unfortunately, session 1 & 2 was not captured, session 4 is on its way. I can't post the videos directly on the blog unless they are submitted to youtube - which I want to avoid for the time.Mathematics and Human Flourishing5/12/2017 Requirements for Ideal Organisms4/12/2017 Every living organism satisfies a few common properties. I want to list them here as a sketch of a possible theoretical foundation for creating life (not necessarily organic life, but artificial life, as some say), based on principles of networks. Organisms are a collection of networks of unit cells (of the same or differing archetypes). Within the network, there is an exchange of substances between cells within a sub-network, and between cells of differing sub-networks. Example: The human body is comprised of several networks, or tissues, of a certain kind of cell. Skin cells, for example, are connected to each other, forming a network. Another network would be that of neurons which allow electrical impulses (energy) to flow through the network. Yet, it is the blood that the circulatory system contains that conveys nutrients to all cells. The circulatory system allows for exchange of chemical messengers between networks as well, providing the foundation for the interconnected system. For a system to mimic an organism, it must share something analogous to the circulatory system i.e., a controlled flow of all substances necessary for the support and communication between networks. This general notion of a circulatory system will be called `nutrio'. The system must also be open - allowing for matter/energy external to the organism to interact - directly or indirectly with various networks within the organism. Example: All living things consume nutrients from the external world. The transfer of substances from the external world must be controlled by the presence of gates or channels. Such gates or channels control the flow into (and out - to be discussed later) the organism. Example: All functional organisms control the influx of external material. When such control is lost, this usually means death or disease. Implications: If there is transfer of some substance without proper channels, the system does not satisfy the requirements. For example, a desktop computer cannot regulate the flow of thermal, chemical, or mechanical energy. In this state, it requires an ideal external environment. The very notion of a cell involves an internal environment that remains stable in a variety of external environments. Hence, there is a notion of stability that every organism must satisfy which is encoded in the requirement above. The substances imported from the external world must always be organized or utilized in a certain way. Again, if this is not true, there is death or disease. Implications: The organism must stably redirect and modify the flux of substances into the organism. I will continue to add and revise. NOTE: An ideal organism (a collection of networks of cells coupled with a nutrio) is one that is always able to redirect energy and matter while maintaining stability. This is obviously idealistic, since the stability of a system depends on the scale of energy. Need proof? Consider the fact that no matter how robust a material may be, and no matter how we augment our own bodies, there is no chance that either would survive explosions involving energies comparable only to the birth or death of large stars. -4/12/17 1/11/18 It has been a while since I have added to this post. However, new studies have given me additional insight. First, I have begun reading "The Puppet of Desire", by Jean-Michel. It is a brilliant piece of work which summarizes Rene Girard's mimetic theory. it does away with psychology being a science of 'the individual' and instead embraces it as a science of the relationship between the 'self' and the 'other', hence "Interdividual Psychology". Secondly, my brief studies in category theory can be applied with little effort. The beauty is not just how well-formulated and supported it is, but also how it reflects phenomena in other fields. Matter is comprised of particles bound together by universal interactions. Biological systems, as described above, also require an interaction between parts to become a whole. While mimetic theory is much more than just a connection between arbitrary parts (I am not giving it full justice here), I do think that mimetic theory lays the philosophical foundation for the mathematical framework one needs to understand how networks give rise to collective, system-level phenomena - like consciousness. This seems to confirm that my emphasis on the existence of the nutrio and gates governing flows across the boundary of the organism is on track; for it is the interaction between the parts that constitute all we need to know about the system. While this is obvious for some, many have disagreed with the idea on a philosophical level. For example, maximization/minimization of energy as a guiding principle for all systems seems to be obvious, but many dispute it. I think it is in the max/min principle that the guiding interactions are given full control. Perhaps the most trivial or zeroth-order formulation of the influence of the interaction upon the system, in its effort to guide and unify parts, is the max/min of energy principle. The Hamiltonian formalism seems to confirm this. Al DanielsHi. I'm a currently a PhD student at the Vermont Complex Systems Center. I prefer not to use social media platforms, so I occasionally share my thoughts here! Archives
December 2018
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