Abstract_Logic

Well, of course. The AI was already created as software, but what I meant by "creating your own chatbot" is that you are producing a chatbot based on your personal settings; bringing it into existence in terms of yourself. It's just like "creating" your RPG character. You're not literally creating it from scratch, just configuring different options to make it exist in terms of yourself.

I recently found a new toy while essentially "mining" the internet for computer science stuff. It uses advanced technology from A.I. and Human-Computer Interaction to simulate the reciprocation of human social interaction. If you click on the first link in my signature, you can chat with my chatbot, CyberDucky. You will find that as you explore different topics of conversation, CyberDucky will exhibit his own personality including a complex response system. You can create your own chatbot, or CyberTwin, if you click on the second link in my signature, go to the Login tab, and then create an account. The personality of the chatbot you create is made possible by answering a series of personality test questions, the answers to which the program integrates into the character of your CyberTwin.

I am aware of the fact that certain species have evolved physical traits that would reduce the likelihood of them being eaten by predators. E.g. certain insects have evolved to mimic plants so that predators may mistake them as such. However, I have been wondering if any species have evolved a certain trait that makes them more attractive to prey, sort of like a luring system. I am mostly referring to species other than humans or anything biologically related to humans. Perhaps I already know a specific instance of this, but it just eludes me at the moment, so when someone mentions one it may just refresh my memory.

I would define geometry as the study of the generalization of spatial structures and of operations on these spatial structures. This definition can include Euclidean spaces, non-euclidean, riemannian spaces, etc, as well as manifolds, supermanifolds, and other spatial structures.

Let [math]X[/math] consist of four elements: [math]X= \{a, b, c, d\}[/math]. Which of the following collections of its subsets are topological structures in [math]X[/math]? [math]1. \emptyset , X, \{a\} , \{b\} , \{a, c\} , \{a, b, c\} , \{a, b\};[/math] [math]2. \emptyset , X, \{a\} , \{b\} , \{a, b\} , \{b, d\};[/math] [math]3. \emptyset , X, \{a, c, d\} , \{b, c, d\}?[/math] Are they all topological structures in X? If they are not, why are they not?

Is the chemical composition of n+1 gases always going to be a gas?

I'm currently reading this book called Set Theory and the Continuum Hypothesis, written by Paul Cohen, which is a model-theoretic investigation of the topics. I'm trying to rediscover the proof of Gödel's Completeness theorem for myself, but I'm kind of stuck on certain details of the proof provided in the book. In the preface, the author mentioned that he did not "polish up" the final draft of the book, so many important details are left out. Although it is written for people with little to no background in propositional logic, the book assumes that one has a background in abstract mathematics, namely in Model theory. I'm only an undergraduate student not yet knowledgeable enough to understand the methods Cohen uses to prove his arguments. So I'm wondering if someone here can help me understand what certain things mean in the proofs. The parts that I've put in red are the parts I'm stuck on. I will quote directly from the book so as to give you a full view of what I'm asking. [math]c_\alpha[/math] and [math]R_\beta[/math] are constant and relation symbols, respectively. I have a very vague idea, but I'm not entirely sure what those parts mean exactly. If someone could help me out here by explaining those parts to me in more detail I would appreciate it. Also, if there are any questions regarding the excerpt from the book I will do my best to answer them. Thank you! Jeffrey

The logical basis of quantum mechanics is the idea of both/and, as opposed to either/or logic. Either/or logic is classical propositional logic, where things are interpreted in terms of 'black and white'. Quantum logic, on the other hand, is the both/and logic, similar to fuzzy logic, where the 'grayness' is taken into account, in this case it would be wave-particle duality. All quantum entities have both a wave and a particle-like nature. In quantum theory, there is something called the superposition principle, according to which quantum entities can experience more than one possible reality at once. So it is generally said that, in the two-slit experiment, a single photon is the superposition of two equally possible realities, i.e. wave-like and particle-like. It is true, scientists do understand it acts like a wave, but that doesn't mean to disregard the particle-like nature of the photon, nor does it mean this phenomenon is not baffling. It is called wave-particle duality simply because the photon behaves like a wave at one point, and a particle at another, so it is easy to see how this can be so baffling to scientists who were so used to the Newtonian world view (i.e. the either/or view). The collapse of the wave function is exactly like what vordhosbn explained. The Schrödinger wave function is a mathematical description of each possible reality associated with any quantum system. Once we attempt to measure (observe) a quantum system, the wave function collapses and only one single reality is experienced (either a wave or a particle). So it appears that whatever it is that draws the line between propositional either/or logic and quantum both/and logic, it definitely has to do with the act of measurement. I would recommend you do a wikipedia search for all the terms I have put in bold face. You might also be interested in the Schödinger's cat experiment, which is a thought experiment involving the wave function and the superposition principle.

Hello Nate. I haven't much experience with Set Theory either, but it is a very intriguing field of study. From what I understand, the aleph numbers are used to represent the cardinality of sets of numbers, i.e. integers, natural numbers, etc. So it would make sense that the alephs cannot form sets themselves because, while they are objects of study within set theory, they are not subjected to the same operations as sets. Your proposal is more along the lines of something that would be called 'Meta-set theory'. And of course, this brings up the issues of the Continuum hypothesis and Russell's paradox. Let's say your proposal is plausible within mathematics, and you have a set of alephs, i.e. a power set of set cardinalities. Then, according to the methods of set theory, you would need a cardinality set for the power aleph set, and also a power-power aleph set for those sets, and so on. This is where things border on absurdity. So your proposal, although very insightful, is unfortunately not plausible within Set theory. But please, don't take my response as an end-to-it-all. I have very little background in set theory, so I think you should hold on to your notions and continue to ask around about them. Good luck to you!

I've just begun learning about category theory. I would love to share ideas with anyone else interested in the topic. Perhaps anyone can recommend some good learning material for it? I've started an introductory book on it, a rather small book of about 200-250 pages. I've finished the first section on general categories, subcategories, pre-categories, morphisms, and other things. I enjoy studying things at the most general level, like category theory, model theory, universal algebra, metamathematics; it intrigues me. I'm more of a generalist than a practitioner, and personally, being a man of pure ideas, I don't believe in anything merely because of its practical value, but rather because of its aesthetic value. One of my favorite quotes: And it is a mistake to think that a mathematical idea can survive merely because it is useful, because it has practical applications. On the contrary, what is useful varies as a function of time, while “a thing of beauty is a joy forever” (Keats). Deep theory is what is really useful, not the ephemeral usefulness of practical applications! - Gregory Chaitin, mathematician and computer scientist

I'm learning College Algebra. I'm wondering how to solve Exponential Equations, such as 8^(X^2 - 2X) = 1/2 8 to the [X squared minus 2X]th power = 1/2 and other equations of that nature.

"Time and space are modes in which we think, and not conditions in which we live." - John A. Wheeler

Maybe I should rephrase the question. Apologies for not making my hypothesis clear enough. The question can be restated as: How much do you think the physical environment influences the development of cognitive structures of the brain? To illustrate: Imagine that nature's constants have all evolved and formed a different, but functional configuration than what they are currently. To what extent would this influence cognitive, including physical and chemical, development of species here on Earth? I apologize if this question seems a bit monogonal from a certain perspective. From a broader, more general perspective, the answer may be strikingly obvious. But when we look at it more specifically, it can seem quite complex. Of course we wouldn't be able to test this hypothesis, but I proposed this question for the sake of mere speculation. From an evolutionary standpoint, we know that the Earth was vastly different in prehistoric times than it is in present times, and, that it is believed that species such as dinosaurs and the first mammals have become extinct due to the fluctuation of certain constants in the prehistoric past. So taking that theory into consideration you might be able to get the gist of what I'm trying to articulate here in this post. I have already formed a possibly conclusive answer to this question, but I am still open to what others thoughts are on this hypothetical scenario.

While learning about Dabrowski's Theory of Positive Disintegration, I began to wonder how our minds would have developed if evolution took on a totally different course. What if our world evolved differently, more differently than we can imagine? Would our minds have developed in the same manner as they are currently? Or would our brains have a totally different function than what we are used to now? If the development of an intelligent mind is precipitated by experience, it would make sense to say that an individual who has experienced the force of gravity on the moon would have a slightly higher developed mind than the individuals who have remain earthbound for their entire lives. Imagine a hypothetical scenario where only a certain amount of earthlings have inhabited the moon. While living on the moon, these individuals began developing a civilization (they began breeding, etc.). Would their offspring have a different form of cognition due to the environmental circumstances in which they have been born and raised? In essence, would they think differently than humans on earth? Of course, due to cultural limitations, they would have a different view of life, after-all having been born and raised on the moon. But the cognitive differences I'm referring to here have a much more complex nature than what certain cultures limit themselves to. I hypothesize that the environmental conditions of the moon would have a much more deeper, complex effect on the cognitive development of its natives than the cognitive differences due to cultural conditions. Therefore, humans born on the moon (or any other planet for that matter) would perceive and conceive of reality in an intrinsically unique manner than the persons born on Earth. I believe the environment can have a profound effect on the way brains develop in humans, or even chimpanzees or dogs or whatever.