Foundations Definition and 116 Threads

I'm preparing for my Foundations of Geometry Course by self-learning topics before the semester starts. I've been reading Geometry: A Comprehensive Course by Dan Pedoe, and it's covered a lot of good topics. Any online resources you recommend?

Not sure if this was posted but I came across a fairly recent online journal specializing on Quantum foundations that some might find interesting: http://www.ijqf.org/wps/wp-content/uploads/2014/08/IJQF-flyer1.pdf http://www.ijqf.org/ Some topics issues that will be published/discussed...

I'm getting interested in mathematics because as a philosopher I am upset with the amazingly poor standards of rigor in my field. I am looking to mathematics for guidance. I would like to formalize philosophy and turn it into a deductive science. I have a deep interest in logic so I decided...

If you have seen interesting recent research papers on foundations/interpretation of these branches of physics, please share your links and thoughts. Argument along ontic versus epistemic lines is not approved--it is frequently a waste of time. So if you please use a separate thread if your...

Folks, A friend and I are interested in finding a forum to discuss the philosophy of the foundations of mathematics. He's a mathematician and I'm a mathematical physicist. Some of the topics we're interested in are understanding intuitionism and understanding Wittgenstein's lectures on the...

This was just posted http://arxiv.org/abs/1308.2206 Energetic Causal Sets Marina Cortês, Lee Smolin (Submitted on 9 Aug 2013) We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose...

I finished reading "Linear Operators for QM" by Jordan a couple of weeks ago, and it was extremely interesting for me. It introduced various topics in functional analysis that are relevant to the foundations of QM (Hilbert spaces, spectral theory, von Neumann algebras, etc.). I was wondering...

1.How did the nucleus evolve? 2.What are the pointers indicating the evolution of eukaryotes from the same branch as archea? 3.Obligate anaerobes, what is the end products? Does it include molecular oxygen? What is it in case of facultative anaerobes? Is there any organism that uses a...

"Foundations of physics" Special Issue: Forty Years of String Theory http://www.springer.com/physics/history+&+philosophical+foundations+of+physics/journal/10701 If this has already been mentioned feel free to delete this post. Articles free through march, A Critical Look at Strings (Carlo...

Author: Behrouz A. Forouzan Title: Foundations of Computer Science Amazon Link: https://www.amazon.com/dp/1844807002/?tag=pfamazon01-20 Prerequisities: Contents:

This paper may be intersting: http://www.springerlink.com/content/d3182t263w74267g/?MUD=MP On the Foundations of Superstring Theory Gerard ’t Hooft Abstract: Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects...

The short summary is that my high school foundations of math were absolutely terrible as I was instructed from the youngest age that mathematics was entirely about computation and that being talented in math meant being able to handle lots of number grinding in your head without a calculator. I...

Homework Statement Prove the following. 4+1+4^-1+4^-2...4^-k = 16/3-1/(3)(4^k) Homework Equations The Attempt at a Solution I confirmed the basis step and proceeded by changing the variable to n and adding n+1. I now have (16/3) - (1/(3)(4^k)) + (1/4^k+1) = 16/3 - (1/(3)(4^k+1))...

I'm looking for a good text on the foundations of GR. Geared towards physicists, but with a focus on the subtleties of the ideas that went into building the theory rather than on applications. Any recommendations? Thanks!

It's known at anyone that, the QM is a powerful instrument investigation about the microworld...since 1930, official year born, the QM has explained a lot of mysterious facts, revealing strange behavior of the mother nature... physicists love QM to the simply mathematical and for the amount...

Hello, Does anyone know of any good books that covers the foundations of mathematics (i.e. mathematical logic, axiomatic set theory, proof theory, model theory, type theory, recursion theory...)? Keeping in mind that I'm still in high school. (Although I'm taking math courses at my local...

Hello. I would like to bring to discussion this paper called "Mathematical Foundations of the Relativistic Theory of Quantum Gravity", by Professor Fran de Aquino, from the Maranhao State University, in Brazil. The paper was published in the Pacific Journal of Science and Technology...

Well this post is "related" two math but I found the chat room to be the most appropriate place for this. Now I found a lecture series on youtube by a mathematician N J Wildberger. He claims that the "Foundations of mathematics" are flawed. The area of mathematics he claims need to be revised...

Can anyone comment on this book?

"Foundations" argument: Silberstein et al engage Hiley-channeling-Bohm Foundations of Physics (ed. 't Hooft) has accepted this Silberstein et al paper for publication. http://inspirehep.net/record/922919?ln=en which seems to me to resurrect some Bohm trends of thought, perhaps in a new form...

Homework Statement View attachment. Homework Equations View attachment. The Attempt at a Solution View attachment. Everything should be in the attachment, i back tracked my working with the answer given on the sheet but i still don't end up with the right solution?

Standard treatments (e.g., Rindler) of the foundations of Special Relativity invoke use of a "rigid rod" or "rigid scale" by an observer to construct his inertial frame -- by (somewhat fictionally) transporting the rod (and also cloning copies of a standard clock at every point in the frame)...

Hey Everyone, I just wanted to ask for a bit of help on this research assignment I have to do. I have to show how Fractal Geometry contributes to the theory that Mathematics was invented. I have been looking into fractal dimensions and the fact that the dimensions we have labelled (1,2 and 3)...

I was intrigued reading * http://en.wikipedia.org/wiki/Quantity_calculus" that after two centuries axiomatization of QC has not been completed, though there are only 5 basic elements and 4[3] concepts: S[tandard],= U[nit], D[imension], Q[uantity]. I suppose nobody here has tackled the problem...

It is frequently stated that path integral formulation of quantum mechanics is equivalent to the more traditional canonical quantization. However, I don't think it is really true. I claim that, unlike canonical quantization, path integral quantization is not self-sufficient. That's because...

Is Abraham and Marsden's Foundations of Mechanics a good book to learn Classical Mechanics? In other words, if I were to go through this book (which I believe is more mathematical than physics-related) would I have a good, intuitive grasp of Classical Mechanics?

Hello, I'm a rising Junior at UC Berkeley, and I'm in a bit of a dilemma for the upcoming semester. I'm a math major, and intend to go to graduate school to pursue a Ph.D in Pure Math, but am not sure about the best path to take. Right now, I've completed the upper division Linear Algebra...

What role does the anthropic principle play in modern cosmology? How can we justify it? (Is it merely good old common sense or does it have a mathematical formulation?) What does it succeed in explaining? Is it scientific? Is it necessary?

After looking at the axiomatic systems of modern mathematics and asking myself what proves they are self consistent I went looking for an explanation and so far I have found only that they have not been proven self consistent nor likely will a proof ever exist. So the possibility of a...

Foundations of "Formal Limits" In Spivak's 4th Edition, one examples says: "The function f(x) = x2 is a little more interesting. Presumably, we should be able to show that f(x) approaches 9 near 3. This means that we need to be small enough to show how to ensure the inequality...

Dear All, Recently I have published a paper on Bell's theorem ASTP 4(20) 945-949 (2010). One can also find it on arXiv as http://arxiv.org/abs/1012.4990. I am interested in a discussion about the results of the paper. The claim of the paper is that mathematically Bell's theorem is...

Hey, I would like to start a discussion about the use of set theory in mathematical physics. I myself have done research in categorical physics and have seen the debates on how it can be an alternate foundation for mathematics. We can discuss here a few things, but try to stick to these...

"The Probing of, Approximation to and Idealization of Structure" for Foundations Hey, Over the past six years I have worked with Lucien Hardy at Perimeter in Waterloo and Prakash Panangaden at McGill. This paper is the culmination of thoughts on physics gleaned from that work...

Hello, Recently I've been attempting to put together a brief book on mathematics. The first section is short and introductory as I lead up into calculus. I kind of feel bad that I skipped over conics, geometric series, permutations and combinations, transformations of functions, and so many...

A discussion arose tonight about why spacers aren't used in the foundations in houses, as opposed to sidewalks where there are gaps every few feet to allow for thermal expansion. Some possible answers were that the foundation would be more constant temperature, or that the concrete was somehow...

http://arxiv.org/abs/1101.5113 Foundations of a theory of quantum gravity Johan Noldus (Submitted on 26 Jan 2011) After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of...

I took the first term of a Foundations of Physics sequence (251) last year, and understood most of the material fairly well. It was calculus based Newtonian mechanics; units and vectors; one-dimensional motion; Newton’s laws; work and energy; momentum and collisions. Since it's been a year...

I enjoy Physics like many and always keep an eye out for new discoveries, but is our understanding of the universe becoming too complicated and involved. We are constantly finding new information that does not fit the current model, but by adding a new constant or variable into the equations it...

Some of the draft chapters of this book are already on Arxiv. The book is scheduled to appear May 2011. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521114400 Many if not all of these were papers presented in a conference in Capetown honoring George Ellis on his 70th birthday...

I'd liked to know whether the postulates of standard QM are still valid in Relativistic QM By postulates I mean what is ussually stated in texbooks as follows 1)Physical states are determined by a vector in sate space E 2)A measurable physical quantity A is described by an observable A acting...

Hi I'm reading this great book Foundations of Analysis by Edmund Landau, a really old book that aims to build the foundations of analysis from basic arithmetic. I'm not that strong on proofing yet but am trying, here is my problem. Using these 5 axioms for the Natural numbers; I) \ 1 \in...

It is a well known view that mathematical logic together with set theory can be used as a foundation for the whole the rest of mathematics. Category theory also has been mentioned as a candidate for this, as an alternative of set theory. But recently I heard (from a non-mathematician) a view...

Let me propose a list of principles of classical dynamics, specifically designed for education, for introduction to novices: - In the absence of any force: objects in motion move along straight lines, covering equal distances in equal intervals of time - Composition of motion: position...

I'm 19 years old and I am in first year computer science. I've really fallen in love with the math that we do (discrete math, linear algebra, multivariable calculus) in this program and I'm thinking of switching majors to math or do a double major in math and computer science.. What I'm...

Is science, alone, the key to addressing the foundations of humanity's problems? Assuming we look at the great implications of what it can do for us.

I`ve started to read on FOM, and unfortunately I found the first paragraph cumbersome to get. Here is the text I started with: http://www.math.psu.edu/simpson/hierarchy.html The first paragraph was: "1. All human knowledge is conceptual and forms an integrated whole. All human knowledge is...

Conjecture: Most of the people doing research in the foundations of maths are 'not good enough' for maths. conjecture here is obviously a joke (but not completely). not good enough as in feel that maths is too difficult to understand (i.e not clear enough, too abstract). There's obviously also...

hey guys I am doing my first semester subject in first year. we're doing a subject on like free body diagrams and like working out like tension in the cables and angles and stuff. i really can't find a textbook with worked solutions and more questions? does anyone know where i can find some? its...

What theory are they? Set theory comes to mind but is that too broad?

I'm interested in understanding foundational issues in QM more deeply. For example, I'd like to be able to read and understand the literature on the Transactional Interpretation of QM and the Many-Worlds Interpretation, as well as the literature on decoherence. What can you recommend for a...