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## [English][Portuguese] Announcement / Aviso

Posted in Educational, Ensino Fundamental, Mathematics, Personal View, Problemas de Matemática, Segundo Grau, Vestibular on October 3, 2009 by Christine

[English] I have decided to run a separate blog on mathematics for Brazilian students, the Matemática Replay!. This blog [Theorema Egregium] continues with the usual material. Thanks.

[Português] Eu decidi manter um blog separado sobre matemática para estudantes Brasileiros, o Matemática Replay!. Este blog [Theorema Egregium] continua com o material usual. Obrigada.

## [Português] Problemas de Matemática do 2o. Grau

Posted in Educational, Mathematics, Problemas de Matemática, Segundo Grau, Vestibular on October 1, 2009 by Christine

Este “post” dá início (tentativamente) a uma série que irá contemplar problemas de matemática para alunos do 2o. grau (ensino médio brasileiro). O público-alvo é de alunos que estão passando por reais dificuldades em resolver problemas. As soluções serão apresentadas detalhadamente e, em seguida, serão propostos problemas similares.

————
Nos problemas do post de hoje, você precisará ter os conceitos de progressão artimética e de números complexos.
————

Você pode baixar gratuitamente os exercícios no link abaixo:

Problemas de Matemática do 2o. Grau – Como Resolvê-los Passo à Passo – Parte 1
[documento PDF, 3 páginas, 100Kb]

Atenção para Copyright na última página!

AVISO: Agora tenho um blog só de matemática, acesse: Matemática Replay!

## [Português] Como resolver problemas de matemática?

Posted in Educational, Ensino Fundamental, Mathematics, Problemas de Matemática on September 21, 2009 by Christine

Escrevi um tutorial de matemática para alunos do ensino fundamental brasileiro, para o 5o. ano (ou 4a. série, pelo regimento anterior), que pode ser baixado gratuitamente aqui.

Dicas de Matemática: Como resolver problemas?
Autora: Christine Córdula Dantas
Tamanho: 1.3 Mb
Número de páginas: 33

AVISO: Agora tenho um blog só de matemática, acesse: Matemática Replay!

## Click-the-Links!

Posted in External Links, Mathematics, Philosophy, Physics, Science on May 28, 2009 by Christine

Dear Readers,

Forgive my long delay in writing here. I spent the last few months wondering whether I would shutdown this blog or not. Well, I have decided that I will not, at least, not yet. So here are a few interesting links that I came across recently:

1) From the [PhilPhys] e-mail list, a talk by Stephen Summers (University of Florida).

“Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State”

Abstract: An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh-Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the vacuum, as well as the striking fact that the modular objects determined by the vacuum state and algebras of observables localized in certain regions of Minkowski space encode a remarkable range of physical information, from the dynamics and scattering behavior of the theory to the external symmetries and even the space-time itself. In addition, an intrinsic characterization of the vacuum state provided by the modular objects is discussed. [Foundations of Physics in Greater Paris]

2) A new issue of Philosophia Mathematica is available online [June 2009; Vol. 17, No. 2], in special:

- Mark Balaguer, Fictionalism, Theft, and the Story of Mathematics

- Francesco Berto, The Gödel Paradox and Wittgenstein’s Reasons

3) New edition of Edge:

What’s Next? Dispatches on the Future of Science (Edited by Max Brockman): “A preview of the ideas you’re going to be reading about in ten years.”

## Solvay Physics Conference 1927

Posted in Astronomy, Cosmology, Educational, Mathematics, Philosophy, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Relativity, Science on February 1, 2009 by Christine

## Unconventional computing

Posted in Biology, Concurrency theory, Cosmology, Mathematics, Philosophy, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Relativity, Science on January 17, 2009 by Christine

Just received.

…………………..

THE SCIENCE AND PHILOSOPHY OF UNCONVENTIONAL COMPUTING (SPUC09)

Cambridge (UK), March 23-25, 2009

SECOND CALL FOR PAPERS

We welcome submissions on topics normally classified under ‘natural computing’ or ‘unconventional computing’ or ‘hypercomputing’ including (but not restricted to) quantum computing, relativistic computing, biology-based computing, analogue computing, and also submissions on the philosophical implications of these new fields for topics including (but again not restricted to) philosophy of mind, philosophy of mathematics, the Church-Turing thesis.

Each presentation should last no more than 30 minutes; a further 10 minutes will be allowed for discussion.

Those wishing to make a presentation should submit by email a 250-word abstract of their paper to Mark Hogarth (mhogarth@cantab.net); enquiries to the same.

Registration fee (yet to be fixed) will be around £100.

Student bursaries are available.

Conference website: http://web.mac.com/mhogarth/Site/SPUC_Conference.html

ORGANISER

Mark Hogarth (Cambridge, UK)

CONFIRMED INVITED SPEAKERS

Selmer Brinsjord (New York, USA))

Jeff Barrett (Irvine, USA)

Philip Welch (Bristol, UK)

Tim Button (Harvard, USA)

Cristian Calude (Auckland, New Zealand))

István Németi (Budapest, Hungry)

Benjamin Wells (San Francisco, USA)

Hajnal Andréka (Budapest, Hungry)

Apostolos Syropoulos (Xanthi, Greece)

Susan Stepney (York, UK)

Bruce MacLennan (Tennessee, USA)

Peter Kugel (Boston, USA)

Mark Sprevak (Cambridge, UK)

Selim Akl (Kingston, Canada)

José Félix Costa (Swansea, UK)

ADVISORY PANEL

Mike Stannett (Sheffield, UK)

John Tucker (Swansea, UK)

Barry Cooper (Leeds, UK)

Sponsored by EPSRC through HyperNet (the Hypercomputation Research Network, EP/E064183/1)

## Something I’d like to do if I were younger….

Posted in Astronomy, Cosmology, Educational, Mathematics, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Relativity, Research, Science on January 16, 2009 by Christine

Just received.

…………………………………………………….

Dear Christine,

I am writing to ask for your assistance in drawing the attention of exceptional, highly motivated students to the Perimeter Scholars International (PSI) program.

PSI is an innovative, Masters level course designed to prepare students for cutting-edge research in theoretical physics. It provides a broad overview, allowing students to choose their preferred specialisation, and extensive tuition in formulating and solving interesting problems.

The due date for applications is February 1st: applications received after this date may still be considered but only as long as places remain available.

A number of outstanding lecturers have already signed up to teach, including for example Yakir Aharonov, Phil Anderson, Matt Choptuik, Nima Arkani-Hamed, John Cardy, Ruth Gregory, Michael Peskin, Sid Redner, Xiao-Gang Wen, and a number of Perimeter Institute research faculty. They will be supported by full-time tutors dedicated to the course.

All accepted students will be fully supported.

For further details, see www.perimeterscholars.org.

Thank you in advance for helping us to make this exciting opportunity known as widely as possible.

With my best wishes,

Neil Turok

Director
Perimeter Institute for Theoretical Physics
Waterloo, Ontario, Canada

## On the Nature of Time — essay competition

Posted in Concurrency theory, Cosmology, Mathematics, Papers, Personal View, Philosophy, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Relativity, Research, Science on November 13, 2008 by Christine

I have submitted an essay to the FQXi competition. If you are interested in reading it, click here.

Title: On the Nature of Time – Or Why Does Nature Abhor Deadlocks?

Essay Abstract

This essay aims at introducing a novel point of view on the nature of time, inspired by a synthesis of three seemingly unrelated concepts: Bergson’s notion of duration, Dijkstra’s notion of concurrency, and Mach’s notion of inertia.

Edit (June 9th 2009): Apparently, the essays on the nature of time are no longer available at the FQXi site. I have made a very few small corrections and modifications in my essay and a new version is available here (pdf file).

## Physical limits of inference – Theories of almost everything?

Posted in Mathematics, Personal View, Philosophy, Physics, Quantum Gravity, Science on October 16, 2008 by Christine

There is a review at Nature’s News and Views section by P.-M. Binder about a recent article by David H. Wolpert from NASA Ames Research Center, entitled “Physical limits of inference“. Binder writes:

A provocative contribution to the logic of science extends the theorems of Kurt Gödel and Alan Turing, and bears on thinking about prediction, the standard model of particles, and quantum gravity.

From the abstract of the paper, one reads

We show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. We call devices with that structure “inference devices”. We present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum-mechanical “uncertainty principle”.

[Yeah, Laplace was wrong even classically, according to my SF novel... ]

and

(…) We informally discuss the philosophical implications of these results, e.g., for whether the universe “is” a computer.

I find it very surprising that this was published in Physica D: Nonlinear Phenomena, and not in a philosophical journal. I have no criticisms against this work in particular (I did not read the paper in full), it is just that it does not seem, from a first impression, a physics paper per se, as much as interesting as it may seem.

Another (somewhat funny, I must admit, but it may be a reflection of my present pessimistic/sarcastic mood) excerpt from Binder’s review is this:

The other limitation is our inability to bring quantum mechanics and gravity into a single theory, although several viable alternative theories are being studied [9]. Quantum electrodynamics, a refinement of quantum mechanics, is defined by just two parameters (the charge and mass of the electron), whereas quantum gravity would require infinitely many parameters, and hence infinite experiments to determine those parameters, making it so far a meaningless theory.

BTW, Ref. [9] above is Wilczek’s book, The Lightness of Being.

## Physics Nobel Prize 2008 announced

Posted in Mathematics, Physics, Quantum Field Theory, Quantum Mechanics, Science on October 7, 2008 by Christine

The prize goes to three Japanese:

Yoichiro Nambu (1/2) “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” and to Makoto Kobayashi (1/4) and Toshihide Maskawa (1/4) “for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature”.

It is somewhat foolish, but I find exciting to see Nobel prizes announced. Congratulations!

Edit: Does anyone have a clue why Nicola Cabibbo did not receive the prize along with Kobayashi and Maskawa?

Edit: See also:

Physics Nobel 2007

## Back into print?

Posted in Mathematics on July 29, 2008 by Christine

If you would like to suggest and/or vote for some out of print math book to come back to print, visit here:

outofprintmath

## Requardt’s papers

Posted in Mathematics, Papers, Physics, Quantum Gravity, Science on July 28, 2008 by Christine

Back in 2005, when I started to read more and more papers on quantum gravity, I have found one paper that really interested (and still interests) me a lot, and was the subject of one of my first posts back at my older blog.

- The Continuum Limit of Discrete Geometries, by Manfred Requardt [http://arxiv.org/abs/math-ph/0507017]

It is a well written paper, with lots of interesting mathematics (Gromov’s geometric group theory, random graphs, etc). As far as I know, it has not been much discussed in other blogs.

Recently, Requardt posted another interesting one, which I am presently reading:

- About the Minimal Resolution of Space-Time Grains in Experimental Quantum Gravity, by Manfred Requardt [http://arxiv.org/abs/0807.3619]

Abstract:

We critically analyse and compare various recent thought experiments, performed by Amelino-Camelia, Ng et al., Baez et al., Adler et al., and ourselves, concerning the (thought)experimental accessibility of the Planck scale by space-time measurements. We show that a closer inspection of the working of the measuring devices, by taking their microscopic quantum many-body nature in due account, leads to deeper insights concerning the extreme limits of the precision of space-time measurements. Among other things, we show how certain constraints like e.g. the Schwarzschild constraint can be circumvented and that quantum fluctuations being present in the measuring devices can be reduced by designing more intelligent measuring instruments. Consequences for various phenomenological quantum gravity models are discussed.

I like his writting style and the various points that he covers in his papers with sensible criticism.

## Bertram Kostant on E(8)

Posted in Mathematics, Physics, Quantum Gravity, Science on July 23, 2008 by Christine

I include here an email from Prof. Bertram Kostant to Ben Wallace-Wells on his view about the E(8) group and some considerations on Lisi’s theory. According to Lisi, this part of the email was permitted to become publically available.

Dear Ben Wallace-Wells,

The following is my response to your queries. In order to answer your question about the Lie group E(8), I found it necessary in the first paragraph to add some historical context. I hope it is not too burdensome to read.

Lie (pronounced Lee) group theory was developed by mathematicians towards the end of the 1800′s. An important accomplishment at that time was also a classification of the simple Lie groups. It turned out there were 4 infinite families and 5 exceptional Lie groups, the largest (containing all the others) of which is E(8). There is an unfortunate double usage here of the word “simple”. There is of course, the everyday usage (eu) meaning easy to understand and a technical use (tu) meaning not built up from other groups. For example, the title of Lisi’s paper is “An Exceptionally Simple Theory of Everything”. His use of Exceptionally Simple is a pun. The exceptional refers to the exceptional Lie groups and simple is (tu). Lie groups started entering physics in a serious way at the beginning of the twentieth century. Perhaps more prominent was Einstein’s theory of special relativity, where the Lie group involved was the Lorentz group. This is a (eu) group and occupies only a very tiny sliver of something as sophisticated as E(8). Also Bohr’s theory of atomic spectra uses the rotation group SO(3) and again is an (eu) and a very tiny sliver of E(8). For the most part, Lie groups were more or less put on the “back burner” by both mathematicians and physicists until the middle of the twentieth century, At that time, it became a serious object of study by mathematicians. I should make it perfectly clear that I am a research mathematician and not a physicist. My speciality is Lie groups and any use of physics terminology here is only what is common knowledge. On occasion I have been motivated by physics – for example, the marvelous development of quantum mechanics by physicists in the 1920′s. I believe that there were some stirrings about Lie groups by physicists in the middle of the twentieth century. I have the following prescient story to tell. I was a visiting member of Princeton’s Institute for Advanced Study in 1955. It was a Good Friday in April and Einstein was looking for the Institute bus to take him back home to 112 Mercer Street. Being Good Friday, the driver was on holiday amd I offered to drive him home. We had a wonderful conversation and at one point he asked me what I was working on. I told him Lie groups. He then remarked, wagging his finger, that that will be very important. Actually, I was quite surprised that he knew who Lie was. About a week later Einstein was dead. In the middle of the twentieth century, physicists developed what is called quantum field theory (Feynman, Schwinger, etc.) Also at that time, the powerful accelerators were producing a zoo of new particles. To deal with this menagerie of particles and to carry forward Einstein’s program of finding a unified field theory (unifying all 4 forces of nature), physicists came up with what is called the Standard Model (Weinberg, etc.) This involved what is called a gauge group. In fact, in the Standard Model, the gauge group is a (eu) simple Lie group. A more refined development was the grand unified theory (GUT) of Glashow and Georgi. Here the gauge group (SU(5)) was more interesting. The GUT theory happily confers a desired fractional electric charge on such exotic particles as quarks. These theories also unified three of the four forces of Nature.

The latter part of the twentieth century also saw the development, by physicists, of string theory. String theory has had vast consequence for mathematics (excluding Lie groups). However, as far as I know, there have been no experimental verifications of the physics involved. (For his work in this area, the mathematical physicist Ed Witten was awarded the most prestigious prize in mathematics.)

A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent “object” in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure. It is easy to arrive at the feeling that a final understanding of the universe must somehow involve E(8), or otherwise put, (tongue in cheek) Nature would be foolish not to utilize E(8). There was a good deal of publicity about E(8) in the last few years when a team of about 25 mathematicians, using the power of present computers and a very complicated program, succeeded in determining all of the vast number of (to use a technical term) characters associated with it. Incidentally, one of the main leaders of the team was an ex-student of mine, David Vogan. It was Vogan who told me about Lisi’s paper. Another person involved here is John Baez. Baez, (a relative of the singer Joan Baez) is a professor of mathematics at the Riverside campus of the University of California. Baez performs a great service to the Math-Physics community by publishing a very engaging weekly report on doings of mathematicians and physicists – explaining latest results in physics to mathematicians and latest results of mathematics to physicists. His week 253 report deals with Lisi’s paper. In effect Lisi is saying that E(8) is the ultimate gauge group. Lisi’s theory makes some astounding claims. Among them is that E(8) “sees” all the elementary particles in the Universe. In addition, Lisi claims that his theory unifies all 4 forces in Nature (the last being gravity) and thereby achieves Einstein’s dream of a unified field theory. String theorists, by and large, heartily dismiss Lisi’s theory. But among some prominent nonstring theorists (e.g., Lee Smolin), the paper has been acclaimed. Incidentally, string theorists utilize E(8), but not as a gauge group. According to Baez’s week 253 report, one of Lisi’s motivations in going to E(8) was that the Glashow-Georgi GUT theory “sees” only one generation of fermions. Apparently there are 3 “generations” of such particles. The Lie group E(8) has a triality construction and I believe that Lisi thought that this may be used to give all 3 generations. Since I had something to do with this triality construction, I became interested in Lisi’s paper. I remind you, I am not a physicist and cannot comment one way or another on the physics involved. However, mathematically, I was able to show, using beautiful results of such finite group theorists as John Thompson, Robert Griess, Alex Ryba and an important input from Jean-Pierre Serre, together with some old results of mine, that E(8) not only “sees” GUT in a natural way, but in fact is itself (viewed through one of the facets) a composite of two copies of GUT. This is the subject matter of what I have been lecturing about. One such lecture was at UC Riverside, which was filmed and put on line by John Baez.

Having seem the film, Lisi sent me an enthusiastic E-mail, saying my results were brand new to him and speculating on what the meaning of the second GUT might be. I am too happy to forward Lisi’s E-mail letter to you, if you wish to see it. At any rate, if there is any physical validity to E(8) as a gauge group, the ball is in the court of physicists to interpret what this doubling up of GUT might mean.

I am happy to cooperate with you on your New Yorker article. However, I think it is best to do this by E-mail and not via phone conversations. I wish to avoid all the misquotations attendant to the New Yorker publication having to do with the solution of the Poincare conjecture.

Bertram Kostant Professor Emeritus of Mathematics at MIT

## Garrett Lisi and Jacques Distler: debates revived

Posted in Mathematics, Physics, Quantum Gravity, Science on July 17, 2008 by Christine

Debates on Lisi’s theory are back being discussed over at n-Category Café from this post on chronologically, so that you can check the exchange progress.

However, it is difficult to tell ahead the end of this story. It appears that some sort of agreement is slowly and painfully being reached, but it is clear that there is still a long way to go.

[Previous posts on Lisi's theory can be found here.]

[Edit 19-Jul-08: An interesting summary by Distler is found in a previous entry from the above mentioned exchange, dated May 22, 2008, and pointed out by Urs Schreiber. It is interesting not only for being a summary of what he interprets from Lisi's theory and the points that he indicate as being problematic, but also because he actually finds what he calls "something kinda cool about the elements of the construction" and that it "would be mildly interesting to see what sort of actions one could build with this construction".]

## Course on Perelman’s proof

Posted in Educational, Mathematics on April 1, 2008 by Christine

Mathematician Terence Tao will be giving the course:

Perelman’s proof of the Poincaré conjecture

He will also include blog posts on the course.

PS – As far as I know, this is *not* an April Fools’ Day joke.

## New discussions on E8

Posted in Group Theory, Mathematics, Physics, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Science on February 25, 2008 by Christine

Recently, John Baez posted over at his blog a talk by Bertram Kostant on the exceptional group E8. It is interesting to follow it and the discussions over there if you are studying Lisi’s recent work. Or not. E8 is interesting per se.

Previous posts on this (on inverse chronological order): here, here and here.

## A new refereed paper

Posted in Concurrency theory, Mathematics, Papers on February 5, 2008 by Christine

A result still coming out from my short time in software engineering… My contribution was mostly from the mathematical side, and the first steps for making a connection with the MSCs.

## List of Books on Quantum Gravity and other helpful tips

Posted in Cosmology, Mathematics, Papers, Physics, Quantum Field Theory, Quantum Gravity, Quantum Mechanics, Science on January 17, 2008 by Christine

I’m writting this post to keep track of books on quantum gravity (and closely related/helpful books). I own only the first one, which I recommend if you are interested in the main conceptual problems of quantum gravity. Regarding the others, I am presently considering purchasing Thiemann and Henneaux & Teitelboim’s books.

There is also Daniele Oriti’s book, which is an edition of several contributions about various approaches to quantum gravity. As it appears, the book has not been released yet. You can learn more about it over at my old blog, Background Independence (scroll down after my two book reviews to find Oriti’s invited post). At that blog you can also find my “Basic Curriculum for Quantum Gravity” (scroll down a little more, after Oriti’s post, or use this direct link to a backup copy of that post, with comments). There, I link to several other helpful books and downloadable tutorials/papers. That list have not been updated. I believe these two papers by Ashtekar are useful recent reviews:

There is also Smolin’s 2006 Lectures on quantum gravity. See here for more details.

## Quantum Gravity Partition Functions in Three Dimensions

Posted in Group Theory, Mathematics, Papers, Physics, Quantum Field Theory, Quantum Gravity on December 7, 2007 by Christine

(Via Woit’s Blog). This is also an interesting paper by Alexander Maloney and Edward Witten: http://arxiv.org/abs/0712.0155

We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the Bekenstein-Hawking entropy and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the Hawking-Page phase transition between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results

Witten has written some months ago a paper in 3D quantum gravity and the monster group (see previous post here). Apparently, such ‘unphysical’ models may be (are supposed to be?) useful to learn about full quantum gravity.

## The Plebanski action extended to a unification of gravity and Yang-Mills theory

Posted in Group Theory, Mathematics, Papers, Physics, Quantum Field Theory, Quantum Gravity, Science on December 7, 2007 by Christine

(Via Physics Forums). This is the new paper by Lee Smolin: http://arxiv.org/abs/0712.0977.

We study a unification of gravity with Yang-Mills fields based on a simple extension of the Plebanski action to a Lie group G which contains the local lorentz group. The Coleman-Mandula theorem is avoided because the theory necessarily has a non-zero cosmological constant and the dynamics has no global spacetime symmetry. This may be applied to Lisi’s proposal of an E8 unified theory, giving a fully E8 invariant action. The extended form of the Plebanski action suggests a new class of spin foam models.

Notice the citation to Lisi’s recent paper.

I read Lisi’s paper and I’ll read this one. Sounds very interesting indeed, and a quite “fast link” to Lisi’s idea, that is, a connection of that idea with the LQG framework.

If you would like to discuss that paper in technical terms, I’ll be glad to host your comments here. Recall that this is a highly moderated, very high signal to noise ratio blog. Be educated.

Update: A personal view can be found here.

## Metaphysical ‘karma’

Posted in Mathematics, Personal View, Philosophy, Physics, Science on October 15, 2007 by Christine

A finite set of mathematical relations is the foundation of reality.

The objetive of science is to find those relations. As a consequence, science also attempts to clarify the ontological status of those mathematical relations. That is, to bring the metaphysical frontier in which they are deeply buried closer into the physical frontier.

If mathematics were reality itself, then reality would be an infinite substance, or an infinite number of substances, which would reflect in the impossibility of building physical laws.

(Ok, I want to believe that).

In any case, somehow, reality emerges to us as a deeply constrained thing. At the same time, science seems to have intrinsic limits to probe reality. Whether the former is a reflection of the latter, or vice-versa, seems to be our inescapable metaphysical ‘karma’.

.

.

See also previous posts (here and here).

## The Universe

Posted in Mathematics, Philosophy, Physics, Quantum Gravity, Science on September 30, 2007 by Christine

The Universe is all that physically exists, its the totality of all things: matter (energy), spacetime; all entities that can be realized, observed, sensed, deduced, measured. All within and outside horizons.

It is the whole, and hence only one by definition.

It is the ultimate reality, and hence only one by definition.

The mathematical — or, for what is worth, even mental — picture of many universes (the multiverse) can only be conceived into a larger “universe” in which the set of multiple universes belong, and hence the multiverse concept inexorably has the limit of an ultimate, “whole universe” or “meta universe”, or “final universe”.

There is only one universe.

The hypothesis of the multiverse has an intrinsic imperfection from its very conception. It is a fragile concept since from simple logic reasoning it always necessarily reduces to an ultimate, “one universe”.

It is an unnecessary hypothesis that I abhor and reject.

## Shut up and calculate?

Posted in Mathematics, Papers, Personal View, Philosophy, Physics, Science on September 27, 2007 by Christine

Tegmark’s new paper… I have no comments for the moment. I didn’t read it.

Update: Just finished reading it. Bad philosophy. Sorry.

## Can you solve it?

Posted in Mathematics on August 18, 2007 by Christine

Rubik’s Cube has approximately 43 quintillion possible configurations (that’s about $10^{19}$). Daniel Kunkle can solve it in 26 moves.

## Upcoming Abel Symposium — 2007

Posted in Algebraic Topology, Mathematics on July 29, 2007 by Christine

I’ve just learned from John Baez that he will be participating in the Abel Symposium this year. The Abel Symposia are organized by the Norwegian Mathematical Society, and you can learn about previous editions here. The program for 2007 is here.

John Baez will be giving a survey lecture on Higher Gauge Theory and Elliptic Cohomology.

Since this is all too much advanced mathematics for me, I content myself with listing below some references that seem to be suitable for my stage of understanding:

- The Heart of Cohomology, by Goro Kato.

- From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes, by Madsen and Tornehave.

These will add to my huge wish list.

BTW, check out Baez’s course on Quantization and Cohomology here:

I’m helping with preparing some figures for this course and trying at the same time to learn something from the process.

Update: John Baez has a new post on his talk over at n-Category Café.

Update: More on Abel Symposium on Baez’s TWF 255.

## Imre Lakatos: theory as a limiting process?

Posted in Mathematics, Philosophy, Physics, Science on July 7, 2007 by Christine

Via philphys list, I have just learned that

An extensive archive of Imre Lakatos’s papers and letters – mostly in English, but some in Hungarian – is held in the British Library for Political and Economic Science at the London School of Economics. Thanks to the generosity of an anonymous donor, Research Fellowships to a total amount of US\$ 25,000 will be available in the calendar year 2007 for scholars wishing to pursue some research project on Lakatos and/or his contemporaries that requires consultation of the archive. The Fellowships will be held at the LSE Department of Philosophy, Logic and Scientific Method which will also provide facilities for the Fellows.

And also, to make thinks more interesting:

Notes for prospective candidates: The LSE Lakatos Archive contains Lakatos’s notes and working papers dating from 1945 and other personal documents, including his correspondence from 1956 with some 1000+ correspondents including Agassi, Carnap, Feyerabend, Kalmar, Koestler, Kuhn, Polanyi, Polya, Popper, Quine, Szabo, Tarski, and many other figures of the philosophical, intellectual and academic establishments of the time.

I think this is an interesting opportunity for a good candidate willing to go a little deeper on the ideas of Lakatos. Since I really knew very little about them, except for a few glimpses from memory about this philosopher, I checked out a Wikipedia article on him, which has a nice summary of his life and ideas.

An interesting passage is:

For Lakatos, what we think of as a ‘theory’ may actually be a succession of slightly different theories and experimental techniques developed over time, that share some common idea, or what Lakatos called their ‘hard core’. Lakatos called such changing collections ‘Research Programmes’. The scientists involved in a programme will attempt to shield the theoretical core from falsification attempts behind a protective belt of auxiliary hypotheses. Whereas Popper was generally regarded as disparaging such measures as ‘ad hoc’, Lakatos wanted to show that adjusting and developing a protective belt is not necessarily a bad thing for a research programme. Instead of asking whether a hypothesis is true or false, Lakatos wanted us to ask whether one research programme is better than another, so that there is a rational basis for preferring it.

So would the conception of a theory be a limiting process? I do not refer here to the process of developing a theory per se, like the struggling years that took Einstein to construct his general theory of relativity. But to the behaviour of paradigm shift: would it be a limiting process, even though sometimes pumby, uneven?

More links on Lakatos:

- Science and Pseudoscience: you can hear the mp3 file or read the transcript.

- Lakatos award: given for an outstanding contribution to the philosophy of science, widely interpreted, in the form of a book published in English during the previous six years. (From this site I have learned about an interesting book, whose author was awarded part of the 2006 Lakatos prize — Harvey Brown, Professor of Philosophy of Physics, University of Oxford, for his book Physical Relativity: Space-time Structure from a Dynamical Perspective).

## Witten on 3D Quantum Gravity and the Monster Group

Posted in Group Theory, Mathematics, Physics, Quantum Gravity, Science on June 29, 2007 by Christine

Are 3D Quantum Gravity and the Monster group fundamentally related?

I’ll take some time to figure this out , so for the moment I’ll be collecting here some links of interest.

Witten’s paper and talk at Strings 07 about 3D Quantum Gravity. [I've posted about this here, where I also indicate links to blogs that are discussing the talks over at Strings 07, so you can send comments to that post as well].

Wikipedia article on the Monster Group.

MathWorld article on the Monster Group.

Baez’s This Week’s Finds # 66, where he gives an introduction to the Monster Group.

Solomon’s paper On Finite Simple Groups and Their Classification.

The Atlas of Finite Group Representations. See, in special, the sporadic groups — the Monster group.

A paper by T. Gannon: Monstrous Moonshine: The first twenty-five years.

Some books:

- Sporadic Groups by Aschbacher.

- Atlas of Finite Groups by Conway.

- Geometry of Sporadic Groups by Ivanov.

- Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics by Gannon (added later).

- Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Ronan; non-technical account (added later).

Update: Here are some very basic questions that I have posted over at PF. Answers are very welcomed.

1. Why is k “an integer for topological reasons”? (k is a parameter that appears in a second term — a multiple of the Chern- Simons invariant of the spin connection — added to the action).

2. Further, what is “holomorphic” factorization? (A pointer to the basic literature on this will suffice). Is it the only possible constraint?

3. He argues that the (naive) partition function Z_0(q) differs from the “exact” Z(q) by terms of order O(q). Would this be correct for any k?

4. He finds that for k=1 the monster group is interpreted as the symmetry of 2+1-dimensional black holes. How sensitive is this result with respect to the value of k, and to respect to the other assuptions used in the derivation?

Update on question #1: Here is the answer by John Baez (as posted over at PF) –

The Chern-Simons action S is invariant under small gauge transformations (those connected to the identity by a continuous path), but changes by multiples of a certain constant c under large gauge transformations. What shows up in path integrals is the exponentiated action exp(ikS) where k is some coupling constant. The consequence is clear: exp(ikS) remains unchanged under large gauge transformations if and only if exp(ikc) = 1, meaning that k has to be an integer multiple of 2 pi / c.

If you set up all your normalization conventions nicely, c = 2 pi, so k has to be an integer.

This stuff is explained a bit more in my book Gauge Fields, Knots and Gravity, in section II.4, Chern-Simons Theory. Also see the end of section II.5.

In 3d quantum gravity, the consequence is that the cosmological constant can only take certain discrete values!!!

It’s quite clear now! It was the phrase “topological reasons” in his talk that seemed mysterious to me.

Update: Question # 2 can be elucidated in this Wikipedia article on the Weierstrass factorization theorem.

Update: There is of course, Lieven le Bruyn’s excellent blog, formely known as “Neverendingbooks”, but recently reformulated into MoonshineMath, focused on the Monstrous Moonshine.

Update: John Baez also indicates this paper by Gannon.

Update: John Baez just wrote about Witten’s new paper on his TWF254 (see the blog entry here).

## Poincaré Conjecture Made Easy

Posted in Mathematics, Science on June 23, 2007 by Christine

I have just learned (via Peter Woit’s blog) about a recent article in Wikipedia, written by Christina Sormani, concerning the Poincaré Conjecture and its solution, given by Griori Perelman and Richard Hamilton (Columbia University).

The article is quite pedagogical and contains excellent graphics, with pointers to other articles, on-line lectures and websites.

## First steps in Quantum Concurrency

Posted in Algebraic Topology, Concurrency theory, Philosophy, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics on March 9, 2007 by Christine

Let us attempt a somewhat primitive reinterpretation of a quantum state as a set of processes.

You can see a process as a function that gives some output from a given input. It’s somewhat like an unitary operator. A given particle state evolves to another as a combined result of a set of many processing, “internally active elements”. Imagine a qubit. A set of quantum states encompassing any possible state between |0> and |1> is here what I call a set of “fundamental processes”.

Internally, a lot of activity is happening to the qubit. The processes are not simply independent agents, but active elements which share finite mutual “resources”. I’m not sure at the present stage what to make of these “shared resources” in such a reinterpreted quantum theory (in LQG, they could be seen as the edges of a spin network: nodes *share* common edges representing spin, so the evolution of spin network states could be seen as a result of how these processes act and share resources, and in the present case is to maintain gauge invariance). In other words, the processes do not act completely independently, but are concurrent in the sense that they need to access some shared resources in order to evolve.

I’m not sure what to do with when you observe the system in such a framework.

Imagine now a n-dimensional space in which every orthogonal axis represents a process. Every point along an axis is a representation of a given quantum state (input) evolving to another (output). For instance, in one axis you could set up the following “scheduling”:

|0> -> |1/sqrt(2)> -> |1> -> |0> -> …

in another axis, this one:

|1/sqrt(2)> -> |1> -> |0> -> |1/sqrt(2)> -> |1> -> …

and so on, so you see there is a quite a large number of possible schedules for the qubit. But, say, two processes could not be at the same “time” sharing the same resources: this translates to some constraint that represents the forbidden usage of (or action upon) the same common resource by different processes which are competing at the same “time” (here, “time” is also to be interpreted in some partially ordered sense).

All possible scheduling (histories) of each of the processes form, combined, a directed topological manifold that encodes *all* the possible histories of a given particle. “Directed” in the sense that there is a local partial order structure imposed on the manifold as the quantum states evolve (a direction of “time”). A point in this manifold represents a superposition of processes (state functions). But since the processes that evolve quantum states must share common resources, there are forbidden regions on the manifold because the processes cannot access the same resource at the same “time”. So there are natural constraints that must be obeyed, and these constraints determine a topological, typical signature of the quantum system in question.

These constraints (that actually forbid the system to go into some kind of “deadlock”) could be seen as correlations/anti-correlations between quantum states, thus providing an interpretation of why energy levels of a harmonic oscillator are quantized, for instance.

There is an emergent field joining topology and concurrency theory — “di”topology — that study these various ditopological manifolds, which carry this extra structure (“di”rection).

It turns out that the idea seems to be easier to grasp when you include gravity. The reason comes from the fact that the scheduling of concurrent processes can be described, as I said, in topological terms by a manifold with a local partial order, a ditopological manifold. And pictorially, spin networks (or spin foams, for what is worth) seem adequate to fit this idea in a more immediate sense because of causality issues.

But that is another story.

## Nature abhors deadlocks

Posted in Algebraic Topology, Concurrency theory, Philosophy, Physics, Quantum Computation, Quantum Field Theory, Quantum Gravity, Quantum Mechanics on January 16, 2007 by Christine

I’ve been working on the idea that quantum systems are inherently concurrent systems (see this previous post under construction). They can be examined under directed algebraic topology (or ditopology) tools (e.g., see here, or google about it).

The most interesting problem to model is quantum entanglement: underlying this phenomenon one abstracts out a quantum state as fundamentally corresponding to a set of concurrent processes. It would be interesting to examine how to restore local realism under this general hypothesis.

One can go further into this and ask whether quantization arises from the idea that, given that quantum systems are seen as concurrent systems, there are naturally forbidden regions in the multi-dimensional state space, where each dimension represents a concurrent process, defined by the fact that these processes locally share “resources” and no two processes can “act” on the shared resources at the same “time”. Forbidden regions correspond to the discretization of nature in the quantum limit.

So nature would fundamentally be a huge deadlock avoidance system.

Update: discussions can be found in the comment section of this blog entry over at n-Cateogry café.

Update: Below follows, for the record, a cut and paste from the discussion over at n-Category café. For the detailed links, please refer to that blog entry (see link above), where the comments appeared.

Christine, I assume the application of directed algebraic topology to concurrent systems is an outgrowth of the work of Herlihy and Shavit, which was done in the late 90s and won the 2004 Gödel Prize.

You might want to communicate with Prakash Panangaden at McGill about your work. He appears to have worked, as a theoretical computer scientist, on concurrent and distributed systems and also on quantum computing, and has a strong interest in the causal structure of general relativity and its connection to abstract notions arising in computer science.

Posted by:
Chris W. on January 17, 2007 1:58 AM |

In terms of applications of general geometrical methods to concurrency, the idea goes back to the 70’s. See Goubault, E. Geometry and Concurrency: A User’s Guide. But you are right to cite the work of Herlihy and Shavit as an evidence of how this subject is getting a lot of attention recently, and giving rise to important developments in the field. It looks a beautiful paper, but I have never studied it in detail.Panangaden also published in gr-qc, and this is one of his most interesting papers, I guess… I don’t know how far this is getting attention, but sounds an original and promissing line of research.

Best regards,

Christine

Posted by:
Christine Dantas on January 17, 2007 11:51 AM

Hi Christine, you probably already know that Carl Petri, one of the founders of Concurrent Systems as a field of study, used to propound the view that an adequate semantics for concurrency would need to be sufficiently broad to also encompass physics.

From what I’ve been reading recently on Anima ex Machina blog he’s updated this position somewhat to a more “out-there” Universe-is-a-Petri-net kind of stance. He might be right! (as might Smolin – I saw your Amazon review!) On the same page I linked you can also find thoughts of Seth Lloyd and some others on this topic from a conference in Berlin last year.

You’re probably also familiar with Vaughan Pratt who clearly thinks very deeply on this sort of topic (although his publications can be frighteningly dense).

When I was a CS student as Glasgow they used to ask us questions like the “big simulation” argument, just to freak us out. I was never able to see why this would confuse a hardy theoretical physicist though — surely they’d be interested (in theory) in the turtle at the bottom of the tower, ie the real simulation that presumably has to simulate itself?!

I’m looking forward to seeing where the quantum lambda-calculus course goes with this kind of thing. Quantum computation seems to rely on arbitrary-precision complex amplitudes — but having gone to all the trouble of defining True and False as morphisms in the course, surely we won’t now be allowed to pull high-precision complex numbers out of the hat? If you were designing a programming language they’d need to be defined and computed themselves somehow… who “computes” these amplitudes that they’re relying on?

Posted by:
Allan E on January 17, 2007 2:09 AM

Hi Allan,

And according to Nielsen and Chuang,

“Quantum computation and quantum information has taught us to think physically about computation (…) we can also learn to think computationally about physics.”

This view is attractive and I believe physics is heading towards this broad idea. I do not have a clue how far this will lead us.

Concerning Petri nets, these and other classical concurrency models have been generalized to the concept of po-spaces (“po” from “partial order”). See Sokolowski, S., Directed topology and concurrency a short overview.

Best,

Christine

Posted by:
Christine Dantas on January 17, 2007 12:21 PM

And concerning the question in your last paragraph, I don’t know how to answer to that… There is a huge gap between a broad idea and the technical details that one has to face in order to make the idea actually work or make sense! But thanks for pointing that out, I’ll have to think about it.

Posted by:
Christine Dantas on January 17, 2007 12:31 PM

Let me see if I understand what you’re getting at. If there are correlations among a set of concurrent processes, they must be constrained to avoid deadlocks. Perhaps the necessary constraints induce correlations and anti-correlations among states and state transitions in the system that resemble correlations among quantum states. These correlations also imply that the system avoid parts of its state space.

You seem to be assuming discretization at the outset, insofar as the number of concurrent processes is finite, and the associated state space is finite. Should I assume that you have in mind a continuous analog of a set of concurrent processes?

Here is a simple and fairly concrete model you might want to examine. Consider the state space to include a set of n Boolean variables, and the concurrent processes to be n Boolean transition functions of two variables that yield a “subsequent” state for each of the variables. The processes (transition functions) share resources in the significant sense that each of the functions operates on two variables, at least one of which might be used as an input by another function. What would constitute a deadlock in such a system, and what is required to avoid it? Is there necessarily a stochastic component to the system’s behavior? That is, does the transition structure have to rearrange itself every so often, in a way that can’t be described deterministically? I realize this is a very sketchy problem formulation.

By the way, with respect to the relevance of algebraic topology, the set of transition functions in this simple model can be considered as defining an abstract simplicial complex; the Boolean variables are the vertices and the functions define the edges. (Remember however that these functions have some internal structure, since we have 16 distinct, albeit interrelated, Boolean functions to choose from.) My previous questions can then be posed as questions about the “moves” that can and must occur within this complex, in order to avoid certain “pathologies” in the evolution of the system. (By the way, in this light, the collection of transition functions can be loosely regarded as a “gas” of edges [1-D!] which is evolving in parallel with and necessarily coupled to a “gas” of Boolean state variables.)

One more point: The Boolean variables are of course undergoing transitions with successive “time steps”. One might ask if one can define a causal order on these transitions or “events”. That is, given one such event, can one say that it was preceded in a well-defined way by another set of events, and followed accordingly by yet another set of events? It is not immediately evident how such a description is to be derived from the transition functions, although one might plausibly expect that it should be possible.

(I have in mind here a complementary description in terms of causal sets. By the way, regarding the compatibility of discreteness based on causal sets with Lorentz invariance, see Discreteness without symmetry breaking: a theorem [1 May 2006].)

Posted by:
Chris W. on January 17, 2007 4:26 AM

Dear Chris W.,

Thanks for this elaborate comment. Your first paragraph summarizes well the broad idea.

And yes, one could assume a continuous “scheduling” of the processes, and also the space could be assumed to be infinite dimensional. What I think is important here is to assume a local partial order – a “po-space”… (I’m interested in ergodic moves…) Examples of such spaces are found here:

* Sokolowski, S., Classifying holes of arbitrary dimensions in partially ordered cubes. Tech. Rep. 2000-1, Kansas State University, Computing and Information Sciences, Aug. 2000. linke here.

* Raussen, M., Geometric investigations of fundamental categories of dipaths. Unpublished, 2001. (sorry, can’t find the link now).

* Gaucher, P., About the globular homology of higher dimensional automata. Cahiers de Topologie et Geometrie Differentielle Categoriques XLIII-2 (2002), 107156. link here.

And thanks for proposing a problem. I guess we all have sketchy ideas for the moment! No problem about that, in fact it is great to know that this is quite an open field for research.

Your comment has given me months to think over! Don’t have much valuable to add for the moment, but thanks a lot.

Christine


text:
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2009-08-19, 16:02   #1189
gd_barnes

May 2007
Kansas; USA

2×5,279 Posts

Quote:
 Originally Posted by mdettweiler Ah, that would make sense. Both G8000 and G7000 crashed a couple of times after the outage, as always seems to happen after an outage. They seem to have stabilized now, though I've put them in a loop so that they'll restart if they do crash again.
They kept crashing Max. Please don't use the phrase "couple of times" when you don't know how many times. Just look in the restart.txt file. There are multiple crashes. I looked at 3 AM CDT this morning and I saw that both had crashed again within the last few hours and were automatically restarted with the loop thing.

You are bound and determined to gloss over this whole issue without doing a detailed look at the exact times and matching up when the rejected results were originally handed out. I took 2 hours last night to do that for you now. How about looking into it this time please?

Please calculate when the 26 rejected results were originally handed out today. I saved them off under an obvious file name. Like I said, I only had time to look at the first 2-3 and those were handed out at 09:55-10:00 CDT on Aug. 18th. Simply take the time that the original result was returned and subtract the # of seconds that it took to return it.

I'm not going to back off on this until we nail it down. I nailed down 10 rejected results to the original power outage. The other 46 still have no explanation. How do we know that they were as a result of yet another crash? We don't. We need to match up exact crash times with times in which the original pairs were handed out.

We seem to have gotten into this habit of glossing over these server problems and that habit needs to end.

I don't know if this will help but it can't hurt:

On port G8000 only, please increase the JobMaxTime to 2 days.

Please tell me how you safely stop the server to do this. If you can let me know how that is done, then I'll do it if it is needed in the future. I now how to change the JobMaxTime and to restart it but don't want to create a problem when I stop it.

Karsten, can we talk you into returning pairs normally instead of ~100 at a time about twice a day? If you need to do so many at a time, how about you write a script to do ~20 each hour for 5 hours or something like that? That may help some.

Gary

Last fiddled with by gd_barnes on 2009-08-19 at 16:06

 2009-08-19, 19:27 #1190 kar_bon     Mar 2006 Germany 24·3·61 Posts i've sent the 2 outstanding pairs at n=957k for GB8000 some time ago and they are in the "last copy off"-file, but the "First unprocessed k/n-pairs" still show one of them! why? was the prune-time not 1 hour? please edit the stats-page for the GB ports to show those settings like the IB ports! PS: the stats updated 14:45 CDT with n=971k! Last fiddled with by kar_bon on 2009-08-19 at 20:08
 2009-08-19, 20:52 #1191 MyDogBuster     May 2008 Wilmington, DE 22×23×31 Posts What has this http://nplb.ironbits.net/ been replaced with? You know, the one with the IB port, all the primes for the day, the first n to process, links to the rejects, results for the day, etc; in the vertical format. Last fiddled with by MyDogBuster on 2009-08-19 at 20:56
2009-08-19, 21:10   #1192
Lennart

"Lennart"
Jun 2007

25×5×7 Posts

http://noprimeleftbehind.net/index.php

Lennart

Quote:
 Originally Posted by MyDogBuster What has this http://nplb.ironbits.net/ been replaced with? You know, the one with the IB port, all the primes for the day, the first n to process, links to the rejects, results for the day, etc; in the vertical format.

 2009-08-19, 21:11 #1193 AMDave     Jan 2006 deep in a while-loop 66610 Posts
 2009-08-19, 21:14 #1194 AMDave     Jan 2006 deep in a while-loop 12328 Posts SNAP!
 2009-08-19, 21:50 #1195 MyDogBuster     May 2008 Wilmington, DE 1011001001002 Posts try http://www.noprimeleftbehind.net http://noprimeleftbehind.net/index.php Not the one's I'm looking for. The one I had in mind did not show the hourly progress. It did show all the primes found for that day listed by each port. It is similar to http://nplb-gb1.no-ip.org/llrnet/ but instead for IB. It did have a like to http://www.noprimeleftbehind.net, but also had links to all current results for the day, rejects, etc. Last fiddled with by MyDogBuster on 2009-08-19 at 21:50
2009-08-19, 22:04   #1196
mdettweiler
A Sunny Moo

Aug 2007
USA (GMT-5)

3×2,083 Posts

Quote:
Okay. I see that G7000 has restarted a number of times, while G4000 and G8000 have not. Note that there's no timestamps on the restart log file, so there's no way to know exactly when the crashes occurred.

As for the rejected results, here's a tally of how many were handed out when:
-10 rejected from marco.bs around 11:00 CDT, 8/18
-20 rejected from kar_bon around 15:39 CDT, 8/18
-21 rejected from kar_bon around 00:37 CDT, 8/19
-5 rejected from marco.bs around 2:23 CDT, 8/19

Note that we can't tell exactly when these were handed out because they were (like many rejected results) listed with a time of 0.0 sec. Correlating with times on the same k/n pairs in the main results files is not helpful in this case, since those could very well have been assigned at a different time.

Note that all of these rejected results are from G8000, a server which did not crash at all. Thus, we can't even circumstantially correlate these with any particular crashes. Even if it had been known to crash, then we wouldn't be able to know when the crashes happened; the time and date of restarts aren't logged.

I know it may seem like I'm glossing over this stuff, but quite frankly, LLRnet doesn't let me do much more than that. It just plain doesn't log enough info. Yes, we redirect the screen output to a file, but that's essentially useless since there's no timestamps on it. Because of this, most server glitches simply have to be glossed over, because any further investigation is just going to waste a lot of time on something that there's not enough information to pinpoint. The glitches usually (as is the case now) will be handled by the server through its normal processes of expiry and reassignment; there's just nothing more we can do except let it run its course.

This is one of the reasons why PRPnet will be very, very nice when it's all ready for production use. It keeps very detailed logs that are of great help when tracing down problems of any sort.

As for the jobMaxTime, unfortunately it's a rather difficult process to stop the server once it's in the loop. I can do it, but in order to verify that the server's actually stopped correctly, I have to do a number of "geek things" that would be really, really hard to explain. Ditto for restarting with the whole loop thing. I've just now changed G8000 to 2 days jobMaxTime; if you need any such changes performed while the servers are in the loop thingy, let me know and I'll do it the absolute soonest that I can. I'd love to tell you how to do it so that it isn't dependent on my availability, but quite frankly, as I said that may be a bit difficult.

Max

 2009-08-19, 22:41 #1197 gd_barnes     May 2007 Kansas; USA 2·5,279 Posts I found calculating when the original pairs (that were later handed out a 2nd time) were handed out to be helpful, even though you couldn't determine when the duplicated pairs (that actually DID reject) were handed out. When the rejected results were returned doesn't help us much. Here's why: Likely the originals and the duplicates were handed out at about the same time. As you could see from the calculated times above, those original pairs were all handed out at 2 distinct times, one of which I was able to correlate almost exactly to the power outage. In other words, this tells me that there was some distinct problem that occurred at those 2 times. Had the original pairs been handed out at more random times, we could not come to such a conclusion. Even if the duplicated pairs had been handed out at distinct times, we couldn't discern such because, as you said, the rejected results don't show how much time was taken. By gleening as much info. as possible through calculations such as this allows us to hopefully cut down on it in the future. Anyway, I agree, it's not easy to gleen much info. from things on LLRnet. I guess we'll have to stop now. One more question: Will getting David's code on to my servers mean that we can avoid the "loop thing" code to restart the servers? If so, that will prevent quite a bit of this "after outage" multiple crashes that we keep encountering. Gary Last fiddled with by gd_barnes on 2009-08-19 at 23:00
2009-08-19, 22:51   #1198
gd_barnes

May 2007
Kansas; USA

2·5,279 Posts

Quote:
 Originally Posted by MyDogBuster What has this http://nplb.ironbits.net/ been replaced with? You know, the one with the IB port, all the primes for the day, the first n to process, links to the rejects, results for the day, etc; in the vertical format.
Quote:
 Originally Posted by Lennart
Quote:
 Originally Posted by AMDave
Quote:
 Originally Posted by MyDogBuster try http://www.noprimeleftbehind.net http://noprimeleftbehind.net/index.php Not the one's I'm looking for. The one I had in mind did not show the hourly progress. It did show all the primes found for that day listed by each port. It is similar to http://nplb-gb1.no-ip.org/llrnet/ but instead for IB. It did have a like to http://www.noprimeleftbehind.net, but also had links to all current results for the day, rejects, etc.

Lennart and AMDave, both of these responses are incorrect and both link to the same incorrect page. Ian asked for the "noprimeleftbehind" link name version of http://nplb.ironbits.net/. If everything is going to roll over to the new server, we need a new link name with "noprimeleftbehind" in it that specifically has this web page in it.

David, are you just going to leave this one link on the old "ironbits" link name or can we expect a new link that has "noprimeleftbehind" in it?

This is an important page that we don't want to lose. I'll Email David with a link to this posting.

Thanks,
Gary

2009-08-19, 22:52   #1199
kar_bon

Mar 2006
Germany

B7016 Posts

Quote:
 Originally Posted by mdettweiler I know it may seem like I'm glossing over this stuff, but quite frankly, LLRnet doesn't let me do much more than that. It just plain doesn't log enough info. Yes, we redirect the screen output to a file, but that's essentially useless since there's no timestamps on it.
so if you need timestamps for the output, try this: http://www.mersenneforum.org/showthread.php?t=10066

i've given those timestamps for the client-side to write this (still using this on my clients):

Code:
[2009-08-20 00:36:21] 2013*2^235548-1 is not prime.  Res64: 0BAAB87826667E2E  Time : 61.858 sec.
[2009-08-20 00:37:23] 2013*2^235595-1 is not prime.  Res64: A6ED66F8AA9036F5  Time : 61.854 sec.
[2009-08-20 00:38:24] 2013*2^235640-1 is not prime.  Res64: 8BCA8E2B12058E30  Time : 61.950 sec.
[2009-08-20 00:39:26]
note: a result and the following timestamp are a pair (couldn't handle this in other order).
so you have to read as.

Code:
[2009-08-20 00:37:23] 2013*2^235548-1 is not prime.  Res64: 0BAAB87826667E2E  Time : 61.858 sec.
[2009-08-20 00:38:24] 2013*2^235595-1 is not prime.  Res64: A6ED66F8AA9036F5  Time : 61.854 sec.
[2009-08-20 00:39:26] 2013*2^235640-1 is not prime.  Res64: 8BCA8E2B12058E30  Time : 61.950 sec.
every line has it's timestamp and result.

perhaps you can change the "server.lua" the same.

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Rates question

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An ambulance travels at 40 mph and can follow a 20-mile route making no stops to get to the hospital. A helicopter travels at one mile per minute, and the air route is 15 miles to get to the same hospital. However, the helicopter takes three minutes for takeoff and three minutes for landing. How many fewer minutes does it take for the helicopter to complete its trip (takeoff, flight and landing) than for the ambulance to complete its trip?

Apr 6, 2020

#1
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Keep in mind that Time=Distance/Speed

Ambulance:

Since the ambulance travels 40 mph, that would be the speed

Since the ambulance travels 20 miles with 0 stops that would be the distance

$$\frac{40}{20}=2$$

The ambulance takes 2 hours to make its journey

Helicopter:

Since the helicopter travels 1 mpm, that would be the speed.

Since the helicopter travels 15 miles, that would be the distance

$$\frac{15}{1}=15$$

The helicopter gets to the hospital in 15 minutes

We can add the 3 minutes for takeoff and landing and that adds 6 minutes to the journey

$$15+6=21$$

The helicopter takes 21 minutes to complete the journey

Since the ambulance takes 2 hours or 120 minutes and the helicopter takes 21 minutes:

$$120-21=99$$

The helicopter will get there in $$99$$ fewer minutes.

Hope this helped!!!

-Ako

Apr 6, 2020


text: Explain the processes involved in a redox reaction and describe what happens to their various components. In disproportionation reactions, a molecule is both reduced and oxidized; these types of reactions are rare. $A + B \rightarrow AB$. Assign oxidation numbers to each of the atoms. In a redox reaction, a spectator ion is an ion whose oxidation number does not change in the course of the reaction. $AB \rightarrow A + B$ . So here, we're forming sodium chloride from sodium metal and chlorine gas. Redox (reduction-oxidation) reactions are those in which the oxidation states of the reactants change. If there is no change in oxidation number, then the reaction is not a redox reaction. To identify a redox reaction, we must first calculate the oxidation number of each atom in the reaction. Sample 4. equation: Fe2O3 + 6 HCl → 2 FeCl3 + 3 H2O. (1) AgNO3 + NaCl ==>AgCl + NaNO3(2) BaCl2 + K2CO3 �==> BaCO3 + 2KCl(3) CuO + CO==> Cu + CO2(4) HCl + KOH �==> KCl + H2O. Identifying redox reactions. For example, the metabolism of sugars to CO2, which stores energy in the form of ATP, is a redox reaction. Keep this in mind as we look at the five main types of redox reactions: combination, decomposition, displacement, combustion, and disproportion. For this question, we're given a reduction-oxidation (redox) reaction. One thing is going to be oxidized if another thing is being reduced, and vice versa. Wiktionary google_ad_slot = "2147476616"; / Archives for Identifying redox reactions. We're asked to identify an answer choice that correctly states what the reducing agent is and what the oxidizing agent is. google_ad_client = "pub-0644478549845373"; (1) CH4 + 2O2 ==> CO2 + 2H2O(2) H2SO4 + Ca(OH)2  ==> CaSO4 + 2H2O(3) MgCrO4 + BaCl2  ==> MgCl2 + BaCrO4(4) Zn(NO3)2 + Na2CO3 � ==> 2NaNO3 + ZnCO3, June 2006-23 Which balanced equation represents a redox reaction? Redox reactions are matched sets: if one species is oxidized in a reaction, another must be reduced. In combustion reactions, a compound reacts with oxygen to produce carbon dioxide, water, and heat. The general form for this reaction is as follows: Boundless vets and curates high-quality, openly licensed content from around the Internet. All the redox reactions can be broken down into two different processes â a reduction process and an oxidation process. 2. In some redox reactions, substances can be both oxidized and reduced. Identifying Redox Reactions. A redox reaction occurs when oxidation and reduction take place in the same reaction. To identify a redox reaction, we must first calculate the oxidation number of each atom in the reaction. Displacement reactions, also known as replacement reactions, involve compounds and the “replacing” of elements. For example, take the equation for the reaction â¦ In this equation, the water is “decomposed” into hydrogen and oxygen, both of which are neutral. Redox reactions take place through either a simple process, such as the burning of carbon in oxygen to yield carbon dioxide (CO2), or a more complex process such as the oxidation of glucose (C6H12O6) in the human body through a series of electron transfer processes. A redox reaction is a reaction that involves both oxidation (the loss of electrons) and reduction (the gain of electrons). This happens as one species is acting as a reducing agent and is oxidised by another species that is acting as an â¦ For the Regents exam, they only ask you to find a reaction that an element changes oxidation number. In H2O2, oxygen has an oxidation state of -1. In the following image, we see methane combusting to release energy. For the Regents exam, they only ask you to find a reaction that an element changes oxidation number. //-->. In H2O, its oxidation state is -2, and it has been reduced. 6 NaOH + 3 Cl2 ---> NaClO3 + 5NaCl +3H2O b. CC BY-SA 3.0. http://en.wiktionary.org/wiki/redox Study the amino acid sequences of the same protein taken from four â¦ Wikipedia In this equation, Cl is reduced and replaces Br, while Br is oxidized. Identifying Reaction Types A redox reaction must involve a change in oxidation number for two of the elements involved in the reaction. Oxidation and reduction reactions or redox reactions are chemical reactions involving a transfer of electrons from one atom in the reaction to another. Identify the oxidizing and reducing agents. General equation:  $A + B \rightarrow AB$, The sum of oxidation states in the reactants is equal to that in the products: 0 + 0 → (2)(+1) + (-2). They occur as single and double replacement reactions. Regents redox reactions have a Free element on one side of a reaction and the same element bonded to something on the other side. The three common redox reactions are discussed below: 1. Oxidation-reduction reaction, also called redox reaction, any chemical reaction in which the oxidation number of a participating chemical species changes. Key Points. We call these oxidation reduction reactions. combustiona process in which a fuel combines with oxygen, usually at high temperature, releasing CO, redoxa shorthand term for “reduction-oxidation,” two methods of electron transfer that always occur together. CC BY-SA 3.0. http://en.wikibooks.org/wiki/General_Chemistry/Types_of_chemical_reactions 2 C 8 H 18 + 2 5 O 2 â 1 6 CO 2 (g) + 1 8 H 2 O. The term reduction comes from the Latin stem meaning â¦ Redox Reactions: A reaction in which a reducing agent loses electrons while it is oxidized and the oxidizing agent gains electrons, while it is reduced, is called as redox (oxidation - reduction) reaction. In this equation, Fe and H as well as O and Cl trade places. Example-          2H2 + O2 --> 2H2O             Free element ---> Bonded element, example 2         2KClO3 --> 2KCl +3O2       Bonded oxygen ----> Free oxygen, Not redox (ions)     K+ + Cl- --> KCl      watch out for the IONS, That is all you need to know for this question, Aug 2008-42 Which equation represents an oxidation reduction reaction? In terms of everyday life, redox reactions occur all of the time around us. Balance charges by using H + (in acidic solution) or OH - (in basic solution). When chlorine gas is bubbled into a solution of sodium bromide, a reaction occurs which produces aqueous sodium chloride and bromine. Boundless Learning Example: Identify â¦ Aug 2004-26 Which reaction is an example of an oxidation reduction reaction? Notice that another way we can write this reaction is by breaking up the ions as if they were dissociated in solution. Combustion reactions always involve oxygen and an organic fuel. The general equation of a combustion reaction is: $\text{C}_x\text{H}_y +\left( x + \dfrac{y}{4} \right) \text{O}_2 \rightarrow x \text{CO}_2 + \dfrac{y}{2}\text{H}_2\text{O}$. Guidelines for Balancing Redox Equations: Determine the oxidation states of each species. Oxygen has been both oxidized and reduced in the reaction, making this a disproportionation reaction. Oxidation-Reduction Reactions. A double replacement reaction is similar to a single replacement reaction, but involves “replacing” two elements in the reactants with two in the products. H 2 O. In displacement reactions, one or more atoms is swapped out for another. In this equation, both H2 and O2 are the molecular forms of their respective elements and therefore their oxidation states are 0. Balancing in a basic solution follows the â¦ Reduction is the gain of electrons or a decrease in oxidation state by a molecule, atom, or ion. Balance all atoms, with the exception of oxygen and hydrogen. 42 Which equation represents an oxidation reduction reaction? identify the reactions as precipitation, ab, or redox: a. Common Redox Reactions. Itâs a good idea â¦ The term oxidation was originally used to describe reactions in which an element combines with oxygen. Decomposition Reaction. As usual, oxidation and reduction occur together. Oxidation is the loss of electrons or an increase in oxidation state by a molecule, atom, or ion. As usual, oxidation and reduction occur together. Oxidation states can be used to identify redox reactions because in any scenario anything that is oxidized losses electrons and anything that is reduced gains an electron. Determine number of electrons gained or lost. A decomposition reaction works quite the opposite to â¦ Such reactions are also known as redox reactions, which is shorthand for red uction- ox idation reactions. In combination reactions, two elements are combined. This can be more easily visualized with lewis structures This is an introduction to oxidation reduction reactions, which are often called redox reactions for short. The term “redox” comes from two concepts involved with electron transfer: reduction and oxidation. They are essential to the basic functions of life such as photosynthesis and respiration. Let's see how to identify the oxidizing and reducing agents in a redox reaction. How to identify redox reactions. This particular resource used the following sources: http://www.boundless.com/ If there is a change in oxidation number, then the reaction is a redox reaction. posted on August 10, 2019. If there is a change in oxidation number, then the reaction is a redox reaction. And so let's start with sodium. Write each half reaction and for each: Balance atoms that change oxidation state. General equation (double displacement): AB + CD → AD + CB. Wiktionary In order to identify whether a reaction is redox or not, you can write separate half equations that show how electrons are lost/gained. These are known as disproportionation reactions. Identifying Oxidizing and Reducing Agents A redox reaction occurs when an electron is transferred from one substance to another. ; A negative â¦ In a galvanic cell, the current is produced by connecting an oxidation reaction to a reduction reaction in an electrolyte solution. A single replacement reaction “replaces” an element in the reactants with another element in the products. It depends on what kind of reaction youâre looking at. These processes are defined as follows: A simple mnemonic for remembering these processes is “OIL RIG”—Oxidation Is Losing (electrons), Reduction Is Gaining (electrons). Cd increases in oxidation state from 0 to +2, and Ni decreases from +4 to +2. Example: The reaction between magnesium metal and oxygen to form magnesium oxide involves the oxidation of magnesium. Second, we apply the definitions of oxidation and reduction. The loss of electrons 2. (8.2.4) Cl 2 (g) + 2 NaBr (a q) â 2 NaCl (a q) + Br 2 (l) Balancing Redox Reactions: Redox â¦ The product is H2O: the oxidation state is -2 for oxygen and +1 for hydrogen. $AB + C \rightarrow A + CB$ . The gain of oxygen 3. In decomposition reactions, a compound is broken down into its constituent parts. Combustion reaction â It is a type of redox reaction which occurs between molecular oxygen and compound to form oxygen-containing products. 2. Example- 2H2+ O2--> 2H2O Free element ---> â¦ Determine what is being oxidized and what is being reduced. 2 Cs + 2H2O ---> 2CsOH + H2 c. 2PF2I + 2Hg ---> P2F2 + Hg2I2 d. Na2SO4 + BaCl2 ----> BaSO4 + 2 NaCl e. MgO + H2O ---> Mg(OH)2 my answers: a. acid base b. redox c. redox d. precipitaion e. redox the correct answers: a. redox b. redox c. redox â¦ Redox Reactions. In fact, much of our technology, from fire to laptop batteries, is largely based on redox reactions. Split reaction into two half-reactions. Sample 3. equation: Cl2 + 2 NaBr → 2 NaCl + Br2, Calculation: 0 + [(+1) + (-1) = 0] $\rightarrow$ [(+1) + (-1) = 0] + 0. Similar to the previous example, H2O has a total oxidation state of 0, with each H taking on a +1 state and the O a -2; thus, decomposition oxidizes oxygen from -2 to 0 and reduces hydrogen from +1 to 0. One real-life example of such a process is the reaction of hydrogen peroxide, H2O2, when it is poured over a wound. Regents redox reactions have a Free element on one side of a reaction and the same element bonded to something on the other side. Decomposition reactions are the reverse of combination reactions, meaning they are the breakdown of a chemical compound into its component elements. google_ad_height = 60; First, we assign oxidation states, or numbers, to all the atoms in the reaction and determine the elements that are changing oxidation state. Redox reactions are oxidation-reduction chemical reactions in which the reactants undergo a change in their oxidation states. The oxidized element increases in oxidation number, while the reduced element decreases in â¦ Any chemical reaction in which the oxidation numbers (oxidation states) of the atoms are changed is an oxidation-reduction reaction. Combination reactions “combine” elements to form a chemical compound. In O2 however, its oxidation state is 0, and it has been oxidized. This is a redox reaction. At first, this might look like a simple decomposition reaction, because hydrogen peroxide breaks down to produce oxygen and water: The key to this reaction lies in the oxidation states of oxygen, however. General equation (single displacement): A + BC → AB + CA. Sometimes, the direction of a redox reaction can be determined by estimating the relative strengths of the reductants and oxidants. CC BY-SA 3.0. http://en.wikipedia.org/wiki/Oxidation-reduction Considering the equation above, we have 2 hydrogen (H) with the total charge +1[Refer the charges of the elements in the above table] and 2 oxygen (O) with the total charge -2 on the L.H.S and 2 hydrogen (H) with total charge +2 and only 1 â¦ And so before you assign oxidizing and reducing agents, you need to assign oxidation states. Combination reactions âcombineâ elements to form a chemical compound. In situations where an electrochemical series is not sufficient to absolutely determine the direction of a redox reaction, the standard electrode potential, E o, can be used. Something is being oxidized. CC BY-SA 3.0. http://en.wiktionary.org/wiki/combustion This occurs because in such reactions, electrons are always transferred between species. CC BY-SA 3.0. http://en.wikipedia.org/wiki/Oxidation-reduction, http://en.wikibooks.org/wiki/General_Chemistry/Types_of_chemical_reactions, https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/. 23 Which balanced equation represents a redox reaction. google_ad_width = 468; Or sometimes "redox" for short. There are three definitions you can use for oxidation: 1. How can you determine if a given chemical reaction is a redox reaction or not? Acid base reactions are characterized by a proton transfer process, similarly oxidation-reduction or redox reactions involve an electron transfer process. Apply the definitions of oxidation and reduction take place in the reaction is breaking. Are lost/gained 2 FeCl3 + 3 how to identify redox reactions one atom in the reaction of hydrogen,. ” an element combines with oxygen in H2O2, when it is how to identify redox reactions over a.... Its constituent parts of -1, one or more atoms is swapped out for another another. Oxidation-Reduction reaction, we must first calculate the oxidation state is -2, it... Dissociated in solution + CA involving a transfer of electrons from one atom in the.! And oxidation when it is poured over a wound term oxidation was originally used to describe reactions which. Occurs because in such reactions, also known as redox reactions current is produced by connecting an process. To a reduction reaction in which the oxidation number, then the reaction is redox or,! Their respective elements and therefore their oxidation states are 0 must first calculate the number... Reacts with oxygen to produce carbon dioxide, water, and Ni decreases from +4 to +2, and has. As redox reactions have a Free element on one side of a reaction, another must be reduced H +., they only ask you to find a reaction and describe what happens to their various components atoms with. Reduction reaction reduction-oxidation ( redox ) reaction can write this reaction is a change in oxidation number, then reaction! Therefore their oxidation states and what the reducing agent is ( reduction-oxidation ) are. Below: 1 assign oxidation states process and an oxidation reduction reaction in an electrolyte solution,... Two different processes â a reduction reaction are three definitions you can use for oxidation 1. Molecule, atom, or ion the general form for this question, we must first calculate the states. Being reduced, and it has been oxidized such reactions are oxidation-reduction chemical involving! Asked to identify an answer choice that correctly states what the oxidizing agent is connecting an reaction! Such as photosynthesis and respiration such as photosynthesis and respiration one or more atoms swapped. An introduction to oxidation reduction reaction in disproportionation reactions, involve compounds and the element! You need to assign oxidation states of each atom in the reaction, making a... One thing is going to be oxidized if another thing is being reduced and! And the same element bonded to something on the other side energy in the reaction Balancing redox Equations Determine... A molecule is both reduced and oxidized ; these types of reactions are oxidation-reduction chemical reactions involving a transfer electrons... Reactants undergo a change in oxidation state by a proton transfer process, similarly oxidation-reduction or redox occur. Also known as replacement reactions, a compound is broken down into its component elements a. 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Reaction that an element changes oxidation number, then the reaction, we must first calculate the oxidation.... Involves both oxidation ( the gain of electrons ) separate half Equations that show how electrons lost/gained!, atom, or ion + CB [ /latex ] Regents exam, only. Each atom in the reaction to laptop batteries, is largely based on redox reactions have a element! H 2 O to describe reactions in which the oxidation state by a molecule, atom, or.! Undergo a change in the reactants change, electrons are lost/gained ) reactions are rare the. It is a reaction is a redox reaction, a compound is broken down into its constituent parts involve electron! Into hydrogen and oxygen, both H2 and O2 are the breakdown a... Which are often called redox reactions into two different processes â a reduction reaction in the., atom, or ion from two concepts involved with electron transfer process not redox! And +1 for hydrogen and Ni decreases from +4 to +2 such a is. A large and diverse how to identify redox reactions of processes body of processes ox idation reactions equation: +! Proton transfer process, similarly oxidation-reduction or redox reactions being reduced charges by using H + ( acidic... One real-life example of such a process is the reaction between magnesium metal and oxygen produce... The products its component elements reactions can be more easily visualized with lewis structures redox... + ( in acidic solution ) species is oxidized in a redox reaction which occurs molecular! Swapped out for another ox idation reactions ( g ) + 1 H. Equation, the direction of a participating chemical species changes laptop batteries, largely. See how to identify an answer choice that correctly states what the oxidizing is. ) + 1 8 H 2 O write each half reaction and describe what happens their. ÂCombineâ elements to form magnesium oxide involves the oxidation of magnesium their oxidation states oxygen is present in reaction. Image, we see methane combusting to release energy reduction-oxidation ( redox ) reaction are rare of... 2 5 O 2 â 1 6 CO 2 ( g ) + 1 8 2...: identify â¦ Balance all atoms, with the exception of oxygen and.... G ) + 1 8 H 2 O the same element bonded to something on other... Combines with oxygen element in the reactants undergo a change in oxidation number, then the reaction a... Also called redox reactions can be both oxidized and what the oxidizing agent is and what is being reduced and... Show how electrons are lost/gained, we must first calculate the oxidation states + 3 H2O also as... Forming sodium chloride from sodium metal and oxygen to form a chemical compound involves oxidation. And heat to find a reaction and describe what happens to their components! And chlorine gas, its oxidation state breaking up the ions as if they were dissociated in solution ]... Is H2O: the reaction of hydrogen peroxide, H2O2, when it is a type of reaction. H2 and O2 are the breakdown of a participating chemical species changes,! Reducing agents, you can write this reaction is a redox reaction is “ decomposed ” into and! Diverse body of processes sometimes, the metabolism of sugars to CO2, which stores energy in the reaction,... You need to assign oxidation states place in the following image, we see methane combusting release... To +2 \rightarrow AB [ /latex ] fact, much of our technology, from fire to laptop,. The reverse of combination reactions how to identify redox reactions which stores energy in the form of,... In which the oxidation of magnesium of such a process is the of. State is 0, and heat O and Cl trade places following image, we must first calculate oxidation! Something on how to identify redox reactions other side such a process is the loss of electrons or a decrease in oxidation,. 2 â 1 6 CO 2 ( g ) + 1 8 H 2 O â¦ Let see... And compound to form magnesium oxide involves the oxidation number does not change in oxidation from!, or ion an answer choice that correctly states what the oxidizing reducing. Way we can write this reaction is a reaction and the same element bonded to something on the side! + 1 8 H 2 O matched sets: if one species is oxidized they were dissociated solution. To another the oxidizing agent is and what the oxidizing agent is from 0 to +2 relative... Oxygen, both H2 and O2 are the breakdown of a participating chemical species.... Has been oxidized the gain of electrons from one atom in the same element bonded to something on other! General form for this question, we must first calculate the oxidation states of the around! One or more atoms is swapped out for another this is an example of such process... Into two different processes â a reduction process and an organic fuel Cl trade places, has. Involve an electron transfer process or not, you need to assign oxidation states to â¦ / Archives Identifying... Into hydrogen and oxygen to produce carbon dioxide, water, and has! And Ni decreases from +4 to +2, and it has been both oxidized and reduced in course! + ( in acidic solution ) Free element on one side of a reaction that an element changes number. Choice that correctly states what the reducing agent is term oxidation was originally used to describe in. Real-Life example of an oxidation state is -2 for oxygen and hydrogen water, and has! These types of reactions are the reverse of combination reactions âcombineâ elements to form a chemical into..., substances how to identify redox reactions be both oxidized and reduced in the reaction is H2O: the oxidation number, the... Decomposed ” into hydrogen and oxygen to produce carbon dioxide, water, and Ni from! The reactant and both products ( single displacement ): AB + \rightarrow...


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 Mentor You can use Gauß' law and symmetry. But if you want to calculate it via an integral, I don't think there is an easier way.


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# How to know the distance of the black hole merger? [duplicate]

I have a question about the detection of the gravitational waves by LIGO. When there is no electromagnetic wave coming from the black holes, then how do they know in which distance it is?

## marked as duplicate by Rob Jeffries, Jon Custer, John Rennie black-holes StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 19 '17 at 5:51

This is not discussed very clearly in the 2015 LIGO paper in which they announced the first observation of gravitational waves. A better explanation is in this review article at p. 20.

There is a quantity $M$ called the chirp mass, which can be expressed in the following three ways:

$$M=\operatorname{function}(m_1,m_2),\qquad[1]$$

$$M=\operatorname{function}(hr,f),\ \text{and}\qquad[2]$$

$$M=\operatorname{function}(f,\dot{f}),\qquad[3]$$

where $h$=amplitude, $r$=distance, and $f$=frequency. Since $h$, $f$, and $\dot{f}$ can all be measured, it follows that one can determine $r$ and constrain the masses. These equations are based on general relativity's predictions of how the process should go. I think these closed-form equations are low-frequency approximations, so in reality they actually estimate the parameters by comparing with numerical simulations. There is also a relation of the form

$$Mm_1m_2=\operatorname{function}(t_\text{chirp},R),\qquad[4]$$

where $t_\text{chirp}$ is the length of the chirp in time an $R$ is the distance between the black holes. I think this is what allows one to constrain the individual masses rather than just $M$. But note that the individual masses are not very well determined in the 2015 event. The physics of equation [4] is simply that if one mass is very small and the other is very big, then radiation is weak, so the orbit persists for a long time.

• Thanks for the explanations. Then I guess what they get to is at first the distance r and then they predict the redshift by it. right? – shadi Aug 19 '17 at 11:12
• Also, this way, the masses cannot be exactly calculated, but just M can be calculated. Could you please tell me what $t_{chirp}$ is physically? What do you mean by the length of a mass in time? – shadi Aug 19 '17 at 11:15


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# Limits. Need recheck.

1. Sep 24, 2011

We have to graph these functions where they are real. (no need to graph where complex)

d)
For d Im getting a point at (1,0) and then half a c shaped graph opening towards the right. Is
this correct?
g)
For g I have 0 on the negative side. and a straight line in the first quadrant. :s Im not sure about this one.

I have to find the limit.
I realize this has two different directional limits positive and negative infinity. does that mean the actual limit does not exist?

Is this very easy? I mean iim confused do i simply have to plug in underroot etc or is it something much more complicated :S

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2. Sep 24, 2011

### HallsofIvy

Staff Emeritus
It looks to me like there is a serious typographical error in this problem! The point of the exercise is to show that, as x gets closer and closer to 2, f(x) gets closer and closer to 4 and then show that you can use the same argument with the general $\epsilon$ as you did with .01 and .001.
(a) asks "What is the value of $x_1$ such that f(x)= 2+ 0.01". That obviously should be "f(x)= 4+ 0.01"! And (b) should be " "What is the value of $x_1$ such that f(x)= 4- 0.01". f(x)= 4+ 0.01 is the same as $x^2= 4.01$. Find $x_1$ by taking the square root of both sides.


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What you need to know

Things to remember:

• It is helpful to think of the time as years first and then convert to other time units.

Before we start, it is important to know how long certain periods of time are.

Time Unit                    Number of Years

1 century                     100

1 millennium                1000

When converting time units into years, we can think of this just like we have when converting measurements.

Time Unit                     Multiply by                   Number of Years

1 century                          100                                         100

1 millennium                    1000                                       1000

What is 7 decades in years?

$$7\times10=70$$

7 decades is the same as 7 years.

What is 2.27 centuries in years?

$$2.27\times100=227$$

2.27 centuries is the same as 227 years.

What is 3.2 millennia in years?

$$3.2\times1000=3200$$

3.2 millennia is the same as 3200 years.

But, like with converting units, we can also go the other way by dividing.

Years to Decades                               Divide by 10

Years to Centuries                             Divide by 100

Years to Millenia                               Divide by 1000

How many decades are there in 75 years?

$$75\div10=7.5$$

There are 7.5 decades in 75 years.

How many centuries are there in 600 years?

$$600\div100=6$$

There are 6 centuries in 600 years.

How many millennia are there in 350 years?

$$350\div1000=0.35$$

There are 0.35 decades in 350 years.

Example Questions

$$6.33\times100=633$$

6.33 centuries is the same as 633 years.

$$4200\div1000=4.2$$

There are 4.2 millennia in 4200 years.