text:
# Mercury’s perihelion and Einstein’s General Relativity

Spyros wrote in response to Alberto’s comment that

GR and Brans-Dicke theory are both relativistic theories of gravitation. It is true that BD can explain the precession of perihelia. However i was referring mainly to the impossibility of explaining this precession using Newtonian mechanics.

I realize that physicists can declare any legal physics theory of gravitation to be “General Relativity” if they wish to do so. Even Newtonian mechanics is General Relativity given appropriate semantic conditions. The way a circle is an ellipse with 0 eccentricity any physics theory is General Relativity with a suitably chosen X = Y condition.

1. The difference between GR and other gravitation theories is academic

According to these pages General Relativity differs from RTG and Brans-Dick theory of gravitation in some important ways:

The relativistic theory of gravitation (RTG) disagrees with the Einstein’s general relativity (GR) in the crucial point: it denies the total geometrization and considers the gravitation on the basis of the classical Faraday-Maxwell’s field approach.

In theoretical physics, the Brans-Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein’s more popular theory of general relativity. It is an example of a scalar-tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity. The gravitational constant G is not presumed to be constant but instead 1/G is replaced by a scalar field φ which can vary from place to place and with time.

In reality, the difference between these theories and General Relativity is academic. General Relativity is so flexible, malleable, plastic and semantic that it can be molded into any shape to prove anything and everything including the existence of god. Physicists use general relativity to map the mind of god into their own careers. Molding General Relativity into a specific shape to prove a physicist’s preferred doctrine is where physics at.

2. General relativity as cargo cult

When physicists talk about the relationship of General Relativity to Mercury’s perihelion they always repeat standard physics mythology without applying even the smallest amount of scientific skepticism to it. But even a superficial questioning of physicists’ interpretation of the precession of Mercury’s perihelion reveals that we are faced with a cargo cult.

In general, any statement that claims that “General Relativity predicts” a natural phenomena is a lie. Einstein’s general theory of relativity is a rubric for an immense collection of statements. Rubrics cannot make quantitative predictions. To say that “general relativity predicts correctly the perihelion of mercury” is as meaningful as saying that “English language predicts that tomorrow it will rain.” Same thing.

3. Only the final unique single formula used in the computation is relevant to the computation

As a rational scientist I ignore derivations physicists use to navigate between legal physics nodes. I look at the operational equations. Philosophical ruminations invented by physicists to rationalize their derivations or their starting point in legal physics have no practical value. I look at the formula that is used to compute astronomical quantities. An astronomical quantity is not computed with a rubric but with one single formula. In this case the formula used to compute the perihelion of Mercury is the equation of the ellipse with an extra term Delta phi. No vestiges of General Relativity remains in the equation of the ellipse after the derivation.

Equation of the ellipse:

$r&space;=&space;\frac{r_0&space;(1&space;+&space;e)}{(1&space;+&space;e&space;\cos(\varphi))}$

Equation of the “general relativistic ellipse!”

$r&space;=&space;\frac{r_0&space;(1&space;+&space;e)}{(1&space;+&space;e&space;\cos(\varphi-\Delta&space;\varphi&space;))}$

The magical Delta phi:

$\Delta&space;\varphi&space;=&space;\frac{6&space;\pi&space;G&space;M}{c^2\:&space;r_0&space;(1&space;+&space;e)}$

4. Where is General Relativity in the ellipse equation?

To endow this Delta phi with general relativistic properties is charlatanism, shamanism and political doublespeak all combined into one. Or legalese.

And where is the famous spacetime of general relativistic physics in this simple equation of the ellipse with a Delta phi? No such thing exists. Physicists talk about spacetimes and fields and geodesics and so on but they eliminate them in order to obtain a practical geometric formula. Physicists tell us that they’ve discovered a fundamental thing called spacetime but when it comes to calculating astronomical motions they will eliminate their spacetime with all the other philosophical furniture they’ve ascribe to nature.

To repeat: physicists will lie through their teeth to defend their faith. In a professional sense, a physicist is a combination of a politician, a cardinal and a lawyer combined into one! The common characteristic of these professionals is that they are all master wordsmiths using semantics to prove their ideology. Mathematical semantics used by physicists is no different than prose semantics used by the others. This fact can be gleaned from the ugliness of the theories designed by physicists. And human knowledge is entrusted to these professional bureaucrats.

I realize that physicists have the authority to define the equation of the ellipse as a relativistic equation. There is nothing to be done about this at this point because we don’t know to whom to transfer physicists’ illegitimate authority on human reason. Yes, professional physicists will call the geometric equation of the ellipse a general relativistic equation because they added their own constants to it and there is absolutely nothing you can do about it.

Might is right. This is true in politics and also in physics.

Physicists have the monopoly on human reason and they use their monopoly to prove their dogma. Physicists are the Doctors of Philosophy who trace their ancestry to the Medieval Doctors of Philosophy against whom a Scientific Revolution was necessary to emancipate human reason from their monopoly.

Let’s look at how physicists obtain the equation of the ellipse from Einstein’s equations.

5. Derivation of the relativistic ellipse for the purpose of saving Mercury’s perihelion

As usual physicists start by writing down a piece of legal physics, in this case, the legal version of non-linear Einstein’s equations. After displaying Einstein’s authority prominently physicists start to eliminate one by one any term, concept or principle that they do not like; pick and choose solutions; cherry pick spacetimes, and add new terms as necessary. All legally, of course, everything is done according to the book.

In physics, the science of physical semantics, non-linear equals linear. In physics, a non-linear equation is simultaneously a linear equation. So these semantic wordsmiths start by writing non-linear equations and then say “let’s assume that our non-linear equations are linear” and work in the “weak field approximation” which is the semantic justification of the principle of equivalence for linearity. The relativistic ellipse equation is built upon many ad hoc but legal hidden assumptions. It is a piece of polemical semantics.

So after a long string of legal assumptions including linearity, spherical symmetry of Schwartzchild and what not, physicists eliminate all of the functionality of Einstein equations and find the ellipse equation with an ad hoc term Delta phi. The ellipse equation is to Einstein’s equation what a bicycle wheel attached to a New York light pole is to a bicycle. Yet, physicists still claim general relativity saves the perihelion because physicists stripped Einstein equations into the ellipse equation.

6. Same formula was derived by Gerber before Einstein

The same equation associated with Einstein’s name that saves the precession of Mercury’s perihelion was found by Gerber prior to Einstein. Einstein claimed that he never heard of Gerber’s solution. So here we have a formula derived from totally nonrelativistic assumptions by another German physicist and dismissed by Einstein and subsequent physicists because Einstein was on the first page of the New York Times but Gerber was not. This is how physics works.

Charlatanism? Yes. But this is just the tip of the iceberg.

7. Le Verrier and Newtonian mechanics

Physics propaganda claims that

1) Nineteenth century French astronomer Le Verrier could not predict Mercury’s small anomalous motion with Newtonian mechanics and

2) Einstein discovered an equation with his miraculous General Relativity and saved Mercury’s precession.

This story of Einstein explaining Mercury’s unexplained precession is mythology. Or fraud. Because we cannot prove the opposite no matter how strong our case is.

Let’s look at what Le Verrier actually wrote. Here’s his theory of Mercury’s motion. What do you see? I see that Le Verrier is not using Newtonian mechanics to model Mercury’s motion. He is just using standard practical astronomy methods to fit observations to a trigonometric model. That’s TRIGONOMETRY. I realize that physicists have the authority to read TRIGONOMETRY as NEWTONIAN MECHANICS but I can’t do anything about that. (Trigonometrical dynamics was invented by Newton himself.) The historical fact is that Le Verrier is not using Newtonian F = GMm/r^2 as physicists assert to compute the precession of Mercury’s orbit. No. He is just fitting observations to trigonometric expansions.

So what does this mean? It means that the cargo cult physics assertion that Einstein’s General Relativity explained something that Newtonian mechanics could not explain is wrong.

Einstein added an ad hoc term to the equation of the ellipse and pretended to derive it from his philosophical principles later to be sanctified under the rubric of General Relativity.

8. Physics is a secular religion

All this proves that physics is a secular religion. Physicists use semantic methods to manipulate mathematical symbols to prove their dogma. General relativistic explanation of the precession of the perihelion of Mercury proves this fact.

As mentioned above, Alberto wrote that there are alternative theories that save the observations equally well. There are alternative theories, yes, and also observations are saved best by the usual method of trigonometric expansions. So why do physicists attribute the perihelion of Mercury issue to General Relativity while there are many other ways to save the same observation more precisely? Because they are the faithful with authority to define. And that’s a dangerous combination.

Mercury’s perihelion is an astronomical issue that can be solved by adding an ad hoc term to Kepler’s rule. And this is what Einstein did.

The fact is that there are trigonometric astronomical methods that save Mercury’s perihelion with smallest residuals that the simplistic ellipse equation cannot match. The general relativistic ellipse equation is a physics textbook trope that will be repeated for ever but it has no practical value.

The more I study methods of physics the more it looks like a legal dogma defended blindly and fanatically by physicists. This is the state of science in the 21st century. State of physics rather, not science.

But of course physicists have the authority to save anything by defining new semantics. Physicists will simply say that the arguments above are historical arguments, and that they do physics, not history and they now have new methods to save the perihelion of mercury.

I, as a physicist, am mainly interested in understanding and explaining how physics works. So what mainly interests me is physics and not the history of physics.

Legal physics says that Mercury’s precession of the perihelion is saved by Einstein’s General Relativity. Any statement to the contrary is wrong by definition. No amount of criticism will ever change physicists’ ownership of the perihelion of mercury.

A perihelion of Mercury problem no longer exists in practice. NASA fits orbits into precise astronomical tables with numerical integration but physicists will perpetuate this mythology to eternity because it has become a bureaucratic habit.

## 8 thoughts on “Mercury’s perihelion and Einstein’s General Relativity”

1. Alberto G. P. says:

Hi Zeynel,

I’ve just read your post. Unfortunately, I’m not a physicist and I don’t have the appropriate knowledge to challenge some of your arguments. But, Why do you think the physicists don’t use logical arguments to formulate their theories? As you know, they use mathematical frameworks. Why do you ignore this fact?

Let me remind you that Mathematical Physics is a enormous field and you can see it as Math if you want. Therefore, Physics has a logical consistency. I agree with the fact that nature is rational is very strange. But, fortunately, Nature is rational (at least from a fundamental point of view). And physicists are scientifics that study nature from a completely rational viewpoint.
I think the results that can be obtained from physical principles are very rationals and objectives. General Relativity has done many predictions which have been confirmed by very precise and difficult experiments. For example, Geodettic effect. Do you think geodetic effect is easy to predict?. I don’t mean to predict it in a qualitative way, which is already very difficult, I’m referring to predict it quantitatively. I think if you don’t use any relativistic field theory, it would be impossible to predict this phenomenon. And the geodetic effect has been measured by a very sophisticated experiment, namely, the Gravity Probe B. I see this like a triumph of human’s mind. You should be proud, because, the humanity has been able to achieve this feat. Thanks to physics, thanks to Physicists.

2. Hi Alberto,

Why do you think the physicists don’t use logical arguments to formulate their theories? As you know, they use mathematical frameworks. Why do you ignore this fact?

In terms of technology it seems like an exciting experiment. But look at this picture. People at NASA are decent enough to put the “spacetime” in quotes. Indeed, the usual, trope of representing spacetime as a grid stretched by a mass at center is nothing more than photoshop physics. It is a metaphor, it is a visualization. Spacetime is fiction. It is fiction because it does not enter the operational formulas.

I’ve investigated in depth the Cavendish experiment, and Coulomb experiment also in some depth, and I’ve look into other historical physics experiments. In all of them I noticed that physicists interpret results to save their ideology.

In the case of gravity probe-B I don’t have the data to analyze the experiment in depth. But, is there a term for spacetime in operational formulas? I bet that there is not. So do you think that the residuals that physicists interpret as due to general relativistic spacetime can be interpreted by other models. By actual reality and not by reified virtual reality called spacetime? I think so.

What Gravity probe-B measures must have simple astronomical explanation.

So I am not doubting that researchers observe a residual in the period of gyroscopes, I only doubt their interpretations.

Here too we see physics mixing with politics. I think NASA’s claim must be investigated by independent hostile parties and non-relativistic astronomical explanation must come first. And under the freedom of informaton act NASA I believe must release all of the information in an intelligible format. Maybe, they do, I don’t know in this case, but they usually make everything available. The problem is to have the expertise to analyze the immense dataset.

Second I don’t believe that “General Relativity predicts” is a logical or rational or mathematical statement. General Relativity is a rubric. It cannot make any predictions. As far as I understand this prediction comes from a philosophical principle included in General Relativity, the equivalence principle, right?

Changes in the spin axis alignment of the gyroscopes are a direct measurement of the geodetic and/or frame dragging effects of general relativity.

This does not make sense. Unless they assume what they are trying to measure there is no GR in this measurement.

According to the laws of Newtonian physics, a perfect gryroscope, which is experiencing no external forces, will not drift. In the GP-B experiment this would mean that once a gyroscope is spinning in alignment with the guide star, it would stay aligned with that star forever.

This is a lie. First of all that’s not Newtonian physics but Newtonian dogma and Newtonian assumptions.

In the early 1960s, based on Einstein’s general theory of relativity, Dr. Leonard Schiff, chairman of the Physics Department at Stanford, predicted that the geodetic and frame-dragging effects would slightly change an orbiting gyroscope’s spin axis alignment in relation to the guide star.

How did he predict? I don’t know. I haven’t read the papers. But the predictions must have come by molding General Relativity into Newtonian mechanics, which means that what is used in essence is Kepler’s rule.

Here are several examples of scientific fraud and lies committed and perpetuated by physicists. Their method is always the same. If the experiments do not confirm their dogma then 1) define a new experiment and/or 2) fit observations to a mathematical framework and call the framework general relativity (or the dogma they are trying to save).

1. Newton and Halley fit three observations of a comet into a parabola and claimed to have computed its orbit from Newtonian dynamics. This is fraud. But it established the method of proving ideology by fitting a curve as a legitimate physics method.

2. Cavendish never observed force or G. But later physicists defined G and started to fit Cavendish data to G. Again, force is not proved. Newtonian mechanics is not proved. Only data is fit to a curve and the fit is called Cavendish experiment.

3. Coulomb faked his results but physicists built a law of nature on Coulomb’s faked experiment. Later, realizing that Coulomb experiment could not be duplicated, they defined another experiment, the hollow sphere experiment, as the Coulomb experiment. Again, measurements are fit into ideology.

4. Einstein’s original computation of Mercury’s perihelion was simply the ellipse equation with an ad hoc term. But physicists accepted this as proof of general relativity. Later they invented Parametrized Post-Newtonian framework which is nothing more than a fit of parameters and has nothing to do with General Relativity. Observations are saved by adjusting the parameters. They set (2+2gamma – beta)/3 to unity and defined it as the general relativistic value. It’s all a charade. Once again, general relativity enters the fit in name only. As a brand.

5. Ligt deflection was not proved by the original observations. But that’s no problem for physicists. They fit subsequent measurement into a mathematical framework and labeled their framework “general relativity.” Nowadays light deflection too is fit to PPN. All these independent fits are associated by marketing methods to General Relativity.

This is not rationalism but politics and marketing. What we see is always “artist’s renditions” and simulated videos and photoshopped spacetimes.

In this video Kip Thorne is explicitly lying. He is using the faked spacetime warp effect that has become real by repetition in the media and is telling us as if this was what really happened, as if light rays were indeed bent by warped fabric of spacetime into a potential well of earth. But this is not true.

A professor of physics, Kip Thorne, is explicitly lying to the public in a NASA press release by showing a photoshopped graphic and claiming that this was what the experiments will measure. If you tell him that he is lying he will refer to one of his papers because this is just a popular account of what happens.

So it is unfortunate that physicists are lying. They are doing the bidding of politicians who pay them and market General Relativity and Einstein as brands.

The evidence is overwhelming. Physicists fit observations into a mathematical framework and call their fit General Relativity.

3. Alberto G. P. says:

‘Spacetime is fiction’

I disagree, Spacetime means that space + time can be described in a unified way using a geometric theory. I agree that space and time seem very different things. For Newtonian mechanics, space and time are different concepts. At the beginning, Einstein didn’t even realize that space and time can be treatise in a same way, from a mathematical viewpoint. Spacetime was a great discovering for human knowledge. Spacetime has a full physical meaning. the curvature of spacetime can be measured. GPB is only a manifestation of this fact.

‘I’ve investigated in depth the Cavendish experiment, and Coulomb experiment also in some depth, and I’ve look into other historical physics experiments. In all of them I noticed that physicists interpret results to save their ideology.’

What are your reasons to think that Coulomb’s law is wrong? Because I could also say that my dog talks with me, and he said that Coulomb’s law is correct. The experiments can be repeated. If you repeat a suitable experiment, you will see that Coulomb’s law is valid. But Coulomb’s law has its own range of validity, although, it wouldn’t mean that Coulomb’s law is wrong.

‘In the case of gravity probe-B I don’t have the data to analyze the experiment in depth’

‘But, is there a term for spacetime in operational formulas? I bet that there is not.’

You bet, you lose, and I win, because I’m going to give you the derivation of the geodetic effect from the Schwarzschild metric. See below.

‘As far as I understand this prediction comes from a philosophical principle included in General Relativity, the equivalence principle, right?’

I think, GR can be derived from the equivalence principle plus the special relativity, but, I am not sure. Therefore, If I am not wrong, the geodetic effect can be derived from this two principles.

‘How did he predict? I don’t know.’

You can see his paper. I think, he started with a Schwarzschild solution and with the equations of motion for this solution
with this, he could predict the Geodetic effect by means of logical-deductive reasoning, namely, using math.

‘In this video Kip Thorne is explicitly lying.’

My thought is just the opposite. And you can see a nice explanation of the geodetic effect by Thorne, here.

‘If you tell him that he is lying he will refer to one of his papers because this is just a popular account of what happens’

He will probably refer to one of the scientific papers, because, in those papers, you could surely find a rational explanation about what he was talking. Zeynel, I accept that politicians lie, it may be true, I can’t accept that physicists lie, because, It is clearly false. I’ve read that physics has open problems. But open problems don’t imply that physicists have to lie. Why do you think physicists lie us? It’s the first time that I read this, and it seems to me hilarious, although, I respect all opinions.

‘Physicists fit observations into a mathematical framework and call their fit General Relativity’

GR is not a Theory of Everything, GR explains the gravitation from a classical viewpoint. GR doesn’t take into the uncertainly principle and therefore, GR can’t explain the quantum gravity. GR is the best theory of gravitation to date. No more.

4. Hi Alberto,

I disagree, Spacetime means that space + time can be described in a unified way using a geometric theory.

My point is that spacetime is one way of measuring distances, it is a choice. And in solar system astronomy it doesn’t appear to be a practical way to measure distances.

I think the reason for this is that in astronomy we can use distance and period. We don’t need space, time or spacetime.

Looking at the links you gave I see that there is no spacetime in practical formulas. That’s why I said that spacetime does not enter this problem.

Space and time are old scholastic forms physicists love to write philosophical commentary on but in practice these forms are not used, distance and period are enough. This is my opinion and I welcome any objections.

I agree that space and time seem very different things. For Newtonian mechanics, space and time are different concepts.

“Newtonian mechanics” is problematic for me. It is a rubric like “General Relativity.” It has no practical meaning. Rubrics are not used to compute astronomical quantities specific formulas are used.

And I don’t really care what Newton wrote in Principia on space and time as philosophical speculations. He may have said time is absolute, space is absolute or that god created space and time, it doesn’t matter. Those are Newton’s scholastic opinions.

I look at how Newton computes astronomical quantities not what he says. But physicists do not care how Newton computed astronomical quantities instead they love to read Newton’s scholastic commentary on space and time in the first few dozens of pages in the Principia and react to them.

Astronomical calculations are in propositions III.4, III.8, I.57, I.58, I.59 and I.60 (more info here). There Newton does not use absolute space or absolute time, he just uses Kepler’s rule to compute simple astronomical quantities. Properties of space and time are not measurable, they are philosophical properties.

Space and time are not needed in practical astronomy. In practical astronomy there is no room for philosophical concepts.

Spacetime has a full physical meaning. the curvature of spacetime can be measured. GPB is only a manifestation of this fact.

But I don’t think GPB is measuring the curvature of spacetime. This is solar system. Weak field. What is measured is the angle of precession.

Why does the gyroscope precess? Because of the motion of the spacecraft. The way, the bending of light was predicted originally by Newton and (Cavendish?) without General Relativity the precession of the gyroscope must have ordinary causes.

General relativity is a marketing tool NASA uses to get funding.

What are your reasons to think that Coulomb’s law is wrong?

Sorry, but, I din’t mean to say that Coulomb’s law was wrong. I was trying to say that Coulomb’s experiment did not prove that electricity obeyed inverse square law. In other words, Coulomb’s experiment did not prove Coulomb’s law because Coulomb faked his results. He just made three measurements. No one could duplicate his results.

Do you agree that physicists insist that Coulomb’s experiment proved Coulomb’s law while Coulomb experiment did not prove it because it was faked?

Yes, thanks. I just skimmed it, I’ll have to read it more carefully. But what I meant was that the actual measurement, the data points NASA obtains.

That’s where the art is. How do they obtain the data? What assumptions do they make? I don’t think any outsider can make sense of the data or how it is reduced.

We have to take their word for it. And that’s fine as long as they don’t assume general relativity and fit the data into general relativity. My impression is that this is what they do. Judging from the press conference and how Thorne explains everything in terms of GR, my impression is that they will fit data to general relativity.

My thought is just the opposite. And you can see a nice explanation of the geodetic effect by Thorne, here.

Thanks for the link. I started to watch it. But when I said Thorne was lying I was talking about the fact that he first starts by saying that the experiment is about a property of spacetime, then he produces the standard “rubber sheet analogy” graphic and calls it space – not spacetime.

And that graphic is a pictorial analogy, it does not represent what is measured. But Thorne explicitly says that radio waves are bent according to his diagram. You don’t think this is lying?

Maybe I am missing something so correct me if I am wrong and I’ll fix the post.

5. Alberto G. P. says:

Hi Zeynel,

Recently, a paper has been posted to the physics arXiv which claims that, maybe, General Relativity can’t explain the precession of Saturn’s perihelion. As you can see, GR doesn’t fit all experimental observations of the gravitational phenomenons, after all. The precession of Saturn’s perihelion is a gravitational phenomenon in the Solar System. Probably, the physicists will say that there is an error in the data analysis, although, it wouldn’t mean that physicists are lying us.

More accurate information here.

6. Recently a paper has been posted to the physics arxiv which claims that maybe general relativity can’t explain the precession of saturn’s perihelion after all.

The precession of Saturn’s perihelion is a gravitational phenomenan in the solar system.

Well, this is open to debate if we take the observational database as the final arbiter. Reading Iorio’s paper that you linked I see that, as I have been writing, observational data is reduced using numerical integration and physicists simply call numerical integration Newtonian dynamical effects, because they don’t want to give up their Newtonian faith.

probably, the physicists will say that there is an error in the data analysis although it wouldn’t mean that physicists are lying us

As far as I can understand from the paper, the residual error is too close to the observational error. And if you notice, as mentioned here, the paper must be very speculative and not supported by the original researcher Pitjeva, but written by Iorio. He explicitly says that the interpretation is his own, not Pitjeva’s.

more accurate info here http://arxiv.org/abs/0811.0756

Title is misleading too. So far nothing is confirmed.

In the paper Iorio implies that the effect may be dynamical:

In this paper I will focus on a recently detected non-standard feature of the motion of Saturn which, if confirmed as a genuine dynamical effect by further, independent analyses, may be added to the list of the Solar System anomalies not explained by known mundane causes.

But this claim is not supported by his table 2 where he lists “dynamical effects” and their analytical expressions.

1. N-body. The first dynamical effect is N-body and its analytical expression is “numerical integration.”

So, Iorio calls numerical integration “Newtonian dyamical effects.” This is a lie. It is true that the tradition goes back to Le Verrier who used trigonometric modelling and called it Newtonian mechanics, as I mentioned in the article. But the fact that it is an old physics tradition to call numerical integration “Newtonian effects” does not make numerical integration Newtonian. This shows how much physics is cargo cult science. In order to save Newton’s authority physicists have been calling numerical integration Newtonian effects caused by the Newtonian force.

2. Solar quadrupole J-2. Looking at the analytical equation, I see that it is an equation based purely on Kepler’s rule. It is geometric application of Kepler’s rule to Sun’s rotation. It is independent of any kind of dynamical, Newtonian or General Relativistic effect. To call this geometric Keplerian equation a dynamical effect is lying, it is a scientific fraud.

3. Small asteroid ring too is modified ellipse equation. So these are standard geometric methods to fit errors in the data. This is how observations are fit, I am not objecting to that, I am objecting to labelling these geometric terms with dynamical names in order to make them the property of physics. Again this tradition goes back to the founder of the profession who stole Horrocks’ trigonometric lunar theory and published it under his own name as Newton’s dynamical lunar theory. The tradition of scientific fraud in physics is an old one and it is continuing with increased levels.

4. TNOs again just an orbital fit.

5. Schwarzschild-like force turns out to be the modified ellipse equation again, as I mentioned in the article. This has nothing to do with General Relativity. Calling something “Schwarzschild” does not make that something General Relativistic. But it will make physics cargo cult.

Look at the term n in that equation. Hidden in n are two Parametrized Post-Newtonian Eddington-Robertson-Schiff parameters gamma and beta. Even adding Eddington-Robertson-Schiff does not make gamma and beta General Relativistic. Even if physicists were to add Einstein’s name as a last resort to gamma and beta they would still be not GTR.

What are gamma and beta? They are free parameters that physicists adjust to eliminate some errors in the data and then they claim to have tested General Relativity! What a charade. I think this is beyond charlatanism.

http://arxivblog.com/?p=702&cpage=1#comment-3252

7. Myrrh says:
8. David Showers says:

Hello, I really appreciate the preceding comments concerning GR. I am not a trained scientist but have always been skeptical of the claims of SR and GR. My skepticism stems from my belief that time is purely a psychological concept devoid of any physical characteristics. In other words, time exists only in the mind of man.

Further, I believe that humans have invented the concept of time in order to deal with the inevitability of death. Time and death are really two sides of the same coin.

If you believe in the hereafter as I do, then in enternity there will no longer be any need for time because death will have been vanquished. Time has no relevance to something that is infinite (eternal life in the hereafter).

Life on earth is finite and from a mathematical perspective may be viewed as a line segment (it has a beginning and an end). We breakup this line segment into equal intervals that we refer to as years or in some cases smaller units of time. Calibrating the line segment in this way allows us to measure our progress toward death. Measuring this progress serves a psychological purpose – unconscioius no doubt. Perhaps it gives us a sense of comfort to know that we can at least measure our position on the continuum of birth to death.

In the hereafter, we may view our life more as a ray – it has a beginning but no end. We cannot breakup something that is infinite like a ray into equal parts as we can with a line segment. Therefore, time has no relevance or usefulness in measuring something that is infinite.

In summary, I believe that time is a human invention that serves a psychological need related to death but has not physical reality. For this reason, I have to be skeptical of any physical theory that incorporates a concept like spacetime.


text:
Logo for Nemo Nisi Mors
Friends in need
Random Quote
Indeed, astrology is not a science at all, but merely a collection of superstitions and hokum that tries to use some of the terminology of astronomy but which rejects the logical thinking that is at the heart of science.
Kaufmann and Freedman
Modified 2019-02-16T12:54:18Z

What is the clock angle? Let us examine the relationships between the hands on an analog clock and their angles calculated in degrees. I will examine both a 12-hour dial as well as a 24-hour dial. I will also present a nice interactive animation to help you understand the relationships.

Note: The 12-hour clock will have its "12" or "0" at the top and "6" at the bottom. The 24-hour clock will have its "24" or "0" at the top and "12" at the bottom.

# Animation of clock angles

Before we dig into the theory, let us first get a visual overview of what clock angles are. In figure 1 we can see an animation of the angles that each hand represent.

Figure 1: Animation of clock angles in an analog clock, using the current Zulu time. You can control the animation by clicking in the figure and then toggle functionality by 'a' (showing angles), 'd' (showing the digital clock), 'f' (showing numbers in face), 'm' (smooth minute hand), 's' (smooth second hand), 'h' (smooth hour hand), 't' (12-hour or 24-hour analog dial) and 'c' (showing texts).

Note: Toggling the digital clock in the animation, between 24-hour and 12-hour AM/PM, is not an option. That is because the 12-hour clock with AM/PM is not an option.

Note: The 12-hour clock will of course use the numbers 0-11 when Zulu time is between 00:00:00 and 11:59:59 and the numbers 12-23 when Zulu time is between 12:00:00 and 23:59:59.

# Definition

Let $$h$$, $$m$$ and $$s$$ denote the current number of hours, minutes and seconds respectively. The hours are, of course, numbered 0-23. The minutes and seconds are numbered 0-59.

Denote the angle for the hour hand $$H^1$$ for 12-hour dial and $$H^2$$ for 24-hour dial, the angle for the minute hand $$M$$ and the angle for the second hand $$S$$. The angles are all measured in degrees and are calculated clockwise from the top.

Note: We will use $$H$$, instead of $$H^1$$ or $$H^2$$, when speaking about the angle of the hour hand in general terms and when it does not matter if it is a 12-hour or 24-hour dial.

Denote the velocity of the hands per time unit as $$X_y$$, where $$X$$ is the hand ($$H$$, $$M$$ or $$S$$) and $$y$$ is the time unit ($$h$$, $$m$$ or $$s$$). The velocity is measured in degrees per time unit. For example, $$M_s$$ denotes the number of degrees that the minute hand moves per second and $$H_m$$ denotes the number of degrees that the hour hand moves per minute.

## The second hand

The second hand rotates one turn, 360°, in 60 seconds. The rotation is therefore $$360°/60 = 6°$$ per second. We also have one turn per minute or 60 turns per hour. This means that it takes 1/6 seconds for the second hand to rotate 1°.

So, for the second hand we have the following three velocities:

S_s = (360°) / 60 = 6°
S_m = 360°
S_h = 360° * 60 = 21600°

The angle for the second hand, $$S$$, equals 0° at 0 seconds, 90° at 15 seconds, 180° at 30 seconds and 270° at 45 seconds. Every 30° for the second hand equals 5 seconds.

## The minute hand

The minute hand rotates one turn, 360°, in 60 minutes. The rotation is therefore $$360°/60 = 6°$$ per minute. We also have one turn per hour or 1/3600 turns per second. This means that it takes 10 seconds for the minute hand to rotate 1°.

So, for the minute hand we have the following three velocities:

M_s = (360°) / (60*60) = (1°)/10
M_m = (360°) / 60 = 6°
M_h = 360°

The angle for the minute hand, $$M$$, equals 0° at 0 minutes, 90° at 15 minutes, 180° at 30 minutes and 270° at 45 minutes. Every 30° for the minute hand equals 5 minutes.

## The hour hand

The hour hand is special and we need to distinguish between the two types of clock faces.

### 12-hour clock

The hour hand rotates one turn, 360°, in 12 hours. The rotation is therefore $$360°/12 = 30°$$ per hour. We also have 1/720 turns per minute or 1/43200 turns per second. This means that it takes 2 minutes (120 seconds) for the hour hand to rotate 1°.

So, for the hour hand, in the 12-hour dial, we have the following three velocities:

H_s^1 = (360°) / (12*60*60) = (1°)/120
H_m^1 = (360°) / (12*60) = (1°)/2
H_h^1 = (360°) / 12 = 30°

The angle for the hour hand, $$H^1$$, equals 0° at 0 (and 12) hours, 90° at 3 (and 15) hours, 180° at 6 (and 18) hours and 270° at 9 (and 21) hours. Every 30° for the hour hand equals 1 hour.

### 24-hour clock

The hour hand rotates one turn, 360°, in 24 hours. The rotation is therefore $$360°/24 = 15°$$ per hour. We also have 1/1440 turns per minute or 1/86400 turns per second. This means that it takes 4 minutes (240 seconds) for the hour hand to rotate 1°.

So, for the hour hand, in the 24-hour dial, we have the following three velocities:

H_s^2 = (360°) / (24*60*60) = (1°)/240
H_m^2 = (360°) / (24*60) = (1°)/4
H_h^2 = (360°) / 24 = 15°

The angle for the hour hand, $$H^2$$, equals 0° at 0 hours, 90° at 6 hours, 180° at 12 hours and 270° at 18 hours. Every 15° for the hour hand equals 1 hour.

## Velocities

Of course, the "three" velocities for each hand are in fact the same. It is the same quantity, denoted with different numerical values and units. We can see that the numerical value for the velocity per hour for each hand is always 60 times higher than the numerical value for the velocity per minute. The velocity per minute numerical value is always 60 times higher than the velocity per second numerical value. Finally, the numerical value for the velocity per hour is always 3600 times higher than the numerical value for the velocity per second. All because one hour equals 60 minutes and one minute equals 60 seconds.

Note: It is the same as 90 km/h denotes the same speed as 25 m/s. Same speed, different numerical values and units. Or that a temperature of 0 degrees Celsius equals 32 degrees Fahrenheit.

These relationships can be expressed as

X_h = 60 * X_m = 3600 * X_s

where $$X$$ is one of the hands ($$H$$, $$M$$ or $$S$$). This is true for both the 12-hour dial and the 24-hour dial.

# Smooth or discrete

The hands can rotate either smooth or discrete. When discrete the hands "ticks" and when smooth the hands rotates continuously.

Let $$u$$ denote the current number of milliseconds (numbered 0-999).

We have the following formulas for calculating the angles:

Discrete
S = 6 * s
M = 6 * m
H^1 = (60 * (h % 12) + m) / 2
H^2 = (60 * h + m) / 4
Smooth
S = 6 * (s + u / 1000)
M = 6 * (m + s / 60 + u / (60 * 1000))
H^1 = (60 * (h % 12) + m + s / 60 + u / (60 * 1000)) / 2
H^2 = (60 * h + m + s / 60 + u / (60 * 1000)) / 4

Note: When calculating $$H^1$$, we have to use modulo 12 of the hour value, since we are using 12-hour dial.

format: plain


text:
# 压缩因子

## 定义

${\displaystyle Z={\frac {p{\tilde {V}}}{RT}}}$

• ${\displaystyle \ p}$  为压力；
• ${\displaystyle \ {\tilde {V}}}$  为气体的摩尔体积
• ${\displaystyle \ T}$  为温度；
• ${\displaystyle \ R}$ 气体常数

${\displaystyle {\frac {P{\tilde {V}}}{RT}}=1+{\frac {B}{\tilde {V}}}+{\frac {C}{{\tilde {V}}^{2}}}+{\frac {D}{{\tilde {V}}^{3}}}+\dots }$

${\displaystyle \ Z_{c}={\frac {p_{c}V_{m,c}}{RT_{c}}}}$

## 参考资料

1. ^ Properties of Natural Gases 互联网档案馆存檔，存档日期2011-02-06.. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document)
• Peter Atkins, Julio de Paula. Atkins' Physical Chemistry 8th ed. Oxford University Press. 2006. ISBN 9780198700722.


text:
# 18: Chemistry of the Environment

Environmental chemistry is the scientific study of the chemical and biochemical phenomena that occur in natural places. It should not be confused with green chemistry, which seeks to reduce potential pollution at its source.

• 18.1: Earth's Atmosphere
• 18.2: Outer Regions of the Atmosphere
• 18.3: Ozone in the Upper Atmostphere
Most of the ozone in the atmosphere is in the stratosphere of the atmosphere, with about 8% in the lower troposphere. As mentioned there, the ozone is formed due to photo reaction. The ozone level is measured in Dobson Unit (DU), named after G.M.B. Dobson, who investigated the ozone between 1920 and 1960. One Dobson Unit (DU) is defined to be 0.01 mm thickness of ozone at STP when all the ozone in the air column above an area is collected and spread over the entire area.
• 18.4: Chemistry of the Troposphere
• 18.5: The World Ocean
Water is the most important resource. Without water life is not possible. From a chemical point of view, water is a pure compound, but in reality, you seldom drink, see, touch or use pure water. Water from various sources contains dissolved gases, minerals, organic and inorganic substances.
• 18.6: Fresh Water
In addition to water, many inorganic substances or minerals are essential to life. These substances ionize in water to form ions and their solutions conduct electricity. Therefore, they are called electrolytes. Because most of these substances are already dissoved in natural water, we list ions instead of the mineral they come from.
• 18.7: Green Chemistry
Green chemistry, also called sustainable chemistry, is an area of chemistry and chemical engineering focused on the design of products and processes that minimize the use and generation of hazardous substances. Whereas environmental chemistry focuses on the effects of polluting chemicals on nature, green chemistry focuses on technological approaches to preventing pollution and reducing consumption of nonrenewable resources.
• 18.E: Chemistry of the Environment (Exercises)
These are homework exercises to accompany the Textmap created for "Chemistry: The Central Science" by Brown et al. These are homework exercises to accompany the Textmap created for "Chemistry: The Central Science" by Brown et al.

Thumbnail: Acid mine drainage in the Rio Tinto River. (Public Domain; Carol Stoker @ NASA via Wikipedia(opens in new window)).

18: Chemistry of the Environment is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by LibreTexts.


text:
# Good evening Eshan sir...This is yester day solution sir.How sir electric field is independent r.Generally E = (1/4π€0) (Q/r^2).I did not understand explain sir.

Eshan
4 years ago
Dear Raju,

It is not true that electric field always follows the relation$\dpi{80} E=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{r^2}$. This is true only for electric field due to a point charge, or due to a uniformly charged solid sphere or spherical shell. In fact electric field due to an infinitely large charged conducting plate with charge per unit areaiswhich is also independent of. In case of infinitely large wire, it is Hence it depends upon the distribution of charges in the given situation.

Here we are asked about the value of ‘A’ such that electric field is independent of. Using the Gauss law, we arrived at an expression of electric field in terms of. Now this has a constant term in addition to a term having dependence as$\dpi{80} \dfrac{1}{r^2}$. But it is given that field must be independent of. So if the coefficient of this$\dpi{80} \dfrac{1}{r^2}$term becomes zero, then the electric field would only have the magnitude$\dpi{80} \dfrac{A}{2\epsilon_0}$. Hence we have put it to zero to find the value of ‘A’.

Hope that helps.


text:
# Math Help - De Morgan's second law

1. ## De Morgan's second law

Hi,

how do I prove De Morgan's second law $(AB)^c = A^c \cup B^c$ by using De Morgan's first law: $(E \cup F)^c = E^c F^c$

Thanks!

2. I do not know the why you have them numbered.
Here is a possiblity.
$\begin{gathered}
\left( {A^c \cup B^c } \right)^c = \left( {A^c } \right)^c \left( {B^c } \right)^c = AB \hfill \\
\left( {AB} \right)^c = A^c \cup B^c \hfill \\
\end{gathered}$

3. Hello,
Originally Posted by lds09
Hi,

how do I prove De Morgan's second law $(A \cap B)^c = A^c \cup B^c$ by using De Morgan's first law: $(E \cup F)^c = E^c \cap F^c$

Thanks!
Start from de Morgan's first law for $A^c$ and $B^c$ :

$(A^c \cup B^c)^c=(A^c)^c \cap (B^c)^c$

$(A^c \cup B^c)^c=A \cap B$ (by noting that $(A^c)^c=A$

Take the complementary of both sides :

$\underbrace{\bigg((A^c \cup B^c)^c\bigg)^c}_{=A^c \cup B^c}=\bigg(A \cap B\bigg)^c$

$A^c \cup B^c=(A \cap B)^c$

This is the second law.


text:
# A ¥9 Trillion Hole Emerges Inside The BOJ's Balance Sheet: "It’s A Pretty Dangerous Situation"

When it comes to accounting conventions, the Fed and the BOJ differ in one major way: unlike the Federal Reserve, the BOJ counts its bond holdings at the purchase price, minus amortization costs. In the old days before NIRP this wasn't an issue because with positive yields, it meant that with time, the value of any central bank bond purchases would accrete through maturity and never lead to a booked loss; however under NIRP, it means that the BOJ is purchasing hundreds of billions in bonds at prices that are so high they guarantee a loss, meaning that by maturity the central banks will face a cumulative loss on the face value of recent bond purchases.

From a purely accounting standpoint, it means that a gap has opened on the BOJ's balance sheet, representing the difference between the book and face value of the central bank's monetizations.

How big is the gap? According to Bloomberg as of August, the delta between the balance sheet and face value has ballooned to some 8.7 trillion yen, or $84 billion. That "gap" is the difference between the 326.7 trillion yen in BOJ bond purchases at face value, and where they are marked on the balance sheet in August, or 335.4 trillion yen. That gap is 42% bigger than before the introduction of negative rates in January, and rapidly rising. At the end of the 2015 fiscal year on March 31, the gap between the two valuations was 6.4 trillion yen and the BOJ wrote down 874 billion yen, according to documents seen by Bloomberg. That was covered by the 1.29 trillion yen in coupon income the bank received that year. However, since the coupon of all current and future purchases are negligible, the BOJ will see limited future current income, and thus will have to resort to other means to plug the balance sheet gap. “These numbers show the distortions of the BOJ’s current policies,” said Sayuri Kawamura, a senior economist at the Japan Research Institute in Tokyo. “The annual amortization losses are going to increase and consume the BOJ’s profits, and the risk is increasing that the bank’s financial stability will be shaken.” As Bloomberg adds, "while not an immediate problem because the BOJ’s income can cover the losses, the widening gap raises questions about the sustainability of the central bank’s bond purchases, which Governor Haruhiko Kuroda has said could be expanded." The BOJ did not have much to say about this troubling decoupling which will eventually require the BOJ to plug the hole: Tadaaki Kumagai, a spokesman for the central bank, said “the BOJ releases half-yearly and yearly accounts,” while declining to comment further. With the gap between the two valuations even larger now, it “would probably be a pretty safe bet” that the losses the BOJ will book for this fiscal year will increase from 2015, according to Naomi Fink, the chief executive officer of Europacifica Consulting. As Bloomberg puts it, "while when those losses may exceed its income is unknown, with the bank buying more high-price, low-income bonds, that time will probably come soon." Fink said that under some scenarios, this could even happen this fiscal year. How much losses can the BOJ absorb? The central bank currently has 2.69 trillion yen in a reserve to draw on to pay for bond losses. “In preparation for an eventual exit from stimulus, the BOJ last year started adding to its reserves to guard against bond losses, but if profits decline, there’s a chance that they won’t be able to continue that,” Japan Research Institute’s Kawamura said. “It’s a pretty dangerous situation now, even before they start to exit." At the current pace it is virtually assured that the BOJ's reserves will be depleted in the not too distant future. At that point the BOJ will have to approah the government to change legislation, allowing it to short up capital for future losses. How the market will respond to such an unprecedented central bank bailout is unknown. ## Comment viewing options Select your preferred way to display the comments and click "Save settings" to activate your changes. time for seppuku part of the samurai bushido honor code 9 trillion here, 9 trillion there, pretty soon you're talking about some serious Mugabe “ ¥9 Trillion Hole “ Hmm… It gives one pause… Just where is the event horizon and when does the whole Ponzi collapse into the singularity? The Japanese made their mistake a long time ago in the 1980's. They kicked the can down the road. The FED did the same thing in 2008 You eventually get something that looks like http://www.sciencecartoonsplus.com/gallery/math/galmath2b.php# The singularity being the Bank of Intl Settlements. Coming soon to a theater near you! Nine trillion yen, that's like a buck fiddy right ? ;-) 9 Trillion missing at the Fed & 9 Trillion missing at BOJ What a coincidence. https://www.youtube.com/watch?v=q9pnc7IXpC0 a tril here a tril there, pretty soon we are talking some real money. Why can't they just press delete on that file? It was created in a similar fashion. We're supposed to get all worked up because the control scheme imposed on us is coming to an end. Oh, they'll try to impose pain all right but if the fingers keep pointing at the perpetrators (the beneficiaries of the fiat printing) then things will work out ok after awhile. Stay on target... It works for email...oh wait! no worries, their new keyboards are en route with re-enforced ctrl and p keys A 9 trillion hole? Hell, no problem, just hit that CNTRL-P button a little more often, cuz up till now it's worked so beautifully hasn't it? www.traderzoogold.blogspot.com Yep, and just so long as the new "money" never gets in the hands of the average citizen, "inflation is contained".... Unfortunately, all stimulus is fungible.... why not just buy all the forests and rivers of the world? should be able to print all the fishes of the sea as well? No big deal. Resident Zero will sign an executive order saying: Let me be clear- we will bail out BOJ. Then he can go golfing. {the risk is increasing that the bank’s financial stability will be shaken} This suggests there's another player who would foreclose on the BoJ. There isn't such a player. Wait! So NIRP is bad for savers not only because they aren't earning interest - and are paying interest mind you - but because the bond's price is inverse to the said rate and is bought at a premium therefor sold at a loss? So is this why safes are being sold at a record pace and gold and silver are leading all asset classes in 2016? My god, what a surprise.... what really is amazing is the sheeple are waking up and stampeding.. shouldn't be long b/4 the hard asset panic of 2016., I think I agree with Jim Rickards - inflation (most of it) will come all at once. There will be exactly ZERO time to react or mitigate against it. No gold available for delivery is the trigger. All wars are fought for gold and when the easy pickings are all gone - Ukraine, Lybia, Venezeula, etc - then a war between super powers will break out. then a war between super powers will break out. well fvk, then all my bennie weenies stocked in the basement at for naught? piss,, shoulda went to the Bahamas with that$

At the current pace it is virtually assured that the BOJ's reserves will be depleted in the not too distant future.

I think I agree with Jim Rickards - inflation (most of it) will come all at once.

Anyone have an approximate D-Day when the yen will hit the fan?

It has to.  Once things inflate from the source, with today's technology, all other markets have to price it in automatically to avoid the guys at the source taking a loss.

Hard to disagree with someone smarter than most people on this planet.

ZH, please Normalize these numbers to (a) the USD and (b) Japan's GDP, to allow us to compare it to the US Debt.

Being math-phillic, I already did it for myself, but many here are somewhat 'maff-phobic' and may require Tyler's 'maff translation'.

maff is my specialty.. let me help.. first we taker the prime number divided by the actual example on page 18 and are given by: x0 = t, x1 = x, x2 = y, and x3 = z which leads us into

Identifying the components of tensor @

or the mixed form,

T ? ? = T ? ? g ? ? , {\displaystyle T^{\mu }{}_{\nu }=T^{\mu \alpha }g_{\alpha \nu },}

or as a mixed tensor density

T ? ? = T ? ? ? g . {\displaystyle {\mathfrak {T}}^{\mu }{}_{\nu }=T^{\mu }{}_{\nu }{\sqrt {-g}}\,.}

and then we JUST HAVE to divide by pie.. French apple is my favorite.. but I also really like cream pies of just about any flavor...

orange juice is good...

I like orange..

So the Central Bank needs to be bailed out....what is strange about that

Just flip all the negative rate bonds to the BOJ... oh wait...

And when the BOJ, the only buyer of JGBs leaves the market? Full blown crisis with rates skyrocketing which quickly far exceed the government's tax base. It all points in one direction: BOJ prints to infinity until it all crashes. As Kyle Bass says, its the most obvious thing on the planet.

If it was ONLY BOJ printing to infinity, maybe we could nip this b/4 global ignition.. but alas the digits are piled high and wide.

Bleachbit on sale now!!

Invite Krugman and Bernanke for a confab and a plate of Fugu prepared by amateurs.

Put the results on Pay Per View - I'd cough up $100 to watch that. 9T Yen. So that's like what, 350 freedom dollars? Just print more money. just do Alt + whatever Japanese symbol for getting screwed "How big is the gap? According to Bloomberg as of August, the delta between the balance sheet and face value has ballooned to some 8.7 trillion yen, or$84 billion."

84B lol

You have a printer, that's worth 0

my printer doesnt spit out much when i press ctrl+AU ??? go figure!

http://ramgold.ilp24.com/20249

And this is where gold's true function in today's modern central banking system will be revealed. For central banks can never go insolvent. Why? Because all they have to do is revalue gold to heal their balance sheets.

except canada, they done pawned off the whole cupboard

Conservation of deflation.  It just goes to show you that no matter what stupid paper tricks are tried, central banks can't stave off the depression forever.

I guess we have to start selling the Yen now. Isn't that what Goldman Sachs and Vipro Markets are expecting us to do. Hell no. Better buy.

All centralbanks will have that kind of losses.

Falling interest causes bigger volume - and other way round shrinks it.

Bigger will not go because interest most is Zero - or nearly.

Indeed problem will be every fast movement of shrinking, what means hiking interstrates.

Therefore Fed should hike carefully and better two little times this year.

It´s a global thing - and a very big one.

they weren't paying attention in the excel goalseek tutorial, tsk tsk tsk

Paperclip Assistant here!

It would appear that you are trying to decimate your country into Smoldering Ruins via Inflation.

Perhaps you should also try:

- Carpet Bombing

- Releasing Genetically Modified Diseases

- Nuking Major Cities and/or Economic Hubs

Killing all the farmers

Then salting their fields lol

I don't understand what the problem is. We already know the BOJ and government are completely bankrupt, but nobody seems to care. It really doesn't matter if the BOJ has negative equity. If people actually cared about things like solvency, they would be running for the doors right now.

As kids,we used to joke about what was after a Trillion?It's a ZILLION

lol. Is this even a fucking story? By October nobody will remember and the black-hole will have been forgotten. The BOJ will type in a few numbers and POW, crisis averted. "Thank god for Abenomics and Krugman endorsed QE" So said the fool and the fraudsters.

I  don't really see what the problem is. The BOJ is a private bank which, unlike the Fed has its shares publicly listed in the Tokyo Stock exchange,  has the extraordinary priveledge of printing unlimited amounts of the Japanese national currency. Now this confetti printer has an accounting loss of a few piddling percentage points in the confetti just printed!! Hell, they will just print more!

Introducing the all new Pat Morita One Quadrillion Yen note!


text:
# 3.1  How would you determine the standard electrode potential of the system $Mg^{2+} | Mg$?

To determine the standard electrode potential of the given system we need to use a hydrogen electrode. In the setup, we shall put a hydrogen electrode as cathode and Mg | MgSO4 as an anode.

Now we will measure the emf of the cell. This emf will be the standard electrode potential of the magnesium electrode.

E°cell = E° right  – E°left
E°left =0 ( The standard hydrogen electrode is always zero)
Hence
$E^{o}cell = E^{o} Mg|Mg^{2+}$

Exams
Articles
Questions


text:
# Core Concepts ¶

There are two main use cases for this software package:

• Backtesting trading systems on historical data

• Deploying trading systems live in real-time

The projects codebase provides a framework for implementing systems to achieve the above. You will find the default  backtest  and  live  system implementations in their respectively named subpackages. All examples will also either utilize the default backtest or live system implementations.

Note

We consider trading strategies to be subcomponents of end-to-end trading systems, which include the application and infrastructure layers.

## Distributed ¶

The platform is also able to be become part of an even larger distributed system, and so you will find that nearly every configuration and domain object can be serialized over the wire using either JSON, MessagePack, or Apache arrow (feather).

## Common core ¶

Both backtest, sandbox and live trading nodes use a common system core. Registering user defined  Actor  and  Strategy  components are then managed in the same way across these environment contexts.

## Backtesting ¶

Backtesting can be achieved by first making data available to a  BacktestEngine  either directly or via a higher level  BacktestNode  and  ParquetDataCatalog  , and then running the system across this data with nanosecond resolution.

A  TradingNode  can ingest data and events from multiple data and execution clients. Live deployments can use both demo/paper trading accounts, or real accounts.

For live trading, extremely high performance (benchmarks pending) can be achieved running asynchronously on a single event loop , especially leveraging the uvloop implementation (available for Linux and macOS only).

## Domain model ¶

A rich trading domain model has been defined, which expresses value types such as  Price  and  Quantity  , up to more complex entities such as  Order  objects - which aggregate many events to determine state.

### Data Types ¶

The following market data types can be requested historically, and also subscribed to as live streams when available from a data publisher, and implemented in an integrations adapter.

•  OrderBookDelta

•  OrderBookDeltas  (L1/L2/L3)

•  OrderBookSnapshot  (L1/L2/L3)

•  QuoteTick

•  TradeTick

•  Bar

•  Instrument

The following PriceType options can be used for bar aggregations;

•  BID

•  ASK

•  MID

•  LAST

The following BarAggregation options are possible;

•  MILLISECOND

•  SECOND

•  MINUTE

•  HOUR

•  DAY

•  WEEK

•  MONTH

•  TICK

•  VOLUME

•  VALUE  (a.k.a Dollar bars)

•  TICK_IMBALANCE

•  TICK_RUNS

•  VOLUME_IMBALANCE

•  VOLUME_RUNS

•  VALUE_IMBALANCE

•  VALUE_RUNS

The price types and bar aggregations can be combined with step sizes >= 1 in any way through a  BarSpecification  . This enables maximum flexibility and now allows alternative bars to be aggregated for live trading.

### Account Types ¶

The following account types are available for both live and backtest environments;

•  Cash  single-currency (base currency)

•  Cash  multi-currency

•  Margin  single-currency (base currency)

•  Margin  multi-currency

### Order Types ¶

The following order types are available (when possible on an exchange);

•  MARKET

•  LIMIT

•  STOP_MARKET

•  STOP_LIMIT

•  MARKET_TO_LIMIT

•  MARKET_IF_TOUCHED

•  LIMIT_IF_TOUCHED

•  TRAILING_STOP_MARKET

•  TRAILING_STOP_LIMIT


text:
# Homework Help: Calculation of a half-life how?

1. Apr 3, 2005

### LoBun

"A radioactive substance has a half-life of 5 days, initial mass of 12kg. How much the original isotope will remain after 10 days?"

This is just an example, the question itself is not important, i just want to know how to solve this type of problems generally.. thank you!

2. Apr 3, 2005

### Jameson

The general form for growth/decay is the model of:

$$A(t) = A_{i}e^{kt}$$

where Ai is the initial amount, k the growth rate, and t is time.

You need to solve for k... so. Set it up like this.

$$6 = 12e^{5k}$$

Solve for k and use the new equation to find any other questions pertaining to this model.

3. Apr 3, 2005

### Staff: Mentor

What's the definition of half-life? In this example, what happens after 5 days?

4. Apr 3, 2005

### LoBun

If im not mistaken..

Half life is the time taken for half the number of nuclides to decay. So, as far as I understand, if the half life is of 5 days, after this time the substance will have half its initial mass.. in this case.. 6kg?

Still somewhat confused..

5. Apr 3, 2005

### Jameson

Look at my post... that's exactly what I have. Can you please indicate what is confusing?

EDIT: The followings posts are probably an easier way to look at the problem. Since 10 days is conveniently twice the half-life, you don't need to use a growth/decay model.

Last edited: Apr 3, 2005
6. Apr 3, 2005

### Data

That is right. The half life is also independent of how many particles you have (within the scale we're discussing here - $\mbox{kg}$). So how much will you have left after 10 days?

Of course, that's just because this particular question is set up such that the answer is obvious (once you understand it). In general you will need to solve an equation to figure out how much remains.

7. Apr 3, 2005

### Staff: Mentor

Right. And what about after another 5 days (for a total of 10 days)?

8. Apr 3, 2005

### LoBun

Maybe because..

..you've confused a few numbers..

Is it supposed to be:

10 = 12e^(5k) ?

9. Apr 3, 2005

### saltydog

May want to check out the "radioactive decay" post in the Differential Equations section. Remember to use enough decimal digits to get an accurate answer (Naeem, are you reading this?).

10. Apr 3, 2005

### Jameson

No.... A(t) is the amount of the substance. The initial amount was 12 kg and after 5 days (t), you have 6 left. I'm fairly certain my method is correct.

This method isn't necessary... if you look at the above posts you'll see why.

11. Apr 3, 2005

### LoBun

Hum..

Would it be.. 1/4 of the initial mass?

12. Apr 3, 2005

### Jameson

Yes, that's correct. :)

Just to show you the method I used, I'll solve this problem for you.

$$6 = 12e^{5k}$$
$$k = \frac{-\ln(2)}{5}$$

Now you have the function
$$A(t) = 12e^{\frac{-t\ln{2}}{5}$$

Plugging in t = 10 you get

$$A(t) = 12e^{\frac{-10\ln{2}}{5}$$
$$A(t) = 3$$

Which is 1/4 of the original amount.

Last edited: Apr 3, 2005
13. Apr 3, 2005

### Data

The equation for an exponentially decaying quantity $I(t)$ is

$$I(t) = I_0e^{-kt}$$

where $I_0 = I(0)$. If the half-life is $T$, what it means is that

$$I(T) = \frac{I_0}{2}$$

In your case, you are given the quantity at time 0 as $12 \mbox{kg}$, so $I_0 = 12 \mbox{kg}$. The half-life is 5 days, so (omitting units for brevity)

$$I(5) = \frac{I_0}{2} = 6 = I_0 e^{-5k} = 12e^{-5k}$$

ie. you're solving

$$6 = 12e^{-5k}$$

for $k$. Once you do that, you need to find $I(10)$. All you need to do to do that is to evaluate the formula for $I(t)$ with $t=10$:

$$I(10) = 12e^{-10k}$$

which isn't a problem now, since you found $k$ in the last step!

Last edited: Apr 3, 2005
14. Apr 3, 2005

### LoBun

So in the case of this question it is pretty much an..

..arithmetic sequence.. :]

Thank you all very much, now im sure i understood the idea and its definitely not as hard as i thought..

15. Apr 3, 2005

### Jameson

No problem.

16. Apr 3, 2005

### Data

Geometric sequence actually. An exponentially decaying quantity is one that is decaying continuously in analogy to the discrete ratio for successive terms of a geometric sequence.


text:
.tabbox {width:400px; margin-top: 15px;margin-bottom: 5px} .tabmenu {width:400px;height:28px;border-left:1px solid #CCC;border-top:1px solid #ccc;} .tabmenu ul {margin:0;padding:0;list-style-type: none;} .tabmenu li { text-align:center; float:left; display:block; width:99px; overflow:hidden; background-color: #f1f1f1; line-height:27px; border-right:#ccc 1px solid; border-bottom:#ccc 1px solid; display:inline;} .tabmenu .cli {text-align:center;float:left;display:block;width:99px;overflow:hidden;background-color: #fff;line-height:27px;border-right:#ccc 1px solid;border-bottom:#fff 1px solid;display:inline; cursor:pointer; color: #810505; font-weight:bold} #tabcontent {width:399px;background-color:#fff;border-left:#CCC 1px solid;border-right:#CCC 1px solid;border-bottom:#CCC 1px solid; height:60px;} #tabcontent ul {margin:0;padding:5px;list-style-type: none;} #tabcontent .hidden {display:none;} Search Browse by Issue Fig/Tab Adv Search
 HOME ABOUT JCST AUTHORS REVIEWERS PUBLISHED PAPERS FORTHCOMING PAPERS

›› 2015, Vol. 30 ›› Issue (4): 859-873.

• Special Section on Data Management and Data Mining •

### Enhancing Time Series Clustering by Incorporating Multiple Distance Measures with Semi-Supervised Learning

Jing Zhou1,2(周竞), Shan-Feng Zhu1,2(朱山风), Member, CCF, ACM, Xiaodi Huang3(黄晓地), Member, ACM, IEEE, Yanchun Zhang1,4,5(张彦春), Member, CCF

1. 1. School of Computer Science, Fudan University, Shanghai 200433, China;
2. Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China;
3. School of Computing and Mathematics, Charles Sturt University, Albury, NSW 2640, Australia;
4. School of Engineering and Science, Victoria University, Melbourne, Victoria 8001, Australia;
5. Shanghai Key Laboratory of Data Science, Fudan University, Shanghai 201203, China
• Received:2015-02-01 Revised:2015-03-25 Online:2015-07-05 Published:2015-07-05
• About author:Jing Zhou received his B.S. degree in computer science from Donghua University, Shanghai, in 2012. He is currently a graduate student of the Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai. His current research interests include time series analysis, data mining, and bioinformatics.
• Supported by:

The work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61332013, 61272110, and 61370229, and the National Key Technology Research and Development Program of China under Grant No. 2013BAH72B01.

Time series clustering is widely applied in various areas. Existing research work focuses mainly on distance measures between two time series, such as DTW-based (dynamic time warping) methods, edit distance-based methods, and shapelets-based methods. In this work, we experimentally demonstrate, for the first time, that no single distance measure performs significantly better than others on clustering data sets of time series where spectral clustering is used. As such, a question arises as to how to choose an appropriate measure for a given data set of time series. To answer this question, we propose an integration scheme that incorporates multiple distance measures using semi-supervised clustering. Our approach is able to integrate all the measures by extracting valuable underlying information for the clustering. To our best knowledge, this work demonstrates for the first time that semi-supervised clustering method based on constraints is able to enhance time series clustering by combining multiple distance measures. Having tested on clustering various time series data sets, we show that our method outperforms individual measures, as well as typical integration approaches.

 [1] Hirano S, Tsumoto S. Cluster analysis of time-series medical data based on the trajectory representation and multiscale comparison techniques. In Proc. the 6th International Conference on Data Mining, December 2006, pp.896-901.[2] Ruiz E J, Hristidis V, Castillo C, Gionis A, Jaimes A. Correlating financial time series with micro-blogging activity. In Proc. the 5th ACM International Conference on Web Search and Data Mining, February 2012, pp.513-522.[3] Tan S C, San L J P. Time series clustering: A superior alternative for market basket analysis. In Proc. the 1st International Conference on Advanced Data and Information Engineering, January 2013, pp.241-248.[4] Mackas D L, Greve W, Edwards M et al. Changing zooplankton seasonality in a changing ocean: Comparing time series of zooplankton phenology. Progress in Oceanography, 2012, 97/98/99/100: 31-62.[5] Lai C P, Chung P C, Tseng V S. A novel two-level clustering method for time series data analysis. Expert Systems with Applications, 2010, 37(9): 6319-6326.[6] Wang X, Smith K, Hyndman R. Characteristic-based clustering for time series data. Data Mining and Knowledge Discovery, 2006, 13(3): 335-364.[7] Zhang X, Liu J, Du Y, Lv T. A novel clustering method on time series data. Expert Systems with Applications, 2011, 38(9): 11891-11900.[8] Zakaria J, Mueen A, Keogh E J. Clustering time series using unsupervised-shapelets. In Proc. the 12th IEEE International Conference on Data Mining, December 2012, pp.785-794.[9] Bagnall A, Janacek G. Clustering time series with clipped data. Machine Learning, 2005, 58(2/3): 151-178.[10] Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E J. Querying and mining of time series data: Experimental comparison of representations and distance measures. Proc. the VLDB Endowment, 2008, 1(2): 1542-1552.[11] Vlachos M, Hadjieleftheriou M, Gunopulos D, Keogh E J. Indexing multi-dimensional time-series with support for multiple distance measures. In Proc. the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, August 2003, pp.216-225.[12] Ye L, Keogh E J. Time series shapelets: A new primitive for data mining. In Proc. the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, June 28-July 1, 2009, pp.947-956.[13] Keogh E J, Pazzani M J. Derivative dynamic time warping. In Proc. the 1st SIAM International Conference on Data Mining, April 2001, pp.1:1-1:11.[14] Jeong Y S, Jeong M K, Omitaomu O A. Weighted dynamic time warping for time series classification. Pattern Recognition, 2011, 44(9): 2231-2240.[15] Marteau P F, Gibet S. On recursive edit distance kernels with application to time series classification. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(6): 1121-1133.[16] Marteau P F. Time warp edit distance with stiffness adjustment for time series matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2): 306- 318.[17] Shao J, Huang Z, Shen H T, Shen J, Zhou X. Distributionbased similarity measures for multi-dimensional point set retrieval applications. In Proc. the 16th ACM International Conference on Multimedia, October 2008, pp.429-438.[18] Sun Y, Li J, Liu J, Sun B, Chow C. An improvement of symbolic aggregate approximation distance measure for time series. Neurocomputing, 2014, 138: 189-198.[19] Qi J, Zhang R, Ramamohanarao K, Wang H,Wen Z,Wu D. Indexable online time series segmentation with error bound guarantee. World Wide Web, 2015, 18(2): 359-401.[20] Lin J, Vlachos M, Keogh E J, Gunopulos D. Iterative incremental clustering of time series. In Proc. the 9th International Conference on Extending Database Technology, March 2004, pp.106-122.[21] Hautamaki V, Nykanen P, Franti P. Time-series clustering by approximate prototypes. In Proc. the 19th International Conference Pattern Recognition, December 2008.[22] Oates T, Firoiu L, Cohen P R. Clustering time series with hidden Markov models and dynamic time warping. In Proc. the IJCAI-99 Workshop on Neural, Symbolic and Reinforcement Learning Methods for Sequence Learning, August 1999, pp.17-21.[23] Ghassempour S, Girosi F, Maeder A. Clustering multivariate time series using hidden Markov models. International Journal of Environmental Research and Public Health, 2014, 11(3): 2741-2763.[24] Izakian H, Pedrycz W, Jamal I. Fuzzy clustering of time series data using dynamic time warping distance. Engineering Applications of Artificial Intelligence, 2015, 39: 235-244.[25] Ramoni M, Sebastiani P, Cohen P. Bayesian clustering by dynamics. Machine Learning, 2002, 47(1): 91-121.[26] Yang Y, Chen K. Temporal data clustering via weighted clustering ensemble with different representations. IEEE Transactions on Knowledge and Data Engineering, 2011, 23(2): 307-320.[27] Yang Y, Chen K. Time series clustering via RPCL network ensemble with different representations. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 2011, 41(2): 190-199.[28] Lines J, Bagnall A. Ensembles of elastic distance measures for time series classification. In Proc. the 14th SIAM International Conference on Data Mining, April 2014, pp.524- 532.[29] Kulis B, Basu S, Dhillon I, Mooney R. Semi-supervised graph clustering: A kernel approach. Machine Learning, 2009, 74(1): 1-22.[30] Huang X, Cheng H, Yang J, Yu J X, Fei H, Huan J. Semisupervised clustering of graph objects: A subgraph mining approach. In Proc. the 17th International Conference on Database Systems for Advanced Applications — Volume Part I, April 2012, pp.197-212.[31] Chen Y, Rege M, Dong M, Hua J. Non-negative matrix factorization for semi-supervised data clustering. Knowledge and Information Systems, 2008, 17(3): 355-379.[32] Shiga M, Mamitsuka H. Efficient semi-supervised learning on locally informative multiple graphs. Pattern Recognition, 2012, 45(3): 1035-1049.[33] Sakoe H, Chiba S. A dynamic programming approach to continuous speech recognition. In Proc. the 7th International Congress on Acoustics, August 1971, pp.65-69.[34] Sakoe H, Chiba S. Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech and Signal Processing, 1978, 26(1): 43-49.[35] Shi J, Malik J. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905.[36] Zhu S, Zeng J, Mamitsuka H. Enhancing MEDLINE document clustering by incorporating MeSH semantic similarity. Bioinformatics, 2009, 25(15): 1944-1951.[37] Fern X Z, Brodley C E. Solving cluster ensemble problems by bipartite graph partitioning. In Proc. the 21st International Conference on Machine Learning, July 2004, Article No. 36.[38] Ghaemi R, Sulaiman M N, Ibrahim H, Mustapha N. A survey: Clustering ensembles techniques. World Academy of Science, Engineering and Technology, 2009, 3(2): 477-486.[39] Huang X, Zheng X, Yuan W, Wang F, Zhu S. Enhanced clustering of biomedical documents using ensemble nonnegative matrix factorization. Information Sciences, 2011, 181(11): 2293-2302.[40] Gu J, Feng W, Zeng J, Mamitsuka H, Zhu S. Efficient semisupervised MEDLINE document clustering with MeSH-semantic and global-content constraints. IEEE Transactions on Cybernetics, 2013, 43(4): 1265-1276.[41] Ji X, Xu W. Document clustering with prior knowledge. In Proc. the 29th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, August 2006, pp.405-412.[42] Ghosh J. Scalable clustering. In Handbook of Data Mining, Ye N (ed.), CRC Press, 2003, pp.247-277.[43] Strehl A, Ghosh J. Cluster ensembles — A knowledge reuse framework for combining multiple partitions. The Journal of Machine Learning Research, 2003, 3: 583-617.
 No related articles found!
Viewed
Full text

Abstract

Cited

Shared
Discussed
 [1] Liu Mingye; Hong Enyu;. Some Covering Problems and Their Solutions in Automatic Logic Synthesis Systems[J]. , 1986, 1(2): 83 -92 . [2] Chen Shihua;. On the Structure of (Weak) Inverses of an (Weakly) Invertible Finite Automaton[J]. , 1986, 1(3): 92 -100 . [3] Gao Qingshi; Zhang Xiang; Yang Shufan; Chen Shuqing;. Vector Computer 757[J]. , 1986, 1(3): 1 -14 . [4] Chen Zhaoxiong; Gao Qingshi;. A Substitution Based Model for the Implementation of PROLOG——The Design and Implementation of LPROLOG[J]. , 1986, 1(4): 17 -26 . [5] Huang Heyan;. A Parallel Implementation Model of HPARLOG[J]. , 1986, 1(4): 27 -38 . [6] Min Yinghua; Han Zhide;. A Built-in Test Pattern Generator[J]. , 1986, 1(4): 62 -74 . [7] Tang Tonggao; Zhao Zhaokeng;. Stack Method in Program Semantics[J]. , 1987, 2(1): 51 -63 . [8] Min Yinghua;. Easy Test Generation PLAs[J]. , 1987, 2(1): 72 -80 . [9] Zhu Hong;. Some Mathematical Properties of the Functional Programming Language FP[J]. , 1987, 2(3): 202 -216 . [10] Li Minghui;. CAD System of Microprogrammed Digital Systems[J]. , 1987, 2(3): 226 -235 .
 ISSN 1000-9000(Print)          1860-4749(Online) CN 11-2296/TP Home Editorial Board Author Guidelines Subscription Journal of Computer Science and Technology Institute of Computing Technology, Chinese Academy of Sciences P.O. Box 2704, Beijing 100190 P.R. China Tel.:86-10-62610746 E-mail: jcst@ict.ac.cn


text:
# mixedmath

Explorations in math and programming
David Lowry-Duda

I moved to the UK to begin a postdoc with John Cremona at the University of Warwick. And for the last four weeks, I have had no internet at my home. This wasn't by choice — it's due to the reluctance of my local gigantitelecom to press a button that says "begin internet service." I could write more about that, but that's not the purpose of this note.

The purpose of this note is to describe the large effects of having no internet at my home for the last four weeks. I'm at my home about half the time, leading to the title.

I have become accustomed to having the internet at all times. I now see that many various habits of mine involved the internet. In the mornings and evenings, I would check HackerNews, longform, and reddit for interesting reads. Invariably there are more interesting seeming things than I would read, and my Checkout bookmarks list is a hundreds-of-items long growing list of maybe interesting stuff. In the middle times throughout the day, I would checkout a few of these bookmarks.

All in all, I would spend an enormous amount of time reading random interesting tidbits, even though much of this time was spread out in the "in-betweens" in my day.

When I didn't have internet at my home, I had to fill all those "in-between" moments, as well as my waking and sleeping moments, with something else. Faced with the necessity of doing something, I filled most of these moments with reading books. Made out of paper. (The same sort of books whose sales are rising compared to ebooks, contrary to most predictions a few years ago).

I'd forgotten how much I enjoyed reading a book in large chunks, in very few sittings. I usually have an ebook on my phone that I read during commutes, and perhaps most of my idle reading over the last several years has been in 20 page increments. The key phrase here is "idle reading". I now set aside time to "actively read", in perhaps 100 page increments. Reading enables a "flow state" very similar to the sensation I get when mathing continuously, or programming continuously, for a long period of time. I not only read more, but I enjoy what I'm reading more.

As a youth, I would read all the time. Fun fact: at one time, I'd read almost every book in the Star Wars expanded universe. There were over a hundred, and they were all canon (before Disney paved over the universe to make room). I learned to love reading by reading science fiction, and the first novel I remember reading was a copy of Andre Norton's "The Beastmaster" (... which is great. A part telepath part Navajo soldier moves to another planet. Then it's a space western. What's not to love?).

My primary source of books is the library at the University of Warwick. Whether through differences in continental taste or simply a case of different focus, the University Library doesn't have many books in its fiction collection that I've been intending to read. I realize now that most of the nonfiction I read originates on the internet, while much of the fiction I read comes from books. Now, encouraged by a lack of alternatives, I picked up many more and varied nonfiction books than I would otherwise have.

As an unexpected side effect, I found that I would also carefully download some of the articles I identified as "interesting" a bit before I headed home from the office. Without internet, I read far more of my checkout bookmarks than I did with internet. Weird. Correspondingly, I found that I would spend a bit more time cutting down the false-positive rate — I used to bookmark almost anything that I thought might be interesting, but which I wasn't going to read right then. Now I culled the wheat from the chaff, as harvesting wheat takes time. (Perhaps this is something I should do more often. I recognize that there are services or newsletters that promise to identify great materials, but somehow none of them have worked better to my tastes than hackernews or longform. But these both have questionable signal to noise.).

The result is that I've goofed off reading probably about the same amount of time, but in fewer topics and at greater depth in each. It's easy to jump from 10 page article to 10 page article online; when the medium is books, things come in larger chunks.

I feel more productive reading a book, even though I don't actually attribute much to the difference. There may be something to the act of reading contiguously and continuously for long periods of time, though. This correlated with an overall increase my "chunking" of tasks across continuous blocks of time, instead of loosely multitasking. I think this is for the better.

I now have internet at my flat. Some habits will slide back, but there are other new habits that I will keep. I'll keep my bedroom computer-free. In the evening, this means I read books before I sleep. In the morning, this means I must leave and go to the other room before I waste any time on online whatevers. Both of these are good. And I'll try to continue to chunk time.

To end, I'll note what I read in the last month, along with a few notes about each.

## Fiction

From best to worse.

• The second best was The Lathe of Heaven by Ursula Le Guin. This is some classic fantasy, and is pretty mindbending. I think the feel of many books of Ursula Le Guin is very similar — there are many interesting ideas throughout the book, but the book deliberately loses coherence as the flow and fury of the plot reaches a climax. I like The Lathe of Heaven more than The Wizard of Earthsea and about the same as The Left Hand of Darkness, also by Le Guin. I read this book in three sittings.
• I read three of the Witcher books, by Andzej Sapkowski. Namely, The Sword of Destiny, Blood of Elves, and Time of Concempt. These are fun, not particularly deep reads. There is a taste of moral ambiguity that I like as it's different from what I normally find. On the other hand, Sapkowski often uses humor or ambiguity in place of a meaningful, coherent plot. The Sword of Destiny is a collection of short tales, and I think his short tales are better than his novels — entirely because one doesn't need or expect coherence from short stories.

I'm currently reading Confusion by Neal Stephenson, book two of the Baroque trilogy. Right now, I am exactly 1 page in.

## Nonfiction

I rank these from those I most enjoyed to those I least enjoyed.

• How Equal Temperament Ruined Harmony, by Duffin. This was told to me as an introduction to music theory [in fact, I noted this from a comment thread on hackernews somewhere], but really it is a treatise on the history of tuning and temparaments. It turns out that modern equal termperament suffers from many flaws that aren't commonly taught. When I got back to the office after reading this book, I spent a good amount of time on youtube listening to songs in mean tone tuning and just intonation. There is a difference! I read this book in 2 sittings — it's short, pretty simple, and generally nice. However there are several long passages that are simply better to skip. Nonetheless I learned a lot.
• A Random Walk down Wall Street, by Burton Malkiel. I didn't know too much about investing before reading this book. I wouldn't actually say that I know too much after reading it either, but the book is about investing. I was warned that reading this book would make me think that the only way to really invest is to purchase index funds. And indeed, that is the overwhelming (and explicit) takeawar from the book. But I found the book surprisingly readable, and read it very quickly. I find that some of the analysis is biased towards long-term investing even as a basis of comparison.
• Guesstimation, by Weinstein. Ok, perhaps it is not fair to say that one "reads" this book. It consists of many Fermi-style questions (how many golf balls does it take to fill up a football stadium type questions), followed by their analysis. So I read a question and then sit down and do my own analysis. And then I compare it against Weinstein's. I was stunned at how often the analyses were tremendously similar and got essentially the same order of magnitude at the end. [But not always, that's for sure. There are also lots of things that I estimate very, very poorly]. There's a small subgenre of "popular mathematics for the reader who is willing to take out a pencil and paper" (which can't have a big readership, but which I thoroughly enjoy), and this is a good book within that subgenre. I'm currently working through its sequel.
• Natures Numbers, by Ian Stewart. This is a pop math book. Ian Stewart is an emeritus professor at my university, so it seemed appropriate to read something of his. This is a surprisingly fast read (I read it in a single sitting). Stewart is known for writing approachable popular math accounts, and this fits.
• The Structure of Scientific Revolutions, by Thomas Kuhn. This is metascience. I read the first half of this book/essay very quickly, and I struggled through its second half. This came highly recommended to me, but I found the signal to noise ratio to be pretty low. It might be that I wasn't very willing to navigate the careful treading around equivocation throughout. However, I think many of the ideas are good. I don't know if someone has written a 30 page summary, but I think this may be possible — and a good alternative to the book/essay itself.

I'm now reading Grit, by Angela Duckworth. Another side effect of reading more is that I find myself reading one fiction, one non-fiction, and one "simple" book at the same time.

Written while on a bus without internet to Heathrow, minus the pictures (which were added at Heathrow).

bold, italics, and plain text are allowed in comments. A reasonable subset of markdown is supported, including lists, links, and fenced code blocks. In addition, math can be formatted using $(inline math)$ or $$(your display equation)$$.


text:
# Can we classify the general linear maps such that for a fixed matrix $A \in M_n(\mathbb R)$ the conjuagation action fixes the first column?

Let $$A \in GL_n(\mathbb R)$$ be fixed. Let us consider the conjugation action by $$G \in GL_n(\mathbb R)$$, i.e., $$G^{-1}AG$$. I would like to see a way to identify the matrices such that the action fixes the first column of $$A$$. That is, what can we say about the set \begin{align*} \mathcal E = \{G \in GL_n(\mathbb R): G^{-1}AGe_1 = a_1\}, \end{align*} where $$e_1$$ is the standard basis vector and $$a_1$$ is the first column of $$A$$. In particular, is the set connected? Let us exclude the trivial case: $$A$$ is a multiple of $$I$$ or $$-I$$.

If we define a linear map $$\phi: M_n(\mathbb R) \to \mathbb R^n$$ by $$X \mapsto (XA-AX)e_1$$, then $$\mathcal E = \ker(\phi) \cap GL_n(\mathbb R)$$.

## 1 Answer

One can not say that $$\mathcal E$$ is always connected.

For $$n=3,$$(and similarly $$n>3$$) let $$A$$ be a matrix with $$a_{i1}=1,\quad \forall i \in \{1,2,\ldots,n\}$$

Then $$\mathcal E$$ contains the identity matrix whose determinant is $$1$$ and it also contains the following matrix with determinant $$-1$$:

$$\begin{pmatrix} 1&0&0\\0&0&1\\0&1&0 \end{pmatrix}$$

According to the previous version of your question about the (semi)group structure of $$\mathcal E$$, observe that if you can prove that $$\mathcal E$$ is a semigroup then it is a group, too. Because the inverse of a every matrix $$G$$, can be written in the form of a polynomial in $$G$$.

I think that $$\mathcal E$$ is not a Lie group because it is contained in a sub vector space $$F$$, the kernel you mentioned, whose dimension is equal to the dimension of $$G$$. Moreover $$Exp(F)$$ is contained in $$\mathcal E$$ But in general case, $$F$$ is not a Lie algebra with the commutator Lie bracket. Please see the comment by Corbennick

• I was in mind probably $\mathcal E$ would have two (or more) components corresponding to the positive determinant and negative determinant. Would you comment on how many components would $\psi(\mathcal E)$ have, where $\psi: B \mapsto B^{-1}AB$ provided $A$ has a real eigenvalue? In this case, the positive and negative determinant would be mapped into the same image. – user1101010 Oct 18 '18 at 16:29
• @user9527 In fact one can generalize your interesting question in the following form: is there a linear subvector space of $M_n(\mathbb{R}$ which intersect $GL_n(\mathbb{R}$ in more than 2 components?Is there an example of this situation with codimension is equal $n$?(In your question that kernel has codimension n) – Ali Taghavi Oct 18 '18 at 16:54
• In $2\times 2$ matrices the matrices of the form $[[x,y],[y,x]]$ intersect $GL_2$ in the subset of the plane with equation $xy\neq 0$, which has 4 components. – YCor Oct 18 '18 at 17:04
• @user9527 Yes. In size $n$, in the subspace of upper triangular matrices, there are $2^n$ components of invertible matrices. – YCor Oct 18 '18 at 17:06
• So, $G\to F$ is an immersion between manifolds of the same dimension, so has an open image; $F$ is the the lie algebra of $G$. – YCor Oct 19 '18 at 12:19


text:
# How to replace mathptmx \sum with CM \sum?

I would like to replace the rather ugly mathptmx \sum operator with the equivalent Computer Modern one.

Here's a compilation of display-style \sum symbols provided by various font packages.

I'd say that the summation symbol provided by the mtpro2 package is closest to the one provided by the Computer Modern family, while still providing the genuine "Times Roman" look. Incidentally, the full mtpro2 package isn't free of charge. However, its lite subset, which is all that's needed to produce the good-looking \sum symbol, may indeed be downloaded free of charge.

Here's the code that generated the preceding four lines (run consecutively for each choice of font family).

\documentclass{article}
\usepackage{array}
%\usepackage{mathptmx}
%\usepackage{newtxmath}
\renewcommand{\rmdefault}{ptm} \usepackage[lite]{mtpro2}
\begin{document}
\begin{tabular}{@{}>{\ttfamily}p{4cm}>{$\displaystyle}l<{$}}
Times Roman, mtpro2 & \sum
\end{tabular}
\end{document}

• Hey, do u think it is possible to use mtpro2's largesymbols with mathptmx? It kind of solves my problem. Oct 26 '15 at 18:07
• @MiladO. - I would use the mtpro2 package instead of mathptmx.
– Mico
Oct 26 '15 at 18:47