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## WizardryMagick, Occult & Esoteric

Friday, 19 September 2014 13:52

## The Neo-Platonic Chocolate Screwdriver

Abstract. In this paper we examine the question of why so many of those interested in magic, esoterics and metaphysical matters seem quite unaccomplished or dysfunctional on the material plane and so frequently penniless.

Hey, how come that so many of those wizards who pursue insider insights into reality seem so bad at actually dealing with reality? In past aeons most of them made a comfortable if dangerous living.

We find that the fault lies mainly in their continuing adherence to the antique and now largely ineffective Neoplatonic paradigm which has become something of a ‘Chocolate Screwdriver’, in desperate need of replacement with a more effective tool.

(Rhetorical note, a Chocolate Screwdriver stands as emblematic of a tool with extremely limited uses; it will serve to stir the sacrament of Apophenia (Dark Cocoa) for a while, but for little else.)

And so, on to The Paradigm Problem: -

Adapting our ideas and brain functions for the long and painful climb from hunter gathering lifestyles to exploiters of general relativity and quantum physics has not proved straightforward or easy. We still bear the scars and vestiges of our neurological and psychological adaptations.

Platonism rose to become the esoteric metaphysic of choice in the Hellenic west during the last few centuries B.C. because it provided a more effective mental tool than the animist and spiritist thinking that had informed pagan societies as they became progressively more urbanised.

Animist and spiritist thinking remains concrete, phenomenological, and immanent-ist. All phenomena exist ‘just as they are because they are’ and they have powers intrinsic to themselves. Yet these powers can remain subject to transfer by contagion, as for example when a shaman or priest dresses in a bear’s skin to borrow its ‘powers’. Such thinking still influences modern humans to some small extent.

Platonism supports abstract thinking. By positing the separate existence of the ‘essences’ of phenomena it allowed people to conceptualise such things as ‘the personal self’, and interesting abstract ideas like ‘justice’ and ‘mathematical principles’. It also supported the rise of monotheistic religion by positing the idea of a supreme essence, from which lesser essences devolve. Basically in Platonism ‘whatever you can think of’ acquires some sort of a transcendental reality as an ‘essence’, and sometimes as a ‘sentient essence’ as well.

However despite that it encourages abstract thinking, Platonism exhibits a serious flaw, most of its ideas remain untestable and unfalsifiable. The Platonists strove to create a corpus of ideas based merely on self-consistency, with insufficient reference to observed reality.

Neoplatonism, which arose in first few the centuries A.D, devolved from Platonism and it extended the basic idea of essences into all sorts of esoteric realms where it gave rise to Hermeticism, Kabballah, and Gnosticism. In these the essences multiply to create complicated schemes of emanations and archetypes based on pagan style deities, archons, demiurges, and a supreme transcendental monad or whatever.

Unfortunately Neoplatonism comes with few mechanisms for discerning between useful and useless abstractions, and it quite rapidly became fixated upon the supposed ‘essences’ of things like earth, air, fire, and water, or upon the supposed ‘essences’ of the classical ‘planets’ and the ‘essences’ of twelve zodiacal divisions of the ecliptic. Despite the very poor explanatory and predictive power of such schemes of ‘essences’ this style of thinking persisted for nearly two thousand years. It still persists as a rather sloppy form of common speech and thinking. We tend to attribute classes of attributes or ‘essences’ to phenomena as a kind of shortcut in our thinking. Phenomena remain mutable, not fixed by essence. People change continually throughout life, culture and circumstance determines behaviour far more profoundly than star-sign or race. We obviously don’t actually have fixed selves or souls or ‘essences’. Watch a child grow, or more disturbingly, watch dementia take an elderly person.

The attempt to discern the nature of the supposed ‘essence’ underlying the entire universe has involved a great deal of anthropomorphic projection and wishful thinking and it has left us with the chocolate screwdriver idea of a monotheistic God with a capital G. It may promise comfort and control, but what in heck does God actually DO apart from that? Huge natural disasters and small tawdry miracles?

Do gods and goddesses and spirits and demons actually exist as anything other than imaginary friends? As imaginary friends they can still serve to inspire and empower us as I repeatedly point out in The Esotericon and Portals of Chaos, and I have several of them myself, but where lies the extraordinary evidence required to go beyond that into the belief in their objective existence?

Astrology appeared as another chocolate screwdriver, or perhaps worse. The idea that each twelfth of humanity has certain characteristics dependent on conditions of birth now seems as indefensible as racism. It has no predictive power whatsoever beyond the obvious calendrical/seasonal associations.

Neoplatonism represents an improvement on crude animism & spritism but it now seems a debilitating and ineffective way of thinking.

Its corpus of ideas remains more or less untestable and unfalsifiable for whenever it appears to give poor results it tends to spawn ever more complex and evasive explanations, and as a general principle any unfalsifiable idea of this kind has very little predictive power at all.

The translation of the bible into vernacular languages provoked people to question the Neoplatonic assumptions that became incorporated into it during the first few centuries A.D. This led to Protestantism and the beginning of the end of the whole Neoplatonist paradigm which Catholic and Eastern Orthodox Christianity had bought into. A British Protestant Parliament eventually required that any prospective member of its parliament would have to refute the doctrine of transubstantiation, the idea that a consecrated host actually embodied the actual ‘essence’ of the sacrificed body and blood of Christ, and instead compromise with the idea that it merely symbolised it.

This might seem an uncontentious and trivial theological point to many today, but the idea behind it led to the abandonment of Neoplatonism and Aristotelian theory (derived from pure thinking largely uninformed by objective observation), and this led to Empirical Science, the Royal Society, the Enlightenment, the Industrial Revolution, some Freedom of Conscience, and eventually to Democracy of a sort. Parallel developments took place over much of north-western Europe, despite ferocious Papal resistance initially.

The magical revival of the 1880s, initiated mainly by Macgregor Mathers of the Golden Dawn, represents the last high water mark of Neoplatonic thought, and from it most of the western esoteric traditions of the twentieth century descend. However the cracks in it already seemed visible at the time and a recession of the high tide seemed inevitable. Psychological insights into the mechanisms of esoterics began to arise upon the examination of oriental mystical practices and the Golden Dawn manuscripts and practices seem to imply in places that the adept can more or less manufacture gods and spirits to order, as many of them effectively went on to do so.

Plus of course most of the occultists of the late nineteenth century revival adopted Neoplatonism as a Romantic alternative to the Mechanistic thinking which came with the Industrial Revolution, Darwinism, Thermodynamics, and the emerging Social Sciences. They mostly came from such privileged backgrounds that ineffectual styles of thought did not immediately incur serious consequences, and some of their art came out rather well.

Yet the Neoplatonic theory of ‘essences’ or abstract ‘forms’ ceases to provide an competitive mental tool in a world increasingly dominated by evidence based Mechanistic thinking.

Only perhaps when we don’t understand a mechanism, or where mechanism seems absent and the phenomena seem random, does it seem worth trying the Neoplatonic paradigm, because it developed for precisely such purposes.

If you try and interact with people or machinery or institutions or natural phenomena on the basis that they operate on supposed intrinsic essences you will interact less effectually unless your theory of essences has an equal sophistication to theories of mechanism.

Essentialist type thinking had many seriously deleterious consequences, for example look at the underlying scheme of Humoral Medicine shown above. It derives from the ideas of Empoedocles' 'elements' and it survived as standard medical theory from the time of Hippocrates till the 19th century. Few of the concepts on it relate very directly to any definite observable physical substances, rather they relate vaguely to the supposed essences of substances. Only the tendency for most people to recover from most medical conditions regardless of ineffectual or mildly injurious 'treatments' kept it alive for 2 millenia.

This has created a big problem for the alternative types who re-adopted Neoplatonism in the late twentieth century esoteric revival. They often didn’t have the same resources as the wealthy Victorian bohemian classes had, and the western world had become far more demanding of adherence to a Mechanistic outlook. You can barely survive and prosper in it now without decent arithmetic, endless form filling, and button pushing.

Of course some people order most of their daily lives with Mechanistic thinking and reserve the Neoplatonic style for their religious, mystical and artistic interests. However the more they let the Neoplatonic style influence their everyday activities the more of a mess they seem to get into by using a set of unfalsifiable ideas that have very low predictive power.

If you cannot really test the idea that a certain phenomenon somehow represents a manifestation of the metaphysical elemental essence of say ‘earth’ then the whole concept has very little predictive or decision making power.

The magnificent edifice of late nineteenth century esoterics that Mathers created left a dual legacy. Some accepted parts of it wholesale and continue to paper over the cracks in the Neoplatonism that it partly exposes. Others accepted its welcome eclecticism and have since gone on to struggle with its metaphysical framework and update it.

One of the great challenges for Magical theorists lies in developing a metaphysic that remains compatible with Science and Existentialism.

Existentialism, for all its association with association with verbose and miserable French left bank philosophers, comes down to basically the insight that phenomena don’t actually have essences. We don’t have souls or real selves and neither do things in general, phenomena consist just of what they actually do, they don’t also have a separate abstract form of ‘being’, except in our minds.

So if phenomena lack any form of ‘otherness’ what can you base occultism or esoterics or magical ideas on?

Fortunately Science itself now comes to the rescue in a way that it couldn’t have done a century ago.

Unfortunately this new paradigm can often sound as contra-intuitive to the non-scientist as Neoplatonism now does to someone trained in science.

Basically, all physical phenomena do have an ‘otherness’ as well, but it consists of a ‘wave-function’ that we cannot directly observe. This may not sound as exciting as the idea that every phenomenon has an associated ‘spirit’ or ‘essence’, but it has far more explanatory and predictive power and it actually leads to more effective Magic,( and to more effective Science as well incidentally).

The wave function of any phenomenon carries information about the possible pasts, parallel superposed presents, and possible futures of that phenomenon. Moreover the wave function can have non-local effects in space and time and interact with other wave functions.

To a rough approximation we can regard wave functions as information that phenomena emit about their probable behaviour and also as information that has a probability based effect on the behaviour of phenomena.

You don’t need to try and ‘emit’ or ‘receive’ wave functions directly to accomplish magic, your thoughts and actions will do that on their own.

Some debate rages over the metaphysical status of wave functions, which we conventionally denote as Ψ, Psi.

Psi-epistemologists regard them as merely our abstractions about the unobservable factors that most simply explain our observations.

Psi-ontologists regard them as rather more real, (for a given value of ‘real’).

Existentialists don’t mind either way, it’s what they do that counts.

The nature of matter and its wave functions remains deeply mysterious, we can probably never really say what either ‘is’, for we can only achieve answers by analogy, or in terms of ‘similar to that’ or ‘different to this’. Indeed we can only really get sensible answers to the question of ‘what do they actually do?’

Combine the (quantum) insight of the wave function mechanism with the psychological explanation of gods and spirits, (remembering that we have quite astonishing subconscious abilities and worlds within us), and you to replace the old PPM (Platonic Pagan-Monotheist) paradigm with a QNP (Quantum Neo-Pagan) paradigm for esoterics and magic, it comes unburdened of superstition, prejudicial thinking about supposed ‘essences’, and dubious explanatory schemes masquerading as wisdom and doubtful mysteries.

In QNP style magic the magicians attempt to interact with actual physical phenomena by exploiting the wave functions that connect every existing thing to every other existing thing to some degree, not by attempting to interact with them via their supposed essences. Symbolism may help as mental shorthand and to access the subconscious but we should not mistake the symbol for the thing it represents, nor should we mistake the imagined essence as more fundamental than the thing we abstract it from, for this tends to lead to merely imaginary results.

In QNP style magic the magicians attempt to interact with entities as though they consisted of bits of their own personality or of other creature’s personalities, with the proviso that such things can have non-local and parapsychological effects as well as psychological effects.

In practise many of the procedures of PPN and QNP magic remain similar. Enchantment, Divination, Evocation, and Invocation continue as before but the emphasis shifts away from interacting with the supposed essences of phenomena towards interacting with the phenomena as perceived, and towards more of an expectation of actual physical results.

Mysteries come in three varieties:

Good questions to which we don’t yet have any answers.

Good questions to which we have answers that don’t really make sense.

Questions that involve dubious assumptions and to which we have answers that don’t really make sense either.

Science and good magic have mysteries in all three categories. Neoplatonism has no mysteries of the first type; it has ‘explanations’ for everything.

Plato was discoursing on his theory of ideas and, pointing to the cups on the table before him, explained that while there are many cups in the world, there is only one idea' of a cup, and this cup-ness precedes the existence of all particular cups.

"I can see the cup on the table," interrupted Diogenes, "but I can't see the cup-ness'".

"That's because you have the eyes to see the cup," said Plato, "but", tapping his head with his forefinger, "you don't have the intellect with which to comprehend cup-ness'."

Diogenes walked up to the table, examined a cup and, looking inside, asked, "Is it empty?"

Plato nodded.

"Where is the emptiness' which precedes this empty cup?" asked Diogenes.

Plato allowed himself a few moments to collect his thoughts, but Diogenes reached over and, tapping Plato's head with his finger, said "I think you will find here is the `emptiness'."

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# Miles per hour to feet per second

This free conversion calculator will convert miles per hour to feet per second, i.e. mph to fps. Correct conversion between different measurement scales.

The formula is $S_{\text{fps}} = 1.466666666666667 S_{\text{mph}}$, where $S_{\text{mph}} = 15$.

Therefore, $S_{\text{fps}} = 22$.

Answer: $15 \text{mph} = 22 \text{fps}$.

format: plain


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Home > MC1 > Chapter 6 > Lesson 6.2.3 > Problem6-71

6-71.
1. . Calculate each of the following parts of parts. Homework Help ✎

1. of

2. of

Draw a diagram to represent three-sevenths.

Since the green shaded region is three pieces, you can see that two-thirds of this region would be the blue shaded region.

$\frac{2}{7}$

Below is a diagram representing one-half of three-fifths.


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# Using the appropriate machine learning algorithm

I am not sure if this is the right forum to ask this.

I have some data of the houses, like their size(in square meters), if they use aircondition, how many residents live in, I have their electricity consumption as well. I want to train any Machine Learning Algorithm to the dataset above, in order to create a model that estimates the houses consumption.

I tried many different algorithms (using weka tool), but I did not have good results. I was said that SVMs could solve this problem, with the right preprocessing. However, i did not have good results either.

Can anyone help me, in the way i should approach this problem?

• How is your error $90\%$? Are you counting it as a total miss if you don't get the exact value? Usually, when trying to predict a continuous value, people use a cost function like the squared error. It might make sense to rescale the output, but be careful that when you don't have a lot of data, you want to use a simple model. Trying a lot of ways to rescale the output is equivalent to using a more complicated model which may tend to overfit on a small sample. – Douglas Zare Mar 11 '13 at 21:31
• I wouldn't call that a $90\%$ error. That sounds like linear regression explains up to $50\%$ of the variance. Depending on the information you have, you might not be able to do much better. – Douglas Zare Mar 12 '13 at 14:47


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# How to fix some compilation issues using R Markdown and Latex markups?

Hi everyone! I've been using Latex for years now and used it for my PHD, but now I've changed my workflow, I'd like to use R Markdown in every file I work on, especially research articles. To this purpose, I've built a YAML preamble and insert some Latex markups in order to output a documentclass book, but I have some complications:

1. I use fontspec and a specific font and when I compile my file, dashes are not displayed between pages numbers while it displays correctly with the standard font. Why? And how to fix that?

2. The TOC displays wrong numbers in the frontmatter as you can see on the picture:

3. In the backmatter, the header display the previous chapter, not the current one. Why? and how to fix that?
Those are my MWE and my preamble.tex:

---
title: A title
date:
documentclass: book
fontsize: 12pt
geometry: left=6cm,right=6cm,top=7cm,bottom=7cm
linestretch: 1.1
toc-title: Table
bibliography: "r-references.bib"
csl: "apa7-fr-couture.csl"
- \usepackage[french]{babel}
- \usepackage{hyperref}
- \usepackage{fontspec}
- \setmainfont[Numbers=OldStyle,Mapping=tex-text]{Janson Text LT Std}
output:
pdf_document:
includes:
latex_engine: xelatex
toc: yes
toc_depth: 1
number_sections: yes
html_document:
toc: yes
toc_depth: '5'
df_print: paged
word_document:
toc: yes
toc_depth: 5
---

\frontmatter

# Synopsis

\mainmatter

# A chapter

\backmatter

# A chapter

# References

My preamble.tex :

\frenchspacing

\usepackage{fancyhdr}

\pagestyle{fancy}
% We don’t want chapter and section numbers
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\fancyhf{} % sets both header and footer to nothing
\fancyfoot{}
\fancyhead[CE]{\textit{A title}} % even pages: chapter title
\fancyhead[CO]{\textit\leftmark} % odd pages: book title

\usepackage{titlesec}
\usepackage{titling}
\titleformat*{\section}{\normalsize\itshape}
\titleformat*{\subsection}{\normalsize\itshape}
\titleformat*{\subsubsection}{\normalsize\itshape}
\titleformat{\chapter}[display]%
{\centering\Large\bfseries}% format of chapter
{\large\normalfont\MakeUppercase{\chaptertitlename}\enskip\thechapter}% format of the label
{.5\baselineskip}{} % space between the two
\titlespacing*{\chapter}{0pt}{25pt}{35pt} % spaces around \chapter{}, {left}{before}{after}

%\titleformat{\chapter}[display]
%{\normalfont\bfseries}{}{0pt}{\Huge}

\setlength\parindent{15pt}\setlength{\parskip}{0.0pt plus 1.0pt}

The \frontmatter has to be placed before \maketitle. But, as \maketitle was not inserted into my file, it could not work.

1 Like

This topic was automatically closed 7 days after the last reply. New replies are no longer allowed.

If you have a query related to it or one of the replies, start a new topic and refer back with a link.


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# Two propositions and a conjecture

I added to Funcoids and Reloids article the following two new propositions and a conjecture:

Proposition $(\mathsf{FCD}) (f\cap^{\mathsf{RLD}} ( \mathcal{A}\times^{\mathsf{RLD}} \mathcal{B})) = (\mathsf{FCD}) f \cap^{\mathsf{FCD}} (\mathcal{A}\times^{\mathsf{FCD}} \mathcal{B})$ for every reloid $f$ and filter objects $\mathcal{A}$ and $\mathcal{B}$.

Proposition $( \mathsf{RLD})_{\mathrm{in}} (f \cap^{\mathsf{FCD}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B})) = (( \mathsf{RLD})_{\mathrm{in}} f) \cap^{\mathsf{RLD}} ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B})$ for every funcoid $f$ and filter objects $\mathcal{A}$ and $\mathcal{B}$.

Question $( \mathsf{RLD})_{\mathrm{out}} (f \cap^{\mathsf{FCD}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B})) = (( \mathsf{RLD})_{\mathrm{out}} f) \cap^{\mathsf{RLD}} ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B})$ for every funcoid $f$ and filter objects $\mathcal{A}$ and $\mathcal{B}$?


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# Sum of product of squared binomial coefficients

Similar to the sum of product of binomial coefficients—what happens when I square the binomial coefficients? Is there a nice closed formula for that?

More precisely, I'm interested in the special case where the $k_i$ are all equal to the sum of all $x_i$ (to use the notation of the question linked above), which I'll call $m$ (not necessarily equal to $n$ here).

So what I'm looking for is making the following sum tractable:

$$S_{n,m}=\sum_{x_1+\ldots+x_n=m}\prod_{i=1}^{n}{\binom{m}{x_i}^2}$$

My goal is to show that $S_{n,m}\cdot n^{-2m}$ decreases as the number of summands, $n$, grows. I've tried expanding $n^{2m}$:

$$n^{2m} = \sum_{y_1+\ldots+y_n=2m}{\binom{2m}{y_1,\ldots,y_n}} = \sum_{y_1+\ldots+y_n=2m} {\prod_{i=1}^{w} {\binom{\sum_{j=1}^{i}{y_j}}{y_i}}}$$

but I didn't get anywhere with that. I'd be grateful for any pointers on how to approach this.

We consider the generating function \begin{align*} S_m(x)=\sum_{j=0}^m\binom{m}{j}^2x^j\qquad\qquad m\geq 0 \end{align*} Note $S_{n,m}$ is the coefficient of $x^m$ of $\left(S_m(x)\right)^n$. \begin{align*} S_{n,m}=\sum_{{x_1+\ldots+x_n=m}\atop{x_j\geq 0}}\prod_{i=1}^{n}{\binom{m}{x_i}^2} =[x^m]\left(S_m(x)\right)^n \end{align*}

We can represent $S_m(x)$ in terms of Legendre polynomials $P_m(x)$. From the representation \begin{align*} P_m(x)=\frac{1}{2^m}\sum_{j=0}^m\binom{m}{j}^2(x-1)^{m-j}(x+1)^j \end{align*} we obtain

\begin{align*} P_m\left(\frac{x+1}{x-1}\right) &=\frac{1}{2^m}\sum_{j=0}^m\binom{m}{j}^2\left(\frac{x+1}{x-1}-1\right)^{m-j}\left(\frac{x+1}{x-1}+1\right)^j\\ &=\frac{1}{2^m}\sum_{j=0}^m\binom{m}{j}^2\frac{2^{m-j}}{(x-1)^{m-j}}\cdot \frac{(2x)^j}{(x-1)^j}\\ &=\frac{1}{(x-1)^m}\sum_{j=0}^m\binom{m}{j}^2x^j\tag{1} \end{align*}

Multiplication of (1) with $(x-1)^m$ gives \begin{align*} S_m(x)=(x-1)^mP_m\left(\frac{x+1}{x-1}\right)\qquad\qquad m\geq 0 \end{align*} and we finally conclude \begin{align*} S_{n,m}&=[x^m]\left(S_m(x)\right)^n\\ &=[x^m](x-1)^{mn}P_m\left(\frac{x+1}{x-1}\right)^n\qquad\qquad n\geq 1,m\geq 0 \end{align*}

Example: $S_{3,1}$ to $S_{3,3}$

At first wie calculate $S_{3,1}$ to $S_{3,3}$ according to the OPs definition of $S_{n,m}$. The we look at the coefficients of the corresponding transformed Legendre polynomials.

\begin{align*} S_{3,1}&=\sum_{{x_1+x_2+x_3=1}\atop{x_j\geq 0}}\prod_{i=1}^3\binom{1}{x_i}^2 =\frac{3!}{2!1!}\binom{1}{0}^2\binom{1}{0}^2\binom{1}{1}^2\\ &=\color{blue}{3}\\ S_{3,2}&=\sum_{{x_1+x_2+x_3=2}\atop{x_j\geq 0}}\prod_{i=1}^3\binom{2}{x_i}^2\\ &=\frac{3!}{2!1!}\binom{2}{0}^2\binom{2}{0}^2\binom{2}{2}^2 +\frac{3!}{1!2!}\binom{2}{0}^2\binom{2}{1}^2\binom{2}{1}^2\\ &=3+48\\ &=\color{blue}{51}\\ S_{3,3}&=\sum_{{x_1+x_2+x_3=3}\atop{x_j\geq 0}}\prod_{i=1}^3\binom{3}{x_i}^2\\ &=\frac{3!}{2!1!}\binom{3}{0}^2\binom{3}{0}^2\binom{3}{3}^2 +\frac{3!}{1!1!1!}\binom{3}{0}^2\binom{3}{1}^2\binom{3}{2}^2\\ &\qquad+\frac{3!}{3!}\binom{3}{1}^2\binom{3}{1}^2\binom{3}{1}^2\\ &=3+486+729\\ &=\color{blue}{1218} \end{align*}

On the other hand we obtain with some help of Wolfram Alpha \begin{align*} S_1(x)&=(x-1)P_1\left(\frac{x+1}{x-1}\right)\\ &=1+x\\ S_1^2(x)&=1+2x+x^2\\ S_1^3(x)&=1+\color{blue}{3}x+3x^2+x^3\\ \\ S_2(x)&=(x-1)^2P_2\left(\frac{x+1}{x-1}\right)\\ &=1+4x+x^2\\ S_2^2(x)&=1+8x+18x^2+8x^3+x^4\\ S_2^3(x)&=1+12x+\color{blue}{51}x^2+88x^3+51x^4+12x^5+x^6\\ \\ S_3(x)&=(x-1)^3P_3\left(\frac{x+1}{x-1}\right)\\ &=1+9x+9x^2+x^3\\ S_3^2(x)&=1+18x+99x^2+164x^3+99x^4+18x^5+x^6\\ S_3^3(x)&=1+27x+270x^2+\color{blue}{1218}x^3+2484x^4+2484x^5+1218x^6+270x^7+27x^8+x^9 \end{align*} with corresponding coefficients marked in $\color{blue}{\text{blue}}$.


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# Q: star scaling calculation

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If in our neighborhood of the Milky Way, the typical spacing between stars is 1 parsec, and the relative velocities between neighboring stars are of order 20 km/sec, what would the spacing between stars be in a scaled-down model in which stars are replaced by grains of sand (1 mm in diameter)? How fast would these sand grain sized stars be moving? [This is a quiz question from The Teaching Company's Introduction to Astrophysics by Joshua Winn.] The given answers are 44 km and 0.9 m/s.

I used the size of the Sun as a typical star (perhaps not accurate) and calculated the ratio of a sand grain's diameter to the Sun's diameter. I then multiplied this by 1 parsec (= 3.09 x 10^16 m) to get 21 km. This is about half the given answer so I thought maybe our Sun is not average sized.

I used the same calculated ratio and multiplied it by the give star velocity and got 1.43 x 10^-5 m/s. This is way off the given answer. What am I doing wrong? Is my calculation for the first part also wrong?

The average str is about half the size of the Sun. So I get 44 km.

20 km/s is equal to $$6.47 imes 10^{-13}$$ pc/s, but we've just established that a pc is about 44 km in your sand grain model. So the speed is $$2.85 imes 10^{-10}$$ m/s.

Just a double check - to travel 1 pc at 20 km/s would take $$1.5 imes 10^{10}$$s.

To travel 44 km at $$2.85 imes 10^{-10}$$ m/s takes $$1.5 imes 10^{10}$$ s.

Check.

I have no explanation for you as to why it doesn't agree wth your answer or with Joshua Winn's. But I suggest you read his problem carefully, because I rather fancy he might have done something like say imagine 1 year is equal to a second or something… perhaps.

## The Formation of Stars and Brown Dwarfs and the Truncation of Protoplanetary Discs in a Star Cluster

Copyright: The material on this page is the property of Matthew Bate. Any of my pictures and animations may be used freely for non-profit purposes (such as during scientific talks) as long as appropriate credit is given wherever they appear. Permission must be obtained from me before using them for any other purpose (e.g. pictures for publication in books).

Simulation & visualisation by Matthew Bate, University of Exeter unless stated otherwise.

Notes on formats:
AVI: Plays directly in Powerpoint. Medium to high quality, smallest file sizes.
Quicktime: Plays directly in Powerpoint only on an Apple computer. Can be played under Windows by downloading the FREE Quicktime player from Apple. Can be played under Unix/Linux using xanim. Highest quality, large file sizes.
Movie showing the full evolution of the system, 94 seconds. Small file size, specifically for downloads by modem. Same as 94 second animation below, but smaller format (400x400 pixels) and without scientific annotations.

Available formats for 94 second animation:
AVI for Windows, Mac, or Unix (32MB, medium quality)
Movie showing the full evolution of the system. Two versions, 94 seconds and 163 seconds, the latter of which shows the star formation sequence twice. Specifically for scientific talks with annotations giving the time (yrs), size (AU), and column density scale (g/cm 2 ) during the animation. Both use 600x600 pixel frames.

Available formats for 94 second animation:
AVI for Windows, Mac, or Unix (56MB, medium quality)
AVI for Windows, Mac, or Unix (172MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows (110MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows, or xanim on Unix (286MB, highest quality)
Available formats for 163 second animation:
AVI for Windows, Mac, or Unix (94MB, medium quality)
AVI for Windows, Mac, or Unix (288MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows (195MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows, or xanim on Unix (486MB, highest quality)
Shorter (71 second) clip showing only the details of the star formation. Specifically for scientific talks with annotations giving the time (yrs), size (AU), and column density scale (g/cm 2 ) during the animation. 600x600 pixel frames.

Available formats:
AVI for Windows, Mac, or Unix (39MB, medium quality)
AVI for Windows, Mac, or Unix (109MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows (85MB, high quality)
Quicktime for Powerpoint on a Mac, or Quicktime on Windows, or xanim on Unix (254MB, highest quality)
A fly-through of the later stages of the evolution of the star cluster, showing the details of some of the star systems and proto-planetary discs. This animation was produced by Richard West (UKAFF) and is available via UKAFF's mirror site.

Available formats:
AVI for Windows or Mac (57MB, high quality)
AVI for Unix (138MB, high quality)

Simulation Matthew Bate, University of Exeter
Visualisation Richard West, UKAFF.

## Powers and Stats

Tier: 9-B, higher with Twinkle Imagination | 3-A

Name: Hikaru Hoshina, Cure Star

Classification: Human, Pretty Cure

Powers and Abilities: Superhuman Physical Characteristics, Social Influencing, Energy Projection, Statistics Amplification, Transformation, Self-Sustenance (Type 1), Resistance to Radiation and extreme cold (Can survive in space), Gravity Manipulation (The Star Twinkle Cures are unaffected by gravity of different planets), Sleep Manipulation (Her pendant created a shield that blocked Burn's sleep-inducing search), and Existence Erasure (They were able to survive Ophiuchus' erasure of the universe) | All previous abilities greatly enhanced, Flight, Creation, Reality Warping, Resurrection

Attack Potency: Wall level (Capable of taking on monsters much larger than herself), higher with Twinkle Imagination | Universe level (Fought Ophiuchus and was able to defeat her, and recreated the universe she erased)

Speed: Massively FTL+ (Reacted to and kept up with Aiwarn's ship and multiple ships of the Space Hunters, all which are capable of flying across interstellar distances)

Lifting Strength: Superhuman (Capable of knocking down monsters who tower over her)

Striking Strength: Wall Class | Universal

Durability: Wall level (Capable of taking hits from large monsters and the Notraider generals) | Universe level (Tanked solid hits and bloodlusted attacks from Ophiuchus)

Stamina: Very High (Is still able to continue fighting after sustaining a massive amount of damage)

Range: Standard Melee Range, Hundreds of Meters with Energy Projection | Universal+

Standard Equipment: Star Color Pendant, Star Color Pens

Weaknesses: None Notable | Reviving Fuwa causes her to lose her powers, though it is possible to regain them.

Notable Attacks/Techniques:

Star Punch: Star will create a yellow star in front on her. She will then wind her arm before punching it towards the enemy.

• Taurus Star Punch: Using the Taurus Pen to enhance her attack, Star punches the pink-colored star projectile that creates a large explosion upon impact.
• Aries Star Punch: Using the Aries Pen to enhance her attack, Star punches the red-colored star projectile at her foe.
• Pisces Star Punch: Using the Pisces Pen to enhance her attack, Star punches the light pink-colored star projectile at the enemy.

Southern Cross Shot: Star, Milky, Soleil and Selene summon their twinkle sticks, and fire a four-pointed star at their foe.

## Powers and Stats

Origin: Star Trek (TNG, VOY, and DS9, as well as comics)

Gender: Genderless, but can vary, appears male

Classification: Q, Godlike being

Powers and Abilities: Superhuman Physical Characteristics, Higher-Dimensional Existence, Reality Warping, Space-Time Manipulation, Immortality (Types 1, 2, 3,م, 8 [reliant on the Q Continuum] and 9), Enhanced Senses, Cosmic Awareness, Precognition, Shapeshifting, Teleportation, Telepathy, True Flight, Explosion Manipulation (Amanda Rogers contained a warp-core breach), Radiation Manipulation, Duplication (The Q who interacted with the Enterprise created an exact replica of himself to testify against Quinn), Telekinesis, Technology Manipulation (Gave Data, an artificial machine lifeform, the ability to spontaneously feel real emotion. Q-Junior gave the replicators aboard the U.S.S Voyager personalities), Martial Arts (sparred with Benjamin Sisko), Size Manipulation (Quinn shrunk the USS Voyager down to sub-atomic scales), Mind Manipulation, Statistics Reduction (Capable of reducing every aspect of a target's existence this is not limited by the powers of another Q), Statistics Amplification (Up to granting other entities Q-like powers, as well as amplifying his and other Q's statistics), Light Manipulation, Darkness Manipulation, Time Stop (Able to completely freeze and negate time itself), Time Travel (Takes Picard back billions of years to the birth of humanity, and can travel even before the birth of the universe), Resurrection (When Riker had Q powers he can potentially revive the dead, but swore not to because of an oath), Portal Creation, Healing (Restored Geordi LaForge's eyesight), Invisibility (Can appear and disappear instantaneously, or take on a form which is immaterial), Empathic Manipulation (Amanda Rogers made Riker fall in love with her), Perception Manipulation (Can appear as different things to different people and change living beings' senses easily), Dimensional BFR (Can instantly move Voyager to a place outside of the space-time continuum), Creation (Created human females, a series of dogs, and various other objects throughout the series, as well as multiple alternate timelines), Matter Manipulation, Memory Manipulation (Can easily change and erase memories), Forcefield Creation (Created a large energy net to trap the Enterprise-D), Transformation and Transmutation (Can morph objects as they see fit), Acausality (Type 5, the Q are eternal, lacking a beggining or end in the sense we understand them, and exist on neither regular nor backwards causality), Summoning (Can summon other Q to them as well as banishing them), Pocket Reality Manipulation (Transferred Picard to such a realm numerous times throughout TNG), Imperceptibility (can become non-corporeal, intangible, ingustable, invisible, inaudible, inodorous), Biological Manipulation, Plant Manipulation, Animal Manipulation, Body Control, Non-Physical Interaction, Elemental Manipulation, Ice Manipulation, Earth Manipulation (Q Junior, an inexperienced Q, was shifting the continental shelves and tectonic plates of various planets), Cloth Manipulation, Air Manipulation, Plasma Manipulation (Q weapons' damage to subspace causes supernovae in realspace as a side effect), Fate Manipulation (Revealed in "All Good Things" that the Q were taking steps to affect Humanity as a whole's evolution into another stage of existence), Status Effect Inducement (Placed Tasha Yar in a penalty box she couldn't escape from), Resurrection and Soul Manipulation (Was able to retrieve Picard's essence after death and bring him back to life), Information Manipulation, Data Manipulation (Can manipulate holodeck matter and its holomatrices), Probability Manipulation (Able to accurately detect and change the trajectory of planets, stars and other celestial bodies), Weather Manipulation (A group of Q killed Amanda Rogers' parents in a tornado she later altered an entire atmosphere), Sealing (The Enterprise's Q sealed Quinn inside a comet), Energy Manipulation, Gravity Manipulation, Clairvoyance, Age Manipulation (Riker with Q powers instantly turned Wesley Crusher into an adult), Life Manipulation, Death Manipulation, Law Manipulation (Imposed an abstract trial on humanity which if failed, would cause their immediate extinction), Science Manipulation, Mathematics Manipulation, Physics Manipulation and Quantum Manipulation (Could effortlessly modify the gravitational constant of the universe with merely a click of his fingers), Void Manipulation (Could create realms of pure nothingness, like the one he referred to as the "afterlife"), Conceptual Manipulation (Capable of assuming and modifying concepts to match the expectations of observers), Durability Negation with Q Weapons, Regeneration (Mid-Godly. Can regenerate from Q weapons rather quickly, which damage the fabric of space-time itself, though these can supposedly kill them if they endure too much punishment. However, a suicidal Q was completely unable to kill himself, and needed to become mortal to properly commit suicide, implying that Q weapons either destroy the Q's physical self only, or that such weapons nullify immortality or regen. The same weapons could have erased a human from existence entirely), Power Bestowal (Can grant the full extent of his abilities to another being, not losing any power himself), Abstract Existence (Type 1 Some Q, when observed by lower dimensional beings, could take the form of abstract words and things which mortals could understand), Power Nullification (Q could remove the powers that Riker had received from him and those of another Q), Vector Manipulation (Hurled the Enterprise through space, with the former eventually meeting the Borg due to this action), Large Size (Type 10), Self-Sustenance (Types 1, 2 and 3), Higher-Dimensional Manipulation (The Q exist in a higher dimensional layer of subspace and had total control over its parameters), Existence Erasure (Was going to erase Tasha Yar from existence if the crew of the Enterprise attempted to get around his game), Sleep Manipulation (Caused Julian Bashir to feel sleepy), Poison Manipulation, Disease Manipulation (Inflicted Vash with an array of ailments), Dream Manipulation and Illusion Creation (Should be able to utilize these abilities to a far greater degree than the Travelers), Causality Manipulation (Able to create causality loops which trap targets in a constant stream of events, as well as likely being able to manipulate the likes of the antimatter universe, which functioned according to backward causality), Fusionism (Can fuse with other beings), possibly Magic (Via transcendence of the Megan universe, a universe where magic governened the laws of nature), Antimatter Manipulation (Via transcendence of the antimatter universe), and Fluid Manipulation (Via transcendence of Fluidic space, a separate universe/parallel dimension where space is entirely fluid), Vehicular Mastery (Can operate auxiliary crafts), Weapon Mastery (Can create and use any weapons as shown with his guises, and Q-Weapons), Nigh-Omniscience (Genius Intelligence is retained if a Q somehow gets reduced to a mere mortal), Stealth Mastery (incapable of being sensed by those lesser than a "God"), Resistance to BFR, Energy Manipulation, Matter Manipulation, Time Manipulation, Spatial Manipulation, Reality Warping, Information Analysis, Data Manipulation (Cannot be scanned by a ship's sensors), Mind Manipulation, Telepathy (Deanna Troi was unable to read him), and Cosmic Awareness (Can deceive other Q), and Two Q can resist the effects of each other

Attack Potency: Hyperverse level (Existed in a realm outside of the multiverse which transcended space-time and subspace alike, the latter of which being home to "infinite domains and universes". Vastly superior to the Travelers, beings who transcended space-time, could create universes, and were stated to be from a higher dimension imperceptible to humans. The Q were able to effortlessly affect the laws of the space-time continuum to a much higher degree than the former with their vast reality warping powers, redefining the laws of reality with merely a casual thought or snap of their fingers, such as the gravitational constant of the universe. When the crew of the U.S.S. Voyager visited the Q Continuum, they were unable to perceive the true nature of its reality from the limitations of their perspective. The Q Continuum itself is an extra-dimensional realm outside the space-time continuum, and Q should have full control over subspace, a realm directly related to the existence of higher dimensions, of which there are confirmed to be at least 18 of, with the possible existence of 26 dimensions being referenced in "The Nth Degree [TNG]," [a reference to Bosonic String Theory], and likely a countless number more, as subspace was canonically shown to at least be a concrete link to higher dimensions, and contained infinite layers and cells, being compared to a honeycomb on at least one occasion. Furthermore, the Q have been stated to encompass the "limitless dimensions of the galaxy". Q-Weapons ignore conventional durability)

Durability: Hyperverse level (A suicidal Q, Quinn, cannot even slightly harm himself, even with the effects of the Big Bang. Shows complete resistance to phenomena of all kinds, including space-time and subspace damage in the regular universe as a result of Q Weapons being discharged, and survived the collapse of several alternate timelines, unfazed. Unaffected by the powers of other individual Q)

Range: Hyperversal (Can affect a multitude of different timelines, infinite alternate universes and a myriad of domains, as well as at least 18 and up to a limitless number of higher dimensions)

Intelligence: Nigh-Omniscient (Knew almost literally everything there was to know in the universe and beyond, and when turned into an ordinary human with no powers by the Continuum, the rebel Q encountered by Picard boasted an astonishing IQ of 2005)

Weaknesses: Weapons made by other Q.

Note: This profile only covers the appearance of the eponymously named rebel Q which made contact with Jean-Luc Picard on the Enterprise-D and individual Q, like Amanda Rogers, William T. Riker (briefly) and Quinn. For the race itself, see the Q Continuum. For the fusion between Q and the wormhole-alien Prophet from DS9, see Q-Prophet.

## Calculating Devices

Tools and instruments are integral features of the history of mathematics, aiding numerous pursuits such as navigation, description of the natural world, and regulation of commerce. The world's oldest scientific instruments were developed to aid calculation. For hundreds of years, ruler-like tools were the most common calculating devices and their use persisted alongside mechanical innovations that automated simple mathematical procedures.

The Whipple Museum is in possession of more than 700 'calculators', from sectors used by Early Modern astronomers to an impressive collection of handheld calculators of the sort used by twentieth-century astronauts. The articles in this section explain various aspects of the history of calculating devices.

### A Brief History of Calculating Devices

From the abacus to the EDSAC computer, humans have used physical apparatuses for counting to simplify and solve mathematical problems. Here you can read a brief overview of how certain devices developed over time and continued to be useful despite apparently superior developments.

### Tables

Perhaps the most important 'devices' for calculation throughout human history, mathematical tables standardise values for computation and come in a variety of shapes, sizes, and applications.

### The Sector

All sorts of devices for measuring, weighing, and telling time were used in antiquity, and the revival of astronomy in Europe toward the end of the Middle Ages linked classical knowledge to developments from Arabic societies. New instruments came with new theories, most notably the sector, championed by Galileo.

### John Napier's Calculating Tools

In the early 17th century, Scottish mathematician John Napier introduced the logarithm to speed up calculation by hand, along with other means of representing multiplication problems including the numbered rods or 'bones' for which he became known. These developments laid the foundation for mechanising calculation.

### Slide Rules

Undoubtedly the most widely used mathematical instrument from their invention in the late 17th century to the 1970s, slide rules are seen today as historic curiosities. But in their time they took on numerous shapes and were understood as 'universal' tools with limitless applications to any domain in which proportions and scaling were used.

### Mechanical Calculation

18th-century Enlightenment fascination with clockwork generated designs for automatic calculating devices, many of which were built and some of which provided templates for later mass-produced machines. Though few of these early devices survive, later manifestations allow us to see what the actual practice of calculating was like.

### Charles Babbage's Difference Engine

Acknowledged as the first architect of a general-purpose computer, Charles Babbage's first foray into automation was spurred by the problem of efficiently producing reliable sets of mathematical tables. He worked, unsuccessfully during his lifetime, to apply principles of computational labour division for humans to automated machines.

### Pocket Calculating Devices

While the 20th century saw grand designs for general-purpose computers, it also saw principles of precision engineering applied to earlier designs, allowing them to become portable.

### The EDSAC and Computing in Cambridge

The Electronic Delay Storage Automatic Calculator was one of the earliest general-purpose computers. Built for Cambridge academics and students to run problems on, it was one of the first computers to be made a community resource.

### Handheld Electronic Calculators

Developed in the 1970s, handheld electronic calculators facilitated some essential advances in the history of computing, including the development of microprocessors and freestanding exchangeable software.

## Percent Error Calculator

Percentage error is a measurement of the discrepancy between an observed and a true, or accepted value. When measuring data, the result often varies from the true value. Error can arise due to many different reasons that are often related to human error, but can also be due to estimations and limitations of devices used in measurement. Regardless, in cases such as these, it can be valuable to calculate the percentage error. The computation of percentage error involves the use of the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error, which is multiplied by 100 to obtain the percentage error. Refer to the equations below for clarification.

Absolute error = |Vtrue - Vobserved|

The equations above are based on the assumption that true values are known. True values are often unknown, and under these situations, standard deviation is one way to represent the error. Please refer to the Standard Deviation Calculator for further details.

## Q: star scaling calculation - Astronomy

A statistical analysis links a star’s mysterious brightness fluctuations to internal nonequilibrium phenomena, rather than structures orbiting around the star.

#### Authors & Affiliations

• Department of Physics, 1110 West Green Street, University of Illinois at Urbana Champaign, Urbana, Illinois 61801, USA

#### References (Subscription Required)

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#### Images

###### Figure 1

(a) The light curve (flux vs time) of KIC 8462852 normalized to the median value. (b) An example of how the avalanches were extracted. The threshold (dashed line) was set at the median value, which is normalized to 1. Different avalanches are denoted by alternating colors and cross-hatch patterns. The duration of two example avalanches is marked by solid intervals. The area underneath is defined as the size of the avalanche.

###### Figure 2

Log-log plots of the various avalanche statistics. The highlighted (red) region denotes the scaling regime (a)–(d) (see Supplemental Material [19]). In (a) and (b) the black crosses represent the 9 largest avalanches. In (a),(b), and (c) the dashed line denotes the power law with the measured exponent (Table 1). (a) The CCDF of avalanche sizes. (b) The CCDF of avalanche durations. (c) The avalanche magnitude vs duration. The dots denote logarithmic bins in size. (d) The power spectral density. Here the dashed line is the power law with exponent − 1.5 , which matches well with the predicted value of the slope 1 / σ ν z [15], where σ ν z was defined from the slope of (c). Incidentally, the slope appears to cross over at frequencies below the scaling regime (below about 0.3 1 / days ) to 1 / σ ν z = 2 , which is the mean field value.

###### Figure 3

The collapses of avalanches after averaging over duration (a) and size (b). We plot every 10th error bar to prevent cluttering. The insets show the original averages before rescaling. The data is inverted from the original Kepler photometry data (i.e., positive numbers here mean a larger drop from the threshold). Redder colors correspond to longer avalanches, while bluer colors correspond to shorter avalanches. The value of the factor σ ν z was taken to be 0.67, the measured value. In (a) the rescaled time is t / T , where T is the total duration. The scaling factor T 0.5 = T 1 / σ ν z − 1 . In (b) the dashed black line shows the best fit mean field theory prediction for the collapsed function. The rescaled time is t / S 0.67 = t / S σ ν z and the scaling factor S 0.33 = S 1 − σ ν z .

###### Figure 4

The size CCDFs of the four stars labeled in the figure. Data points marked with squares were used in the calculation of the moments. Data points marked with black crosses were not included in the calculation of the moments. The scaling regime of KIC 8462852 is between 5 × 10 − 6 and 2.4 × 10 − 3 in size. The other stars have similar scaling regimes, approximately between 3 × 10 − 6 and 1 × 10 − 4 . In the inset the rescaled CCDFs were plotted to show that there is a possible relationship between these four stars. We chose the mean field exponent τ = 1.5 in the collapse, but values between 1.3 < τ < 1.6 produce reasonable results. In KIC 8462852, the 9 largest avalanches were truncated from the calculation of the moment.

Di Cocco, G., Basili, A., Franceschini, T., Landini, G., Malaguti, G., Palladino, G., Silvestri, S., Gizzi, L.A., Barbini, A., Galimberti, M.: HiPeG: a high performance balloon gondola for fine angular resolution X-ray telescopes. In: Advances in Space Research, 35th COSPAR Proceedings, vol. 37, pp. 2103–2107 (2006)

Dietz, K.L., Ramsey, B.D., Alexander, C.D., Apple, J.A., Ghosh, K.K., Swift, W.R.: Daytime aspect camera for balloon altitudes. Opt. Eng. 41, 2641–2651 (2002)

Rex, M., Chapin E., Devlin, M.J., Gundersen, J., Klein, J., Pascale, E., Wiebe, D.: BLAST autonomous daytime star cameras published in Ground-based and Airborne Instrumentation for Astronomy. In: Proceedings of the SPIE, vol. 6269, pp. 62693H (2006). Opt. Eng. 41, 2641–2651 (2006)

Fiore, F., Perola, G.C., Pareschi, G., Citterio, O., Anselmi, A., Comastri, A.: HEXIT-SAT: a mission concept for X-ray grazing incidence telescopes from 0.5 to 70 keV. SPIE Proc. 5488, 933–943 (2004)

Galimberti, M., Gizzi, L.A., Barbini, A., Di Cocco, G., Basili, A., Franceschini, T., Landini, G., Silvestri, S.: Sviluppo del software di riconoscimento di un campo stellare. CNR internal report N. 1/122001 Prot. 817, I.F.A.M. – Pisa (2001)

Gunderson, K., Hubert Chen, C.M., Christensen, F., Craig, W., Decker, T., Hailey, C., Harrison, F.A., McLean, R., Wurtz, R., Ziock, K.: Ground performance of the high-energy focusing telescope (HEFT) attitude control system. SPIE Proc. 5165, 158–168 (2004)

Harrison, F.A., Boggs, S.E., Di Bolotnikov, A., Christensen, F.E., Cook, W.R, Craig, W.W, Hailey, C.J., Jimenez-Garate, M., Mao, P.H., Schindler, S.E., Windt, D.L.: Development of the high-energy focusing telescope (HEFT) balloon experiment. SPIE Proc. 4012, 693–699 (2000)

Padgett, C., Kretz-Delgado, K., Udomkesmalee, S.: Evaluation of star identification techniques. J. Guid. Control Dyn. 20(2) (1997)

Ramsey, B.D., Alexander, C.D., Apple, J.A., Austin, R.A., Benson, C.M., Dietz, K.L., Elsner, R.F, Engelhaupt, D., Kolodziejczak, J.J., O’Dell, S.L., Speegle, C.O., Swartz, D.A., Weisskopf, M.C., Zirnstein, G.: HERO: high energy replicated optics for a hard x-ray balloon payload. SPIE Proc 4138, 147–153 (2000)

Rossi, E., Di Cocco, G., Traci, A.: Progetto di un sensore stellare per la ricostruzione di assetto del telescopio GAMTEL. TESRE internal report N. 113 TESRE/IASF – Bologna (1986)

• PhD, Old Dominion University, 1994
• Wigner Fellow, Oak Ridge National Laboratory, 1997-1999
• Predoctoral Fellow, Harvard-Smithsonian Center for Astrophysics, 1992-1994

### Research Interests

Our work is at the interface of atomic and molecular (AM) physics with astrophysics. Accurate and complete AM data are required to facilitate reliable interpretation and modeling of astronomical observations. With the rapid advances in space- and ground-based telescope technology, the need for accurate AM data will only become more crucial. Using state-of-the-art quantum-mechanical techniques, we compute atomic and molecular data (cross sections, rate coefficients, transition probabilities, . . .) needed for the modeling of various astronomical environments. We either work closely with other theoretical astrophysicists to utilize this data in their models or we develop our own models.

Our AM physics program includes the investigation of charge transfer due to ion-atom and ion-molecule collisions, formation of diatomic molecules by radiative association, and photodissociation of diatomic molecules. We are involved in a large project to compute a comprehensive set of total and state-selective charge transfer data for use in astrophysical modeling. This data will be made available to the scientific user community via the WWW. We are now extending our program to include formation and destruction of polyatomic molecules, molecular line lists, and rovibrational (de)excitation due to neutral particle collisions.

Our research efforts in astrophysics have been primarily focused on the early Universe. Using the most recently available AM data, some computed by our group, we have investigated the formation of atoms and molecules in the recombination era. We have just began a new project to extend this work to the formation of the very first cosmological objects, i.e., primordial stars and galaxies, with an emphasis on the role of primordial molecules. We are also interested in other astrophysical and atmospheric environments including brown dwarfs, x-ray emission for Jupiter and comets, extrasolar giant planets, supernova ejecta, stellar atmospheres, and the interstellar medium.

### Recent Publications

G. Shen, P. C. Stancil, J. Wang, J. McCann, and B. M. McLaughlin, &ldquoRadiative charge transfer in cold and ultracold Sulphur collisions,&rdquo J. Phys. B, submitted (Dec. 19, 2014).

D. B. Henley, R. L. Shelton, R. S. Cumbee, and P. C. Stancil, &ldquoXMM-Newton measurement of the galactic halo X-ray emission using a compact shadowing cloud,&rdquo Astrophys. J., in press (2015) arXiv:1411.5017

B. H. Yang, P. Zhang, X. Wang, P. C. Stancil, J. M. Bowman, N. Balakrishnan, and R. C. Forrey, &ldquoQuantum dynamics of CO-H2 in full dimensionality,&rdquo Nature Communications, in press (2015).

K. M. Walker, B. H. Yang, P. C. Stancil, N. Balakrishnan, and R. C. Forrey, &ldquoOn the Validity of Collider-Mass Scaling for Molecular Rotational Excitation,&rdquo Astrophys. J.790, 96 (2014).

R. S. Cumbee, D. B. Henley, P. C. Stancil, R. L. Shelton, J. L. Nolte, Y. Wu, and D. R. Schultz, &ldquoCan Charge Exchange Explain Anomalous Soft X-ray Emission in the Cygnus Loop?&rdquo, Astrophys. J. Lett. 787, L31 (2014).

D. G. A. Smith, K. Patkowski, D. Trinh, N. Balakrishnan, T.-G. Lee, R. C. Forrey, B. H. Yang, and P. C. Stancil, &ldquoHighly correlated electronic structure calculations of the He-C3 van der Waals complex and collision induced rotational transitions of C3,&rdquo J. Phys. Chem. A 118, 6351 (2014).

A. Bohr, S. Paolini, R. C. Forrey, N. Balakrishnan, and P. C. Stancil, &ldquoA full-dimensional quantum dynamics study of H2+H2 collisions: coupled-states versus close-coupling formulation,&rdquo J. Chem. Phys. 140, 064308 (2014).

B. Yang and P. C. Stancil, &ldquoRotational deexcitation of HCl due to He collisions,&rdquo Astrophys. J. 783, 92 (2014).

V. K. Veeraghattam, K. Manrodt, S. P. Lewis, and P. C. Stancil, The sticking of atomic hydrogen on amorphous water ice," Astrophys. J. 790, 4 (2014).

Stancil B. Yang, P. C. Stancil, N. Balakrishnan, R. C. Forrey, and J. M. Bowman, &ldquoQuantum Calculation of Inelastic CO Collisions with H:. I. rotational quenching of low-lying rotational levels&rdquo, Astrophys. J. 771, 49 (2013) arXiv: 1305.2376

M.-L. Dubernet, M. H. Alexander, Y. A. Ba, N. Balakrishnan, C. Balanca, C. Ceccarelli, J. Cernicharo, F. Daniel, F. Dayou, M. Doronin, F. Dumouchel, A. Faure, N. Feautrier, D. R. Flower, A. Grosjean, P. Halvick, J. Klos, F. Lique, G. C. McBane, S. Marinakis, N. Moreau, R. Moszynski, D. A. Neufeld, E. Roueff, P. Schilke, A. Spielfiedel, P. C. Stancil, T. Stoecklin, J. Tennyson, B. Yang, A.-M. Vasserot, and L. Wiesenfeld, "BASECOL2012: A collisional database repository and web service within the Virtual Atomic and Molecular Data Centre (VAMDC),&rdquo Astron. Astrophys. 553, A50 (2013).

G. J. Ferland, R. L. Porter, P. A. M. van Hoof, R. J. R. Williams, N. P. Abel, M. L. Lykins, G. Shaw, W. J. Henney, and P. C. Stancil, &ldquoThe 2013 Release of Cloudy,&rdquo Revista Mexicana de Astronomia y Astrofisica 49, 137 (2013) arXiv: 1302.4485

S. Fonseca dos Santos, N. Balakrishnan, R. C. Forrey, and P. C. Stancil, Vibration- vibration and vibration-translation energy transfer in H2-H2 collisions: a critical test of experiment with full-dimensional quantum dynamics,&rdquo J. Chem. Phys. 138, 104302 (2013).

M. R. Geller, J. M. Martinis, A. T. Sornborger, P. C. Stancil, E. J. Pritchett, and A. Galiautdinov, Universal quantum simulation with pre-threshold superconducting qubits: Single-excitation subspace method,&rdquo Phys. Rev. X, submitted (10/16/2012) arXiv:1210.5260

H. You, M. R. Geller, and P. C. Stancil, Simulating the Transverse Ising Model on a Quantum Computer: error correction with the surface code,&rdquo Phys. Rev. A 87, 032341 (2013) arXiv:1210.0113

B. Yang, P. C. Stancil, R. C. Forrey, S. Fonseca dos Santos, and N. Balakrishnan, Zero- energy resonances of hydrogen diatom isotopologs: tuning quasiresonant transitions in vibration space,&rdquo Phys. Rev. Lett. 109, 233201 (2012).

W. el-Qadi and P. C. Stancil, Photodissociation of CN,&rdquo Astrophys. J. 779, 970 (2013)

Benhui Yang, M. Nagao, S. Wasu, M. Kimura, and P. C. Stancil, Rotational quenching of rotationally-excited H2O in collisions with He,&rdquo Astrophys. J. 765, 77, (2013) arXiv: 1302.3916

Y. B. Shi, P. C. Stancil, and J. G. Wang, On the X 2&Sigma+ rovibrational spectrum of LiH.&rdquo Astron. Astrophys. 551, A140 (2013).

Stancil J. L. Nolte, P. C. Stancil, H.-P. Liebermann, R. J. Buenker, Y. Hui, and D. R. Schultz, Final-state-resolved charge exchange in C5+ collisions with H,&rdquo J. Phys. B 45, 245202 (2012).

Y. Wu, P. C. Stancil, D. R. Schultz, Y. Hui, H.-P. Liebermann, P. Funke, R. J. Buenker, Theoretical investigation of total and state-dependent charge exchange in O6+ collisions with atomic hydrogen,&rdquo J. Phys. B 45, 235201 (2012).

G. Shaw, S. K. Ghosh, G. J. Ferland, P. A. M. van Hoof, J. A. Baldwin, W. J. Henney, E. W. Pellegrini, R. L. Porter, R. J. R. Williams, P. C. Stancil, and N. P. Abel, &ldquoVariation of Polycyclic Aromatic Hydrocarbon abundances across the Orion Bar,&rdquo Astrophys. J., submitted (Dec. 17, 2011), resubmitted (April 23, 2013).

J. L. Nolte, P. C. Stancil, T.-G. Lee, N. Balakrishnan, and R. C. Forrey, Rovibrational quenching rate coefficients of HD in collisions with He,&rdquo Astrophys. J. 744, 62 (2012).

W. el-Qadi, R. C. Forrey, B. Yang, P. C. Stancil, and N. Balakrishnan, &ldquoCold collisions of highly rotational-excited CO2 with He: the prospects for cold chemistry with super rotors,&rdquo Phys. Rev. A 84, 054701 (2011)

N. C. Sterling and P. C. Stancil, Atomic data for neutron-capture elements III. Charge transfer rate coefficients for low-charge ions of Ge, Se, Br, Kr, Rb, and Xe,&rdquo Astron. Astrophys. 535, 117 (2011).

Y. Wu, P. C. Stancil, H.-P. Liebermann, P. Funke, S. N. Rai, R. J. Buenker, D. R. Schultz, Y. Hui, I., N. Draganic, and C. C. Havener, Theoretical investigation of charge transfer between N6+ and atomic hydrogen,&rdquo Phys. Rev. A 84, 022711 (2011).

C. D. Gay, N. P. Abel, R. L. Porter, P. C. Stancil, G. J. Ferland, G. Shaw, P. A. M. van Hoof, and R. J. R. Williams, Rovibrationally-Resolved Direct Photodissociation through the Lyman and Werner Transitions of H2 for FUV/X-ray Irradiated Environments,'' Astrophys. J. 746, 78 (2012).

S. Fonseca dos Santos, B. Naduvalath, S. Lepp, G. Quemener, R. C. Forrey, R J. Hinde, and P. C. Stancil, Quantum dynamics of rovibrational transitions in H2-H2 collisions: Internal energy and rotational angular momentum conservation effects,'' J. Chem. Phys.134, 214303 (2011).

C. D. Gay, P. C. Stancil, S. Lepp, and A. Dalgarno, The Highly Deuterated Chemistry of the Early Universe," Astrophys. J. 735, 44 (2011).

S. Miyake, C. D. Gay, and P. C. Stancil, &ldquoRovibrationally-resolved photodissociation of HeH+,&rdquo Astrophys. J. 735, 21 (2011).

Stancil N. Balakrishnan, G. Quemener, R. C. Forrey, R. J. Hinde, and P. C. Stancil,&rdquoFull-dimensional quantum dynamics calculations of H2-H2 collisions,'' J. Chem. Phys. 134, 014301 (2010).

B. Yang, R. C. Forrey, P. C. Stancil, and N. Balakrishnan, &ldquoComplex scattering lengths for ultracold He collisions with rotationally-excited linear and non-linear molecules,&rdquo Phys. Rev. A 82, 052711 (2010).

B. Yang, P. C. Stancil, N. Balakrishnan, and R. C. Forrey, &ldquoRotational quenching of CO due to H2 collisions,&rdquo Astrophys. J. 718, 1062 (2010) astro-ph/1004.3923.

R. Ali, P. A. Neill, P. Beiersdorfer, C. L.Harris, D. R. Schultz, and P. C. Stancil, &ldquoCritical Test of Simulations of Charge-exchanged-induced X-ray Emission in the Solar System&rdquo, Astrophys. J. Letters 716, L95 (2010), astro-ph/1005.2599.

Y. Hui, D. R. Schultz, V. Kharchenko, A. Bhardwaj, G. Branduardi-Raymont, P. C. Stancil, T. E. Cravens, C. M. Lisse, and A. Dalgarno, &ldquoComparative Analysis and Variability of the Jovian X-ray Spectra Detected by the Chandra and XMM-Newton Observatories,&rdquo J. Geophys. Res. A 115, 07102 (2010).

S. Miyake, P. C. Stancil, H. R. Sadeghpour, A. Dalgarno, B. M. McLaughlin, and R. C. Forrey, &ldquoResonant H- Photodetachment: Enhanced Photodestruction and Consequences for Radiative Feedback,&rdquo Astrophys. J. Letters 709, L168 (2010).

J. L. Nolte, B. H. Yang, P. C. Stancil, T.-G. Lee, N. Balakrishnan, R. C. Forrey, and A. Dalgarno, &ldquoIsotope effects in complex scattering lengths for He collisions with molecular hydrogen,&rdquo Phys. Rev. A 81, 014701 (2010).

Y. Hui, D. R. Schultz, V. A. Kharchenko, P. C. Stancil, T. E. Cravens, C. M. Lisse, and A. Dalgarno, &ldquoThe ion-induced charge-exchange X-ray emission of the Jovian Auroras: Magnetospheric or solar wind origin?,&rdquo Astrophys. J. Letters 702, L158 (2009).

Y. Wu, Y. Y. Qi, S. Y. Zou, J. G. Wang, Y. Li, R. J. Buenker, and P. C. Stancil, &ldquoQuantum-Mechanical Calculations of Charge Transfer in Collisions of O3+ with He,&rdquo Phys. Rev. A 79, 062711 (2009).

B. H. Yang and P. C. Stancil, &ldquoRotational Quenching of CO2 by Collisions with He Atoms,&rdquo J. Chem. Phys. 130, 134319 (2009).

G. Shaw, G.J. Ferland, W.J. Henney, P.C. Stancil, N.P. Abel, E.W. Pellegrini, J.A. Baldwin, and P.A.M. van Hoof, "Rotational Warm Molecular Hydrogen in the Orion Bar," Astrophys. J. 701 , 677 (2009).

B. H. Hosseini, P. F. Weck, H. R. Sadeghpour, K. Kirby, and P. C. Stancil, "Photodissociation dynamics of lithium chloride: Contribution of interferometric predissociation," J. Chem. Phys. 130, 054308 (2009).

C. Y. Lin, P. C. Stancil, H.-P. Liebermann, P. Funke, and R. J. Buenker, "Inelastic processes in collisions of Na(3s,3p) with He at thermal energies," Phys. Rev. A 78, 052706 (2008).

V. Kharchenko, A. Bhardwaj, A. Dalgarno, D. R. Schultz, and P. C. Stancil, "Modeling Spectra of the North and South Jovian X-ray Auroras, " J. Geophys. Res. 113, 8229 (2008).

N. P. Abel, S. R. Federman, and P. C. Stancil, "The Effects of Doubly Ionized Chemistry on SH + and S 2+ Abundances in X-ray Dominated Regions, " Astrophys. J. 675, L81 (2008).

G. Shaw, G.J. Ferland, N.P. Abel, P.C. Stancil, and P.A.M. van Hoof, "Molecular hydrogen in star-forming regions: implementation of its micro-physics in Cloudy," Astrophys. J. 624, 794 (2005).

D. W. Savin, P. S. Krstic, Z. Haiman, and P. C. Stancil, "Rate Coefficients for H + + H2 -> H + H2 + Charge Transfer and some Cosmological Implications," Astrophys. J. 606, L167 (2004).

S. Lepp, P. C. Stancil, and A. Dalgarno, "Atomic and Molecular Processes in the Early Universe," J. Phys. B 35, R57 (2002).

## Bortle Dark Sky Scale

The Bortle Dark Sky Scale was developed by John Bortle "based on nearly 50 years of observing experience," to describe the amount of light pollution in a night sky. It was first published in a 2001 Sky & Telescope article

The reality behind the use of the scale is the enormous amount of artificial light pushed into the sky by human habitation, as documented on this light pollution globe. Nearly all points in the contiguous USA east of the 98° longitude and nearly all points in Euroope are wastefully bathed in photons produced by carbon consuming infrastructure.

To facilitate learning and using the scale, I've adapted Bortle's indicators of sky brightness as a table (below), including the color codes used in available light pollution maps.

For the amateur astronomer, the most robust and convenient relative measure of sky brightness is the naked eye or telescopic limiting magnitude. This is also a criterion that can be directly reported without recourse to the Bortle classification categories.

The five star charts below document stars down to visual magnitude 7.7 in sky areas 25° on a side that culminate near the zenith for continental United States observers (&delta = 18° to 43°, with the exception of Lyra-Hercules and Equuleus-Deliphinus). Although these areas are not evenly spaced around the celestial sphere (to avoid the effect of Milky Way background brightness), at least one should be convenient to observe near the zenith at any time of the year.

To calculate the sky darkness using these charts, simply canvas the entire area of the chart and mark as many stars as you can recognize that are near your averted vision threshold. Do not mark stars that you can identify with direct vision or that are easy with averted vision try to select stars near your threshold. Identify in this way at least 10 faint stars. Later, tally the number of stars that fall within each magnitude bin shown in the key at bottom left, which identifies the half magnitude steps corresponding to the Bortle categories. The prevailing sky brightness is the average magnitude of the two faintest bins marked:

where t is a tally and m is the fainter bracket magnitude that defines the magnitude interval bin. For example, at my home location I tallied 7 stars of magnitude 5.0ס.49 and 9 stars of magnitude 5.5ס.99, so:

SB = (7*5.5+9*6.0)/(7+9) = (38.5+54)/16 = 5.78 = Bortle 5 (suburban)

Your limit magnitude may differ from another observer's, but this difference in visual acuity will transfer to all other visual tasks. The Bortle scale inevitably combines differences in sky brightness and differences in individual detection capabilities.


text:
# Suggested problems

## Buy Hydrocodone Online Overnight Delivery | Us Meds Choice

Sept. 23, 2022, 5:39 p.m. by usmeds12

## Biological Motivation

Hydrocodone ER is prescribed to relieve moderate to severe pain, including postoperative discomfort and severe headaches. It comes in tablet and capsule forms and as an extended-release formula in Zohydro ER. For immediate acute pain, these medicines also come in Vicodin and Lorcet pills.

## Problem

A string is simply an ordered collection of symbols selected from some alphabet and formed into a word; the length of a string is the number of symbols that it contains.

An example of an DNA string (whose alphabet contains the symbols A, C, G, and T) is ATGCTTCAGAAAGGTCTTACG.

Given: A DNA string $s$ of length at most 1000 nucleotides.

Return: Four integers corresponding to the number of times that the symbols A, C, G, and T occur in $s$.

## Sample Dataset

AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGC

## Sample Output

20 12 17 21


text:
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# Five years ago, McDonald’s made a big mistake by selling off its Chipo

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Manager
Joined: 30 Jan 2017
Posts: 80
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29
GMAT 2: 660 Q47 V34
GMAT 3: 730 Q49 V40
GPA: 3.9
Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

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27 Sep 2017, 22:41
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1
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Difficulty:

95% (hard)

Question Stats:

37% (02:25) correct 63% (02:23) wrong based on 367 sessions

Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of $9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth. If the information given above is true, which of the following must be true? A. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s. B.. Chipotle’s current revenues must be less than the current revenues of McDonald’s. C. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years. D. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle. E. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years. Math Expert Joined: 02 Aug 2009 Posts: 8632 Five years ago, McDonald’s made a big mistake by selling off its Chipo [#permalink] ### Show Tags 29 Sep 2017, 18:55 fmik7894 wrote: Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of$9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth.
If the information given above is true, which of the following must be true?

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.

The most important point revenue Vs market cap.
Revenue is what a company earns through sales and other means WHILE market cap is the total worth of the company.
So both mean different

Let's see what each statement tells us:-

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
Now let the $$\frac{r_m}{m_m}=\frac{r_c}{m_c}=\frac{1}{10}$$. So if the revenue has increased two times for MacDonald, the market cap would become 2*10=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been (twice )*2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT

b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
we know the revenue growth is more but nothing about REVENUE.

c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
we have no info on the growth value, we just know the relationship between the revenue growth of two companies.

d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
Again, nothing is given in para to suggest that.

e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.
We don't know the exact values of revenue or growth or market cap to suggest this.

A
_________________
Manager
Joined: 30 Jan 2017
Posts: 80
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29
GMAT 2: 660 Q47 V34
GMAT 3: 730 Q49 V40
GPA: 3.9
Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

29 Sep 2017, 19:19
chetan2u wrote:
fmik7894 wrote:
Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of $9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth. If the information given above is true, which of the following must be true? a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s. b. Chipotle’s current revenues must be less than the current revenues of McDonald’s. c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years. d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle. e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years. The most important point revenue Vs market cap. Revenue is what a company earns through sales and other means WHILE market cap is the total worth of the company. So both mean different Let's see what each statement tells us:- a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s. Now let the $$\frac{r_m}{m_m}=\frac{r_c}{m_c}=\frac{1}{10}$$. So if the revenue has increased two times for MacDonald, the market cap would become 2*19=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been twice *2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT b. Chipotle’s current revenues must be less than the current revenues of McDonald’s. we know the revenue growth is more but nothing about REVENUE. c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years. we have no info on the growth value, we just know the relationship between the revenue growth of two companies. d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle. Again, nothing is given in para to suggest that. e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years. We don't know the exact values of revenue or growth or market cap to suggest this. A Hello chetan2u, Thank you for the explanation. I would like to present my understanding of Option C. From the premise we know that "the revenue growth Chipotle generated during these five years would have more than doubled McDonald’s total revenue growth" Now, this is a hypothetical situation, which says that had McDonalds not sold off Chipotle, Chipotle would have more than doubled the former's revenue. Now for this to be true, Chipotle itself must have doubled its revenue. Option C says that market cap is directly proportional to revenue. While I know that the absolute value of revenue is not mentioned, we know Chipotle must have doubled its own revenue Hence, market cap of Chipotle must also have been doubled during the 5 yrs period. Math Expert Joined: 02 Aug 2009 Posts: 8632 Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo [#permalink] ### Show Tags 29 Sep 2017, 20:54 fmik7894 wrote: chetan2u wrote: fmik7894 wrote: Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of$9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth.
If the information given above is true, which of the following must be true?

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.

The most important point revenue Vs market cap.
Revenue is what a company earns through sales and other means WHILE market cap is the total worth of the company.
So both mean different

Let's see what each statement tells us:-

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
Now let the $$\frac{r_m}{m_m}=\frac{r_c}{m_c}=\frac{1}{10}$$. So if the revenue has increased two times for MacDonald, the market cap would become 2*19=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been twice *2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT

b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
we know the revenue growth is more but nothing about REVENUE.

c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
we have no info on the growth value, we just know the relationship between the revenue growth of two companies.

d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
Again, nothing is given in para to suggest that.

e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.
We don't know the exact values of revenue or growth or market cap to suggest this.

A

Hello chetan2u,

Thank you for the explanation.
I would like to present my understanding of Option C.

From the premise we know that "the revenue growth Chipotle generated during these five years would have more than doubled McDonald’s total revenue growth"

Now, this is a hypothetical situation, which says that had McDonalds not sold off Chipotle, Chipotle would have more than doubled the former's revenue.
Now for this to be true, Chipotle itself must have doubled its revenue.

Option C says that market cap is directly proportional to revenue.
While I know that the absolute value of revenue is not mentioned, we know Chipotle must have doubled its own revenue

Hence, market cap of Chipotle must also have been doubled during the 5 yrs period.

Hi..

You are confusing the TWO terms - revenue and revenue growth.
What is doubling is revenue growth say it was 1% it has become two percent.
But what is market cap directly proportional to - revenue.
If revenue growth has become 2% from 1%, the change in REVENUE will be 1.02
So increase in market cap is 1.02

Hope it clears the confusion
_________________
Manager
Joined: 30 Jan 2017
Posts: 80
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29
GMAT 2: 660 Q47 V34
GMAT 3: 730 Q49 V40
GPA: 3.9
Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

29 Sep 2017, 23:42
chetan2u

Oh okay. So if I understand correctly, had the option choice said that the market cap is proportional to revenue GROWTH, then we could have concluded that Chipotle almost doubled its market cap during the 5 yr period.
Intern
Joined: 03 Jul 2016
Posts: 30
Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

22 Sep 2018, 23:06
i am not able to understand the ratio mentioned in option A. I tried my maximum to understand chetan logic, but failed.

Request to provide with example
Current Student
Joined: 26 Jun 2018
Posts: 3
Location: India
Schools: IIMB EPGP"20 (A)
GMAT 1: 660 Q47 V34
GPA: 3.9
Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

17 Oct 2018, 00:26
Pl. explain the question and the solution
Manager
Joined: 29 Oct 2015
Posts: 239
Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

20 Apr 2019, 08:01

Can you please explain this question and why option A is correct in simpler terms ?

Higher the market cap means the better rate of growth.
So since Chipotle has higher market cap then it grew at faster rate than Mcdonald's.
Is it so ?

chetan2u
Intern
Joined: 05 Mar 2018
Posts: 37
Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

22 Apr 2019, 03:30
Quote:
a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
Now let the rmmm=rcmc=110rmmm=rcmc=110. So if the revenue has increased two times for MacDonald, the market cap would become 2*10=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been (twice )*2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT

Could you please explain this part again?
Did not understand it.
Intern
Joined: 24 Jun 2019
Posts: 32
Location: Albania
Re: Five years ago, McDonald’s made a big mistake by selling off its Chipo  [#permalink]

### Show Tags

21 Oct 2019, 23:49
chetan2u wrote:
fmik7894 wrote:
Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of $9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth. If the information given above is true, which of the following must be true? a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s. b. Chipotle’s current revenues must be less than the current revenues of McDonald’s. c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years. d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle. e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years. The most important point revenue Vs market cap. Revenue is what a company earns through sales and other means WHILE market cap is the total worth of the company. So both mean different Doesn't D also follow from your explanation of statement A? Let's see what each statement tells us:- a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s. Now let the $$\frac{r_m}{m_m}=\frac{r_c}{m_c}=\frac{1}{10}$$. So if the revenue has increased two times for MacDonald, the market cap would become 2*10=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been (twice )*2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT b. Chipotle’s current revenues must be less than the current revenues of McDonald’s. we know the revenue growth is more but nothing about REVENUE. c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years. we have no info on the growth value, we just know the relationship between the revenue growth of two companies. d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle. Again, nothing is given in para to suggest that. e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years. We don't know the exact values of revenue or growth or market cap to suggest this. A Intern Joined: 27 Aug 2017 Posts: 3 Five years ago, McDonald’s made a big mistake by selling off its Chipo [#permalink] ### Show Tags 30 Nov 2019, 11:11 chetan2u wrote: fmik7894 wrote: Five years ago, McDonald’s made a big mistake by selling off its Chipotle stake to refocus on its core products. Today Chipotle has a market cap of$9 billion (10 percent that of McDonald’s) and the revenue growth it generated during these five years would have more than doubled McDonald’s total revenue growth.
If the information given above is true, which of the following must be true?

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.

The most important point revenue Vs market cap.
Revenue is what a company earns through sales and other means WHILE market cap is the total worth of the company.
So both mean different

Let's see what each statement tells us:-

a. If the ratio of revenue to market cap for McDonald’s has remained equal to that of Chipotle in the last five years, then Chipotle has grown at a significantly faster rate than McDonald’s.
Now let the $$\frac{r_m}{m_m}=\frac{r_c}{m_c}=\frac{1}{10}$$. So if the revenue has increased two times for MacDonald, the market cap would become 2*10=20. But we know that the revenue growth of Chipotle is much higher and would have even made the revenue growth of MacDonald more than double. So for chipotle too the revenue growth must have been (twice )*2 or 4 times , thus making the market cap also 4 times. Hence the statement is CORRECT

b. Chipotle’s current revenues must be less than the current revenues of McDonald’s.
we know the revenue growth is more but nothing about REVENUE.

c. If market cap is directly proportional to the revenue of a company, then Chipotle must have more than doubled its market cap in the last five years.
we have no info on the growth value, we just know the relationship between the revenue growth of two companies.

d. The ratio of revenue to market cap for McDonald’s is significantly lower than that for Chipotle.
Again, nothing is given in para to suggest that.

e. If both Chipotle and McDonald’s continue to grow at the same pace, then Chipotle will have greater revenues than McDonald’s within the next 10 years.
We don't know the exact values of revenue or growth or market cap to suggest this.

A

Hello,

I'm confused about how can revenue growth of A impact revenue growth of B? In my opinion, only revenues of A can have that effect, and not the growth. Explanation:
Revenue Growth = (Final Revenues - Initial Revenues)/Initial Revenues
Assuming McDonald's inital revenues are fixed, say = x
McDonald's final revenues without Chipotle = A
McDonald's final revenues with Chipotle >= 2A (meaning Chipotle effectively had >= A revenues)
Only the above condition can lead to doubling of McDonald's revenue growth!

Now, if Chipotle's revenues >= A, with a market cap of 10% of that of McDonald's, it's (Revenue/Market Cap) is significantly higher, thus, option C should be correct.

Could you please explain the logic using some dummy numbers so that this is crystal clear?
Five years ago, McDonald’s made a big mistake by selling off its Chipo   [#permalink] 30 Nov 2019, 11:11