I never have an issue with words. As Glennon Doyle Melton said, “Reading is my inhale, and writing is my exhale.”

However, over the past three weeks I’ve become frozen. My fingers are stiff, stuck to the keys like ice, the words crowded behind them like bodies shoved against locked doors with no way out.
My mind is sluggish, dizzy, unfocused, caught up in the whirlwind of emotions ruling my thoughts.
My body is on edge. While the color of my skin and my orientation grants me privilege to be shielded from much of the hate that has been brought into the light during the past year and a half, I am not blind to overlook the direct change and consequences that have roared into many of my friends’ and loved ones’ lives.

We have slim, weak glimmers of hope about the outcome. We have the mid-term elections. We have the few in Congress who are fighting tooth and nail to uphold the Constitution in the midst of the bought bureaucracy.

But still, we must be ready.

We must be ready to fight for our friends and family. If we have privilege, we must use it to its fullest to protect those that our broken society has marginalized and attempted to silence. The disenfranchised must be heard over us. We have been heard long enough. I have been comfortable in my privileged zone for far too long.

There are so many emotions trying to break free, sort themselves out, but there is not time.
The marathon as begun. The starting shot went off as soon as America swore in its 45th president. Already, our lands, our schools, our liberties, our equalities have been attacked, and we said no. We wrote, we marched, we called, we tweeted, shared, and posted. However, we cannot lose that fire. We cannot hold it so tightly that we get burned, letting it slip through our fingers to get crushed under foot. We have years left.
There is a difference between being angry and staying furious: a flash, an explosion that flings you into movement, or a quiet, seething heat that is stoked daily, kept hot and ready for the journey that lies ahead.

So research, plan, strategize, learn, and stay armed- armed to the teeth with books, statistics, quotes, dates, facts, figures, undeniable proof. Check sources twice, three times, and prepare yourself.
Study history, learn from the past, listen always, and build your arsenal.


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Bond Finally Posted Following Birth Injury Lawsuit Verdict

The experienced Illinois childbirth negligence lawyers at our firm know that it takes continued advocacy to ensure that clients receive the legal representation they need from the beginning of a case to the end. Unlike the frequent misguided portrayals made by those seeking tort reform, defendants in civil actions-including birth injury lawsuits-usually throw up every defense possible and use stalling tactics to fight efforts to hold negligent wrongdoers accountable for the consequences of their actions. The need to fight through the legal stall tactics is one reason why it is important for victims of these injuries to seek out experienced legal professionals who have consistently seen these cases through to the end.

For one thing, investigation and analysis must be conducted before the suit is even filed so that proper information can be included in a complaint. The complaint is the formal legal document filed by the plaintiff which initiates a civil action. After the complaint is filed defense attorneys often try to get the lawsuit thrown out of court on technicalities by filing a motion to dismiss. If the plaintiff survives that then discovery is conducted where information is collected on both sides. Near the end of the discovery process defense lawyers often try to defeat the measure again by filing a motion for summary judgment. It is only is the plaintiff withstands that attempt that the case actually goes to trial.

Of course, there are no guarantees that a jury will return a verdict for the plaintiff. Both sides have the ability to present their side of the story, and the plaintiff retains the burden of proof. Essentially that means that in the event of a “tie,” the defendant wins. However, even after a jury returns a verdict for a plaintiff, work must be conducted to ensure that the victim actually receives the award to which they are entitled. Many insurance companies, hospitals, and defendants attempt to use stall tactics even after money is owed to block the collection. It takes focused, experienced legal professionals to follow the case all the way through and ensure that victims actually receive what they are entitled in as efficient a manner as possible.

For example, last week the Trib Today published a story on the stall tactics conducted by one insurance company that delayed as long as possible after a birth injury lawsuit led to a verdict for a plaintiff. After losing a $9.7 million medical malpractice case, an insurance company appealed, but they refused to post a bond which was required for that appeal. The delay in posting the bond meant that the plaintiff’s attorneys began action against in the individual doctor involved in the case-even though the judgment was supposed to be paid by the insurance company. Eventually, only after a filing a lawsuit claiming that they were not required to post a bond (over a year after the verdict), did the company finally do as required.

Our Illinois birth injury lawsuits are experienced professionals who have followed through on countless cases for victims to ensure that they actually receive the funds that they are owed in a timely matter. Winning a verdict or reaching a settlement means little to the plaintiff’s until they actually receive the redress required.

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my jaw is wracked with mindlessness.
a blank ocean lurches beneath my skull.
I chew on teeth and problems

hangs from my temples.
I push nails through shaking fingers

sounds are far away.
you will find me clenched up under the waves
Today I feel electric grey
I hope tomorrow, neon black
Last edited by Ganoosh at Mar 1, 2015,
You could look into seratonin boosters
Be excellent to each other ☺
this is simple and straightforward, but strong. i like the third line of the first stanza, particularly "chewing on teeth". it's a good metaphor and i can relate to that (and all of this really).

the second stanza is my favorite, particularly because of the last line. it doesn't say where you're pushing your nails (and what are the nails? fingernails? literal nails?), but the setup in the rest of the stanza creates a nice, implied imagery.

i also like how your last stanza is shorter than the rest. maybe not in word count, but in the number of the lines- it reads much more quickly. it adds a sense of finality to the poem, and provides a full perspective of the image you are creating. what i mean by this, is that most of the images you show are fairly isolated to certain parts of the body, particularly those relating to the head. then the last line comes in, and i see the whole person.

the title misspelling feels appropriate, however i'm not sure if it was intentional (i'm guessing it was). you could read it as self-loathing or sarcasm. some kind of mockery. i like creative use of grammatical errors, it's interesting sometimes.

the only criticism i can give is to perhaps stray away from sea and ocean related metaphors in relation to this kind of subject matter, but that's up to you. i don't mind it personally, i just see it a lot and it feels a little derivative.

Quote by Paully1
You could look into seratonin boosters

*selective serotonin reuptake inhibitors
Last edited by Dregen at Mar 5, 2015,
Thanks for the feedback! I really appreciate it. The title was intentional, I was loaned a book of Jack kerouacs haiku and he used to call them pomes for whatever reason, so it was just my little personal nod to what I've been reading lately. I wrote the first stanza actually as a haiku itself after his style, but then it turned into more.

I wanted to give a sense of the far away sounds like when you are underwater, and also give a double meaning to the waves in the last line; under the sound waves, and also like under the waves in the ocean. And both of those positions would happen to be beneath my skull. So I don't know if that worked or not but that was the intention.

If there's anything you want me to take a look at just let me know
Today I feel electric grey
I hope tomorrow, neon black


Local Selling Tips

Selecting a Realtor®: Your most important decision when selling your home is the selection of the person you choose to represent you. The job of your Sales Associate is to support you in selling your home with the best possible terms, and to aid you through the entire process. Your Sales Associate will explain the process of selling a home, and familiarize you with the various activities, documents and procedures that you will experience throughout the transaction. Tips For Selecting A Realtor: Your Real Estate Professional should be: Aware of the complicated local and state requirements affecting your transaction. Effective in multi-party, face-to-face negotiations. Highly-trained, with access to programs for continued learning and additional certifications. Resourceful in attracting the largest possible pool of potential buyers. Knowledgeable in the technology resources that facilitate the transaction. Assisted by a fully-staffed marketing department. Supported by professional legal counsel. Developing a Marketing Strategy: In order to sell your home quickly and on with the best possible terms, it's necessary to prepare your home for the market. This process includes: Deciding when to put your home on the market. Establishing a strategic price based on recent comparable sales, local market conditions and your motivation to sell. Estimating probable net proceeds. Advising you on how to make your home more appealing to potential buyers. Marketing Your Property: Ordering a "FOR SALE" sign to be placed prominently on your property. Installing a lock box to make it easy for agents to show your home. Submitting your home to the regional Multiple Listing Service for immediate exposure to the real estate community. Arranging Sales Associates in the area to tour the home. Developing a flyer/brochure highlighting the features and benefits of your home. Promoting your home at the appropriate Association(s) of Realtors' for maximum exposure to other cooperating agents. Holding open houses when appropriate. Contacting your neighbors to promote the property. Advertising your property on our regular office schedule meetings. Featuring your property on our web site and REALTOR.com. Asking clients and colleagues if they know of possible buyers. Managing the Transaction: You'll appreciate having a strong advocate on your side during the transaction! Negotiating the Offer: Your Sales Associate will immediately present and explain all offers to you. You will be able to accept, reject, or counter any offer presented. During the negotiation process, your Associate will leverage their experience and skills to advocate your interests: Reviewing the contract and obligations before you sign. Explaining how contingencies and release clauses work. Protecting you from signing a "blank check" for unknown problems or repairs. Defining legal disclosure requirements. Orchestrate the offer process for "back-up" offers, if necessary. Throughout the negotiation, your Sales Associate will provide you with a professional, objective point of view; but the final decision of accepting an offer is yours. After the Offer is Accepted: Once an offer is accepted, your Sales Associate will manage all the details to make the process as stress-free and efficient as possible: Staying in contact with the buyer's agent to ensure a smooth escrow. Following up on the progress of the buyer's loan. Monitoring all contingency removal deadlines. Assisting you if a conflict with the buyer arises. Finalizing and Closing the Transaction: Finalizing the process includes reviewing all closing documents and ensuring both parties have copies. When the transaction has closed, your Sales Associate will deliver the closing check to you and the keys to the new owner.


Title: Automated Epileptic Seizure Detection from Electroencephalogram Signals
Authors: Jindal, Komal
Upadhyay, Rahul (Guide)
Keywords: EEG
Epilipsy Detection
Machine Learning Technique
Waelet Transform
Issue Date: 5-Sep-2017
Abstract: iii ABSTARCT Epileptic seizure is one of the brain’s disorder which can be automatically diagnosed by measuring and analys ing the non - linear and non - stationary behaviour of brain electrical activity. It is a transient symptom of excessive or synchronous neuronal activity of human brain. It is a group of disorders of human brain which has affected a large part of world’s popul ation. Epileptic seizure disturbs usual pattern of neuronal activity that causes interruption of consciousness, weird sensation and muscle fits. Early recognition of epileptic seizure helps in improving the physiological condition of patient. Human brain e lectrical activity varies with various physiological and neurological conditions and is recorded by multiple scalp mounted electrodes. The record of human brain electrical activity is called Electroencephalogram (EEG) signals. The Electroencephalogram (EEG ) signals are employed to diagnose various human brain disorders. The Electroencephalogram (EEG) signals contain necessary information for early diagnosis of epilepsy and epileptic seizures. In epilepsy, the nerve cells send out high amplitude electrical impulses and the impulses generate events called seizures. In the past, these EEG signals were diagnosed for any brain disorders by visual examination. However, visual examination is susceptible to errors and requires good understanding of EEG activity. T his research work presents an autonomous system, which is capable of detecting epileptic seizure from EEG signals automatically. The proposed system is carried out in three methodological steps viz. pre - processing, feature extraction and classification. T he purpose of pre - processing is to organize the data in an orderly manner and to remove noise. Whereas , feature extraction step extracts time - spectral features for proper representation of seizure and non - seizure signals. Further, the extracted features are then fed to the machine learning algorithms for detection of seizure and non - seizure EEG signals. The proposed system of automatic seizure detection is validated on publicly available dataset and the results show high detection ability of the proposed system. In present work, different feature extraction techniques have been employed and analysed for efficient classification. A comparative study for proposed feature extraction methods is performed in terms of classification efficiency. In this work, Sup port Vector Machine and Artificial Neural Network classifier have been used for classification of Electroencephalogram signals associated with different physiological condition.
Description: Master of Engineering -ECE
URI: http://hdl.handle.net/10266/4828
Appears in Collections:Masters Theses@ECED

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Planting Chilies – Short Procedure Text with Generic Structure

Do you like chilies?  Yes most of us like chilies to get a hot taste when chewing some meals.  A text on how to plant chilies is best sample for a procedure text. A text on how to plant, how to cook, how to write, how fix, and other how to texts are mostly written in imperative sentences. The way in which the imperative sentence organized into  a whole meaningful text, is called generic structure. Here we give you a very short example of procedure text

How to Plant Chilies

procedure text how to plant
Imperative sentences to build a procedure text example

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0 to 3V Adjustable Output Power Supply

0 to 3V Adjustable Output  Power Supply circuit diagram

This is an LM317 based adjustable voltage regulator with a maximum output of 3V and 1.5A. The output voltage depends on the VIN, R1 and R2 values, so the circuit can be modified to use with a maximum output of greater than 3V. The maximum current output is also independent of the circuit design, it is related to the package options. In this circuit, LM317T, which is capable of transferring up to 1.5A, is used.

Since the internal reference voltage of the LM317 regulator is 1.25V, the output voltage can be also minimally 1.25V. One way to overcome this problem is using a reference voltage source built on two diodes. But this approach is mostly suitable for 1.5V to 15V regulators since the sensitivity becomes poor for the low voltage outputs less than 1.5 . On the other hand, diodes have temperature dependent forward voltages.


Shabbat as a Reminder of Creation

Heschel draws out the implications of the idea that we rest in memory/imitation of God's primeval rest at the end of Creation.

When the Romans met the Jews and noticed their strict adherence to the law of abstaining from labor on the Sabbath, their only reaction was contempt. The Sabbath is a sign of Jewish indolence, was the opinion held by Juvenal, Seneca, and others.

In defense of the Sabbath, Philo, the spokesman of the Greek-speaking Jews of Alexandria, says, “On this day we are commanded to abstain from all work, not because the law inculcates slackness. . . . Its object is rather to give man relaxation from continuous and unending toil and by refreshing their bodies, with a regularly calculated system of remissions to send them out renewed to their old activities. For a breathing spell enables not merely ordinary people but athletes also to collect their strength with a stronger force behind them to undertake promptly and patiently each of the tasks set before them.”

Here the Sabbath is represented not in the spirit of the Bible but in the spirit of Aristotle. According to the Stagirite, “we need relaxation, because we cannot work continuously. Relaxation, then, is not an end”; it is “for the sake of activity,” for the sake of gaining strength for new efforts. To the biblical mind, however, labor is the means toward an end, and the Sabbath as a day of rest, as a day of abstaining from toil, is not for the purpose of recovering one’s lost strength and becoming fit for the forthcoming labor. The Sabbath is a day for the sake of life. Man is not a beast of burden, and the Sabbath is not for the purpose of enhancing the efficiency of his work. “Last in creation, first in intention,” the Sabbath is “the end of the creation of heaven and earth.”

Three acts of God denoted the seventh day: He rested, He blessed, and He hallowed the seventh day (Genesis 2:2-3). To the prohibition of labor is, therefore, added the blessing of delight and the accent of sanctity. Not only the hands of man celebrate the day; the tongue and the soul keep the Sabbath. One does not talk on it in the same manner in which one talks on weekdays. Even thinking of business or labor should be avoided.

Labor is a craft, but perfect rest is an art. It is the result of an accord of body, mind, and imagination. To attain a degree of excellence in art, one must accept its discipline, one must adjure slothfulness. The seventh day is a palace in time which we build. It is made of soul, of joy and reticence. In its atmosphere, a discipline is a reminder of adjacency to eternity. Indeed, the splendor of the day is expressed in terms of abstentions, just as the mystery of God is more adequately conveyed via negationis, in the categories of negative theology which claims that we can never say what He is, we can only say what He is not. We often feel how poor the edifice would be were it built exclusively of our rituals and deeds which are so awkward and often so obtrusive. How else express glory in the presence of eternity, if not by the silence of abstaining from noisy acts? These restrictions utter songs to those who know how to stay at a palace with a queen.

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How A Whale Awakened My Spirituality

Why Jews Eat Round Challah For the New Year

A sweet and symbolic tradition for the Jewish New Year


Desert Botanical Garden

1201 N. Galvin Parkway, Phoenix, AZ 85008 - United States

Museum Day Hours of Operation: 7:00 am ‐ 8:00 pm

Desert Botanical Garden is a living museum with more than 50,000 plants from around the world. For nearly 80 years, Desert Botanical Garden has been teaching and inspiring visitors from the local community and around the world, providing research, exhibits and more, designed to help us understand, protect and preserve the desert’s natural beauty. Everything the Garden does reflects this passion for connecting our community with the beauty and wonder of desert plants.

Discover the tranquil vibrancy of desert plants nestled amid the red rocks of the Papago Buttes. Visitors can stroll through five thematic trails to explore the fascinating beauty of the Sonoran Desert, from towering cacti and alluring succulents to brilliant wildflowers and lush trees. Scroll through the Garden's calendar so not to miss festive events and dazzling exhibitions. Delve deeper to learn about desert landscaping, nature art, cooking and wellness and more through the Garden's various adult and children's classes.

Get Directions


Other Subjects

Geography Year 7

Students in Year 7 will study one of the most contentious issues of the modern day population. They will investigate how the population increase affects everyone today and what the future holds if nothing is done about it. Students will look at the case study of China and investigate what extreme measures were put into place to try and slow population growth. This country will then be compared to the superpower of the United States of America. Students will study its place in the world and whether it warrants the label “superpower”. Students will also investigate the movement of people from Mexico to America and why this movement is so influential for both countries. Students finish the year by exploring the world of Natural Disasters, including how and why they occur and the destruction and benefits they can bring.

Geography Year 8

In Year 8 pupils study the less economically developed country of Kenya in Africa. Students study both physical and human aspects of this diverse country before focusing on, and contrasting two tribes. Students in Year 8 are involved in a field trip to Henley River and Rowing Museum to gain first-hand experience of rivers and flooding. This triggers an independent project on a case study of their choice. The majority of the year is dedicated to the study of deserts, forests, and grasslands otherwise known as Biomes. There is a focus on Tropical Rainforests, Hot deserts and Savanna regions. Each Biome is investigated in groups then presented to the class. The final topic of the year is a country study of Italy in Europe. Students explore its landscape, cities, trade and tourism industry.

History Year 7

Students commence Year 7 by studying the six key skills of History; causation, chronology, diversity, evidence, interpretation and significance. Each skill is looked at in detail and forms the basis of every lesson studied. Once the skills are gained students apply this to how towns and society have changed from AD40 – 1100 before studying the Normans and their conquests, and significant characters of this era. Pupils undertake an independent study on the formation of castles before looking at the English Crusades which took place across Europe. The year is concluded with students examining the Kings and Queens of the Middle Ages.

History Year 8

In Year 8, pupils acquire knowledge of 16th and 17th Century British History including Queen Elizabeth and the politics that linked to her reign. Following this students cement their skill of chronology by exploring how towns in Britain changed since 1750 until the modern day. The formation and importance of the railways is discussed and the use of children as a workforce scrutinised. This theme links closely to the following topic of the British Empire and the slave trade, where students have the chance to make a documentary about the trade and its abolition. Students complete Year 8 by looking at the history of Emigration including how this process has established Britain into the country that it is today.

Science Year 7

In Year 7, pupils learn about cells, reproduction, acids and alkalis, chemical reactions, separation techniques, particle theory, the rock cycle, the solar system, energy resources and sustainable living forces. Throughout each topic, pupils will carry out investigative work and are encouraged to research and evaluate the information they need to supplement their learning.

Science Year 8

In Year 8, pupils study the digestive and respiratory systems of the body, the action of microbes, the interaction of organisms within ecosystems, the transfer of energy as heat, light and sound, the effects of levers and pressure, the periodic table and the formation of compounds as described through word and symbol equations. In preparation for beginning their GCSE courses at upper school, we continue to develop and refine investigative skills, especially the evaluation of data and research.

Music Year 7

Year 7 pupils start by revisiting the main elements of music. They learn about how these elements are used as a means of providing interest and contrast in the works of established composers and also develop a more critical approach to their own music-making. Composition work is developed through an emphasis on the importance of having a clear structure and through the use of chords and harmony. Pupils learn how to use chords and learn about musical impressionism with its emphasis on chromatic discords. The Gamelan music of Indonesia is introduced as an example from another musical culture of how sounds can be put together in unusual ways to create atmospheric effects.

Music Year 8

In Year 8 pupils build on the knowledge they have already acquired by working with more extended musical structures. They learn about the music of other cultures – notably the music of the Caribbean and Afro-American Blues music. Through these topics they develop their improvisational skills and work at developing more sophisticated compositions. A range of musical styles and genres is also introduced with the aim of encouraging appreciation of a wider musical spectrum. Singing skills are also developed, including a greater emphasis on part-singing, and through practical and listening tests at the end of the year pupils are assessed before moving on to prepare for exam courses in their Upper Schools.

Art Year 7

In the Autumn term Year 7 study Pop Art focusing on the artist Andy Warhol. They use their knowledge and understanding to produce a large Pop Art painting based on Liquorice Allsorts. During the Spring term pupils will study wartime art, researching the artist Henry Moore and discovering what conditions would have been like during an air raid. Pupils will explore a range of different media and learn to experiment in the style of Moore. During the Summer term pupils will experience technical drawing, working with both two and single point perspective to create a fantasy city looking at the idea of Utopia. They will also learn about historical animation creating their own Zoetrope animated sequence. Pupils refine and improve skills in painting, drawing, mixed media and technical drawing.

Art Year 8

In the Autumn term Year 8 study illustration, focusing on a selection of poems including the Jabberwocky. They explore a range of different media and illustrators to create an exciting final illustrated painting. Pupils will also have the opportunity to look at Pop-up techniques to make their final piece more challenging. During the Spring term pupils will research the artist Ben Nicholson and the Cubists discovering layering techniques within collage and painting. Pupils will refine their ability in observational painting and drawing to produce a large scale mixed media still life. Once completed in the Summer term pupils will focus on abstracting their work to create a Cubist final piece. Selected pupils will also research philosophy in art reading Plato’s Republic. They will create a final response using their knowledge and understanding developed from their readings. Pupils will refine skills in observational drawing, collage, painting, oil pastel, chalk, ink, sculpture and illustration.

Design & Technology Year 7

In Year 7 pupils design and make two products; a Cushion Cover in Textiles and a Trinket Box in Resistant Materials. Their Cushion Cover includes the technique Reverse Applique based on the Mola work by the Kuna Indians; this develops pupils’ skills on the sewing machine and enables them to construct a product from a pattern piece. In Resistant Materials the pupils’ work with both natural and manmade materials and use a variety of skills including measuring and marking out accurately and finishing techniques.

Design & Technology Year 8

In Year 8 pupils design and make two products; a Beanie Hat in textiles and an Abstract Clock in Resistant Materials. In Textiles they work with a variety of fabrics and techniques including Applique and Computer Aided Design to produce their final product. In Resistant Materials the pupils use a wide variety of tools and equipment to complete their Abstract Clock based on the work of Piet Mondrian. Their design work includes Isometric drawings and modelling.

Life Skills in KS3

Pupils have the opportunity to develop self-understanding, a healthy lifestyle and an understanding of the society in which they live. They explore the social and emotional aspects of learning, friendship, values, management of money, drugs awareness and speaking skills. Life Skills contributes to citizenship: understanding about becoming informed citizens, developing skills of enquiry, communication, participation and responsible action.

During Anti-bullying week the whole school takes part in the same activities and learning.

Windsor Youth Talk will deliver sessions on the subject of self-esteem and a project on smoking in Year 7 and sessions on the subjects of bullying, domestic violence and self-esteem in Year 8.

Pupils are taught mostly in single gender groups and receive 180 minutes of Physical Education per week. During this Key Stage pupils are taught a range of subjects which enable them to develop their interest in a range of activities, encouraging their involvement in extra-curricular clubs in school and later in life:

They will develop:

  • Tactics and strategies in individual and team games as well as techniques across a range of activities.
  • Ability to perform in Dance and Gym.
  • Ability to work individually and as part of a team when solving problems.
  • Ability to self and peer assess in order to move their learning forward independently.

All pupils will take part in a number of activities during the Key Stage; these include Netball, Football, Hockey, Rugby, Gymnastics, Dance, Basketball, Volleyball, Badminton, Fitness, Cross Country, Athletics, Rounders and Cricket.

All students take part in House Matches.

Pupils in Year 8 are also given the opportunity to become Sports Leaders developing leadership skills such as organisation, communication and teamwork. This helps build confidence and self-esteem as they take on the responsibility of leading their peers and younger pupils within our family of First Schools.

RE Year 7

The topics covered by Year 7 pupils are answering the following questions: What is RE? How and why do people worship in a Christian Church? How can they move forward in a modern society to draw new members in? As Christian Churches have been seen as centres where the community can gather in the past, is this the way forward, and if so, why? What would a new Church Community look like? What facilities would it need to have to draw everyone in? Can churches still maintain some traditional forms of worship and still provide these new facilities?

Pupils try to design a place of worship for themselves that encompass some of their ideas including designing a church building for all Christians. During the summer terms they look at the question; ‘can one person make a difference?’ They choose to study one of the great religious or cultural leaders who have brought about a huge change in society through selfless acts. People like Mother Teresa, Ghandi or Martin Luther King.

RE Year 8

Year 8 study Buddhism throughout the first two terms looking at the Eightfold Pathway, Three Universal truths, Four Noble Truths and finally the Five Moral Precepts. They are asked to compare some aspects of what they have learnt with some moral teaching from other religions. Why was Gotama Buddha so special? What is a Buddhist goal in life? What are we doing to the environment? Is it right to eat animals? This leads pupils on to other ethical issues to do with the planet and forming opinions about basic human rights.

Pupils make informed responses to questions of identity and experience. In some topics they will explain how some forms of religious expression are used differently by individuals and communities; they will explain how selected features of religious life and practice make a difference to the lives of individuals and communities. Pupils make informed responses to people’s values and commitments (including religious ones) in the light of their learning. In Year 8 we consider what we really value in life and what it means to be “fully alive” and evaluate a range of guidance in order to enable pupils to form their own personal views. We examine the difference between going on a journey as a tourist or a pilgrim; whether one person can save the world, and whether prayer or meditation can work for us. Pupils develop their citizenship skills through study of some religious law, values and moral responsibility.


The Tragic Fall Of Macbeth

Essay by PaperNerd ContributorHigh School, 11th grade October 2001

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The play Macbeth by William Shakespeare presents a tragic journey from which escape is deadly. The tragic occurrences relate to Aristrotle's tragic hero. Aristrotle's Tragic Hero is defined as a character who is noble and virtuous. He allows his weaknesses to replace his honest heart, and because of this, he becomes a potential evil character. There are three main elements that define a tragic hero. The character must have a high social status, and be admired for his greatness. A tragic flaw, which dismantles his imperial status, must be evident in his personality. A tragic downfall must occur where the character displays actions provoked by his tragic flaw, usually ending the character's life. In the play Macbeth , by William Shakespeare, the character Macbeth is a definitive portrayal of Aristrotle's Tragic Hero.

Macbeth has the heart and mind of a compassionate person throughout descriptions and actions of his character early in the play.

He exhibits much strength and loyalty to his country. Macbeth, Thane of Glamis, is introduced as a strong, fearless soldier to his King. This is shown through the decisive words, "For the brave Macbeth-well deserves that name-/Disdaining fortune, with his brainish'd steek/Which smoke'd with bloody execution,"ÃÂ(1.2.16-18), Macbeth acts with much heroism in his battles, and fights nobly for his King. In addition, Macbeth is given special honours and his social status rises to Thane of Cawdor. This is because the King sees Macbeth's loyalty to the crown, and the Thane of Cawdor at that present time had dishonored him tremendously. The king reveals his distaste in the present Thane of Cowdor when he says, " No more that Thane of Cawdor shall deceive/Our blossom interest. Go pronounce his present death,/and with his former title greet Macbeth."ÃÂ(1.2.65-68). Macbeth is extensively known for his brave heart, and this has...


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- Stats
- Maybe implement DB::BulkDeleteForRange(start_key, end_key)
that would blow away files whose ranges are entirely contained
within [start_key..end_key]? For Chrome, deletion of obsolete
object stores, etc. can be done in the background anyway, so
probably not that important.
- There have been requests for MultiGet.
After a range is completely deleted, what gets rid of the
corresponding files if we do no future changes to that range. Make
the conditions for triggering compactions fire in more situations?


The Normal Distribution is AbNormal

Posted on Updated on

I gave a talk on this topic exactly two years ago at my undergraduate institution, the Indian Institute of Technology, in Chennai (India). The speech is here, with the powerpoint presentation accompanying it The Normal Distribution is Abnormal And Other Oddities. The general import of the speech was that the Normal Distribution, which is a statistical distribution that applies to random data of a variety of sorts, that’s often used to model the random data, is often not particularly appropriate at all. I presented cases where this is the case and the assumption (of a normal distribution) leads to costly errors.

Mr. Olbers and his paradox

Posted on Updated on

Why is the night sky dark? Wilhelm Olbers asked this question, certainly not for the first time in history, in the 1800s.

That’s a silly question with an obvious answer. Isn’t that so?

Let’s see. There certainly is no sun visible, which is the definition of night, after all. The moon might be, but on a new moon night, the moon isn’t, so all we have are stars in the sky.

Now, let’s make some rather simple-minded assumptions. Suppose the stars are distributed equally throughout space, at all previous times too. Why do we have to think about previous times? You know that light travels at 300,000 \: km/s, so when you look out into space, you also look back in time. So, one has to make some assumptions about the distribution of stars at prior times.

Then, if you draw a shell around the earth, that has a radius R and thickness \delta R, the volume of this thin shell is 4 \pi R^2 \delta R.

Shell Radius R

Suppose there were a constant density of stars n stars per unit volume, this thin shell has n 4 \pi R^2 \delta R stars. Now the further away a star is, the dimmer it seems – the light spreads out in a sphere around the star. A star a distance R that emits I units of energy per second, will project an intensity of \frac{I}{4 \pi R^2} per unit area at a distance R away. So a shell (thickness \delta R) of stars at a radius R will bombard us (on the earth) with intensity \frac {I}{4 \pi R^2} n 4 \pi R^2 \delta R units of energy per unit area. This is = I n \ \delta R units of energy per unit area.

This is independent of R!. Since we can do this for successive shells of stars, the brightness of each shell adds! The night sky would be infinitely bright, IF the universe were infinitely big.

Some assumptions were made in the above description.

  1. We assumed that the stars are distributed uniformly in space, at past times too. We also assumed, in particular,
  2. isotropy, so there are no special directions along which stars lie.
  3. We also assumed that stars all shine with the same brightness.
  4. We didn’t mention it, but we assumed nothing obscures the light of far away stars, so we are able to see everything.
  5. In addition, we also assumed that the universe is infinite in size and that we can see all the objects in it, so it also must have had an infinite lifetime before this moment. Since light travels at a finite speed, light from an object would take some time to reach us; if the universe were infinitely old, we’d see every object in it at the moment we look up.
  6. We also assumed that the Universe wasn’t expanding rapidly – in fact with a recession speed for far away stars that increased (at least proportionately, but could be even faster than linear) with their distance. In such a universe, if we went far enough, we’d have stars whose recession speed from us exceeds the speed of light. If so, the light from those stars couldn’t possibly reach us – like a fellow on an escalator trying hard to progress upwards while the escalator goes down.

There are a tremendous number of population analyses of the distribution of light-emitting objects in the universe that make a convincing case (next post!) that the universe is isotropic and homogeneous on enormously large length scales (as in 100 Mega parsecs). We don’t see the kind of peculiar distributions that would lead us to assume a conspiracy of the sort implied in point 2.

We have a good idea of the life cycles of stars, but the argument would proceed on the same lines, unless we had a systematic diminution of intrinsic brightness as we looked at stars further and further away. Actually, the converse appears to be true. Stars and galaxies further away had tremendous amounts of hydrogen and little else and appear to be brighter, much brighter.

If there were actually dust obscuring far away stars, then the dust would have absorbed radiation from the stars, started to heat up, then would have emitted radiation of the same amount, once it reached thermodynamic equilibrium. This is not really a valid objection.

The best explanation is that either the universe hasn’t been around infinitely long, or the distant parts are receding from us so rapidly that they are exiting our visibility sphere. Or both.

And that is the start of the study of modern cosmology.

The Great American Eclipse of 2017

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I really had to see this eclipse – met up with my nephew at KSU, then eclipse chasing (versus the clouds) all the way from Kansas to central and south-east Missouri. The pictures I got were interesting, but I think the videos (and audio) reflect the experience of totality much better. The initial crescent shaped shadows through the “pinholes” in the leafy branches,

With the slowly creeping moon swallowing the sun

Followed by totality

and the sudden disappearance of sunlight, followed by crickets chirping (listen to the sounds as the sky darkens)

I must confess, it became dark and my camera exposure settings got screwed up – no pictures of the diamond ring. Ah, well, better luck next time!

This is definitely an ethereal experience and one worth the effort to see it. Everybody and his uncle did!

Mr. Einstein and my GPS

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I promised to continue one of my previous posts and explain how Einstein’s theories of 1905 and 1915 together affect our GPS systems. If we hadn’t discovered relativity (special and general) by now, we’d have certainly discovered it by the odd behaviour of our clocks on the surface of the earth and on an orbiting satellite.

The previous post ended by demonstrating that the time interval between successive ticks of a clock at the earth’s surface \Delta t_R and a clock ticking infinitely far away from all masses \Delta t_{\infty} are related by the formula

The gravitational potential \Phi(R)=-\frac{G M_E}{R} is a {\bf {negative}} number for all R. This means that the time intervals measured by the clock at the earth’s surface is {\bf {shorter}} than the time interval measured far away from the earth. If you saw the movie “Interstellar“, you will hopefully remember that a year passed on Miller’s planet (the one with the huge tidal waves) while 23 years passed on the Earth, since Miller’s planet was close to the giant Black Hole Gargantua. So time appears to slow down on the surface of the Earth compared to a clock placed far away.

Time for some computations. The mass of the earth  is 5.97 \times 10^{24} \: kg, Earth’s radius is R = 6370 \: km \: = 6.37\times 10^6 \: meters and the MKS units for G = 6.67 \times 10^{-11} \: MKS \: units. In addition, the speed of light c = 3 \times 10^8 \frac {m}{s}. If \Delta t_{\infty} = 1 \: sec, the clock on an orbiting satellite (assumed to be really far away from the earth) measures one second, the clock at the surface measures

\Delta t_R = (1 \: sec) \times (1 - \frac {(6.67 \times 10^{-11}) \:  \times \:  (5.97 \times 10^{-24} )}{(6.37 \times 10^6 )\: (3 \times 10^8 )^2})

this can be simplified to  0.69 \: nanoseconds less than 1 \: sec. In a day, which is  (24 \times 3600) \: secs, this is 70 \times 10^-6 = 60 \: \mu \: seconds (microseconds are a millionth of a second).

In reality, as will be explained below, the GPS satellites are operating at roughly 22,000 \: km above the earth’s surface, so what’s relevant is the {\bf {difference}} in the gravitational potential at 28,370 \: km and 6,370 \: km from the earth’s center. That modifies the difference in clock rates to 53 \: nanoseconds per second, or 46 \: microseconds in a day.

How does GPS work? The US (other countries too – Russia, the EU, China, India) launched several satellites into a distant orbit 20,000 \: - 25,000 \: km above the earth’s surface. Most of the orbits are designed to allow different satellites to cover the earth’s surface at various points of time. A few of the systems (in particular, India’s) have satellites placed in a Geo-Stationary orbit, so they rotate around the earth with the earth – they are always above a certain point on the earth’s surface. The key is that they possess rather accurate and synchronized atomic clocks and send the time signals, along with the satellite position and ID to GPS receivers.

If you think about how to locate someone on the earth, if I told you I was 10 miles from the Empire State Building in Manhattan, you wouldn’t know where I was. Then, if I told you that I was 5 miles from the Chrysler building (also in Manhattan), you would be better off, but you still wouldn’t know how high I was. If I receive a third coordinate (distance from yet another landmark), I’d be set.  So we need distances from three well-known locations in order to locate ourselves on the Earth’s surface.

The GPS receiver on your dashboard receives signals from three GPS satellites. It knows how far they are, because it knows when the signals were emitted, as well as what the time at your location is.  Since these signals travel at the speed of light (and this is sometimes a problem if you have atmospheric interference), the receiver can compute how far away the satellites are. Since it has distances to three “landmarks”, it can be programmed to compute its own location.

Of course, if its clock was constantly running slower than the satellite clocks, it would constantly overestimate the distance to these satellites, for it would think the signals were emitted \: earlier than they actually were. This would screw up the location calculation, to the distance travelled by light in 0.53 \: nanoseconds, which is 0.16 meters. Over a day, this would become 14 kilometers. You could well be in a different city!

There’s another effect – that of time dilation. To explain this, there is no better than the below thought experiment, that I think I first heard of from George Gamow’s book. As with {\bf {ALL}} arguments in special and general relativity, the only things observers can agree on is the speed of light and (hence) the order of causally related events. That’s what we use in the below.

There’s an observer standing in a much–abused rail carriage. The rail carriage is travelling to the right, at a high speed V. The observer has a rather cool contraption / clock. It is made with a laser, that emits photons and a mirror, that reflects them. The laser emits photons from the bottom of the carriage towards the ceiling, where the mirror is mounted. The mirror reflects the photon back to the floor of the car, where it is received by a photo-detector (yet another thing that Einstein first explained!).

Light Clock On Train

The time taken for this up- and down- journey (the emitter and mirror are separated by a length L) is

\Delta t' = \frac{2 L}{c}

That’s what the observer on the train measures the time interval to be. What does an observer on the track, outside the train, see?

Light Clock Seen from Outside Train

She sees the light traverse the path down in blue above. However, she also sees the light traveling at the same (numerical) speed, so she decides that the time between emission and reception of the photon is found using Pythagoras’ theorem

L^2 = (c \frac{\Delta t}{2})^2 - (V \frac {\Delta t}{2})^2

\rightarrow  \Delta t = \frac {2 L}{c} \frac{1}{\sqrt{1 - \frac{V^2}{c^2}}}

So, the time interval between the same two events is computed to be larger on the stationary observer’s clock, than on the moving observer’s clock. The relationship is

How about that old chestnut – well, isn’t the observer on the track moving relative to the observer on the train? How come you can’t reverse this argument?

The answer is – who’s going to have to turn the train around and sheepishly come back after this silly experiment runs its course? Well! The point is that one of these observers has to actively come back in order to compare clocks. Relativity just observes that you cannot make statements about {\bf {absolute}} motion. You certainly have to accept relative motion and in particular, how observers have to compare clocks at the same point in space.

From the above, 1 second on the moving clock would correspond to \frac {1}{ \sqrt{1 - \frac{V^2}{c^2}} } seconds on the clock by the tracks. A satellite at a distance D from the center of the earth has an orbital speed of \sqrt {\frac {G M_E}{D} } , which for an orbit 22,000 km above the earth’s surface, which is 28,370 \: km from the earth’s center, would be roughly

\sqrt { \frac {(6.67 \times 10^{-11} (5.97 \times 10^{-24})}{28370 \times 10^3} }\equiv  3700 \: \frac{meters}{sec}

which means that 1 second on the moving clock would correspond to 1 \: sec + 0.078 \: nanoseconds on the clock by the tracks. Over a day, this would correspond to a drift of 6 \: microseconds, in the {\bf {opposite}} direction to the above calculation for gravitational slowing.

Net result – the satellite clocks run faster by 40 microseconds in a day. They need to be continually adjusted to bring them in sync with earth-based clocks.

So, that’s three ways in which Mr. Einstein matters to you EVERY day!

Master Traders and Bayes’ theorem

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Imagine you were walking around in Manhattan and you chanced upon an interesting game going on at the side of the road. By the way, when you see these games going on, a safe strategy is to walk on, since they usually reduce to methods of separating a lot of money from you in various ways.

The protagonist, sitting at the table tells you (and you are able to confirm this by a video taken by a nearby security camera run by a disinterested police officer), that he has managed to toss the same quarter (an American coin) thirty times and managed to get “Heads” {\bf ALL} of those times. What would you say about the fairness or unfairness of the coin in question?

Next, your good friend rushes to your side and whispers to you that this guy is actually one of a really \: large number of people (a little more than a billion) that were asked to successively toss freshly minted, scrupulously clean and fair quarters. People that tossed tails were “tossed” out at each successive toss and only those that tossed heads were allowed to toss again. This guy (and one more like him) were the only ones that remained. What can you say now about the fairness or unfairness of the coin in question?

What if the number of coin tosses was 100 rather than 30, with a larger number of initial subjects?

Just to make sure you think about this correctly, suppose you were the Director of a large State Pension Fund and you need to invest the life savings of your state’s teachers, firemen, policemen, highway maintenance workers and the like. You get told you have to decide to allocate some money to a bet based made by an investment manager based on his or her track record (he successively tossed “Heads” a hundred times in a row). Should you invest money on the possibility that he or she will toss “Heads” again? If so, how much should you invest? Should you stay away?

This question cuts to the heart of how we operate in real life. If you cut out the analytical skills you learnt in school and revert to how our “lizard” brain thinks, we would assume the coin was unfair (in the first instance) and express total surprise at the knowledge of the second fact. In fact, even though the second situation could well have happened to every similar situation of the first sort we encounter in the real world, we would still operate as if the coin was unfair, as our “lizard” brain would instruct us to behave.

What we are doing unconsciously is using Bayes’ theorem. Bayes’ theorem is the linchpin of inferential deduction and is often misused even by people who understand what they are doing with it. If you want to read couple of rather interesting books that use it in various ways, read Gerd Gigirenzer’s “Reckoning with Risk: Learning to Live with Uncertainty” or Hans Christian von Baeyer’s “QBism“. I will discuss a few classic examples. In particular Gigirenzer’s book discusses several such, as well as ways to overcome popular mistakes made in the interpretation of the results.

Here’s a very overused, but instructive example. Let’s say there is a rare disease (pick your poison) that afflicts 0.25 \% of the population. Unfortunately, you are worried that you might have it. Fortunately for you, there is a test that can be performed, that is 99 \% accurate – so if you do have the disease, the test will detect it 99 \% of the time. Unfortunately for us, the test has a 0.1 \% false positive rate, which means that if you don’t have the disease, 0.1 \% of such tested people will mistakenly get a positive result. Despite this, the results look exceedingly good, so the test is much admired.

You nervously proceed to your doctor’s office and get tested. Alas, the result comes back “Positive”. Now, ask yourself, what the chances you actually have the disease? After all, you have heard of false positives!

A simple way to turn the percentages above into numbers, suppose you consider a population of 1,000,000 people. Since the disease is rather rare, only (0.25 \% \equiv ) \: 2,500 have the disease. If they are tested, only (1 \% \equiv ) \: 25 of them will get an erroneous “negative” result. However, if the rest of the population were tested in the same way, (0.1 \%=) \: 1000 people would get a “Positive” result, despite not having the disease. In other words, of the 3475 people who would get a “Positive” result, only 2475 actually have the disease, which is roughly 72\% – so such an accurate test can only give you a 7-in-10 chance of actually being diseased, despite its incredible accuracy. The reason is that the “false positive” rate is low, but not low enough to overcome the extreme rarity of the disease in question.

Notice, as Gigirenzer does, how simple the argument seems when phrased with numbers, rather than with percentages. To do this using standard probability theory, one writes, if we are speaking about Events A and B and write the probability that A could occur once we know that B has occurred as P(A/B), then

P(A/B) P(B) = P(A)

Using this

P(I \: am \: diseased \: GIVEN \: I \: tested \: positive) = \frac {P(I \: am \: diseased)}{P(I \: test \: positive)}

and then we note

P(I \: am \: diseased) = 0.25\%

P(I \: test \: positive) = 0.25 \% \times 99 \% + 99.75 \% \times 0.1 \%

since I could test positive for two reasons – either I really among the 0.25 \% positive people and additionally was among the 99 \% that the test caught OR I really was among the 99.75 \% negative people but was among the 0.1 \% that unfortunately got a false positive.

Indeed, \frac{0.25 \%}{0.25 \% \times 99 \% + 99.75 \% \times 0.1 \%} \approx  0.72

which was the answer we got before.

The rather straightforward formula I used in the above is one formulation of Bayes’ theorem. Bayes’ theorem allows one to incorporate one’s knowledge of partial outcomes to deduce what the underlying probabilities of events were to start with.

There is no good answer to the question that I posed in the first paragraph. It is true that both a fair and an unfair coin could give results consistent with the first event (someone gets 30 or even 100 coin tosses). However, if one desires that probability has an objective meaning independent of our experience, based upon the results of an infinite number of repetitions of some experiment (the so-called “frequentist” interpretation of probability), then one is stuck. In fact, based upon that principle, if you haven’t heard something contrary to the facts about the coin, your a priori assumption about the probability of heads must be \frac {1}{2}. On the other hand, that isn’t how you run your daily life. In fact, the most legally defensible (many people would argue the {\bf {only}} defensible) strategy for the Director of the Pension Fund would be to

  • not assume that prior returns were based on pure chance and would be equally likely to be positive or negative
  • bet on the manager with the best track record

At a minimum, I would advise people to stay away from a stable of managers that simply are the survivors of a talent test where the losers were rejected (oh wait, that sounds like a large number of investment managers in business these days!). Of course, the manager that knows they have a good thing going is likely to not allow investors at all for fear of reducing their returns due to crowding. Such managers also exist in the global market.

The Bayesian approach has a lot in common with our every-day approach to life. It is not surprising that it has been applied to the interpretation of Quantum Mechanics and that will be discussed in a future post.

Fermi Gases and Stellar Collapse – Cosmology Post #6

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The most refined Standard Candle there is today is a particular kind of Stellar Collapse, called a Type 1a Supernova. To understand this, you will need to read the previous posts (#1-#5), in particular, the Fermi-Dirac statistics argument in Post #5 in the sequence. While this is the most mathematical of the posts, it might be useful to skim over the argument to understand the reason for the amazing regularity in these explosions.

Type 1a supernovas happen to white dwarf stars. A white dwarf is a kind of star that has reached the end of its starry career. It has burnt through its hydrogen fuel, producing all sorts of heavier elements, through to carbon and oxygen. It has also ceased being hot enough to burn Carbon and Oxygen in fusion reactions. Since these two elements burn rather less efficiently than Hydrogen or Helium in fusion reactions, the star is dense (there is less pressure from light being radiated by fusion reactions in the inside to counteract the gravitational pressure of matter, so it compresses itself) and the interior is composed of ionized carbon and oxygen (all the negatively charged electrons are pulled out of every atom, the remaining ions are positively charged and the electrons roam freely in the star). Just as in a crystalline lattice (as in a typical metal), the light electrons are good at keeping the positively charged ions screened from other ions. In addition, they also use them in turn to screen themselves from other electrons; the upshot is, the electrons behave like free particles.

At this point, the star is being pulled in by its own mass and is being held up by the pressure exerted by the gas of free electrons in its midst. The “lattice” of positive ions also exerts pressure, but the pressure is much less, as we will see. The temperature of the surface of the white dwarf is known from observations to be quite high, \sim 10,000-100,000 \: Kelvin. More important, the free electrons in a white dwarf of mass much greater than the Sun’s mass (written as M_{\odot}) are ultra-relativistic, with energy much higher than their individual mass. Remember, too, that electrons are a species of “fermion”, which obey Fermi-Dirac statistics.

The Fermi-Dirac formula is written as

P(\vec k) = 2 \frac {1}{e^{\frac{\hbar c k - \hbar c k_F}{k_B T}}+1}

What does this formula mean? The energy of an ultra-relativistic electron, that has energy far in excess of its mass, is

E = \hbar c k

where k c is the “frequency” corresponding to the electron of momentum c k, while \hbar is the “reduced” Planck’s constant (=\frac {h}{2 \pi}) (here h is the regular Planck’s constant) and c is the speed of light. The quantity k_F is called the Fermi wave-vector.  The function P(\vec k) is the (density of) probability of finding an electron in the momentum state specified by \hbar \vec k . In the study of particles where their wave nature is apparent, it is useful to use the concept of the de Broglie “frequency” (\nu = \frac{E}{h}), the de Broglie “wavelength” (\lambda=\frac {V}{\nu} where V is the particle velocity) and k=\frac{2 \pi}{\lambda}, the “wave-number”  corresponding to the particle. It is customary for lazy people to forget to write c and \hbar in formulas, hence, we speak of momentum k for a hyper-relativistic particle travelling at speed close to the speed of light, when it should really be h \frac {\nu}{c} = h \frac{V}{\lambda c} \approx {h}{\lambda} = \frac {h}{2 \pi} \frac{2 \pi}{\lambda} = {\bf {\hbar k}}.

Why a factor of 2? It wasn’t there in the previous post!

From the previous post, you know that fermions don’t like to be in the same state together. We also know that electrons have a property called spin and they can be spin-up or spin-down. Spin is a property akin to angular momentum, which is a property that we understand classically, for instance, as describing the rotation of a bicycle wheel. You might remember that angular momentum is conserved unless someone applies a torque to the wheel. This is the reason why free-standing gyroscopes can be used for airplane navigation – they “remember” which direction they are pointing in. Similarly, spin is usually conserved, unless you apply a magnetic field to “twist” a spin-up electron into a spin-down configuration. So, you can actually have two kinds of electrons – spin-up and spin-down, in each momentum state \vec k . This is the reason for the factor of 2 in the formula above – there are two “spin” states per \vec k state.

Let’s understand the Fermi wave-vector k_F. Since the fermions need to occupy momentum states two-at-a-time for each, and if they were forced into a cube of side L, you can ask how many levels they occupy. They will, like all sensible particles, start occupying levels starting with the lowest energy level, going up till all the fermions available are exhausted. The fermions are described by waves and, in turn, waves are described by wavelength. You need to classify all the possible ways to fit waves into a cube. Let’s look at a one-dimensional case to start

Fermion Modes 1D

The fermions need to bounce off the ends of the one-dimensional lattice of length L so we need the waves to be pinned to 0 at the ends. If you look at the above pictures, the wavelengths of the waves are 2L (for n=1), L (for n=2), \frac{2 L}{3} (for n=3), \frac {L}{2} (for n=4).  In that case, the wavenumbers, which are basically \frac {2 \pi}{\lambda} for the fermions need to be of the sort \frac {n \pi}{L}, where n is an integer (0, \pm 1, \pm 2 ...).

Fermion Modes 1D Table

For a cube of side L, the corresponding wave-numbers are described by \vec k = (n_x, n_y, n_z) \frac {\pi}{L} since a vector will have three components in three dimensions. These wave-numbers correspond to the momenta of the fermions (this is basically what’s referred to as wave-particle duality), so the momentum is \vec p = \hbar \vec k. The energy of each level is \hbar c k. It is therefore convenient to think of the electrons as filling spots in the space of k_x, k_y, k_z.

What do we have so far? These “free” electrons are going to occupy energy levels starting from the lowest k = (\pm 1, \pm 1, \pm 1) \frac{\pi}{L} and so on in a neat symmetric fashion. In k space, which is “momentum space”, since we have many, many electrons, we could think of them filling up a sphere of radius k_F in momentum space. This radius is called the Fermi wave-vector. It represents the most energetic of the electrons, when they are all arranged in as economically as possible – with the lowest possible energy for the gas of electrons. This would happen at zero temperature (which is the approximation we are going to work with at this time). This comes out from the probability distribution formula (ignore the 2 for this, consider the probability of occupation of levels for a one-dimensional fermion gas). Note that all the electrons are inside the Fermi sphere at low temperature and leak out as the temperature is raised (graphs towards the right).

It is remarkable and you should realize this, that a gas of fermions in its lowest energy configuration has a huge amount of energy. The Pauli principle requires it. If they were bosons, all of them would be sitting at the lowest possible energy level, which couldn’t be zero (because we live in a quantum world) but just above it.

What’s the energy of this gas? Its an exercise in arithmetic for zero temperature. Is that good enough? No, but it gets us pretty close to the correct answer and it is instructive.

The total energy in the gas of electrons is (in a spherical white dwarf of volume V = \frac {4}{3} \pi R^3, with 2 spins per state, is

E_{Total} =  2 V  \int \frac {d^3 \vec k}{(2 \pi)^3} \hbar c k = V \frac {\hbar c k_F^4}{4 \pi^2}

The total number of electrons is obtained by just adding up all the available states in momentum space, up to k_F

N = 2 V \int \frac {d^3 \vec k}{(2 \pi)^3} \rightarrow k_F^3 = 3 \pi^2 \frac {N}{V}

We need to estimate the number of electrons in the white dwarf to start this calculation off. That’s what sets the value of k_F, the radius of the “sphere” in momentum space of filled energy states at zero temperature.

The mass of the star is M. That corresponds to \frac {M} { \mu_e m_p} full atoms, where m_p is the mass of the proton (the dominant part of mass) and \mu_e is the ratio of atomic weight to atomic number for a typical constituent atom in the white dwarf. For a star composed of Carbon and Oxygen, this is 2. So, N = V \frac {M}{\mu_e m_p} = V \frac {M}{2 m_p}.

Using all the above

E_{Total} = \frac {4\pi}{3} R^3  \frac {\hbar c}{4 \pi^2} \left(  3 \pi^2 \frac {M}{\mu_e m_p \frac{4\pi}{3} R^3 }\right)^{4/3}

Next, the white dwarf has some gravitational potential energy just because of its existence. This is calculated in high school classes by integration over successive spherical shells from 0 to the radius R, as shown below

Spherical Shell White Dwarf

The gravitational potential energy is

\int_{0}^{R} (-) G \frac {\frac{4 \pi}{3} \rho_m r^3     4 \pi r^2}{r} dr = - \frac{3}{5} \frac {G M^2}{R}

A strange set of things happen if the energy of the electrons (which is called, by the way, the “degeneracy energy”) plus the gravitational energy goes negative. At that point, the total energy can become even more negative as the white dwarf’s radius gets smaller – this can continue {\it ad \: infinitum} – the star collapses. This starts to  happen when you set the gravitational potential energy equal to the Fermi gas energy, this leads to

the R (radius) of the star drops out and we are left with a unique mass M where this happens – the calculation above gives an answer of 1.7 M_{\odot}. A more precise calculation at non-zero temperature gives 1.44 M_{\odot}.

The famous physicist S. Chandrasekhar, after whom the Chandra X-ray space observatory is named, discovered this (Chandrasekhar limit) while ruminating about the effect of hyper-relativistic fermions in a white dwarf.

He was on  a cruise from India to Great Britain at the time and had the time for unrestricted rumination of these sorts!

Therefore, as is often the case, if a white dwarf is surrounded by a swirling cloud of gas of various sorts or has a companion star of some sort that it accretes matter from, it will collapse into a denser neutron star in a cataclysmic collapse precisely when this limit is reached. If so, once one understands the type of light emitted from such a supernova from some nearer location, one has a Standard Candle – it is like having a hand grenade that is of {\bf exactly} the same quality at various distances. By looking at how bright the explosion is, you can tell how far away it is.

After this longish post, I will describe the wonderful results from this analysis in the next post – it has changed our views of the Universe and our place in it, in the last several years.

Coincidences and the stealthiness of the Calculus of Probabilities

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You know this story (or something similar) from your own life. I was walking from my parked car to the convenience store to purchase a couple of bottles of sparkling water. As I walked there, I noticed a car with the number 1966 – that’s the year I was born! This must be a coincidence – today must be a lucky day!

There are other coincidences, numerical or otherwise. Carl Sagan, in one of his books mentions a person that thought of his mother the very day she passed away in a different city. He (this person) was convinced this was proof of life after/before/during death.

There are others in the Natural World around us (I will be writing about the “Naturalness” idea in the future) – for eclipse aficionados, there is going to be a total solar eclipse over a third of the United States on the 21st of August 2017. It is a coincidence that the moon is exactly the right size to completely cover the sun (precisely – see eclipse photos from NASA below)

Isn’t is peculiar that the moon is exactly the right size? For instance, the moon has other properties – for instance, the face of the moon that we see is always the same face. Mercury does the same thing with the Sun – it also exhibits the same face to the Sun. This is well understood as a tidal effect of a small object in the gravitational field of a large neighbor. There’s an excellent Wikipedia article about this effect and I well explain it further in the future. But there is no simple explanation for why the moon is the right size for total eclipses. It is not believed to be anything but an astonishing coincidence. After all, we have 6000 odd other visible objects in the sky that aren’t exactly eclipsed by any other satellite, so why should this particular pair matter, except that they provide us much-needed heat and light?

The famous physicist Paul Dirac discovered an interesting numerical coincidence based on some other numerology that another scientist called Eddington was obsessed with. It turns out that a number of (somewhat carefully constructed) ratios are of the same order of magnitude – basically remember the number 10^{40}!

  • The ratio of the electrical and gravitational forces between the electron and the proton (\frac{1}{4 \pi \epsilon_0} e^2 vs. G m_p m_e) is approximately 10^{40}
  • The ratio of the size of the universe to the electron’s Compton wavelength, which is the de Broglie wavelength of a photon of the same energy as the electron – 10^{27}m \: vs \: 10^{-12} m \: \approx 10^{39}

On the basis of this astonishing coincidence, Dirac made the startling observation that this could indicate (since the size of the universe is related to it’s age) the value of G would fall with time (why not e going up with time, or something else?). Whereas precision experiments in measuring the value of G are beginning now, there would have been cosmological consequences if G had indeed behaved as 1/t in the past! For this reason, people discount this “theory” these days.

I heard of another coincidence recently – the value of the quantity \frac {c^2}{g}, where c is the speed of light and g is the acceleration due to gravity at the surface of the earth (9.81 \frac{m}{s^2}), is very close to 1 light year. This implies (if you put together the formulas for g, and 1 light year), a relationship between the masses of the earth, the sun, the earth’s radius and the earth-moon distance!

The question with coincidences of any sort is that it is imperative to separate signal from noise. And this is why some simple examples of probability are useful to consider. Let’s understand this.

If you have two specific people in mind, the probability of both having the same birthday is \frac{1}{365} – there are 365 possibilities for the second person’s birthday and only 1 way for it to match the first person’s birthday.

If, however, you have N people and you ask for any match of birthdays, there are \frac {N(N-1)}{2} pairs of people to consider and you have a substantially higher probability of a match. In fact, the easy way to calculate this is to ask for the probability of NO matches – that is \frac {364}{365} \times \frac {363}{365} \times ... \frac {365 - (N-1)}{365}, which is \frac {364}{365} for the first non-match, then \frac {363}{365} from the second non-match for the third person and so on. Then subtracting from 1 gives the probability of at least one match. Among other things, this implies that the chance of at least one match is over 50% (1 in 2) for a bunch of 23 un-connected people (no twins etc). And if you have 60 people, the probability is extremely close to 1.

Probability Graph for Birthdays

The key takeaway from this is that a less probable event has a chance to become much more probable when you have the luxury of adding more possibilities for the event to occur. As an example, if you went around your life declaring in advance that you will worry about coincidences ONLY if you find a number matching the specific birth year for your second cousin – the chances are low that you will observe such a number – unless you happen to hang about near your second cousin’s home! On the other hand, if you are willing to accept most numbers close to your heart – the possibilities stealthily abound and the probability of a match increases! Your birthday, your age, room number or address while in college, your current or previous addresses, the license plates for your cars, your current and previous passport numbers – the possibilities are literally, endless. And this means that the probability of a “coincidence” is that much higher.

I have a suggestion if you notice an unexplained coincidence in your life. Figure out if that same coincidence repeats itself in a bit – a week say. You have much stronger grounds for an argument with someone like me if you do! And then you still have to have a coherent theory why it was a real coincidence in the first place!

Addendum: Just to clarify, I write above “It is a coincidence that the moon is exactly the right size to completely cover the sun …” – this is from our point of view, of course. These objects would have radically different sizes when viewed from Jupiter, for instance.


Linda Welcome

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About me

Industry Marketing
Occupation Entreprenuer
Location Ellington, Connecticut, United States
Introduction Well...let's see. I would rather be with my grandchildren than anyone else in the entire world. I'm definitely naive and obsessive/compulsive. My eyes are brown. My hair is getting very gray. I'm way too plump. I almost like everyone. I wish I were younger but knew what I know now!
Interests Loving my grandchildren, knitting, mousemaking, crocheting, sewing, reading, cross-stitching, and teaching
Favorite Movies Wedding Date, When Harry Met Sally, Pretty Woman, Sense and Sensibility, Emma, Pride and Prejudice...Yep, I' a Romantic Fool
Favorite Music Sinatra, Taylor, Groban, Buble, so many more...
Favorite Books Savannah Blues, Emma, Pride and Prejudice

If there's no I in team, why is there meat?

Because it contains all the same letters.


Carolina Culinary Cuisine

Carolina Primavera

Chefs of Carolina puts a Cackalaky twist on this classic Italian dish.  Fresh, locally produced pasta, produce and seafood were purchased at local farmer's markets and fisherman's wharf and used in this tasty dish.

What is Artichoke Relish?

Artichoke relish or Jerusalem Artichoke relish or Sunchoke relish is a Carolina favorite that consists of Jerusalem artichokes, onions, and bell peppers pickled with vinegar, mustard seed, turmeric, and other ingredients.

Black Sea Bass

Black Sea Bass is a unique fish with a wonderful texture and flavor. Black Sea Bass has firm white meat that is flaky and a delicate and unique flavor. Balckfish can be cooked several ways including frying, roasting, baking, broiling even grilling. Chefs will often cook the fish whole or with the skin on as it gives a good presentation.

Carolina Chicken Bog

What exactly is Chicken Bog?

Chicken Bog is comfort food. Chicken Bog is stick-to-your-ribs goodness! Yet to put it simply, Chicken Bog is a type of pilaf dish. But it is really much more than that.

What is Chow-Chow?

There are many different types of chow-chow from varying regions but in the Carolinas the relish primarily consists of chopped cabbage, onions, and peppers pickled in a brine of vinegar, mustard seed, turmeric and other ingredients.

Carolina Blue Crab

Blue Crab has been important to the culinary traditions of the Carolinas since people inhabited the area. Its scientific name means Beautiful Savory Swimmer and if you’ve ever seen them swim you’d know why. Many of the great seafood recipes of the Carolinas have Blue Crab in them.

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An Overview on E-Correspondence Unit

E-Dealings Unit effectively benefits from information technology so that it can continuously enhance and develop Deanship. Based on new systems, the administration fulfills and develops all procedures to facilitate gaining information. It also collects and saves all s 1008 tatistical information and data concerning the affairs of teaching staff members and employees. Additionally, it provides officials and researchers true and authentic statistical information and data.


Tuesday, July 22, 2008

not as radical as I thought. . .

It looks like my boss might have been surfing the web . . .

Generation V

My boss has a new buzz word he is using "Generation V" . He sees that there is a new class of people, a generation not bounded by age or birth - but instead bounded by the experience of using computers. This is an interesting idea. There are people who are active users of the Internet, blogging, social networking tools, and so on. There are other people who are not, and likely never will be. This set of differences is larger than the similarities that might exist across a age group.

Any other opinions on this concept?