Number theory is a branch of mathematics that focuses on the properties and relationships of numbers. It plays a crucial role in reference education, providing students with a solid foundation for further mathematical exploration. For instance, consider the case study of Sarah, a high school student struggling to understand algebraic equations. By studying number theory concepts such as prime numbers and divisibility rules, Sarah not only gained a deeper understanding of algebra but also developed problem-solving skills that extended beyond her math class.
In reference education, number theory serves as an essential tool for developing critical thinking and analytical reasoning abilities. Through the study of number patterns and their applications, students are exposed to logical reasoning strategies that can be applied across various disciplines. This academic style of learning cultivates intellectual curiosity and encourages students to approach problems from multiple angles. Moreover, by exploring topics like modular arithmetic and Diophantine equations, learners gain valuable insights into abstract mathematical concepts that lay the groundwork for future studies in advanced branches of mathematics such as cryptography or computer science.
Overall, the incorporation of number theory in reference education provides students with opportunities to develop both foundational mathematical skills and broader cognitive abilities necessary for success in academia and beyond. By engaging with this fascinating field of mathematics, learners acquire problem-solving techniques and enhance their ability to think critically and analytically. They learn to approach problems systematically, breaking them down into smaller components and applying logical reasoning to find solutions. This skill set is not only valuable in mathematics but also in other subjects and real-life situations. Number theory also encourages creativity as students explore different strategies and approaches to solve problems. By studying number patterns, students develop an intuition for numbers, which can aid in making connections between different mathematical concepts. Furthermore, the abstract nature of number theory challenges students to think outside the box and consider unconventional approaches to problem-solving. Overall, incorporating number theory in reference education equips students with a versatile skill set that can be applied across various disciplines and fosters a deeper understanding and appreciation for mathematics as a whole.
History of Number Theory
Number theory, a branch of mathematics that focuses on the properties and relationships of numbers, has a rich and fascinating history. To illustrate its relevance, let us consider the famous case study of Fermat’s Last Theorem. In the 17th century, Pierre de Fermat proposed this conjecture, stating that there are no three positive integers a, b, and c that satisfy the equation an + bn = cn for any integer value of n greater than two. This tantalizing problem intrigued mathematicians for over 350 years before it was finally proven by Andrew Wiles in 1994.
The development of number theory can be traced back to ancient civilizations such as Babylonian and Egyptian cultures, where basic arithmetic operations were performed using various numerical systems. However, it was not until around the 6th century BCE when Pythagoras and his followers made significant progress in understanding irrational numbers and their relationship to geometry. As time passed, prominent mathematicians like Euclid, Diophantus, and Fibonacci further expanded upon these ideas and contributed to the foundation of number theory as we know it today.
To appreciate the significance of number theory throughout history, consider the following emotional bullet points:
- Number theory has provided solutions to real-world problems such as encryption algorithms used in cybersecurity.
- It has played a crucial role in developing techniques for prime factorization, which is vital for cryptography.
- Mathematical concepts originating from number theory have found applications in diverse areas including computer science and physics.
- By exploring patterns within numbers themselves, number theory encourages abstract thinking and fosters analytical skills.
Additionally, let us examine a table showcasing influential mathematicians who made notable contributions to number theory:
|Pythagoras||Developed theories on rational and irrational numbers||6th century BCE|
|Euclid||Introduced the concept of prime numbers||3rd century BCE|
|Diophantus||Pioneered algebraic methods in number theory||3rd century CE|
|Fibonacci||Studied the properties of his self-named sequence||13th century CE|
In conclusion, the history of number theory is a testament to humanity’s enduring pursuit of understanding and exploring mathematical concepts. From ancient civilizations to modern-day mathematicians, this discipline has evolved over centuries, unraveling mysteries and inspiring new avenues of research. Understanding its historical context not only enhances our appreciation for number theory but also highlights its relevance as we delve into its importance in education in the subsequent section.
Moving forward with the discussion on the “Importance of Number Theory in Education,” it becomes evident that the legacy of this field stretches far beyond mere academic curiosity.
Importance of Number Theory in Education
Transitioning from the previous section on the history of number theory, it is evident that this field of mathematics holds significant importance in education. To illustrate its relevance, let us consider a hypothetical scenario where a middle school teacher introduces her students to prime numbers during a math lesson. The students are intrigued as they discover the unique properties and applications of prime numbers, sparking their curiosity and deepening their understanding of mathematical concepts.
The incorporation of number theory into education offers several benefits for students at different academic levels. Here are some key reasons why number theory holds such importance:
Development of critical thinking skills:
- Encourages logical reasoning and problem-solving abilities
- Promotes analytical thinking through pattern recognition
- Enhances deductive and inductive reasoning capabilities
Fostering creativity and curiosity:
- Inspires students to explore beyond textbook problems
- Engages learners by presenting puzzles and challenges
- Cultivates an environment conducive to questioning and inquiry
Building a strong foundation in mathematics:
- Deepens conceptual understanding of arithmetic operations
- Provides a bridge between algebraic expressions and real-world scenarios
- Strengthens computational fluency through mental math exercises
Preparing for advanced fields:
- Equips students with essential knowledge for higher-level mathematics courses
- Lays the groundwork for future studies in cryptography, computer science, or engineering
- Develops problem-solving strategies applicable across various disciplines
To further emphasize the significance of incorporating number theory into education, we can examine the following table:
|Benefits of Number Theory||Impact on Students|
|Enhanced critical thinking skills||Improved problem-solving abilities|
|Increased curiosity and creativity||Deeper engagement with mathematics|
|Stronger foundational understanding||Higher success rates in math|
|Preparation for advanced fields||Broader career opportunities|
In conclusion, the importance of number theory in education cannot be overstated. By integrating this branch of mathematics into curricula, educators can cultivate critical thinking skills, foster curiosity and creativity, build strong mathematical foundations, and prepare students for advanced studies or careers. The subsequent section will explore real-life applications where number theory finds practical use.
Transitioning to the next section on “Applications of Number Theory in Real Life,” we delve into how these theoretical concepts find relevance beyond the classroom setting.
Applications of Number Theory in Real Life
Section H2: Applications of Number Theory in Real Life
Real-life applications of number theory showcase the practical relevance and impact this field has on various aspects of our daily lives. One such example is the encryption algorithms used in secure communication systems. Public key cryptography, a widely-used method for securing online transactions and communications, relies heavily on number theory concepts.
Consider an example where two individuals, Alice and Bob, want to exchange sensitive information over the internet. They each have a pair of keys – a public key that anyone can see and use to encrypt messages, and a private key that only they possess to decrypt those encrypted messages. The security of this system hinges on the difficulty of factoring large composite numbers into their prime factors – a fundamental problem in number theory known as integer factorization.
The real-life applications of number theory extend beyond just encryption algorithms. Here are some other areas where number theory plays a crucial role:
- Cryptocurrency systems like Bitcoin utilize advanced mathematical principles based on number theory to ensure the integrity and security of digital transactions.
- Error-correcting codes, which are essential in data storage devices like CDs or DVDs, rely on mathematical properties derived from number theory.
- Prime numbers find practical application in fields ranging from computer science (primality testing) to physics (quantum mechanics).
These examples highlight how number theory is not confined to abstract mathematics but has tangible implications in our everyday lives. By exploring its applicability in diverse domains, we gain insights into both the theoretical foundations and practical significance of this branch of mathematics.
In the subsequent section about “Fundamental Concepts in Number Theory,” we will delve deeper into the core principles underlying these real-world applications.
Fundamental Concepts in Number Theory
Applications of Number Theory in Real Life have demonstrated the practicality and relevance of this branch of mathematics. Now, let us delve into the fundamental concepts that form the backbone of number theory.
One key area where number theory finds applications is in cryptography. For example, consider RSA encryption, a widely used method for secure communication online. In this system, two large prime numbers are multiplied to generate a public key, while their factors remain secret as the private key. The security lies in the difficulty of factoring large numbers into primes without knowledge of these primes themselves. This application showcases how number theory can protect sensitive information from malicious actors.
To gain further insights into number theory’s significance, we shall explore some essential concepts within it:
- Prime Numbers: These integers greater than 1 possess no divisors other than 1 and themselves.
- Divisibility: It refers to an integer evenly dividing another integer without leaving any remainder.
- Modular Arithmetic: This arithmetic deals with operations on remainders when one number is divided by another.
- Diophantine Equations: Named after ancient Greek mathematician Diophantus, these equations involve finding integer solutions for variables rather than general real or complex values.
Let us visualize this information through a table highlighting different properties related to divisibility:
|Divisible by 2||14||Ends with an even digit|
|Divisible by 3||243||Sum of digits is divisible by 3|
|Divisible by 5||105||Ends with either ‘0’ or ‘5’|
|Divisible by both 2 and 3||18||Satisfies both criteria above|
As we conclude our exploration of fundamental concepts in number theory, it becomes apparent that studying these principles provides a solid foundation for further exploration of the field. In the subsequent section, we will delve into the contributions made by famous number theorists and their lasting impacts on mathematics.
Next Section: Famous Number Theorists and Their Contributions
Famous Number Theorists and Their Contributions
Transitioning from the fundamental concepts in number theory, we now turn our attention to the incredible contributions made by famous number theorists throughout history. To bring these achievements closer to home, let us consider a case study involving Pierre de Fermat. In 1637, Fermat famously wrote in the margins of his copy of Diophantus’ Arithmetica that he had discovered “a truly marvelous proof” for what is now known as Fermat’s Last Theorem. This tantalizing claim captured the imagination of mathematicians for centuries until it was finally proven by Andrew Wiles in 1994.
As we delve into the world of famous number theorists, several notable figures emerge who have left an indelible mark on this field. These individuals have not only advanced our understanding of numbers but also revolutionized other areas of mathematics through their profound insights. Let us explore some key figures and their remarkable contributions:
- Carl Friedrich Gauss: Known as the Prince of Mathematicians, Gauss made significant advancements in algebraic number theory and modular forms.
- Évariste Galois: Despite dying at a young age, Galois laid the foundation for group theory and established a connection between symmetries and equations.
- Alan Turing: Renowned for his groundbreaking work in computer science and cryptography, Turing applied number-theoretic techniques to solve complex problems during World War II.
- Sophie Germain: A self-taught mathematician, Germain overcame gender barriers to contribute significantly to elasticity theory and prime numbers.
To gain further insight into the accomplishments of these prominent thinkers, let us examine Table 1 below:
Table 1: Notable Number Theorists and Their Contributions
|Pierre de Fermat||Pioneered modern number theory; proposed numerous conjectures|
|Carl Friedrich Gauss||Developed the fundamental theorem of arithmetic; made discoveries in modular forms|
|Évariste Galois||Established the connection between symmetries and equations through group theory|
|Alan Turing||Applied number-theoretic techniques to cryptography and computer science|
|Sophie Germain||Made significant contributions to elasticity theory and prime numbers|
In summary, the field of number theory owes much of its progress to the brilliant minds who have dedicated their lives to exploring its intricacies. Their innovative ideas continue to shape mathematics as a whole, inspiring future generations of mathematicians.
As we look ahead to the future of number theory research, it becomes evident that these past achievements provide a solid foundation for further exploration and discovery.
Future of Number Theory Research
Transitioning from the previous section on famous number theorists and their contributions, it is evident that number theory has had a profound impact on various fields. One example that highlights this influence is the encryption algorithms used in modern cybersecurity systems. Cryptography relies heavily on number theory concepts such as prime factorization and modular arithmetic to ensure secure communication over networks.
To further understand the significance of number theory in modern applications, let us explore some key areas where its principles are employed:
- Cryptography: As mentioned earlier, encryption techniques based on number theory provide a fundamental layer of security for sensitive information transmitted digitally.
- Coding Theory: Error-correcting codes rely on mathematical structures derived from number theory to detect and correct errors during data transmission.
- Cryptocurrency: Digital currencies like Bitcoin utilize cryptographic protocols underpinned by advanced concepts from number theory to secure transactions without relying on central authorities.
- Data Compression: Algorithms based on number theoretic principles enable efficient compression methods, reducing file sizes while preserving data integrity.
To illustrate the importance of these applications, consider the following table showcasing real-world instances where number theory plays a crucial role:
|Online Banking||Protects financial transactions against unauthorized access using robust cryptographic mechanisms.|
|Satellite Communication||Ensures reliable communication between satellites and ground stations through error correction codes.|
|Secure Messaging||Enables encrypted messaging platforms that safeguard privacy and prevent unauthorized interception.|
|Medical Imaging||Efficient image compression techniques reduce file sizes while maintaining diagnostic accuracy.|
As we can see from these examples, the incorporation of number theory into various domains has revolutionized how we approach different challenges within our technologically-driven society. Its practical implications extend beyond academia, making it an essential subject with far-reaching consequences.
In light of these observations, it becomes evident that number theory continues to shape the future of research and technological advancements. Exploring its applications in emerging fields such as quantum computing or machine learning holds immense potential for further innovation. The ever-growing need for secure communication, efficient data processing, and reliable systems ensures that number theory will remain a vital discipline within mathematics, driving progress across multiple domains.


Peer pressure is one of the topics that many parents fear. It makes them think of losing control over their teens. What these parents fail to understand is that facing this issue of peer pressure in the early stage can prove very health in the lives of their teens.
Research has shown that peer pressure is the major contributor in many teen vices such as smoking, deterioration in academics, teen drinking, and generally substances abuse. We cannot say that peer pressure is entirely negative as there are some aspects of it that prove positive in the lives of many teens.
Peer pressure in teens
Alienation from the family
One of the major effects of peer pressure is that it alienate the teens from their family. What does this mean? It simply means that instead of the child keeping close to his or her parents, they will choose other companies of their choice. This is very dangerous as it will make them feel that their parents are an obstacle in their achieving best relationship with their peers. It this habit that leads to teen repulsion.
Losing interest in education
It is said that education is the key to life. Can you imagine your teen refusing to study? What does it mean? It probably means a ruined life. This is how destructive peer pressure could be. However, this does not just happen; it happens when your teen gets into the company of those people who does not understand the value of education.
Negative behaviors, in this case, is a wide term that is used to refer to all vices that your kid can engage in when in the company of bad teens. This negative behaviors and habits make the teen disrespect their parents and finally, the lives succumb to negativity. Some of these behaviors that young people may find themselves in due to peer pressure includes indulgence in smoking, early sexual activities which can result in unwanted pregnancies and transmission of STDs, alcohol and substances abuse.
On the hand, peer pressure can also have some positive effects on the youths. So this, therefore, means that the company that your teens associate with is critical as it can either impact negatively or positively on your kid. Some of the positive impacts of peer pressure include;development in communication skills improved academic performances, developed and helpful human skills. With all this information, as a parent, you have a responsibility to watch over the company that your teens choose.


Lisbon’s pogrom of 1506
In 1506, Easter in Lisbon was forever marked by a tragic event. Between 4000 and 5000 people were killed and, some of them, after being tortured, accused of being Jews.
Portugal is country of tolerance, is part of the Portuguese heritage.
That being said it doesn’t mean that there are no problems concerning tolerance, of course, there are. But, in the actual world, I can consider Portugal as being a country where differences, towards the majority, are well accepted.
However, on 19 April 1506 something happened that was going to be remembered as the Pogrom of Lisbon or the Easter Massacre.
For the context and details, I will call your attention to the Wikipedia’s description that I find quite useful: https://en.wikipedia.org/wiki/Lisbon_massacre
Please pray for the end of all kinds of discrimination.


At the heart of this resource on the French sociologist and philosopher Emile Durkheim, provided by Professor Robert Alun Jones of the University of Illinois, is its bibliographic section. Included are both a complete chronological bibliography of Durkheim's published works, and an alphabetical bibliography of hundreds of items about Durkheim. An explanation of the process involved in producing these bibliographies is provided at the site. This site also features two full texts (French only at this time), highlighted by a set of lecture notes taken by the philosopher Andre Lalonde from a course given by Durkheim in 1883-84. A brief biography of Durkheim, a timeline, a list of lecture courses taught by Durkheim, and a glossary of pertinent terms are available. Much content at the site is informed by Steven Lukes' Durkheim: His Life and Work: A Historical and Critical Study.
(no comments available yet for this resource)


One aspect of our psychological growth is the movement from dependence to independence to interdependence. In the final part of this three-part series, we look at interdependence — what it is and how it creates a whole new way of relating to others.
Part 3: Interdependence
Our culture values independence — and this is a value I share. My interest is in helping people find their gift. I enjoy meeting those who have developed their own style — whether in an art form or in their way of life. Meeting a person with a sense of who they are is refreshing.
Independence is important. Unless people can challenge their tradition and develop their own style then the tradition becomes stale. We are stuck simply repeating the past, a past that becomes less and less relevant to how we live. In this way, simply repeating the past leads to the death of the tradition. Without innovation, without people developing their own style, any art form is doomed to sterility. And any individual’s life will simply be a repetition of their life at a particular age. We get stuck with nothing but the ‘good old days’. I don’t see anything wrong with reminiscing, but I do think it is a problem if we feel that nothing has happened in our lives ever since. Independence is needed to renew our traditions and keep ourselves fresh.
Interdependence adds another element. Independence is focused on the individual. The independent person may work with others but this is mainly for their own enjoyment and benefit. Interdependence goes beyond this.
Firstly, interdependence recognises the limitations of independence. Interdependence sees that independence is not separate to dependence but is a way of responding to it. Independence is not doing away with our need for hugs but refining how we ask for and give them. The way we walk is dependent on gravity, the way we talk is how we use our language — not being without it. While independence sees the individual as distinct, interdependence sees how this distinct individual relates to the world around: how their style chooses from and modifies the options available.
Secondly, interdependence seeks goals and projects bigger than the individual. Many of the crises confronting us at the moment (ecological catastrophe and appalling social inequity) are about more than individuals. They are about how individuals relate to each other and groups. This includes rules of trade, laws and resources used in transport (petrol rather than electricity, electricity generated by coal rather than winds or waves) and how groups (parliaments, companies) make decisions.
To make a better world means collaboration — interdependence. It means finding how individuals can contribute and work together for the good of all. This can sound utopian but is I think our everyday experience.
It is common for both people to feel enriched after a good conversation. An innovator, businessperson and marketing whiz can do more together than either one separately. (Should I mention satisfying sex?) From a casual hello to moments of shared intimacy to the building of mutual projects, mutual benefit (interdependence) is the rule rather than the exception.
I think it is worth saying that competition is often dependent on and legitimised by interdependence. Firstly any competition is dependent on shared rules. Without these rules (and people sticking to them) there can be no winner. Markets exist because there are legal rules. People can work for a promotion because they know what is expected. Any competition relies on a shared sense of reality and what the rules are. And there are usually penalties for breaching them — from penalties in sport to imprisonment. In one sense competition is a form of interdependence.
That competition is not enough is acknowledged when people assert that it is by competition that we all improve and benefit. This is to say: competition is not good in itself — it is a way for all of us to gain. Whether this assertion is always true I think is doubtful. A lot depends on how the competition is conducted — and how the rewards are shared around. A sport that was only concerned with the grand final wouldn’t last long. A company where only the most productive employee was paid wouldn’t be viable. Competition is legitimate because it leads to mutual benefit — this is acknowledging the reality that we are, all of us, interdependent.
Interdependence means having a sense of our own contribution and uniqueness. It means respecting the other’s gift too. And it means that we can collaborate for mutual benefit. And the examples of it are all around us.
To develop interdependence I think means:
- Embracing our dependence. This means knowing what we need and desire. This can be as simple as knowing we’re thirsty or the lovers’ passionate desire for each other.
- Valuing our independence. Knowing that we have a particular way of being and doing and having a sense of what we can contribute.
- Moving to the place where we work together. Knowing that we depend on and contribute to each other. Appreciating our own and others independence, where our own and others strengths and limitations are valued and become part of a bigger story.
Where do you see interdependence in your life? Have there been especially precious moments of interdependence for you? Let me know in the comments.
All clinical material on this site is peer reviewed by one or more clinical psychologists or other qualified mental health professionals. This specific article was originally published by Dr Greg Mulhauser, Managing Editor on .on and was last reviewed or updated by


by Torben Gronning, Patricia Sohl and Thomas Singer
Visual Resources Vol. XXIII, No. 3, September 2007, pp. 245-267
This article describes the history of the recently digitized and online accessible Archive for Research in Archetypal Symbolism (ARAS), from its 1930s origins at the famous Eranos annual conferences of eminent scholars in Ascona, Switzerland to the present. The purpose, function and structure of the collection are explained and illustrated with an example. ARAS is compared with other art image databases, and its unique features are elucidated. The article argues that the heritage and focused purpose of ARAS has allowed it to successfully address common iconographic challenges and that the online resource (www.aras.org) adds important new dimensions to the user experience.
Keywords: Iconography; archetypal symbolism; cross-cultural symbols; Fröbe-Kapteyn, Olga (1881-1962); Jung, Carl Gustav (1875-1961).
When a filmmaker needed inspiration for her award-winning animated film, she found it in the Archive for Research in Archetypal Symbolism. When a theater director looked for ideas for sets and costumes, he consulted the archive, as did an artist developing a survey of masks throughout world history and a theologian looking for an androgynous figure of Christ. Numerous analytical psychologists and psychotherapists regularly consult the archive to explore their own and their clients' dreams by analyzing the symbolic imagery of these dreams in a process of self-discovery.
The Archive for Research in Archetypal Symbolism, often just called ARAS, has a most interesting history, rooted in the Eranos meetings of the early 1930s, when world-renowned scholars from many fields gathered for discussions that touched on the history of religion, the history of art, anthropology, psychology, sociology and archaeology. Images to illustrate the topics of these cross-disciplinary meetings formed the beginning of the ARAS archive, and the Eranos heritage became the foundation for developing the nomenclature used in ARAS's image classification.
ARAS has since developed into a rich collection of 17,000 annotated photographic images of human creative expression, purposefully selected from every culture, spanning the 30,000 years of human history since the Ice Age. With its cultural, historical, anthropological and psychological commentary, ARAS has become over time a unique tool for academics, researchers, scholars, artists, writers, historians, anthropologists, analytical psychologists, psychotherapists, students, and the general public alike.
Early History of ARAS and Eranos
The conception of ARAS dates back to the 1930s and is intrinsically linked to the Eranos Society and its creator, Olga Fröbe-Kapteyn (Figure 1). She was born in 1881 of Dutch parents in London where her father Albert Kapteyn, an avid photographer, was the director of the Westinghouse Brake and Signal Company. Her mother was a philosophical anarchist, a writer on social questions, and a friend of playwright George Bernard Shaw and anarchist Prince Kropotkin. Olga Fröbe-Kapteyn studied applied art in Zürich and helped in her father's darkroom. She became a young widow when her husband Iwan Fröbe, the Austrian musician, was killed in a plane crash in 1915 while testing an aerial camera for the Austrian army. She had twin
Figure 1 Olga Fröbe-Kapteyn in the 1930s. Photograph by Margarethe Fellerer. Courtesy of Eranos Foundation Archives, Ascona-Moscia, Switzerland.
daughters, born after the death of her husband.1
Around 1920, Olga Fröbe and her father went for a recreational stay to the Monte Verita sanatorium in the Swiss village of Ascona, located on the western bank of Lake Maggiore, a setting of great natural beauty looking south into Italy. Ascona had since the late nineteenth century developed into a gathering place for artists, writers, dancers, political radicals, utopians and gurus, including Lenin, Trotsky, Mikhail Bakunin, Prince Kropotkin, Hermann Hesse, Stefan George, Rudolf Steiner, Mary Wigman, Isadora Duncan, Hans Arp, Paul Klee, Emil Jannings, Emil Ludwig, and Erich-Maria Remarque. Albert Kapteyn bought a house overlooking the lake, Casa Gabriella (Figure 2), for his daughter and provided funding for her to live in reasonable comfort.
Olga Fröbe's great interest was spiritual research, and she built a lecture hall and a guesthouse on her grounds in 1928. After a short and unsuccessful attempt at running a school for spiritual research, she developed the idea of founding a meeting place for East and West. In 1932 she went to Marburg to visit Rudolf Otto, the prominent German theologian, scholar of mysticism and comparativist of Eastern and Western religions. Otto was very receptive to her plan for a lecture program and proposed the name "Eranos," which in Greek means a shared feast.
For the next sixty-six years this annual lecture program, begun in August 1933 and called the "Eranos Tagungen" (Eranos meetings), would assemble many of Europe's leading intellectuals in Ascona to give scholarly lectures about their latest insights in the fields of religion, philosophy, history, art and science. The imaginative and inspiring force
Figure 2 Casa Gabriella, Ascona, Switzerland in the 1950s. Photograph by Margarethe Fellerer. Courtesy of Eranos Foundation Archives, Ascona-Moscia, Switzerland. Archetypal Symbolism and Images 247.
of mind and the unfailing rigor of scholarship2 brought forward ideas often "on the edge."3 The lectures were published after each year's conference in the Eranos- Jahrbuch (Eranos Yearbook).4 Olga Fröbe-Kapteyn was the publisher of each Eranos yearbook from 1933 to 1961, the year before her death. Six volumes of selected Eranos lectures, translated into English and edited by Joseph Campbell, were published in 1954-1968 as part of the Bollingen Series.5
The subject of the first two-week Eranos conference in 1933 was "Yoga and Meditation in East and West," held in the lecture hall now named "Casa Eranos." Among the speakers were the scholars of Indian art and religion Heinrich Zimmer and G.R. Heyer, the Buddhist scholar Caroline Rhys Davids and the Sinologist Erwin Rousselle.6
Psychiatrist and founder of analytical psychology Carl Gustav Jung (Figure 3), reluctant at first, decided to participate when he saw the lecturer list and realized that "those are all my friends!"7 Jung would become a regular contributor each year to the two-week conference in late August. Jung remained a fundamental figure in the organization of the conferences due to the fertile influence of his analytical psychology-referred to as a "spiritus rector" by Eliade in 1955. Although
Figure 3 Carl Gustav Jung in the late 1940s. Photographer unknown. Courtesy of Thomas B. Kirsch, MD, Palo Alto, CA.
the symposia were not "Jungian," they focused on the core idea of "archetypes" in human life.8
Despite the difficulties of the pre-war years, the Eranos conferences took place without interruption. Planning for next year's conference would begin as soon as one year's conference was over. Olga Fröbe was the impresario and organizer, although she insisted that Eranos was without plan or program. She decided the theme, invited the speakers, organized the announcements and printing of programs, booked accommodations, planned catered lunches and dinners, made traffic arrangements with local authorities.
A conference typically included anywhere from seven to twelve half-day lectures, delivered in German, French or English, and attended by up to two hundred persons. The afternoons were open for informal discussions, sailing on the lake, excursions in the area or reading. An equal representation of first-time speakers and speakers with previous Eranos experience assured renewal and continuity through the years.
The scholars from the early years and their expertise demonstrate the cross-cultural nature of the Eranos experience: Heinrich Zimmer (Indian religious art), Károly Kerényi (Greek mythology), Mircea Eliade (history of religions), Jung and Erich Neumann (analytical psychology), Gilles Quispel (Gnostic studies), Gershom Scholem (Jewish mysticism), Henry Corbin (Islamic religion), Adolf Portmann (biology), Herbert Read (art history), Max Knoll (physics) and Joseph Campbell (comparative mythology).9
Olga Fröbe had a lively interest in finding and collecting images to illustrate the topic of each year's meeting, which in addition to the first year's "Yoga and Meditation in East and West" (1933) included such titles as "The Gestalt and Cult of the Great Mother" (1938), "The Hermetic Principle in Mythology, Gnosis, and Alchemy" (1942), "The Mysteries" (1944), "Spirit and Nature" (1946) and "Man and Time" (1951).10
In 1935 she systematically began to collect pictures that exemplified archetypal themes as a complement to Jung's writings. She later explained that "Those who feel the truth of the old Chinese conception that all that happens in the visible world is the expression of ideas or images in the invisible might do well to consider Eranos from that point of view." She traveled to the great libraries in Athens, Rome, Paris, London and elsewhere in Europe, finding and purchasing photographs of ancient frescoes and other paintings, sculpture, manuscript illumination and primitive folk art. These she classified according to archetypal themes in what became known as the "Eranos Archive," located for want of other space in her bedroom at Casa Gabriella.11
The 1938 Eranos conference on "The Great Mother" included an exhibition of large photographs from the Eranos Archive (Figure 4). Hildegard Nagel took the pictures back for an exhibition at the Analytical Psychology Club in New York, thus facilitating Eranos' debut in America.12 The exhibited pictures later became the basis of Erich Neumann's book The Great Mother: An Analysis of the Archetype (New York: Pantheon, 1955). Figures 5, 6 and 7 show expressions of the Great Mother archetype from three different cultures and time periods.
With financial assistance from benefactors Mary and Paul Mellon of Pittsburgh, both deeply involved in Eranos and later the founders of the Bollingen Foundation Archetypal Symbolism and Images 249 created to assure a wider audience for Jung's work,13 Olga Fröbe traveled to Rome in 1938 to obtain photos of an illuminated manuscript of the Divine Comedy kept in the Biblioteca Apostolica Vaticana Library.14 She wrote to Mary Mellon that she was "going to collect every archetypal representation I can find, ... [e.g.] the Crucifixion, the Baptism, the Descent into Hell, the Resurrection, the fight with the Dragon." She continued to Amsterdam, London, Paris, Bonn, Trier and Berlin, "picture-hunting everywhere."15
At the start of the Second World War, Olga Fröbe was contemplating what to do with her Eranos archive. She learned of the Warburg Institute - moved in 1934 to London from Hamburg because of the Nazi danger - and its library, which seemed a good fit for her collection. After the war, in 1946, she began to send her photographs to London, and in 1956 the Warburg Institute accepted her entire collection. She gave photographic duplicates of the archive (made at Bollingen expense) to Jung (who shortly before his death gave it to the Jung Institute in Zürich) and to the Bollingen Foundation in New York, which was, at that time, supporting numerous scholars in their quest for the meaning of symbolism and publishing the works of Jung.16
Jessie E. Fraser, Librarian of the Analytical Psychology Club in New York, was entrusted with editing and cataloging the archive. In 1959, her proposal for a cataloging scheme found support with members of the Eranos Conference, and the Bollingen Foundation decided to make the archive a special project and increase their grant.17 In 1960, the archive was renamed the Archive for Research in Archetypal Symbolism (ARAS), reflecting the many additions to the original Eranos collection.
Figure 4 Swiss journalist and publicist Fritz René Allemann viewing the Eranos Archive in 1939, featuring archetypal representations related to the process of rebirth. (The Eranos Conference 1939 was entitled "The Concept of Rebirth in the Cults and Religions of Various Times and Peoples.") Photograph by Margarethe Fellerer. Courtesy of Eranos Foundation Archives, Ascona-Moscia, Switzerland.
In the development of keywords to reflect archetypal themes, Jessie Fraser collaborated with analytical psychologist Joseph L. Henderson in San Francisco, who worked with Jung and wrote a chapter in Man and His Symbols.18
In 1969, the Bollingen Foundation gave ARAS to the C.G. Jung Foundation for Analytical Psychology in New York, who undertook a ten-year development project funded by Jane Abbott Pratt and the Frances G. Wickes Foundation. The archive grew and had, in 1977, reached 25,000 representations, of which 12,000 were mounted, numbered and in various stages of completion and 8,000 finished.19 Copies of the collection were housed at the C. G. Jung Institutes in San Francisco and Los Angeles. These three Jungian centers are the founding members of National ARAS.
The Bingham Foundation and many other donors were instrumental in supporting the continued expansion of the collection in the 1980s, and also made possible the writing and publication of two scholarly volumes, Encyclopedia of Archetypal Symbolism I-II, based on approximately 200 selected images from ARAS.20
In 2003-04, the New York collection of 17,000 images and 20,000 text
Figure 5 The Goddess Ninhursag ("Lady of Birth") c.2017-1763 BC. Terracotta, 10.2 cm high. Origin: Babylonian Period, Return of Amorites to Babylonia, Time of Isin and Larsa Dynasties. Provenance: Iraq. ARAS Record 2Bh.004. Repository: Iraq Museum, IM 9574, Baghdad, Iraq.
commentaries was scanned. About 45,000 catalog cards from the New York and San Francisco collections, which had continued its own further development since the early 1980s, were combined to produce 10,000 different keyword-based archetypal themes. Private donors funded this large project that ultimately resulted in ARAS becoming available as an online subscription-based resource (www.aras.org) in 2005.
Purpose of ARAS: Use and Amplification of Symbols and Images
Although the creation of the Archive for Research in Archetypal Symbolism was motivated by Jung's discovery and description of the "archetype," the use of ARAS goes well beyond Jungian psychology. However, ARAS owes a tremendous debt to Jung's basic idea of archetypes and the collective unconscious. Jung was the particular proponent of a broadly archetypal point of view that insists upon common human or transpersonal and symbolic connections transcending cultural and theological boundaries.21
One might argue that from an iconographic classification point of view Jung's concepts have created the essential foundation for the nomenclature
Figure 6 Minoan Deity or Worshipper. Terracotta. Origin: Pre-Hellenic Era, Crete, Post Palace Period, Late Minoan IIIa, b, c (Achaeans in Crete). ARAS Record 3Ce.002. Courtesy of Archeological Museum Herakleion, Crete, Greece.
developed to categorize the ARAS image content. The term "archetype" means "original pattern from which copies are made," and it appeared in European texts as early as 1545. It derives from the Latin noun archetypum and from the Greek noun arkhetypon, meaning "pattern, model," and the adjective arkhetypos, meaning "firstmolded," from arkhe- ("first") + typos ("model, type, blow, mark of a blow").22
Jung explains how the collective unconscious-humankind's shared psychic foundation patterning all expressive endeavors-rests on "archetypes" or "primordial images" (CW 8: 229).23 Jung was not the first to discover and formulate this idea of the archetype. Anthony Stevens explains how Jung acknowledged his debt to Plato, describing archetypes as "active living dispositions, ideas in the Platonic sense, that perform and continually influence our thoughts and feelings and actions" (CW 8: 154).24
For Plato, "ideas" were mental forms superordinate to the objective world of phenomena. They were collective in the sense that they embody the general characteristics of groups of individuals rather than the specific peculiarities of one. Thus, a particular dog has qualities in common with all dogs (which enable us to classify it as a dog) as well as peculiarities of its own (which would enable its master
Figure 7 The Goddess Tlazolteotl. Aplite speckled with garnets, 20.2612 cm. Provenance: Mexico. Origin: Mexico, Aztec. ARAS Record 8Bd.017. # Dumbarton Oaks, Pre- Columbian Collection, Washington, DC.
to recognize it). So it is with the archetypes: they are common to all humankind, yet each person experiences them in a unique and personal way.
The German astronomer Johannes Kepler (1571-1630) believed that his delight in scientific discovery was due to the mental exercise of matching ideas or images already implanted in his mind by God with external events perceived through his senses. Kepler's "inner ideas" that lie "under the veil of potentiality" and are "derived from a natural instinct and are inborn" are clearly akin to Jung's "primordial images."25 It is speculated that Jung may have been influenced in his thinking about archetypes by the German ethnologist Adolf Bastian (1826-1905), who studied the myths, folklore and customs of humankind all over the world. Bastian was impressed by the similarity, which existed between many of the themes and motifs he encountered wherever he went. He noticed, however, that these universal themes - which he called Elementargedanken (elementary ideas) - invariably manifested themselves in local forms peculiar to the group of people he happened to be studying: these he called Volksgedanken (ethnic ideas).26
Archetypes transcend culture, race and time. Thus, in Jung's view, the mental events experienced by every individual are determined not merely by personal history, but by the collective history of the species as a whole (biologically encoded in the collective unconscious), reaching back into the primordial mists of evolutionary time.27 Jung made it a point to distinguish between the archetype-as-such and the archetypal images, motifs and ideas, which the archetype gives rise. One cannot "see" the archetypes themselves-only their indirect manifestation in or as images, motifs and ideas associated with or stemming from the archetypes. In his writings, Jung explained archetypes in the following ways:
The term "archetype" is often misunderstood as meaning a certain definite mythological image or motif ... on the contrary, [it is] an inherited tendency [i.e., ability, potential] of the human mind to form representations of mythological motifs-representations that vary a great deal without losing their basic pattern. ... This inherited tendency is instinctive, like the specific impulse of nest-building, migration, etc. in birds. One finds these representations collectives practically everywhere, characterized by the same or similar motifs. They cannot be assigned to any particular time or region or race. They are without known origin, and they can reproduce themselves even where transmission through migration must be ruled out. (CW 18: 523; emphasis in original)
...besides [the intellect] there is a thinking in primordial images, in symbols which are older than the historical man, which are inborn in him from the earliest times, and, eternally living, outlasting all generations, still make up the groundwork of the human psyche. (CW 8: 794)
As the products of imagination are always in essence visual, their forms must, from the outset, have the character of images and moreover of typical images, which is why ... I call them "archetypes." (CW 11: 845)
...[Tribal] lore is concerned with archetypes that have been modified in a special way. Another well-known expression of the archetypes is myth and fairytale. (CW 9(1): 5,6)
It is the manifold expressions of these archetypal images and symbols that make up the ARAS collection. The collection probes the universality of archetypal themes and provides a testament to the deep and abiding connections that unite the disparate factions of the human family.
Harry Prochaska, who served as San Francisco ARAS's curator 1978-1992, defined "symbol amplification" as the elaboration of the historical and cultural matrices of a symbol in its variant forms so that one develops a larger sense of its polyvalences. This process is different from subjective association. Association stems from one's personal biography projected on to the symbol. In the associative process, symbolic meaning may be legitimately and absolutely personal, carrying a value, which no one else shares nor needs to share. Amplification, however, leads to significant clues which lie in the cultural unconscious, for each of us is born into a culture as well as into a family. Amplification and association are parallel pathways to symbolic meaning.28
Prochaska quotes Mircea Eliade who states that "The essential problem is to know what is revealed to us not by any particular version of a symbol, but by the whole of the symbolism."29
Circumambulation-"a walk around the image"-is a term used to describe the interpretation of an image by reflecting on it from different points of view. Circumambulation differs from free association in that it is circular, not linear. Where free association leads away from the original image, circumambulation stays close to it. Jung uses the term "circumambulation" in his commentary on The Secret of the Golden Flower,30 where he defines it as a "psychological circulation" or "movement in a circle around oneself" so that all sides of the personality become involved (CW 13: 38). In the mandala, Jung saw a uniting symbol or an archetype of wholeness.
German physicist and Nobel laureate Wolfgang Pauli (1900-1958) offered a related description of the creative method of scientific discovery, when he talked about "continuously taking up an issue, thinking about the object, then putting it back down again, then gathering new empirical material, and continuing this, if necessary, for years. In this way, the subconscious is stimulated by the conscious, and only in this way, if at all, can something come of it."31
The ARAS archive is especially useful to analytical psychologists and psychotherapists or anybody interested in amplifying images that emerge in dreams. The process begins when one is struck by a particular image, wondering why that particular image appeared and what it means. We do know that each image is carefully chosen by the psyche as a means of communicating specific information about the dreamer's state of development and attitude. One could say that the image is a key with the potential to unlock a particular door leading to greater knowledge or consciousness about the dreamer. ARAS gives the analyst or the dreamer a means of discerning which door the key fits. What is revealed through the study of the many visual examples of the images and their cultural, historical and psychological amplifications helps to enlarge our understanding of the symbolic image. And it is our relationship to the symbol that effects the deep change or transformation of our being.32
The use of the archive often begins with the decision to explore a particular image, whether the image originates from a dream, an idea to use in an artistic creation, a cultural study, a research paper or project, or simply to explore the richness of the archive. The search results in multiple examples that demonstrate how the same image is expressed in different times, cultures and mediums. It is this commonality that helps to distill the meaning of the image. The search may lead one off on various tangents, circling around the meaning, fleshing it out until one finally comes to an understanding of what it means. An excitement and enthusiasm often accompanies the search, carrying one along on a fascinating and enlightening journey through the world of symbolic images.33
The ARAS homepage (www.aras.org) illustrates this variety with two examples. One example shows the results of a search for the archetypal theme "lion";34 the other is an animated collage of images associated with the archetypal theme "snake on tree."35 Both examples let the user enjoy the full richness of the images on their own and discover how many cultures and eras have expressed a common idea, each in their own ways.
Ami Ronnberg, who in 1979 continued Jessie Fraser's work on the classification of the archive's images and became curator in 1984, describes how the interconnectedness of symbols often guides the imagination in the process of circumambulation: "Begin with a thread, follow a lead, look up similar ideas, and move intuitively around a symbol or a dream."36


How music became an industry: on 'Selling Sounds'
Among the fascinating examples of early music-industry advertising reproduced in "Selling Sounds," the most striking is a 1913 image that pairs a photograph of legendary tenor Enrico Caruso, costumed for "Aida," with one of his Victor Red Seal recordings. “Both are Caruso," the text reads, adding that the owner of the disc hears the singer in his own home "just as truly as if you were listening to him in the Metropolitan Opera House." For author David Suisman, this identification of a living, breathing person with an inert hunk of shellac that encodes his voice isn’t merely a clever promotional ploy, but an emblem of a century-old transformation in the ways that we understand, experience and consume music.
Subtitled "The Commercial Revolution in American Music," Suisman's book (Harvard University Press) focuses on the 1880s through the mid-1920, a period that saw the growth of sheet-music publishing from a printer's sideline to a wildly profitable New York-based industry, the rise of the player piano, and its displacement in American homes by the even more easily operated gramophone. These innovations made professionally composed and performed music available to a wider range of Americans than ever before. At the same time, music increasingly became something to be passively appreciated rather than actively made. (This story could have been different, if Edison's wax cylinders, which allowed convenient home recording as well as playback, had won out over Emile Berliner’s disc technology.) Suisman also emphasizes the extent to which regional and vernacular sounds were crowded out by the centralized distribution of mass-produced scores (and later records), though he notes that the new technologies would later preserve the folk traditions of players and singers who didn’t or couldn't notate their songs.
Even the category of "popular song" was a child of commerce. Though individual songs had become "hits" since the days of American minstrels and the English music halls, it wasn’t until the 1910s that the writers and publishers of Tin Pan Alley organized their production and promotion into a consistently profitable enterprise. As the lengthy narratives of older balladry gave way to short, catchy choruses meant to be remembered in seconds and forgotten in weeks, these commodities formed the cornerstone of what could be called, for the first time, an American music "industry." The melodies were often sentimental, but their authors were not. Suisman cites Irving Berlin’s dicta that "the songwriter must look upon his work as a business," as well as vaudevillian Bert Williams's assertion that popular melodies "were mostly made up of standard parts, like a motor car."
With new things to sell came new ways of selling, from the public "song-plugging" of the sheet-music era to the Victor Co.’s canny use of "Nipper," the dog that cocked an ear to “His Master’s Voice,” in one of the 20th century’s most recognizable corporate trademarks.
Phonograph manufacturers were also in the advance guard of consumer credit, specialized store window displays, and celebrity endorsement. Even more significantly, music publishers and songwriters led efforts to expand the law’s conception of intellectual property. A 1924 photograph depicts Berlin, John Phillip Sousa and operetta composer Victor Herbert preparing to lobby Congress for royalties on radio broadcasts of their music; to this day, their spiritual (and sometimes actual) descendants rally the troops when valuable copyrights are threatened by the Constitution's pesky "limited term" clause.
Though the story Suisman tells is a broadly familiar one, he has assembled valuable reminders of something many would rather ignore; namely, the extent to which the music we hear, and how we hear it, has less to do with our personal preferences than with what a large, well-organized sector of business makes available to us. Most listeners – and, I’d wager, artists – would surely prefer to see their musical experiences as a respite from capitalism, not a function of it. Still, it would be hard to deny that phenomena from the selling of youth culture back to itself in the form of rock and roll to the rise of ringtones as a tiny, publicly audible lifestyle indicator (and a fresh income stream) are rooted in structures and processes whose origins Suisman describes.
That said, Suisman sometimes overreaches in laying bare the nefarious consequences of his “revolution,” as when he claims that the “disembodiment” of music from its making was the “very purpose” of piano rolls and phonograph records. If so, why tie them so closely to the image of the performer, as in Victor’s Caruso ad? Suisman at times allows that popular song “brought real pleasure into people’s lives, and [that] through the music people formed meaningful social bonds.” These concessions read begrudgingly, as way-stations to his insistence that “the music industry was not connected or responsible [to its audience] except through the market.” Such bona fides, which owe an acknowledged debt to Marx’s concept of commodity fetishism and Theodor Adorno’s dismal view of “the culture industry,” are reproduced frequently -- even mechanically -- throughout the book.
I happened to read "Selling Sounds" not long after the death of two figures (among many others) whose careers complicate Suisman’s pessimistic outlook. Guitarist Les Paul, who died Aug. 13, invented the process of recording “sound on sound,” first on disc and then on multi-track tape. With this and other inventions, Paul did as much as anyone to make recorded music into an artistic medium in its own right. Thirteen days after Paul’s passing came that of Ellie Greenwich, who penned (with Jeff Barry) such girl-group gems as “Be My Baby” and “Leader of the Pack” as a staffer for companies housed in the Brill Building, the last stronghold of New York’s songwriting industry. Though these artists, like any artist at any time, would have produced something different, or nothing at all, under other conditions, they did their best work from within the belly of the technological-cum-corporate beast. More than that, their music has proved far more durable than the ephemeral assembly-line products suggested by "Selling Sounds." The existence of such work is another strain within the tangled history of American popular music, though not one that Suisman’s instrument is well-equipped to play.
-- Franklin Bruno
Photos taken by Takomabibelot via Flickr
Franklin Bruno is the author of "Armed Forces" (Continuum Books); his most recent recording is Local Currency (Fayettenam Records). He lives and writes in Jackson Heights, Queens, and sometimes blogs at http://nervousuntothirst.blogspot.com.


How to Start Recycling Plastic Waste at the Workplace
The Ministry of the Environment in Finland realised the problem with plastic waste and was among the first WWF Green Offices to begin recycling plastic. What does it require from the office to start collecting plastic waste?
“When we realised that plastic waste was not yet collected at our office, we just had to act. Continuous news of the harmful impacts of plastic made it a topical issue,” says Aino Pietarinen, Senior Officer at the Ministry of the Environment .
Previously, plastic waste generated at the Ministry of the Environment office, such as empty yoghurt containers, food packaging and plastic bags, ended up incinerated with mixed waste. Now, it continuous its life in the form of recycled plastic. The content of the office collection containers is transported to Fortum’s plastic plan in Riihimäki, where the different types of plastic are sorted, washed and processed into recycled plastic.
“Plastic is no good if incinerated. Without a doubt, it had to be recycled,” Pietarinen says.
The biggest benefit of recycling plastic is that it allows decreasing the production of virgin plastic, which consumes oil and lots of energy. The carbon footprint of recycled plastic is up to 85% lower than that of virgin plastic.
The Most Ecological Ministry
The Ministry of the Environment has been a member of the WWF Green Office network since 2011. The Ministry has a designated team to implement the Green Office actions in its day-to-day operations.
“Green Office has been very important to the Ministry of the Environment, as it has provided us with encouragement, support and advice. It has laid down the foundation for being an ecological ministry and has concretely promoted our environmental activities,” says Pietarinen, who is both the Green Office contact person and the chair of the ecology team.
Revising the waste collection system and sorting instructions and improving internal communications have been goals of the office’s environmental programme since the beginning of this year.
Steps to Plastic Collection at the Office
The Helsinki Region Environmental Services Authority HSY, for example, has made plastic sorting possible in residential buildings in the Helsinki region since 2016. However, starting the collection at workplaces still requires a degree of initiative.
“To my mind, here the most challenging thing about the entire process was having to ask several parties if we can simply start to collect it. Finally, when the ecology team, that is our Green Office team, took to it, nobody had anything against it.”
“First, I checked that the provider of waste management collects plastic. We ordered the collection containers from the company responsible for cleaning and I agreed on the pick-up times. I made sure that all floors of the office had sufficient numbers of containers, as plastic packaging waste is the biggest fraction of all waste. Now, the containers are easy to reach and marked well. In addition, the cleaners were informed of the new waste collection type,” Pietarinen explains.
Before the collection of plastic waste at the office really got started, the recycling instructions had to be updated.
“It is important to communicate about the changes in a comprehensible way to the personnel. The revised recycling instructions are displayed on office walls and more extensively in a recycling booklet. They were visualised and laid out in co-operation with the communications department.”
Ask the Waste Management Provider About Plastic Waste Collection
In Finland, lots of work remain in correct recycling. According to the Finnish public service broadcasting company, Yle, the huge mountain of slag caused by the incineration of waste at the Ämmässuo landfill could be up to one-half smaller had all recyclable waste, paper, board, glass, metal and plastic, found their way to the right bin.
“In addition to getting people to understand the importance of sorting, another challenge is that not all waste management providers yet offer plastic waste collection to businesses and organisations,” says Mikko Kuiri, Partnership Manager at WWF Green Office.
In fact, Kuiri encourages Green Offices to increase the demand for it.
“Start by asking the provider of waste management at your workplace whether plastic waste could be collected. If it is not possible, I recommend that you remind the waste management company that their competitors already offer this option. This way, businesses and organisations could be drivers of change.”
Text: Emmi Karhiaho


Donald Campbell Dewar (21 August 1937 – 11 October 2000) was the first First Minister of Scotland from 1999 until his death in 2000. He was the first person to hold the position of First Minister following the establishment of the Scottish Parliament in 1999.
Early life[change | change source]
Dewar was born and raised in Glasgow.
In government[change | change source]
After the 1997 General Election, Dewar was in a position which John Smith (leader of the Labour Party, 1992-1994 and a good friend of Dewar) would never have thought possible. He was able to start the process to split Scotland from the United Kingdom, and worked endlessly on creating the Scotland Act, popularly known as Smith's "unfinished business". When ratified, this was to give Scotland its first Parliament for nearly 300 years.
First Minister of Scotland[change | change source]
The first elections to the Scottish Parliament were held on 6 May 1999, with Dewar leading the Scottish Labour Party against their main opponents, the SNP under Alex Salmond. He was elected as the MSP for Glasgow Anniesland. Although Scottish Labour won the most seats, they did not have a majority in Parliament to allow them to form an Executive without the help of a smaller party. A deal was agreed with the Scottish Liberal Democrats to work together, with Dewar agreeing to their demand for the abolition of up-front tuition fees for university students.
On 13 May, Dewar was nominated as First Minister, and was officially appointed by the Queen on 17 May at a ceremony in the Palace of Holyroodhouse. He later travelled to the Court of Session to be sworn in by the Lord President and receive the Great Seal of Scotland.
On 16 June, Dewar set out the legislative programme for the Executive which included: an Education bill to improve standards in Scottish schools; land reform to give right of access to the countryside, a bill to abolish the feudal system of land tenure; and a bill to establish National Parks in Scotland.
Death and funeral[change | change source]
In April 2000, Dewar was admitted to hospital for tests on his heart, following a previous test where a minor irregularity was discovered. In May 2000, he later had surgery to repair a leaking heart valve, and was forced to take a three month break from Parliament, with Deputy First Minister, Jim Wallace taking over as Acting First Minister. He returned to work on 14 August 2000.
Dewar dealt with the exams results fiasco and the lorry drivers strike, and attended the Labour party conference in Brighton in September, but at the end of September told the historian Tom Devine in Dublin that if there was no surge of the energy of old, he would have to reappraise the situation within a few months time.
On 10 October 2000 around lunchtime, Dewar sustained a fall. He seemed fine at first but later that day suffered a massive brain hemorrhage which was possibly triggered by the medication he was taking after the heart surgery. Donald Dewar died the following day, at 12.18pm, in Edinburgh's Western General Hospital. He was 63 years old.
Dewar's funeral service was held at Glasgow Cathedral, amid scenes of mourning unknown for a politician in Scotland's largest city. He was cremated on 18 October 2000, and his ashes were scattered at Lochgilphead.
Although he has become something of a political legend, Donald would have abhorred any attempt to turn him into some kind of secular saint. He would have been horrified at a Diana-style out-pouring of synthetic grief at his untimely death. -- Iain MacWhirter, Sunday Herald, October 15, 2000.
References[change | change source]
- "PR deal will end councils stranglehold", The Guardian
- "UK Politics- Dewar appointed as first minister", BBC News, May 17, 1999
- Dewar's statement to Parliament, BBC News
- "Dewar undergoes heart tests", BBC News, 25 April 2000
- "Dewar takes post-op steps", BBC News, 11 May 2000
- "First Minister returns to the fray", BBC News, 14 August 2000
- "Donald Dewar", Electronic Scotland, October 2000


Image Source: Melissa Farlow, National Geographic
Well, okay, Groundhog Day is tomorrow. But, as I won't be blogging tomorrow, I wanted to get a word in edgewise on this most noblest of astronomical holidays.
For those of you who may live in a country not blessed with such a glorious holiday, let me explain the day. On February 2, the legendary groundhog, a furry woodland animal that looks exceptionally cute but is not always the most friendly of the beasts, awakens from its winter hibernation and sticks its head out of the ground. If the groundhog sees its shadow, it is spooked (not being among the most clever creatures) and runs back in its hole to sleep for another six weeks. If it doesn't see its shadow, it happily scampers about, and we get an early spring.
Of course, this legend has little to do with reality. The fact is that, whether or not the groundhog sees its shadow, there are another six weeks of winter. Look at your calendar, count 6 1/2 weeks into the future, and you'll see the first day of spring. Now count backward 6 1/2 weeks, and you'll see the first day of winter. Groundhog Day is halfway between the winter solstice and the spring equinox. And that is not coincidence!
These days halfway between an equinox and a solstice are called the cross-quarter days. They used to play a large role in pagan cultures (and still do among neo-pagan religions). We even have "holidays" on or near three of the four cross-quarter days: Groundhog Day, May Day, and Halloween.
What does a cross-quarter day mean for us? Not too much -- most of the northern hemisphere is in the middle of a cold winter, hoping that spring will come soon, and the southern hemisphere is enjoying summer vacation, and hoping that summer lasts a little longer. Around now you will probably start to notice the days getting noticeably longer pretty quickly. Around the winter solstice, the length of the day stays pretty constant for a while, but as the Earth continues to speed around our sun, the sun will appear to rise higher in the sky (for those of us living in the north), the days will get longer, and, eventually, the temperatures will get a bit warmer.
I make a big deal out of days like this, I realize. It's because the seasons are one of the most obvious links we have to the larger Universe around us, and one that most Americans don't understand. And it's a hard picture to grasp -- we are on a tiny ball of a planet that spins once a day and goes in circles around our parent sun once a year, which itself is orbiting the Milky Way galaxy every 250 million years, and our galaxy which is moving around our neighbor galaxies and slowly falling toward a cluster of galaxies 60 million light-years away. We're in constant motion, most of it extraordinarily slow by galactic standards. But we can sense some of it -- our planet's spinning, and its motion around the sun -- and these motions intimately affect our lives. Once we can grasp that, we've started to open our minds to a much larger universe around us.


Back to search results
|Print this page|
Constitution of the Nisga'a Nation
|Date: ||1 January 2000|
|Subject Matter:||Self Government|
|Summary Information: |
|The Constitution of the Nisga'a Nation was ratified November 6, 1998 and took effect May 11, 2000. The Constitution outlines the founding provisions of Nisga'a, new governance structures, land and resources ownership and individual rights. The Constitution is the enactment of many provisions of the Nisga'a Final Agreement.|
|Detailed Information: |
|The Constitution of the Nisga'a Nation includes a declaration of the Nisga'a Nation which expresses the history and culture of Nisga'a People. Chapter 1, Founding Provisions, also lists key values of the Nisga'a and connections to land. Chapter 2 outlines citizen's rights, ranging from rights of access to election rights. Land and resources are dealt with in Chapter 3, which affirms the role of the Nisga'a Treaty as the basis of land claims.|
Nisga'a Governance is outlined in Chapters 4, 5 and 6. Chapter 4 states the governing principles and the goals of the Nisga'a Nation, as well as the composition of Nisga'a government. The details of the Nisga'a Lisims Government, legislative and executive, are found in Chapter 5. Chapter 6 describes the composition of Nisga'a Village Governments.
The composition and power of the Nisga'a Finance Committee, as well as budget requirements are detailed in the Financial Administration chapter. The Constitution also includes principles for Public and Financial Administration. The remaining chapters of the Constitution relate to other institutions, dispute resolution, and general provisions regarding constitutional amendment.
Was this useful? Click here to fill in the ATNS survey


Probably the most obvious way humans are altering the planet is by building cities, which are essentially vast stretches of man-made materials—steel, glass, concrete, and brick. But it turns out most cities are not good candidates for long-term preservation, for the simple reason that they're built on land, and on land the forces of erosion tend to win out over those of sedimentation. From a geologic perspective, the most plainly visible human effects on the landscape today "may in some ways be the most transient," Zalasiewicz has observed.
Humans have also transformed the world through farming; something like 38 percent of the planet's ice-free land is now devoted to agriculture. Here again, some of the effects that seem most significant today will leave behind only subtle traces at best.
Fertilizer factories, for example, now fix more nitrogen from the air, converting it to a biologically usable form, than all the plants and microbes on land; the runoff from fertilized fields is triggering life-throttling blooms of algae at river mouths all over the world. But this global perturbation of the nitrogen cycle will be hard to detect, because synthesized nitrogen is just like its natural equivalent. Future geologists are more likely to grasp the scale of 21st-century industrial agriculture from the pollen record—from the monochrome stretches of corn, wheat, and soy pollen that will have replaced the varied record left behind by rain forests or prairies.
The leveling of the world's forests will send at least two coded signals to future stratigraphers, though deciphering the first may be tricky. Massive amounts of soil eroding off denuded land are increasing sedimentation in some parts of the world—but at the same time the dams we've built on most of the world's major rivers are holding back sediment that would otherwise be washed to sea. The second signal of deforestation should come through clearer. Loss of forest habitat is a major cause of extinctions, which are now happening at a rate hundreds or even thousands of times higher than during most of the past half billion years. If current trends continue, the rate may soon be tens of thousands of times higher.
Probably the most significant change, from a geologic perspective, is one that's invisible to us—the change in the composition of the atmosphere. Carbon dioxide emissions are colorless, odorless, and in an immediate sense, harmless. But their warming effects could easily push global temperatures to levels that have not been seen for millions of years. Some plants and animals are already shifting their ranges toward the Poles, and those shifts will leave traces in the fossil record. Some species will not survive the warming at all. Meanwhile rising temperatures could eventually raise sea levels 20 feet or more.
Long after our cars, cities, and factories have turned to dust, the consequences of burning billions of tons' worth of coal and oil are likely to be clearly discernible. As carbon dioxide warms the planet, it also seeps into the oceans and acidifies them. Sometime this century they may become acidified to the point that corals can no longer construct reefs, which would register in the geologic record as a "reef gap." Reef gaps have marked each of the past five major mass extinctions. The most recent one, which is believed to have been caused by the impact of an asteroid, took place 65 million years ago, at the end of the Cretaceous period; it eliminated not just the dinosaurs, but also the plesiosaurs, pterosaurs, and ammonites. The scale of what's happening now to the oceans is, by many accounts, unmatched since then. To future geologists, Zalasiewicz says, our impact may look as sudden and profound as that of an asteroid.
If we have indeed entered a new epoch, then when exactly did it begin? When did human impacts rise to the level of geologic significance?
William Ruddiman, a paleoclimatologist at the University of Virginia, has proposed that the invention of agriculture some 8,000 years ago, and the deforestation that resulted, led to an increase in atmospheric CO2 just large enough to stave off what otherwise would have been the start of a new ice age; in his view, humans have been the dominant force on the planet practically since the start of the Holocene. Crutzen has suggested that the Anthropocene began in the late 18th century, when, ice cores show, carbon dioxide levels began what has since proved to be an uninterrupted rise. Other scientists put the beginning of the new epoch in the middle of the 20th century, when the rates of both population growth and consumption accelerated rapidly.
Zalasiewicz now heads a working group of the International Commission on Stratigraphy (ICS) that is tasked with officially determining whether the Anthropocene deserves to be incorporated into the geologic timescale. A final decision will require votes by both the ICS and its parent organization, the International Union of Geological Sciences. The process is likely to take years. As it drags on, the decision may well become easier. Some scientists argue that we've not yet reached the start of the Anthropocene—not because we haven't had a dramatic impact on the planet, but because the next several decades are likely to prove even more stratigraphically significant than the past few centuries. "Do we decide the Anthropocene's here, or do we wait 20 years and things will be even worse?" says Mark Williams, a geologist and colleague of Zalasiewicz's at the University of Leicester in England.
Crutzen, who started the debate, thinks its real value won't lie in revisions to geology textbooks. His purpose is broader: He wants to focus our attention on the consequences of our collective action—and on how we might still avert the worst. "What I hope," he says, "is that the term 'Anthropocene' will be a warning to the world."


My dear students, I want to apologize for my long absence. I guess that I had had the flu. For one month I did not feel well, and I frequented the hospital.
The last week, when I felt worse, I decided to meet one of my students who is a medical doctor now. She examined me thoroughly, and she gave me a strange piece of advice. She said that I had to have a walk every day; I had to make pauses every half an hour when I use my laptop. I could not believe. However, I tried.
What I would like to advise you is to have a walk at least once a day, for 20 minutes minimum. Just give it a try. You can have a walk after or before your English homework. I hope that my easy homework won’t take more than half an hour, and you could see something else, but not your computers.
Finally, let’s start with your exercises!
Change to Present Perfect (some of my phrases are not used in correct grammar; I have written them as an example):
- We are three years passed by. – We have been students for three years now.
- I did a lot of things.
- Did they find the umbrella?
- She had walked there before us.
- You had tried everything.
Change to Present Perfect Continuous:
- I was studying for two hours. – I have been studying for two hours.
- We were talking without any break during the whole day!
- You are waving hand to the crowd of strangers.
- She is looking through the window.
- They were creating new projects.
Change the sentences to Past Perfect:
- She has done her exercises. – She had done her exercises.
- We have trained a lot!
- They have done many exercises.
- I haven’t come to their place.
- Have you thought about that case?
Change the sentences to Past Perfect Continuous:
- They have been dancing. – They had been dancing.
- I have been swimming in the pool.
- You have been talking to me.
- She has been changing her dresses.
- We have been walking in the garden.
Find out the grammar for this lesson here.
You will find more exercises and more practice here.


Homograph attacks are a way to deceive someone into thinking they're communicating with a legitimate user by using characters that look visually similar to others that aren't in the same character set.
This means someone could use the Cyrillic letter "e" in place of the Latin character "e". For example the usernames below look the same, but are using different characters:
Some spellcheck tools and text editors make these differences more apparent by highlighting the letters or word, but when on a website or display without that functionality it will appear to be the exact same.
Wickr is hoping to prevent this type of spoofing by warning a user that the username contains mixed character sets. eg. Cyrillic vs Latin. You'll see a warning like below when communicating with a user that has mixed characters in their username.
<username> has been flagged for potential spoofing by using mixed encoded
characters in their username. We recommend you verify this user before engaging
in sensitive communications, or block them. Learn more about Homograph Attacks.
We hope this can help identify that someone may be trying to impersonate someone else by using these visually similar characters. Always be sure you're communicating with someone you trust. We'd recommend using the verification feature to prevent this sort of attack, as well as knowing that on Wickr, you cannot message yourself.
Please reach out to firstname.lastname@example.org if you have any questions or feel we can help!


A sheet of material formed into a curved surface, like a dome or an eggshell, can support a surprisingly large load. Researchers have known for decades how to calculate the way spherical shells respond to external forces. Now, two separate teams writing in Physical Review Letters have used experimental and theoretical methods to better understand how the geometry of nonspherical shells relates to their stiffness. In addition to guiding structural designs, the results can help researchers interpret mechanical measurements on objects ranging from viruses to blimps.
Shells appear in natural forms ranging from the protective protein enclosures around viruses to birds’ eggs and in manufactured forms ranging from table tennis balls to architectural domes. Their combination of light weight and high load-bearing capacity results directly from their geometry, but scientists have not found it easy to work out a full mathematical description of this apparently simple connection.
Pushing a pencil point gently against an egg triggers a complex mechanical reaction. The material of the eggshell bends rather easily, so a tiny depression forms at the point of contact. However, flattening out the convex surface pushes the nearby shell outward, squeezing the shell material in directions radiating away from the point of contact. The eggshell resists this lateral compression much more strongly than it resists bending. As a result, it’s harder to deform the more highly curved surface at the tip of an egg than the more gently curved surface of the side of the egg.
For strictly spherical shells, the relationship between bending, compression, and geometry was described mathematically more than sixty years ago. But for more complicated shapes, engineers have come to rely on computer simulations.
Pedro Reis and his team at the Massachusetts Institute of Technology (MIT) in Cambridge set out instead to find basic rules for these deformations experimentally, using new three-dimensional printing techniques to create molds for making precisely shaped “eggshells.” “Being able to 3D-print molds and using fast-curing elastomers allowed us to move much faster in the experiment,” says Reis. The researchers made a series of ellipsoidal shells from different materials and with different shapes, injected them with pressurized fluid, and measured the deformation as they poked them with a narrow tip. Initially, the team intended to explore large deformations and breakage, expecting that for small deformations, “everything must be known,” Reis says. “Little by little, we realized that was not quite the case.”
The simplest case, beyond the sphere, is the “polar” region of a symmetric ellipsoid of revolution, which, like the tip of an egg, has the same curvature in all directions. In this case, the measurements confirmed that the indentation of an ellipsoid is the same as for a sphere with matching curvature. Pressing on the side of the egg is subtly different, however, because the curvature is no longer the same in all directions. The researchers found that the deformation in this case was equivalent to that of a sphere with curvature equal to the average of the curvatures along the “waist” and the long axis of the egg. This way of characterizing the curvature allowed the team to model the stiffness of the ellipsoidal shell by using the known relationship between applied force and depth of indentation for a spherical shell. Moreover, says Reis, their analysis applies to any nonspherical convex shell, since the average curvature at any location can be defined in a similar way.
A second international collaboration has also been studying this problem, supplementing theoretical analysis with numerical simulations. Their original motivation, says Arezki Boudaoud of the University of Lyon in France, was to see if they could determine the internal pressure of plant cells by observing how they indented when prodded. They had previously calculated how internal pressure modifies the indentation response of a spherical shell. “I thought that this would have been worked out somewhere in the literature,” says Boudaoud. “It wasn’t the case.”
Learning of the work by the MIT team, Boudaoud and his colleagues developed a more sophisticated mathematical analysis that applies to nonspherical, pressurized shells. Overall, says Boudaoud, their conclusions agree well with the simpler arguments of the MIT team. But he says “it’s still an open issue” how best to quantify the curvature when it is not the same in all directions. In some cases, instead of the simple average used by the MIT team, the simulations and theoretical analysis by Boudaoud and his colleagues favor using an average based on the product, not the sum, of the curvatures in the principal directions. Experiments of the type conducted by the MIT team cannot easily distinguish between the two possibilities because it’s hard to make long, thin ellipsoids where the two averages would differ significantly.
“This is an exciting time for the mechanics community, because there’s a bunch of new experimental tools … to make structures in all shapes and sizes and materials,” says Douglas Holmes of Virginia Tech in Blacksburg. The new work suggests ways in which it may be possible to exploit geometry to modify structural properties. “Instead of trying to come up with better, stronger, and tougher materials to use, maybe if we redesigned the shape of the material, that would have the same effect.”
Don Monroe is a freelance science writer in Murray Hill, New Jersey.


(WINdows Future Storage) The code name for a unified storage subsystem that was expected in Windows Vista but never completed. Using a relational database and XML meta-data, WinFS was designed to go beyond the hierarchical view that Explorer presents to the user. It would have let users index and combine heterogeneous data formats such as files, folders, email and contacts. Data would be searched like a search engine, which yields results in different formats (HTML pages, documents, etc.).FS Is Not a File System
Because "FS" is in the name, WinFS was often mistaken for a new file system. WinFS was designed to sit on top of the NTFS file system, and software developers would write to the WinFS programming interface (API). See NTFS.


By the time World War II began on September 1, 1939, Germany had purged itself of its Jewish professors, scientists, and scholars. Some of these academics, deprived of their livelihoods by the Nazis, found refuge in the United States. But in this new world, they faced an uncertain future.
A few dozen refugee scholars unexpectedly found positions in historically black colleges in the American South. There, as recent escapees from persecution in Nazi Germany, they came face to face with the absurdities of a rigidly segregated Jim Crow society. In their new positions, they met, taught, and interacted with students who had grown up in, and struggled with, this racist environment.
The exhibit draws the obvious parallels between the German anti-Jewish laws and the social, legal and political segregation and disenfranchisement of African-Americans in the United States. The exhibit highlights some of the refugee-scholars' early acts of civil disobedience (before it was even called "civil disobedience") in solidarity with their students.


Do You Know How Much You’re Really Borrowing?
Borrowing money is never an ideal solution to cashflow problems. But in today’s world, many of us have no choice. Whether we take out loans, have credit card debt, or get payday loans, money borrowing is a way of life in many households. Before borrowing money, however, it’s essential that you understand exactly how much you’re borrowing. And things might not be as simple as you think.
Borrowing Isn’t Simple
If you borrow £20 from you friend, you pay him back £20 the next time you see him. Easy. But borrowing from a company (a bank, credit card company, or loan provider) isn’t as simple as that. Obviously, these companies need to make money, so you’re going to end up paying back more than you borrow.
You probably know about interest, and can make a fair guess that if you borrow £1000 from your credit card company you’re going to be paying back more than £1000. But how much you pay back isn’t just a question of interest. There are actually five different things that affect your payback amount.
What Affects How Much You Pay Back
Let’s say you need a loan of £2000 to pay for a big family holiday. You’ll probably fund this by paying for your vacation on your credit card. Or maybe you need to do some work on your house, so you borrow £5000 from you bank. Either way, you’re going to be paying back more than you borrowed. How much you pay back is determined by five things:
- The loan amount: e. the total amount that you borrowed
- The fees: these are extra charges that the company adds to the cost of your loan to cover things like administrative expenses
- The repayment schedule: whether repayments are monthly or if there are lump sum payments
- The loan length: how long you need the money for and when you can pay back the amount by
- The interest rate: the percentage of the loan that the company adds to the total fees as a fee for borrowing the money
How does each of these things influence your borrowing? Let’s look at each of them in more detail.
The Loan Amount
This one is simple, if you borrow £500 then you’ll pay back at least £500. If you borrow £5000 then you’ll pay back at least £5000. However, there’s an added point here in that many companies charge different interest rates depending on how big the sum is that you want to borrow. It may end up costing you a lot more to borrow £501 than it does to borrow £499 simply because the institution you’re borrowing from charges a certain interest rate for loans up to £500 and a larger interest rate for loans above that amount.
Another simple one. Most institutions charge fixed fees for processing loans and administrative costs. When borrowing you should always ask about fees and check the small print of any contracts as well. These fees are unavoidable, unfortunately.
The Repayment Schedule
Whilst many institutions require monthly payments, not all do. And even if you do have monthly payments, some lenders also accept “lump sum” payments where you can pay off a big chunk of your debt at one time. In most cases (and counter-intuitively) you’ll usually end up paying MORE in interest if you pay lump sums than if you pay regular monthly payments. A regular monthly repayment schedule tends to be the cheapest way to borrow money. A big lump sum payment can mean much higher interest rates.
A Note on Minimum Payments
Whilst we’re talking about payment schedules, it’s important to mention minimum payments. Some companies, particularly credit card companies, have something called a minimum payment. This means that there’s a minimum you can pay each month without getting a penalty, but you can also pay more if you like. Paying only the minimum payment on a loan is NOT a good idea, you should always pay more if you can.
A minimum payment is usually a percentage of how much you’ve borrowed, which means it gets lower over time as you pay off your loan. Paying only the minimum payment means it will take you MUCH longer to pay off your loan, which in turn means you’ll be paying interest for longer, and that means that the total amount you end up paying back is more.
Even adding an extra £10 to the minimum monthly payment will help save you money in the long run!
The Loan Length
The shorter the length of your loan, the less money you’ll pay in interest over the course of the loan, which means you’ll pay less to borrow money overall. It might be tempting to go for a longer loan term since monthly payments will be lower, but in truth, that shorter loan is a better plan.
Don’t believe it? Hypothetically, let’s say you borrow £5000 at an APR (we’ll get to explaining APR in a moment!) of 11.72%, which is pretty standard. Over the course of a three-year loan, your monthly payments will be £165.40, which comes to a total of £6631 over three years. On a five year loan, on the other hand, your monthly payments might be only £110.52, but that comes to a total of £7298 by the end of the loan period!
The Interest Rate
If you borrow money you’ll be charged interest on that sum until you’ve finished repayments. This adds a lot to the cost of borrowing. Interest rates on loans are given in a percentage with the abbreviation APR (which stands for “annual percentage rate of charge”). As you can probably guess, the lower that percentage, the better since you’ll end up paying back less money over the course of your loan.
A Note on APR Rates
Many loan companies, credit card companies, and banks advertise quite heavily, and most will include an APR in their advertisements. Be aware that UK law only requires companies to give 51% of their customers their advertised APR. Just because a company advertises a great APR does NOT mean that you will receive it! Always check your APR before signing for a loan.
So How Do I Know How Much I’m REALLY Borrowing?
Borrowing £5000 isn’t just a question of paying back £5000. You’ll need to take into account all five of the above factors to figure out the overall cost of borrowing the amount that you need. This can involve some complicated maths, but there are loan calculators available online to help you out. You can find a couple of examples here and here, though most banks and credit card companies also have loan calculators on their websites.
Be aware that these loan calculators are only a guide and may not give you the exact amount you’ll end up paying back (many of them don’t include fees from the company that you’re borrowing from, for example). They’ll give you a good idea of what you’re getting into, but it’s up to you to check all the possibilities before signing for that loan or spending on your credit card.
Before You Borrow
Borrowing money can be an expensive business, and it’s very easy to get into debt if you don’t realise the true cost of borrowing. It’s important that before you borrow (or run up your credit card) that you consider a few things.
The first of these considerations is whether or not you really need to borrow money at all. Is what you’re planning on buying essential? A family holiday might sound nice, but is it really worth getting into debt for? Especially when that holiday is going to end up costing you way more than the ticket price. Also consider whether you can better pay for what you need through savings or even a personal loan from a family member, rather than needing to pay fees and interest to a lending institution.
And obviously, you’ll need to take a look at how much your repayments are going to be using all the above factors before committing to borrowing!
How Much Can You Repay?
The key important factor when borrowing money isn’t how much you can borrow, or how much you can afford to pay each month, or which bank you use, or anything else. There is one over-riding question that you have to ask yourself before borrowing:
How Much Can I Afford to Repay?
You’ll need to work out the total cost of borrowing a sum taking into account APR, loan length, and everything else before deciding that you want to sign on the dotted line!


Laser-induced Breakdown Spectroscopy
Laser-induced Breakdown Spectroscopy (LIBS) is an emission spectroscopy technique that provides an elemental fingerprint of the sample under investigation.
A LIBS measurement starts with an energetic laser pulse. The laser pulse is tightly focused onto the sample of interest to form a plasma. From this plasma highly discrete colors of light are emitted, called emission lines; these lines are characteristic for the elements present in the sample. A spectrometer unravels the different colors emitted from the sample and creates a spectrum. A digital camera captures the spectrum and dedicated software translates the emitted spectrum into the composition of the sample. Because all elements emit light at characteristic frequencies when excited, LIBS can in principle detect all elements, limited only by the amount of energy present in the plasma and the wavelength range of the used spectrometer.