Wednesday, October 31, 2018

Are humans contributing to global warming?

I believe that humans are contributing to global warming. This post is a collection of reasons and quotes to support my belief. There are 7 quotes divided into 3 sections.

A. Industrial human activities release greenhouse gases into the atmosphere
B. The amount of greenhouse gases in the atmosphere affect the temperature on Earth
C. The temperature on Earth is increasing faster now than any other time in human history

A. Industrial human activities release greenhouse gases into the atmosphere


Intergovernmental Panel on Climate Change:
1. "Anthropogenic greenhouse gas emissions have increased since the pre-industrial era, driven largely by economic and population growth, and are now higher than ever. This has led to atmospheric concentrations of carbon dioxide, methane and nitrous oxide that are unprecedented in at least the last 800,000 years." (Climate Change 2014 Synthesis Report Summary for Policymakers)

David Attenborough:
2. "When I was a boy in the 1930s, the carbon dioxide level was still below 300 parts per million. This year it reached 382, the highest figure for hundreds of thousands of years." (Climate change is the major challenge facing the world, The Independent, 2006)

Rebecca Lindsey:
3. "Based on air bubbles trapped in mile-thick ice cores and other paleoclimate evidence, we know that during the ice age cycles of the past million years or so, atmospheric carbon dioxide never exceeded 300 ppm. Before the Industrial Revolution started in the mid-1700s, atmospheric carbon dioxide was 280 ppm or less." (Climate Change: Atmospheric Carbon Dioxide, 2024)

B. The amount of greenhouse gases in the atmosphere affect the temperature on Earth


Intergovernmental Panel on Climate Change:
4. "Without the natural greenhouse effect, the average temperature at Earth's surface would be below the freezing point of water. Thus, Earth's natural greenhouse effect makes life as we know it possible." (IPCC Fourth Assessment Report: Climate Change 2007, FAQ 1.3 What is the Greenhouse Effect?)

U.S. Energy Information Administration:
5. "When sunlight strikes the Earth's surface, some of it radiates back toward space as infrared radiation (heat). Greenhouse gases absorb this infrared radiation and trap its heat in the atmosphere, creating a greenhouse effect that results in global warming and climate change." (Energy and the environment explained, Greenhouse gases, June 2014)

C. The temperature of Earth is increasing faster now than any other time in human history


Barack Obama:
6. "2014 was the planet's warmest year on record. Now, one year doesn't make a trend, but this does: 14 of the 15 warmest years on record have all fallen in the first 15 years of this century." (State of the Union Address, 2015)

World Meteorological Organization, United Nations:
7. "The global average temperature in 2022 is estimated to be about 1.15 (1.02 to 1.28) °C above the 1850-1900 average." (Eight warmest years on record witness upsurge in climate change impacts, 2022)

Sunday, October 28, 2018

Fundamentals of phenomenology


Photo source: Wikimedia Commons

This post is a collection of quotes about phenomenology. There are 23 quotes divided into 9 sections. The painting above is by Giovanni Ambrogio Figino titled Metal Plate with Peaches and Vine Leaves (1594).

A. Phenomenology is the study of immediate perception (3)
B. All knowledge begins with phenomenology (2)
C. Direct perception in the present moment is fact (1)
D. Memory is a bookcase that we can grab knowledge from (3)
E. The six main senses are vision, hearing, touch, taste, smell and thought (3)
F. Most thoughts mimic the other five senses (2)
G. Reality is full of details (3)
H. Reality is full of potential concepts (3)
I. The feeling of good is mysterious (3)

A. Phenomenology is the study of immediate perception


Charles Sanders Peirce (1839-1914, philosopher):
1. "That artist's observational power is what is most wanted in the study of phenomenology." (Pragmatism and Pragmaticism, 1903)

Edmund Husserl (1859-1938, philosopher):
2. "To begin with, we put the proposition: pure phenomenology is the science of pure consciousness." (Brainyquote.com)

Edmund Husserl (1859-1938, philosopher):
3. "A new fundamental science, pure phenomenology, has developed within philosophy: this is a science of a thoroughly new type and endless scope. It is inferior in methodological rigor to none of the modern sciences." (Pure Phenomenology, 1917)

B. All knowledge begins with phenomenology


William Stanley Jevons (1835-1882, economist):
4. "In a certain sense all knowledge is inductive. We can only learn the laws and relations of things in nature by observing those things." (The Principles of Science, 1874)

Simone Weil (1909-1943, philosopher):
5. "Although people seem to be unaware of it today, the development of the faculty of attention forms the real object and almost the sole interest of studies." (Reflections on the right Use of School Studies with a View to the Love of God)

C. Direct perception in the present moment is fact


John Stuart Mill (1806-1873, economist):
6. "Whatever is known to us by consciousness, is known beyond possibility of question. What one sees or feels, whether bodily or mentally, one cannot but be sure that one sees or feels." (A System of Logic, 1843)

D. Memory is a bookcase that we can grab knowledge from


Philip Roth  (1933-2018, novelist):
7. "Memories of the past are not memories of facts but memories of your imaginings of the facts." (The Facts: A Novelist's  Autobiography, 1988)

Francis Buller (1746-1800, judge):
8. "Some instances of strength of memory are very surprising." (Coleman v. Wathen, 1793)

Henri Bergson (1859-1941, philosopher)
9. "Without this survival of the past into the present there would be no duration, but only instantaneity." (An Introduction to Metaphysics, 1903)

E. The six senses are vision, hearing, touch, taste, smell and thought


Leonardo da Vinci (1452-1519, artist):
10. "The eye, which is called the window of the soul, is the principal means by which the central sense can most completely and abundantly appreciate the infinite works of nature; and the ear is the second, which acquires dignity by hearing of the things the eye has seen." (Quoted by The Notebooks of Leonardo da Vinci by Rudolf Flesch)

Michel Foucault (1926-1984, philosopher):
11. "The painter is turning his eyes towards us only in so far as we happen to occupy the same position as his subject. We, the spectators, are an additional factor." (The Order of Things: An Archaeology of the Human Sciences, 1970)

Martin Heidegger (1889-1976, philosopher):
12. "We ourselves are the entities to be analyzed." (Being and Time, 1927)

F. Most thoughts mimic the other five senses


Robert Andrew Wilson, Frank Keil:
13. "However, the central role of imagery in theories of mental activity was undermined when Kulpe, in 1904, pointed out that some thoughts are not accompanied by imagery..." (The MIT Encyclopedia of Cognitive Sciences, 2001)

Temple Grandin (1947-now, professor):
14. "To understand animal thinking you've got to get away from a language. See my mind works like Google for images. You put in a key word; it brings up pictures. See language for me narrates the pictures in my mind." (NPR: A Conversation with Temple Grandin, 2006)

G. Reality is full of details


Baruch Spinoza (1632-1677, philosopher):
15. "The more reality or being a thing has, the greater number of its attributes." (Ethics, 1677)

Laurence Sterne (1713-1768, novelist):
16. "Digressions, incontestably, are the sunshine; and they are the life, the soul of reading; take them out of this book for instance, you might as well take the book along with them." (The Life and Opinions of Tristram Shandy, Gentlemen)

George Henry Lewes (1817-1878, literary critic):
17. "...it is in the selection of the characteristic details that the artistic power is manifested." (The Principles of Success in Literature, 1865)

H. Reality if full of potential concepts


Ferdinand de Saussure (1857-1913, linguist):
18. "Without language, thought is a vague, uncharted nebula. There are not pre-existing ideas, and nothing is distinct before the appearance of language." (Cours de Linguistique Generale, 1916)

Albert Einstein (1879-1955, physicist):
19. "By means of such concepts and mental relations between them, we are able to orient ourselves in the labyrinth of sense impressions." (Physics and Reality, 1936)

Peter Strawson (1919-2006, philosopher):
20. "Part of my aim is to exhibit some general and structural features of the conceptual scheme in terms of which we think about particular things." (Individuals, 1959)

I. The feeling of good is mysterious


Jacques Lacan (1901-1981, psychologist):
21. "Desire, a function central to all human experience, is the desire for nothing nameable. And at the same time this desire lies at the origin of every variety of animation." (Goodreads.com)

G. E. Moore (1873-1958, philosopher):
22. "If I am asked, 'What is good?' my answer is that good is good, and that is the end of the matter. Or if I am asked, 'How is that to be defined?' my answer is that it cannot be defined, and that is all I have to say about it." (Principia Ethica, 1903)

Simone Weil (1909-1943, philosopher):
23. "There is a reality outside the world, that is to say, outside space and time, outside man's mental universe, outside any sphere whatsoever that is accessible to human faculties. Corresponding to this reality, at the centre of the human heart, is the longing for an absolute good, a longing which is always there and is never appeased by any object in this world." (Draft for a Statement of Human Obligation, posthumous)

Saturday, October 27, 2018

Top 12 questions in economics


Photo source: Wikimedia CommonsWilfredorCC0 1.0

This post is a ranking of what I believe are the most important questions in economics. I define economics as the study of production, distributions and consumption of goods and services.
  1. What goods and services should the government provide?
  2. What economic activity should be regulated or illegal?
  3. Does increased taxes on high-income earners hurt economic growth?
  4. How can poor countries escape poverty?
  5. How can rich countries increase growth?
  6. Should poor individuals receive welfare?
  7. Should governments in rich countries increase aid to poor countries?
  8. Does increasing the minimum wage hurt economic growth?
  9. Should the government subsidize innovative technologies?
  10. Should the government guarantee a job to everyone?
  11. Should the government increase spending during recessions?
  12. Should the government increase the money supply during recessions?

License: CC BY-SA 4.0

Wednesday, October 24, 2018

Quotes about economics

This post is some of my quotes about economics. There are 12 quotes listed below.

Econ Factbook


1. "Econfactbook.org is a economic data website that attempts to bring greater transparency to the world economy... The format of Econ Factbook is designed to eliminate excess statistics and only display the structure of an economy. By focusing on the structure, I believe it can help people better understand an economy." (Transparency and the world economy, 2018)

2. "I hope that someday every city and state in the world could have their own page using the same format. Currently economic data about localities is very difficult to find on the internet and I believe centralizing this data in a clear format would be useful." (Transparency and the world economy, 2018)

3. "The format of Econ Factbook is based on the circular flow of income model. The format has a section for each of the five main economic sectors: households, companies, government, banks and the central bank. Each section has a few statistics to illustrate the condition of that sector. In addition to these sections, the format has a section for employment, industries and international accounts." (Transparency and the world economy, 2018)

Current events and academic economics


4. "My undergraduate economics education has been very useful to me and I learned great information. I'm happy to have learned many demand and supply graphs along with other mathematical theories. But as a whole, analysis of current events was not the focus. In order to know what was going on in the real world, I had to read The Economist and other publications outside of class." (Current events and academic economics, 2018)

5. "That's not to say that academic economists completely ignore current events; there are some examples of great current event analysis in economic journals. But as a whole, I believe that current events is of secondary importance within academic economics." (Current events and academic economics, 2018)

6. "Before the financial crisis, there should have been academic economists devoted to analyzing exotic financial products in the actual financial system. These economists would have published papers maybe as early as 2005 to ring the alarm about the widespread fraud subprime mortgage securities. Although this type of work would have been useful, it was largely absent." (Current events and academic economics, 2018)

7. "I believe economists would benefit from reading The Big Short by Michael Lewis. The book explains how hedge fund manager Michael Burry was able to predict the subprime mortgage financial crisis long before anyone else. On the other hand, academic economists were largely blind to the impending crisis." (How to predict a financial crisis, 2017)

Economic statements


8. "I believe the goal of economics is to make accurate representations of economic phenomena. I regard this is the purpose of any branch of knowledge." (Evaluating economic statements, 2017)

9. "When I think about economics, I divide the discipline into five types of statements. Here are the five types: what economic policy should be, historical economic phenomena, current economic phenomena, future economic phenomena, general economic phenomena." (Five types of economic statements, 2018)

10. "Building a DSGE model is cool, but it's only a statement. I believe it's more important to find evidence that supports or disputes an economic statement in order to determine its accuracy." (Evaluating economic statements, 2017)

Confounding variables


11. "There are real mechanical relationships in the social realm that accurately fit mathematical equations. Although I think such relationships exist, I'm more inclined to believe that the vast majority of social reality does not operate mechanistically. There are too many confounding variables in the social realm that can't be inserted into a mathematical equation." (Current events and academic economics, 2018)

12. "Applying the scientific method (i.e. controlled experiments) to social reality is a difficult task. Quasi-experimental methods are worth developing, but we should always be wary about unseen confounding variables. Despite these difficulties, I believe that there are real economic relationships that can be discovered using econometrics." (Current events and academic economics, 2018)

License: CC BY-SA 4.0

Tuesday, October 23, 2018

Quotes about knowledge and language

This post is some of my quotes about knowledge and language. There are 12 quotes below. An updated version of this post can be found at this link: Collection of quotes from Knowledge and Representation

Principles


1. "Principles constitute the outline of our knowledge. We can add to this list of principles and create dynamic systems. In this regard, principles help organize our thoughts into coherent structures." (What is a principle? 2018)

2. "I enjoy collecting quotes and organizing them into clear structures. To me, structured quotes usually stick in my mind stronger than continuous prose. Even when I write normally, I try keep my paragraphs short and clear." (Quotes and the organization of thoughts, 2018)

Reason


3. "It's important to know the reasons why you believe something and be able to point to pieces of evidence that support your argument. The benefit of this method is that it forces a person to be explicit about why they believe a certain thing." (What is an argument? 2018)

4. "The first step is to figure out what exactly is being debated. This would be to determine a statement that one side believes is true while the other believes is false. Surprisingly, this can be difficult in some cases but its a necessary pre-requite." (What is bias? 2018)

5. "The second step is for each side to provide a list of concise reasons why they hold their belief. Each side should be limited to about 5 reasons. Each reason should be clearly stated and consist of no more than a few sentences. This enables the structure of the belief to become transparent." (What is bias? 2018)

6. "Instead of arguing against a morphing argument, we can hold each side still and dissect each belief. In this regard, we can discover that some reasons are false or have a weak connection to the proposition." (What is bias? 2018)

Language


7. "I believe that language is formed through establishment rather than usage. For example, imagine that we have a a million different color shades and we want to give a word to each shade. In this situation, we could name every color a separate number. This process would establish many word-concept relationships. Although we wouldn't use every color shade, the meanings would still remain." (What is establishment? 2018)

8. "I believe that almost every word in the English language has multiple meanings... For example, the word 'for' could indicate a length of time or an occasion in a series. Another example, the word 'in' could mean that something is surrounded by something else or refer to a condition." (What is literal? 2018)

9. "Instead of trying to differentiate between objective and subjective statements, I think of statements existing along a continuum. I believe there are too many unseen misinterpretation traps to safely conclude that a statement is 100% objective (except for mathematics and logic symbols). As a resolution, I believe we should use the word 'objective' in a subjective manner." (What is objective? 2018)

10. "These examples show that being perfectly literal is somewhat of an elusive task. For most words, it's not clear what the primary meaning is. In this regard, we can only subjectively choose what we believe is most literal meaning." (What is literal? 2018)

Cogito


11. "I exist. Consciousness exists. Experience exists. A sense exists. A perception exists. Reality exists. Time exists... I believe that these seven propositions are necessary for any hallucination to happen. In this regard, even the most elaborate hallucination could not negate any of these propositions." (What is a fact? 2018)

12. "If the self didn't exist, there would be nobody to view the hallucination. If consciousness didn't exist, the hallucination wouldn't have been seen. If experience didn't exist, the hallucination wouldn't have been endured. If a senses didn't exist, there would be no way to access data about the hallucination. If a perception didn't exist, the hallucination wouldn't have been perceived. If reality didn't exist, there would be nothing. If time didn't exist, there would be no seconds to experience the hallucination." (What is a fact? 2018)

License: CC BY-SA 4.0

Monday, October 22, 2018

Top 8 questions in epistemology


Photo source: Wikimedia Commons, Karolspacja
Photo license: CC BY 4.0

This post is a ranking of what I believe are the most important questions in epistemology. I define epistemology as the study of knowledge.
  1. How do reasons support a belief?
  2. What can we know with absolute certainty?
  3. What are the limits of knowledge?
  4. Does a priori knowledge exist?
  5. Is all knowledge subjective to a degree?
  6. Does all knowledge rely on intuition to a degree?
  7. What is the scientific method?
  8. Is science always true?

License: CC BY-SA 4.0

Sunday, October 21, 2018

Top 8 questions in the philosophy of language


Photo source: Wikimedia CommonsLadakh
Photo license: CC BY 2.0

This post is a ranking of what I believe are the most important questions in philosophy of language. I define language as written or spoken symbols.
  1. How does a word get its meaning?
  2. How do words in a sentence combine together to create meaning?
  3. Can language be absolutely true?
  4. Do perfect definitions exist?
  5. What words are absolutely objective?
  6. What sentences are absolutely objective?
  7. Do concepts exist in transcendental reality?
  8. Do humans have pre-wired grammar?

License: CC BY-SA 4.0

Saturday, October 20, 2018

Top 32 words to define in philosophy

Photo license: CC BY 2.0

I believe that many of the disagreements in philosophy are caused by a divergence on the meaning of a word. To make things more difficult, if you look up the definition of a word in multiple dictionaries, you often won't find a clear consensus. For this reason, I believe that defining words is an important endeavor in philosophy.

The most famous example of this is the debate over the meaning of 'science', which is known as the 'demarcation problem'. Defining 'science' is particularly important because the word 'science' carries weight and significance. Many people regard science as the best method for establishing knowledge about reality. But if you ask the average person, 'What is the definition of science?' they probably won't provide a clear and satisfactory answer. For this reason, many philosophers have attempted to establish a clear meaning of 'science'.

The rest of this post is a ranking of what I believe are the 32 most important words to define in philosophy and I have provided my definition for each word. A longer list of definitions can be found at this link.

1. Philosophy: study of fundamental nature
2. Reality: actual state of affairs
3. Science: 1. method of establishing knowledge through controlled experiments; 2. study of any subject related to physics, chemistry or biology
4. God: conscious being who created reality
5. Knowledge: correctly justified true belief
6. True: attribute of being an accurate representation of reality
7. Phenomenology: study of immediate perception
8. Experience: totality of past and present senses
9. Truth: 1. accurate representation of reality; 2. actual state of affairs
10. Religion: belief in or worship toward a divine supernatural power
11. Understanding: 1. condition of knowing the explanation of something; 2. condition of having competent knowledge in something
12. Consciousness: faculty that enables a being to be aware of experience
13. Reason: 1. process of forming conclusions using explicit reasons or premises; 2. something intended to support the accuracy of a proposition; 3. something that explains something else
14. Language: written or spoken symbols
15. Fact: 1. something known with absolute certainty; 2. something known with absolute certainty with the exception of hallucinations and extreme coincidences
16. Belief: something accepted to be true
17. Mind: faculty that enables a being to have beliefs, sense replications, emotions and a subconscious
18. Mathematics: study of numbers, lines and shapes
19. Art: expression of imagination and/or ability
20. Physics: study of matter, motion, force, space and time
21. Intuition: process of forming beliefs based on unclear reasons
22. Logic: process of forming conclusions using objective reasons or premises
23. Being: 1. essential self; 2. way something is
24. Concept: mental general representation
25. Sense: faculty that retrieves data
26. Thought: conscious belief, memory retrieval, sense replication or emotion
27. Meaning: 1. underlying representation; 2. underlying significance
28. Ontology: study of the way something is
29. Explanation: 1. description of why something happened or happens; 2. description that makes something clear
30. Soul: conscious transcendental being
31. Description: linguistic representation
32. Analysis: detailed examination of something with the purpose of drawing conclusions

License: CC BY-SA 4.0

Friday, October 19, 2018

Top 18 questions in philosophy


Photo source: Wikimedia Commons, Georges Noblet
Photo license: CC BY-SA 2.5

This post is a ranking of what I believe are the most important questions in philosophy. I define philosophy as the study of the fundamental nature.
  1. Why is there something rather than nothing?
  2. What am I?
  3. What is the meaning of life?
  4. Why does good feel good?
  5. Why does suffering exist?
  6. Does God exist?
  7. Do people have free will?
  8. How does consciousness work?
  9. Is everything made out of matter?
  10. Do people have souls?
  11. What happens after death?
  12. How do reasons support a belief?
  13. What can you know with absolute certainty?
  14. Can reality exist without a conscious observer?
  15. Are other people conscious?
  16. Why am I me and not somebody else?
  17. Why is it now and not some other time?
  18. Are inanimate objects conscious?

License: CC BY-SA 4.0

Sunday, October 14, 2018

Jean-Francois Lyotard and knowledge production


Photo source: Wikimedia Commons, Bracha Ettinger
Photo license: CC BY-SA 2.5

Jean-Francois Lyotard (1924-1998) was a French philosopher best known for his analysis of knowledge distribution and postmodernism. Wikipedia says,
"His interdisciplinary discourse spans such topics as epistemology and communication, the human body, modern art and postmodern art, literature and critical theory, music, film, time and memory, space, the city and landscape, the sublime, and the relation between aesthetics and politics." (Wikipedia: Jean-Francois Lyotard, 7.1.21 UTC 20:05)
The rest of this post is some quotes from Lyotard.

Postmodernism


"I define postmodern as incredulity towards metanarratives." (The Postmodern Condition: A Report on Knowledge, 1977)

Knowledge as a commodity


"Knowledge is and will be produced in order to be sold, it is and will be consumed in order to be valorized in a new production..." (The Postmodern Condition: A Report on Knowledge, 1977)

Art and the sublime


"I shall call modern that art which... presents the fact that the unpresentable exists. To make visible that there is something which can be conceived and which can neither be seen nor made visible." (Goodreads.com)

"The sublime is not mere pleasure as taste is - it is a mixture of pleasure and pain... Confronted with objects that are too big according to their magnitude or too violent according to their power, the mind experiences its own limitations." (Peregrinations Law Form)

John Rawls and justice

John Rawls (1921-2002) was an American political philosopher best known for his analysis of justice and the 'original position' thought experiment. Economist Will Hutton said,
"This means society should build what Rawls calls an 'infrastructure of justice' that ensures everyone has access to key primary goods - some reasonable level of income and material wellbeing, opportunity and basic rights and liberties - which allow them to consider they have been given a proper chance to achieve full membership of society."
Writer Steven M. Smith said,
"Rawls is a philosopher for our time. His desire is to render both theoretically and practically legitimate and redistributivist polices of the prosperous North Atlantic welfare states." (The Philosopher of Our Times, The New York Sun, 2007)
The rest of this post is some quotes from Rawls.

Original position


"A just society is a society that if you knew everything about it, you'd be willing to enter it in a random place." (AZQuotes.com)

Justice


"The concept of justice I take to be defined, then, by the role of its principles in assigning rights and duties and in defining the appropriate division of social advantages." (A Theory of Justice, 1971)

"A conception of justice cannot be deduced from self evident premises or conditions on principles; instead, its justification is a matter of the mutual support of many considerations, of everything fitted together into one coherent view." (A Theory of Justice, 1971)

Equality


"This organizing idea is that of society as a fair system of social cooperation between free and equal persons viewed as fully cooperating members of society over a complete life." (Political Liberalism, 1993)

"In all sectors of society there should be roughly equal prospects of culture and achievement for everyone similarly motivated and endowed. The expectations of those with the same abilities and aspirations should not be affected by their social class." (A Theory of Justice, 1971)

Jacques Lacan and structuralism

Jacques Lacan (1901-1981) was a French psychoanalyst best known for his contributions to structuralism and the philosophy of language. Literary critic Norman Holland said,
"Lacan's most widely quoted maxim is, 'The unconscious is structured like a language' and like that sentence, Lacan's whole oeuvre rest on a certain idea of language. His proclaimed 'return to Freud' meant remedying Freud's failure to use 'modern' linguistics. 'Modern' linguistics for Lacan, however, means a turn-of-the-century linguistics - specifically, Ferdinand de Saussure's." (The Critical I, 1992)
The rest of this post is some quotes from Lacan.

Structuralism


"Meaning is produced not only by the relationship between the signifier and the signified but also, crucially, by the position of the signifiers in relation to other signifiers." (Goodreads.com)

"Nature provides - I must use the word - signifies, and these signifies organize human relation in a creative way, providing them with structures and shaping them." (The Four Fundamental Concepts of Psycho Analysis, 1978)

"For the signifier is a unit in its very uniqueness, being by nature symbol only of an absence." (AZQuotes.com)

Language


"The man who is born into existence deals first with language; this is a given. He is even caught in it before his birth." (Interview, 1957)

"I always speak the truth. Not the whole truth, because there's no way, to say it all. Saying it all is literally impossible: words fail. Yet it's through this very impossibility that the truth holds onto the real." (Goodreads.com)

"The real is what resists symbolization absolutely." (The Seminar of Jacques Lacan: Freud's Papers on Technique)

"As is known, it is in the realm of experience inaugurated by psychoanalysis that we may grasp along what imaginary lines the human organism, int he most intimate recesses of its being, manifests its capture in a symbolic dimension." (AZQuotes.com)

Subconscious


"The knowledge that there is a part of the psychic functions that are out of conscious reach, we did not need to wait for Freud to know this!" (AZQuotes.com)

"Discontinuity, then, is the essential form in which the unconscious first appears to us as a phenomenon - discontinuity, in which something is manifested as a vacillation." (The Four Fundamental Concepts of Psycho Analysis, 1978)

"The unconscious is structured like a language." (AZQuotes.com)

Desire


"...Desire, a function central to all human experience, is the desire for nothing nameable. And at the same time this desire lies at the origin of every variety of animation." (Goodreads.com)

Wolfgang Amadeus Mozart and melody


Photo source: Wikimedia Commons, Joseph Sonnleithner

Wolfgang Amadeus Mozart (1756-1791) was an Austrian composer best known for his contributions to Classical period of music. Composer Carl Ditters von Dittersdorf said,
"Mozart is undoubtedly one of the greatest of original geniuses, and I have never known any other composer to posses such an amazing wealth of ideas. I wish he were not so spendthrift with them. He does not give the listener time to catch his breath, for no sooner is one inclined to reflect upon a beautiful inspiration then another appears ever more splendid, which drives away the first, and this continues on and on, so that in the end one is unable to retain any of these beauties in the memory." (Autobiography, 1799)
The rest of this post is some quotes from Mozart.

Music


"The music is not in the notes, but in the silence between." (Goodreads.com)

"I choose such notes that love one another." (AZQuotes.com)

"Melody is the essence of music." (Quoted in Reminiscences of Michael Kelly... by Henry Colbern)

"...the most necessary, most difficult and principal thing in music, that is time..." (Letter to Leopold Mozart)

"The best way to learn is through the powerful force of rhythm." (AZQuotes.com)

"The organ is in my eyes the king of all instruments." (Mozart's Letters)

Creation


"I am never happier than when I have something to compose, for that, after all, is my sole delight and passion." (AZQuotes.com)

"You know that I immerse myself in music, so to speak - that I think about it all day long - that I like experiments, studying, reflecting." (Goodreads.com)

"I pay no attention whatever to anybody's praise or blame. I simply follow my own feelings." (Goodreads.com)

"Neither a lofty degree of intelligence nor imagination nor both together go to the making of genius. Love, love, love, that is the soul of genius." (Goodreads.com)

"I really do not aim at any originality." (AZQuotes.com)

Religion


"God is ever before my eyes. I realize his omnipotence and I fear his anger; but I also recognize his compassion, and his tenderness towards his creatures." (AZQuotes.com)

Enrico Fermi and nuclear physics


Photo source: Wikimedia Commons, U.S. Department of Energy

Enrico Fermi (1901-1954) was an Italian physicist best known for creating the first nuclear reactor. Novelist C. P. Snow said,
"If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom. If this sounds like hyperbole, anything about Fermi is like to sound like hyperbole."
The rest of this post is some quotes form Fermi.

Nuclear weapons


"Such a weapon goes far beyond any military objective and enters the range of very great natural catastrophes... The fact that no limits exist to the destructiveness of this weapon makes its very existence and the knowledge of its construction a danger to humanity as a whole. It s necessarily an evil thing considered in any light." (Official General Advisory Committee report for the Atomic Energy Commission, 1949)

"Whatever Nature has in store for mankind, unpleasant as it may be, men must accept, for ignorance is never better than knowledge." (Goodreads.com)

"Actually there was no choice. Once basic knowledge is acquired, any attempt at preventing its fruition would be as futile as hoping to stop the earth from revolving around the sun." (Collected Papers of Enrico Fermi, 1939-1954)

"It is clear that the use of such a weapon cannot be justified on any ethical ground which gives a human being a certain individuality and dignity even if he happens to be a resident of an enemy country." (Goodreads.com)

Nuclear science


"Although the problem of transmuting chemical elements into each other is much older than a satisfactory definition of the very concept of chemical element, it is well known that the first and most important step towards its solution was made only nineteen years ago by the late Lord Rutherford, who started the method of the nuclear bombardments." (Nobel lecture, 1938)

Johann Sebastian Bach and God


Photo source: Wikimedia Commons, Elias Gottlob Hausmann

Johann Sebastian Bach (1685-1750) was a German composer best known for his contributions to Baroque music. Pianist Glenn Gould said,
"The prerequisite of contrapuntal art, more conspicuous in the work of Bach than in that of any other composer, is an ability to conceive a priori of melodic identities which when transposed, inverted, made retrograde, or transformed rhythmically will yet exhibit, in conjunction with the original subject matter, some entirely new but completely harmonious profile." (So You Want to Write A Fugue, 1963)
The rest of this post is some quotes from Bach.

Music and God


"Like all music, the figured bass should have no other end and aim than the glory of God and the recreation of the soul; where this is not kept in mind there is no true music, but only an infernal clamour and ranting." (Quoted in Bibel und Symbol in den Werken Bachs by Ludwig Prautzsch)

"I play the notes as they are written, but it is God who makes the music." (Goodreads.com)

"Music is an agreeable harmony for the honor of God and the permissible delights of the soul." (Goodreads.com)

"The final aim and reason of all music is nothing other than the glorification of God and the refreshment of the spirit." (Goodreads.com)

Meditation


"Ceaseless work, analysis, reflection, writing much, endless self-correction, that is my secret." (AZQuotes.com)

Wilhelm Rontgen and X-rays


Photo source: Wikimedia Commons, Nobel Foundation

Wilhelm Rontgen (1845-1923) was a German physicist best for producing and detecting electromagnetic radiation in a wavelength also known as X-rays. Weapons scientist Otto Glasser said,
"Rontgen was an experimental physicist of the old school and built most of his own equipment... It was Rontgen's custom, when beginning new investigations, to repeat important experiments made previously by others in the same field." (Wilhelm Conrad Rontgen and the Early History of the Roentgen Rays, 1934)
The biographical profile by the Nobel Foundation says,
"Rontgen retained the characteristic of a strikingly modest and reticent man... He was always shy of having an assistant, and preferred to work alone."
Below is one of Rontgen's first X-ray photographs of Albert von Kolliker's hand in 1896. Photo source: Wikimedia Commons


The rest of this of this post is some quotes from Rontgen.

Discovery of X-rays


"Having discovered the existence of a new kind of rays, I of course began to investigate what they would do... It soon appeared from the tests that the rays had penetrative power to a degree hitherto unknown. They penetrated paper, wood, and cloth with ease; and the thickness of the substance made no perceptible difference, within reasonable limits." (The New Marvel in Photography, 1896)

"In a few minutes there was no doubt about it. Rays were coming from the tube which had a luminescent effect upon the paper... It seemed a first a new kind of invisible light. It was clearly something new, something unrecorded." (The New Marvel in Photography, 1896)

"If the hand be held between the discharge-tube and the screen, the darker shadow of the bones is seen within the slightly dark shadow-image of the hand itself." (On a New Kind of Rays, 1895)

"I was working with a Crookes tube covered by a shield of black cardboard. A piece of barium platino-cyanide paper lay on the bench there. I had been passing a current through the tube, and I noticed a peculiar black line across the paper." (The New Marvel in Photography, 1896)

Edward Jenner and vaccinations


Photo source: Wikimedia Commons

Edward Jenner (1749-1823) was an English physician best known for creating the first smallpox vaccination. Wikipedia says,
"Jenner is often called 'the father of immunology' and his work is said to have 'saved more lives than the work of any other human'. In Jenner's time, smallpox killed around 10 percent of the population, with the number as high as 20 percent in towns and cities where infection spread more easily." (Wikipedia: Edward Jenner, 8.21.21 UTC 19:16)
The rest of this post is some quotes from Jenner.

Benefit to mankind


"While the vaccine discovery was progressive, the joy I felt at the prospect before me of being the instrument destined to take away from the world one of its greatest calamities [smallpox], blended with the fond hope of enjoying independence and domestic peace and happiness, was often so excessive that, in pursuing my favourite subject among the meadows, I have sometimes found myself in a kind of reverie." (Quoted in The Life of Dr. Jenner, 1827)

"I shall endeavor still further to prosecute this inquiry, an inquiry I trust not merely speculative, but of sufficient moment to inspire the pleasing hope of its becoming essentially beneficial to mankind." (AZQuotes.com)

"I hope that some day the practice of producing cowpox in human beings will spread over the world - when that day comes, there will be no more smallpox." (AZQuotes.com)

Disease


"The deviation of man from the state in which he was originally placed by nature seems to have proved to him a prolific source of diseases." (Goodreads.com)

Joseph Lister and antiseptics


Photo source: Wikimedia Commons, Weltrundschau zu Reclams Universum

Joseph Lister (1827-1912) was an English surgeon best known for his pioneering work in antiseptic surgery. Physician Clifford Allbutt said,
"Lister saw the vast importance of the discoveries of Pasteur. He saw it because he was watching on the heights, and he was watching there alone." (The Encyclopaedia Britannica, 1911)
Wikipedia says,
"Applying Louis Pasteur's advances in microbiology, Lister championed the use of carbolic acid as an antiseptic, so that it became the first widely used antiseptic in surgery." (Wikipedia: Joseph Lister, 8.21.21 UTC 12:37)
The rest of this post is some quotes from Lister.

Antiseptics


"Bearing in mind that it is from the vitality of the atmospheric particles that all the mischief arises, it appears that all that is requisite is to dress the wound with some material capable of killing these septic germs, provided that any substance can be found reliable for this purpose, yet not too potent as a caustic." (On a New Method of Treating Compound Fracture, 1867)

"But when it has been shown by the researches of Pasteur that the septic property of the atmosphere depended not on the oxygen, or any gaseous constituent, but on minute organisms suspended in it, which owed their energy to their vitality, it occurred to me that decomposition in the injured part might be avoided without excluding the air, by applying as a dressing some material capable of destroying the life of the floating particles. Upon this principle I have based a practice." (On the Antiseptic Principle in the Practice of Surgery, 1867)

Surgery


"If the love of surgery is a proof of a person's being adapted for it, then certainly I am fitted to be a surgeon; for thou can'st hardly conceive what a high degree of enjoyment I am from day to day experiencing in this bloody and butchering department of the healing art." (Letter to his father, 1853)

"It is our proud office to tend the fleshly tabernacle of the immortal spirit, and our path, rightly followed, will be guided by unfettered truth and love unfeigned." (AZQuotes.com)

Gregor Mendel and genetics


Photo source: Wikimedia Commons

Gregor Mendel (1822-1884) was a German biologist best known for his pioneering work on genetics. Biologist David P. Clark said,
"The birth of modern genetics was due to the discoveries of Gregor Mendel (1823-1884), an Augustinian monk who taught natural science to high school students in the town of Brno in Moravia. Mendel's greatest insight was to focus on discrete, clear-cut characters rather than measuring continuously variable properties, such as height or weight. Mendel used pea plants and studied characteristics such as whether the seeds were smooth or wrinkled, whether the flowers were red or white, and whether the pods were yellow or green, etc." (Molecular Biology, 2010)
The rest of this post is some quotes from Mendel.

Traits


"That no generally applicable law of the formulation and development of hybrids has yet been successfully formulated can hardly astonish anyone who is acquainted with the extent of the task and who can appreciate the difficulties with which experiments of this kind have to contend." (Experiments in plant-hybridisation, 1865)

"The striking regularity with which the same hybrid forms always reappeared whenever fertilisation took place between the same species induced further experiments to be undertaken..." (Experiments in plant-hybridisation, 1865)

"Experiments on ornamental plants undertaken in previous years had proven that, as a rule, hybrids do not represent the form exactly intermediate between the parental strains." (Experiments in plant-hybridisation, 1865)

"The course of development consists simply in this; that in each generation the two parental traits appear, separated and unchanged, and there is nothing to indicate that one of them has either inherited or taken over anything from the other." (Letter to Carl Nageli, 1867)

"In this generation, along with the dominating traits, the recessive ones also reappear, their individuality fully revealed, and they do so in the decisively expressed average proportion of 3:1, so that among each four plants of this generation three the dominating and one the recessive characteristic." (Experiments in plant-hybridisation, 1865)

Saturday, October 13, 2018

William Harvey and the heart


Photo source: Wikimedia Commons, Daniel Mijtens

William Harvey (1587-1657) was an English physician best known for his analysis of blood circulation. Robert Willis says,
"Harvey was not content merely to gather knowledge; he digested and arranged it under the guidance of the faculties which compare and reason... Harvey appears to have possessed, in a remarkable degree, the power of persuading and conciliating those with whom he cam in contact.
Neuroscientist Robert Willis said,
"Few would have predicted that the discovery of the circulation of the blood woudl have hanged the way philosophers view the world, theologians conceive of God, or astronomers look at the starts, yet all of that happened." (The Fabric of Mind, 1985)
The rest of this post is some quotes from Harvey.

Heart


"This organ deserved to be styled the starting point of life and the sun of our microcosm just as much as the sun deserves to be styled the heart of the world. For it is by the heart's vigorous beat that the blood is moved, perfected activated, and protected from injury and coagulation. The heart is the tutelary deity of the body..." (De Motu Cordis, 1628)

"The blood in the animal body is impelled in a circle and is in a state of ceaseless motion... and that it is the sole and only end of the motion and contraction of the heart." (On the Motion of the Heart and Blood, 1628)

"I finally saw that the blood, forced by the action of the left ventricle into the arteries, was distributed to the body at large, and its several parts, in the same manner as it is sent through the lungs, impelled by the right ventricle into the pulmonary artery, and that it then passed through the veins and along the vena cava, and so round to the left ventricle in the manner already indicated." (Quoted in the Works of William Harvey)

Demonstration


"When in many dissections, carried out as opportunity offered upon living animals, I first addressed my mind to seeing how I could discover the function and offices of the heart's movement in animals through the use of my own eyes instead of through the books and writings of others." (De Motu Cordis, 1628)

"I profess both to learn and to teach anatomy not from books but from dissections; not from positions of philosophers but from the fabric of nature." (Dedication of Dr. Argent and Other Learned Physicians)

Epistemology


"There is no science which does not spring from pre-existing knowledge, and no certain and definite idea which has not derived its origin from the senses." (Quoted in The First Anatomical Disquisition on the Circulation of the Blood by Willis and Bowie)

"The studious and good and true, never suffer their minds to be warped by the passions of hatred and envy, which unfit men duly to weigh the arguments that are advanced in behalf of truth, or to appreciate the proposition that is even fairly demonstrated." (Dedication of Dr. Argent and Other Learned Physicians)

Alexander Graham Bell and the telephone


Photo source: Wikimedia Commons, Moffet Studio

Alexander Graham Bell (1847-1922) was a Scottish inventor and scientist best known for creating the first practical telephone. Wikipedia says,
"[Bell's] research on hearing and speech further led him to experiment with hearing devices which eventually culminated in Bell being award the first U.S. patent for the telephone in 1876... Many other inventions marked Bell's later life, including groundbreaking work in optical telecommunications, hydrofoils and aeronautics." (Wikipedia: Alexander Graham Bell, 8.21.21 UTC 00:26)
The rest of this quote is some quotes from Bell.

Telegraphy


"Watson... if I can get a mechanism which will make a current of electricity vary in its intensity, as the air varies in density when a sound is passing through it, I can telegraph any sound, even the sound of speech." (AZQuotes.com)

"Grand telegraphic discovery today... Transmitted vocal sounds for the first time... With some further modification I hope we may be enabled to distinguish... the 'timbre' of the sound. Should this be so, conversation viva voce by telegraph will be a fait accompli." (AZQuotes.com)

"The day will come when the man at the telephone will be able to see the distant person to whom he is speaking." (AZQuotes.com)

Discovery


"When I have worked a long time on one thing, I make it a point to bring all the facts regarding it together before I retire." (Interview in How They Succeeded; Bell Telephone Talk, 1901)

"Concentrate all your thoughts upon the work at hand. The sun's rays do not burn until brought to a focus." (Interview in How They Succeeded; Bell Telephone Talk, 1901)

"You cannot force ideas. Successful ideas are the result of slow growth. Ideas do not reach perfection in a day no matter how much study is put upon them." (Interview in How They Succeeded; Bell Telephone Talk, 1901)

Antonie van Leeuwenhoek and microscopic life


Photo source: Wikimedia Commons, Jan Verkolje

Antonie van Leeuwenhoek (1632-1723) was a Dutch microbiologist best known for his contributions to microscopy and the discovery of many microscopic organisms. Antiquarian Martin Folkes said,
"We have seen so many, and those of [Leeuwenhoek's] most surprising discoveries, so perfectly confirmed by great numbers of the most curious and judicious observers, that there can surely be no reason to distrust his accuracy in those others which have not yet been so frequently or carefully examined." (Account of Mr. Leeuwenhoek's Microscopes, 1723)
The rest of this post is some quotes from Leeuwenhoek.

Microscopic life


"...I judge that some of these little creatures were above a thousand times smaller than the smallest ones I have ever yet seen, upon the rind of cheese, in wheaten flour, mould, and the like." (Letter to the Royal Society, 1674)

"...we see little living animals and see their legs and must judge the same to be ten thousand times thinner than a hair of my beard, and when I see animals living that are more than a hundred times smaller and am unable to observe any legs at all, I still conclude from their structure and movements of their bodies that they do have legs." (Letter to N. Grew, 1678)

"I observed certain animalcules, within whole bodies I saw so quick a motion as to exceed belief; they were about the size of a large grain of sand, and their bodies being transparent, that the internal motion could plainly be seen. Among other things, I saw in the body of one of these animalcules a bright and round corpuscle, placed near the head, and in which a very wonderful swift motion was to be seen, consisting of an alternate extension and contraction. This particle I concluded to be the heart." (AZQuotes.com)

"If we reflect that a small creature such as this is provided, not only with external members, but also with intestines and other organs, we have no reason to doubt that a like creature, even if a thousand million times smaller, may already be provided with all its external and internal organs... though they may be hidden from our eyes." (Letter to the Royal Society, 1685)

Is reality infinitely microscopic?


"How little do we discover in comparison of those things which now are and forever will be hidden from our sight? The whole of which I am fully persuaded no one will ever be able to dive into, and to explain their causes and effects." (Brainyquote.com)

"How inscrutable and incomprehensible are the hidden works of Nature!" (Brainyquote.com)

James Watt and thinking


Photo source: Wikimedia Commons, Carl Friedrich Breda

James Watt (1736-1819) was a Scottish inventor best known for his contributions to the stream engine. Economist Jeremy Rifkin said,
"James Watt patented his steam engine on the eve of the American Revolution, consummating a relationship between coal and the new Promethean spirit of the age, and humanity made its first tentative steps into an industrial way of life that would, over the next two centuries, forever change the world." (Quoted in The Hydrogen Economy)
Chemist Humphry Davy said,
"Those who consider James Watt only as great practical mechanic form a very erroneous idea of his character: he was equally distinguished as a natural philosopher and a chemist, and his inventions demonstrate his profound knowledge of those sciences, and that peculiar characteristic of genius, the union of them for practical application." (Quoted in Proceedings of the Public Meeting held at Freemasons Hall, 1824)
The rest of this post is some quotes from Watt.

Thinking


"I can think of nothing else than this machine." (Letter to Dr. Lind, 1765)

"I had gone on a walk on a fine Sabbath afternoon... I was thinking upon the engine at the time, and had gone as far as the herd's house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder." (Quoted in Reminiscences of James Watt by Robert Hart)

"When once the idea of the separate condensation was started, all these improvements followed as corollaries in quick succession, so that in the course of one or two days the invention was thus far complete in my mind, and I immediately set about an experiment to verify it practically." (Notes on Professor Robison's Dissertation on Steam-engines, 1769)

Steam engine


"It now appeared that the cylinder of the model, being of brass, would conduct heat much better than the cast-iron cylinders of larger engines (generally covered on the inside with a stony crust), and that considerable advantage could be gained by making the cylinders of some substance that would receive and give out heat slowly." (Notes on Professor Robison's Dissertation on Steam-engines, 1769)

"I perceived that, in order to make the best use of steam, it was necessary - first, that the cylinder should be maintained always as hot as hot as steam which entered it; and, secondly, that when the steam was condensed, the water of which it was composed, and then injection itself, should be cooled down to 100 degrees, or lower, where that was possible." (Notes on Professor Robison's Dissertation on Steam-engines, 1769)

"There still remained another source of the destruction of steam, the cooling of the cylinder by the external air, which would produce an internal condensation whenever the steam entered it, and which would be repeated every stroke; this I proposed to remedy by an external cylinder, containing steam, surrounded by another of wood, or of some other substance which would conduct heat slowly." (Notes on Professor Robison's Dissertation on Steam-engines, 1769)

Joseph-Louis Lagrange and arithmetic


Photo source: Wikimedia Commons

Joseph-Louis Lagrange (1736-1813) was an Italian mathematician best known for his contributions to analysis, number theory and classical mechanics. Writer Johann Wolfgang von Goethe said,
"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange." (Wilhelm Meister's Wanderjahre, Zqeites Buck)
Mathematician Dirk Jan Struik said,
"Full use of Lagrange's own calculus of variations made the unification of the varied principles of statistics and dynamics possible - in statistics by the use for the principle of virtual velocities, in dynamics by the use of D'Alembert's principle." (A Concise History of Mathematics, 1948)
The rest of this post is some quotes from Lagrange.

Arithmetic and geometry


"An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity." (Dans Les Lecons Elementaires sur les Mathematiques, 1795)

"As long as algebra and geometry proceed along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection." (Dans Les Lecons Elementaires sur les Mathematiques, 1795)

"We have already various treatises on Mechanics, but the plan of this one is entirely new... The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure." (Quoted in Mathematics, from the points of view of the Mathematician and of the Physicist, 1912)

Applied knowledge


"I regarded as quite useless the reading of large treatises of pure analysis: too large a number of methods pass at once before the eyes. It is in the works of application that one must study them; one judges their utility there and appraises the manner of making use of them." (Quoted in Moniteur Universel by J. F. Maurice)

History of science


"Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish." (Introduction to Astronomy by F. R. Moulton)

"It took them only an instant to cut off that head, but France may not produce another like it in a century." (Quoted in Annual Editions: Western Civilization by William Hughes regarding the beheading of Antoine Lavoisier)

Pierre de Fermat and number theory


Photo source: Wikimedia Commons

Pierre de Fermat (1607-1665) was a French mathematician best known for Fermat's Last Theorem and his contributions to number theory and calculus. Physicist Isaac Newton said,
"I had hints of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract equations, directly and invertedly, I made it general." (Quoted in Isaac Newton by Louis Trenchard More)
Regarding Fermat's Last Theorem, Wikipedia says,
"In number theory, Fermat's Last Theorem... states that no three positive integers A, B, and C satisfy the equation A^N + B^N = C^N for any integer value of N greater than 2. The cases N=1 and N=2 have been known to have infinitely many solutions since antiquity." (Wikipedia: Fermat's Last Theorem, 8.11.21 UTC 03:24)
Mathematician Andrew Wiles wrote the proof to Fermat's Last Theorem in 1993, which was regarded as a major event in the history of mathematics. Wiles said,
"The best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem." (Nova Interview, 2000)
The rest of this post is some quotes from Fermat.

Number theory


"There is scarcely any one who states purely arithmetical questions, scarcely any one who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? ... If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof..." (Letter to Frenicle de Bessy, 1657)

"It is impossible for any number which is a power greater than the second to be written as a sum of two like powers." (AZQuotes.com)

"To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible..." (AZQuotes.com)

"...given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square." (Letter to Frenicle de Bessy, 1657)

Alan Turing and artificial intelligence


Photo source: Wikimedia Commons

Alan Turing (1912-1954) was an English computer scientist and mathematician best known for contributions to computers and artificial intelligence. Philosopher Jerry Fodor said,
"Beyond any doubt, the most important thing that has happened in cognitive science was Turing invention of the notion of mechanical rationality." (The Trouble with Psychological Darwinism, 1998)
Mathematician James Wilkinson said,
"Turing had a strong predilection for working things out from first principles, usually in the first instance without consulting any previous work on the subject, and no doubt it was this habit which gave his work that characteristically original flavor." (Some Comments from a Numerical Analyst, 1970)
The rest of this post is some quotes from Turing.

Artificial intelligence


"If one wants to make a machine mimic the behaviour of the human computer in some complex operation one has to ask him how it is done, and then translate the answer into the form of an instruction table. Constructing instruction tables is usually described as 'programming'." (Computing Machinery and Intelligence, 1950)

"We may hope that machines will eventually compete with men in all purely intellectual fields. But which are the best ones to start with? Many people think that a very abstract activity, like the playing of chess, would be best. It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English." (AZQuotes.com)

"It seems probable that once the machine thinking method had started it would not take long to outstrip our feeble powers... They would be able to converse with each other to sharpen their wits. As some stage therefore, we should have to expect the machines to take control." (Goodreads.com)

"I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted." (Computing Machinery and Intelligence, 1950)

Turing test


"A computer would deserve to be called intelligent if it could deceive a human into believing that it was human." (AZQuotes.com)

Mathematics


"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings." (System of Logic Based on Ordinals, 1938)

"...we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions." (System of Logic Based on Ordinals, 1938)