S2EP6: Exploring the study methods of the (other) inventor of calculus

The Autodidactic Podcast
S2EP6: Exploring the study methods of the (other) inventor of calculus
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Hello and welcome to the Autodidactic podcast, season 2 episode 6.

This week I’ll be talking about a German autodidactic who one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history.

Who? It is Gottfried Wilhelm Leibniz (1 July 1646–14 Nov 1716) a prominent German polymath and one of the most important logicians, mathematicians and natural philosophers of the Enlightenment.

A contemporary Denis Diderot an eighteenth-century French atheist and materialist said: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one’s books and go die quietly in the dark of some forgotten corner”

As a representative of the seventeenth-century tradition of rationalism, Leibniz developed, as his most prominent accomplishment, the ideas of differential and integral calculus, independently of Isaac Newton’s contemporaneous developments. Mathematical works have consistently favoured Leibniz’s notation as the conventional expression of calculus.

He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal’s calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in a device called the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of nearly all digital (electronic, solid-state, discrete logic) computers, including the Von Neumann machine, which is the standard design paradigm, or “computer architecture”, followed from the second half of the 20th century, and into the 21st.

Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, and history.

He wrote in several languages, primarily in Latin, French and German but also in English, Italian and Dutch.

Leibniz was born in Leipzig on July 1, 1646, two years prior to the end of the Thirty Years War, which had ravaged central Europe. His father, Friedrich Leibniz, was a jurist and professor of Moral Philosophy at the University of Leipzig, and his mother, Catharina Schmuck, the daughter of a professor of Law.

Leibniz’s father died in 1652, and his subsequent education was directed by his mother, uncle, and according to his own reports, himself. He was given access to his father’s extensive library at a young age and proceeded to pore over its contents, particularly the volumes of ancient history and the Church Fathers. His father’s library enabled him to study a wide variety of advanced philosophical and theological works—ones that he would not have otherwise been able to read until his college years.

Access to his father’s library, largely written in Latin, also led to his proficiency in the Latin language, which he achieved by the age of 12. While young, Leibniz immersed himself in history, poetry, maths, and other subjects, gaining knowledge in many different fields.

At the age of seven, Leibniz entered the Nicolai School in Leipzig. Although he was taught Latin at the elementary school, Leibniz had taught himself far more advanced Latin and some Greek. As he progressed through school he was taught Aristotle’s logic and theory of categorising knowledge. Leibniz was clearly not satisfied with Aristotle’s system and began to develop his own ideas on how to improve on it. In later life Leibniz recalled that at this time he was trying to find orderings on logical truths which, although he did not know it at the time, were the ideas behind rigorous mathematical proofs.

In 1661, at the age of fourteen, Leibniz entered the University of Leipzig. It may sound today as if this were a truly exceptionally early age for anyone to enter university, but it is fair to say that by the standards of the time he was quite young but there would be others of a similar age. He studied philosophy, which was well taught at the University of Leipzig, and mathematics which was very poorly taught. Among the other topics which were included in this two year general degree course were rhetoric, Latin, Greek and Hebrew. He graduated with a bachelors degree in 1663

Leibniz then went to Jena to spend the summer term of 1663.

At Jena the professor of mathematics was Erhard Weigel but Weigel was also a philosopher and through him Leibniz began to understand the importance of the method of mathematical proof for subjects such as logic and philosophy. Weigel believed that number was the fundamental concept of the universe and his ideas were to have considerable influence of Leibniz. By October 1663 Leibniz was back in Leipzig starting his studies towards a doctorate in law. He was awarded his Master’s Degree in philosophy for a dissertation which combined aspects of philosophy and law studying relations in these subjects with mathematical ideas that he had learnt from Weigel. A few days after Leibniz presented his dissertation, his mother died.

Despite his growing reputation and acknowledged scholarship, Leibniz was refused the doctorate in law at Leipzig. It is a little unclear why this happened, but Leibniz was not prepared to accept any delay and he went immediately to the University of Altdorf where he received a doctorate in law in February 1667.

Leibniz dedicated his working life to serving two German families that were very important to the society of the time. He had proposed to a plan to revitalize and protect German-speaking countries after the devastating and opportunistic situation left by the Thirty Years’ War. Although the elector listened to this plan with reservations, Leibniz was later summoned to Paris to explain the details of the plan.

In the end, this plan was not carried out, but it was the beginning of a Parisian stay in Leibniz that lasted for years. This stay in Paris allowed Leibniz to be in contact with several well-known personalities in the field of science and philosophy. Having been in contact with all these specialists, he realized that he needed to expand his areas of knowledge.

Leibniz decided to follow a self-education program. This program had excellent results, even discovering elements of great importance and transcendence, such as his investigations linked to the infinite series and his own version of differential calculus.

The reason why Leibniz was summoned to Paris did not take place and Leibniz was sent to London for a diplomatic mission to the government of England. During these years he took the opportunity to present to the Royal Society an invention he had been developing since 1670. It was a tool through which it was possible to make calculations in the field of arithmetic. After witnessing the operation of this machine, the members of the Royal Society appointed him an external member.

While in London, he learned that the elector Juan Felipe von Schönborn for whom he worked had died, and Leibniz had to find another occupation. Leibniz began working as a private justice counsellor for the House of Brunswick. While Leibniz dedicated himself to providing his services to the House of Brunswick, they allowed him to develop his studies and inventions, which were in no way linked to obligations directly related to the family.

Then, in 1674 Leibniz began to develop the conception of calculus. Two years later, in 1676, he had already developed a system that was coherent and that saw the light of day in 1684.

1682 and 1692 were very important years for Leibniz, as his documents were published in the field of mathematics.

During the first decade of the 1700s, the Scottish mathematician John Keill indicated that Leibniz had plagiarized Isaac Newton in relation to the conception of calculus. This accusation took place in an article written by Keill for the Royal Society.

This institution then carried out extremely detailed research on both scientists to determine who had been the author of this discovery. It was eventually determined that Newton was the first to discover calculus, but Leibniz was the first to publish his dissertations. Today historians believe both men made the discoveries completely independently and both are credited with the invention of calculus.

The last part of Leibniz’s life was plagued by the controversy. In 1714, George Louis of Hanover became King George I of Great Britain. Leibniz had a lot to do with this appointment, but George I was adverse towards him.

Leibniz died in Hanover on November 14, 1716. He was 70 years old. Leibniz never married, and his funeral was only attended by his personal secretary. George I did not attend his funeral, which shows the separation between the two.

So what can we take away from Leibniz? Well he had two periods of intense self-learning. The first as a child in his fathers library, and the second from 1672 in Paris. Leibniz studied mathematics and physics under Christiaan Huygens a Dutch scientist in 1672 and it was Huygens who encouraged to read and gave him an extensive reading list. This list included, works of many famous mathematicians such as Pascal and Descartes.

In both of these periods he read extensively. Like many of my previous podcasts about famous autodidactics reading was a keystone for Leibniz as well. Ray Bradbury a writer I featured recently called the library his college. For Leibniz reading was a critical method for extending his knowledge. Leibniz didn’t just read in a single area of knowledge, he read extensively in all areas he was interested in.

In this podcast let’s focus on becoming more prolific readers. If you’re listening to this then you’re probably already doing a lot of study and like most people you’re short of time. Using what we know about Leibniz and his two periods of intensive study let me propose some things to help become voracious readers.

First, make a list of books to read.

Leibniz started both his periods of intense self-study with reading lists. The first was his intention to read all the books in his fathers library. You can picture him as a young child entering the room, pulling the book from the top most shelf on the left wall, and working his way around the room book by book. The second period he was given a list to start with by a friend and mentor.

It doesn’t really matter how you get a starting list, you’ll come across other books as you read. Or you might find a topic mentioned in one book which leads to another set of books. But the trick is to have a list of books you’ll be reading next. From your starting list, just keep adding more and more books as they appear on your radar.

Set a reading goal.

Have a target for how many books you’ll read, and how many pages or chapters per day. But most importantly set a daily goal. For example 20 pages every day.

Always have a book handy.

Like the famous advert said, “Don’t leave home without it.”. Always have something to read with you. I know someone who used to rip books into 20 pages. Then carry around the 20 page sections to read in his pocket. Personally I don’t think I could bring myself to destroy a book like that, but it worked for him and he read all the time.

In addition to books, try audio books.

I used to listen to some audio books while driving from the Great Course company. It is very useful to have a book to listen to when driving alone, since you’re not wasting any time.

Make reading a priority.

You need to put reading in a higher category than other things you might be doing now. Park the TV or the Xbox, stop using Instagram and read instead.

Set a deadline for each book.

When you don’t set a deadline to complete your book, there isn’t a sense of urgency, and when something isn’t urgent, you tend to procrastinate and your books get left on the shelves untouched and unread. Set a deadline to avoid this problem. You can have a general deadline like complete any book you open in 2 weeks.

Read in layers.

For non-fiction books you may want to read contents page, headers, etc. first. You can find more information in the autodidactic podcast, Season 1, Episode 7: Textbook Study Methods. I’ll put a link in the show notes.

Well that is all for this week.

If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also, please feel free to email me at rick@autodidactic.info, or leave feedback on the website autodidactic.info.

Thank you very much for listening.

https://www.burrosabio.net/gottfried-leibniz-biography/

https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

https://plato.stanford.edu/entries/leibniz/

https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz

http://www.themarginal.com/emc2/gottfried_wilhelm_leibniz.htm

https://www.thefamouspeople.com/profiles/gottfried-w-leibniz-536.php

S2EP5: Exploring the study methods of Thomas Henry Huxley

The Autodidactic Podcast
S2EP5: Exploring the study methods of Thomas Henry Huxley
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Hello and welcome to the Autodidactic podcast, season 2 episode 5.

This week I’ll be looking into a British autodidactic named Thomas Henry Huxley who was born on the 4th of May 1825 and died 29 June 1895. Huxley was a biologist and anthropologist specializing in comparative anatomy. He was known as “Darwin’s Bulldog” for his advocacy of Charles Darwin’s theory of evolution.

His father taught mathematics and was assistant headmaster at a school in Ealing which Thomas Henry attended for a brief period. But after his father lost his job he no longer attended school. For his general education Huxley was largely self-taught; while still in his teens he read extensively, particularly in science and metaphysics, and gained a facility in reading German and French. He learned Latin, and enough Greek to read Aristotle.

Though raised as an evangelical, Tom devoured books of a distinctly anti-evangelical nature written by subversives such as William Lawrence and David Hume and William Paley. Though he wanted to grow up to be an engineer, he became a medical student instead–at the advanced age of 12, he was introduced to medicine as apprentice to brother-in-law Dr. John Scott. This began his life-long commitment to investigating the engineering of the body, to anatomy, morphology, physiology.

He was apprenticed to his sister Ellen’s husband, John Charles Cooke, a medical materialist. Transferred to a London dockside practitioner early in 1841, Huxley was shaken by the lives of his pauper patients. As an apprentice, he would walk the streets of the East End on his way to patients, observing the dreary and dangerous life lived by the poor.

In September 1842 Huxley and his brother James were awarded free scholarships at Charing Cross Hospital. The lecturer on physiology, Thomas Wharton Jones, had a strong influence on Huxley’s interest in physiology and anatomy and helped teach him methods of scientific investigation. Under Wharton Jones’ guidance, Huxley published his first scientific paper demonstrating the existence of an unrecognized layer in the inner sheath of hairs, a layer that has been known since as Huxley’s layer.

He passed his first exams at London University, but didn’t present himself for the second exam and consequently didn’t qualify for a degree. However, this first exam results were enough to allow him to apply for the Royal Navy. Huxley was too young to apply for the Royal College of Surgeons for a license, but because he was deeply in debt he applied for the navy. He was interviewed by Sir William Burnett, the Physician General of the Navy, who arranged for his competence to be tested and he was made Assistant Surgeon on the HMS Rattlesnake.

The Rattlesnake left England on 3 December 1846 and, once they had arrived in the southern hemisphere, Huxley devoted his time to the study of marine invertebrates. He began to send details of his discoveries back to England, where his papers were published by a friend Edward Forbes.

The value of Huxley’s work was recognised and, on returning to England in 1850, he was elected a Fellow of the Royal Society. In the following year, at the age of twenty-six, he not only received the Royal Society Medal but was also elected to the Council. Huxley, who had learned German when he was a teenager and had begun serious scholarly investigation of German science upon his return to England. He regularly corresponded with, and sometimes had as household guests, Anton Dohrn, Ernst Haeckel, Dr. Leuckart and other German biologists.

Huxley effectively resigned from the navy (by refusing to return to active service). In 1851 recently returned from the Rattlesnake voyage, was so desperate for a job that he applied to the University of Toronto. Fortunately for England and perhaps for science, Toronto rejected him in favor of a politician’s relative. In July 1854, he became Professor of Natural History at the Royal School of Mines and naturalist to the British Geological Survey in 1855. He was active in the British scientific circles for the remainder of his life.

He was also Fullerian Professor at the Royal Institution; Hunterian Professor at the Royal College of Surgeons; President of the British Association for the Advancement of Science; President of the Quekett Microscopical Club; President of the Royal Society; Inspector of Fisheries; and President of the Marine Biological Association.

In 1890, he moved from London to Eastbourne where he edited the nine volumes of his Collected Essays. Finally, in 1895, he died of a heart attack (after contracting influenza and pneumonia), and was buried in North London.

When Huxley himself was young there were virtually no degrees in British universities in the biological sciences and few courses. Most biologists of his day were either self-taught, or took medical degrees. When he retired there were established chairs in biological disciplines in most universities, and a broad consensus on the curricula to be followed. Huxley was the single most influential person in this transformation.

Huxley was also a major influence in the direction taken by British schools: in November 1870 he was voted onto the London School Board. In primary schooling, he advocated a wide range of disciplines, similar to what is taught today: reading, writing, arithmetic, art, science, music, etc.

Of all his public speaking Huxley was most interested in the serious of workingmen’s lectures which gave regularly, beginning in 1855, by which he wanted “the working classes to understand that Science and her ways are great facts for them.”

While Huxley is best known for his defense of Darwin’s hypothesis, he did not accept it uncritically and did not consider that the problem was finally settled nor that natural selection was by any means proven as the mechanism. For Huxley it remained a hypothesis because of the lack of experimental proof.

Huxley’s close friends were Charles Lyell, whom he met shortly after his return from the voyage, Herbert Spencer, Michael Foster, John Knowles, Charles Darwin, Joseph Hooker, and John Tyndall. The number of letters exchanged between Huxley and these people hints at the degree of closeness.

Later an idea came to these friends: to institute a club, Huxley’s title for which was Blastodermic. The first meeting of the X Club, as it came to be designated, was in January of 1864. The club became an admired and feared cabal, since it not only had the talent to write most of a scientific encyclopedia, but from its members came four Presidents of the Royal Society, five Presidents of the British Association for the Advancement of Science, officers of the Royal College of Surgeons and many societies, the London Mathematical, the Chemical, the Geological, the Ethnological.

According to its members, the club was originally started to keep friends from drifting apart, and to partake in scientific discussion free from theological influence. A key aim was to reform the Royal Society, with a view to making the practice of science professional.

The scientific eminence, social status, hard work, and political astuteness of the X Club’s members were all essential to the group’s success. By electing one another to office and through effective networking, these men were influential in scientific societies and became leading advisers to the government. As popular lecturers, contributors to elite journals, and textbook writers, they were among the prime interpreters of science for the industrializing and secularizing society of Victorian England

What can we take away from Huxleys life and learning? Firstly like all the autodidactics and polymaths I’ve reviewed so far he had an insatiable love of reading. He also was hard-working and dedicated. I can tell you as a fellow language learner, Huxley’s learning of multiple languages, German, French, Greek, and Latin was not mean feat and would have consumed many hours of study, reading and practice.

The Foreign Service Institute (FSI) has created a practical reference for people interested in learning a foreign language. The list contains difficulty ratings and the estimated number of classroom hours necessary to learn each language at a semi-proficient level.

German is rated as a category 2 language and considered to be similar to English. The FSI estimates that German takes approximately 30 weeks, or 750 classroom hours to learn. This study was conducted on a group of language students who spent 25 hours per week in class, and three hours daily on individual practice.

Without a teacher or modern methods such as electronic flashcards and working only with books and meetings, Huxley would have had a much more difficult time, and probably would have spent longer. Remember that a bachelor’s degree in most areas can require between 124 to 128 college credits particular to a specific program of study. Where as a C2 – CEFR certification in German is estimated at well over 1500 hours of study.

So we know that Huxley had dogged determination and great motivation to learn a language. We know he was a vicarious reader. But one thing we can also take away from Huxley’s life and study practices is his network of people. Huxley was a prolific correspondent and wrote letters all his life. Starting in his early years while studying and corresponding with various mentors.

In addition, the creation of the X-Club was specifically designed to have a peer system. Today we’d call this a Mastermind Group. Napoleon Hill, his classic book Think and Grow Rich, coined the phrase “mastermind group” and pointed out that the most successful people throughout history had a personal “Board of Advisors” that helped them reach their goals. Huxley was one of these people.

Surrounding himself with like minded people, and creating a network of friends and mentors via correspondence was a core feature in Huxley’s life and learnings. These mastermind groups have been around a long time. One of the people I previously reviewed, Ben Franklin established a group called “The Junto” in 1727 who met together for mutual improvement by discussing moral, political, and scientific topics of the day.

As a self-learner you may struggle with a topic and it is often good to get an outside perspective on the issue. For example, yesterday I sent some computer code to a friend asking him for help. He didn’t give me the answer, but managed to start me down the correct path to get the answer myself. Often when you have a knotty problem to figure out, just explaining the problem to someone else will trigger the answer to pop up into your head without them saying a word.

If you research a Napoleon Hill mastermind group, it will be different from what I’m proposing for an autodidactic. Typically the groups outlined by Hill are for career progression and business mentoring. What I’m suggesting is more like what Huxley used in his youth. A group of people who are knowledgeable in a subject your are learning and would be willing to assist you. It is also helpful if you know something they are learning so you can pay them back, but often people will assist you simply from kindness or friendship.

Huxley corresponded via letter with knowledgeable people in his field of study. Asking questions and having discussions about what he was learning.

A few years ago I was looking into statistics and wanted to do a small experiment. I read a number of books on the subject and had a general idea how to go about it, but didn’t know any specifics. I decided to write the author of one of the books I was studying, a professor at the University of Bath. I sent an email and told him I was reading his book, and why I was reading it. I asked the specific question about my project and hoped for an answer. Not only did he reply he advanced some suggestions for improvements in my project and we continued to correspond via email for a few weeks.

You can have a group of mentors for your own learning. You need to identify people who could help you, and may want to help you. Remember that you shouldn’t badger people into helping you, nor depend on a few people. But here are some ways you can start to pull together a learning mastermind group.

  1. Create a list of people who are knowledgable.
  2. Determine the best way to communicate with these people.
  3. Determine what you can do for them.
  4. Have a hotseat.

A diverse group has been proven to be a far better way to solve our problems than one or two individuals. Groups that are too much alike find it harder to keep learning, so try to diversify. For example, if you’re learning computer programming having a mathematician around would be extremely helpful to you.

Communication could be as a group, or to individuals. You might decide to meet with your six friends who are all learning the same subject as you each week. Or you might decide to create a WhatsApps or Signal group in order to share learnings and problems. You might decide that you’d rather meet one-to-one or use email correspondence for communications.

Determine what you can give back to these people. It might be that you don’t have anything to give back, but they help simply because they enjoy helping others. Don’t abuse people for your personal gain, try to help them if you can. Always be available to answer their questions if they have them.

If you’re going to meet regularly have a hot-seat that rotates through all the members so they can ask questions about their issues and seek answers from the group.

Remember that while the authors of books, professors, or other people might seem to mighty to answer your simple questions, they are people just like you. A rather famous, but insightful saying is; Don’t ask, don’t get.

Well that is all for this week.

If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also, please feel free to email me at rick@autodidactic.info, or leave feedback on the website autodidactic.info.

Thank you very much for listening.

References:

https://mathcs.clarku.edu/huxley

https://en.wikipedia.org/wiki/Thomas_Henry_Huxley

S2E4: Polymathy and Autodidactics

The Autodidactic Podcast
S2E4: Polymathy and Autodidactics
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Hello and welcome to the Autodidactic podcast, season 2 episode 4. I had an email in my mailbox this week from a listener named Kenyatta (forgive me if I have mispronounced your name). She was wondering about my definitions of Autodidactic, Polymath, and self-learner. So I thought I would expand a little on these terms this week, and how I tend to use them.

She also asked why I ask for donations. Well that one is easy to answer, I don’t have any corporate sponsor, and I pay for all the podcast hosting and things myself. So the donation is just if someone liked the show, and wanted to show their appreciation by buying me a coffee.

Back to Kenyatta’s musings. I’ll give you the dictionary definitions then talk a little more about each one.

  1. Self-Learner – Learning done by oneself, without a teacher or instructor.
  2. Polymath – a person of great learning in several fields of study.
  3. Autodidactic – a person who has learned a subject without the benefit of a teacher or formal education; a self-taught person.

So you can see that a self-learner and an autodidactic are actually the same. It is someone who learns by themselves. While this might mean they are learning one thing only, they could be learning in multiple fields. Autodidactics then may or may not be a polymath, and a polymath, may or may not be an autodidactic.

In this podcast I try to explore techniques and methods for self-learning and hopefully this is of some use to either type of autodidactic, polymath or non-polymath. But one assumption that I have a tendency to make is that many people who are listening to the podcast are more likely to be polymaths and trying to learn skills in multiple fields.

Using myself as an example; I self-learn mathematics, electronics, programming, metal working, knife-making, cooking, and languages. While I’m certainly no expert in all of these, I enjoy working in these disparate fields. As a writer I find it helps to have a broad knowledge of a lot of topics in order to write characters convincingly.

Autodidacticism and self-learning we’ve covered, but let me explore polymathism with you.

A polymath is from the Greek and means “much learned”. So this is a person who has knowledge in multiple fields of study, but might not be self-taught. In the renaissance, a period in Europe covering the 14th through the 17t centuries, started in Italy in the late middle ages. The idea of a “Uomo Universale” or universal man was someone who could play musical instruments, speak many languages, write poetry, paint and so on.

Normally these ideal persons were nobility or sons of nobility and required a rounded universal education. Interestingly, the idea of a universal education was essential to achieving polymath ability, hence the word university was used to describe a seat of learning. The idea behind a university was not to specialise but to give a general well-rounded education to these young courtiers so they cound then go forward and specialise in a specific field.

Marching forward to the 21st century we find a renewed interest in polymathy in the scientific community. Robert Root-Bernstein worked in the area of polymathy and two other types of categories which were the specialists and the dilettante. He regards a specialist as someone who has great depth in a subject with without a breadth of knowledge, and a dilettante is someone who has superficial knowledge of many subjects. However, the dilettante unlike the polymath has acquired these skills without any regard to understanding broader applications or implications and without integrating knowledge across these fields.

So for Robert Root-Bernstein a polymath is someone who has knowledge in multiple fields, but can “put a significant amount of time and effort into their avocations and find ways to use their multiple interests to inform their vocations”.

Robert Root-Bernstein argues in favour of polymathy. The argument that universality of domain favours the creative processes. Which means other interests outside of the primary domain can feed the mental tools required to generate creative ideas. A prime example often cited is Albert Einstein and his love of the violin. Einstein once said that if he hadn’t been a scientist, he would certainly have been a musician.

In “Life Stages of Creativity”, Robert and Michèle Root-Bernstein suggest six typologies of creative life stages.

  • Type 1 represents people who specialize in developing one major talent early in life (e.g., prodigies) and successfully exploit that talent exclusively for the rest of their lives.
  • Type 2 individuals explore a range of different creative activities (e.g., through worldplay or a variety of hobbies) and then settle on exploiting one of these for the rest of their lives.
  • Type 3 people are polymathic from the outset and manage to juggle multiple careers simultaneously so that their creativity pattern is constantly varied.
  • Type 4 creators are recognized early for one major talent (e.g., math or music) but go on to explore additional creative outlets, diversifying their productivity with age.
  • Type 5 creators devote themselves serially to one creative field after another.
  • Type 6 people develop diversified creative skills early and then, like Type 5 individuals, explore these serially, one at a time.

So why is there a decline in polymathy since the middle ages? Well Peter Burke, Professor Emeritus of Cultural History and Fellow of Emmanuel College at Cambridge believed that due to the rapid increase in knowledge from the 17th century onwards with was increasingly difficult from an individual to master as many disciplines as before. Professor Burke warns that in the age of specialization, polymathic people are more necessary than ever.

Michael Araki is a professor at Universidade Federal Fluminense in Brazil, who sought to formalise the polymathic development. Professor Araki’s work shows although there are many different perspectives and definitions of a polymath, they generally assert three elements which are; Breadth, Depth, and Integration.

Breadth means a comprehensive knowledge of the subjects, rather than a narrow specialisation. This is the primary indicator of a polymath. Depth refers to the accumulation of knowledge, as opposed to the dilettantes superficial knowledge. Finally there is integration which requires connecting, articulating and synthesising knowledge from different frameworks.

How do I use these terms? Well I’m assuming that you wouldn’t listen to this podcast unless you are a self-learner, or my mother. I also make the assumption that my listeners are studying in multiple fields of study. But even if you aren’t a polymath, I need to try to make my podcasts relevant to the person studying biology as it is to the person studying avionics just because of a diversity of listeners.

Also I think that a lot of people who are willing to put in the effort to self-learn, to be an autodidactic will naturally want to study and understand more than one topic.

Autodidacticism is simply education without the guidance of subject matter experts such as teachers or professors. In general an autodidactic has chosen the topic themselves and might be trying self-learning for the first time. When you need to select your own study material, create your own study plans and find the time yourself, it is useful to know that you’re not alone and that many people have trodden this path before. There is a well worn path, you just need someone to point it out to you.

It might be as an autodidactic you’re studying independently as a complement or an alternative to formal education. For example, learning how to program a computer could be a skill which is a complement to work you’re already doing.

In this pandemic lots of people are using their newly acquired spare time to learn other topics they have an interest in. A 2016 Stack Overflow poll reported 69.1% of software developers appear to be self-taught and I suspect in the current climate these numbers will only increase.

Well that is all for this week. It was a bit shorter than normal, but hopefully enjoyable. Next week I plan to return to the investigation of an autodidactic and try to ascertain their methods and adopt them for us to use.

If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also, please feel free to email me like Kenyatta did to rick@autodidactic.info, or leave feedback on the website autodidactic.info.

Thank you very much for listening.

PolymathWikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc.

S2E3: Exploring the study methods of a famous American Writer

The Autodidactic Podcast
S2E3: Exploring the study methods of a famous American Writer
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Hello and welcome to the Autodidactic podcast, season 2 episode 3. I’m happy to say that I’m appearing on another podcast soon. I was interviewed by Kris Brohom from Actual Fluency Podcast about my language learning activities and advice for people studying during the pandemic. I’ll put links in the podcast transcription on the autodidactic.info website.

This episode I’m going to be looking into the study habits of a great writer and autodidactic. Before I tell you his name, let me read a quote from him.

“Libraries raised me. I don’t believe in colleges and universities. I believe in libraries because most students don’t have any money. When I graduated from high school, it was during the Depression and we had no money. I couldn’t go to college, so I went to the library three days a week for 10 years.”

He is one of the most celebrated 20th- and 21st-century American writers, and worked in a variety of genres including fantasy, science fiction, horror, and mystery fiction. I’m speaking of Ray Douglas Bradbury (born August 22, 1920, died June 5, 2012). He was born in in Waukegan, Illinois to Esther Bradbury a Swedish immigrant and Leonard Bradbury who was a telephone lineman.

Bradbury’s most famous works include “Fahrenheit 451” and “Something wicked this way comes.”

Bradbury began writing his stories at age 11 (1931), during the Great Depression—sometimes writing on the only available paper, butcher paper. Bradbury was a firm believer in writing something every day. One incident which Bradbury attributed to his lifelong writing habit was, in 1932, when a carnival entertainer, one Mr. Electrico, touched the young man on the nose with an electrified sword, made his hair stand on end, and shouted, “Live forever!” Bradbury wanted to be immortalised forever through his writing.

Bradbury remarked, “I felt that something strange and wonderful had happened to me because of my encounter with Mr. Electrico … [he] gave me a future … I began to write, full-time. I have written every single day of my life since that day 69 years ago.”

In addition to writing Bradbury was a keen prestidigitator, otherwise known as a magician. As a boy, Bradbury attended several performances by Blackstone the Magician and, in 1931, was given a book on magic for his eleventh birthday. He was soon performing his own magic act for various service clubs and lodges, and was invited to appear at the Veterans of Foreign Wars Hall on Christmas Eve.

In high-school Bradbury was a member of the drama club and was a keen actor. Bradbury married his wife in 1947 and they were married for 56 years until her death in 2003. His wife was the first and only woman he’d ever dated, and they had four daughters. Bradbury never obtained a driver’s license, but relied on public transportation or his bicycle. Bradbury witnessed a fatal car accident when he was 16. Later he said:

“I saw six people die horribly in an accident. I walked home holding on to walls and trees. It took me months to begin to function again. So I don’t drive. But whether I drive or not is irrelevant. The automobile is the most dangerous weapon in our society—cars kill more than wars do.”

Bradbury was a strong supporter of public library systems, raising money to prevent the closure of several libraries in California facing budgetary cuts. He said “libraries raised me”, and shunned colleges and universities, comparing his own lack of funds during the Depression with poor contemporary students. Bradbury permitted the publication of “Fahrenheit 451” in electronic form provided that the publisher, Simon & Schuster, allowed the e-book to be digitally downloaded by any library patron. The title remains the only book in the Simon & Schuster catalogue where this is possible.

It took Bradbury just nine days to write Fahrenheit 451—and he did it in the basement of the UCLA library on a rented typewriter. (The title of his classic novel, by the way, comes from the temperature at which paper burns without being exposed to flame.)

Bradbury remained an enthusiastic playwright all his life, leaving a rich theatrical legacy, as well as literary. Bradbury headed the Pandemonium Theatre Company in Los Angeles for many years and had a five-year relationship with the Fremont Centre Theatre in South Pasadena. Not only was Bradbury highly creative with language—he was also an exceptional visual artist. He would use the basement office as his studio, doodling, sketching, and painting.

He once said that when he died, he planned to have his ashes placed in a Campbell’s Tomato Soup can and planted on Mars. A more fitting memorial is the one NASA gave him when they landed a rover on Mars a few months after Bradbury’s death in 2012: They named the site where Mars Curiosity touched down “Bradbury Landing.”

So what can we take away from Ray Bradbury that would help us as autodidactics? The first is obviously the use of libraries and reading. He was at the library three days a week for 10 years. Even if he spent only an hour or two, he still invested between 520 and 1040 hours of time in the library. But from other statements he made while doing fund raising for libraries we can see that he invested a lot more time than that. He said:

“I read everything in the library. I read everything. I took out 10 books a week so I had a couple of hundred books a year I read, on literature, poetry, plays, and I read all the great short stories, hundreds of them. I graduated from the library when I was 28 years old. That library educated me, not the college.”

So Bradbury in the 10 years he invested time in the library he read about 5200 books. You can see from this quote that he was investing that reading time focused on his primary interest which was writing and theatre. Earl Nightingale said many years ago that one hour per day of study in your chosen field was all it takes. One hour per day of study will put you at the top of your field within three years. Within five years you’ll be a national authority. In seven years, you can be one of the best people in the world at what you do. Bradbury did it for 10 years, and for more than an hour.

To paraphrase self-help guru Brian Tracy: Read all you can about your field. Subscribe to the executive book clubs and book summaries. Build your own library of important books in your field. Never be cheap about your education. If you read one hour per day in your field, that will translate into about one book per week. One book per week translates into about 50 books per year.

As autodidactics much of our primary focus will be on using books for learning. Even if you’re learning a more physical skill such as sailing or painting there are numerous books written by professionals in your area of interest. If you’re interest is more academic then the library shelves are full of things you need.

Where I live the library provides an online catalogue of all their books, not just in my local library, but all the libraries run within the district I live in. They allow me to place an order for any book in any of the 75 libraries under their control and they will deliver it to my local library for me to walk over and pickup. While not every library provides this type of service, it is certainly worth investigating what is available to you via your local library.

Libraries contain not only books for study, but audio and visual works as well. If you’re learning a language then there is a good chance you can pick up some courses at the library with audio included.

Another thing we can take away from Ray Bradbury is the concept of Synergistic Learning. I don’t mean some kind of new-age buzzword. But rather knowledge gained in pursuit of one area, often has application in others. Bradbury introduced a concept of magic or mystery into many of his stories, and used the plays and poems he’d read to help give his writing a more lyrical feel. He applied his writing to a number of areas. In fact Bradbury’s first pay as a writer was for a joke he sold to comedian George Burns.

Being an autodidactic typically means that you’ll be learning more than one topic. These topics of interest can spread over a widely divergent set of things, but can be related. Synergistic learning is simply looking at your various topics of interest and seeing if there is any common ground. If there is you can focus on that area and gain knowledge in two interests not just one. For example, many topics need a good knowledge of maths.

Often we think of self-study as being simply sitting at a desk with a textbook. While that is valid, it isn’t the only thing that should be done. If you’re interested in Nutrition Science. You shouldn’t just be reading textbooks, you should try to also read websites, government guidelines, weight watchers magazines, cooking books, watch YouTube cooking channels, read about agriculture techniques, gardening books, wine and food magazines, etc.

Don’t narrow your focus too much, try to keep an open approach. You can focus when you start to get overwhelmed with information, but having a wider general knowldege of the subject will benefit you when you narrow your focus as well.

Well that is all for this week. If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also let me know if you find these explorations of the methods used by other autodidactics useful, and if there is someone in particular you’d like me to research. As always you can leave feedback on the website autodidactic.info, or send me an email to rick@autodidactic.info.

Thank you very much for listening.

Actual Fluency Podcast

S2EP2: Exploring the study methods of Ben Franklin.

The Autodidactic Podcast
S2EP2: Exploring the study methods of Ben Franklin.
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Hello and welcome to the Autodidactic podcast, season 2 episode 2. I’d like to apologise for the delay in getting this weeks episode out. I ran into some technical issues and also getting a quiet area to do the recording. Hopefully I’ll be able to be more consistent in future.

This week I’m going to start delving into the lives and study methods of autodidactics through the ages and into modern times. I’m going to start with a person who most listeners inside the United States would need no introduction. I haven’t yet worked out the format of these podcasts about autodidactics, but I will generally start with telling you a little about the person, what they accomplished, and what we know of their methods. Then I’ll try to dig a little deeper into the methods they used and relate it to what we can emulate today.

The person I’m going to talk about today is Benjamin Franklin. Ben Franklin was born in what would become the United States on January 17, 1706 and died on April 17, 1790. Franklin was an American autodidactic and one of the Founding Fathers of the United States. He was a leading writer, printer, political philosopher, politician, postmaster, scientist, inventor, humorist, civic activist, statesman, and diplomat. Franklin became a successful newspaper editor and printer in Philadelphia, the leading city in the colonies, publishing the Pennsylvania Gazette at the age of 23.

Benjamin Franklin became a luminary in everything from politics to physics, and he did this without modern educational techniques such as schools, teachers, or the Internet.

Franklin was a prodigious inventor, but Franklin never patented his inventions. Probably the first advocate of opensource/open knowledge movement he wrote: “… as we enjoy great advantages from the inventions of others, we should be glad of an opportunity to serve others by any invention of ours; and this we should do freely and generously.”

Franklin studied, electricity, ocean currents, population and demography, wave light theory, meteorology. He was an avid chess player, and with a friend learned Italian. The loser of these matches had to perform some task given by the winner, such as reciting sections of Italian grammar, or 100 animal names at the next meeting.

Ben Franklin’s autobiography can give us many clues about the man and how he used his time and many of his writings are available online to read. I’ll put links to his writings at the end of the transcript on the autodidactic.info website.

Although there is a lot to learn from his writings, I believe that Franklin had two methods we can emulate as autodidactics. The first is known today as “deliberate practice” and the second is measurement or monitoring.

Of all the things Franklin does these two things lend themselves most to self-study and autodidactism.

First let’s look at deliberate practice. What is it?

Deliberate practice refers to a special type of practice that is purposeful and systematic. While regular practice might include mindless repetitions, deliberate practice requires focused attention and is conducted with the specific goal of improving performance. What sets deliberate practice apart from other training methods is a rigorous sequence of ongoing performance assessment, tailored goal-setting, and systematic skill-building informed by expert feedback.

Franklin shows us how he used deliberate practice when he taught himself to become an author and better writer. Let me read an excerpt from his autobiography.

About this time I met with an odd volume of the Spectator. It was the third. I had never before seen any of them. I bought it, read it over and over, and was much delighted with it. I thought the writing excellent, and wished, if possible, to imitate it. With this view I took some of the papers, and, making short hints of the sentiment in each sentence, laid them by a few days, and then, without looking at the book, try’d to compleat the papers again, by expressing each hinted sentiment at length, and as fully as it had been expressed before, in any suitable words that should come to hand. Then I compared my Spectator with the original, discovered some of my faults, and corrected them.

—Benjamin Franklin, Autobiography

Here Franklin is doing what is known as “deliberate practice” in order to improve his writing. K. Anders Ericsson likens it to how artists practice by trying to imitate some famous work. Mathematicians are taught to attempt to prove most theorems themselves when reading a book or paper — even if they can’t, they’ll have an easier time compressing the proof to its basic insight.

Deliberate practice can be used to learn any skill from music to computer programming.

Let’s use some examples of how you could use deliberate practice for something other than writing as Franklin does.

Many people are self-taught programmers who use a programming textbook to learn a programming language. But if you just read the book and cover to cover you’ll not get the maximum value from it. Instead when you come to a section in a chapter showing a small snippet of code to open a file. Look at the snippet, close the book and actually try to create the program yourself without opening the book. Chances are you’ll fail, however when you open the book back up you’ll be able to compare your work against the snippet. You’ll get some immediate feedback about where you’ve gone wrong.

Otherwise when studying you can use this method by simply reading a page of the book you’re learning from, a recorded lecture, etc. Close the book or pause the video/audio and try to write down everything you’ve just read or listened to. Try not to do a summary, but to remember everything. It would be tedious to reproduce and entire book verbatim but this method would give immediate feedback about knowledge gaps. It might show you that the information you’ve missed tends to always been at the end of paragraphs, so you can modify your behaviour to focus on the end of paragraphs as well.

But deliberate practice is bigger than this. The exerpt I read from Franklin didn’t cover the three primary things you must do for deliberate practice. Mostly because Franklin himself had done the other steps “off camera”.

The three steps are:

  1. Have a specific goal, and break it down – Break down what you want to know or practice into a well defined small amount. For a textbook this might be into chapters for example.
  2. Create a plan – Have a written plan for how you’re going to practice, with times and a schedule. For example, you might decide on a chapter per week, with X number of exercises.
  3. Get a coach (or some form of feedback) – this is probably the most important thing to have. Remember Franklin used the original Spectator articles as feedback to compare against his own writing. You also need some type of feedback mechanism. In the programming example you have the authors version of the file opening snippet.

When you do your plan you need to keep your goal in mind. When you break this down into practice sessions you need to have a goal in mind for each section.

Goals like:

  • Play or sing a certain song at a specific speed with no mistakes three times in a row.
  • Memorise the first 10 digits of pi.
  • Type at 50 words per minute with no errors.
  • Summarise each page of the textbook with no gaps.

If you’re interested in deliberate practice I recommend the book Peak by K. Anders Ericsson

The other area we can emulate from Franklin is tracking or monitoring of progress. Franklin had a little book where he would track his errors each day, monitoring himself to try to improve.

A phrase most managers in most companies will immediately recognises is “You get what you measure.” It’s human nature to shoot for the objectives set, and it is human nature to pay attention to the metrics which are being measured. However, a word of caution here. You need to make sure that you’re measuring the correct thing, or that the instrument you’re using to measure is correct. Just measuring time studying doesn’t indicate amount learned.

Sir Arthur Eddington, an English astrophysicist, told a short story involving a scientist studying fish by pulling them up with nets. After checking all the fish hauled up, the scientist concludes that there is a minimum size of fish in the sea. But the fish seen were determined by the size of the holes in the net, the smaller ones having slipped through, unmeasurable. The instrument you use affects what you see.

So you need to think carefully about what you are trying to learn and try to find a way to measure your ability.

If you are learning from a textbook you might create a simple form to fill out at the end of each chapter with some questions rating from 1-7 where 1 is defiantly not, and 7 is defiantly yes. Some statements might be:

“I understand ALL the concepts in this chapter.”

“I found this chapter easy.”

This type of survey would let you judge how well you learned from this book, and if you should re-read, or find an easier or more difficult resource.

If you were learning a skill such as learning how to remember names you might score yourself 2 points for all names remembered and -1 point for any name forgotten. Then you review your scoreboard each week, plotting it to spot trends. You might discover you typically fail to remember when introduced to a group of people at the same time, but are ok individually. Then you can use deliberate practice to focus on remembering names at group introductions.

If you were learning photography you might have your photos scored based on framing, lighting, focus, filtering, exposure, etc. Then you design practice sessions with deliberate practice on the elements you score low in.

For monitoring you need to:

  • Break down and list your goal into things which can be measured.
  • Eliminate things from the list who’s measurement isn’t essential
  • Be clear on what you need to measure, why you are measuring it, and how you’ll measure it.
  • Schedule periodic reflections on the measures
  • Design repetitive, deliberate practice to overcome measured defects.

Remember you can’t improve what you don’t measure, but measuring the amount of time spend generally isn’t useful. Review what you’re measuring in order to design better practice, and review your measures to ensure you’re still measuring essential matrix.

Well that is all for this week. If you enjoy the show, please give a rating on the platform you’re using to listen, and please share the podcast with friends and family who might be interested. Also let me know if you find these explorations of the methods used by other autodidactics useful, and if there is someone in particular you’d like me to research. As always you can leave feedback on the website autodidactic.info, or send me an email to rick@autodidactic.info.

Thank you very much for listening.

Writings of Ben Franklin

NOTE: I apologize for the transcript not being 100% accurate this week, I had some difficulties getting it out.

S2EP1: Season Two Introduction – The Why

Welcome back to the first episode of Season Two. I’ll be talking about the plans for this season, and why you should be an autodidactic.

The Autodidactic Podcast
S2EP1: Season Two Introduction - The Why
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Hello and welcome back to the autodidactic podcast, episode 1 season 2. If you’re a returning listener Welcome back! If you are new to the podcast then welcome aboard.

This episode I want to just give a brief introduction to the new season and the types of things I’ll be covering. Let me start by quoting the first few lines of a Rudyard Kipling poem.

I KEEP six honest serving-men
(They taught me all I knew);
Their names are What and Why and When
And How and Where and Who.

Season one of the podcast was focused primarily on how to study and various methods to use. This season I’d like to explore two of Kipling’s honest serving men, Why and Who. So I’ll do this episode on why being an Autodidactic is a good goal to pursue and the remainder of the season I’ll focus on Who.

Therefore, the season will primarily focus on Who. The reason for this is that I believe if we look at some autodidactics such as Charles Darwin, Benjamin Franklin, Malcolm X, and many others we can try to discover and adopt their methods for learning.

In many cases it is difficult to find any record of the methods which they used for study. Some are relatively easy to find information about, for example Ben Franklin wrote about his methods in his autobiography. Others we’ll have to find through research and contemporary writings.

I would also like to attempt to interview some living autodidactics and try to understand their methods.

But first let’s get into the Why of becoming autodidactic and what I mean when I talk about an autodidactic.

An autodidactic is a person who is a life-long learner and while they might study for to enhance their careers or job prospects when I speak of an autodidactic I’m talking about someone who doesn’t just learn for work purposes. A Uomo Universale an ideal developed in Renaissance Italy which considers humans limitless in capacity for development and that everyone should embrace knowledge and develop their capacities to the full. Exemplified by Leonardo da Vinci (1452–1519), whose gifts were in the fields of art, science, music, invention, and writing.

Many of the benefits and reasons why someone should be autodidactic will apply to both autodidactics and anyone who is learning by themselves.

The first two reasons are ones that everyone can relate to, they are time and money. Self learners can save money by not enrolling in formal courses and time as well. The reason a self learner can save time is they focus on what they don’t know and can skip information they already know. While in a classroom environment you would have to sit while the lecturer brings others up to speed with things you already know.

Self-learning is neither location constrained nor time-bound. With proper planning and tools you can do your study anywhere and at any time.

Another often over looked advantage is tangents. Self-learners are allowed to go off on a tangent and then return later, since they have no constraints. For example, while studying computer science you might spark and interest in basic electrical systems and spend a few months on a tangent where you learn more about electrical systems and maths related to electricity before returning to your computer studies.

When you contrasts this with formal education where you have to attend the classes or miss out, the obvious benefits of self-learning becomes apparent.

Then there are the emotional benefits. A sense of accomplishment and pride. It will also make you happier according to Vanessa King, a positive psychology expert. Scientific research from the 1990s shows, a challenged, stimulated brain may well be the key to a vibrant later life. These studies have also shown a link to learning and the delay or negation of mental and physical ailments and diseases.

The one thing in life which is guaranteed is change. Change is the only constant around us, and in modern society the pace of change continues to increase. Many people believe that the economy of the future will require people who can continue to learn new skills and continue to adapt. This is because many jobs are already being automated out of existence. Lifelong learning enables us to keep up with society’s changes – especially the technological ones.

An autodidactic with the notion of Uomo Universale will pick topics and skills to learn outside of the work they do. A relentless focus on building a single skill is not, for most people, the best formula for leading a happy life.

So these are some benefits for becoming autodidactic. Thanks for listening, and I hope you’ve enjoyed the podcast. I’m always interested in hearing what you’d like me to discuss. So as always you can email me at rick@autodidactic.info, or you can leave a comment on the website: https://autodidactic.info