Don’t Doubt Descartes

Statue of the philosopher in Descartes, France

If you took an intro to philosophy course or even if you never took philosophy, the one phrase you might know is “I think therefore I am.” That comes from the man known as “the Father of Modern Philosophy,” – René Descartes.

Descartes was born in 1596 in La Haye en Touraine in central France. The city is now named for him. His book, Meditations on First Philosophy, was on the required reading list for my first philosophy course.

Descartes had not been a healthy child and spent a lot of time in bed. He was sent to Jesuit schools and got a degree in law. He moved to the Netherlands and he did most of the writing he is known for in the 20 years that he lived there.

Queen Christina of Sweden invited him to Stockholm to be her tutor. She was 23 and he was in his 50s. While in Stockholm, he came down with pneumonia which caused his death.

When he wrote that famous phrase in 1637, what did he mean? He wrote it as “Je pense donc je suis.” and it was often written in Latin as “Cogito ergo sum” and translated to Englis as “I think therefore I am.”

It is a summary statement from his Discourse on the Method. He was thinking and writing about some of his ideas about science which included theories (like those of Galileo) that were controversial at the time. His intention was to write a proof showing that skepticism about the laws of nature is necessary for understanding nature.

This “methodological skepticism” meant he would reject any idea that could be doubted. Them he would need proof for the idea so that it could be accepted as knowledge.

In all this doubt, he could even doubt his own existence. One thing he could not doubt was the existence of his own thoughts. If he was doubting, he was thinking. If he was thinking, then he existed.

“Of philosophy, I will say nothing, except that when I saw that it had been cultivated for so many ages by the most distinguished men; and that yet there is not a single matter within its sphere which is still not in dispute and nothing, therefore, which is above doubt, I did not presume to anticipate that my success would be greater in it than that of others.”

Zero Is Not Nothing

“If you look at zero you see nothing;
but look through it and you will see the world.” – Robert Kaplan

“an O without a figure” – William Shakespeare, King Lear

“Where did you go?”
“Then why are you late?”
– exchange between a father and son
on a Sumerian clay tablet from 5000 years ago


I remember vividly when one of my sons at age 5 realized that zero was very important. He has a mathematical mind (he ended up in the finance world) and it hit him that nothing in math works without zero. He would discover in the years to come that it plays a role in many other things too.

It is a symbol of what is not there. Add a zero with any number and it does not change. Add a zero to the end of any number and it increases. A bit of a paradox.

This concept was invented (or is the proper word “discovered”?) in pre-Arab Sumer. It got a symbolic form in ancient India.

It obviously is mathematical but it figures then into other areas as large as the universe itself.  Mathematician Robert Kaplan follows this symbol’s history in his book The Nothing That Is: A Natural History of Zero. It is partially a cultural tale, part scientific discovery, part law of nature and it has a few strokes of Romance.

The Sumerians counted by 1s and 10s but also by 60s. That’s not so foreign to us if you consider our 60 minutes in an hour and that 6 × 60 = 360 for the degrees in a circle. Kaplan reminds us hat we have a bunch of number systems: 12 for months in a year, 7 for days in a week, 24 for hours in a day and 16 for ounces in a pound or a pint. All these systems were our ways of trying to make sense of the universe. and gigantic concepts like Time.

Our ancestors pre-zero were clearly handicapped in dealing with large sums. (Kaplan says to try multiplying CLXIV by XXIV.) The mathematically astute Greeks didn’t really have zero. It was Indian mathematicians who treated zero like any other number, instead of as a symbol.

I find math fascinating but have always been math-phobic and always struggled with math courses once we got past the arithmetic and into algebra and beyond. So, I enjoyed the story of zero. For example, how in the Middle Ages, zero comes to western Europe via Arab traders.

It was considered “dangerous Saracen magic” and associated with the Devil. But those who worked with numbers every day were not only the rare mathematicians but any merchants or money lenders.

All this leads to double-entry bookkeeping, equations, the invention of calculus, and the scientific revolution. Leap into our lifetimes and most people know that computers see everything as zeros and ones.

Kaplan’s other books were on the library shelf besides this one and they are all math-related. The other title that got my attention is The Art of the Infinite. (It has a subtitle that may seem impossible to some of us: “The Pleasures of Mathematics.”) I do recall that for me as a child it wasn’t so much zero that caught me by surprise as it was infinity.
I think I have come to understand zero. I’m not sure I have any greater grasp of infinity than I did as a child. In the same way that I now know much more about the stars and the heavens than I did as a child, I still look up at the night sky with a childlike wonder and know I will never understand it all. Others know far more than me and yet they will never understand all of it. In physics and cosmology, whether the Universe is infinite is still an open question. My lack of knowledge and my wonder are infinite.

I asked earlier if zero is discovered or invented, and it turns out that this was a question famously debated by Kurt Gödel and the Vienna Circle. Kaplan writes, “The disquieting question of whether zero is out there or a fiction will call up the perennial puzzle of whether we invent or discover the way of things, hence the yet deeper issue of where we are in the hierarchy. Are we creatures or creators, less than – or only a little less than — the angels in our power to appraise?”

Other cultures, disconnected from Mesopotamia, Greece, India, or Europe, such as the Mayans, also had to discover zero. (Ah, “discover” – and so I have revealed my answer to that question.)  As infinity began as a philosophical concept before it became mathematical, zero moved from math to philosophy.

Nothingness as a philosophical term is a huge topic of its own. Nothingness is the general state/domain/dimension of nonexistence. It is where things pass to when they cease to exist. But it can also be where they come into existence, as in some cultures where God is understood to have created the universe ex nihilo, “out of nothing.”

Nothing is infinite.

Yes, I see the paradox.

book cover

Hozro and Hiraeth

“Everything is connected. The wing of the corn beetle affects the direction of the wind, the way the sand drifts, the way the light reflects into the eye of man beholding his reality. All is part of totality, and in this totality man finds his hozro, his way of walking in harmony, with beauty all around him.”
Tony Hillerman, The Ghostway

balanced stones
Image by daschorsch

I came upon two new words recently that come from very different places and cultures, but both resonated with my state of mind this past week.

Hozro is the Navajo word meaning to be in harmony with one’s environment, at peace with one’s circumstances, and free from anger or anxieties. If that isn’t enough, it means you are walking in harmony, content with the beauty all around him.”

It is about balance; about personal and communal beauty that adds its voice to the whole blended ensemble of creation.

Hozho is about real-world harmony and balance in the trenches of life, not the weekend retreat, ”don’t-worry-be-happy varieties.” In the novel Sacred Clowns, Jim Chee, a Navajo detective, is the way author Tony Hillerman explores what it is like to be born among the Dine’ and live on the reservation through novels of mystery. Chee explains hozho in this way:

“This business of hozho… I’ll use an example. Terrible drought, crops dead, sheep dying. Spring dried out. No water. The Hopi, or the Christian, maybe the Moslem, they pray for rain. The Navajo has the proper ceremony done to restore himself to harmony with the drought. You see what I mean? The system is designed to recognize what’s beyond human power to change, and then to change the human’s attitude to be content with the inevitable.”

In hozho, harmony and balance are real and it is a realistic goal in life. You don’t find this harmony outside or in things. You find in your own heart and mind.

Not everyone I know could accept this philosophy. Some people I know want to change the world. That is not the wrong thing to do. There are things that need changing and some of them you yourself can change or at least help change. You could view hozho as acceptance. “I can’t change the climate so I just accept it.”

Adjusting ourselves to reality is an easier and certainly less stressful way to live. It seems to me that this philosophy is more about the things we can’t change. Unhappy about how the weather has “ruined your plans” this weekend? You can’t change it, so adjust yourself.

There is also a belief in certain inevitabilities in hozho. Certain things are going to happen – aging and death amongst the big ones – and fighting to change these things is harmful. I don’t think it means to ignore your health and habits and “come what may” but to battle aging every day makes what life you have left less enjoyable.

nostalgia photos
Image by Michal Jarmoluk

On the other side of the world, I found hiraeth, a Welsh word that has no direct English translation. I found it defined as a combination of homesickness, grief, and sadness over the lost or departed. The closest synonyms in English seem to be “longing, yearning, nostalgia, or wistfulness.” For the Welsh, it seems to be those feelings about the Wales of the past, but the concept is not uniquely Welsh.

The etymology is that it is derived from hir and aeth and literally means “long gone.” The word appears in the earliest Welsh records, including early Welsh poetry. This is not a new feeling.

The word came into the English language in the 19th century. Historically, from 1870 to 1914, approximately 40% of Welsh emigrants returned to Wales. Was it hiraeth?

These two words and their larger meanings don’t seem similar to me. In fact, I see them as opposites in a way. That longing for things long gone in hiraeth is a yearning for things that can never return, such as a lost loved one, or the world, real and imagined, of your childhood. Those kinds of feelings certainly would not enhance any harmony or balance in your life. It means an unacceptance of some inevitabilities.

Everything is connected. The past is settled. You have the present to live in. The future is not completely undetermined but you have the ability to change some of it. If you believe in an afterlife, you are determining what it will be today.


Virginia’s Relativity

                 Virginia Woolf at age 20


Doing some research reading on Virginia Woolf for a post yesterday about her novel To the Lighthouse, I came across an article that made what seemed like a weird connection between Woolf and Albert Einstein.

Imagine this: Virginia has a conversation with poet William Butler Yeats. It is 1934. Yeats wanted to talk about her very experimental novel from 1931, The Waves. Yeats’ interpretation of it was mystical and he had visions of “the Occult.”

She wrote in her diary after the conversation that you “can’t unriddle the universe at tea,” She also noted that Yeats had said that “Neither religion or science explains the world. The occult does explain it.”

Virginia was more interested in science than the occult. She was interested in physics and astronomy. Albert Einstein’s Special and General Theories of Relativity were news in 1905 and 1915 respectively and astronomer Arthur Eddington proved (observationally) relativity in 1919, and it became something heard by (but not really understood by) the general public.

What might a novelist do with Einstein’s theory that events in time are not the same everywhere for everyone? It could certainly change how you used time as a narrative structure.  That is what is happening in To the Lighthouse and the article’s author sees the influence in her Orlando, and The Waves, which are two novels I don’t know very well.

Virginia – and others in and out of the literary world – were influenced by Einstein’s view that this is a non-linear, probably godless and probably impossible to fully understand the world and universe.

The article goes into much greater detail but what seems to at least partially have created some of the popularity of his theories in the culture was that they were just so damned counter-intuitive. They turned earlier ideas upside down.

Did Woolf read Einstein’s work? Not clear. She might have just heard it in conversation with friends like philosopher Bertrand Russell who published the ABC of Relativity in 1925. Maybe she read some of the many newspaper accounts. 

Did it get her thinking in such a way about narrative that the character Orlando in that same-named novel is a boy in Shakespeare’s time but later wakes up as a woman in the 20th century? Time in the novel is relative and it moves much more slowly for Orlando than for the rest of his/her world. That’s a paradox that Einstein suggests, though not in such an extreme fashion.

Yeats wanted her to consider that there is a world beyond this one we see. Einstein would agree, but he wouldn’t explain any of it as mystical or having to do with religion. Either would Woolf, who would have a character in Mrs. Dalloway say that “there were no Gods; no one was to blame; and so she evolved this atheist’s religion of doing good for the sake of goodness.” It’s a philosophy of simplicity and seeing the marvelous in every day.

And yet, her life ended in suicide. She finished her last novel and fell into another depression as she had before. It was the start of World War II and her London home was destroyed during the Blitz. Her diary was full of thoughts about death. Woolf was overtaken by mental illness throughout her life and was institutionalized several times and attempted suicide at least twice. Her illness may have been bipolar disorder, for which there was no effective intervention during her lifetime. On March 28, 1941, she filled her overcoat pockets with stones, walked into the River Ouse near her home and drowned. She left a suicide note, addressed to her husband:

I feel certain that I am going mad again. I feel we can’t go through another of those terrible times. And I shan’t recover this time. I begin to hear voices, and I can’t concentrate. So I am doing what seems the best thing to do… 
I can’t go on spoiling your life any longer. I don’t think two people could have been happier than we have been.  V

Occam’s and Other Razors

William of Ockham.png
William of Ockham CC BY-SA 3.0, Link

I was explaining recently to someone a reference in the program The Undoing to Occam’s razor. It’s a pretty well-known problem-solving principle, sometimes called the principle or law of parsimony. It states that simpler explanations are more likely to be correct and that you should avoid unnecessary or improbable assumptions.

But why a “razor”?  The principle is attributed to William of Ockham (or Occam), an English Franciscan friar, scholastic philosopher, and theologian, who is believed to have been born in Ockham. But the principle had nothing to do with his shaving habits.

In philosophy, a razor is a principle or rule of thumb that allows one to eliminate (“shave off”) unlikely explanations for a phenomenon, or avoid unnecessary actions.

There are several other razors or razor-like principles that you hear referenced or applied less often.

Paul Grice, a philosopher of language, also has a razor principle of parsimony. Parsimony refers to the quality of economy or frugality in the use of resources. For linguistic explanations, conversational implications are to be preferred over semantic context. This gets more complicated than Occam’s Razor. Grice worked in pragmatics, a subfield of linguistics and semiotics that studies how context contributes to meaning.

I am a fan of the simpler Hanlon’s razor: Never attribute to malice that which can be adequately explained by stupidity.

Hitchens’s razor seems appropriate to much in the news the past decade: What can be asserted without evidence can be dismissed without evidence.

Hume’s Guillotine is a larger and more complex razor: What ought to be cannot be deduced from what is. “If the cause, assigned for any effect, be not sufficient to produce it, we must either reject that cause or add to it such qualities as will give it a just proportion to the effect.” Hume’s law or Hume’s guillotine is the thesis that, if a reasoner only has access to non-moral and non-evaluative factual premises, the reasoner cannot logically infer the truth of moral statements.  This is also less-interestingly called the is-ought problem.

The Sagan Standard is a neologism abbreviating the aphorism that “extraordinary claims require extraordinary evidence.” It is named after Carl Sagan who used that exact phrase on his television program Cosmos, though he was not the first to state it. It illustrates a core principle of the scientific method and of skepticism.

Karl Popper’s falsifiability principle: comes from the philosophy of science. For a theory to be considered scientific, it must be falsifiable. For example, the statement “All swans are white” is falsifiable because “Here is a black swan” contradicts it. That seems clear. But what about “All men are mortal”? It is not falsifiable because, unlike a swan being black, a man being immortal is not an inter-subjective property—there is no shared procedure to systematically conclude to immortality. You can think about that one for a bit.

The exciting Newton’s Flaming Laser Sword (I’m not making up these names.), states that “If something cannot be settled by experiment or observation, then it is not worthy of debate.” It is also known by the less exciting name of Alder’s Razor.


That Dialogue on Opposing World Systems

Galileo, Copernicus
Galileo and Copernicus    (Gilgub/Flickr)

The title “Dialogue Concerning the Two Chief World Systems” certainly sounds like a heavy topic. It was heavy in 1632 when Galileo published it. The two systems were the Ptolemaic and the Copernican theories of cosmology. It is less controversial and easier to understand today.

Ptolemy, following the tradition of Aristotle, believed that the Earth was the center of the universe, and everything — Sun, Moon, planets, and stars — revolved around it.

Copernicus, on the other hand, posited that the Sun is the center of the universe, and though we seem to be standing still, we are in fact hurtling through space as we circle the star.

I used to have a quotation in my middle school classroom for my students that said “You are not the center of the universe” – Copernicus. Nicholas didn’t say exactly that quote, and he wasn’t specifically referencing my young teen students, but it was a good point-of-departure quote for discussion.

Galileo had spoken with Pope Urban VIII earlier and discussed his tide theory as proof that the Earth moved through space – not that the Sun was the center of the universe. The Pope granted him permission to write “Dialogue on the Tides” but that the Copernican theory should be treated as hypothetical in the book. Wisely, Galileo wrote the book as a series of discussions between two philosophers. One believed in Copernicus, one believed in Ptolemy, and a neutral but well-educated layman served as a moderator. That got it past the Catholic censors.

But Galileo was Copernican all the way and the popular book did not please Pope Urban VIII who had Galileo tried by the Inquisition. They ruled that he was “vehemently suspect of heresy” and too close to endorsing Copernican theory and the book was placed on the Catholic Church’s Index of Forbidden Books.

Galileo was ordered to recant and recite weekly psalms of penitence. He spent the rest of his life under house arrest, and none of his later books were permitted to be published in his lifetime.

The Dialogue on Opposing World Systems remained on the Index of Forbidden Books until 1835. Change is slow in religion – but not in science.

Further Reading

The Essential Galileo