Essential Thinkers #2 Pythagoras of Samos, Mystic and Mathematician

Probably born around the mid-sixth century BC no exact date is known as to when Pythagoras lived. Despite his name being familiar to every schoolchild for Pythagoras’ Theorem, which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the remaining two sides, it is likely that this was known both to the Babylonians – where Pythagoras is thought to have travelled in his youth – and the Egyptians.

Pythagoras was a somewhat shadowy figure and like Socrates after him wrote nothing himself, preferring to leave his students to document his thoughts. Reputed to be a mystic as well as a thinker, the school he founded would nowadays be thought of as a religious cult that taught many unusual and strange doctrines including, notoriously, the veneration for – and abstinence from eating of – beans. Pythagoras also preached reincarnation and the transmigration of souls and is largely responsible for the modern belief in numerology, later popularised by Nostradamus.

According to Pythagoras, the ultimate nature of reality is number. This idea developed out of his theory of music, in which he proved that the intervals between musical tones could be expressed as ratios between the first four integers (the numbers one to four). Since part of Pythagoras’ religious teaching consisted in the claim that music has a special power over the soul, infused as it is into the very fabric of the universe, the belief that number is the ultimate nature of reality quickly followed.

The Pythagoreans went on to venerate certain numerical patterns, especially the so-called ‘tetractys of the decad.’ The tetractys is a diagram that represents the first four numbers in a triangle of ten dots:

Both the triangle and the number 10 – the decad – became objects of worship for the Pythagoreans. In Pythagorean thought, the number 10 is the perfect number because it is made of the sum of the first four integers, as shown in the tetractys. The integers themselves were thought to represent fundamental ideas – the number one representing the point, two the line, three the surface and four the solid. Further, it was thought that there were ten heavenly bodies – five planets, the sun, the moon, the earth and a mysterious and invisible ‘counter-earth’ (probably invented to make the celestial number up to ten) all revolving around a central fire.

After Pythagoras’ death, his school splintered into two camps. One maintained his religious and mystical teachings, while the other concentrated on his mathematical and scientific insights. The latter continued to believe the nature of the universe must be essentially arithmetical. Units of number, points, were somehow thought to possess spatial dimensions and be the ultimate constituents of objects. An idea later criticised by both Parmenides and Zeno. The Pythagorean cosmology also encountered grave problems due to one of Pythagoras’ own discoveries. For Pythagoras had shown how the ratio of the diagonal through a square to its sides could not be expressed as a whole number. The problem of ‘the incommensurability of the diagonal’ led to the discovery – or invention, depending on your philosophical point of view – of irrational numbers. Though a major problem for the Pythagorean cosmogony, irrational numbers have proven a major and lasting development in mathematical thinking.

[Summarized from Philosophy 100 Essential Thinkers by Philip Stokes, 2012. Also watch Brief History of the Pythagorean Theorem https://www.youtube.com/watch?v=PrjTkWGLk2Q]

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Essential Thinkers #1 Thales of Miletus, the First Analytical Philosopher

Credited as the first philosopher of Ancient Greece, and therefore the founder of Western philosopher, Thales hailed from the Ionian seaport of Miletus, now in modern Turkey. Miletus was a major centre of development for both science and philosophy in Ancient Greece. Thales, probably born somewhere around 620 BC is mainly remembered as the pre-Socratic philosopher who claimed that the fundamental nature of the world is water. Aristotle mentions him, as does Herodotus, and these are really our only accounts of Thales’ background. However, his significance as a philosopher is not so much what he said, but his method. Thales was the first thinker to try to account for the nature of the world without appealing to the wills and whims of anthropomorphic, Homerian gods. Rather, he sought to explain the many diverse phenomena he observed by appealing to a common, underlying principle, an idea that is still germane to modern scientific method. He is also credited by Herodotus with correctly predicting that there would be a solar eclipse in 585 BC during a battle between the Medes and the Lydians. As such, Thales can with some justification be thought of as the first natural scientist and analytical philosopher in Western intellectual history.

Thales had other modern traits, for it also seems that he was something of an entrepreneur. According to one story, Thales made a fortune investing in oil-presses before a heavy olive crop – certainly he would have had to be wealthy in order to devote time and thought to philosophy and science in seventh century BC Ancient Greece.

According to his metaphysics, water was the first principle of life and the material world. seeing that water could turn into both vapour by evaporation and a solid by freezing, that all life required and was supported by moisture, he postulated that it was the single causal principle behind the natural world. In a crude anticipation of modern plate tectonics, Thales professed that the flat earth floated on water. Aristotle tells us that Thales thought the earth had a buoyancy much like wood, and that the earth floated on water much like a log or a ship. Indeed, many floating islands were said to be known to the sea-farers of Miletus, which may have served as either models or evidence for Thales’ theory. He even accounted for earthquakes as being due to rocking of the earth by subterranean waves, just as ship may be rocked at sea. From the port of Miletus he would have been familiar with the phenomenon of sedimentation, possibly believing it to be the spontaneous generation of earth from water, an idea held as recently as the 18^th century.

Having sought to give a naturalistic explanation of observable phenomena, rather than appealing to the wills of gods, Thales claimed that god is in all things. According to Aetius, Thales said the mind of the world is god, that god is intermingled in all things, a view what would shortly appear contemporaneously in a number of world religions, most notably Buddhism in India. Despite his metaphysical speculations being clearly mistaken, it seems that Thales was a modern thinker in more ways than one, pre-empting many ideas in religion, philosophy and science.

[Summarized from Philosophy 100 Essential Thinkers by Philip Stokes, 2012. Also watch Thales of Miletus in 5 Minutes https://www.youtube.com/watch?v=iiyGnaBnIqk]

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Benjamin Franklin's 13 Virtues in Life

Throughout history, people have been concerned about figuring out their values and trying to live by them. Benjamin Franklin (1706-1790), the American printer, author, diplomat, and scientist, was one of the writers of the Declaration of Independence. He also helped draft the U.S. Constitution. In his autobiography, Franklin explains how he tried to change his behaviour by describing and then trying to live by his values, which he called “virtues.” How are Franklin’s value applicable today? Which is Franklin’s values do you share?

The Thirteen Virtues

1)    Temperance: Eat not to dullness. Drink not to elevation.

2)    Silence: Speak not but what may benefit others or yourself. Avoid trifling conversation.

3)    Order: Let all your things have their places. Let each part of your business have its time.

4)    Resolution: Resolve to perform what you ought. Perform without fail what you resolve.

5)    Frugality: Make no expense but to do good to others or yourself, i.e. waste nothing.

6)    Industry: Lose no time. Be always employed in something useful. Cut off all unnecessary actions.

7)    Sincerity: Use no harmful deceit. Think innocently and justly; if you speak, speak accordingly.

8)    Justice: Wrong none by doing injuries or omitting the benefits that are your duty.

9)    Moderation: Avoid extremes. Forbear resenting injuries so much as you think they deserve.

10) Cleanliness: Tolerate no uncleanliness in body, clothes, or habitation.

11) Tranquillity: Be not disturbed at trifles or at accidents common or unavoidable.

12) Chastity: Rarely use venery* but for health or offspring – never to dullness, weakness, or the injury of your own or another’s peace or reputation.

13) Humility: Imitate Jesus and Socrates.

[Taken from: Franklin Benjamin, The Autobiography of Benjamin Franklin and Selections from His Other Writings. New York: Random House, 1994, pg. 93-95. *Sexual activity.]

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How to Increase Synapses In Your Brain

Back in the 1970s a neuroscientist by the name of Bill Greenough did some experiments with rats and their living accommodation. One poor group of rats drew the short straw and ended up living alone with nothing to do. The other group were bestowed and comparatively plush surroundings. They had exercise wheels, ladders to climb, and other rats to talk to. Greenough called it ‘the rat equivalent of Disneyland.’ These lucky rats soon became noticeably more physically and socially active, as far as laboratory rats can.

Things became really interesting when their brains were later examined. The ‘enriched’ environment rats had 25% more synapses (connections between a neuron and another cell) per neutron than their poor relatives. These additional synapses meant the rats were cleaverer and quicker to find their way through mazes and were able to learn landmarks faster.

[Source: Make Your Brain Work (2013) by Amy Brann. Pg. 26]

By enriching your world – be physically active and be more socialable,

you are going to upgrade your brain, making it easier and quicker

for you to work things out in the future.

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Focus Repetition Will Make You Think Faster

But then, Caesar from 'Planet of the Apes' is too smart

Michael M. Merzenich is famous for many experiments with monkeys. In one he trained a monkey to touch a spinning disk with a certain amount of pressure for a certain amount of time. The monkey was then rewarded with a banana pellet reward. The monkey’s brain was mapped before and after the experiments. What happened has huge implications. The overall area of that particular map in the monkey’s brain got bigger. This makes sense as more brain resources are being dedicated to the more frequently carried out tasks. The individual neuron’s receptive fields got smaller – more accurate – and only fired when small corresponding parts of its fingertip touched the disk. So there were more accurate neurons available to do this task.

Here’s where things get really fascinating. Merzenich found that as these trained neurons got more efficient they processed faster. This means that our speed of thought is plastic. Through deliberate, focused repetition our neurons are being trained to fire more quickly. They also don’t need to rest for as long between actions. Imagine how much more powerful and effective you would be if you could think quicker. It doesn’t even stop there, the faster the communications, the clearer, so more likely to fire in sync with other fast communications ultimately making more powerful networks. More powerful networks or messages make it more likely we’ll remember something.

[Source: Make Your Brain Work (2013) by Amy Brann. Pg. 24]

So if you want the benefit of faster thinking capacity

and the ability to recall things easily in the future,

then you need to pay conscious attention to one thing at a time.

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