The Birth of Calculus - Newton and Leibniz

Before you run away in fear of having seen the word calculus, let me preface this entry by saying that you don't have to understand how it works, or even be able to do it, to understand and appreciate why it's important and why calculus represents one of the greatest intellectual achievements of human history: the modern world would not exist without it. You may choose to turn a blind eye to it, but that doesn't make it go away, so why not embrace it?

And while you probably know that it was invented, that's right... invented, by two geniuses, Newton and Leibniz, working (mainly) independently of each other, do you know the differences in their approaches? If you've never quite had an appreciation for the beauty and elegance of math, the following short documentary, should be able to change that:

And if you don't know anything about the priority dispute between these two men, here is a short introduction to that regrettable nightmare:

Did you know both Newton and Leibniz were first-borns? From the perspective of evolutionary psychology, it makes a lot of sense why their priority dispute got so heated and cantankerous. Now Wallace and Darwin, on the other hand, were way later-borns, and look how that turned out :)

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Standing on the Shoulders of Giants

This famous phrase, made famous by Sir Isaac Newton, and celebrated ever since, may have been a public attempt at modesty and historical gratitude that was sure to endear him to, and inspire, subsequent generations of natural philosophers, but it may also have been a little bit of an underhanded insult to Robert Hooke, just the kind of thing Newton would do when his gigantic and fragile ego was wounded if anyone dared to question some of his ideas...

Still, the phrase has taken on a life of its own, and it is now used to describe the incredible scientific and technological progress that has taken humanity to the unique position of being able to question its own origin and place in the universe, and to actually start to answer those questions, change its environment, make its dreams more ambitious and then make those dreams come true. The following captivating video is a beautiful celebration of the cumulative knowledge and insight we've gained about ourselves and the universe in only a few centuries, and the amazing feats we've accomplished as a result, by standing on the shoulders of giants:

Hope you're inspired!

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The Fabric of the Cosmos - The Illusion of Time

In the first episode of the Fabric of the Cosmos series, we learned a little bit about the weirdness of space, so hopefully that massaged your brain enough for something even weirder: time.

Philosophers and scientists have been trying to understand what time is since antiquity, and one thing that they have found is that it's incredibly difficult to say anything about time without already presupposing it in some sort of viciously circular argument. Nevertheless, curiosity drives us to ask questions that we then have to test by conceptual analysis and by empirical means, and we often find out that these come in conflict with each other in ways that elude simple solutions.

There are philosophical accounts of time (and I'll provide a short introduction soon), as well as scientific accounts, most of which are based to various extents on some of the incredible insights to come out of Einstein's theories of special and general relativity.

So fasten your seat-belts as Brian Greene takes us on a tour to understand some of the deepest of mysteries: What is time? Does the past exist? Does the future? Can we change the future? Can we travel back in time? If so, can we change the course of history? And hey, if you can go back in time and meet your former self, which one is really you? That last one is more of a philosophical question, just to show you how badass we are :)

If your head isn't spinning by now, then you might want to get yourself checked into a hospital :)

And if you want to watch the original from NOVA, here it is:

Watch The Fabric of the Cosmos: The Illusion of Time on PBS. See more from NOVA.

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The Fabric of the Cosmos - What Is Space?

That's probably not the first question that comes to mind for most people when they wake up in the morning, but it is definitely one that has kept some of the greatest minds of all time awake at night. What exactly is space? Is it a substance? Is it merely a relationship between objects? Whatever it is, is it static or dynamic, absolute or relative, immanent or transcendent? If there no physical objects in the universe, would empty space still exist, or is that an incoherent question, like asking what happened before the beginning of time? Join Brian Greene in a fascinating (if gimmicky) exploration of one of the most fundamental scientific and philosophical questions in this first episode of The Fabric of the Cosmos:

And in case the youtube video stops working at some point, here's the original from NOVA:

Watch The Fabric of the Cosmos: What Is Space? on PBS. See more from NOVA.

For more related videos, check out the Elegant Universe Tag.

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A Brief History of Mathematical Geniuses

Math, unfortunately, is usually taught, and consequently thought of, as a set of cold, bloodless tools to solve practical and theoretical problems that are somehow removed from real lived experience.

However, the truth of the matter is that math has a fascinating and mesmerizing life of its own, and those who have really confronted its secrets have found it to be a source of love, respect, admiration, inspiration, despair, confusion and wonder. Whatever else it may be, math is not boring... not if you actually pay attention.

In the following set of short documentaries, which you should definitely share with your mathophobe friends, Professor Marcus du Sautoy explores the lives, the insights, the contributions and the influence of some of history's greatest mathematicians.

Newton and Leibniz:
     

Leonard Euler:
     

Joseph Fourier:
     

Evariste Galois:
     

Carl Friedrich Gauss:
     

The Mathematicians who helped Einstein:
     

Georg Cantor:
     

Henri Poincare:
     

Hardy and Ramanujan:
     

Nicolas Bourbaki:
     


What other mathematicians would you have included in this list?

And for a touching and fascinating biography/tribute to Cantor, don't forget to check out the spectacular documentary Dangerous Knowledge.

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Neil DeGrasse Tyson - The God of the Gaps

There are many reasons why lots of otherwise reasonable people don't 'believe' in the theory of evolution. Yes, some of it has to do with their religious background and with a lack of basic education concerning science generally and evolution specifically, but that can't be the whole story.

Part of it also has to do with the way our minds work. For instance, we have a natural tendency to think teleologically (in terms of goals, purposes and design) and in terms of agency (there must be some intentional mind or subject behind any given phenomenon), and so we commit a basic category mistake when we apply these modes of thinking (the manufacture of industrial and commercial goods) to non-teleological phenomena (like biological complexity and organic processes).

But it doesn't stop there. The problem is that as evolved creatures, we have inherited a set of cognitive quirks and biases that conferred our ancestors with practical benefits that are not always conducive to the attainment of truth. To add insult to injury, our cognitive biases often lead us to commit logical fallacies, like the God of the Gaps argument.

In the following fascinating and amusing presentation, Neil deGrasse Tyson explains how even some of the greatest scientific minds of all time, people whose education and intelligence are unimpeachable, when confronted with the limits of their own knowledge and understanding, quickly retreat to this pernicious mode of poor thinking. In the process, he draws some deliciously thought-provoking lessons.

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Lecture 2 - Introduction to Modern Philosophy

After a brief introduction to ancient philosophy and the intellectual revolution started by Galileo and Descartes in the 17th century, Professor Millican begins to provide a concise and fascinating summary of the intellectual developments and questions that the new science and philosophy would produce.

To begin with, we start with an account of Thomas Hobbes. Hobbes is mostly famous for his political philosophy, but in the context of this course, his importance is due to his thorough commitment to a naturalistic and scientific account of everything, including minds. His materialism, as you might imagine, was immediately understood to imply atheism, which is why he received the dubious distinctions of being considered the monster of Malmesbury, as well as the cause of certain natural disasters. Pretty powerful for a guy who didn't believe in hocus-pocus :)

Being dissatisfied with the Cartesian account of matter as extended space, Robert Boyle would produce a theory of matter as being composed of tiny corpuscles. He also introduced the idea of empty space, thereby clearing the conceptual landscape for Sir Isaac Newton to come up with his universal laws of motion. Newton's predictive success was unimpeachable, but his instrumentalist introduction of the notion of a 'force' of gravity got many wondering whether we were back to postulating obscure and occult explanations a-la Aristotle or a-la Christianity. Wisely, Newton claimed not to understand the nature of such a force ("I feign no hypothesis"), only that its postulation (right or wrong) helped him describe the phenomena experienced with more accuracy than any previous thinker. David Hume would jump on this idea soon.

Finally, we move on to John Locke's empiricism, as well as to Malebranche's occasionalist attempt to explain the necessary connection behing causal inferences, and to Bishop Berkeley's idealism as a response to the skepticism that kept coming from all directions.

Click here to see the course slides.
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