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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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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Bach Visualized Through Math

You've no doubt heard the claim that some of the greatest musicians of all time had an intuitive sense for mathematical proportion and harmony. It's no coincidence, for instance, that the musical scale was invented by that most eccentric of mathematicians, Pythagoras.

And if you're familiar with your Leibniz, you might remember that he once claimed that "music is the pleasure the human mind experiences from counting without being aware that it is counting."

Well, the following animation beautifully illustrates this abstract claim in as concrete a way as it is possible to do...

And if you need the sound of a more familiar rendition, we aim to please:

And why stop at music? Take a look at the the fibonacci sequence throughout nature.

May your day be blessed with beauty... and math :)

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Lecture 8 - Personal Identity

Science is great when it comes to discoveries and studies about the physical world. It requires lots of work and dedication, analytic skills to test various hypotheses, and a wealth of creativity to figure out how to conduct experiments to tell the merits of one explanation from those of another. For all of that, however, and without implying any denigration, it's also somewhat easy because you have the physical world itself to check your results against. If you think dropping heavy objects will float, the universe itself will let you know you're wrong...

Philosophical research, on the other hand, is more difficult because the object of our studies is concepts, and concepts will not smack you upside the head when you're wrong. Take one simple example for comparison: in science, you might study how something changes, and you can easily imagine the set of tools you might need to do the job. In philosophy, you'd study the nature of change itself. How on earth do you do that???

And the investigation of change is one of the philosophical questions par excellence, tracing its history all the way back to Heraclitus and Parmenides. In this final lecture, Professor Millican explores the question of personal identity: assuming that you do exist, what does it mean to say that your past self and your present self are the same person? How can it be the case that something that changes is still the same thing? That sounds like a logical contradiction, and yet pre-reflectively at least, this is what we all assume to be true.

Click here to see the course slides

And more awesome stuff on this and related questions, check out the Brainspotting tag.

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Julian Baggini - What Does It Mean to Be "You"?

The metaphysical question of personal identity is, to my mind, one of the most interesting and important there are in the philosophical literature. An obvious part of its importance has to do with the fact that many other philosophical, psychological, social and ethical issues depend on the answer to the question of whether the self exists and what it is.

Consider a thought experiment formulated by Leibniz: suppose you have the option to choose to have all the riches, talents, fame, good looks and lovers you desire, but on one condition: that you forget absolutely everything about yourself up to that point. Would you do it? If you answer is no, that implies that you think that whatever you are, your conscious experience and memories seem to be a necessary part of being you. So, no memories = no you. The new rich, talented, beautiful person would effectively be someone else. Imagine then a case of assault in which the victim loses all memory. Should this now count as murder?

In the following presentation, Julian Baggini explores the question of the self, whether it exists, whether it's an illusion, and whether we should understand an illusion as something that's not there, or as something that's simply not quite what we normally take it to be, but which is there nevertheless.

And if you want to listen to the whole thing, including an interesting Q&A, you can listen to it here:

For more on this issue, check out the Brainspotting series.

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