10 May 2010

What is Enlightenment?

The motto of the Enlightenment is not a thing of the past. It is modern and will always be so:
Aufklärung ist der Ausgang des Menschen aus seiner selbst verschuldeten Unmündigkeit. Unmündigkeit ist das Unvermögen, sich seines Verstandes ohne Leitung eines anderen zu bedienen. Selbstverschuldet ist diese Unmündigkeit, wenn die Ursache derselben nicht am Mangel des Verstandes, sondern der Entschließung und des Muthes liegt, sich seiner ohne Leitung eines anderen zu bedienen. Sapere Aude! Habe Muth dich deines eigenen Verstandes zu bedienen! ist also der Wahlspruch der Aufklärung.
Enlightenment is man's release from his self-incurred tutelage. Tutelage is man's inability to make use of his understanding without direction from another. Self-incurred is this tutelage when its cause lies not in lack of reason but in lack of resolution and courage to use it without direction from another. Sapere aude! "Have courage to use your own reason!" - that is the motto of enlightenment.
So the message of the Enlightenment is not, simply, the lack of reason but the lack of ability to use one's reason. Reasoning independently and with courage is what the motto of the enlightenment is. "Sapere aude" means "dare to know" and, by extension, dare to use your own reason, independently, without the guidance of somebody else, free of external influences even (or, perhaps, especially) when these influences are part of an established "tradition".

The message of the Enlightenment should be read and understood by all, even people working in the Academia (teachers and administrators alike).

Here is the original first page from Imanuel Kant's essay "Beantwortung der Frage: Was ist Aufklärung? -- Berlinische Monatsschrift, Bd. 4, 481-494, 1784".

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What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant