David Berlinski - The advent of the algorithm (2000)

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For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake-there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?

David Berlinski
Validity is the touchstone of inference, and truth of judgment: the fact that vichyssoise is cold ratifies the judgment that vichyssoise is, indeed, cold, and the judgment that vichyssoise is cold expresses the fact that vichyssoise is cold.

David Berlinski
Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

David Berlinski
Some philosophers see into themselves, and some into their times; still others forge an alliance with the future.

David Berlinski
Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

David Berlinski
Bystanders wandered in and out of the merchant's stall, passing the time, talking of dreams they might purchase. Workers and slaves stooped from labor asked timidly for dreams of wine and ease. Women asked for dreams of love, and men for dreams of women.

David Berlinski
For all the great dreams profitlessly invested in the digital computer, it is nonetheless true that not since the framers of the American Constitution took seriously the idea that all men are created equal has an idea so transformed the material conditions of life, the expectations of the race.

David Berlinski
Leibniz endeavored to provide an account of inference and judgment involving the mechanical play of symbols and very little else. The checklists that result are the first of humanity's intellectual artifacts. They express, they explain, and so they ratify a power of the mind. And, of course, they are artifacts in the process of becoming algorithms.

David Berlinski
At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.

David Berlinski
The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they proceed from separate places in the imagination.

David Berlinski
In the end, every scheme and every science is justified by itself or it is not justified at all.

David Berlinski
The motion of the mind is conveyed along a cloud of meaning.~ There is this paradox that we get to meaning only when we strip the meaning from symbols.

David Berlinski
More than sixty years ago, mathematical logicians, by defining precisely the concept of an algorithm, gave content to the ancient human idea of an effective calculation. Their definitions led to the creation of the digital computer, an interesting example of thought bending matter to its ends.

David Berlinski