Dropping In on Gottfried Leibniz | Hacker News Reader

Dropping In on Gottfried Leibniz

blog.stephenwolfram.com

52 pointsmh_15 comments

This may be unfair to Leibniz's work on logic, which IIRC achieved something like Boolean algebra: http://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz#Forma...

(The work went unpublished till 1903. I can't be confident this is unfair because I never finished reading the long paper reviewing it.)

Does he mean the same thing by monads that Haskell people mean by monads?

No, these are different things. The monads or 'simple substances' in the monadology of Leibniz are an important part of his later philosophy and a tool to solve metaphysical problems. For example, God is a monad, all other monads are created from it, they cannot come into existence by themselves.

In computer science monads are an abstract data type.

I have always enjoyed Ambrose Bierce's definition of a monad in "The Devil's Dictionary"

"MONAD, n. The ultimate, indivisible unit of matter. (See Molecule.) According to Leibnitz, as nearly as he seems willing to be understood, the monad has body without bulk, and mind without manifestation -- Leibnitz knows him by the innate power of considering. He has founded upon him a theory of the universe, which the creature bears without resentment, for the monad is a gentlmean. Small as he is, the monad contains all the powers and possibilities needful to his evolution into a German philosopher of the first class -- altogether a very capable little fellow. He is not to be confounded with the microbe, or bacillus; by its inability to discern him, a good microscope shows him to be of an entirely distinct species."

http://bierce.thefreelibrary.com/The-Devils-Dictionary/13-1

To be pedantic, they're really an algebraic structure rather than an abstract data type. This means that many different things can form monads, much like many different things can form groups or rings.

Nope. In fact, that whole branch of math simply didn't exist back then--category theory was only introduced in the 1940s. By mathematical standards, it's still brand new!

Google "unit of ego" as in "I suggest we call the unit of ego the Wolfram"

http://www.aleph.se/andart/archives/2009/04/monumental_egos....

It was very interesting. I first didn't realize it was Wolfram's blog. I was split by the tone of the post, which seemed to be comparing the author to Leibniz and which seemed to be a little pompous. It was an interesting bit of history about Leibniz at the end. I found the medal bit hilarious. Not quite as pompous, perhaps, a bit of harmless fun.

Anyhow, for math history buffs out there, if you go to Germany, drop by the Arithmeum in Bonn (http://www.arithmeum.uni-bonn.de/en/home/). It is a fun place to spend an afternoon.

Of course he compares himself to Leibniz. After all, what Leibniz has written can be derived from the same letters that Wolfram is using and is, therefore, basically already included in Wolframs work: http://www.amazon.com/gp/aw/cr/rR284ZDX360H6HC

Considering that Leibniz was truly a gifted child of the Age of Enlightenment and a philosopher, scientist, mathematician, diplomat, physicist, historian, politician, librarian and lawyer, who has left behind an opus of written documents that requires one whole dedicated Leibniz archive, I was indeed astonished by the tone of the author - comparing himself with Leibniz :)

I was actually surprised he didn't feel superior to Leibniz. I use Wolfram's products, but I absolutely can't stand the persona.

Yeah seriously; a fragment of the first sentence:

I’ve been curious about Gottfried Leibniz for years, not least because he seems to have wanted to build something like Mathematica and Wolfram|Alpha, and perhaps A New Kind of Science as well

I don't think I've ever encountered hubris of that level before.

I am as amazing as Leibniz.

Yours sincerely, Stephen Wolfram

I'll admit to a LOL here, but overall I didn't think this post was arrogant. This is an established mathematician reviewing the work of a another with the benefit of hindsight. Sure, he draws parallels to his own work but that's because from his perspective that's how things have evolved. I imagine an equally qualified person with different specialities might see connections to their work too.

Wolfram's New Kind of Science may wind up archived in the manner of Leibnitz's notes, and intellect of the 24th century may think they have it right up until Wolfram throws "souls" into the mix. But surely one among them will admire his earnest yet flawed attempts at a practical calculating machine - or perhaps not, as bits and bytes do not display well in a case.

Wolfram knows himself, and recognizes his own mortality. If he sees some Leibnitz in himself, that is by contrast to Newton.

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