It has been noted that one needs only 39 digits of Pi to make a circle the size of the observable universe accurate to one atom of hydrogen.
Today is the birthday of one of my personal heroes.
Augusta Ada King, Countess of Lovelace
Ada was the only legitimate child of the English poet, Lord Byron. Born in the 1800s, she was part of a world that didn’t have many female scientists and mathematicians like her.
Why was she badass?
Among her many other accomplishments, Ada is widely considered to be the world’s first computer programmer.
In 1842–43, Ada translated an Italian manuscript on Charles Babbage’s proposed Analytical Engine, the very first design for a Turing-complete general purpose computer. With the article, she appended a set of notes explaining the Analytical Engine’s function.
This was difficult, considering other scientists did not actually grasp Babbage’s concept. The notes she left were longer than the manuscript itself and included, in complete detail, a method for calculating a sequence of Bernoulli numbers with the Engine.
When the first complete Babbage Analytical Engine was completed in 2002, her method was found to successfully and efficiently run on it. Yes, the algorithm she wrote in the notes of a translation she did, for a computing device the likes of which had never been seen and that had not even been built and wouldn’t be tested until 150 years after her death.
Although it is a bit silly, I like to think that one can trace a long line of female computer programmers down from Ada Lovelace. I learned my first programming languages from my mother. I’ll tear down any chauvinist who says girls can’t code.
Oh, sure, the program worked. But it still took 159 years to compile.
Brought to you by intothecontinuum:
To paraphrase Boolos paraphrasing Gödel paraphrasing himself:
It is true that 2 plus 2 is 4. I hope you can at least believe that much. Of course, it can be proved ⊢ that 2 plus 2 is 4. It can also be proved that it can be proved ⊢⊢ that 2 plus 2 is 4.
Moreover, it can be proved that it can be proved that it can be proved ⊢⊢⊢ that 2 plus 2 is 4. We could continue in this seemingly trivial manner, but what we are hoping for is that 2 plus 2 is not 5. Fortunately, it can be proved ⊢ that 2 plus 2 is not 5, and that too can be proved ⊢⊢.
Now just to be on the safe side what we really should ask is if it can be proved that it can’t be proved ⊢⊬ that 2 plus 2 is 5…. It can’t! ⊬ ⊢⊬… In fact, no claim of the form “claim X can’t be proved” can be proved.
So thanks to Gödel … it can be proved that if it can be proved that it can’t be proved that 2 plus 2 is 5, then it can be proved that 2 plus 2 is 5.
⊢(⊢⊬X→⊢X)I would rather take an incomplete theory over a [unquestionably wrong, self-]inconsistent one any day. Wouldn’t you?
… pretty tanpura drones in the pitches of
A, respectively (which I suggest listening to with eyes closed and nice headphones).