I not so think as
you dumb I am at least I
don’t think so … maybe
I have never understood math.
It was a long time until I got it that mathematics and arithmetic were not the same thing.
In his book, Who Got Einstein’s Office by Ed Regis, a history of the Institute for Advanced Study at Princeton where this feller got the idea that all the smartest people in the world could be brought together in one spot and think great thoughts and something great would happen, writes that: “To the uninitiated, mathematics is the paradigm of certainty, a model of rational perfection and absolute truth.”
I am not even real sure that that sentence means.
Like I said, I never understood math.
I had this creepy ability to read an algebra story problem then stare at the wall for awhile and write down the answer.
But could I follow the expected formula of writing out how I came by my answer of declaring variables and x + x * y – 100 then … and finally scribbling QED at the bottom of my paper?
Nope, couldn’t do it.
Which set me apart from my family who are a bunch of math nuts.
There are 11 kids in my family and we all attended Grand Rapids Creston High School.
Four or five of my brothers and sisters brought home the annual Math Trophy, a trophy coincidently named after the math teacher our Dad had when he went to Creston.
According to legend, Dad got a C.
One Thanksgiving weekend, I took all our kids over to my Mom’s to see all my family members who were in town for the holiday.
We got there to find a dozen of my brothers and sisters and nieces and nephews sitting at the big table … in silence, heads bowed over pieces of paper.
My brother Bobby looked up, he actually became a math teacher, saw me and said, “Grab some paper. We’re doing a calculus problem.”
I shook my head and tried to explain that I had looked at calculus problems before and gave up as they didn’t end with an = sign.
Honestly I cannot you tell what a calculous equation means in any way shape or from and down deep, I got’s no desire to learn.
SO it was some satisfaction that when I read Who Got Einstein’s Office, I came across Kurt Gödel.
Mr. Gödel was considered to be the second biggest name at the Institute for Advanced Study after Prof. Eisenstein and the two were great friends.
According to Wikipedia: Kurt Friedrich Gödel was a logician, mathematician, cosmologist, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly influenced scientific and philosophical thinking in the 20th century (at a time when Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor.
Gödel’s discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel’s incompleteness theorems two years later, in 1931. The incompleteness theorems address limitations of formal axiomatic systems. In particular, they imply that a formal axiomatic system satisfying certain technical conditions cannot decide the truth value of all statements about the natural numbers, and cannot prove that it is itself consistent. To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
I am not sure what most of that means but I guess it states he was pretty smart.
From reading Mr. Gödel’s profile in Who Got Einstein’s Office, it also it fairly clear that the man was pretty much a nut to the point that he felt someone was out to poison him so, logically, he stopped eating.
His friend, Prof Einstein, tried to get him to eat to no avail and Mr. Gödel starved himself to death, dying in a hospital weighing less than 80 lbs.
Also from what I gather, all that accomplishments listed by Wikipedia, the Gödel numbering and such all happened BEFORE he came to Princeton in 1953.
There is a great story about Mr. Gödel in 1947 appearing before a Judge (With Einstein at his side) for his citizenship hearing and the Judge asked if Mr. Gödel thought what had happened in NAZI Germany could happen in the US and Mr. Gödel answered “Oh, yes, I can prove it” and started to layout what became known as Gödel’s loophole, a supposed “inner contradiction” in the Constitution of the United States that would allow a dictatorship. Mr. Gödel was just getting started with his explanation before the Judge headed him off with moved to another question. Sadly no version of the loophole exists.
Mr. Gödel published some work now then, nothing like his earlier stuff, until his death in 1978 but for the most part he worked in his office, filling notebook after notebook after notebook with, what else, notes called the Arbeitshefte [working notebooks] of Kurt Gödel.
When he died, Institute for Advanced Study boxed up his old office and put it into storage where the Arbeitshefte sat, untouched for years.
In March, 1982, one John Dawson, a mathematician at Penn State asked to see the notebooks and Institute for Advanced Study came back and asked if Mr. Dawson might want to catalog the collection and Dawson took the job.
Mr. Dawson was thrilled saying, “You couldn’t just leave the man’s lifework, his intellectual corpus, moldering down in some basement where it’s going to vanish into the mists of time.”
In the book, Mr. Regis writes: So it’s quite understandable that a bit of excitement is welling up inside John Dawson’s breast as the secretary jangles the keys to the archival cage and swings the door open in front of him. The Godel papers are right over there, up against the far wall. It’s pretty dark back there, but you can see well enough. There are two tall file cabinets and then stacks and stacks of cardboard boxes … there must be about sixty of them. They’re piled up six feet high, in row upon row stretching across the room.
John Dawson wonders to himself: What in the world’s in all those boxes?
And what was in all those boxes?
” … books, journals, manuscripts, and countless personal records of every description, including family photographs, clothing bills, apartment rental contracts, housecleaning bills, everything, anything. “There was an envelope of receipts from his wedding, right down to a counter check for a glass of beer. Coal bills from when he was in Vienna, month after month of utility bills, library slips-it was unbelievable.”
And what about those notebooks, the Arbeitshefte?
” … these books filled with page after page of unintelligible writing. It was in no language that John Dawson had ever seen; even the alphabet was unfamiliar. There were these strange loopy figures and zigzags and dots …. What did they mean? Dawson didn’t know.”
It was like Stephen King’s The Shining with boxes of manuscript all filled with “The quick red fox jumps over the lazy brown dog.”
… books filled with page after page of unintelligible writing.
Mr. Dawson stayed with and “It took John Dawson two years to go through all sixty boxes of Godel’s personal papers and documents. He sifted through and catalogued every last scrap of them, and now any scholar can go to Princeton and, piece by piece, trace through the flotsam and jetsam of the life and work of Kurt Godel.”
And the notebooks?
Dawson finally figured out what these are. They’re Godel’s notes on various subjects, written in an obsolete German shorthand called “Gabelsberger,” named after Franz Xaver Gabelsberger, its inventor. Later, Dawson discovered a “Rosetta stone” in the form of Godel’s shorthand textbook and practice workbooks, and even located an expert on Gabelsberger in New York City, a photographer by the name of Hermann Landshoff. It will be a while before all Godel’s notes are decoded, though. There are lots of them, and Godel made some of his own alterations to the shorthand.
It reminded me of the story of the Diary of Samuel Pepys, a 10 year diary of life in England in 1660 that were written in a personal shorthand as well. The six physical diaries were donated to Cambridge and sat on a library shelf until 1819 when this feller, John Smith (no kidding) spent three years decoding the writing. In an ending a librarian will love, when he was also done, they found the codebook to the diaries, in the lirbary, on the shelf ABOVE the other six books. Apparently in the 200 years the books sat on the shelves, someone pulled out the codebook and said, ‘Ain’t this interesting!’ and put it back … on the wrong shelf … but I digress.
You might well ask, why am I telling you all this?
Well, I’ll tell you.
The Arbeitshefte are back in the news.
According to the article, Ahead of his time’: AI helps unlock discoveries hidden in notebooks of man who transformed maths by Alex Bellos, who writes about mathematics for the Guardian:
Since 2017, the Finnish logician Jan von Plato has led a project at Helsinki University to understand the contents of 16 notebooks that Gödel wrote in the early 1940s. This material – the “workbooks” – is 1,009 pages of densely written text about maths and logic. Much of it is written in a German shorthand, Gabelsberger, that was obsolete even when Gödel was using it.
Progress in the mathematical understanding of the text was painfully slow – about a page a week – until September, when von Plato enlisted the help of the AI model Claude. Within a couple of days, Claude had provided a comprehensive digest of the entire material, revealing Gödel had proved hundreds of theorems that no one knew about.
The most famous logician of modern times had, in fact, discovered significantly more than anyone had thought.
Gödel changed the course of logic because he revealed the limits of mathematical knowledge. His incompleteness theorems show that in all mathematical systems there are true statements that can neither be proved or disproved. Yet while this result was a blow to previous generations of logicians, who had hoped that all truths were verifiable, Gödel’s work pushed the field in new directions, inspiring Alan Turing to write his 1936 paper that began the theory of modern computation.
Von Plato said he had started his Gödel project in 2017 because he was facing mandatory retirement from Helsinki University. “What should I do to make myself indispensable? Oh yes, I’ll start reading Gödel’s enigmatic shorthand pages!” He received a €2.5m (£2.1m) grant from the European Research Council, taught himself Gabelsberger shorthand – “I am one of only six people who can read it in the world” – and assembled a small team.
It’s a fascinating story and makes me consider the magic of AI.
In this case, the article makes the point, the Mr. Godel recorded everything but most likely, even Mr. Godel could not process all he was thinking at the same time, over time.
AI was able to take the Arbeitshefte as a whole and connect bits of work with other bits of work and make statement that Mr. Godel proved in part, but not at the same time.
Quoting Von Plato, “What strikes me especially is that he starts from ideas. He’s not like someone who plays with formulas and hopes to arrive somewhere. He has very, very clear ideas, and then he’s methodical. Step after step he goes ahead and he manages to fulfil the aims that he has in this formal work.”
I can appreciate the work.
I can appreciate the genius.
I love the story.
But I still don’t understand one word of what it means.
I not so think as
you dumb I am at least I
don’t think so … maybe
