I am sorry if I sound a bit confused. I don't speak English well and I am far more familiar with the mathematical terms in German. And I am confused by Solomoff induction.
My main point is the vast mathematical difference between "only" infinite (abzählbar unendlich) sets like the rational numbers or the computable numbers and the sets that are uncountable (überabzählbar) like the real numbers or the power set of the natural numbers.
If I have the set of real numbers between zero and one and "take" one number "randomly" I should "get" a non - computable number - in other words something that's existence is more than doubtful. I certainly can not give a sample for that.
These numbers were not named "irrational" for nothing.
Perhaps this is only about the word particular in "particular infinite input string". Something like "you can take it only if it exists". But should it not be formulated like that? It feels to me like smuggling the whole concept of real numbers in by the backdoor.
What if you use instead the following sentence:
"More precisely, suppose that a particular input string x0 of unknown length is about to be fed into U.
However, you know nothing about x0 other than that each term of the string is either 0 or 1."
Would that form into be a sort of weak Solomoff induction? Or would the thing than collapse into complete nonsense?
Now, I thought a little about my own comment and asked myself two questions.
For whom did I write it?
Now, first to mind comes my heroine ,Emmy Noether, the inventor of this little, uncomplete and so useful axiom system - the group and its derivates.
Second is Mileva Einstein-Marić, who wrote a bunch of papers together with her later husband. The last ones were published under the name "Einstein", because they were already married by then.
He got the nobel prize for them. He took the honor ( I think, he might have been into the anti atom movement by then ). He gave her the money. Was it only to keep care of one of their sons?
Or was it a overlooked sign to the world? Einsteins opinion of the stupidity of humens is well known.
And geometry (see Noether) must have been a big thing by the time Mileva studied mathematics.
The third group I wrote this for, I can only think on in bitterness:
The women in Iran. They must fight for their right not to be pounded to death, just because someone thougt he or she saw a hair outside the burkha.
In all the wars and dying that goes on right now, this is one I think is a bit overlooked: girls of fourteen or fifteen years fighting for the right just to be.
With whos voices exept my own can I speak with?
One is a voice of the past: Selma Lagerlöf, the nobel prize winner, who 1911 gave a speech for the womens right movement in sweden. I think the title in English must be something like "home and country".
The other voice is Douglas Hofstaedter, whos "metamagicum" I always enjoyed, subchapter seven. Since I read it in German, it might be different to the english version, he took great care with the translation especially in this chapter.
Hello, this looks very interesting to me. So I want sort of making a mark on it, so that I can find it later. At the moment I can´t do much out of personal reasons. I am a newbie here, barely knowing what this "bayesian thing" is about.
But knowing a bit about making a sound axiom system, I have a feeling there could be some work done to make the "table", the axiom system all this stands on, a better one.
My wordpress blog ( and I have still to learn how to write one) holds at the moment only my "resurrected" thesis and doctoral thesis from about 30 years ago. In german at that. I had to dig up the old latex files, then make pdf files out of it. Since latex changed a lot, I could not resurrect the correct pictures yet.
Just marking this for myself, so that I can find it later, at the moment real, deep mathematical thinking is not possible and actually I should not even handle this forum. But this just looked to interesting.
Hermiones Voice
Where am I? What has been done to me?
In the Harry Potter Original I was the smart one of the trio. I could have been sorted into Ravenclaw because of my smartness, but ended up in Gryffindor because of my courage.
I gave courage to smart girls and women to speak out. I fought alongside two boys, always thinking, learning and looking ahead.
I helped fight the dementors, the deep depression Rowling must have known, even if Harry was most vulerable to it.
And now? I am "emotional good", barely good enough for the phoenix test.
Why didn´t I win the "enders game" battle in the middle of the series.
Even then I was seen more of a thing two boys fight over, not a human.
I was there to be protected, to be made into a unicorn or whatever. I, along with the other girls were there to be raped or cherished, proteced or loved.
Am I a thing here, not seen as a human beeing? Wasn´t this what Terry Pratchett warned against again and again?
I am a woman, like roughly half of humanity. I am a human beeing. This is not a story I wish to be in.
That would not be rational.
The problem I see here is that you are trying to use functions at all. Take the years/GDP line. If your measure the GDP once a year, you should use a bloc graphic.
Else you have a lot of imaginary points per month, day and hour, that, in reality, are not there. Take black friday - lots of changing , take holidays, when the shops are closed - little changing.
Days - lots of changing, nights - little changing. And you can´t really know the GDP for the next year - there can always be a drastic change.
Take the cannabis/homeowner plot graph on the other hand. You have a lot of (x,y) pairs (homeowners, cannabis supporters)
Some of these points have the same place on the x - axis, but different places on the y - axis. That is the reason you can´t just draw a function through all this points.
Such a set of points is called a relation in mathematics. Just because you can draw a line through them does not mean you should.
And just because it is customary to draw orthogonal x- and y- axes in mathematics does not mean that is always the best way.
Especially If the points of a relation are not stochastically independent it might not be a good idea.
After all, you draw on a euclidean plane and your are free which axes to chose on a euclidean plane.
My secret garden or why my garden is not well-kept
I talk of a real garden here - my garden, a place for me to rest, to see flowers, birds and butterflies, to read in.
Years ago, before my time, it was a well-kept garden.
There was a lot of grass and some bushes, and that was it, easy to maintain, well kept.
Because I like flowers, i tried this and that, some things thrived and others died and it was never the garden I planned in the beginning.
I never planted the clover and the moss that creeped into the grass. In the beginning, I tried to fight it, but suddenly I began to understand that the garden won life trough it. There suddenly were bees and little flowers in the grass.
I despised roses in the beginning. They seemed like plastic flowers to me. But then I discovered the old roses, roses who did the one thing a rose to my mind should do : they smell. All the roses in my garden have different smells.
I have plants I never planted, but I like them. I even like dandelion, even if I have to fight it every year.
There will be dandelion anyway. A bit of fighting is necessary, because else the garden would have only dandelion.
I took my gardening philosophy a bit from "the secret garden" from Burnett and a bit from chinese and japanese gardens, including new plants, if they take root, only rooting out the ones that try to overtake the garden or that I know are poisenous.
This year, because of clima change, a lot - even the big tree I love so - has to go. I don´t know which flowers will thrive next year. I wait and see.
I know this: in the oh so well kept gardens in my childhood there were no sweet smells and nothing was allowed to grow, if it was not planted in that exact place.
Let the new seeds, that fly in, place to grow. Don´t root them out, because they are not what you expected.
A garden can be too well kept to be a living, thriving thing.
Been there - well not exactly the same but depression, panic attacks, all that, yes a long time. Try a mixture of patience and looking at your fears.
If the fear is too big, don´t look. Try existing, try doing something nice or even something necessary and concentrate on that.
Try looking at your fear again.
What is the worst that can happen? You fear beeing overrun by a car?
Your fear is solid, don´t try to fight it with bravery, just train yourself to be EXTRA careful.
You fear you could fall into a thorny bush by the wayside? Go that way anyway, fight your fear with bravery at a time you have the nerve for it.
Perhaps take a tetanus shot before.
Have a lot of patience with yourself.
Still fighting myself.
I am proud of me. I had a long fight. I exist. And at the moment it is even fun existing!
Tomorrow - who knows?
Finding your way between scylla and charybdis, be proud of yourself.
Sorry, found my mistake. For Solomonoffs induction the input string has to be computable. Therefore it is not from a uncountable set, only from an infinite one.
Confusion solved.