AxiomWriter

LESSWRONG
LW

AxiomWriter — LessWrong

Replying toThe power of finite and the weakness of infinite binary point numbers

The power of finite and the weakness of infinite binary point numbers

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.

Replying toThe power of finite and the weakness of infinite binary point numbers

AxiomWriter2y

The power of finite and the weakness of infinite binary point numbers

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... (read more)

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The power of finite and the weakness of infinite binary point numbers

AxiomWriter

Take a sequence of the numbers 0 and 1. You can interpret this sequence as a real number between zero and one.

Just write 0.( your sequence).

This can be interpreted as a binary number.

For instance 0.1101 is $1 / 2 + 1 / 4 + 0 / 8 + 1 / 16$ .

Now, I have read here about the might of irrational numbers, whose sequences go on and on, never ending, containing all the knowledge in the world.

I see two difficulties with that form of thinking.

It is not at all difficult to construct an irrational number, that contains nearly nothing at all. Take 0.101001000100001000001...... as an example. I seriously doubt it contains even one little story, let alone all books in the world.
To contain all books in the world

... (read 396 more words →)

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Replying toChapter 122: Something to Protect: Hermione Granger

AxiomWriter2y

Chapter 122: Something to Protect: Hermione Granger

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... (read more)

Replying toMy PhD thesis: Algorithmic Bayesian Epistemology

AxiomWriter2y

My PhD thesis: Algorithmic Bayesian Epistemology

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... (read more)

the underestimation of circular thinking

AxiomWriter

There is a great and often underappreciated danger in logic thinking itself.

That is the danger of circular reasoning. The easiest example goes:

If A is true then so is B.

If B is true, than so is A.

Therefore A and B are true.

Because it seems so easy to spot, it is vastly underestimated.

But what if hundreds of theorems and variables are involved?

It is not only possible, it is more than likely, that circular reasoning is involved somehow.

Say your intuition goes against the conclusion you have drawn.

You begin to test your logic, going this way and that way through all the theories and variables,

training your own brain to believe in them.

Proofs of the existence of... (read 301 more words →)

A dialog with the axiom of choice

AxiomWriter

preliminary remark: the axiom of choice ( Auswahlaxiom in Germany) can be formulated this way:

For all sets $M$ there is a selection function, that assigns for all elements of the power set $P$ $(M)$ exept $\emptyset$ an element of the corresponding subset of $M$ .

It is assumed to be true in many areas of mathematics. Besides its "job" of giving elements of infinite sets, it has equivalent formulations to give "upper bounds" (Lemma of Zorn) and others. It is crucial in functional analysis in many ways.

In the following dialogue I tried to clarify a bit to myself, what this axiom means and why I do not entirely trust it.

Beware: It is an axiom, not a proven theorem. All that is proven... (read 1519 more words →)

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Replying toChapter 122: Something to Protect: Hermione Granger

AxiomWriter2y

Chapter 122: Something to Protect: Hermione Granger

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... (read more)

Replying toUsing axis lines for good or evil

AxiomWriter2y

Using axis lines for good or evil

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,... (read more)

Replying toWell-Kept Gardens Die By Pacifism

AxiomWriter2y

Well-Kept Gardens Die By Pacifism

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... (read more)

A definition that counts (newbie, trying to find my place and my voice, no native english speaker)

AxiomWriter

I often read in this forum about AI, and often about the term "giving training data" to a AI,, while the term "programming a AI" means configuring a computer ( or robot or whatever) really means "someone is creating a AI".

Now a AI, is rhoughy the same as a natural neural network, which I will call an NI

Humans just took an idea evolution already created and modified it a bit.

Now, look at different NI. There are of course insects and crocidiles, birds and rats ( and their intelligence is often underrated by humans).

But let us look at the most general NI that existist: a human baby.

It is a bit different then a... (read more)

Replying toAnxiety vs. Depression

AxiomWriter2y

Anxiety vs. Depression

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... (read more)

LESSWRONG
LW

LESSWRONG
LW

Is there a possibility to activate an english spellchecker for the drafts?

the underestimation of circular thinking

A definition that counts (newbie, trying to find my place and my voice, no native english speaker)

A dialog with the axiom of choice

AxiomWriter

AxiomWriter

The power of finite and the weakness of infinite binary point numbers

the underestimation of circular thinking

A dialog with the axiom of choice

Is there a possibility to activate an english spellchecker for the drafts?

A definition that counts (newbie, trying to find my place and my voice, no native english speaker)

AxiomWriter

Is there a possibility to activate an english spellchecker for the drafts?

the underestimation of circular thinking

A definition that counts (newbie, trying to find my place and my voice, no native english speaker)

A dialog with the axiom of choice

AxiomWriter

AxiomWriter

The power of finite and the weakness of infinite binary point numbers

the underestimation of circular thinking

A dialog with the axiom of choice

Is there a possibility to activate an english spellchecker for the drafts?

A definition that counts (newbie, trying to find my place and my voice, no native english speaker)