Re: One and Zero

Hi Arik,

> I think I would have got it on the first go were it explained like you
> did now. Also you did not cover the part about them being like
> parallel lines - did you mean the two lines f(x)=0 and f(x)=1?

Yes.  Or you can define it as f(x,y)= x^y, and only f(0,y) and f(1,y)
will be straight, parallel lines.  For any other x it will not be a
straight line.

> > By the way, one and zero are the only numbers (integer, real or
> > complex) who remain the same when multiplied by themselves (or powered
> > by a positive number except one):
> >
> > x^2 = x <=>
> > x^2 - x = 0 <=>
> > x * (x-1) = 0
>
> Well, you can design a 2nd order polynomial for every two numbers,
> like for 2 and 3:
>
> x^2-5x+6=0

I was referring to numbers who remain the same when multiplied by
themselves, and therefore x^2 = x.

> > The whole idea of articles such as this one is that I'm challenging
> > deterministic logic, claiming that it is inconsistent.
>
> I'm sorry but I didn't understand how you prove your claim.

It's complicated.  In short, my claim is that if Godel's
incompleteness theorem is true, then the theory is not consistent (not
only incomplete).  And Godel's incompleteness theorem is true for any
deterministic logical theory who is not trivial.
[http://www.cs.auckland.ac.nz/CDMTCS/chaitin/georgia.html]

But it is worth proving in more details.  I'll think about it.  If you
want, you can read my view about it in other articles, such as the
following two:

http://www.speedy.net/uri/blog/?p=20
http://www.speedy.net/uri/blog/?p=22

I also came to the conclusion that the speed of light is not constant,
and more generally speaking that constants don't exist.  I wrote about
it a few articles:

http://www.speedy.net/uri/blog/?cat=3

> Yes, I meant drugs, but drugs are not the only way to achieve these
> states. You didn't answer my question about the article having the
> stream-of-consciousness quality - is that how you created it?

I read your question again, but I don't understand what you mean by
"stream of consciousness".  Can you explain?

> What were you in for? Schizophrenia?

Technically, yes.  They call it schizophrenia.  But I don't like their
definitions so much.  Let's say I'm different than them, I think
differently, and I behave differently.  I also did things which seem
illogical to most people, and actually I admit it was a mistake.  So
they decided I'm "sick" and I need "treatment".  I don't consider it
treatment, I consider it punishment for being nonconformist and doing
"strange" things.  I also don't consider myself as sick (not
physically and not mentally).

> Again the language issue - if you use your own personal language to
> describe the world, expect people to misunderstand you. To interact
> with people you have to share some of their reality, and language
> plays an important role here (I'm an Israeli living in the US, so I'm
> painfully aware of that). If you don't share enough of other people's
> reality, you will be misunderstood. If you don't have enough control
> over yourself to share in enough of other people's reality, you might
> find that people will tend to push you away from society.

I know.  But I allow myself to make exceptions once in a while.  I
define my own terms sometimes.  If people know me, they will
understand what I mean when I say google.  I don't have to do
everything like everybody else.

> Ah! That's much more like it. An article about a single subject
> following up on the subject from start to end. I liked that one more
> than the one you wrote your original email about. I've seen this
> argument before - creating a 1:1 transformation between an idea and a
> natural number - and my response to that is: Copyright is not about
> the idea itself. Copyright is about the ability of the author to pick
> the *right* number out of the infinite pile of numbers and say - this
> is it. Because, frankly, most of the pile is garbage.

I know.  If you're the first one to discover something and publish it,
you can be considered sometimes as the one who "invented" it or
"created" it.  Because the chances of two people to publish exactly
the same book, or melody, is almost zero.  That's why our society
allows copyrights.  But to have copyright on a file means having
copyright on a number.  For example, there are prime numbers known as
"illegal primes".

Thanks, and I'm glad you liked my article.

Actually, my articles are written in a logical order.  The first one
is called "The axiom of choice" [http://www.speedy.net/uri/blog/?p=1].
 If you read them in the order I wrote them, maybe they will make more
sense to you.  But not all of them are on the same topic, you don't
have to read all of them if you don't want to.  I wrote most of them
last month (except the first two, which I wrote about two years ago).

Uri.