Exploring the Unity of Mathematics: From Ptolemy to Copernicus and Beyond

[moshek]

Thank you Phoenixthoth.

I will be back only on saturday.

Have a good and mostly intersting,
time here.

My Best regard
Moshek

 

[phoenixthoth]

what are you talking about? do i know you? right about what?

 

[moshek]

Phoenixthoth,

I was really attract to you
when you were wondering in this forum,
how mathematics will look
in the next millennium

If you answer me on that way,
than you really don't know me.

moshek

 

[phoenixthoth]

then i think i know you. yes, it will be interesting to see where math goes indeed.

 

[moshek]

If so,

It will be my real pleasure to share that with you here,
but before I start do that let me ask you

Do you have some idea about that?
[?]

 

[enigma]

moshek,

Please use the private message system for communications directed at a specific member.

 

[moshek]

Ok Anigma,

As i wrote once, if we want to discuss really
how mathematics sound be in the next millennium
we must see that all of the known books
in mathematics have the fundamental form of Euclid books,
"The Elements".

A right question is can we write mathematics,
in a different way ?


Moshek

 

[moshek]

H(x)

Phoenix Hi, Saturday

About a month ago (27.11) it was publish in the BBC on line that a very young student ( 22) solved Hilbert 16 th' problem. unfortanly there it look that there is a mistake in here prove but let’s give E.O the credit of trying.

Hilbert 8 th' problem is the famous Reiman hypothesis ( 1859) and we know about few mathematician that are very close today to reach this very high mission.

The third problem that is still consider unsolved ( 20 were solved) is the 6 problem of Hilbert.

But we must understand that Hilbert ask this question 5 years before Einstein discover relativity and quantum mechanics.

The new melinuma of mathematics will create by the real and common effort to solve this mostely and very mystery problem of D.Hilbert.

Best
Moshek

 

[phoenixthoth]

a proposed direction in the theory of everything that has to do with so-called "self-aware structures":

http://www.physicsresource.com/showproduct.php?product=37&sort=1&cat=2&page=1

i bet that math will latch onto this idea in connection with mind-theorists to try to figure out the smallest structures that have self-awareness structure. i bet this is something that will become important in the future. and then it will not just link physics and math but also theories of mind. indeed, that's more of "everything" than just uniting the four forces into one equation. in addition, perhaps the theory of everything should be the theory of the universal set.

 

[moshek]

You are rigth

Thank you Phoenixthoth,

I will study,
what you sent here,
it is really
very interesting.

I will replay to it
on Saturday.

 

[moshek]

Dear phoenixthoth,

Thank you for the link to the theory on everything.
it is really mostly interesting paper.

I believe like you that
the hidden connection between mathematics
and physics will come from biology.

As i told you you are right!

Best
Moshek

 

[phoenixthoth]

this is the paper moshek is talking about:
http://alephnulldimension.net/toe.pdf

actually, thank max tegmark!

if his theory is on the right track, then it may unite consciousness with the rest. and if what i know about consciousness is on the right track, it really would be a theory of everything; just need to work out the hologram part of reality, if it is a hologram.

cheers

 

[moshek]

Intelligent life

Thank you for letting me know about Max Tegmark
he is extraordinary thinker of our time.

I think that his new theory relate to
what i something that i wrote in 2000
after i heard Alain Connes the inventor
of Non-commutative Geometry
At U.C.L.A conference "100 to Hilbert":


Moshek

---------------------------------------------------------------------
Intelligent life

Planet Mar's was connected twice to the search of man for intelligent life. First was the effort to understand the retrograde movement of Mars on the background of the night sky. second was a mistake that identify cannel on is face done by other culture. maybe there is connection between Mars to the search of life in the area of mathematics.
Thousand year's ago people observed that Mars is going sometime in the opposite direction relative to the stars. Mars is moving slowly on the background of the night sky so you can distingue the different every day, suddenly he stand and then start to go in the opposite direction. Then he stop again and continue his regular direction.
For explaining this strange movement the astronomer invented complex system of wheels so that Earth is in the center . the most complicate system was invented by Talmy and it included 12 wheels. But 400 year's ago Copernicus invent a new revolutionary idea so that put the sun in the center of the world and not the planet earth. In this observation the explanation to the movement of mar's became very simple and it base on some interaction of movement between mar's and earth. This is how the science revolution started and it was with many hard struggle. The follower of Copernicus, Galilo and Newoton base the science way of thinking by a development of a new suitable mathematics.
The top of this way of thinking bring in the 20 century to the development of two central theory: Relativity and Quantum theory. These two theory's change the way man understood himself in the world. We are not passive observer in the phenomena , and we have some active part that base on the interaction that between us and the world. Is there a way to establish similar principle in the rational area of mathematics? By first looking it look that there is no way for doing this. The world of mathematics seems to be absolute and exist without man. But from the other side we know that here is today some need to develop a new looking to mathematics that can bring to more understanding of the relation between mathematics and the world of phenomena. This was express in the lecture of Alein Connes who develop 20 year's ago Non commutative Geometry, and consider as one of the leading mathematician in the world today. "… we need today a new understanding in mathematics that it's source is not necessarily come from logic but more on the geometry." This end the last lecture in the conference "100 to Hilbert" . This conference was to point another famous lecture of Hilbert in Paris in 1900. Hilbert end his lecture by drawing a vision to discover an organic unity of mathematics.
A Common looking on those two important conference like two eye's, one took place in Paris and the other in Los-angels, with a different of 100 year's in time arise the question if and how is moving mathematics , like mars, on the background of the culture of mankind. This is how arise the problem that not solved yet , of the inherent hidden connection between mathematics and the real world. But like the observation of Copernicus that aloud us to put the Sun in the center of our world and by this to understand more simply the interaction between the Earth and mar's, we can point to a third eye's that solved the mathematical problem. The new common center of mathematics and physics is the discovery of the organic unity of mathematics , intelligent life.

 

[moshek]

Phoenixthoth:

As you see
It took me
some day's
to think about
the mysteries equation in:

www.rense.com/general46/stan1.html

well,

You cannot understand them directly
only in the languge of "Mount Analogue"
when Non Euclidian mathematics
is develop in some planet
in the universe.
Take for exapel: Earth.

The Alien come
and make some sight
for the members
of this planet


Moshek

 

[phoenixthoth]

very interesting site. I'm definitely not sure that it's not a hoax but the equations are interesting to me. i give a fairly detailed interpretation on the site linked to in my signature under "math" "miscelleneous" "mystery equations."

 

[moshek]

Dear Phoenix,

You gave in your forum
a very interesting explanation
to these equation.

But still you look on them in Newton way of thinking
seeing mathematics only as modeling of the universe.

please read:

www.math.rutgers.edu/~zeilberg/Opinion56.html

Best
Moshek

 

[phoenixthoth]

if max tegmark is right ( http://www.hep.upenn.edu/~max/multiverse1.html ) then math is more than the model of the universe but is, in some sense, the universe.

the pythagoreans believed reality at its deepest level is mathematical in nature.

 

[moshek]

A very nice view.
If you don't mind
let's stay one more week
just for think about that.

Thake care
Moshek

 

[moshek]

You are right again Phoenix,

The attitude to use mathematics for modeling the universe fail completely. We and our consensus are parts of this universe. This is why the discovery of non Euclidian geometry (1823) is only firts step in the death of the Euclidian mathematics base on axioms etc...

Moshek



http://www.math.rutgers.edu/~zeilberg/Opinion43.html

http://www.icm2006.org/#

 

[HallsofIvy]

Is that the theme from "twilight zone" I hear in the background?

 

[moshek]

"Twilight zone"

Please explain me
what it is?

Thank you.

 

[selfAdjoint]

A classic old TV show from the fifties that had weird and upsetting stories and a menacing voiceover narration - and a very distinctive theme music. So reference to it is kind of a put down, at least on a site like this one. In face to face discussion, people will just hum the theme. Even the youngest generations know it, it has entered the folklore.

 

[moshek]

Thank you Self-Adjoint:

I invite you
to see the face:

www.ma.huji.ac.il/~moshek/the%20face.htm[/URL]

And see you next saterday

Moshek

 

[HallsofIvy]

Thank you, Self-Adjoint!

Yes, it was a put-down! I want that clearly understood!

 

[moshek]

HallsofIvy,

I will be glad to hear your opinion about:


www.math.rutgers.edu/~zeilberg/Opinion43.html


thank you
Moshek

 

[HallsofIvy]

No, you would NOT be glad to hear my opinion!

 

[moshek]

Well, It is not my opinion!
So How do you know that
in advance?

Moshek

[?]

 

[phoenixthoth]

maybe that's what HOI meant, that they'd agree with the opinion as well as disagree with you.

 

[moshek]

maybe i really don’t know what they are meaning
i think it is always better to say thing directly.

 

[phoenixthoth]

i've read the first few paragraphs and i can see why HOI may have objected.

is creativity logical? i'd say, "not always."

however, when it comes time to write down the results, the proofs should be based on some form of logic though not neccessarily a strict, machine-level, programming language.

my suspicion is that even creativity and lateral thinking is still logical just super high-level

in terms of higher-level languages, we have the following structure:
the kernel of understanding

the possibly totally logical language of creativity

the language of advanced proofs (where the vast majority of the words are difficult to concisely define in a few words)

the language of proofs (more details are spilled out here and one need not be an expert in the field to accept the proof)

the formal proof language (machine language)

binary code.

the problem is that when a higher level language is projected onto a lower level one, the lower level one is almost always, if not always, longer and more complicated. the debatable question is at what level should we communicate results? we should never use either extreme, that much is clear. in other words, i can't publish in a journal: my understanding is this, period, and here are my results. and we can't publish binary code and expect a human to understand it though in order to ever get computers to prove things and/or do proof theory, then a lower level language ought to be used. what i don't know for sure is exactly what language one ought to use for proofs.

think about it: there is no such thing as a proof, ever. mathematical proofs, at least, are just words. how many verbs can you insert into the sentence so that it makes sense: "words _____?" can words love? can words kill? can words do anything? can words prove?

"proofs" do one of the following things: pass the set criteria for rigor and correctness, not, or something in between. someone writes down a proof but a human has to judge it for correctness. the words in themselves don't prove; it is the reader and writer who prove.

"proofs" are an attempt to articulate that kernel of understanding and stimulate the reader's kernel so that they will also understand. once the reader has matched the kernel of understanding enough, by a preset criteria, then the reader will judge the "proof" to be "valid."

the bottom line is that if the language is too high for humans, that kernel of understanding just won't get transferred. it's not a matter of "should it" or "could it": it typically doesn't unless the reader already has that kernel.

what seems to be the most efficient technique for transferring that kernel of understanding is for the author to write in a medium level language. but when that author talks to his friend who's also an expert, listen to their conversation. it's at a much higher level language and they can prove things to each other with much more efficiency.

i use the word "kernel" on purpose so that it resembles actual computers. if we are self-aware mathematical structures, then we might literally have kernels. i wonder if our kernels are "written" in a high level language or a low level language or something in between...

 

[moshek]

Dear Phoenix,

I meet Doron.z at the conference "The unity of mathematics" in the honer of Israel Gelfand 90 birtday, At Harvard university.(sep2003)

Doron got the AMS prise few year's ago.
I also recomand to read his 56 opinion about

"The disunity of mathematics"

www.math.rutgers.edu/~zeilberg/OPINIONS.html

Thank you for your first opinion
to his 43 opinion about the need to
search for some Non-eclidian mathematics.

I will study that and respond to you
on Saterday

take care
Moshek

P.S:
To HallsofIvy remak about some T.V program. as far as i can see it T.V is an invention that with minimum effort reduse for the maximum the intelligent of the observer.

 

[moshek]

Dear phoenix,

Your Kernel is really nice but still similar to the circles of Ptolemy to describe the retrograde movement of mars.

So as Copernicus discover, we need today to put the center of mathematics not in logic but more on it organic unity with is the principle of duality ( Complementary as Organic wrote) and it geometric interpatation of the Klein Bottle as positive interpatation to Goedel theorem.

My regard
Moshek