khaled

I'm not good at physics anyway, but, I think that the theories about the universe and its expanding, those kind of theories were not made because we saw the expand, ..etc. Because all of that is impossible for us to notice in the general form .. so instead of going from observations, they went from astrology basics, observations around the earth ...

no idea ...

you can then call it "Random Genetic Programming", since the genetic evolution process is fully random

first .. the expansion is the step of moving from one solution to another, one program to another

second, are you aware that you are not really doing genetic programming, you only do "random mutation optimization", because

genetic programming is not random walks, or just mutations

also, you have to be aware that all methods, including this, are used to find an approximated solution .. because N != NP

I'm an avid user of Chrome with MSE and Rapport as security and I've yet to get hit by a virus and I'm quite cavalier about clicking links. I am safe in the knowledge that I have whole-system images to fall back on if I get hit or it screws up...images are virtually a cure all. Macrium Reflect Free or Norton Ghost (not free) are good imagers and have good reliability records. I've yet to use a backup to recover from malware yet though. Adding a website checker like WOT is a good idea as well to warn you of dodgy sites beforehand.

1. WOT is not a certification good enough for security, based its rating system can be manipulated by threats, unlike Certification Authorities such as enTrust, ..etc

2. a browser will no longer become safe, if you install an add-on/toolbar which is neither made by the browser dev team, nor certified by a formal authority

3. proxy application/services will make you anonymous to others, but not secured, because all of your data are migrated through a specific server,

thus if you put critical data on that connection, you are exposed to danger ...

-- you know that hackers can steal data from your system, without even reading it ...

I forgot to include differential geometry, which needs differential topology and advanced ring theory. That should include super-manifolds. Supersymmetry will certainly be covered in theories of everything.

 

Do you want me to be more specific, or to include more advanced topics?

=Uncool-

.. are there any more advanced topic ?

But books take you by the hand, and start at something relatively basic, and build it up from there.

 

Don't worry, each book only teaches you a tiny bit about maths... it's gonna take a lot more than the 4 books DJBruce wrote down to learn "everything in mathematics".

 

If you want to be able to upgrade your maths skills from what you describe, to a level able to work and understand the quantum mechanics, then I would advise you first to let go of the idea that 4 books are too much. You're probably looking at more than 4 books. Also, if the money for 4 books is too much, then you might want to look at used books (Amazon has used books at lower prices).

 

You're looking at quite an endeavour, so you might as well realize what resources you need to achieve it: lots of time, dedication and also some books. And possibly a teacher too.

 

It takes regular students in a university a couple of years to learn and properly apply the maths. It'll take you even longer if you do it alone (unless you're a genius).

I'm currently only a bachelor in computer science .. but, just like great scientists, I'm a scientist in more than one field, Logic, Computer Science, Artificial Intelligence, Psychology, Philosophy, Theoretical Computer Science, Theoretical Physics, and Mathematics -- and that's why I want to learn everything .. I've my whole life to this,

I believe if I become good at all mathematics, I will be able to do researches in all of my fields in high level, knowing all kind of models I can utilize to solve a problem, or work a model ..etc

ps. thanks uncool for the list, but I will need to see the complete list, of everything in math .. even complex topics such as super-manifolds, supersymmetry, ..etc

Yes.

 

To be optimal the start of the series of numbers the program outputs when evaluated should be as close as possible to the input series.

 

Of lower importance but that when most programs output series starts correctly becomes significant is program length which should be as short as possible.

 

Have I made it clear what happens inside a program when it runs? The list of instructions in my first post.

I'm afraid it's not, you have to show your algorithms:

- the algorithm to obtain an initial solution

- the algorithm of the expansion

- the algorithm of the mutation process

- the algorithm for f(P): evaluating how optimal is program P

I'm not really good at neural networks, but you have to specify, since there are many types of neural networks ...

I'll draw you my idea, and you can think of it,

good luck,

I agree with StringJunky, and add .. Chrome is not good for safe browsing, given it's developed by Google itself ...

I suggest using Firefox, under Linux ...

You can ask -- Who are programmers that had huge impact on computer systems ?

To me, I think of Linus (Linux inventor)

using XML files is to use structural informations offline, but online use require that you put all those data on the database, and do SQL queries to do search ...

in HTML 5, there is <video> tag that allow you to stream a video .. for something more advanced, you have to program that using Flash, ..etc

Unix-based Systems are secure by default .. I suggest Ubuntu for a regular use, and Fedora (Red Hat) for server development use

In Ubuntu, you will find in the menu, Ubuntu Software Center .. which is where you can find an application you need, and if you choose one it will download & install automatically, sometimes you are asked for configurations, or authorization ...

Important tips for secure system:

- make a non-readable password, 8+ characters, mixed (at least 1 number, 1 lower-case, 1 upper-case)

- don't write down your password on a paper or on your system (this is worse)

- when making backup or sending a critical data online, or even through any medium, use encryption

- don't leave your computer open, and leave .. close your computer, and when you return open it

good luck,

Globalization is the use of shared data among several units at some level .. while Localization means using private data locally,

C++

int X = 1 ; // global

void function ()
{
    int X = 2 ; // local

    ::X = X ; // export data to global variable
}

void f2 ()
{
    printf("%d", X); // this will print ' 2 '
}

If you work on a Unix-based OS, they need the root privileges, nothing less ...

and If you are working on Windows, make sure you have a Security System, not just an anti-virus !

well, first .. I asked for the order of mathematical topics\courses, not books, in order to reach a level to understand Quantum Theory ...

besides, I don't know how I'm going to jump from specific types of calculus into Analysis on Manifolds, not even knowing Numerical\Functional analysis ...

I need something general, if I can simplify it in a phrase "I want to learn everything in mathematics, what is the path" ...

So, in this case, you are not doing a Tree Search, you are doing a Local Optimization over a Function [math]f(P) = \; how \; optimal \; is \; program \; P[/math]

I'd call it Local Random Genetic Optimization, but you might get stuck in loops, with no use of history .. the other solution around is to provide

an incremental progressive algorithm, or else just stay with the random mutations .. and make some constraints to guide it,

good luck

"time is considered a dimension, the time-flow is constant .. but what is different is how different objects realize time" -- my speculations

So, I think that using a clock to organize our works, is based on using the time-flow of the clock machinery asynchronously ...

in NLP (Neural Language Programming), there is a complex techniques to experience slow realization of time-flow for short amount of time,

which, as theory says, can be utilized between time & time, to do some things, such as avoid a bullet, taking a critical escape path, accelerate an indirect punch

[math]Eph = \frac{hc}{\lambda}[/math]

[math]\frac{Eph \lambda}{Eph} = \frac{hc \lambda}{Eph \lambda}[/math]

[math]\lambda = \frac{hc}{Eph}[/math]

So,

[math]

\int_0^t (\gamma^{1/\kappa}-i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds = \int_0^t (\gamma^{1/\kappa}-(i\zeta{w}(1-t/s)_+^{H} \times i\zeta{w}(1-t/s)_+^{-1/2}))^{\kappa}ds

[/math]

[math]

= \int_0^t (\frac{\sqrt[\kappa]{\gamma} - (i\zeta{w}(1-t/s)_+^{H}}{\sqrt{i\zeta{w}(1-t/s)_+})})^{\kappa} ds

[/math]

Let's talk about limits and bounds,

Program size = m Bytes, Max Program size = 200 Bytes

Max Expansion size = Max(m) x Max Elements = 200 x 1000 = 200,000 Bytes ~ 195.3 KB

If you keep all data, without removing past states, your space complexity becomes exponential

and your search continue only for 100 steps only ...

So, if you keep all data, for R runs, Total Size = [math]\sum_{i = 0}^{R}{d^i} = \sum_{i = 0}^{100}{{(195.3)}^{i}} = 1.1 E 220 TB[/math] -- which is a tremendous space

if you keep only a branch of the tree, Total Size = [math]d \times R = 195.3 \times 100 = 19 MB[/math] -- reasonable

Advice: try to minimize Expansion Size, Increase Max number of steps,

-- Consider Progressive Merge and Semi-Random Mutation, that way your search covers a wide area of possibilities, and it allows random progression limited by general direction

good luck

So, simply you are working on Genetic Programming, so what is the search you are using ? .. ex: Simulated Annealing

and this search is to optimize a Program, where a Program is a set of Instructions, an Instruction is an unsigned 8-bit Integer

Number of Instruction types = 2^8 = 256

Program [math]P = \{ I_1, I_2 .., I_m \}[/math] where [math]m = ?[/math]

So, what is the value of m, is it static, dynamic, or a range of values ?

-- is your search linear, exponential, local, or guided ?

-- what is the size of your buffer, queue, list .. in terms of Max Number of Programs ?

-- do you keep previously processed states (Programs) ? .. so that you don't go over the same one once again, & don't get stuck in loops

-- how did you define SELECTION, MERGE, and MUTATION functions, in terms of algorithm ?

good luck

Here is a concise presentation of Ptolemy's Table of Chords.

--------------------

From the Μεγιστη

 

 

This is a table from the Ptolemy's Almagest as translated in Arabic. The picture is stolen from a presentation in greek page 39, I was not able to find the original picture. (maybe copyright issue?)

The sheet contains information about celestial horoscopes, such as Aries, Taurus, Gemini, ..etc

this sounds weird, so they knew how to calculate angles for the zodiac system

Also, about how ancients calculated sin(90), and zero was invented by indian scientist .. I think if you think about it,

Greek have their representation of numbers .. I = 1, V = 5, & X = 10 .. so, sin(90) in greek is simply sin(XXXXXXXXX) = I

.. also, I think they have a symbol for zero (nothing), and based on how they represent the numbers, I think zero

in greek is simply a gap .. 0 = __, 1 = I, 2 = II, 3 = III, ..etc

I'm computer science researcher, but I'm not really good at math, that I want to improve myself,

I studied: Basic Calculus, Basic Geometry, Discrete Mathematics, Basic Linear Algebra, Basic Probability & Statistics

I know how to get math courses, but in what order should I go .. I want to know the path where I can then understand Quantum, Super mathematics, ..etc

best regards, khaled

I'm a computer scientist, so I'd say Logic, Discrete Mathematics, Analysis, Model Theory, Number Theory, Algorithms, with some interest in Geometry, and Quantum Theory ...

To me, while I was still a bachelor student in computer science, which was five years, and since the second year, I have started to write researches in Logic, Algorithms, and Model Theory .. I was in the third year, I had no idea about scientific scholarships and researchers around the world meeting in conferences .. I wrote tens of papers, most were no good, but considered a start of realizing that I need to be good in the field to start writing researches .. and that I need to meet specialized people to help me in, In my senior year, I published a paper, with not much notations, about one of my attempts to do Randomness Generation ...