So, I'm thinking about incompleteness today

[linuxboy]

... And I decide to visit Stephen's site


http://www.stephenwolfram.com/


apparently he has published a new book with his findings on cellular automata with a discussion of how mathematics fails in analyzing the physical world because of its level of abstraction and not an algorithmic, patterned approach using actual cellular data.

Now I'm no expert in theoretical physics, but I think that if he is right, it will mean huge changes in the way we look at the world and the way out collective education system approaches science. What he's saying is that an expansion of current mathematical approaches based on the real world and how it operates gets us away from the pesky problem of irrational numbers and the like using traditional rules of algebra.


I haven't read the book yet, but it sounds fascinating. What do you think?


Cheers ! 🙂

 

[datalink7]

Here for some thoughts on it.

 

[Angrymarshmello]

I'm too uneducated to make an educated statement, sorry

 

[linuxboy]

hmm, I missed that thread. I wasn't even aware he was ready to publish anything. Weird. But exciting stuff, I can't wait to read this. It's my bored times wading through calculus and Newton's ideas finally put to good use in an abstract model I can enjoy. Wonder if he's right?


Cheers ! 🙂

 

[Atrail]

Are irrational and imaginery numbers the same or similar?

 

[Heisenberg]

An irrational number is one that has essentially a random sequence of numbers following the decimal point to infinity. An imaginary number involves the square root of -1.

 

[bmd]

Originally posted by: Atrail
Are irrational and imaginery numbers the same or similar?

Well, I know they aren't the same, I'm not sure how "similar" you could consider them.

Irrational numbers can't be expressed as the quotient of two whole numbers (right?), such as pi or e. Imaginary numbers involve "i", where i = root(-1).

Edit: Heisenberg beated me!

 

[Atrail]

square root of 1 = i
i^2 = -1

 

[bmd]

Originally posted by: Atrail
square root of 1 = i
i^2 = -1

square root of 1 = 1
i = root(-1)

 

[Heisenberg]

i = (-1)^1/2

Edit: Win one, lose one. bmd beat me this time. 🙂

 

[Atrail]

gothca

 

[Geekbabe]

haven't read the book yet, but it sounds fascinating. What do you think?

LOL,I think I got scared that I'd wandered off and gotten lost over in the Highly Technical
forum again ! 😀

 

[bmd]

Originally posted by: baffled2

haven't read the book yet, but it sounds fascinating. What do you think?

LOL,I think I got scared that I'd wandered off and gotten lost over in the Highly Technical
forum again ! 😀

Yeah... My dad bought the book for me and so far I've flipped through all the pretty patterns but haven't really managed to actually read any parts of it yet.

 

[gopunk]

Originally posted by: datalink7
Here for some thoughts on it.

touche

 

[bizmark]

Originally posted by: Atrail
Are irrational and imaginery numbers the same or similar?

Another thing about irrational numbers. There's a subset of those numbers that are 'transcendental'. These are numbers that are not 'algebraic' over the rational numbers. Algebraic means that it solves some polynomial equation with coefficients only in the given set. To give an example, the square root of 2 is not transcendental, because it is algebraic over the rational numbers: you can come up with a polynomial with coefficients only in the rational numbers, whose solution is the square root of 2. E.g. x^2-2=0. There is no such equation for any transcendental number. The most commonly used transcendental numbers are pi (3.14159...) and e (2.71828...).