Beyond, and below the dimensions

[Kevin_Ahab]

Okay, if Jonathan Bowers is here, he would know best, but, anyways.

All dimensions are defined by exponents. i.e Tetraspace is x^4, whereas in general, x^n is dimensions. Now, x^^n, is tetration. Several spaces are definable by tetration, infinite in fact:

x^x^n - Super Dimensions
x^x^x^n - Trimensions
x^x^x^x^n - Quadremensions
etc. etc.
And n can be anything.

From what I interpret, this is analogous to linear, planar, realmar, flunar spaces in dimensions BUT I MAY BE WRONG.

Then you can go onto pentation: x^^^n. Spaces can be defined by this.
This goes on and on and on etc. etc..


THIS IS EXTREMELY HARD TO UNDERSTAND, IT CONFUSES ME IMMENSLY, DO NOT GET ME WRONG, IT IS JUST A GENERAL INTRODUCTION.


Anyways, I was wondering, I know this does not fit exactly here, what are spaces BELOW dimensional spaces - i.e. spaces defined by multiplication, addition and (maybe) counting?

Some would say a plane is defined by multiplication, I disagree, but if I am wrong tell me, some say a line is defined by addition, I disagree, but if I am wrong tell me.

Also, are there any other spaces defined by exponents besides dimensions.

THANKS IN ADVANCED FOR HELPING MY SEVERELY CONFUSED MIND.

[bo198214]

I am not quite sure what you mean by defining spaces for example by tetration. If you are after higher arithmetic operations like tetration, then I am currently writing my thesis about it, so possibly I can answer some questions. This topic was also already here discussed on this forum.

[houserichichi]

I'd love to read your thesis if you need an editor or constructive criticism.

[Kevin_Ahab]

I am not quite sure what you mean by defining spaces for example by tetration. If you are after higher arithmetic operations like tetration, then I am currently writing my thesis about it, so possibly I can answer some questions. This topic was also already here discussed on this forum.

Your topic was FASCINATING, but I (almost, I think) fully understand the function. I literally mean spaces defined by it.

Consider: dimensions are defined by exponents. x^n. A size ten tesseract, for instance, is simply 10^4. NOT THAT SOLUTION (10 * 10 * 10 * 10 = 10000), literally, that is an "Array." A 10 by 10 by 10 by 10 thing.

members.cox.net/hedrondude

Jonathan Bowers (one of my heroes) explains better than me.

Anyways, spaces must be defined by tetration, too!

[PWrong]

So you're trying to find a geometric interpretation of tetration, is that it? All I can think of is a box, where the number of dimensions of the box is equal to the size of the box. It's difficult, because you need an interpretation of a fractional dimension.

[jinydu]

Kevin_Ahab, I think you misunderstand. When mathematicians write things like R^n, they don't literally mean that R is being multiplied by itself R times (after all, how would you even define that?). What they mean is the set of all objects made up of n elements in R in a particular order. So R^n is not literally exponentiation.

[houserichichi]

I think R^n by this Jonathan Bowers guy is standard symbols used in a nonstandard way, ie nonstandard notation. I don't know how to interpret things like x^^^x outside of arrow notation which is defined on number not the spaces that contain the numbers.

[bo198214]

Any references to texts of Jonathan Bowers?

[houserichichi]

He's an amateur mathematician (according to wikipedia) and this is his webpage.

[bo198214]

Unfortunately is "Beyond dimensions" not established yet ...
Where did you read about it?

PS: Didnt know that it is Polyhedron_Dude, though he is not very active here.

[Kevin_Ahab]

He's an amateur mathematician (according to wikipedia) and this is his webpage.

His new one is http://members.cox.net/hedrondude/
Unfortunately, it seems he abandoned the section relating to this.