CTK Exchange
CTK Wiki Math
Front Page
Movie shortcuts
Personal info
Awards
Terms of use
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Recommend this site

Manifesto: what CTK is about Search CTK Buying a book is a commitment to learning Table of content Products to download and subscription Things you can find on CTK Chronology of updates Email to Cut The Knot Recommend this page

CTK Exchange

Subject: "Moving through a 4D space"     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange This and that Topic #896
Reading Topic #896
Chris
guest
Apr-29-09, 07:21 AM (EST)
 
"Moving through a 4D space"
 
   Hello Alex Bogomolny,

My name is Chris, and I am a high school student, fascinated by the fourth dimension.
At first I thought it was impossible, even mathematically, but then I thought: If sqrt(x^2+y^2) gives the distance between a point and the Origin in 2D, and sqrt(x^2+y^2+z^2) gives the distance between a point and the Origin in 3D, then perhaps sqrt(x^2+y^2+z^2+w^2) gives the distance in 4D.

I started searching the internet, and after a while I found your Java aplets on https://www.cut-the-knot.org/ctk/Tesseract.html. I find this absolutely fascinating.

I was wondering: If a tessaret can be rotated in four dimensions, perhaps it is also possible to let objects interact with eachother in 4D. perhaps it is possible to assign values to an object: depth, height, length, hyperDepth. and then use the same programs used for making for example three dimensional gaming programs, and adapt them to the fourth dimension, to simulate a real time four dimensional environment.

Also, perhaps it is possible to then develop a virtual camera within the program, that 'films' this virtual 4D environment, and projects it onto a 2D image, for your screen, the same way we use it to film virtual 3D environments in for example computer games. Is this possible, to film it in 2D? or would it have to be 3D, because 2 dimensions difference is just too much? we can show 3D on 2D images, but not 3D on 1D, so perhaps 4D on 3D can be done, but 4D on 2D cannot.

Perhaps my ideas are crazy, but I have been thinking about this for very long, without being able to get my mind off of it, and I just wanted to share it.

Chris


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
alexbadmin
Charter Member
2366 posts
Apr-29-09, 07:33 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: Moving through a 4D space"
In response to message #0
 
   >then perhaps sqrt(x^2+y^2+z^2+w^2) gives the distance in 4D.

That is definitely the case. In fact, in spaces of higher dimensions (beyond 4) the distance is measured in the same manner.

>I started searching the internet, and after a while I found
>your Java aplets on
>https://www.cut-the-knot.org/ctk/Tesseract.html. I find this
>absolutely fascinating.

Thank you. Truth be told, I, too, spent a lot of time with those applets.

>I was wondering: If a tessaret can be rotated in four
>dimensions, perhaps it is also possible to let objects
>interact with eachother in 4D. perhaps it is possible to
>assign values to an object: depth, height, length,
>hyperDepth.

Of course.

>and then use the same programs used for making
>for example three dimensional gaming programs, and adapt
>them to the fourth dimension, to simulate a real time four
>dimensional environment.

Yes, probably. Depends on how this programs are written.

>Also, perhaps it is possible to then develop a virtual
>camera within the program, that 'films' this virtual 4D
>environment, and projects it onto a 2D image, for your
>screen, the same way we use it to film virtual 3D
>environments in for example computer games. Is this
>possible, to film it in 2D? or would it have to be 3D,
>because 2 dimensions difference is just too much? we can
>show 3D on 2D images, but not 3D on 1D, so perhaps 4D on 3D
>can be done, but 4D on 2D cannot.

Wikipedia has a good article on 4d and reeferences

https://en.wikipedia.org/wiki/Fourth_dimension

>Perhaps my ideas are crazy,

No, not at all. Modern physics, based on the string theory, implies that the world we are living in is actually 20D or so.

>but I have been thinking about
>this for very long, without being able to get my mind off of
>it, and I just wanted to share it.

Thank you


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to have a look at the old CTK Exchange archive.
Please do not post there.

Copyright © 1996-2018 Alexander Bogomolny

Search:
Keywords:

Google
Web CTK