Table of Contents



 

Hyperspheres, Hyperspace, and the Fourth Spatial Dimension






Subtitle: A Look at the Universe as a Higher-Dimensional Brane World



 
   
 







Title Page/Introduction, Links to Other Sites, Latest Updates









The Two Reader's Digest Condensed Essays





Short Essay #1: The Transformation of the Conventional Model of the Universe into a "Brane-World" via the Extra Dimension Theorem


Short Essay #2: Is There Physical Evidence for a "Large" Fourth Spatial Dimension?







Main Sequence of Essays


 

 
Essay #1: A Hierarchy of Structures - Circle/Sphere/Hypersphere
 

Essay #2: Perceptions in Hyperspace: How the Antipode Affects our Observations
 

Essay #3: The "Finite But Unbounded" or "Brane-World" Universe

Subtitle of Essay #3: The Extra Dimension Theorem

 
 
Essay #4, Part I: A Brief Discussion of Quasars 




  
Essay #4, Part II: Quasars in the Mid Three Range of Reshifts
 

Essay #5: Anomalous Observations in Deep Space



Essay #6: Conventional, Radio, Infra-Red, and Lyman-Alpha Galaxies

Essay #7: Absorbers


Essay #8: Putting It All Together...Counterimages?    Maybe!
 

Essay #9: Final Comments


  
 




 

Appendices

  

    
 
  1. Embeddedness - When is it OK? (Essay #1)
  

  2.  How the Fourth Spatial Dimension Relates to the
First Three (Essay #1)
  
  3.  How to Create a Hypersphere (Essay #1)
  
  4.  Brief Comments of Willem de Sitter and Albert
Einstein on Curved Space. (Essay#2)
  
  5. More Recent References to Cosmological Models with
an Antipode (Essay#2)
  
  6. Hyperspace as a Gigantic Lens: 1/cosθ
and 1/(cosθ)2 (Essay #2)


    (If you get θ rather than the Greek letter for theta, take the link to Appendix 11 below.)

  
  7. Sources for Alignment Errors in "Counterimages" (Essay #2)
  
  8. A Few References Mentioning Perception of Objects
Near an Antipode (Essay #2)
  
  9. Do It Yourself Cosmology: Ned Wright's Javascript (Essay #3)
  
    Subtitle of Appendix 9: The Cosmological Parameters (Essay #3)
 
  10. A "Round Trip" in a Collapsing Hypersphere (Essay #3)
  
  11. The Greek Alphabet (on Internet Explorer and Netscape) (Table of Contents)

  12. A Brief Note on Methodology: The NVSS Distribution/Expectation Table

 

 

[When you hit the "Return" link at the end of each appendix,
you'll go back to the part of the main essay from which the link to the respective
appendix was made.   The essay in parentheses following the appendix shows the essay which has  the link to that appendix.] 

   
 






  List of Figures:  


(The parentheses indicate the file in which the figure appears.)




Fig. 1: Around and Around (Short Essay #1)

Fig. 2: Flat or Curved?  (Short Essay #1)

Fig. 3: Friedmann Space or Riemannian Space? (Short Essay #1)

Fig. 4: Same Space? (Short Essay #2)

Fig. 5: Or Different Space. (Short Essay #2)

Fig. 6: From Friedmann to Riemannian Space (Short Essay #2)

Fig. 7: The Standard Mercator Projection (Essay #1)

Fig. 8: The Polar Projection (Essay #1)

Fig. 9: S2 Projected Onto V2 (Essay #1)

Fig. 10: Embeddedness: S3 Projected Onto V3 (Essay #1)

Fig. 11: Appearance of a cloud on a spherical surface (Essay #2)

Fig. 12: Appearance of "Standard Candles" on a spherical surface (Essay #2)

Fig. 13: The Perception of an Exponentially Increasing Distribution on a Hypersphere (Essay #2)

Fig. 14: The Lyman-Alpha Forest - Is there an Explanation in Topology? (Essay #7)

Fig. 15: The Normal Distribution (QSO Appendix #4)

Fig. 16: Counterimages: The Most Likely Red Shifts to Find Them (Essay #8)






 



  Quasar Tables:  






Table 1: Veron 11th, RD = .25 to .41, z = .303 to .607 (QSO/AGN)

Table 2: Veron 11th, RD = .42 to .58, z = .607 to 1.085 (QSO/AGN)

Table 3: Veron 11th, RD = .59 to .75, z = 1.085 to 2.039 (QSO)

Table 4: Veron 11th, RD = .76+, z = 2.039++ (QSO)

Table 5: 2QZ in Veron 11th, RD = .25 to .41, z = .303 to .607 (QSO/AGN)

Table 6: 2QZ in Veron 11th, RD = .42 to .58, z = .607 to 1.085 (QSO/AGN)

Table 7: 2QZ in Veron 11th, RD = .59 to .75, z = 1.085 to 2.039 (QSO)

Table 8: 2QZ in Veron 11th, RD = .76+, z =  2.039+ (QSO)

Table 9: SDSS in Veron 11th, RD = .25 to .41, z = .303 to .607 (QSO/AGN)

Table 10: SDSS in Veron 11th, RD = .42 to .58, z = .607 to 1.085 (QSO/AGN)

Table 11: SDSS in Veron 11th, RD = .59 to .75, z = 1.085 to 2.039 (QSO)

Table 12: SDSS in Veron 11th, RD = .76+, z =  2.039+ (QSO)

Table 13: Veron 10th, RD = .76+, z = 2.039++ (QSO)

Table 14: Veron 9th, RD = .76+, z = 2.039++ (QSO)


 





 QSO Appendices 


 
 
    
Appendix 1: Table Guide 
    
Appendix 2: Table Terminology 
    
Appendix 3: Table Construction
 
    
Appendix 4: Standard Deviation (σ)