Hyperdimensions Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 03/04/2017, 10:31 AM Hi, everyone! The oldest dimensional base units like i[0]=1, i[1]=i (imaginary unit), i[2] and i[3] (quaternions), i[4] ... i[7] (octonions), i[8] ... i[15] (sedenions) ... etc. is called ancient-dimensional base units (by me). The less old dimensional base units where the indeces can be any real is simply called old-dimensional base units. Its PARI/gp code looks like this one: Code:twist(p,q)={ L=ceil(1.4426950408889634*log((max(q+1,p+1)))); res=1;sta=1; if(round(p)!=p||round(q)!=q,p*=2^60;q*=2^60;L+=60); p=round(p);q=round(q); T=[1,2,3,4;2,2,5,6;3,6,3,5;4,5,6,4;5,6,6,6;6,5,5,5]; for(i=0,L,j=L-i-1;k=2*bittest(p,j)+bittest(q,j)+1;sta=T[sta,k]); if(sta==4||sta==6,return(-1),return(1)); } xor(x,y)={return(bitxor(round(x*2^60),round(y*2^60))/2^60)}So i[x] i[y] = twist(x;y) i[x xor y] And for instance the graph of i[y] = i[1] i[x] looks like this: https://www.dropbox.com/s/81rxif99w7j50u...D.bmp?dl=0 As you can see the sign of the function is alternating. Okey, so these were the old-dimensional numbers. The so-called hyperdimensional base units are base units whose indeces can be complex, quaternion ... so simply old-dimensional numbers. For example these are hyperdimensional numbers: i[1+i+i[2]] i[i[0.5]-3] i[0.3+i[100]-i[7]+i[pi]] My question is that how to multiplicate two hyperdimensional base units according to the T matrix above in the code? I think we should extrapolate the T matrix to 3D matrix, but how? Xorter Unizo tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 03/09/2017, 01:23 PM I really do not know what you are talking about ... Regards Tommy1729 Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 03/09/2017, 07:53 PM (This post was last modified: 03/09/2017, 07:54 PM by Xorter. Edit Reason: grammar ) (03/09/2017, 01:23 PM)tommy1729 Wrote: I really do not know what you are talking about ... Regards Tommy1729 I call the complexes, quaternions, octonions, sedenions ... etc. ancient dimensional numbers. (But it is not so important.) Look: https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia.org/wiki/Octonion https://en.wikipedia.org/wiki/Sedenion And here is a summation for N-dimension: http://jwbales.us/ We have a 2^n dimensional space with base units. These are the dimensional base units whose multiplication is that I am interested in. I found some formulas to calculate it. But I must step toward into the so-called hyperdimensional spaces with its hyperdimensional base units. I would like to know how I can multiplicate two of hyperdimensional base units. Are we closer to understanding? Xorter Unizo « Next Oldest | Next Newest »