My personal approach to Vectors

Motivated by personal feedback by @EDILSON CARVALHO  and 
an excellent presentation of @Michael Braam  related to Vector Search I'd like to share
my personal approach to Vectors.

When I started and met vectors with 256, 384, and over 1200 dimensions - I felt lost.
However my example Vector-inside-IRIS - a simplification of iris-vector-search - worked fine.
 
In order to understand the mechanics behind it, I decided to start in small steps.
Our common 3 dimensions describe our physical world quite fine.
Even the half 4th dimension (no negatives) added by Einstein is not to hard to follow.
Cosmologic string theory with 0 to 11+ dimensions was a real border line to me.

So back to start : => 2 dimensions are enough for a beginner.
Geographic coordinates provide a nice starting point with sufficient test data.
VECTOR_COSINE() function was my primary target in my example geo-vector-search

The range of results from -1 to +1 is easy to interpret in a quasi-flat projected map.
That's basic mathematics and its transposition to an additional dimension is not a miracle.

But what about some hundred dimensions?

;#1
-.0104943, .01472898, .07107521, .07168121, -.0937807, .05828459, .04451195, -.1045385, -.0110124, -.0240547, -.0032111, -.0030188, -.0414225, -.1092015, .02203945, -.0129255, .14087346, .04734043, -.0181046, -.0458297, .02323769, .02859951, .01124321, .00857456, -.0049756, -.0144282, -.0846236, -.0284645, -.0147692, -.0989931, .04880870, .01899284, -.0176833, .04763242, -.0808972, -.0604988, .05757499, -.0638228, .04217084, .03707900, .03757081, .03086806, .02773610, .02082979, -.0495735, -.0337784, -.0438372, -.0827000, -.0018084, -.0072785, -.0797550, -.0055747, -.0551242, -.0918905, .01140710, -.0115834, -.0088469, -.0445509, .02972822, .04385065, .04125113, .01189815, .01809763
;#2
-.0340279, -.0930349, -.0356242, .03200291, .07393958, -.0164658, -.0218968, .01392244, -.0069597, .02677908, -.0800164, .07227557, -.0430033, -.1134698, -.0561500, -.0520939, -.0306403, .00750979, -.0345837, .03335380, -.0438071, -.0088005, .03423582, .00794844, .01172804, .05204785, .04179215, .01768089, -.0489745, -.0031708, -.0349655, -.0482467, .08090461, -.0596610, -.0565769, -.0043313, .01015284, .07152537, .04189436, -.0475862, -.0171517, .03899634, -.0705699, -.1133416, .08019342, .02138555, .01466019, .00184080, -.0905641, -.1039420, -.0290395, .02753796, .01674868, -.0259464, -.0107869, -.0407411, -.0120343, -.0636389, .00047146, .01514394, -.0694578, -.0204190, -.0024446
;#3
.00350692, .09432639, .01641871, .09951058, .10459023, .00019239, -.0823584, -.0022799, -.0227801, -.0023362, -.0397562, .07449327, -.1137044, .09173037, .08620572, -.0881805, -.0111093, -.0316556, -.0044012, -.1248759, -.0897788, .03191807, -.0147239, -.0198379, -.0849955, -.0026861, .02628867, -.0523788, -.0398543, -.0080245, .06736382, .01456158, .04700677, -.0171667, -.0217174, .06761254, -.0070750, .02879706, .01109632, .02541129, -.0384420, .00410159, .05145533, .06493697, -.0924961, -.0422163, -.0739539, .06107471, .06070494, -.0044191, .00238501, -.0182966, .03546700, .05925614, -.0361021, .09686610, .02930910, .01282224, .02953721, -.0526526, .03977891, .00501585, .00717564

the example here is shortened for readability

After thinking it over for some time I found a personal image:

• When I search for a target in Google Maps that is not just around the corner I get a choice of routes offered.
• the shortest one, the fastest one, the one with the least fuel consumption,   public transport, ... 
• and I make a choice according to my needs
• interpreting the dimensions of my vectors as numbered intermediate steps to my target I would get a similar picture
• And by VECTOR_COSINE I get the best proposal

LLM experts may laugh about my simplification.
But to me, it's a picture beyond abstract mathematics and confusing language theories.
And I believe my simple picture based on a daily used process in car driving
helps to understand how results are found.

NOTE: I still have no idea of HOW those vectors are calculated as long as it's consistent.
It was important for me to understand how the matching works.