I saw a youtube short, tiktok like video of a metal sphere being attracted multiple times slower towards the earth when passing through a long metal tube from eddy currents causing motion resisting fields, I commented, “This makes me think of an outer space touchless satellite relocator, have a moving belt of powered electromagnet mini satellites at a circle around the big satellite, have each mini satellite be an electromagnet, and push and pull the big satellite forward a vector direction to a new location or orbital height. The mini satellites propel forward causing continuous drive field on the big satellite, This also makes a touchless magnetic broom to gather and sequester space junk., the sphere travelling vastly slower through a tube with a motion resisting external field could be utilized to separate all kinds of materials because of diamagnetic repulsion, grind up recycleables without sorting, then use diamagnetism to sort them as they circle around and around at a torus, could just possibly also sort chemical products, touchlessly sort living cytes, and maybe even magnetically sort/steer electrophoresis of proteins and other chemicals., Youtube also says magnetic response is used medically I also commented, if you use a cube magnet to traverse the tube will it automatically orient itself a particular side/pole up to respond to the field. using the right hand rule of EM you could find the direction right, from electricity's perspective at all 720 degrees of a sphere. the direction right could have the additional meaning of opposite or with gravity right. with towards North always being right.
A youtube video tries to figure out what a 4D sphere looks like/goes together/is really, I commented: its possible that the math of a 3D vector, now maybe called a tensor could be described as that mapping where if any direction of the tensor (or three or four fingers spreading) always connects back to the origin of the individual rays of each linearity of the three or four ray tensor. a smoothly connected surface that does that would be a kind of 4D sphere. as a bonus, youtube just told me about a completely new kind of way of being 2 or three dimensional, which is what mathematicians call a blade, where as compared with a plane from the intersection of any two vector rays to make a 2d plane area from the diamond/square the vectors make together, so just find out if a 3D space made with 3/4 ray tensors ever makes a 3D blade, which would be an unexistent, or perhaps existent but new to my awareness/physics new way to be an extra dimension different than 3 dimensions, a 3d'' if the 3D i live in is called 3D' (3D prime), so if you feel vague, you could define a topology where 3D' sphere is a possible 4D hyperdimensional blade, then if you want to, arrange the three D prime sphere blades to all be capable of interconnection, then just as the awesome mathematician at the youtube video says, that could Look Like a 4D sphere, just a blade composition 4D blade, there is lots more, like negative number blades making negative 3 dimensional space, or complex number like mixed positive and negative ray attribute tensor spaces, noting that 2^3 is 8, there might be at least 8, or 9+ (blade tensor effects) or many more distinctly different 3D sphere forms, or 8-9+ completely different ways to be a 3D sphere. so the number of things that is a way a 4D sphere could go together if made from 3/4 ray tensors is likely much larger than 8-9+

I once enumerated 14+ things that have a nonlinear time attribute like delayed choice quantum eraser forms, time asymmetric K leptons, and what wikipedia calls time crystals, and many others, a new to me use of these is that time, as a single dimension, considered as a ray, suddenly becomes a vector when there is a time novelty, and two vectors intersecting form a plane or blade, that suggests that causlity and time traversal puzzles, and technologies if it is possible to make a composited 2D time blade, from plural human linear times, or previously described plural 14+ kinds of time technologies/objects

youtube video of gecko feet polymer tape that is unsticky when touched, but when placed on a shperical surface then turned upside down adheres to the surface, thinking of different angles and forms of the gecko feet microtexture, I commented: Good for vehicle windows, anti-sticky at most of the surface, reversed under each shingle patch to be sticky, sheds condensation rapidly from most of the viewing area, has a shingle base just big enough to sticky an entire gravity roll-off water droplet, you get a windshield, or camera lens/video lens that rolls off water and functions without distortion during rain. This could also be used at vehicle and airplane surfaces to shed water, improving mileage. Could possibly be used to increase the velocity and effectiveness of water collecting drinkable/agricultural water from rain condensers, keeping water from evaporating off the condenser surface, and the condensed water shedding always leaving fresh cooling/deliquescent/electrowetting surface to grab more water out of the air, some edits from video comment

Hi Madja, I was hoping to pay you to advertise your fiverr service, not do a service that quora pays you for. The ad attracts people just like me, with a lot of hours of work for you, and the same activity you do for me now. are you sure you do not want to do it. I am like your free english as a first language advertisement writer so you can attract more fiverr jobs! It is kind of like a tip that comes with a multi hour job. also, you could put up hundreds of advertisements, except each would have a unique paragraph from me so fiver would like them

I think bivectors might be the name for two vectors whose rays intersect each other creating a plane, but two corner angles/brackets nested together might overlap as vector angle area spaces, possibly creating blades, or things different than blades and different than planes, if you have two rotating angle bracket vectors, like hands of a time piece next to another time piece, sometimes pointing towards each other making a rhombus (plane generating), sometimes making nested angle brackets (blades and other things), sometimes opposite, making nonmeeting non extra dimension generating >< (unless they are embedded on a 3 space like sphere or volumetric saddle or torus, where they then meet up and make a curved plane, or, amazingly, a new undulating (volumetric saddle)form of dimensionality,, at physics, being able to rotate a duotimepiece image from >^ to/from ourspace <> vector planes, also to >< dimensional excluders creates new forms of 3D space fissions and fusions which might be portable to 3D actual physics new forms of fission and fusion, making new energy sources, possibly something could be done with relations between relativity frames of reference, and turning the ricci tensor from a smooth but FEAish image to a stochastic >^V< rotationg vectors or tensors math space, sometimes they align or dealign to modify or disintegrate 4D spacetime, making new time technologies possible with patterned rather than stochastic replacements of the ricci tensor of <V^>

I think bivectors might be the name for two vectors whose rays intersect each other creating a plane, but two corner angles/brackets nested together might overlap as vector angle area spaces, possibly creating blades, or things different than blades and different than planes, if you have two rotating angle bracket vectors, like hands of a time piece next to another time piece, sometimes pointing towards each other making a rhombus (plane generating), sometimes making nested angle brackets (blades and other things), sometimes opposite, making nonmeeting non extra dimension generating >< (unless they are embedded on a 3 space like sphere or volumetric saddle or torus, where they then meet up and make a curved plane, or, amazingly, a new undulating (volumetric saddle)form of dimensionality,, at physics, being able to rotate a duotimepiece image from >^ to/from ourspace <> vector planes, also to >< dimensional excluders creates new forms of 3D space fissions and fusions which might be portable to 3D actual physics new forms of fission and fusion, making new energy sources, possibly something could be done with relations between relativity frames of reference, and turning the ricci tensor from a smooth but FEAish image to a stochastic >^V< rotationg vectors or tensors math space, sometimes they align or dealign to modify or disintegrate 4D spacetime, making new time technologies possible with patterned rather than stochastic replacements of the ricci tensor of <V^>

commenting on a video about how “are multivectors invertable” then “proves” they arent with a math solving process where a squaring of 1+vector1 is one, but a squared multivector is 2, 2 does !=1, but popping it up that way could do the comment: or, maybe with an additional math term, or maybe just as is it spontaneously pops off and up out of the 2D vactor dimension, where two vectors together generate a 2D plane, into thrilling three dimensions, pop it up again to generate a 4...5,6,7,8,9+ dimensional space, pop it some other way and make string theory math dimensions

a magnetic levitation 3d field opposite to a a body that does levitation exterior opposite-of-a-three ring towards gravity gimbal that then completely compensates for bodies resisting motion from acceleration near gravity (F=MA) newtonian physics makes it so that any bodies in the middle of the anti-gimbal omit resisting motion, making them hypermotional, but only with their own energy or applied energy, zeroer zero-G, true zero G rather than microgravity, this could be used at gravity wave detectors, new force measurement detectors, scales, kilogram definitionalizations, and completely new detectors of new physics forces that are previous to being measured, verified, and known, it might even be a new non-RF/EM sundet gene effect detector, or remotely possibly, but maybe not, relativity jitter detector
comment on a reply, “@angelmendez-rivera351
12 days ago
@shoam2103 The answer to your question is no. In general, it is not possible to define the geometric product in terms of "more elementary" or "more familiar" products. The geometric product is itself just defined axiomatically. It is what other products are defined in terms of, instead. This is like how, when you learn grade school arithmetic, the counting function, also known as the successor function, cannot be defined in terms of more elementary functions. Rather, it is itself the most fundamental and most elementary non-trivial function when it comes to simple arithmetic structures, and so, it can only be defined axiomatically
“ to a youtube video about vector products that the video maker thinks , I commented to the reply: that contributes to my thoughts on how godels incompleteness theorem a=!A contains a steplike computery process step, you've called it with its math name , sucessor function, is axiomatic rather than proven, now to excitedly look up sucessor function on wikipedia to find out if there are 2D or curving or looping or fractal successor functions. Cool! thanks for your great comment.” to a video on “The geometric product is not the sum of the inner and outer products!” that reply is to, “@angelmendez-rivera351
12 days ago
@shoam2103 The answer to your question is no. In general, it is not possible to define the geometric product in terms of "more elementary" or "more familiar" products. The geometric product is itself just defined axiomatically. It is what other products are defined in terms of, instead. This is like how, when you learn grade school arithmetic, the counting function, also known as the successor function, cannot be defined in terms of more elementary functions. Rather, it is itself the most fundamental and most elementary non-trivial function when it comes to simple arithmetic structures, and so, it can only be defined axiomatically”, looking up successor functions at wikipedia, wikipedia says, “Several constructions of the natural numbers within set theory [or math more parsimonious than set theory][utilizing succession]”…For example, John von Neumann constructs the number 0 as the empty set {}, and the successor of n, S(n), as the set n ∪ {n}. The axiom of infinity then guarantees the existence of a set that contains 0” That brings up the idea of beyond turing machine computers and math to build new computers with, an amusing variant on the jocular “what if arrays didn’t start at zero, started at one” programmers say