OneWorldOneNumber

Not even sure how to begin with something " imaginary" and build insight through questions on this, " seriously." From my book on Elementary And Intermediate Algebra, page 584. Talks about the ideas behind the use of a number that is a square root of -1 also referred to as i Uhmmm, Ok.....So then " where did complex numbers come from then?? The page goes onto to mention how negative numbers do not have negative squared roots... Understood, however then it says: Larger number systems that contain the " real number systems" " Real number - Wikipedia" is designed so that negative numbers do have squared roots. Ok....... Who was this designer??? And why are Larger numbers able to do this??? Hope i made sense here...

From what I gather " from the 2 book images", it seems that water " is used as a base" to understand the "bonding" of soil or its mass relationship to force? So force I assume is homogenous at any scale??? Another notion, i see a gradient too, meaning from large thick pieces of soil, to less thick to less thick, until the most finest pieces of soil are found at the top... In other words from dense to less dense and least dense... I will further research the links provided, I want to fully understand this... Great information! Thanks for making the logic more clear, it makes 100% sense! I can't help but to ask, please correct me if i'm wrong. Because of the "scale factor" ie, our accuracy "homogenous issue" at molecular levels, dealing with electrostatic forces from micro to macro, can we " assume" forces in general are homogenous? Just as our methane molecule example you can hand out one molecule of methane, I assume you can do the same with force, because shouldn't force be "logical?" Shouldn't force be an observation at any scale???

I see mineralogy books are quite expensive but worth paying for considering the rich information they contain.. Id personally invest in this field 1st before tackling on physics. You stated: Note that we live in a 3D world so we really need to work in terms of volume not area. This came to mind: About " volume 3d, and cubic centi-meters or "units these represent." for my grid example " 4th comment" with the green shaded area that represents non-homogenous location.... Some further insight... When you say, 3d as volume, do we "still consider this "a complete body of mass?" isn't this the same as our homogenous issue? Should it be "individual 3d Volumes<--- as plural? I'm thinking ""intermolecular forces??""" but i'm not too sure now because of the homogenous issue. Another notion, what would these masses be relative to? Earth's gravitational attraction is rather weak i've read.

Has there been any research to prove this scientifically and/or visually other than an electron microscope or another "way" to show that this is true?

Very well understood and thanks! One of the reasons I placed a green shade in my grid with the x in the boxes " above 4th comment " was incase I needed to understand an individual molecule.. In this i mean, our homogenous " issue." So with this new information, would this green shaded area vary in: density? mass? electro static force? Since we are now dealing with molecules, I assume the entire grid "sponge cake" varies in the aforementioned not just the shaded area, is this correct?

I really want to make sure i am on the same page with you.. Is homogenous something that is "balanced" or synchronized with something else? I'm seeing elements and compounds appear to share this same property?? From google search: What are some homogeneous examples? Examples of homogeneous elements are: nitrogen in a balloon, mercury in a thermometer, or gold in an ingot. Compounds can be homogeneous. Examples of homogeneous compounds are: carbon dioxide in a balloon, water in a bottle, or plastic forming an electric socket. I just want to note, of the nitrogen in a balloon and carbon dioxide in a balloon and the others behave either gas like or fluid like?? Now i cannot resist to ask: Does Homogenous also deal with " ions" like those in sodium chloride? There spacing and formation I mean. Also, what I mean is how they " arrange" and re-arrange themselves " the atoms" I mean " at random. Here is what I mean. Sodium Chloride (NaCl) Crystal | PhysicsOpenLab When I "visualize" something homogenous i envision this image of something x that has the same value through a topology at every point in " the mass" of the clay. I'm not to sure if this means " without gravitational forces" from earth though because anything with mass is influenced by it. This is a great reply and thank you, I will research everything you have stated and study it in detail to further understand this..

Does clay remain uniform even when you pound it, shape it or mold it with a "Pot Wheel? " I have looked online for information and "did find" some resourceful information, but "visually" such as a "lattice" or other uniform topologies I am "very" confused. Here is what I mean: Here is an image: Wikimedia-Commons.png (2000×736) (d1whtlypfis84e.cloudfront.net) The reason i'm confused is in due part of the spacing in-between the particles themselves" "What Governs This?" I guess im asking about electron configuration, or electro static attractions from particle to particle, " IE" Ionic Solids, if this helps.. Here is an image: 2 (2213×1167) (mtstatic.com) Here is my question "answered by Wikipedia" but I really would like to confirm this here, as " i was under the impression" that clay is like "glass" and glass is an "Amorphous Solid" not uniform " a " Super Cooled Fluid" and fluids are " from what I know" not Uniform rather chaotic. Topology - Wikipedia In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending. Hope I made this clear enough....Thnks In Advance!