bijective connection

[AntonioLao]

The connection to external reality as philosophically believed can be accomplished subjectively or objectively. For those who preferred advocating subjectivity, they will eventually realize that knowledge is merely subjective from personal idiosyncrasy and individuality and that there is no external or objective truth. For those who insisted on the doctrine of objectivity, they believed that the external world exists independently of the mind and cannot be influenced by personal feelings or opinions.

In the precise mathematical definition of continuous spacetime transformation from one region to another connected region, the connection is called injective if there is a one to one connectivity while if one member of the codomain (a set of well defined elements) is the image of at least one member of the domain (a larger set of well defined elements) then it is defined as an “onto” or surjective connection. At most surjectivity implies many-to-one connection. Injectivity can be used to define a linear function while surjectivity for nonlinear functions. Nonetheless, a connection that is both injective and surjective becomes a bijective connection.

[labelwench]

Based on your opening post, and the definitions you have supplied for the words used, I would contemplate that many human beings have a bijective connection to the way in which they experience the universe.

Inanimate forms would enjoy at least an injective connection to the universe itself, and all forms have some degree of surjectivity between each other and having the universe in common.

That's my thumbnail summary for further contemplation.

Thank you for an interesting post and some new words, Antonio.

[Lloyd Gillespie]

I see subjective math knows as much as it ever does__Nothing__when eliminating the larger external objective Universe__of any possible experimental proofs__The major problem it's had, for the last 100+ years...

[labelwench]

I see subjective math knows as much as it ever does__Nothing__when eliminating the larger external objective Universe__of any possible experimental proofs__The major problem it's had, for the last 100+ years...

Now, Lloyd, just because I don't do spatial and conceptual math, doesn't imply that I can't attempt to have a conversation with a mathematician. My subjective math skills may be poor, but I am excellent at budgeting and balancing accounts.

[Lloyd Gillespie]

Lorrina, I wasn't addressing your skills__I was addressing the subjective only, math issue...

[labelwench]

Perhaps I could prevail on your language skills in asking if you have more detail to add to Antonio's use of the terms injective, bijective and surjective? You seem to be a walking encyclopedia on the history of words and their usage, and it is ever so much more interesting to learn these things from people than just wandering off and doing more research on my own.

I've got some chores to do and wood to split after I shovel a path to my woodpile, so I'll check back later to see if you have taken me up on the invite.

[Lloyd Gillespie]

Hi Lorrina, and the way I use injection, bijection and surjection is in mapping one concept or model to another. The three classes stand for partial one to one mappings, directly and indirectly partial mappings, and including both directly and indirectly mapped up to isomorphism, or where one concept matches and transforms into the new concept or model. It's the logical or mathematical matching and mapping of one idea to another, according to the number of possible matchings. It can be used as either mathematical or logical mappings. If one starts with a pure measurement of a known objective entity first__it works best__In other words concepts and ideas must be both rational and empirical to start with, or they be subjective intuitions and imaginations, which may not pertain to reality...

Put simply, it's like painting a sphere by numbers, when the numbers exist only on a separate flat sheet of paper, as a pattern__you have to transfer the mapping number points from the flat sheet to the sphere__can be tricky... All modern flat global maps are done with this mathematics__Peirce was the first to do the quincuncial maths, which is a very similar idea, except he developed the algorithm for it... http://en.wikipedia.org/wiki/Peirce_quincuncial_projection

It's technically explained here...Link...




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[labelwench]

Thank you very much, Lloyd, and I will study those links after a sleep, and before shift, which will give me something to ponder while we are stocking the shelves like demented elves.

The reason I ask you to expand on what Antonio has presented is for the assistance it gives me. Your way with words, your dialogue style and your links aid me to understand better at least some of what Antonio presents, the shortcoming being mine on these subjects.

When persons become very accomplished in any field of learning, it becomes more difficult sometimes to share one's knowledge and concepts, as others do not have the same frame of reference.

I perceive you both as very interesting and experienced gentlemen, though your opinions may vary on many topics.

Thank you both for taking the time to reply and share your expertise.

Oh, I see you have added an image! Excellent! I am tactile and visual, and enjoy multi-textured learning.

[labelwench]

As we approach that time of year, some Christmas cookies for you gentlemen......

[AntonioLao]

Thank you for an interesting post and some new words

If I can make you understand these new words for aiding me in formulating a physical theory of quantized spacetime then I have done the "impossible."

You are correct that human understanding follows a bijective connectivity. This is more so in our conscious effort to understand the existence of God. And if God is the first and foremost mathematician then I would be interested in understanding the math God uses.