Despite public opinion being what it is, Evolution is not a theory. Evolution is a process that is evidenced by the diversity of living forms, the diversity of the fossil record, the diversity of our cultures, religions and so forth. Evolution is, quite simply, a label we apply to the gradual change of something over time. It is literally the Möbius strip of the general change away from current states and forms into differing states and forms.
Evolution itself is not a theory.
The means of the change is.
When a biologist stands up behind a podium or lectern and says something about the “Theory of Evolution,” they are doing the public a great disservice. They are simplifying and truncating the actual theory, the theory of evolution by means of natural selection, to the now colloquially understood phrase. Not only does it allow the confusion of the public understanding of what Charles Darwin did, allowing them to believe that he came up with this process out of whole cloth and that the phrase, terms, and concepts just didn’t exist prior to his inventing them, but it makes it more difficult for us all to communicate about the theory.
Ill illustrate this with a story.
Recently in my Linear Algebra course we were discussing how to confirm that a given Transformation is in fact Linear and my instructor said there are two tests that must be executed. One of them is linear addition, and the second is the scalar multiplication, as shown here.
As with all students of this day and age I wanted to simplify my notes, as it occurred to me… scalar multiplication is a linear test, so why do we need to bother with both? When I asked, my instructor tried a few things, but suffice to say, it didn’t seem to make a difference. Luckily this was on a Friday and I had two days to think about the situation, please follow my logic.
Given that v and u are vectors, and we have to follow WOLOG (WithOut Loss Of Generality), scalar multiplication is really just addition of a second term that is just the first scaled. So the scalar test can be rewritten as …
While this does not test all elements in the universe of the vector space that u and v live within, since the universe has to include the scalar multiplied values of u within it. That is to say that while you cannot rely on the Scalar test to confirm that it is linear you can rely on the addition test because it will already include all elements of the scalar test.
This is a lot like the deductive logic puzzles on the LSAT where you walked through a series of characteristic statements and were asked to draw a conclusion…
Some students are male. All males have penises.
Therefore, some students have penises.
To rehash, this is my argument:
1. The vector u must exist within a closed vector space.
2. One of the requirements of a closed vector space is being able to multiply by an arbitrary constant (AKA Scalar Multiplication).
3. Therefore, no matter the vector chosen for u, its scalar values have to exist within the closed vector space.
The good news is, on Monday when my instructor, Mr. Frank Soler who has a doctorate but does not like to be called a doctor and has my appreciation for it, couldn’t find an example of a transformation that passed the addition test and failed the scalar test, under the standard definition of scalar multiplication because of what I have described above so I don’t need to bother with this second test. Scalar multiplication is a distributive application of multiplication. The problem is, the scalar multiple applies to all elements in the vector. His solution was to redefine the term as follows:
But wait, redefining scalar multiplication breaks all that we have come to know and love =( Our use of the dot product makes use of the scalar multiplier and that isn’t to mention all of the other work throughout vectors that just doesn’t make sense. The purpose of the scalar multiplier is to scale the vector some arbitrary length. All of our graphing, and for that matter graphic, needs come down to scalar multipliers being applied to the normalized orthogonal unit vectors to reach a point without too much complication.
It didn’t take long, but when he redefined this he quickly found an example that passed the linear test but failed the scalar test. Unfortunately for him though, this change completely invalidates all that we had learned, so I defined my answers on our next quiz as the correct ones and wrote it as such, so I’m sure I got them correct. I’ll find out on Monday if my redefinition is as useful as his was.
The reason we have this evolved language is to facilitate communication. Why overcomplicate things by making it so when I say car I mean truck, bus and so forth when each of those things have their own terms to set them apart (I admit I have no idea what category the SUV falls into, oh wait). If I were to grab hold of a term, like tree, and call all buildings I come across trees as well I have effectively ruined the purpose of the term. This misuse is similar in fashion to what I originally applied to the term Love was well as Conservative.
When a scientist chooses to lop off “by means of natural selection” they are doing the same, albeit much more self-defeating, act that someone who chooses to call a building a tree is. They may be saving themselves from having to say those horribly heavy and facially contorting five words, but as a far as our film world has brought us, thanks Blade…