ALine

ok, sooooo this looks like some weird math. Like the formation of these neural structures are analogous to mathematical structures. so wait, the closer neurons dendrites are to the main cell body, the more it affects the neurons firing rate? Does this change the potential activation function of the neuron? Making it higher or lower, depending on how close it is to the neurons cell nucleus?

Ye! helps out a whooooole lot. If I were to give a general reference understanding to this I would call it a kind of "spark gap" which requires a certain amount of "charge" in order to "fire." This previous statement is used in order to give myself an understanding of what behaviors it associates to also seen.

I have been trying to simulate a neuron for a self project to improve on my skills as a circuit designer, however I am having trouble understanding the circuit for a neuron. below is the circuit model The way I am interpreting it is the 2 variable resistors are actually potentiometers and the are, I think, self regulating or tuned by a user and the input and output currents are the overall neurons models input and outputs. However what I do not understand is how this leads to the neuron actually firing. Much help would be appreciated.

yeahhhhhhh, ok so back when I posted this I was medicate and it felt like it analogously unlocked something in my brain to make every problem appear obvious. Had to go to the hospital actually. But I am good now, it gave me a lot of time to think and reflect. Leading me to the conclusion that I like to collect knowledge and I should be able to do so without the need for medication.

ahhh, ok. This makes a lot of sense to me. So would mathematics be like a wire framing for any "reality"? Like say for example you are in another universe that does not have the same laws as we do "here." Would mathematics still be able to describe those laws in order to form understandable theories?

ok so right now I my understanding of mathematics is " A structural formation thing that overlays on top of reality in order to form unique structures from the observed structures." Like an wireframing of reality and the use of imagination to create and develop new wireframes. Does this sound close to what mathematics as a field accomplishes?

Immm actually a senior, I have been doing electrical engineering up until now and decided to transfer because I was not doing so hot and that I was good at math. Proofs hit me like a freight train in understanding. Thanks mans I just get this feeling that mathematics is like, as stated before, like everything else. From art to science to engineering, it is just more intrinsic. The formation of some thing using simpler things. But I will keep working at it until I get to that graduate level of understanding :D. like one giant formless puzzle....thing.

(Also the statement "A systematically purist style is out of the question" peeked my interest, why is this so? It gives the inclination that for the formal definitions of mathematics and logic , one must use a systematically purist understanding in order to concieve of the notions of each field, however once you actually look into each field a pragmatic approach is taken. The latter statement makes sense, because if you were to attempt to develop new systems outside of the previously defined axioms then there would inevitable chaos. Or am I incorrect in making the previous statement?) < please do not answer this question until I am less ignorant of the field. apologies for jumping around so every straight line which is not passing through origin, that being (0,0), is affine? Does that mean that every line which does not pass through the origin is affine? Is that why in linear algebra all the lines come from the origin? So is normal algebra affine algebra? Are non-linear equations all just apart of affine algebra? What else am I missing. I have so many questions now.

So if I am reading this right, also look at the wiki, affine spaces are single point representations of linear transformations between points on a Euclidean space. Like if you have deltaX = X2 - X1, in this affine space this would represent a single point? Also, good read, however I am having a few problems fully absorbing the information of the first text. Thanks for the info Also if the above statement in which I have made is true then would that mean that because they are only transformations points in affine space would be real if the points in the Euclidean space are also real? Also Apologies for not keeping it to a single thread, will try to remember for next time.

Hey whats up, question, Is there some underlying linear understanding for how one may go about understanding mathematical proofs? for example Definitions -> Postulates -> Theorems -> Proofs -> etc. Like is there a universal path of understanding for some logical statement? The reason I ask is because when reading a little of "Journey into Mathematics" and the Elements it would continuously go through this process like one thing is built on top of another. That is cool and all but is there like an existing quantifiable formula for this process? Thank you for your time

Thank man, I never thought that math could be so exciting. I only assumed it was just rate relationships. Ye Continue the cycle of increasing complexity until brain equals explosion.

So I am taking my first proofs class this semester along with an application of it in mathematical statistics and I got to say. This is pretty awesome. Why have I never seen this stuff before in my lower level mathematics courses. Like it provides general reasoning and evidence for each mathematical equation. I am currently reading over "Journey into mathematics-an introduction to proofs" by Joseph J. Rotman and it answer ssooooo many questions. Like a proof for that cosine equation that was just given to me. I thought it involved like some super human levels of mathematics. It turns out it just uses the pythagean theorem and some geometry identification and relationship forming. Also I am reading "The Elements" by Euclid for class as well, picked it up because it looked kind of cool when I was younger and it turns out I needed it later on, nice coincidence. Turns out it is now my favorite book. Like a book that you do not want to pick up because you know you will not be able to put it down. Like my biggest issue in my math classes was that I did not understand how the conclusion was reached. Like omg, this is the most I have learned in a long time. (source: Family guy) (reason for use: for dramatic comedic appeal ) Is this what math is? finding patterns and relationships in order to develop unique structures in order to better understand the interworks of different behaviors being observed?

I remember learning about vectors where order matters as well. Is it roughly the same concept, but instead of just scalar values it has vector values and those vectors values make it obvious the underlining mathematics involved? Also I keep hearing about the importance of the divisor. Why is that? (model association question) - would the divisor be related to set theory in any way? Like if you divide a number by its divisor would that be the same as taking a section or a sub set from an overall given set. image ref below p.s. apologies for my jump in reasoning. I am a daredevil when it comes to drawing conclusions. Also I feel as though this is getting off topic. Is there any way this can be moved to an area which would satisfy its new topic? Like general discussion?

Yep, I just jumped the shark on that one.

I was thinking about it further, and what if instead of it being 3|1= 1-1-1 it is instead, 3|1= -1-1-1. Like instead of it using positive numbers it just used the negative equivalency, so 3|1=-(3*1). Ex: 3|1 = -1-1-1 = -3 and -(3*1) = -(1+1+1) =-3. So it would maybe act like multiplication but just in the negative axis.

@SenseiOhhhh, so you used it as a method in order to determine if it is a legal operation in terms of mathematical. Through the modeling of it to determine if it breaks this "no divisor equals 0" rule? Apologies, I did not know that is what you were going for with your code.

1 resp) yep, sorry about that 2 resp) yep I had no idea the order gave rise to different interpretations. Learn something new every day. The more I think about it the more feel as though it should be 1|3 = -3 or 3|1 = -1-1-1 instead of 1-1-1 because I do not think that it would make any sense to have a positive 1 in front while the rest are negatives. Apologies for not giving specifications toward my reasoning for this. Not well versed in the field of mathematics and justifications. I do not think that it would really have a need. Just an idea so if someone discovers a need for it then far be it from me to stop them.(assuming this is not just some crazy idea) Had no idea....will need to look into that. @Sensei Nice code man.

So I was sitting there on my thinking chair, metaphorically, and I was thinkin to my self. if you could represent 1*3 = 3 as 1+1+1 = 3 then could you represent 1-1-1 with a symbol just as how 1+1+1 has the * symbol? ex usage of the concept: 1|1 = 1-1 1|4 = 1-1-1-1 or 4 2|6 = 2-2-2-2-2-2 or 6-6 in contrast to 1x1 = 1 1x4 = 1+1+1+1 or 4 2x6 = 2+2+2+2+2+2 or 6+6

ah yes, breaking the fabric of reality I see.

So the Fourier transform is like a subset of the Laplace transform, in where it only deals with sinusoidal periodic functions and where Laplace transforms deal with all kinds of continuous functions? Am I getting that correct?

thank you, I will take it to heart.

yep, I do not quite fully understand it, however I kind of get the gist of it.