I want to create a map on how different sciences and mathematics interrelate in order to learn as much as possible as effectively as possible (leaning concepts strongly in one field that will apply to others). Philosophy is included because progression should be made from old to new. Graph is incomplete and spotty, I haven't worked on it much.
Basic resources I've used: yEd graph editor (would like to do books, the slip of paper looking thing, off to the side of the main path - any other editor that could do this or a setting for this one?) Bertrand Russel book on philosophy Veeky Forums wiki (not completely through) A math guide I saw posted before
What I'm asking for is any references that would be helpful for filling this out, any previous knowledge tree things, or better graph software
Right but I'm trying to figure out how some bits of everything are related to other bits of everything
Joshua Hall
Monitoring this. I hadnt thought about this, there has to be some research on this
Evan Nguyen
Even if you could somehow order fields from the most to least "fundamental", it doesn't imply that the pedagogically correct approach is to study them in that direction.
For a simple example, most of classical physics and QM can be collapsed into a Standard Model, but no one seriously suggests learning that before you learn about electromagnetism.
Likewise, in mathematics, concepts in category theory have many applications to other fields of math, and can help simplify other ideas in those fields. But even the most radical categorists would tell you that >leaning concepts strongly in one field that will apply to others is not something you would want to do with their subject.
Christopher Lewis
>Even if you could Algebra is required for basic physics, going through AP chem and AP bio would likely make learning biochem easier, etc. >it doesn't imply Right, not if you're trying to get excellence in one field, but knowledge is formed through practice and enhanced through increased relation. >can help simplify other ideas This is the goal. I understand that the best way to become an engineer wouldn't be through advanced math, but that learning about it may help. The best way to become a good chef probably wouldn't be through studying chemistry, but I'm sure there's some interrelation.
If you have any ideas, please contribute. I'd love to have a Khanacademy-like roadmap of knowledge. I'm making this map for personal reasons (aspiring to become a polymath) but I can see uses for anyone who wants to learn.
Sebastian Harris
Man, the math part is wrong, you start from the foundaments of math, metamathematics, category theory and group theory; then you link metamathematics to metaphysics and to philosophy. Then you link group theory to Number theory which leads you to sums and prime numbers, sums and operations lead you to element theory (algebra) that disperses into linear, non-linear and multilinear algebra and equations, equations leads to functions, functions to limits, limits to calculus. Then analitically you study Space Theory that disperses as topology and geometry, geometry leads to trigonometry, trigonometry to vectors and vectors combines with calculus to create vectorial calculus. Vectors, trigonometry, functions and calculus leads into Classical Physics that everyone knows how it's made. Newtonian Mechanics and Electromagnetism leads to Relativity. Back to math you study Modeling Theory that it develops as Statistics and Probability. Classic Mechanics and Electromagnetism lead to Particle Physics and Particle Physics with Probability expands as Quantum Mechanics. Quantum Mechanics and Special Relativity creats Quantum Field Theory; General Relativity and Quantum Mechanics create String Theory and String Theory evolutes as M-Theory. Particle Physics leads to Chemistry, Chemistry leads to Biology, Neuro-science leads to Psychology and all the rest
Ryan Cox
You fucked up the economics part. For basic macro/micro economics you will need algebra. For intermediate micro you will need calc. Not psychology. Never got past that. Econ minor.
Julian Gutierrez
I took your suggestions as best as I could and meshed them with to create this. I think I got it right, feel free to correct me. The original had notes designating literature to be read, I can add that in later, for now I just want to get the fields down. Where does discrete math, multivariable calc, and algorithms come in?
Possible orderings: - difficulty (more in line with pedagogy) - generality
Note: Just in case some part of you is doing this with a vision of being omnicompetent/a universal polymath, then it may be worthwhile having a parallel process of investigating the mechanics of intelligence and learning.
So, spending a portion of your time charting the world of knowledge and another portion of your time building a craft that can go ever faster and hold more in its cargo space.
Jaxson Green
Thank you for the resources. >universal polymath That is the goal. Lifespans are increasing, Musk is trying to get BMI's going (based on an interview with Tim Urban, he may also go for increasing lifespans), knowledge is always increasing.
To continue to learn as you get older requires more experience and knowledge to rely on - you have patterns and pathways already formed that you can apply to other disciplines. One of my goals is to form as broad of a base intellectually as I can while also getting as much depth as I can, in an expanding reverse pyramid covering breadth and depth on X and Y. I'm not sure where I'll start the point, maybe physics or math.
Cameron Long
Take a look at MIT OCW's course listings, and use the listed prerequisites of those classes to help you map things out.
If you want to study the courses in order of covering the "prerequisite" elemental topics first, you should mimic the sequence of classes for various majors at good universities.
Ethan Flores
Check out Scott Young's MIT challenge videos on YT and his own personal blog. He outlines how he taught himself the MIT Electrical and Computer Engineering degree in just one year.
Jaxson Miller
from a physics grad student, it seems this is mostly based off of the education system steps and not how they are actually intertwined. something I noticed in undergrad is that even though math is required in physics, the different disciplines of physics are often more closely related to more specific mathematics topics. ie: quantum is literally an application of linear alg and pde due to operators and applying wave eqs to an L2 hermertian space.
Michael Rivera
You are correct, the end goal is to learn through books and other education materials out there now. I plan to have some kind of searchable note system, maybe OneNote, to take notes and then maybe a similar graph after I learn the material to intertwine things. >different disciplines of physics are often more closely related to more specific math topics This is something I want to account for; individual kite shapes are where I'd like to branch off, but I would still like to show relations to earlier subjects that are not directly linked, see "Calculus" to "Intermediate MicroEconomics" in That looks pretty damn impressive, thank you. Good idea. I've done some stuff like grabbing course books that I can work through, it's surprising how much you can find online - I went through the Sci wiki for some, the math picture in for others, then I've also got the AP Info repository for 5 steps to a 5 and other entry level things (Taking and passing mock AP tests will be of the same value to me as completing prerequisite courses for college if the credits would transfer; my model will likely be RIT, as this is the school I'll be attending come Fall).
Jacob Anderson
Its funny to see this thread, because just a few days ago I thought about this. A map of the entire knowledge of mankind in a tree diagram. My approach to learn new things on my own was always to follow the events of history chronologically. That way I see why and under which circumstances something was discoverd or invented. Most importantly I see what knowledge these great minds could build own, what was already there before them. For example in mathematics you start with counting, adding and substracting, the need for fractions, then multiplying,etc. Ägyptian math, then Babylonian math and then Greek math, etc.
I guess the most important skill for your purpose is to be able to learn efficiently. I would start there and search for non pseudoscience articles.
I also think that maybe in the future it should be possible to organize all the knowledge by a computer.
Tyler Flores
Guys, there is a thing, its called knovel.com
It has a search bar and gazillion scientific books it searches for the term.
Knowledge is entirely irrelevant today, unless you posess unique access to unique knowledge that only you are able to utilise, which is next to impossible.
Joseph Bennett
Been planning on doing this myself, OP, although keeping it to myself. I started with math, and was planning on moving to quantum mechanics after thoroughly learning probability theory, and working my way up from there.
I was planning on taking it one step at a time, though, so I don't have a large list filled out. Nonetheless, monitoring thread.
James Jones
>to create this. I think I got it right, feel free to correct me. The original had notes designating literature to be read, I can add that in later, for now I just want to get the fields down.
I like it =)
Gabriel Parker
I found this: A few months old, nothing seems to have come out of it. >Knowledge is entirely irrelevant today I'd argue otherwise. I want to learn. I also don't have as much time as I need to learn all that I want, which is why I'm trying to figure out dependencies and prerequisites to take care of those in one swoop - from there I should be able to branch off.
I'm also doing this for anyone similar-minded, there's some other people monitoring the thread: As for I can understand wanting to follow the events chronologically, it's a good idea for understanding, I'm just concerned that it would take too much time. Maybe having a background in history from 6,000BC to present would accelerate the process. As far as learning efficiently, research shows the following: Spatial relations to information, gathered through taking notes and writing things down
Spaced repetition, through something like Anki
Firm understanding of basics, fundamentals. Yesterday I read through all of The Art of Learning, this is something Josh Waitzkin really stressed - focus on the simple aspects. For chess, start with the endgame. Then learn how to combine different topics together. I believe this project will give a firm understanding of the basics through covering prerequisites - learning algebra before trying to jump into advanced physics - so I think I'm good on that end.
If anyone has a background in some subject area - math, physics, chem, economics (this is an odd one, I'm not sure how much it actually counts as a science) - please help out with logical progression through this topic.
Jackson Collins
>economics (this is an odd one, I'm not sure how much it actually counts as a science
the dismal science ;)
Robert Moore
You should read Barbara Oakley's "A Mind for Numbers" to prepare yourself for studying independently, especially science and math fields of knowledge.
