Creating The Simple Math of Everything
Eliezer once proposed an Idea for a book, The Simple Math of Everything. The basic idea is to compile articles on the basic mathematics of a wide variety of fields, but nothing too complicated.
Not Jacobean matrices for frequency-dependent gene selection; just Haldane’s calculation of time to fixation. Not quantum physics; just the wave equation for sound in air. Not the maximum entropy solution using Lagrange Multipliers; just Bayes’s Rule.
Now, writing a book is a pretty daunting task. Luckily brian_jaress had the idea of creating an index of links to already available online articles. XFrequentist pointed out that something like this has been done before over at Evolving Thoughts. This initially discourage me, but it eventually helped me refine what I thought the index should be. A key characteristic of Eliezer’s idea is that it should be worthwhile for someone who doesn’t know the material to read the entire index. Many of the links at evolving thoughts point to rather narrow topics that might not be very interesting to a generalist. Also there is just plain a ton of stuff to read over there—at least 100 articles.
So we should come up with some basic criteria for the articles. Here is what I suggest (let me know what you think):
The index must be short: say 10 − 20 links. Or rather, the core of the index must be short. We can have longer lists of narrower and more in depth articles for people who want to get into more detail about, say, quantum physics or economic growth. But these should be separate from the main index.
Each article must meet minimum requirements in terms of how interesting the topic is and how important it is. Remember, this is an index for the reader to gain a general understanding of many fields
The article must include some math—at minimum, some basic algebra. Calculus is good as long as it significantly adds to the article. In fact, this should probably be the basic rule for all additions of complex math. Modularization also helps—i.e., if the relatively complicated math is in a clearly visible section that can be skipped without losing anything significant from the rest of the article, it should be ok.
Baye’s Rule
Supply and Demand (probably with effects of price controls, incidence of tax, etc., and limitations)
Economic Growth (Solow Growth model with limitations/implications)
If you do happen to come across something worth considering for the index, by all means, update the wiki. (a good place to start looking would be at Evolving Thoughts...) Perhaps we should add a section to the wiki for articles that we think are worth consideration so we can differentiate them from the main list. What thoughts do you have (about all of this)?
making a general primer on “the story of what humans understand thus far” with bias towards those concepts that have the broadest applicability is one of my goals.
Areas to cover: thermodynamics, focusing on entropy. natural selection. supply and demand. bayesian statistics, focusing on how the scientific method is a subset of bayesian reasoning. a primer on primate signaling and group dynamics. a “just so” stories version of the list of common fallacies and the list of cognitive biases available on sites like wikipedia.
in fact, include just so stories for every concept listed. of course eventually the intended target should realize “just so” stories don’t count as evidence, but the presentation will help introduce everything to a broader audience and also make it more accessible to children.
oh and the basics of game theory.
Make sure to include something about Big-O notation; I’m always surprised at how little it’s generalized beyond algorithms.
Huh? It’s already beyond. :-) Big-O notation is about the behavior of functions as their argument goes to some limit. Sometimes the function of interest is the running time or space requirement of an algorithm, sometimes it’s something else, like the asymptotic of a sum.
In what way can Big-O notation be generalized beyond algorithms? Perhaps it would be useful to define ‘Big-O notation’ and ‘algorithm’.
Choice Under Uncertainty (Is this suitable?)
(Non-cooperative) Game Theory
This may be somewhat tangential, but a bit of graph theory would do wonders, especially theory related to recognizing deceptive or misleading graphs.
Careful. The term “graph theory” is usually used to refer to a specific branch of mathematics which I don’t think you’re referring to.
My mistake, I was referring to the Edward Tufte stuff. Thank you for correcting me.
As I suggested in the last post on this topic: examples.
They don’t even have to be serious examples, but examples of how one might use the basic math, and hopefully examples that are easy to follow but not an obvious usage. For example, the time-to-genetic-fixation example might be: you have 20 friends, half of whom have a pet rock. How many years until pet rocks have drifted into extinction etc.
Various types of optimization)?
Evolving thoughts link is down. Archive.org link
Why re-invent the wheel this has already been done if I understand correctly for example in a bit of a more specific case “Fundamental Formulas of Physics”.
“Fundamental Formulas of Physics” is just a list of formulas without much explanation.
So—more of something to put on your shelf next to Abramowitz and Stegun than a textbook, then.
has something this general been done already? We’re talking everything from physics to computer science to economics. It’s the simple math of everything. If you show me, I’ll believe you, but for now I remain skeptical.
A page named “basic maths”, explaining “essential” concepts would be great. I don’t know if it is possible, but i would want the explanations to be theoretical—the way eliezer explains bayes, basically something for the generalists who can’t learn maths by looking at equations!!
Thirded. What should be essential? Algebra and some basic calculus? Anything more?
Yes, and probably a detailed probability lesson. I was very good at maths in high school, but now after 10 years after highschool, i have totally lost touch. Though i still know the concepts, i get a bit lost when people start talking in “p” terms out of nowhere. I would like to follow everything.
Seconded, with the caveat that it’s called “Basic Math”. Or to compromise, “Basic Mathematics”.
I realise it should be basic “math”. For some strange reason almost 99% of people here in india say maths. We are taught by teachers as maths. People invariably say I like maths, not math. Its just so ingrained by now that i wrote that in spite of knowing that its “math”. Probably a thing like your comment is what my brain was waiting for, it would be more “brainy” before writing maths again :)
There is no right or wrong about the matter, only convention. In Britain, India, and many other places, the conventional abbreviation is maths. In the United States, it is math.
But thomblake’s suggestion of “Basic Mathematics” at least sidesteps having to choose.
In the spirit of compromise, I suggest “Basic Mathematic”, the one option that noone likes. (Ever looked up where the abbreviation “UTC” came from?)
thanks for tellin that. I should have looked up before saying that
Ok, I have to be honest this entire idea makes me cringe, it seems a bit to much like a cheap get out of learning the math idea. Maybe I am biased because I actually am a mathematician but these kind of ideas I think are dangerous since you take away an important bar of admission to fields like physics. If you don’t understand why the math is an important bar of admission look at the google groups physics group.
To be honest I think someone would be better off spending their time learning calculus at minimum then trying to read this kind of general overview. I think what is likely to happen is that either the math will be to simple and muddles the field to the point of being useless or its so complex that nobody can follow it. A good case and point you can understand quantum physics if you understand algebra but your going to be hopeless in a discussion about it without understanding things like the differential equations. Of course there are other fields which you have to know the math, from some of my own experience, fluid mechanics.
For my own part I think required math should include at minimum: Advanced Calculus (not that “calculus class” you took in high school it doesn’t count) Differential Equations Linear Algebra Abstract Algebra Set Theory (basic at least) Number Theory
I think with these you probably can figure a lot of the more complex math out.
I am sure I am leaving a couple out but you get the idea.
While I also don’t see the point in the enterprise, and think many of the specific suggestions misguided, you misinterpret its intent. Read the original post for an explanation. The point isn’t to learn math “in a simple form”, but to explain some of the most important facts about the world with at least a bit of mathematical rigor and expressive power.
Oh I get it. I would make the same point either way especially when the idea comes from a non math person. Whenever a non math person says this kind of thing it should make anyone who has done their due diligence cringe.
If you can’t do the math so for the physics if partial differential equations are beyond you then you shouldn’t be talking about physics. There are many fields where knowing the “drop-dead” math is not sufficient to qualify one to talk about it.
Now I know you will all vote me down, I am rocking the boat.
Do you expect a person to end up worth off as a result of learning about some subject to less than certain level of detail? If it’s better to learn a little than not at all, it’s probably better to learn a few facts written in math than no facts written in math at all. It seems that you have to agree with one or the other.