Sharing

I meet many people who stopped paying attention in Math, anywhere between 4th and 12th grade and, years later, got their interest piqued again. This happened to me too, and I know the feeling that it is too late. And I know that it isn't, particularly with the resources of the web. I'm posting an email I wrote to a friend. It is a post-calculus curriculum. If you made it as far as 11th grade before fading out, you can start here. You'll pick up the trig again as a result of getting back in, sort of piecemeal, the rest you can get guided through in the courses. This is more of a roadmap through MIT's OCW. everything is there: HW, tests, lectures, slides, readings (or books to buy) and answers to all the HW and tests. If you haven't made it as far as calc but want a roadmap through everything up to it, let me know and I'll put something together.

Here is the letter:

"

Lucky you, OCW not only has a complete linear algebra class, but it has full video lectures AND it is taught by the amazing Gilbert Strang. He is the Mr. Roger's of Linear algebra. I took Numerical Methods with him at MIT and he started the course off talking about his 4 favorite matrices. When I was taking linear algebra at Berkeley, having never even heard of the guy, friends were watching these lectures to help them understand what was going on in the local class which was taught entirely differently.

Watching the lectures will be nice enough, but to really benefit from

this stuff, you should do the HW

http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm

Here are all the math class, with all the All Class on the left sidebar.

http://ocw.mit.edu/OcwWeb/Mathematics/index.htm

It is lucky that you learned, back in the day, 'everything up to'

calculus, because there isn't really a one stop shop for full pre-calculus courses. MIT assumes precalc and all that trig. Though you have likely forgotten your trig and a bunch of your algebra, it won't be prohibitive to pick up again, and you can ask me to clarify steps, and the internet Does have all the bits and pieces scattered about. http://mathworld.wolfram.com/ is a great resource. Wolfram is an important egomaniac who has done some cool stuff.

Given a foundation just up to calc, I prescribe the following

four-unit plan to Catching You Up. The goal is to give you the fairly conventional ladder up to taking courses with proofs. That is when you really start seeing the beauty of mathematics, and when equations stop having numbers in them. The first three units form a sort of bottle neck, with intertwined prereqs, after that, you can branch off in all kinds of directions: more applied or more abstract or more fun. If you want to skip straight to courses with proofs, you can do that, just let me know and I'll revise this to take out all the courses that use numbers in their equations, though you should give this a try. If you want a Unit 0, just to get you psyched and ease you in, take 18.781 Theory of Numbers . Number Theory was my favorite math.

Unit 1

18.01 Single Variable Calculus (or 18.013) 18.06 Linear Algebra

Unit 2

18.02 Multivariable Calculus 18.03 Differential Equations

Unit 3

18.05 Introduction to Probability and Statistics 18.100A Analysis I

Unit 4

pretty much whatever you'd like. Everything below is in math, but from here you can learn Real Physics and Engineering of all kinds. Physics tends to start as three courses: Classical Mechanics, E&M (electricity and magnetism) and then Quantum (which MIT teaches concurrently with statistical mechanics, which is excellent). None of these requires all of the above prereqs, but just the process of doing them all is great preparation for all of these, and, importantly, all of the above are considered a minimal foundation (though I haven't taken analysis and have never had a proper DE (Diff Eq)(differential equations) course. Recommendations: 18.781 Theory of Numbers (Great!!) 18.04 Complex Variables with Applications 18.100B Analysis I 18.152 Introduction to Partial Differential Equations 18.353J Nonlinear Dynamics I: Chaos 18.901 Introduction to Topology 18.950 Differential Geometry "

So, taking the T in Boston, mostly up and down Cambridge, I've been in the habit of entering the car that will end up being closest to where the exit will be at my destination station. I've observed that the best car is usually the last car. So a simple rule of thumb to shave a valuable 15 seconds off your commute is "Ride the last car on the subway."

When I am trying to explain how it is an okay thing for a person to be attracted to very specific things, I tend to say that 'You can't control what you like'. But when I remember Epictetus' Enchiridion, I repeat the mantra, that how you feel is the only thing you control. I still have to figure out how I really feel and come up with a model that reconciles these two beliefs.

Brief notes on much of the work presented at this bi-year's lecture series:

• Properties of numbers in base 10
• Proof that irrational number to irrational power can be rational
• Q&A Re: Tax and inheritance
• Arctic String Figures
• How to sharpen a chisel
• Some cultural differences between Japan and the US
• Brief history of the Jim Henson Company
• Insider Trading
• Film of Peter Greenaway
• An incident of interest in the structure of thought
• Tones in Mandarin
• Infinite Plus One
• DIY Backpacking
• The Yeti
• Food preservation technique
• 3d modeling and thought
• Rangolis, Kolum
• The Hollow Earth

I've had an image of an old man, who takes small shuffling steps, who is mild and invisible, orchestrating his own dischordant death in broad daylight. He shuffles down a relatively quiet city street of his home, through a busy tight apartment building, down its claustrophobic halls to the roof. The movers he hired earlier that day, under the pretense to his neighbors of finally moving to the country farm to prance in the fields, have a pulley all set up to get his threadbare furniture down through his luxuriant bay window. His piano is hanging outside the building from the pulley assembled and braced on the roof. Slowly, with arthritic hands the geriatric suicidal saboteur connects a release lever to five stories of stiff twine.

He shuffles back down the cramped stairwell to the sidewalk, one step at a time, carefully using the railings and his cane near the false step on the third floor. He steps out into the sun, the same one that illuminates the dust floating in his ancient apartment. He shuffles to a spot under his window, three stories down. Tulips grow there during the spring, dandelions sublet during the summer. He turns around, with the street on his left, people brushing by on the sidewalk. A few feet away he is passed faster by cars with anonymous drivers. He waits patiently for the side walk, pretending to be senile. The sidewalk takes 90 minutes to clear. He takes as deep a breath as he can manage, puts on as big a smile as he can manage. He tries to think of people to say goodbye to as he realizes that he is about to say hello to every ancient face that came to mind. And then he pulls the rope.

I thought that old man would be me. But Yelena proposed 'overdose of knowledge' as the cause of my death and now this dream must fade as I paint a new portrait of the end.

So there is this rule of thumb in biology, that ontology recapitulates phylogeny. A developing embryo seems to (roughly) follow a miniature course of evolution, resembling in form its genetic ancestors as it grows into an adult of whatever species. It is an observation, not a law, and one that I've wondered about.

I just found a new instance of it in a pedagogical question. Take a highly developed and complex part of physics. So parts are very intuitive, some features are very subtle and counter intuitive. Now try to teach it.

The question is, do you teach it the way it is, or the way it developed? Should a student follow an abridged guided version of history or take the knowledge, complete and self consistent as it is, and pick up where current knowledge leaves off? The problem with the first is that there are many things that are not true, which nevertheless account for everything a student knows at a certain point and make sense. Later such stepping stones turn out to be false (incomplete is a better word), and get nuanced by something more complicated.

The latter is inadequate because understanding is not the uploading of information to a brain, nor a list of facts. Understanding a subject means knowing what is primary, what is subtle, what is important and tricky and obvious and given, and what comes from what. And the history of a field is going to go through this same process. That said, we don't teach phlogiston or other well developed, long discredited and largely forgotten attempts at comprehending the world. Does individual learning recapitulate the development of scientific understanding?

Obviously, the answer isn't going to be one or the other. What happens is a dense mix of both. The question is interesting because it brings up more:

• Why do we see individuals retracing the history of a field in their own development?
• What steps get repeated and which skipped?
• What is the difference between a community learning something unknown and an individual learning something known?

It was this last one that gave me the most intriguing idea: Compared to the environment I am in now, my distant ancestor organisms developed in a much different environment than the one I developed in.

In the language of pedagogy, The process I will go through is different than the process my academic forefather will go through because what is already known is different. Presumably, the mistakes and discoveries that get repeated in my learning are the more important ones out of all mistakes and discoveries that were made for the end result I'm approaching.

The idea of end result is tricky tying this back to the biological inspiration. Thats about as far as I am pondering all this.

I went to the Boston Skillshare and shared how to make a few toiletries:

Q-tip

Everyone thinks this is sketchy, but I love it. It is such a simple example of how we have left even the simplest human traditions to 'specialists' and corporations, to the point where it doesn't even occur to us that these things not only can be made in ten seconds, but were until maybe 40 years ago. Intructions copied from myself

"

My ears were all clogged up with wax, to the point of itchiness. My pinky is too big, so I tried to steal a q-tip from my roommates without their noticing, but they didn't have any. Ear candles are a little overboard, so I tried a toothpick but that is scary, poking around in your ear with a toothpick.

How can I make it less scary? I took the toothpick, dug around for a cotton ball, and rolled the toothpick against the fluff of the cotton. It turns that that this was nothing less than reinventing the qtip, the exact qtip!

It worked? Of course it worked, that is what a qtip is, they are so inconscpicuous, and so complete; they are so There, that I never thought of them as something that can be *made*. Not so mystical. No patented qtip technology. Why did I never know that? How did that knowledge get lost to humanity? Well, I guess that with both ends cushioned, noone heard this presumably timeless knowledge drop and slip through the cracks of time.

Making them gives you a steady hand and an intuition for fluff, you are basically spinning thread, but only a few inches of particularly fluffy thread. And I broke off the sharpest bit o' tip from the carefully machined splinter that served me, (otherwise its still just a tiny bit scary).

In Your Ear!

"

Handkerchiefs and Dispenser

Handerkerchiefs are easy. Go to the thrift store and buy threadbare tshirts. linen is best, cotton second. Avoid stretchy, sheer, thick or dense fabrics. Choose pretty ones. Cut the t-shirts to hell. There you are. Next is to figure out how to get thin, careful hems. Handkerchiefs are a practical habit to keep up if you have a whole bunch. Shirts, underwear and pants are not a limiting factor in my laundering, but socks are, so I keep more socks than anything else. Similarly, you should keep lots of kerchiefs, because you don't want a really snotty one, because the best thing about kerchiefs is offering them to others, unless they refuse to take it on grounds of its snottiness.

So, having a whole bunch, where do you keep them? How about in a tissue box? Fold them the same way Kleenex fold and you've got a dispenser, even with the magical 'the next one peeps out when you take the first' action! How? It is too easy, just fold them ove each other so one hanky pulls the next partway out with it. The length of the description betrays the simplicity, but only because descriptions of physical operations are cumbersome in words.

Fold all kerchiefs to the width of the box and lay the first lengthwise. Lay the second in a line with the first, overlapping half way. Fold the uncovered part of the first hanky over the overlapping half of the second. Now you have a free half of the second and a small stack of the first over the second over the first. Take you third, put it halfway on the stack and fold the free end of the second over it. Continue until you have a stack.

Stuff the stack into an old tissue box, or even an upsidedown yogurt container with the bottom cut out. It works, its great.

Toothbrush

Use a stick that you chew on. I use licorice stick from the Harvest market. In Vedic tradition it is neem, in Islam it is siwak. You can get the latter at Arab grocery stores. They are naturally antiseptic, its been tested. As a rule of thumb, any plant with bitter roots should provide branches or roots suitable from brushing with. Like Olive? neat! You can also dip the tip in baking soda if you want.

Razor

You could buy a straight razor, i think you can get them for as little as 25$. I just made a simple disposable one using cheaper but higher quality blades. Go to a store that sells old fashioned safety razor blades, I used Boston's Levitt and Pierce. Then, seriously, I thumbtacked it to a stick that I cut at an angle. And it works. I could still touch it up more, to give the cleanest shave of all, and I post it if I do, but in the meantime, that will do you. Instead of 10 bucks for five blades (2 bucks a piece) it is 2 bucks for 10 blades (.25 cents a piece).

I tried hardware store razor blades, and, atleast the ones we are all familiar with, are not sharp enough. There may be some suped-up kinds with tricky alloys that do the job, if so, they are a better choice than the safety razor blades, which are more expensive than hardware stores blades and very thin and flexible (which is bad).

A Common View

The Great Artists have endured time because they are beautiful, because of their strength and universal appeal. Very little art or music made in recent years will endure in the same way, because it is less beautiful.

The Point:

As individuals and small groups gain a larger share in determining a generation's canon of beautiful things, fads will become more common in society because only large institutions have the inertia (and resistance to change) to carry one generations's canon into the future.

The Angle:

I was at dinner with some fascinating people* and Howie the composer was a big fan of emphasizing experiential universals (and therefore universal reactions to music (and therefore an argument for universal beauty, or at least universal communication through music)). By universal I only mean human, but all humans, builtin sense of beauty. His opinions seemed to be mostly a reaction to the excessive relativism of the last century. I lean more towards relativism, but I was listening.

One assumption he was making was that The Greats have lasted because they are beautiful, because of their strength and universal appeal. He expressed doubt that any art or music made in recent years will weather the centuries that the late great composers have. I agree, but …

A confound occurred to me, one worth investigating (if investigable). Institutions carry ideas and traditions through generations. Their size influences their resistance to change and their ability to carry art through human time. There is no arguing that this will be a factor (in addition to Beauty) that carries art forward through generations and lends a sense of universality and concensus to such cultural artifacts. By this mechanism 'lost artists', are artists that got dropped by institutions and rediscovered only by research. Presumably such artist's work didn't 'speaks' to its birth culture and didn't get in the canon.

This culture is seeing an interesting trend due in large part to technology. Large institutions get larger and Small ones get smaller and more numerous (Analogously, designers have noticed that Photoshop has made good design better and bad design worse). Since any institution, large and small, can only carry a finite (and small) number of cultural artifacts forward as canonical, the number of cultural artifacts carried forward by large institutions will be small relative to the number of artifacts carried forward by small institutions and the total number of artifacts. I will put my focus on the role of small institutions in carrying work forward.

Individuals are more empowered than ever before. Small institutions are gaining an larger stake/share in selecting the contents of collective conciousness. But small institutions don't last. They have limited power to carry cultural artifacts through the vast stretches of time necessary to lend such work an air of universal appeal.

Fads are works that don't stay relevant beyond a generation. Perhaps (and is there even a circumstantial way to test this?) as people get more empowered and large traditional institutions contribute a smaller share of those artifacts which a culture finds relevant, fads will become more the norm. This will happen because of how ideas get passed on through time, not because today's culture isn't producing sufficient beauty or sufficiently universal beauty.

An interesting implication is that we can't use the ephemerality of fads as evidence of their lack of 'substance'. I don't think Howie will like that, but an important caveat in any talk of culture is that no cause is THE cause, and I am only putting this forward as a factor in the mess of factors that makes society into the complicated beast that society is.

Testability

There is evidence in support of this already (though falsifiability is what we are after). I wonder if there is any way to test the following hypothesis. A Model?

*notes to self

• Howie = Howard Frazin (composers in red sneakers) and Anna = Anna Willieme. Mother has no pictures of Anna's dream book. Strange; Internet should not have failed.
• Much restraint to not use the word 'meme', which is still too arcane for non-obnoxious use in discourse. Atleast for me.

Boston:

• I just found an amazing one On Mass Ave, between Central and Harvard Sqs. [1] Impressive, thick, tall, serious, and I've biked by it every day for two years without noticing it.
• Sighting by Abe Lateiner: ""I found an awesome tree. Check it out. It doesn't appear that awesome from the satellite, but I passed it last night and it is the bomb diggity. It's near my new place. I propose that when it gets a little warmer, you come over one evening for tree climbing followed by a picnic in the park which is right next to it.
• Sighting by Dana Malas: "I have to take you to this park by the green monster"

This is the beginning of my work at this unreasonably long address

Maybe someone will make the trek to read it one day.

-seth