Festivals of Light

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Hanukkah is called “The Festival of Lights”, but it certainly isn’t the only one – just like flood myths, festivals of light are commonplace in many cultures. Unsurprisingly, they tend to be held in the winter. It is one of the great joys of humanity that it responds to external darkness with internal light, but it makes me wonder what the origin is – the message. Is it defiance of the weather or the long night? An innate comfort defined by a basic human need? A reminder that winter is only transient? A prayer for an easy season? It’s an interesting thing to think upon while driving past all of the decorations. As children, some of us are afraid of the dark – we flee from it. Here, as adults, we appear to be taking a stand against it, however – repelling or perhaps even defiantly challenging it.

Nope, still not getting it

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In another example of society not getting it, spinoffs (or should I say variations) of Wikipedia, typically revolving around correction of one of its perceived flaws by somehow restricting access to articles, are sprouting up on the web. Of course, this is more akin to a traditional online encyclopedia, such as Encarta, than Wikipedia, whose very existence is due to the success of using an unrestricted editing process (although it has a fair deal of informal schism and an unacknowledged but well-defined hierarchy within its ranks, as I found out when I was an active contributor – I was one of the first to realize it and that is why I am no longer an active contributor). Wikipedia proves that this model works very well, but some people seem to miss the lesson.

The most ironic ones are the ones that start with Wikipedia’s articles as a base. “Sure, your model doesn’t work, but we’ll use it for what will likely form the majority of content in our encyclopedia”.

(Update: Just saw this a day after posting. Woof!)

More is less

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I’m noticing that the more information you put into a paper, the more the reviewers demand (example: add an ROC curve to your new results in addition to class accuracies and suddenly they ask why you didn’t compute one for the old results that you’re citing as well!) This is probably why papers also tend to get needlessly long, which was the subject of another post some months back. Sort of stupid, but that’s what you get for getting people started on your ideas. The ironic thing is that the more a paper gets people to think about similar issues, the more successful it probably is – and yet because of this phenomenon, the less likely it is to be accepted!

If this hypothesis is correct, it would not only indicate that peer review causes rejection of perfectly good papers spontaneously, but that it actively seeks good papers to reject.

Summarizing Roark in One Line (plus a bunch of extra analysis)

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Perhaps I’m putting a bit of my own spin on it as well:

“The thinker creates. The parasite destroys.”

It’s the fundamental question of any utilitarian philosophy: by existing, do you add anything? Or do you take away? Is the world better or worse for your influence on it? True, destruction makes way for new creation, but it’s foolish to praise the effects of a fire or earthquake because they enable people to build more houses, for example – better to credit the builders for the very human feat of creating in spite of the destructive forces that oppose them.

Thus it is desirable to destroy only as much as is required to replace with a better creation. Anything further is gratuitous, unnecessary, …even evil.

And thus the principle of additivity finds its application and its grounding in utilitarian philosophy (perhaps with some Objectivism thrown in, though Rand’s aim was to create a philosophy for living according to one’s own principles within society, while my aim is to create a philosophy for the act of creation itself).

Rand defines the worth of society as the amount of freedom it affords its citizens. It’s a good definition, but I’d also factor in the amount of unnecessary destruction it requires for creation (or even just life in general) – destruction of the environment, destruction of people’s fortunes, destruction of people’s ideas, etc. Anything that doesn’t need to be cleared for creation shouldn’t be.

Slowly, the concept of Panidealism is being fleshed out (through the usual method of subconsciously generating unrelated ideas and tying them together in surprising ways, or “painting a house with a paintball gun”). It’s going to be quite a philosophy when I’m finally ready to write it up. Unfortunately, I don’t think it will happen before I graduate.

(Update: Why do I always add an “e” to the end of his name? Subconsciously, “Roark” just lacks a sort of linguistic “balance”).

Motor learning rates

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While testing my hypothesis on motor learning rates, I noticed that while there does appear to be a variance in the slope from person to person, some of the data appears not to make much sense. In particular, one person had a POSITIVE slope in his frontal lobe.

Now, what that essentially means is that this person had to do more and more processing with each repetition of the task. Tasks require less cognitive processing with each repetition; this is how we learn to do things like walk.

So what on earth is a positive slope supposed to signify? 🙂

SVMs: Why so popular?

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SVMs are a nice technique, but they’re slow (O(N3)) and often give worse classification results than techniques such as radial basis function networks or even bagged / boosted kNN, Bayes, and/or decision tree models. So why are they so popular?

Simplifying the closed form of linear regression

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Here’s one that must already exist:

Linear regression is given by the closed matrix form:

θ = (XTX)-1 XTY.

We have a rule we can apply here: (AB)-1 = B-1 A-1
Which gives us: θ = X-1 (XT)-1 XT Y.

But the transpose and its inverse cancel, yielding the identity matrix when multiplied.
This leaves us with:

θ = X-1 Y.

Now, surely there must be some reason that it’s not taught this way. Is it because this requires X to be a square matrix? Can we use a pseudoinverse instead to solve this?

Update: Indeed we can. Now I understand why it’s presented that way; the pseudoinverse is given by (XTX)-1 XT! Therefore, we can also just say the optimal parameters are given by X+Y, where X+ is the pseudoinverse.

“Reinvention is talent crying out for background”, I suppose.

Reading and another Einstein quote

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Here’s another one that I think is good advice for scientists:

“Reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.”
–Albert Einstein

The idea is one I’ve long held, though it flies in the face of conventional ideas: reading is useful to learn only what other people have thought. After a while, however, you need to move on to creating your own thoughts, using other people’s thoughts only as stepping stones – if at all. There’s no novelty to be found in the thoughts of others – they’re better at thinking in their own ways than you are.

Concentrating too much on the past will only prevent you from expending the effort in more useful ways.

Learning anything at any age

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I’ve held these beliefs for a while, but kept them fairly private. Since a major theme of mine during the last year and a half has been the necessity of an appropriate educational system for nurturing great thinkers, I think I’ll state them in the open:

We really must, as a society, move beyond the “no child left behind” mentality. We cannot afford to slow classes down more and more in order to cater to the slowest learners. It does a great disservice to the normal children and a far greater one to accelerated learners. The manifestations of this are pretty plain: boredom, lack of focus on work (but not a general lack of focus), preference for self-devised side projects, frustration, detachment, etc. If these abound in a classroom, chances are the work is too slow.

The worst culprit, however, is not No Child Left Behind. It’s the concept of a grade. Even at young ages, mental ability is not uniform. It is absolutely unfair to group all children of a certain age into a single grade, learning all the same materials, and then to keep them there for a fixed amount of time. Sorry, but if a student learns multiplication halfway through 1st grade, for instance, he really should not need to keep learning it for the rest of the academic year – move the work up to something more appropriate for the student’s background.

The rest of this will concern math, because it’s the area I’ve tutored most extensively. However, it can be applied to any field in a similar manner, taking appropriate safety precautions in fields such as chemistry, of course. (“You know how to use a bunsen burner, now let’s work with some HCl!” is probably not a good idea).

From my own experience as a student and a tutor, I bet we’ll see students learning algebra in 3rd or 4th grade in such a system. I started learning it at 8, but I had no help in the matter (as usual; I’ve always had to do everything on my own), so I bet we could teach it even earlier, at least to the mathematically gifted. Taught properly, rules from arithmetic supply the intuition – things like multiplication and division being inverse operations, associativity, and even binomial multiplication (FOIL) on simple things that the student can verify conventionally, including showing how it emerges from the distributive property, such as (5 + 1) * (4 + 3) = 5(4 + 3) + 1(4 + 3) = 5*4 + 5*3 + 1*4 + 1*3 = 42. Anyone who knows simple addition and multiplication can of course verify this simple example by adding 5 and 1, 4 and 3, and then multiplying the resulting 6 and 7, which allows the student to verify for himself that the identity does indeed work on this example. After this is done, generalize by moving onto variables.

Once basic algebra is mastered (and it doesn’t need to take years), introduce the basics of calculus. If you’re feeling really adventurous, it’s probably an ideal time to introduce some abstract algebra as well – right after a student finishes generalizing numbers to variables, they’ll be in the right mindset to generalize variables to teach them to generalize algebra itself – to get rid of the whole “number” thing and just talk about systems.

Logarithms and things are all special cases in calculus and can be safely ignored until the students learn about them (their “special” properties really arise from the definition of the operators anyway). Limits are easy to teach – use a number line and terminology like “gets closer and closer”. And DO NOT tell me you can’t teach someone d/dx(x^n) = n x^(n-1) as soon as they know algebra, because I won’t buy it. If they can learn the quadratic formula, they can certainly learn how to differentiate a polynomial.

Integrals are taught pretty well as-is (Riemann sums and the Fundamental Theorem of Calculus give good intuitive foundations for the concept), but again, far too late. It should be 7th / 8th grade sort of stuff at the latest.

The idea is to teach students enough that they can learn the rest, then move on and let them learn the rest (with help, if necessary). Exactly how much is “enough to learn the rest” varies from student to student and must be recognized on an individual basis.

Forcing homework upon them isn’t going to help them learn the rest, either. They should be encouraged, but not coerced. Students start out wanting to learn – in my own experience, the younger my proteges, the more enthusiastic they were about learning science, engineering, and/or math. Associating boring and repetitive work with such subjects for years eventually turns most people off to it (or worse, makes them think they can’t do it when they really can). The high school and college students tended to be the least enthusiastic, because they had the choice of (a) rote study or (b) an active social life. Assignments force them to the choice while providing very little benefit. Einstein states that “it is a miracle that curiosity survives formal education”, but, scientist that he was, he hasn’t seen the casualties.

Ultimately, it is society that suffers.

Yes, I’m aware that Montessori came up with a similar idea, but I’ll stop saying it when I see people acting on it. It doesn’t matter whether the idea already exists if people don’t do anything with it. Further derivation just serves to underscore the need for an implementation.

More evidence for my Theory of Synchronized Spontaneity – 2008

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It’s about a month early this year, but all of the freelance requests are hitting me all at once again. It’s interesting to watch the patterns, because my (passive) freelance search is generally sparse throughout most of the year (which is fine because I usually have lots of other things to do, some of which already pay me), but becomes very active for about 3 months in the year – usually January/February, May, and July. It’s very clumpy.

Also, two more recruiters contacted me. That is right on schedule this year; November-December is when it usually begins 🙂

I wonder whether there’s some underlying subconscious cue that causes particular behavior, or if there’s just a periodic need that I’m not aware of. Nonetheless, I find it extremely interesting that society has a circadian rhythm (although I’ve always personified it in every other way, I’ve never ascribed physiological characteristics to it). Seriously. This sort of stuff makes me want to become a sociologist.

This is something I formulated a few years/iterations ago called the Theory of Synchronized Spontaneity. It was also the basis for my 11th Psychological Postulate (which is a few years old by this point): “Given the choice, people tend to perform similar tasks at similar times.”