Monthly Archives: December 2007

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.”

More on the Wizard's Rules, and a surprising connection

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While looking up information on the aforementioned Wizard’s Rules to see whether my guess of “Confessor”‘s theme was accurate, I stumbled upon an interesting explanation of the First Rule that was apparently given in the book:

“People are stupid, they will believe anything, either because they want it to be true or because they are afraid it is.”

Wizard’s First Rule: Chapter 36, Page #397, US Hard Cover (revealed by Zeddicus Zu’l Zorander).

* Explanation by Zeddicus Zu’l Zorander: “People are stupid; given proper motivation, almost anyone will believe almost anything. Because people are stupid, they will believe a lie because they want to believe it’s true, or because they are afraid it might be true. People’s heads are full of knowledge, facts, and beliefs, and most of it is false, yet they think it all true. People are stupid; they can only rarely tell the difference between a lie and the truth, and yet they are confident they can, and so are all the easier to fool.”

(Wikipedia)

It is clear from the explanation that I owe somewhat of an intellectual debt here. The rule itself doesn’t even need explicit mention (we’re all stupid, and all genius is but a lesser form of stupidity), but the explanation is helpful. One of the foundational principles of my “panidealist” philosophy is the inability to fully estimate the objective range of applications of an idea. This is a particular flavor of the last sentence in the explanation (although I strengthen “rarely” to “never”). Although that principle was largely observed from experience (it was practically shoved down my throat whenever I attempted to explain my research on the divisor function and I would have thought of it, Wizard’s Rule or not, because it was simply made so clear to me again and again), this doubtless counts as an additional influence on that aspect of my philosophy. Credit where it’s due; I’ll cite Goodkind in my Treatise 🙂

Keyboard minimalism, taken to its extreme – a review of the DiNovo Edge.

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The Logitech DiNovo Edge is a very interesting keyboard.

The first interesting thing about it is the MSRP: $199. For a keyboard. A month ago, I thought “who would be crazy enough to pay $200 for a keyboard?” Well, lower the price to $100 ($150 on Tigerdirect and a $50 mail-in rebate) and apparently I am. It figures that I’d be typing this on one.

Now, the reason I went for it is because I wanted a keyboard I could type comfortably on for hours – after all, I’m spending a good chunk of time writing a very long thesis, and when I’m not doing that, I’m usually typing something else. The keyboard is also supposed to have excellent Bluetooth wireless quality (it does; it hasn’t missed a single keystroke yet) and a very slim profile (again, it does). It’s truly a joy to type on.

Other features include a volume slider that I thought would be cooler than it really is and a trackpad that functions as a fully working mouse (albeit not a very good replacement for one – it’s meant for people who like to couch surf on their “media PCs” and whatnot).

Finally, Logitech’s name also carries it a long way; there are not many companies that can charge this much for a keyboard and get away with it. Logitech users such as myself will generally pay more because of the reputation for quality that the products have established.

However, I am beginning to become wary of Logitech’s keyboards, because along with the reputation for quality, they have a nasty habit of removing essential keys from the keyboards. For example, on this $200 keyboard, there is no numpad. It’s completely absent. Num lock, of course, is gone too, since there is no number pad to lock. SysRq no longer exists, but the only function that key ever served was to generate an interrupt that was handled by the BIOS in case the OS scheduler froze up or something. The home, end, delete, page up, and page down keys are arranged differently, but this is something that veteran Logitech users will be used to already; Logitech loves to rearrange these keys. In total, there are only 84 keys left on this keyboard. Most layouts have around 104.

Possibly aside from the loss of the numpad and the inability to 10-key (although I’ve been using the top row long enough to 10-key it fine regardless), the greatest omission that Logitech may have made is the menu key. It simply isn’t on this keyboard, requiring the use of the far less graceful Shift + F10 shortcut. In its place is an “Fn” key, which (you guessed it) gives you access to a bunch of “media” / “Internet” keys (and four customizable ones above F9-F12).

The right Windows key is also missing, but many other keyboards don’t have this either, so it’s far from unusual.

Finally, a more minor criticism is that the trackpad, though it has a scrolling area, is difficult to scroll. Not really an issue if you use it with a mouse.

Overall, the typing feel alone is enough to justify the price, high as it is, but the lack of a menu key almost breaks the deal (it would except that I mapped that “media center” key with the Windows logo at the top to Shift + F10, essentially making it my new menu key). The keys are low and respond in a similar manner to most laptop keyboards, but don’t suffer from the spacing issues of a laptop keyboard. It actually seems to have increased my typing speed by 10-20 WPM.

So, the pros:

Very nice feel.
Aesthetically pleasing.
Integrated mouse and volume control.
Slim profile.
Excellent wireless connection quality.

Cons:
$200 is WAY TOO MUCH.
The mini adapter that comes with the keyboard is specific to the keyboard; it can’t be used as a general bluetooth adapter.
The numpad and menu key are absent; these were useful.
The trackpad, particularly when scrolling, is difficult to use.
The volume gauge is actually just a fancy pair of “up”/”down” buttons. I was hoping for an actual volume meter.
Only two keys on the keyboard can be customized without having to hit Fn.