Category Archives: Philosophy

Applications

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If one more person asks me why my work on the divisor function is applicable, I am going to scream! I’ve been mentioning Robin’s Theorem (proving a bound on the divisor function is equivalent to proving the Riemann Hypothesis) as an example of what can be done with this, but that is not why I did this research.

If Dali had to justify his paintings to the powerful, we would not have “The Persistence of Memory”. If Beethoven had to justify his works to the elite, we would not have the Moonlight Sonata. The simple act of expression is a reflection of the beauty in the soul.

It is the same with mathematics. I don’t know how significant my result is (though I am sure that it is at least novel and suspect that it has a moderate degree of significance… probably not enough to prove the Riemann Hypothesis), and probably never will due to society’s refusal to accommodate my wish to pursue multidisciplinary training, but I don’t care, because I’ve effectively reduced the amortized time complexity of calculating the divisor function for sequentially-increasing values to O(n) (calculating it the old-fashioned way, by multiplying over the primes, is polynomial) in a most elegant way.

That suffices for me. If it doesn’t suffice for you, I’d say you are, mathematically, at a handicap against those with an innate sense of mathematical beauty. At the very least, you’ll lack the passion that we have.

Oh, and this doesn’t only apply to math. If you only concentrate on application, a whole world of beauty is closed to you.

Ruminations Over Salad for "The Optimization of Systems"

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While eating at the local Wendy’s (basically the only source of food that is open past 2 PM in all of Templetown – words cannot describe how much I hate this city), I noticed two important things:

  1. Potentials (Materials, Ideas, Things that aren’t yet in their final Form) always existed in one form or another since the birth of the universe, yet are only usable after undergoing a change or series of changes. The essence is eternal, but the structure is only transient. For example, “this salad did not exist yesterday”: certainly the salad as an assembled component did not, but the lettuce, tomatoes, and partially hydrogenated soybean oil did exist. Even before they existed in those forms, they existed as part of a plant. The First Law of Thermodynamics guarantees this.
  2. Wendy’s now serves breakfast.

Expanding more on the Potentials, this should be a very intuitive, even downright obvious, idea. What makes it interesting is the particular framing of my thoughts: I realized that this could be used to derive a potential function (as in the amortized analysis technique) that serves as a “signature” of the changes physical objects undergo. I need to develop the idea further, but it’s something to talk about if I ever get around to writing “The Optimization of Systems”.

The two types of "social" sites

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I’ve had this theory kicking around in my mind since before this blog started, but since it wasn’t around then, I never posted it.

There are two types of “social” sites: those where one person naturally invites others (exosocial) and those where others are required for one to join (endosocial). Quite simply, an exosocial site attracts people as population grows, while an endosocial site attracts users only once a critical population is reached.

Why is this important? Well, an endosocial site (such as HireGeeks) requires heavy marketing as a catalyst, since no one will come until people are already there. Exosocial sites do not create such dependencies between a user and the rest of the population (though they might build one between two individual users), and are free to grow almost unchecked.

That’s why HireGeeks was a stupid shoestring business. Technically, that is some of the nicest Perl code I’ve ever written, but it means nothing if I can’t attract two separate groups of people to the site at the same time.

Panidealism

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I’ve found a catchy name for what I had previously referred to as the “principle of additivity” in my Treatise on the Objective Reality of Ideas (which is falling behind schedule; sorry): “Panidealism”. It’s the position that any idea, even a ridiculously stupid one, has an intrinsic inestimable value. The reasoning is fairly simple: either an idea “works”, in which case it is worth something on its own, it does not, in which case knowing that it does not is itself worth something, or we’re not sure, in which case we will ascertain and reaffirm the status of other ideas in the process of seeking it.

In other words, there is no such thing as a bad idea, hence the name. This should be somewhat intuitively familiar to other compulsive brainstormers 🙂

To give an example, suppose I said rainbows end in pots of gold. This is probably false, but if we knew it was, we would be better off, because now we can derive “rainbows do not end in pots of gold”. If we didn’t know, we’d look for rainbows, and perhaps discover, say, that they are circular when viewed from above – also a useful fact.

Water unnecessary

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From news.com.au, a professional statement of a position I’ve held since I heard the “water must be present for life” dogma:

“NASA’s current approach to “follow the water” is logical assuming alien life is comparable to that on Earth – based on water, carbon and DNA – but the “life as we know it” approach could easily miss something exotic, the US National Academy of Sciences panel advised.”

Ah, vindication.

Sapir-Whorf Hypothesis

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I have quite a few problems with this hypothesis. It isn’t that the hypothesis is flawed – quite the contrary, actually: this hypothesis is so obvious that it really doesn’t deserve to be named after two people who, incidentally, were not the first to discover or write about it. Another problem I have is that it’s needlessly specific. It can be summarized in three words as “language influences thought”, when a much more general hypothesis (the one I arrived at as a child and later incorporated into my psychological postulates) is “expression influences thought”. Finally, the hypothesis is needlessly unidirectional: to argue that expression is not a product of thought, formal system that it is, is ludicrous. Therefore, an even stronger statement is “expression and thought influence each other”.

I needed to be born 50 years ago, when the obvious things weren’t all discovered yet. But then, perhaps I would have died in childbirth had that happened.

Renaissance Transhumanism

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Renaissance humanism is a holistic philosophy that states that to be fully “human”, one should strive for perfection in all things. The ideal of this philosophy was the polymath, embodied by people such as Leonardo da Vinci.

That ideal is considered all but impossible to fulfill these days, since the breadth and depth of knowledge has grown enormously in the past century. Except for some small interdisciplinary research efforts, which typically span at most two disciplines and usually involve specialized experts in both fields collaborating, hyperspecialization is now the norm.

One solution to this state, which I believe pathological and suboptimal, is to raise the intellectual capacity of thinkers to meet this larger and more complex body of knowledge. Though there is no doubt in my mind that talented individuals can function as polymaths (so long as society tolerates them), most thinkers either cannot or will not. I strongly believe that if intellectual capacity is augmented, we will see the return of the polymath… so long as people are still willing to pursue beauty wherever it lies.

That may not be a good thing, for transhumanism could as easily destroy our sense of humanity as augment it. The tradeoff might not be worth it.