Just a quick shout out to my friend Steve Olson; who is doing the Wendy’s kick for a million tomorrow night. He got his name drawn, then made it past the quarter and semi finals to get a chance to kick for the chance of winning a bunch of prizes tomorrow.
See the quarter final here; the semi final here.
I will post the final video as soon as it’s up. Good luck Steve!
Edit: You made a good effort Steve. Here’s the final video.
I came across an interesting article, which was written way back in 1960 by Eugene Wigner, titled The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I wouldn’t normally reply to the deceased, but a few people have mentioned the article and support the viewpoint that it is a remarkable coincidence that we have laws of physics which can be expressed nicely by mathematics. I have had other discussions in which it was argued that the existence of laws of physics points to a higher intelligence of some sort (usually referred to as god).
The article excellently sums itself up in it’s conclusion,
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.
and I couldn’t disagree more (alright, maybe I could if he were a creationist or similar). To begin with, in much the same way that the universe is not fine tuned for life, mathematics as a whole is not particularly suited for describing reality. There have been many more mathematical theorems in history which are not used to describe any aspect of reality than those that have.
Mathematics is, at it’s most basic, an extension and continuation of formal logic. Because of this, some branch of mathematics can be used to describe any logically consistent system. Given that mathematics is just the study of logical conclusions, anything that obeys logic can be described by math. The fact that any particular bit of math applies to a particular situation in reality is mere coincidence. The only “remarkable” condition for the effectiveness of mathematics is that the universe be consistent. And, as we know from mathematics, if the universe had one inconsistency, then it would have to have every conceivable inconsistency (and probably some you can’t conceive of as well). Given that we have never observed even a single inconsistency, we can reasonably assume (though never completely prove, thanks Gödel!) that we live in a consistent universe. As such, it is perfectly reasonable (in fact, inevitable) that mathematics be so effective in the natural sciences.
My wife and I bought a new house, and I’ve been extremely busy with moving/renovating/repairs lately that I haven’t had any time to post. Hopefully I’ll be able to start posting more regularly again.
Since that unveiling of Wolfram|Alpha, I have heard a few people complain that it can’t do this, that, or the other thing which Google, Wikipedia, or Mathematica can currently do, and therefore Google, Wikipedia, or Mathematica will remain their first choice for everything. To them, I have this to say:
You guys who expect it to be Google + Wikipedia + Mathematica + fluent in English are just setting up unreasonable expectations. If I build a new power plant and expect it to match the energy output of the sun, I’ll be disappointed too.
It was designed to be first and foremost a computation engine. It’s not intended to replace Wikipedia, or Google, or Mathematica. Read here for more details. Note a few things:
Goals
Wolfram|Alpha’s long-term goal is to make all systematic knowledge immediately computable and accessible to everyone.
It’s not intended to be a dictionary, or a math/physics text, or anything of the sort. It’s meant to give you immediate access to data, and be able to offer some relevant graphs and computations with that data. It doesn’t have all the worlds data in it yet (and probably never will, considering how fast data is generated), but it has a lot.
Our goal is to accept completely free-form input
I think considering that I can’t even understand what some people type onto the internet, it will never be completely free form. They’re going to try to get as close to that as possible. They do this much better than Wikipedia, but perhaps not as well as Google (though you don’t get the proverbial digital diarrhea of websites that you do from Google). It needs some work to perfect, and I expect this to improve over time, though as long as there are people typing things online which I can’t make sense of, I don’t expect their algorithm to make sense of it either.
As of now, Wolfram|Alpha contains 10+ trillion of pieces of data, 50,000+ types of algorithms and models, and linguistic capabilities for 1000+ domains
This should make it abundantly clear that it’s designed for retrieval and calculation of data, rather than general definitions/education.
Future
Wolfram|Alpha, as it exists today, is just the beginning. We have both short- and long-term plans to dramatically expand all aspects of Wolfram|Alpha, broadening and deepening our data, our computation, our linguistics, our presentation, and more.
This is, like Wikipedia, a never ending effort. There will always be more to add, as well as simply changing things to better reflect the expectations of the current generation of users. It’s impossible to release it completely “finished”, since it will never be completely finished.
Wikipedia, Mathematica, Wolfram|Alpha, and Google are all very different. Each one excels at some things, and fails at others. You don’t search Wikipedia for instructions on how to sew, you don’t ask Mathematica to define terms for you, you don’t ask Google to solve differential equations, and you don’t ask Wolfram|Alpha for introductory calculus lessons. There is some overlap between each of them, but as long as you use each of them as they were intended, you’ll be able to get the most out of all of them.
I got up this morning, checked my feeds, and found that ScienceDaily has a new article up. They claim that Einstein was wrong, and that his theory of relativity (the first clue that there’s a problem should come from the fact that they don’t differentiate between special and general) is inconsistent. Their source? A professor of politics. Through most of the article, I found myself wondering if they would ever actually give an example. They finally do, the so-called “Clock Paradox”. What they call the clock paradox is actually just a restatement of the Twin Paradox, which was long ago resolved in both special and general relativities (actually, it was never a problem in general relativity, because GR can use non-inertial frames).
This “paradox” can, in fact, be tested yourself. Just take a really accurate clock with you to the top of a mountain, leave one at home, and when you get back, the one you took with you will be behind the one you left home. Rank him on the crackpot index, and post your results in the comments.
Well, I finished the first day of my new workout routine. I survived… barely. I can’t touch my shoulders right now. Tomorrow will be my first day of cardio.
In his 1912 book The Problems of Philosophy, Bertrand Russell wrote the following three laws of thought, which he considered “self-evident logical principles”.
These all, at first glance, seem self-evident. However, upon closer inspection it turns out that all three are wrong (or at least, are limited in scope). In most common cases, Russell is correct, and all three apply. Any time a mathematician does a proof by reductio ad absurdum
then 
cannot be true, but #3 states that if is not true, then 
must be true).
1. Law of Identity: Whatever is, is.
The law of identity holds if we only restrict ourselves to equivalence relations (it is, in fact, one of the three properties in the definition of equivalence relations, the other two being symmetry and transitivity). If we consider all possible relations it may or may not hold. It is trivial to find an example which does not hold: the “less than” operator. 
is clearly not true. Relations which have this property are called reflexive relations, but they certainly do not make up all possible relations. When considering more complex relations than “equals” or “less than”, it is worthwhile to check if you are dealing with a reflexive relation or not, rather than to assume that all relations are reflexive.
2. Law of Noncontradiction: Nothing can both be, and not be.
The law of noncontradiction is actually an assumption on the theory you are working within, the assumption of consistency. Unfortunately, thanks to Gödel, given a sufficiently complex logical theory, it is impossible to prove that it is consistent (or rather, if you can prove that it is consistent, then it is inconsistent). Further, not all logical systems are consistent, so this clearly doesn’t hold in all cases.
3. Law of Excluded Middle: Everything must either be, or not be.
For the law of excluded middle, we will look at Russel’s paradox, given a consistent logical system. Russel’s paradox is roughly this: Define the set of all sets which do not contain themselves, and then ask if this set is a member of itself. Formally:
?
Assume for a moment that 
holds, that is, is a member of itself. In that case, by the definition of , is not a member of itself, 
. As well, if holds, then is not a member of itself. In that case, by the definition of , is a member of itself, .
If we assume that #2 holds, that is, we cannot have 
, then we must have neither nor, .
If on the other hand, we assume that #2 doesn’t hold, then the theory is inconsistent, and everything can be proven true and not true. If 2 doesn’t hold, then there exists at least one 
such that 
. Given , we know that the statement 
must be true for any 
. But given 
and we conclude that . The same holds for 
, therefore, letting 
, 
, and #3 doesn’t hold.
Notes:
I am aware that my treatement of #3 uses the assumption of #3 in it’s proof (that is, I assumed either #2 or not #2) this is perfectly acceptable, since if the assumption is wrong, we are already done.
A treatment of #3, which is less interesting, can be seen with the statement “This statement is false”. Symbolically: 
.
This is meant to be an interesting discussion of formal logic, rather than a thorough treatment of the subject, which would take several university courses, and even then you wouldn’t cover it all. As such, it is far from rigorous, intentionally so.
I’ve decided that I’ve been out of shape for long enough, and I want to be in as good (or better) condition as when I was doing martial arts. To this end, I’m adopting a new fitness regimen. To keep myself honest will be posting semi-regular updates on here. If I start to fail, please guys, let me know. I’m hereby giving you guys permission (and requesting you) to nag me about it.
Hopefully with you guys nagging me, and me posting about it on here, I’ll stick with it until it becomes a habit. That’s always been the hard part for me, getting going. I’ll do well for the first couple of weeks, and then I’ll find an excuse or two to miss one workout, then another, and before I realize what’s happened, I’m not working out at all anymore. Once I get going, and do it for a few weeks it becomes a habit, and is very easy to stick with, at least until something majorly rearranges my life (like a new job, going back to school, getting married, or having a child), and then I often fall off the wagon.
I’ll be using both weight training and cardio work. I’ll be lifting on Mondays, Wednesdays, and Fridays, with at least a 45 minute bike ride or run on Sundays, Tuesdays, and Thursdays (and also on Saturdays, time and energy permitting). I picked up a heart rate monitor so that I can make sure I’m pushing hard enough to get benefits, but not so hard that I can’t finish my 45 minutes. If anyone else thinks they should be in better shape, feel free to post your efforts and progress in the comments.
Up until recently I didn’t think anyone actually believes in astrology. I thought it was something people read for fun, and didn’t really pay much attention to, kind of like fortune cookies. Apparently I was naive. They even have their own “scientific” journal. I am ashamed to admit that I had no idea so many people took this nonsense so seriously (I prefer to think that rather than being naive, I am simply too much of an optimist, but maybe that’s just a nicer way of phrasing the same thing).
How it supposedly works is a bit of a mystery to me. Some say it works by magical vibrations, despite the fact that space is a vacuum and therefore incapable of transmitting vibrations. Others claim it works through gravity, either direct gravitational pull on us, despite the fact that the gravitational pull from the midwife or doctor delivering the baby is the same order of magnitude as that of the moon or the stars (gravitational forces drop off like 
), or gravitation affects the magnetic properties of the sun, which affects us, despite the fact that the magnetic fields from the electronics in the room are orders of magnitude larger (magnetic fields drop off faster than 
, though the exact expression depends on the structure of the magnet).
What brought about this sudden realization, you might ask? I was at work Saturday (I work at a bookstore) removing books for return from the “Astrology/New Age” section, when I casually commented to one of my coworkers that the books belong in the “Fantasy” section. Imaging my chagrin when she got upset with me. She then proceeded to try to “convert” me to astrology. The single bit of evidence she presented: “Remember when Mars was really close to Earth last year, and there was that series of murders? Well, Mars makes people more violent.” That’s it, that was the entirety of her argument. A single bit of anecdotal evidence (which I’m taking her word that it is actually true, I don’t, in fact, remember any such string of murders off hand). No statistics. Not even a proposed mechanism of action. At least some people try to use statistics. I attempted an explanation of why astrology doesn’t work, and the flaws in her short argument but was met with a wall of incomprehension. I walked away, shaking my head.
At least one of us learned something today.
B.C. gives naturopaths right to prescribe drugs. These people are not medical doctors, they have not completed a medical degree (they have their own degree program which glosses over a few medical terms before jumping into the quackery), and do not have the understanding of pharmacology required to prescribe drugs. Further, they have no understanding (because in many cases the studies have never been done) of the interactions between the herbs they normally prefer to use and the drugs they may be prescribing. Your doctor will usually tell you to avoid herbal “medications” while you are on actual medication because the interactions have not been extensively studied.
To make matters worse, midwives are now allowed to perform acupuncture for pain relief of women in labour. Never mind that accupuncture doesn’t work. There is no anatomical basis for the acupuncture points, or the meridian lines, chi energy, and other nonsense the points are based on. That’s right, let’s stick ineffective needles that don’t work into women who are trying to give birth. Good work British Columbia!