I may be retiring this blog

I'm literally the only person who cares, since (as established many times) all my readers are imaginary. If somehow one of you is not imaginary and forgot to tell me, this is for your benefit too, I guess. Also if anyone happens by this blog on an accidental google search and for some unaccountable reason likes what I write and wants more.

I'm not the same person who started this blog, almost seven years ago. And that's a good thing, too; it would be pretty fucking sad if my thought process hadn't changed since I was 18. Most of things I complained about in this blog now don't really bother me, or at least I wouldn't care enough to write about. Many of the thoughts I've posted I've since changed my mind about, or restated in different ways, or don't seem relevant anymore.

This once tried to be an atheist blog. I'm still an atheist, but that seems much less important. That one question has been answered, let's move on.

When I realised how limited the atheist memespace was, I tried my hand at scepticism in general, and later on the rationalitysphere. I'm still working that last one, but the work I have here is not really a good example of that (especially everything before I read Less Wrong, but a good deal of what's after as well).

 At one point this tried to be a writing blog; clearly that failed, and although I intend to go back to that, I've been "intending to go back to that" on and off for years. No reason to expect this time will be the one. And all the fiction I've posted here sucks, but I knew that even back then.

The point is: when I read back, I cringe a bit. I think that's about as healthy a reaction as one can have to a younger self. I've posted here a bit recently, testing the waters, but there's no reason to keep at it.

I have a Tumblr account now, which I got basically because it was a convenient way to follow some people. Still, having it empty bothered me, so I started using it. I've since posted a couple of longer form things I would have usually posted here. Which means, I have a platform for thinking out loud that isn't burdened with my past dumb stuff (yet!).

So yeah. It would seem Untheism is no more. I liked it while it lasted.

As a final note, if for some reason you need to interact with my online presence, I'm on twitter, the aforementioned tumblr, and I'm usually hanging out on the forum I admin, FQA. Also, anyone using the name "Sigmaleph" anywhere on the internet is probably me.

Bye!

Death is bad, 2

I fully expected the last post to be a one-shot, but then Scott Alexander wrote a thing on ethics offsets:

Some people buy voluntary carbon offsets. Suppose they worry about global warming and would feel bad taking a long unnecessary plane trip that pollutes the atmosphere. So instead of not doing it, they take the plane trip, then pay for some environmental organization to clean up an amount of carbon equal to or greater than the amount of carbon they emitted. They’re happy because they got their trip, future generations are happy because the atmosphere is cleaner, everyone wins.
We can generalize this to ethics offsets. Suppose you really want to visit an oppressive dictatorial country so you can see the beautiful tourist sights there. But you worry that by going there and spending money, you’re propping up the dictatorship. So you take your trip, but you also donate some money to opposition groups and humanitarian groups opposing the dictatorship and helping its victims, at an amount such that you are confident that the oppressed people of the country would prefer you take both actions (visit + donate) than that you take neither action.

 The concept is probably unappealing to a certain sort of person, but not me. My sort-of-utilitarian, definitely-consequentialist mind is 100% on board with the idea. Or at least, it was, until:

GiveWell estimates that $3340 worth of donations to malaria prevention saves, on average, one life.
Let us be excruciatingly cautious and include a two-order-of-magnitude margin of error. At $334,000, we are super duper sure we are saving at least one life.
So. Say I’m a millionaire with a spare $334,000, and there’s a guy I really don’t like…

 (Scott further specifies that you are a master criminal that will never get caught, it looks like death by natural causes so you don't waste police time, etc. or that you further offset those costs with more and more donations, as one in principle could)

So. As is its wont, my brain broke down on that one. One part of my mind says "Well, which world would you rather live in? The one where this mysterious millionaire didn't save all those lives, at the expense of killing one person? By any reasonable standard, that's a better world to live in: if death is bad, then saving lives is good, and saving more lives is better" The other part mostly yells "but murder is bad!".

The key insight here, as far as I can tell, is that my intuitions on morality break down somewhere in the vicinity of murder. I can be OK with the idea of killing one person to save many others (e.g. the trolley problem) because you didn't put the person in the tracks. I can even be OK with the fat man version of the trolley problem, because it's not your fault that's the only way to save five people. But I'm not OK with this. Where's the difference?

The obvious candidate is "But you have another available course of action: not murdering anyone, and donating the money anyway. That's clearly better." And that's true, and if true it applies equally to all ethics offsets, not just re: murder. And I agree: if it comes to me, the obvious ethical decision is not to murder anyone and donate almost all my money to the most efficient charity. No question. But people don't actually do the most ethical action if it's too inconvenient. 

Suppose I am building an ethics system to be used by imperfect humans, and some of those humans happen to be murderous millionaires. Suppose that those murderous millionaires would obey "don't murder anyone" as a rule, and would also obey "If you want to murder someone, donate X amount of money to charity to offset you murder", but they would not accept "Don't murder anyone, and also, donate all your money to charity". Sitting in this position, it seems to me, my brain can relax and think right: this is a trolley problem. The trolley was set in motion by some very peculiar quirks of the psychology of hypothetical millionaires, but it's no less trolley-ish. I still have several lives on one metaphorical track, and one on another. Sucks for the one.

I'm not sure what this means for the problem I discussed last post, (i.e. a good way to ground "killing people is bad" without resulting in life maximization), other than further confirmation that I can't trust my intuitions on killing people to be consistent.

Death is bad (but I'm not sure why)

(thoughts prompted by this post on utilitarianism and abortion)

I would urge you to read the linked article on its own, especially if you self-identify as an effective altruist or utilitarian or somewhere on that philosophical area. But for the purposes of this blog, there's an argument there that goes like this: Murder is very bad. Most people who support abortion are sure that killing a 1st trimester foetus is not murder, but they should also be aware that there a lot of people who disagree with them. Therefore, they should not be 100% certain* that abortion is not murder. Therefore, if you admit something like a 1% chance that abortion is in fact murder, and therefore very bad, and if you put numbers on "very bad" (that's where the utilitarianism comes) it's very hard to make the math come out "abortion is good". (unless you are dealing with extreme cases like abortion to save the life of the mother/foetus will not survive/etc.)

Political disclaimer: My support for legal abortion has less to do with "abortion is morally good" and more with "abortion will happen anyway but if legal it's safer" and "we should probably give people the right to decide how their body is used as a matter of principle, even if they will decide to do bad things with them". "If it's bad it should be illegal" is not a principle I endorse in the general case. So no, I'm not trying to make or endorse an argument for banning abortion.

Back to the argument. There a number of obvious responses, like:

"I'm not an utilitarian and I don't think you can do math on life and death", in which case I would love to have a longer argument with you on the subject but this post is not the place, or

"I am, in fact, very much certain that foetuses are not people and killing them is not murder, less than 0.01% chance I'm wrong", or

"Well, obviously in conclusion abortion is wrong", which I think are both interesting positions and I'll address in a moment.

In the "put numbers on very bad" part above, the author uses Quality-Adjusted Life Years (QALY). The argument is that if it turns out abortion is murder, it costs the foetus ~76 years of life, on average. Here's the part where my brain, and my philosophy, goes nuts:

What if a foetus isn't a person? Aren't we missing out on exactly those same ~76 QALY anyway?

There's a philosophy that says no. You can only care about real people, not potential people; those 76 QALY only matter if the person who would have lived them already exists.

If you accept that, yay. You can go back one level to the previous argument and try to figure out the expected personhood of a foetus, which I'm sure must be a barrel of laughs. My problem is that I'm not sure I can.

If I'm certain of anything in meta-ethics, it's consequentialism: the idea that "good" or "bad" is about states of the world. The right action is the one that results in the best state of the world, and nothing else. Not which laws you follow, not which virtues you exercise, just how the world is.

In particular, if "person X exists" is a good state of the world, we should bring it about; if not, we shouldn't. But the "fuck you, potential people" principle says otherwise: If you already exist, then states of the world where you don't mean you were killed, so that's bad. But if you don't already exist, then states of the world where you don't exist are neutral. There's no reason to care about you in the future if you don't exist now.

It seems like a very weird twist on consequentialism: The same state of the world can go from good to bad depending on when you ask the question. That's a very ugly feature I don't really want in my metaethics.

But if you reject that, not only do you have to worry about abortion, but suddenly everything from contraception to not having sex falls in the same bucket: You are not taking action to make a person come into existence, this is the same as taking action to remove a person from existence (since they both result in world states where a person doesn't exist), ergo you are a murderer.

Which brings us to a nasty conundrum: If I want to be remotely consistent about ethics, then either I admit that murder is not always that bad, or I have to stop blogging right now and go impregnate as many women as possible. Since the second option sounds like a lot of work and would probably end badly for everyone involved (except our future children, who are being saved from counterfactual murder!), let's look at the first one.

Why is killing people bad? 

... honestly, I'm not sure. I'm far more certain of the fact of "don't murder" than of any philosophical justifications for it, presumably because hominid brains evolved to have an innate sense of morality where we don't kill each other all the time, because social animals that kill each other all the time don't really work too well.

Like, there's the making people sad argument: if I kill you, your friends and family will be very sad, and making people sad is bad, therefore don't do it. And that's all well and good, except that if that's all it should mean it should be alright to kill people with no friends, or people who have lots of enemies who would be happy to seem the die. It does seem to allow not having sex, since people who don't exist yet don't have friends to care, so that's at least a point in favour.

There's the preferences argument: as a general rule, people's preferences being fulfilled is good, all other things being equal. People prefer not to die, ergo, don't kill them.

But that falls prey to the potential people problem just as well: hypothetical people would most likely also enjoy existing, ergo, if we care about their preferences we should bring them into being. Should we only care about the preferences of people who exist right now? If so, then that raises intriguing questions about the future: are we supposed to stop caring about what happens to the planet after the last currently-living person dies? After all, the people who would be alive then have no moral weight right now. 

It seems to me that I intuitively care about people who don't exist, like, I would think it's very bad if the world a thousand years from now is every human being living a miserable existence. But I don't worry about my potential children not existing. My brain parses "not existing" and "it existed and then stopped" as very different things, even though the end result is the same.

It would then seem there are two choices: 

Existence is not inherently valuable, and I need a good ethical grounding for why murder is bad that I don't have,

or,

We are morally obligated to maximise the number of people who exist, and will exist.

I'm currently defaulting to the first one, hence the title. This just might be because the second one is weird and uncomfortable, and I would really like a good answer for this. But I don't have it.

*As a general rule, you should not be be literally 100% certain of anything, for reasons I may have gone over in the past. Here though, I don't mean just "technically this could all be an illusion created by a trickster demon" but "There is a small but measurable chance you are wrong".

More alpha-negatrons!

Pal Sahota apparently found my previous post and may have taken offence at me using the words "crackpot physics" to describe his hypothesis. Over Twitter, he asks:

@sigmaleph Has @google paid you? Over 8900 views & many Profs & Phd's re-tweeted it. Its a hypothesis & could be wrong.Your qualifications?
— Pal Sahota (@searchasyoutype) March 15, 2014

 I would've replied through the same medium, but I find the character restriction rather, well, restricting.

So, point 1: No, Google hasn't paid me. Presumably this question was prompted by the fact that he claims he invented search-as-you-type and Google stole it from him. My post was purely for the love of making fun of bad physics and there were no venal interests whatsoever. 

Also, if Google wanted to discredit him, I'm sure they could've found someone with a much greater audience than me. My readership is largely non-existent.

Point 2: What does the number of views have to do with anything?

Point 3: Were any of those professors and PhDs physicists? That seems relevant. Also, a retweet is not an endorsement.

Point 4: It could be wrong, yes. Further, it actually is wrong. Of that I have already spoken.

Point 5: I don't have a degree in physics yet, though I'm working towards one. Thus, the only qualification I claim is that I know much more about physics than Pal Sahota.

This is evident by looking at his theory. The very format of his argument is flawed, relying overtly in qualitative verbal arguments rather than quantitative mathematical reasoning. There's exactly one equation in the entirety of the alpha-negatron document, Einstein's famous E=mc², and his attempt to fit it into his theory is severely flawed (I elaborate on that in my previous post, see the second bullet point)

Anyone actually doing physics would, at the very least, make some rough calculation showing, for example, that the alpha-negatrons actually do mediate an interaction of the same order of magnitude as gravity (or any other of the millions of effects he attributes to his pet particle). That he doesn't means he either can't do it, or he doesn't even know what a physics theory looks like.

Anyone who were to seriously propose a theory in physics would, at the very least, get past the 19th century. His particle is clearly classical in behaviour, ignoring pretty much everything in quantum physics except for occasional lip service.

And that's just the generalities of the thing. I brought up plenty of specific mistakes even a lowly physics student like myself should catch, like claiming light is a longitudinal wave or ignoring that the mass/proton number ratio is not constant in all elements (or between different isotopes of the same element). I even provided references to famous experiments that invalidate his theory, like the Michelson-Morley interferometer or Millikan's oil drop.

Those are my qualifications, Pal Sahota. You're welcome to challenge them.

Alpha Negatron

Anyone up for some crackpot physics? No? Just me then.

Pal Sahota has a theory that he claims unifies "gravity, magnetism, electromagnetic radiation and time", which is nice. Someone should probably let him know that magnetism and electromagnetic radiation have been unified for a while now, but still.

I took the liberty of looking over this document up on scribd, and I noticed a few odd things, so I decided to give him a hand with some constructive criticism.

So, Pal's bright idea is that, by studying nature, he noticed " there is a basic pattern like fractal which keeps repeating itself" and therefore space isn't empty. He doesn't say what that pattern is yet, but we'll get to that later. Anyway, space isn't empty, because it's filled with particles he calls "alpha negatrons", which as far as I can tell are like the pre-quantum idea of the electron except a lot smaller and with a proportionally smaller charge. He actually says it's "infinitely smaller", but that would mean it's charge is zero and could not do all the wonderful things it does. I'll assume "infinitely" was figurative and it's simply much smaller, though it sure would be nice to have an order of magnitude.

Anyway, these alpha negatrons are negatively charged (hence the name) and so they repel each other. Pal seems to think these would lead them to arrange themselves in an evenly spaced 3D matrix, which seems odd because all the other negative and positive charges (like protons and electron) would be guaranteed to disrupt that, but sure, whatever. Frankly his argument is irrefutable. I'd guess my first question would be why negative charges much smaller than than of an electron didn't irrevocably screw up Millikan's experiment¹, but I'm sure Pal can explain that.

Next, Pal says that the nucleus of the atom and the electron spin around themselves by analogy to the solar system, which is that fractal pattern he mentioned earlier. Of course, there is the minor problem that the planetary model of the atom is wrong and has been obsolete for 90 years or thereabouts², but it's an understandable mistake. After all, popular images of the atom are still using the planetary model, and you could hardly expect someone to go study physics beyond a pop-sci level when they are so busy developing revolutionary new theories. He's also somewhat liberal in his use of the word "fractal", when referring to a pattern that appears twice (or once) as opposed as to at infinitely many levels of resolution. But other than completely ignoring all of physics after the 1920s there's not much to nitpick here. Oh, right, there's also the fact that we know that the premise being pushed is known to be wrong, also because of that pesky quantum physics³. But that's it, at least until the next few sentences of the paragraph.

There, Pal tells us that the nucleus is "infinitely larger" than the electron (once again being figurative, I'd guess) and that's why it has a much greater influence on the alpha negatrons. I would nitpick and say that being that the interaction with the ANs is electromagnetic, the fundamental property that matters is not "size" (whatever that means in this context) but rather electric charge, and that is in fact very similar in both parts of the atom⁴. But I'm sure this won't affect his theory greatly.

When the time comes to explain electromagnetic radiation, Pal says that "Similar to sound waves, electromagnetic waves propagate through the alpha-negatron matrix utilizing compression and rarefaction", which is not quite right. First, because we know that electromagnetic waves propagate through the electromagnetic field, and if they had a medium like the AN matrix we would've noticed⁵. Second, because sound waves are longitudinal but electromagnetic waves are transverse, i.e. they do not propagate through compression and rarefaction of anything. If they did, we would not have polarization of light. But this fundamental misunderstanding of the basic nature of electromagnetic waves should not cause one to doubt the soundness of the theory.

Next in this parade of explanations is gravity, which Pal describes as a fundamentally electromagnetic phenomenon where protons attract alpha negatrons which attract other protons, and thus matter with protons attracts other matter with protons. Also waves. Curiously absent is an analysis of how the electrons in matter with their negative charges would interfere with this, or any order of magnitude calculation to show this would result in the gravitational constant we see, or any math of any other kind for that matter. But this is physics, why would we need to get maths involved?

Pal is clever enough to explain that gravity appears proportional to mass because the number of protons increases with mass, which is almost true. He fails to account for the fact that different elements (or different isotopes of the same element⁶) have different ratios between charge and mass, so we should observe varying ratios between weight and mass depending on chemical make-up of objects. But this difference would be small and if there's something we know is that precise measurement is kind of a "meh" thing for scientists.

As if all those explainings were not enough, there is a quite extended treatment of magnetism which is so undoubtedly correct it's not even worth detailing, except to mention it's based on "whirlpools" of alpha negatrons and completely disregards electromagnetic theory on what should happen to charges in motion. But then, what has standard electromagnetic theory accomplished, other than being generally considered one of most successful theories in physics and the template all field theories are modelled after? Surely alpha negatron supersedes it in every aspect.

Pal even takes a crack at wave-particle duality in  the photon, explaining it away by saying that it doesn't exist, and boldly asserts that in alpha negatron theory energy travels in wave packets. It seems curious that he borrows this property from quantum theory without bothering to explain why it should be so in alpha negatron theory. It hardly seems worth mentioning that the photoelectric effect cannot be explained through classical waves (such as those in AN theory), which is one of the reasons quantum theory was developed and the idea of the photon came about. I cannot wait to see how he will most definitely account for this.

During his conclusion, Pal takes a tour of all the complex physical phenomena his theory sorts out. These are just a few examples:

• The speed of light is constant because the separation between alpha negatrons in the matrix is constant (certainly not invalidated by the fact that alpha negatrons could not possibly remain at fixed distances around charged particles)
• E=mc². Isn't it just a huge coincidence that the speed of light would show up there? Well, alpha negatrons save the day again, by saying that the transference between energy and mass happens through the AN matrix so the speed of light shows up. I don't see the point in bringing up that the equations for special relativity were in fact trying to explain why electromagnetic waves behave as they do so it's quite natural that the c factor would appear. Much less, that saying that the rate of transference determines the proportionality constant is somewhat like saying that the exchange rate from dollars to euros is determined by how fast the transaction is processed.
• Relativity and the effects of gravity on time. The rate of passage of time depends on how fast things move through the alpha negatron matrix, which varies because gravity is protons!
• The quantification of electron orbitals! Because alpha negatrons create forces that balance out exactly at the specified orbitals for no reason given!

Frankly it seems there's nothing alpha negatrons can't explain. I'm sure they could even explain things that aren't actually true, because that's just how great alpha negatrons are.

In summary, I wholeheartedly and without reservations recommend alpha negatron theory be considered an unqualified success as a unified theory of everything, and frankly it's a crime Pal Sohata doesn't already have one or two Nobels in physics.


¹ Millikan showed that electric charges always appear as the multiple of a certain charge, which was determined to be the charge of a single electron. If something with a much smaller charge was around, we'd expect to see things a much more continuous range of charges, rather than the discrete separation we observe.

² Quantum mechanics shows that electrons can't be thought of as tiny balls orbiting around the nucleus because they aren't tiny balls at all and they don't have a defined position and momentum.

³ There is a quantum mechanics thing called spin, which people thought at one point had something to do with  the nucleus or the electron spinning around themselves, but was later shown to be fundamentally different.

⁴ Depending on the element, the charge of the nucleus can be identical (Hydrogen) or about a hundred times greater (elements at the end of the table) than that of one electron. And electrons usually don't show up alone, but rather atoms tend to have enough electrons to balance out their nucleus. 

⁵ Here I refer to the Michelson-Morley experiment, which attempted to detect what was then called the luminiferous aether, a proposed medium for electromagnetic waves that was disproved and led to the development of special relativity by this fellow named Albert Einstein. If the AN matrix was a medium for electromagnetic waves, Michelson would've detected it in his experiment.

⁶ An isotope is an atom which has the same number of protons but different number of neutrons as another atom. For example, a regular hydrogen nucleus is just one proton, but in a deuterium nucleus there's also a neutron. If those neutrons didn't matter gravity-wise, all isotopes should weigh the same and, for example, heavy water (where the regular hydrogen is replaced by deuterium) should not be heavier than regular water. Someone might want to look into that, see if we'll have to change the name.

How not to fix the problems with science

Once again, people have said something on the internet, and driven me to say others things in reply. Today's something is How the Scientific Method Silences All Ways of Knowing That Are Not White and Male, by Taeha Condon. If you know me at all*, you know this won't be a glowing review.

One would assume the article is about how they are some ways of knowing that are not White and Male, and the scientific method silences them. One would be wrong. It is in fact about how the author doesn't quite understand what the scientific method is but likes to blame it for everything anyway.

Problem the first: the author confuses quantification with the scientific method. Or at least I think she does, because otherwise I cannot explain why she continually rages against modern society's tendency to measure and quantify and considers that a criticism of the scientific method.

The core of the scientific method is "test your hypotheses", not "put a number to it". Numbers can be precise and amenable to statistical analysis and a lot of other nice things that make them useful for scientific research, but they are not what science is about. So when your title talks about problems with the scientific method and your primary argument is "we're using too many numbers", I'm gonna be somewhat disappointed.

Could one blame the scientific revolution for the abundance of quantifiable measures in today's world? Yeah, definitely. Partly because people use numbers to lend an air of sciencyness, and therefore legitimacy to their nonsense, but mostly because numbers work and science showed us that most conclusively. The author claims that "[w]e have relied on numbers and quantifiable solutions for too long, and clearly, they are not working", but then again quantifiable solutions have taken us to a world with vaccines and the Internet, so they are doing pretty fucking good, if you ask me. If "We've been doing this for a long time and the world is not perfect yet" is an argument against quantifiable solutions, then it's also an argument against agriculture, writing and democracy.

So problem the first is actually two-pronged: Quantifiability is not some sort evil demon, and it's not the same thing as the scientific method

Problem the second: You know those titular "all ways of knowing"? I am struggling to find any way of knowing in the text other than the scientific method**. Sure, the author alludes to "Aboriginal [...] ways of knowing that account for the interconnectivity of land, spirituality, country and kin", but doesn't actually say what they are or describe how they work. But they must be better than science, since they account for all that stuff! And science doesn't! For some reason.

Why would there be some ineffable, science-proof quality to interconnectivity of land et al.? I have no idea. Can you not formulate testable hypotheses about it? Or is it just that it doesn't look like the sort of thing you find in a lab with microscopes and test tubes?

Problem the third: The author consistently asserts that science is a white male way of knowing. And I'll grant that science has a gender problem; it's mostly a male dominated field, women's contributions are under-appreciated and boys are encouraged to pursue STEM careers much more than women. This has been said a thousand times before. You know how you don't go about solving that problem? By claiming that empirical thinking is a male thing and women are made for intuition and feeling. In fact, that strikes me as exactly the sort of thing that caused the problem in the first place.

Telling women that they cannot be scientists? That the single most successful way of knowing humankind has found is not their thing? That they are not built for logic and analytical thinking? That's one of the most unfeminist memes our society has. When you spread that meme, you are part of the problem.

So, in summary:
1) Learn what science actually is.
2) If you're gonna talk about how science stifles other ways of knwoing, kindly provide an example of one that has been successful to a level at least comparable to the scientific method
3) And for the love of all the nonexistent gods, there are enough sexist assholes telling women science is not for them. We don't need more.



*Which of course you do not.

**I am strongly reminded of learning about Feyerabend in my Introduction to Scientific Thought class in college.

FSTDT Forums...

A long time ago, in the mysterious times known as 2006, my younger self came across a website. It was funny, and it appealed to various interests that teenage me happened to be developing in that very moment. It was a website about making fun of stupid people, mostly stupid people that said stupid things in ways relating to taking religion waaaay too seriously. Seriously enough that one might call them fundamentalists, or even fundies. That website was called Fundies Say the Darnedest Things, or FSTDT.

One might simply dismiss it as a humour site, one of a billion that populate the webs, but there was more to it. It had a community of really smart people (or so they seemed, to me), who said things I hadn't known then and now find obvious, and yet it seems they still need saying. Even when I eventually grew tired of reading the quotes they collected, the community that lived in its forums kept my interest. It would be fair to say that if I hadn't met those people when I did, this blog would likely not exist, and I perhaps would be a very different person.

I've been in and out of this community, in the past. At times when I needed a break from the internet in general, at times when I grew disillusioned with the people, but I returned every time, because I liked it there. My latest return was earlier this year, around April. Not long afterwards, the current webmaster made an announcement that he wished to retire from administering the forum and focus only on running the website itself, so he was looking for a replacement.

This wouldn't be the first time there was a change in administration; indeed, he had taken over the website back in 2009 when the then-owner burnt out and rather unexpectedly shut everything down. She, in turn, had received the website from its creator, who passed away at an unfairly young age. That was before my time, though.

In any case, the webmaster started a thread in the forums asking for candidates, and said there'd be a more or less democratic process: those candidates that got a reasonable amount of endorsements would spend a trial period as moderators, and then maybe there'd be a general election. I submitted myself as a candidate, not expecting much but thinking I would like to see what people would say about me.

To my continuing amazement, I won. I was apparently the only candidate credible enough to make it to the trial phase, I passed it more or less uneventfully, and I became the forum admin.

Now, like I mentioned, the webmaster kept control of the website itself, I just handled the community at the forums. Which suited me just fine, since it was the only part I visited anyway. Being that it still was his website, though, he warned me that he kept a kill option on the forums if things went too far out of hand. I figured this wasn't something likely to come up.

So, retiring from his position as admin, the webmaster still kept posting as a regular forum user. He took the chance, after leaving the position of power, to say things on a couple of subjects that he really couldn't have said when he was in charge. I thought, sure, a chance to get past some old forum drama, this should be a good thing, right?

It didn't go well. People got angry at the things he said. He got angry at the things people said to him. At some point, it seemed the discussion might die down and we could all move past it, but no. Instead, it came to the point where he didn't want to associate with the forums in any way. Including having them in his website.

So he told me he was killing the forums, and gave me a chance to make a new place for them. After a period of lots of panic, and with the help of the people hosting us, I managed to secure us a new home. We even got to keep the forums mostly the same, with a different address and name being the most significant change

FSTDT continues to exist, but there no longer are any FSTDT Forums. Instead, Frequently Questioned Answers is now an independent community, which for some weird reason has me as an admin. I still feel like I'm not exactly sure how I ended up in charge, even though I just told you.

Thoughts I have during class, 2

After an introduction to the uncertainty principle, and a clarification that some of the common examples for it are not quite true:

"Huh, that makes a lot more sense now. It's not that position and momentum are there but we can't measure them because of quantum magic. Position and the wave number k are Fourier conjugate variables, and by De Broglie's postulates k equals momentum divided by h-bar, so of course if one is highly focused the other is very spread out, and in the limit you have one as a Dirac delta and the other as a wave over all space. I wonder why science popularizers don't discuss it this way, it's not that complicated...


...oh, right, Fourier transforms."

Oh, hey

As has become a sort of tradition by now, I've noticed the state of abandonment of the blog once again and decided to revive it. Mostly, I blame the fact that I haven't been writing a lot, lately. Also, my last computer died in early January and I only got a new one a couple of weeks ago. Lost with that computer, incidentally, is all or most of my latest story, which was actually coming along nicely before everything went kablooey. 'Nicely' to be considered relative to my usual standards of creative output, that is.

While I muster the will to rewrite it or wait for a miracle to bring it back from the depths of a busted hard drive, here's a story from math class.

* * *

We are discussing how a particular mathematical transformation (a linear map) affects a rhombus. The computer shows first a parallelogram, then what appears to be a straight line. "Of course, this is actually a very thin parallelogram, not a line", says the professor."What would it imply, if it was an actual straight line?", she asks, while she tries to use the zoom tool to demonstrate.

The answer comes to mind, even before she has finished asking: "the matrix would not be invertible". Right behind me, another student says the same thing. The professor confirms this is so. Meanwhile, I am thinking, furiously, "How the fuck did I know that?"

It's not that it's an odd thing, or an unfamiliar subject. A few moments later, I figured out a couple of satisfactory answers as to why it must be so. It's just that, the moment I knew it, I had not gone through any of the intermediate steps in my mind. The answer seemed obvious in itself, as though a cached thought. And yet, as far as I recall, I have not come across this particular kind of question before. Did I do so and forget? Or did I just happen to have a cool flash of mathematical intuition?



Mathematical details, for those so inclined: A linear map is, for our purposes, a function that given a vector returns another vector, with some properties. Namely, if X and Y are vectors and f is a linear map, then f(X+Y)=f(X)+f(Y), and if k is a real number, then f(k*X)=k*f(X). We'll be working with vectors in R², which can be thought of as arrows in a plane.  Every linear map has an associated matrix, and iff the map has an inverse map (i.e, a map g such that g(f(X))=X for all vectors X) then the associated matrix is invertible (i.e., there is another matrix which, multiplied by it, returns the identity matrix). If you don't know what a vector or a matrix are, I suggest Wikipedia, an algebra class, or giving up. The idea above of applying the map to a rhombus means, essentially, that you apply the map to the vectors of every point of the rhombus and see what happens. In practice, all you actually need to do is apply it to the vertices of the rhombus and then connect the dots.

Now, the reasons a rhombus couldn't be turned into a line by an invertible matrix can be expressed in many ways. The first, is that it would imply that the transforms of all the corners of the rhombus are in a straight line. Because of the second property above, all vectors in the same straight line (which are all multiples of each other) also go to a straight line after mapping. If two separate lines in the rhombus go to the same line in its map, that implies there are different vectors that are being mapped to the same vector. A function that takes two inputs and sends them to the same output cannot have an inverse function. Therefore, the matrix associated with the map cannot be invertible.

Another way of looking at it is that if the map turns a two-dimensional figure such as a rhombus into a one-dimensional line, there must be some direction in space it makes zero. (This is by no means rigorous proof, just the sort of thing that would be stored in my brain and influence my intuitions). A linear map always maps zero to zero, so if there is another vector that also goes to zero, it cannot have an inverse.

A third way, which came to mind on the bus ride home, is that the determinant of the transformation of a matrix tells you how it changes areas after transforming. (This is only obvious to me because it's an important part of the change of variable theorem in integration. Being a physics student, calculus is something I use much more often than algebra). A straight line has area zero, which means the determinant of the transformation is also zero, and there's a theorem that states that if the determinant is zero, the matrix is not invertible.

Ateísmo+

Hace un par de semanas, la blogger Jen McCreight publicó un poste proponiendo un nuevo movimiento dentro del ateísmo. En particular, un movimiento que vaya más allá de estar en contra de la religión (el Nuevo Ateísmo estilo Dawkins) y se manifieste sobre cuestiones como racismo, sexismo y homofobia.

El contexto es todo el quilombo que hubo en la blogosfera atea en el último año donde ciertos elementos misóginos de la comunidad se hicieron muy visibles (googleá "Elevatorgate"). Naturalmente, los elementas más socialmente progresivos quieren que la comunidad sea más inclusiva. Como resultado, sale el Ateísmo+. Ateos que además se preocupan por otras cosas.

Vale aclarar: ateísmo sigue significando lo mismo. No creés en dios, sos ateo. Esta es la base de un enorme número de críticas al movimiento A+, que ateísmo no requiere ninguna preocupación por derechos iguales o lo que sea.

Y es cierto. Los misóginos son tan ateos como los feministas. Sin embargo, el asunto es que nadie dijo lo contrario. A+ no intenta redefinir el ateísmo sino que juntar a un grupo de personas que tienen preocupaciones comunes (y que les jode esa onda en el resto de la comunidad).

Por cierto, algo parecido ya pasaba con el Nuevo Ateísmo. La gracia de la parte de "nuevo" era la idea de pasar de simplemente no ser religioso a a combatir activamente la religión como una fuerza negativa, algo que tampoco es parte de la definición del término.

Así como el Nuevo Ateísmo reconoce que no creer en dioses nos lleva (a algunos) a querer combatir la religión, el A+ extiende esa idea a otros asuntos. Reconocer la influencia de la iglesia sobre los derechos LGBTQ lleva a muchos ateos a combatir a su favor. Reconocer la cultura patriarcal de las religiones más importantes nos lleva al feminismo. Y así sucesivamente.

Tengo un cierto optimismo sobre este movimiento. No puedo declarar demasiado, visto y considerando que existe hace dos semanas, nomás, pero me interesa ver como evoluciona, y si puede no solo agregarle conciencia social al ateísmo sino también un punto de vista escéptico a la lucha por las minorías. Veremos que onda.



(este poste me vino al la cabeza en respuesta a esto, donde el autor critica al A+ en base a que "el ateísmo es una posición filosófica, no idelógica". Completamente cierto, completamente irrelevante.

Para quienes les interese el tema, atheismplus.com tiene un foro bastante activo donde ahora mismo se está discutiendo qué es y que debería ser el A+. Solo en inglés por ahora.)

The power of the human soul

"Oh yes, the complex is entirely self-sufficient. Food, water treatment, electricity, we handle it all ourselves. Right here in this very building, as a matter of fact"

"Is that so? How exactly do you manage that?"

"Well, we harness the power of the human soul.This structure is the result of years of hard work, of research, of trial and error. I've lost track of how many designs I tried until I settled on this one, but it's paid off, let me tell you. It's the largest, most efficient soul distillery in the world!"

"Soul... distillery?"

"Of course, the process has little to do with distillation in the technical sense, but the name has stuck. That large tower in the middle houses an aether vortex of billions of souls, which are progressively run through a series of subsystems which ultimately provide all we need to subsist."

"What?! How?"

"The main product of the process is a sort of nutritious sludge, obtained from the deepest essence of the souls. The necessary steps are mostly a series of filters inscribed in runes of ancient power and a centrifuge and some, um, other steps, but anyway, in the end we get our main food source. It has some wonderful properties, it's healthy, and filling, and has some curious side-effects at the, uh, higher concentrations some of us take"

"I'm sorry, you're telling me you eat souls-"

"Not just eat, no, like I said earlier, the sludge's just one of the products of the system. The vortex functions as a turbine, too, that's how we power the complex, and there are other byproducts of the refining of the soul we take advantage of for various purposes. Fertilizers for what little farming we do, building materials, disinfectants, some other things..."

"But, I... you mentioned billions of souls, right? How does that even work, where do the souls come from?"

"Oh, that was my biggest problem in the early stages. My first soul processing system was designed for harvesting them one at a time, can you believe that? Sure, it worked as a proof-of-concept and for the early research, but if I wanted any significant volume? The logistics issues alone gave me nightmares. Fortunately I didn't give up, I had many other ideas. The aether vortex, for example! In the initial designs, it was supposed to suck in all the recently deceased souls floating around, which would in turn power up the vortex even more, so it would cover a wider area, and so on and so forth."

"In the initial designs."

"Right. Eventually it became apparent that there simply wasn't anywhere on the planet with enough population density to power the system like that, and the problems with even getting it running where just too many. Frankly, the sheer numbers involved would have doomed any scheme I or anyone else tried. A single soul produces at best a few millilitres of anything useful, and I simply didn't have a large enough source available. That is, until I thought of wanking"

"...come again?"

"Wanking. Turns out sperm have souls, too! Well, half-souls, really, the other half is in the ovum. Not terribly well developed, either, only a fraction as juicy as that of a developed human being, but at a couple hundred million per ejaculation, it doesn't really matter. I could power the entire thing myself if necessary!"

"..."

"I don't, if that's what you're wondering. No, most of the male elders do their part. We engage in certain practices that, uh, ensure we have the highest quality spiritual children, so to speak"

"So... the basis of the entire community... is the semen of the elders..."

"The condensed essence of the proto-souls contained in the semen of the elders, yes."

"You know, when I write about this, I'm gonna tell them 'the power of the human soul' is a metaphor for solidarity and working as a group"

"Seems like it would be wise."



------


Sometimes I just need to write things.

A word of warning

What I'm going to do today is leave a note so that if at any point anyone finds themselves in the situation I did one month ago, they might find this post and save themselves some panicked guesswork.

One of the CDs I shot lasers at

Let's rewind one month, then. I am shooting lasers at CDs. And I don't mean in the usual "use the laser to read the information encoded in the CD" sense. Nor the slightly less usual "use the laser to burn the information onto the CD" sense. I mean I grabbed a CD, stripped away part of the label and reflective layer, and aimed an He-Ne laser through the resulting transparent opening into a wall.

Spots of light caused by diffraction

Why would we do such a thing? The short answer is that CDs (and optic discs in general) work as diffraction gratings. The rough idea is that diffraction gratings allow you to divide a beam of light into a lot of beams of light, and since all those beams of light have the same source , they can interfere with each other in a way that is simple to calculate and visualise*. In particular, what you see when you shoot lasers through a CD is a number of bright spots on the wall behind. One of them is located exactly where it would be, if the CD was just an ordinary piece of transparent plastic. Just trace a straight line from the laser to the wall, and there you go. The other spots are located on either side, at places that can be found with something called the grating equation.


The grating equation relates the angle of the position where the bright spots are, the wavelength of the laser, and something called the "period" of the grating. In a CD, that amounts to the distance between two consecutive grooves, AKA the track pitch.


I already know the wavelength of the laser I'm shooting at the CD, and I can figure out the angle of the bright spots by measuring a couple of distances and using trigonometry. Which means that I can use all this data to measure the track pitch of a C. A distance, incidentally, that a bit of prior research on people who had done similar experiments had shown to be 1.6 micrometers  (a micrometre or micron is a unit of length equal to the millionth part of a metre. It has the symbol μm)

So, as I was saying, I am shooting lasers at the CD. I mark the location of the spots, measure all the relevant distances, do all the relevant math, and find a result: 1.49 μm. Well damn. That's not good.

But wait!, you're thinking. Aren't we talking about a difference of 0.1 microns? A tenth of a millionth of a metre? That's a minuscule difference!


It sure might seem that way, but the measurement I was doing was supposed to be much, much more precise. Specifically, with an error margin of 0.02 μm. A result of 1.49 ± 0.02 means that the biggest possible value for the track pitch, given all those measurements, is 1.51. 


So I recheck all my math, measure the distances again, etc, but nothing changes. and I start to get worried. All the other further things I was supposed to do with that CD would be completely pointless, with such a large error. I needed to know what was wrong! 


And so I turned to the internet, and explored the issue, and what do I come across? Well, that the ubiquitous figure of 1.6 μm that everyone keeps quoting is not, in fact, quite so. Certainly, there are CDs with that track pitch. Those are what we call 74 minute CDs. The much more common in modern times 80 minute/700 MB CD, why, that has a 1.5 μm track pitch.


The industry standards for CDs say that track pitch has to be 1.6 ± 0.1 μm, so of course, many assume that 1.6 is the most common. Certainly that was the case with every single previous experiment on the subject I'd checked previously. What happens is that nowadays, CD players are more reliable than they were when the CD was first created, so you can have a CD with grooves closer to each other and you won't have any trouble playing it. A tighter track pitch means more information can be stored in the same space, so naturally you want to take advantage of that and go to the lower end of the allowable range. Thus, 1.5 μm track pitch CDs.


You hear me, people of the future who might consider doing experiments with CD diffraction? The groove spacing or track pitch for a 700 MB / 80 minute CD is 1.5 μm! Don't let everyone else mislead you!





* In theory, there is no requirement that light be from the same source to interfere. In practice, however, what happens is that any observable effects of interference between different sources lasts for too short a time to be seen.

In which Ashes is recorded for future use

This is apropos of nothing, but this idea has been worked into my mind and I feel like recording it here, because it might have some future use. Or not. It's here, either way. It's a simple system I call "Ashes", based on its two main symbols, the dash and the asterisk.

The rules are as follows:

1. -- is a valid sequence
2. ** is a valid sequence
3. You can add - to the end of a valid sequence ending in --
4. You can add * to the end of a valid sequence ending in **
5. If you have a valid sequence composed entirely of asterisks, and a valid sequence composed entirely of dashes, you can insert a copy of the dashes sequence between every asterisk of the asterisk sequence
6. If you have a valid sequence that contains the fragment -*-, you can add # to both ends and remove all the asterisks.

You'll notice you can have sequences of any length greater than 1, as long as they are composed entirely of dashes or entirely of asterisks, thanks to rules 1-4. For example:
---
-----
-------
*****
***
**

Rule 5 allows you to combine them. For example, combining the first and the fourth would result in

*---*---*---*---*
You could use the second with the fifth and the third with the sixth, getting

*-----*-----*

*-------*

And so on and so forth.

Rule 6 is the closer, where the # symbol appears. Using it with those above we would get

#------------#

#----------#

But we cannot use rule 6 on  *-------* to get #-------#, because at no point does -*- appear in *-------*.


There is a reason behind this bizarre set of rules, of course, some interesting property behind the chains that can and can't appear. It seems obvious to me, actually, but that's probably because I thought it up so it would fulfil that express purpose. I suspect it is not immediately clear to most other people. It might be a fun riddle, I don't know.

The answer is ROT13'd here:

Vs bar gnxrf frdhraprf bs qnfurf orgjrra unfurf naq pbhagf gur ahzore bs qnfurf, gur bayl (cbfvgvir vagrtre) erfhygf lbh pna'g rire trg ner gur cevzr ahzoref naq 1. Va bgure jbeqf, rirel unfu frdhrapr unf n pbzcbfvgr ahzore bs qnfurf.

This serves no purpose, so far, other than as an illustration of a pattern hidden in rules that don't refer to it directly.

Evaluation: 0-TAPIR 2

First, I'd like to make it clear that the recent pause in updates was due to laziness in writing Evaluations, not the story itself. Plus I had exams until yesterday. Anyway.

No title yet, as you can see, though I haven't focused much on one. It might become apparent once the story moves forward a little, or not, in which case I'll just makes something up. But let's hope it doesn't come to that.

The writing moves on at a decent rythm, at least decent for me. I've played this part of the story many times in my head (this is the novel I've been wanting to write for years, though to be fair most of what I've written so far is relatively new), so no lack of ideas for a while now. It's getting exposition-y, but frankly as far as I can see there's no alternative for that. Hopefully it isn't too annoying, otherwise I'd have to reconsider the entire story... but let's not go there.

Wordcount: 2865

Since last time: 1521

Evaluation: 0-TAPIR

What the hell is 0-TAPIR, you ask? A working title. Project TAPIR is what I like to call the novel I've been wanting to write for many years now and restarted several times. What I've got right now is a prequel of sorts to it, a story that happens in the same continuity involving some of the main characters. Hence the zero. (The zero goes at the beginning because otherwise it messes up the Evaluation count.

0-TAPIR is specifically the story of Mielen (name subject to change), but also in a way the story of why the world is as it is. A small part, because she wasn't there for a lot of it, but that's to be filled by other characters. Mielen's story has changed a lot throughout the years, most of the changes meant to remove clichés and depower her, because damn was she absurdly powerful originally. Now, she's might actually be at a disadvantage against some people! I'm so proud of myself.

Wordcount: 1344

Evaluation: Countdown 2

Many thousands of years ago, I used to do this thing where I posted weekly updates of my ongoing writing projects. It's back, baby!

Sort of. I've only written a handful of paragraphs yesterday, due to terminal laziness and lack of inspiration. Mostly laziness. But still, I'm back, and hopefully I'll get my shit back together.

Wordcount: 225

Total: 820

ProofThatGodExists.org

Moving past that little bit of math the other day, we turn to philosophy, which is like math except much less precise, much less useful and a lot more open to discussions by laypeople in altered states of consciousness. Also a more common subject of my blogginations.

As you have no doubt cleverly deduced from the title, there is a website called proofthatgodexists.org, and it claims to have proof of God's existence. The even cleverer may suspect I disagree, and that an explanation of that disagreement will be in fact the main point of this post. You are entirely correct.

The format of the website is quite simple. At each stage, you are faced with a number of propositions, 4 at first and 2 at all other steps, and you have to choose one. If you choose the wrong one (as determined by the author), you are directed to a page explaining your foolishness and urging you to choose the right one. As you progressively accept the propositions deemed correct, you are guided to a final "proof" which takes these propositions as premises and God's existence as a conclusion.

It should be noted that I don't necessarily disagree with the premises. I may be hesitant on a few, but essentially all feel correct or close enough. It's just the final reasoning I object to. So while I say a thing or two about them, the really important part is just the proof. Skip to that if you want to.

Didn't skip? OK, then, we start at step 0, faced with 4 options regarding absolute truth. They are:

1) Absolute truth exists: This is the option deemed correct by the author, and mostly I agree. I wouldn't say I'm sure, but it certainly seems my best guess.

2) Absolute truth does not exist: This leads to a page titled "Absolute truth does not exist" with two options: Absolutely true and False. Both lead to the same place, a page with the title "This is not a glitch (think about it)", and shows the same 4 options that at the beginning. Of course, the author refuses to consider the possibility that the non-existence of absolute truth is relatively true.

3) I don't know if absolute truth exists: The page you get is exactly the same as if you had clicked the prior option, only with a correspondingly different title. Both options again lead to the "think about it" page. Again, the author's insistence on binary propositions leaves the obvious answers out.

4) I don't care if absolute truth exists: The followup is just a "thank you for visiting" page with an "exit" button that links to Disney. Is knowledge apathy highly correlated with being a Disney fan? Mysteries of life.

Like I said,I essentially agree here, so I moved forward to an introductory page which has some blahblahblah about how the existence of God should be obvious but anyway here's some proof and whatnot. Moving right along, we get to step 1, about logic: 

1) Laws of logic exist: While one might quibble about what "existing" means for a logical law, once again I essentially agree.

2) Laws of logic do not exist: The page claims that either you arrived at this conclusion using logic, or it was an arbitrary decision and you might choose otherwise next time. Once again, this is not strictly exhaustive, one might come to decisions using non-logical but time-invariant reasoning. People do not, in fact, use logic alone to come to most decisions, but it's not really a point worth arguing.

Onwards to step 2 (electric boogaloo), which deals with the subject of mathematics:

1) Laws of mathematics exist: This is actually equivalent to step one. Math is just logic, wherein you say that, given some axioms, something is necessarily true or necessarily false. Accepting logic is accepting math, and viceversa. So I again agreed.

2) Laws of mathematics do not exist: This point essentially says that you use math all the time, so you can't deny it and be consistent. I agree, though one might argue about the subtleties of using math vs declaring math to be law, etc.

Which leads us to step 3, which leaves the purely logical domain and enters the empirical one:

1) Laws of science exist: Agreed, with the usual provisions on what it means for a law to exist, etc. But, yes, I do believe laws of science are real and useful, otherwise I wouldn't be trying to become a scientist.

2) Laws of science don't exist: It redirects to a page with the same argument as above, except for science instead of math

And then step 4 which takes us to the complex field of ethics:

1) Absolute moral laws exist: This one is tricky. I'm a moral realist, i.e. I consider right and wrong to be objective concepts. Results of quirks of the evolution of humans as sapient social animals, ultimately, but nonetheless real. What I am not is a deontologist, i.e. someone who believes that morality is a set of rules that must be obeyed absolutely, which is what one usually thinks when talking about moral laws. But nonetheless there are laws concerning right and wrong, or at least one law, which says (roughly) "calculate the possible consequences of your actions, weigh them according to what you value, and do the best thing possible". So I agree or disagree depending on what exactly is meant. This is ultimately of little relevance to the final proof, though.

2) Absolute moral laws do not exist: This leads to a second set options, asking whether raping children for fun is absolutely wrong or not. I actually can conceive of situations where raping children for fun would, in fact, be the right thing to do. They are convoluted and ridiculously improbable, of course, but still. If you pick "not", the next page goes on about how moral subjectivism is bad and blah. I could respond to it (I used to be a moral subjectivist, and had seen similar arguments before), but it would get long and boring.

Steps 5, 6, and 7 are on the nature of all these laws previously mentioned. Step 5 deals specifically with their materialness :

1) Laws of logic, mathematics, science and absolute morality are immaterial: I prefer "abstract" to "immaterial", since the latter implies they are made of something, which just isn't so. But in any case, sure, they certainly aren't objects made of matter. They are things that hold true about things that are made of matter, (or about other abstract entities).

2) Laws of logic, mathematics, science and morality are material: Leads to a page asking you to say where in nature you can actually find them and blah.

Step 6 deals with universality:

1) Laws of (etc.) are universal: I don't really consider something to be a law (in the sense used here, not the legal one) unless it is, in fact, universal. A law which only works in some circumstances is not a law, just a special case of a greater, actual law. So yeah, sure.

2) Laws of (etc.) are individual: Once again our friend ignores a vast number of possibilities. There are a number of different scales between universal and individual. But anyway, leads to a page using the same "you assume X to live your daily life so you can't deny it".

Step 7 is highly similar to its direct predecessor, but this time it's about change:

1) Laws of etc. are unchanging: Again, if laws change over time they are just special cases of laws that dictate their behaviour at each time.

2) Laws of etc. are changing: Leads to the typical argument.

And finally, we arrive at step 8, the part that is the purported proof rather than just the building up the premises.

The argument begins as follows, and I quote:

To reach this page you had to acknowledge that immaterial, universal, unchanging laws of logic, mathematics, science, and absolute morality exist. Universal, immaterial, unchanging laws are necessary for rational thinking to be possible. Universal, immaterial, unchanging laws cannot be accounted for if the universe was random or only material in nature.

A random universe can very well be lawfully random. The Copenhagen interpretation comes to mind. And I don't see why a purely material universe can't have statements about it that are true yet not material themselves, I mean that's what most materialists mean by material universe, myself included. So this "cannot be accounted for" thing is just glaringly lacking in justification. When you consider the long essays over ultimately inconsequential things, this is quite annoying (I say ultimately inconsequential, because you don't really need to agree to all the laws put forth, it's enough to agree with one set of them for the purposes of the argument)

It continues to say:

The Bible teaches us that there are 2 types of people in this world, those who profess the truth of God's existence and those who suppress the truth of God's existence. The options of 'seeking' God, or not believing in God are unavailable. The Bible never attempts to prove the existence of God as it declares that the existence of God is so obvious that we are without excuse for not believing in Him.

Because obviously, someone who doesn't already believe God exists gives half a shit about whether the Bible allows us not to believe, or whether it considers God to be evident. I mean, the Revelation of Ungod teaches us that gods don't exist, but I don't expect that to sway the author of this piece.

Anyway, that is followed by some corresponding Bible verses (Romans 1:18-21, if you're interested), and then the remark:

The God of Christianity is the necessary starting point to make sense of universal, abstract, invariant laws by the impossibility of the contrary. These laws are necessary to prove ANYTHING. Therefore...

Whoa, mate. How the fuck d'you figure that? Even accepting your premise that a material universe isn't enough, why does the starting point need be a god, let alone your god? This claims to be a logical proof, so what possible chain of reasoning based on the premises so far results in "The God of Christianity", a complex proposition not mentioned once in any premise? Someone doesn't understand what "logical proof" is, methinks. New elements don't just jump out of thin air.

The final statement of the proof is "The Proof that God exists is that without Him you couldn't prove anything." It gets its own page and all. And while I could argue the finer points of whether you actually can prove anything at all, that's not really where the proof fails. At each step there were subtle points that can be argued to death, but it's useless to get bogged down on that when there's that giant gaping hole in the argument.


So putting aside my hesitation at some of the premises and whatnot, my refutation of this "proof" is short and simple: There's no reason given why a material universe doesn't account for universal law, and there's even less reason to assume the only thing that does is one particular God. Anything else would be nitpicking.


It's disappointing. With all the build-up and extensive arguing for each mostly obvious premise, the final steps of the proof, the most vital and the most controversial, are stated outright with no reasoning behind them.

Slicin' spheres

Illustrative MS Paint diagram 1

Imagine a spherical structure of radius r, which has within it multiple circular floors (see illustrative MS Paint diagram 1). You want to know the total area of those floors. The area of a circle is pi*radius^2, so you can easily calculate the surface of a floor located in the exact centre, since its radius is the same as that of the sphere, but the other floors are trickier. Let's say that all the other floors are separated by a distance h. How do we find the total area?

The most obvious approach is to find a formula for the radius of each floor, plug it into the pi*r^2 formula, and repeat for each floor. Let's try that, first.

Illustrative MS Paint diagram 2

Take a look at our second MS Paint diagram, with coloured lines labelled x, r, and h. The green r length and red h length we already know (and are, in fact, r and h, i.e. the radius of the sphere and distance between floors). You can see that the blue x line is the one whose length we want to know, the radius of a circle located at a distance h from the centre. X, r, and h form a right triangle, so by Pythagoras' theorem, we know that x^2 + h^2 = r^2. From which we can deduce that x^2 = r^2 - h^2. We could take the square root to find out the value of r, but we don't need to. Why? Because all we want x for is to replace it in the circle formula pi*radius^2, where it is already squared.

Illustrative MS Paint diagram 3

Replacing, we know that, for a circular section of a sphere at a distance h from the centre, the area is pi*(r^2-h^2). That's the floor directly above the centre, at any rate. It's also the floor directly below the centre, since they are the same size. But we want to know the total surface, so we need to know all floors. So what we do is we name each floor by the scheme in diagram 3, and amend the formula to be pi*[r^2-(n*h)^2], where n is the floor number. That way, we are in effect doing the same thing that in the paragraph above, but replacing each h with n times h. So, for floor 1, the formula remains unchanged. For floor 2, we use twice h rather than just h, because it's twice as high. Notice that, cleverly enough, for floor 0 the formula is just the old pi*r^2. Also notice that I gave some of the floors negative numbers, but I could just as well have made them positive. It doesn't make a difference, because n^2=(-n)^2.

So there we have our complete formula,, for every n floor. Now it's a relatively simple matter of replacing every floor in the formula, and adding them all up. Easy if you have 3 floors, to be sure, but what if you have more?

Well, in the original problem I considered, the radius was 150m and the distance was 3m. That is to say, ~50 floors in each direction. Admittedly, at that point I declared myself too lazy, left the person who was asking me the question with the general formula, and told them that if they wanted it they could do it themselves. (They didn't, but I remembered what little I have of skill with Python and wrote a short script to do it for me). But I then thought of this simple trick to compute an approximate answer. It's useful if you don't need an exact answer and can't ask a computer or another person to do it for you. In fact, it's because I was surprised the trick worked so well that I ended up writing this blog post.

Image stolen from Wikipedia

The reason I thought of this trick is because the idea of slicing up a sphere in lots of smaller pieces and adding them up reminded of the concept of an integral. Very rough explanation: An integral is something you can use to calculate the area below a curve. The idea is that you divide the area into small rectangles, whose surface is easy to find. The more rectangles, the closer you get to the exact value. See diagram to the right, which this time I didn't make myself in MS Paint but rather took from Wikipedia*. You're welcome. Anyway, the same principle can be used for volumes (and happens to be something I've been doing in class a lot, lately). The trick we need for today's problem is to go backwards from an integral. I'll explain how that works in a moment.
 

Illustrative MS Paint diagram 4

So let's go back to the beginning. You've got a sphere and many parallel slices, whose area you want to know. You already know the radius of the sphere , so you can easily find its volume as 4/3*pi*r^3. And then you think: "I have all these parallel slices at the same distance of each other. I bet that if I took each slice, made it into a cylinder, and stacked them all on top of each other I'd get something very similar to the sphere". You can imagine something like our 4th illustrative MS Paint diagram. The red is the stacked cylinders, black is the actual sphere (I know they look like rectangles on a circle, I don't feel like adding 3d effects and the idea is the same). Anyway, you can see that is a reasonable approximation, though of course not perfect. The more slices, the better the approximation, so for the ~100 slices of my original problem this is more than good enough.

So, you add the volumes of the cylinders and get a result that is close to the volume of the sphere. But what are you doing when you are adding the volume of the cylinders? Well, a cylinder's volume is height times area of the base. So we have base area of the first cylinder (ba1) times its height (h1), plus those of the second (ba2*h2), plus those of the third (ba3*h3)... But wait, all those h1, h2, h3 are the same, so we can just call it h. So we have: Volume of the sphere ~= ba1*h + ba2*h +ba3*h +.... The symbol ~= means "approximately equal".

With me so far? We have everything multiplied by h, so we can just write it as volume of the sphere ~= h*(ba1 + ba2 + ba3 + ba4 + ...). But what is this sum of ba's? The sum of the base areas of all the cylinders. And what is the base area of those cylinders? It happens to be the area of the circular sections we were trying to calculate in the first place!

So we just divide both sides of the equation by h, and we have that (volume of the sphere)/h ~= sum of the areas of the circular sections. And the volume of the sphere, I remind you, we already know from its radius. So this long explanation adds up to a very simple formula, which is the biggest advantage of this method: It's ridiculously easy to use. Just take r and h, and plug them in here:
.

As for that "approximately", how approximate is it? In my original problem, radius = 150 m  and h = 3 m, the result I got from my Python script is 4,711,917.9068 (pi to ten decimal places, just because that's as much as I know from memory). Using the formula above, I get 4,712,388.9804. That's an error of about 0.01%. So, y'know, pretty good. Considering the result I reported to the person who asked me was "about 4,700,000 m^2", far more accurate than I needed.


To my imaginary readers, I promise I will get back to writing fiction rather than math and shitty .bmps. Eventually.


*The image's copyright holder is Wikipedia user KSmrq. Since it's under a Creative Commons Attribution-Share Alike license, so is this individual post.