Pi Day! (Pi Randomness, and the Case for Tau) [Pre-Release Text]

[This is really just my script for a video that I wanted to do, but I couldn't in time. (Update: I know I said I'd have it the day after, but that has not come to pass. It should be up soon, but I don't have a specific date yet.) Some things may be hard to understand without visual aids and mathematical formatting.]

Happy Pi Day! In case you didn't figure, Pi Day comes from the first three digits of pi: 3.14. This yields the date 3/14 in month-day form, or March 14.

Those who don't go with the month-day form, and go with day-month instead can still have their day with Pi Approximation Day, 22 July, which looks just like the approximation 22/7 for pi in day-month form.

But let's get back to Pi Day. The only way this works is in decimal form, which most of us use. But what if we tried a different base, say 2? Binary is just as important in our modern (computerized) world, so let's go with that.

Pi begins with the binary expansion 11.00100100. Of course, we could pick out different numbers of digits to get the date we want, say, the first two, 1 and 1, and celebrate Binary Pi Day on New Year's. But that doesn't capture the essence, just as 3/1 doesn't do it for Pi Day.

So we'll maximize the number of digits to take. A month in the Gregorian Calendar requires 4 binary digits, with range 0 to 15, to be represented. A day requires 5 binary digits, with range 0 to 31.

So let's do that. If we use month-day, we have 1100 and 10010, resulting in 12 and 18 in decimal. Mark your calendars for December 18! Or, if we use day-month, we have 11001 and 0010, or 25 and 2. We've barely passed 25 February. Set your sights for next year!

There's a lot more to be said about pi, but I think what I might say has been said before. I might do something soon about it. But now, let's set our sights on a related constant: tau.

Tau is equal to 2 pi. Equivalently, it is the ratio of a circle's circumference to its radius. That formula for circumference, C = 2 pi r, becomes C = tau r.

Before we continue, I'd like to say that, though Tau Day (6/28) is not the same as Pi Day, they both agree for binary. Since tau is just pi multiplied by 2, the binary representation is simply shifted over one place value: 110.0100100... So December 18 and 25 February should really be Binary Pi/Tau Days!

Moving on. There are lots of reasons why tau works better than pi. You can go ahead and read "The Tau Manifesto" (which should be linked) [http://tauday.com/tau-manifesto], or continue reading. (I do have to admit that much of this is taken from there.)

Well, if tau works better then pi, why do we use pi in the first place? The answer is practicality. Put simply, it's much easier to measure a circle's diameter than its radius. Engineering specifications for circular forms are usually given as a diameter, with its own special symbol (okay, not really special as it resembles a few other symbols with distinct uses).

But that's why we use pi. But enter modern mathematics, where circles are considered by their radii, not their diameters. (Seriously, if you see "d" in math class, you're either dealing with distance or differential calculus [and possibly both]).

So we should use tau. It clears up formulae, as we've already seen with circumference: C = tau r. The period of the sine, cosine, secant, and cosecant functions is... 2 pi? How about just tau! As a consequence, we can write angular frequency omega = tau frequency f. As a consequence of that, here's one for the physicists: no more dealing with that pesky formula for the reduced Planck's constant. Reduced Planck's constant h-bar = Planck's constant h / tau! Much simpler!

Next we return to what brought us here in the first place: circles. Radians are excellent for measuring angles since they simply represent the ratio of the arc length to the radius. That is, radian angle theta = arc length s / radius r. So, how many radians does a full circle subtend? 2 pi radians. How about tau radians! So a quadrant of a circle subtends 1/4 tau radians, which reveals the quarter aspect. 1/2 pi radians? What?

Oh, the grand Euler equation: e^(pi i) + 1 = 0. The famous equation relating five of the greatest numbers in mathematics, derived from Euler's formula: e^(xi) = cos x + i sin x. Pi still has its stronghold... Not exactly. This is just a more elegant way of saying e^(pi i) = -1, which doesn't look too good with that negative sign. Even better, we can say e^(tau i) = 1. Okay, the zero is gone, but it was only there in the original one to get rid of the negative sign. We can re-introduce it by considering Euler's formula: e^(tau i) = 1 + 0i.

And finally, we come to the most contentious formula in the battle between tau and pi: area of a circle. A = pi r^2. A = 1/2 tau r^2? Doesn't look too good, does it?

Well, that's true, but... Tell me, in physics, how far does an object travel, starting at rest with a constant acceleration, in a given amount of time? Answer: distance x = 1/2 acceleration a (time t)^2. Similarly, what is its kinetic energy? energy E = 1/2 mass m (velocity v)^2. These two formulae are clues to what's going on.

To fully answer this, we're going to need calculus. Let's start with the distance problem. Acceleration is the second derivative of position, so d^2x/dt^2 = a, which is a constant as established earlier. Integrating, we have dx/dt = at + C. Since velocity is just the first derivative of position, we have v = at + C. To find the value of C, note that the object is initially at rest, so v(0) = 0. 0 = a(0) + C, so C = 0. We're left with dx/dt = at. Integrating again, we have x = 1/2 at^2 + C. We'll assume that the object's initial position is 0, so C = 0. Finally, we have x = 1/2 a t^2.

We can use this to derive the formula for kinetic energy, and we will see that it retains the 1/2 factor from the formula we just derived for position. Kinetic energy is essentially the work needed to bring an object to a certain velocity. Work W = force F distance x. We'll assume a constant force to simplify things, so that implies a constant acceleration. Force F = mass m acceleration a, and we already have x = 1/2 a t^2, so W = (ma)(1/2 a t^2) = 1/2 m a^2 t^2. But since v = at for an object initially at rest and undergoing constant acceleration, the formula can be simplified to W = 1/2 m v^2. Since kinetic energy is equal to this work, E = 1/2 m v^2.

Now, how does this apply to the area of a circle? It works with one proof for the formula for the area of a circle. We'll break up the circle into concentric rings (or annuli, singular annulus, if you will).

Let's consider one of these rings (annuli). Let's call the radius of this ring little r (to distinguish it from big R, the radius of the whole circle) and the width dr. The area is roughly equal to that of a rectangle of length that is the circumference of the ring (it doesn't matter inside or outside; since this is calculus, we'll make these rings infinitesimally thin), and height dr. Remember that tau is the ratio of circumference to radius, so the length is tau r. So the area of this ring is tau r dr.

Summing up these circles with integral (0 to big R) tau little r dr, we have 1/2 tau R^2. As "The Tau Manifesto" states at the end of the section exploring this formula: "If you were still a pi partisan at the beginning of this section, your head has now exploded."

creation.com's article on atheism

creation.com has a lengthy article all about atheism. the descriptions of atheism in sections 1-3 are fairly innocuous (at least what I read). let's check out different.

Morality and ethics

As to the question of whether atheists can make absolute moral statements, this is tantamount to the first year theology student who, when asked, “Do you believe in infant baptism?” responded, “Sure I do; I’ve seen it done.” Yes, atheists can make any statements about anything at all--the question is: are the statements viable? [emphasis in original

this is pretty stupid. anyone can make statements about anything, and the same question has to be asked.

Atheists make epistemic statements about morality but do not provide an ontological premise for ethics. [Footnote: Epistemology refers to the study of the nature of knowledge; what it is, and its scope/limitations., etc. Ontology refers to the study of the nature of being, existence, or reality in general. (emphasis in original)] That is to say that they can muse upon issues of morality and come to any conclusion that they please. However, these turn out to be arbitrary personal preferences that are expressed as dogmatic assertions.

I'm not quite sure about the epistemological/ontological whatnot, but since we do not look to a higher power for a source of morality, we perhaps do make arbitrary statements on morality. but who's to say religious people don't do the same? if it turns out that deities don't really exist, then their morality also simply comprises "arbitrary personal preferences."

“Q.E.D.” is the Latin term quod erat demonstrandum which means “that which was to be demonstrated,” in other words; tautology or circular logic. [Concerning Darwinian evolution of morality.]

just plain bull! that is the literal Latin meaning, but it is supposed to mean that the original statement that was set out to be proven has been proven. for example, to prove the Pythagorean theorem, you would first have to state what exactly you must prove, that the square of the length of the hypotenuse (longest side) hypotenuse is equal to the sum of the squares of each of the lengths of the other two sides. you would them set out to prove it, and once you reach the conclusion identical to the first, you write "Q.E.D."

Another supposed basis for ethics is that “an action is unethical/immoral if it causes harm to others.” Thus, it is the nature of the consequence caused by the action that determines whether an action is ethical or unethical. The fundamental problem with this definition of ethical behavior is that an action ceases to be unethical if no adverse consequences are experienced. As such, nothing is inherently wrong; an action is only wrong if it causes harm to another.

Consider the example of adulterous behavior: under the “do no harm” definition of ethical behavior, adultery is wrong because it harms the other party in the marriage (i.e., the faithful spouse). This harm can include mental anguish, the spread of disease to the faithful party and the loss of affection from the adulterous party. An additional adverse consequence includes unwanted pregnancies outside of the marriage. However, what if an adulterous act did not lead to those outcomes (e.g., a husband, who has had a vasectomy, occasionally has sexual relations with women free from sexually transmitted diseases while on trips to foreign cities)? In such an instance would adultery cease being unethical? Would the husband’s behavior turn from ethically neutral to unethical only if he were to confess his adultery to his wife, or if he was otherwise caught, thus causing her mental anguish?

again, bull. this is like saying petty theft isn't illegal or wrong until somebody finds out! still, harm is done since the business or what-have-you that got its property stolen loses money. with the adultery example, the outside sex could lead to a less satisfying relationship with the faithful spouse, which would lead to "mental anguish," just the same.

Furthermore, the atheist has no basis for saying that it is wrong to harm others anyway. Why should it be wrong to harm others? This supposed basis for ethics fails at this very point.

intuition! once again, if it turns out that deities don't really exist, then religion's base of ethics fails as well

Atheists such as Richard Dawkins have trouble finding logical reasons to denounce rape as unacceptable behavior.

how about this? I think we can agree that rape harms the person being raped, usually a woman. how and why, though? this comes down to the process of courtship and mating in humans as well as other animals. females tend choose mates carefully, since they can bear fewer offspring in their lifetime. to disturb this careful selection would be harming her. therefore rape is wrong.

Uncreated creator?

to quickly sum up, the atheist argument presented is that God must have been created by something, if religious people say that everything has a cause or creator. the response is that God is eternal, and thus does not need a creator or cause. they also point out that atheists assert that matter and energy are eternal, and thus do not need causes, which is the same as religion's argument

fine by me! I personally do not bring up this argument, as I acknowledge that some things are eternal and do not need causes, such as the theoretical multiverse proposed by physicists, of which out universe is only a part.

Arguments for God's existence

the cosmological argument asserts that the universe must have a creator. again, I point to the multiverse.

[the teleological argument, aka the argument from design]

1. All designs imply a designer
2. There is great design in the universe
3. Therefore, there must be a Great Designer of the universe

proponents of natural selection will argue that premise #1 is obviously false. plus some may argue that #2 isn't necessarily true. next!

[the ontological argument]

1. God is defined as a being than which no greater can be conceived.
2. Such a being can be conceived.
3. If there were no such being in reality, then a greater being--namely, a being than which no greater can be conceived, and which exists--can be conceived.
4. Yet nothing can be greater than a being than which no greater can be conceived.
5. Therefore a being than which no greater can be conceived--i.e., God--must exist.
6. God is the entity of which nothing greater can be thought.
7. It is greater to be necessary than not.
8. Hence, God exists necessarily.

[emphasis in original]

this, frankly, is a steaming pile of bull excrement, masquerading as a chocolate cake. please refer to my other post concerning this argument. in short, conceiving of a being that actually exists does not make it actually exist! also, "greatness" is subjective

[Dostoevsky’s argument from the consequences of positive Atheism]

1. If atheism is true then man is “the chief of the earth.”
2. If man is “the chief of the earth” then he can abandon absolute standards (i.e., morality)
3. If man can abandon the absolute standards then “everything is permissible.”
4. Therefore, if atheism is true, everything is permissible.

this argument really fails at premise #3. ever heard of moral relativism? secular ethics? please see my post on this as well

[the argument from joy]

1. Every natural innate desire has a real object that can fulfill it.
2. Human beings have a natural, innate desire for immortality.
3. Therefore, there must be an immortal life after death

what?!?! please check premise #1 and get back to me.

[Ronald Nash's argument from numbers] An argument proposed by Ronald Nash is known as the argument from numbers [emphasis in original]. This is how Ronald Nash explained it:

“...when I used to teach philosophy to undergraduate college students, I would sometimes ask them to tell me what the number one is. They would usually reply by writing some of the many symbols we use such as ‘1’ or ‘I’. I would then explain that such symbols are not really the number we are seeking but are only convenient ways we use to refer to the real number one. No wise person should ever confuse a symbol for something with the thing itself.

So what then is the number one? The first step is to recognize that the number one is a concept.

What is a concept? The short answer is that it is an idea.

The next step is to ask where the concept of oneness exists. The idea of oneness, like all ideas, exists in minds.

The third step is to note that the number one is eternal. If someone has trouble with this claim, ask when the number one began to exist.

Not only has the number one always existed, it is impossible for the number one ever to change. If the number one were ever changed, it would cease to be the number one. After all, if the idea of oneness changed, let us say, into the number two, then it would no longer be the number one.

So where are we? I believe we can show many people that the concept of oneness is an eternal and unchanging idea that exists in some mind. And, the only kind of mind in which this kind of eternal and unchanging idea could exist must be an eternal and unchanging mind. When I reach this point in my little example, some student in the back of the classroom usually raises his hand and asks if I am talking about God.”

This argument is very interesting in that it can be employed in the service of various considerations. For example, you may replace the term “the number one” with “the laws of logic” and produce a similar argument.

the concept of the number one is not "eternal," but rather developed by humans at some point in the past. the Wikipedia article on "natural numbers" has an introduction to formalizations of the natural numbers (0, 1, 2, etc.), which show that there are actually different realizations of this concept, meaning that the concept of the number one is, in fact, mutable (i.e. changeable).

Science

Although the scientific endeavor has nothing to offer atheism, atheists have co-opted it and employed it as a façade which they wrap around atheism in order to make it appear as if it is deserving of the merits of scientific respectability.

The contradiction in the atheist’s attempt to employ science towards their end is:

1. They claim that science only deals with the material and therefore, has nothing to say about the immaterial or supernatural.
2. They claim that science has disproved the immaterial or supernatural.

Despite this, some atheists claim that the way that science disproves the immaterial or supernatural is by increasingly finding material causes for material effects. However, this does not trouble the Christian because God created the material realm and it follows logically that material effects will have material causes and such causes and effects do not exclude the immaterial or supernatural such as God, or miracles.

personally I do not say that science "disproves" theism, but simply that it renders it unnecessary.

Society

it seems that atheists are generally less charitable than religious people, as liberals than conservatives. well, that sucks! but, hey, people aren't perfect. atheists should give more to charity, and I applaud those who already do.

it also seems that atheists have more health problems and rates of suicide attempts, due to less happiness, supposedly. but this is not a reason to convert. personally I am quite happy as an atheist, and if others aren't, and seek religion as the answer, that's fine by me.

In “...an effort to determine changes occurring between 1968 and 1978 in the percentage who approved of legal abortion in Canada under 6 possible conditions of pregnancy” agnostic/atheist students were amongst the least likely to draw a distinction between the following conditions under which abortion would be considered, “1st set of conditions (harm to mother’s health, possible child deformity, pregnancy from rape)...2nd set of conditions (out-of-wedlock pregnancy, economic inability to support child, unwanted child).”

so what? it just depends on one's view of abortion, and when developing human life actually becomes a person, between conception and birth. it doesn't have to do with the reason. take this example: an insect is not a person, so it shouldn't matter if I'm killing it because it's harming me in some way or simply because I want to.

another claim is that atheists say that societies without religion will be more scientific, intelligent, and maybe civilized, but atheists tend to be more superstitious. again, that sucks! but what is the cause? plus, I personally don't believe in such superstitions.

Atheism has no moral imperative for honesty so it is not surprising that atheists figure prominently in fraud and deception, although it is difficult to find statistics on this issue.

There are many examples just in the history of the promotion of evolution. A particularly notorious example is that of Ernst Haeckel, a “free thinker” (atheist) who fraudulently doctored drawings of embryos of various creatures to make them look almost identical and then claimed that this was evidence for evolution. He made at least two other fraudulent claims regarding the origin of life and a non-existent ape-man. He helped lay the foundations for Nazism in Germany.

again, please read about morality without religion, above, for nontheistic sources of morals such as honesty. and yes, Haeckel was a fraud, but that does not discredit atheists as a whole, not to mention the rest of the huge pile of evidence for evolution!

well, that's it for now! but note that this is only a bit more than half of the whole article, so I might have more in the future.

first comment to creation.com

creation.com is a fairly well-known site that supports creationism and discusses Christian teachings. I submitted a comment on this article about how the theory of evolution is linked to moral decline based on a survey conducted in Australia. my original comment is reproduced below for your information, and in case it is not published on their site, or is modified.

The premise of the argument made by this article requires the assumption that the actions described, namely: premarital sex and abortion, are actually immoral.

Challenge 1: Explain the basis of these assumptions.

Challenge 2: Give a secular explanation of said assumptions.

(Note: The designation of the above tasks as "challenges" is sarcastic. However, I still request that you perform them.)

If Challenge 2 cannot be met since it is believed that morals can only come from religion, that is utterly false. There are various systems of morals and ethics that do not require religious teachings.

in case you didn't already figure, I personally do not regard those actions as immoral

evolution's "circular reasoning"

browsing various areas, I've noticed that one argument that people often make against the theory of evolution is circular reasoning in the principle of "survival of the fittest." the argument generally goes like this:

the theory of evolution states that the fittest animals will survive, and that those that survive are the fittest. this is circular reasoning, and thus evolution is wrong

this is merely the definition of biological "fitness", stated twice. how this really comes into the big picture of evolution is this:

those, that are deemed the fittest, survive and are able to pass on heritable traits (in the form of genes) to the next generation. therefore those traits that lead to fitness and survival become more common over time

are we good here?