This article was sent to me recently and I was asked to provide my opinion of it. The article is written by Dr. Richard Parker, M.D. and it’s titled “A Physician Comments on Abortion and the Morning After Pill.” As might be expected, Parker’s position is pro-abortion. However, his philosophical failings become immediately apparent in the first paragraph. Parker states:

I was recently confronted in the Emergency Department with a situation I rarely encounter: a woman requesting “the morning after pill.” Since I practice in a largely conservative state, for a few minutes I introspectively debated whether I should provide her with such a prescription (italics mine).

The portion I emphasized above demonstrates Parker’s first problem. He is looking at this issue as a political issue. But while the issue has been used by politicians, determining the ethics of abortion has nothing to do with politics. Therefore, the fact that Parker lives in a “largely conservative state” ought to have exactly no bearing upon his actions from an ethical perspective. (It might be relevant if he was dealing with a legal issue; but since the so-called “Morning After Pill” is legal in the US, that’s a non-issue here.)

Secondly, Parker displays his ignorance of the rights of man when he writes:

The anti-abortionist position also fails to recognize that human beings are granted rights qua man’s status as a rational animal, not qua animal.

There are several problems with this. Let’s start with the fact that if we consistently hold to this, then we MUST say that those people who are “more rational” than others have more rights. That is, under this theory, an imbecile does not have the same human rights as a genius. In fact, the smarter one is the more rights a person must have.

Furthermore, it means that adults will by and large have more human rights than children, as most adults are far more rational than most children. As a result, our ethical conditioning to save children before adults in the case of fire, for instance, is not only wrong but evil. If an infant and his mother are caught in a burning building, the ethical choice for the firemen is to save the more rational of the two. Let the infant burn, rescue the mother. But this obviously goes against most of our common ethics (regardless of whether you hold to a Biblical world view).

Further, rationality must be measurable in order for it to have any meaningful usage in Parker’s dictum. But this presents a problem for Parker because whatever tests we use to determine rationality would have to occur when he is conscious. If Parker is asleep, we cannot test his rationality—he would score exactly the same as a non-rational rock! Therefore, if I kill him while he’s asleep I have not killed a rational human being at all under his definition. Therefore, if we are consistent with his ethic, no murder has occurred.

Finally, Parker’s claims about the rationality of the person are identical to the views of those who defined slaves as non-persons. Black slaves were considered less-rational than whites, and therefore whites could own them. If we take Parker’s position that rights come about based on something that is not linked to our humanity but instead to some other ontological feature, then human rights cease to be human rights and instead become whatever rights the ruling political class allows. In Parker’s case, human rights become rational rights. And as soon as we change rights in this manner we can begin to exclude whomever we deem unfit.

Additionally, I must point out that the Christian response to Parker is that human rights are not “granted” at all, but exist due to the fact that humans are created in the image of God.

Parker also tries to make a distinction between the actual and the possible. He writes:

In reality, the potential is not the actual, nor is an entity’s parts the same as the entity itself and rights can only be granted to actual rational entities.

Again, Parker treats human rights as if they can somehow be “granted.” But if they are granted that implies a grantor. What grants those rights to us? If he says it’s the law, then all that needs be done is that we modify the law. If the law grants rights, we can change the law to say, “People named Parker can be executed” and that would not be unethical. If it’s the consent of the people, we can still get enough people together to say, “People named Parker can be executed.” Is that not what every oppressive regime does? Hitler’s Germany decided Jews had no right to life, so they could be killed. How is this a violation of the rights of Jews unless the “grantor” of the right is something beyond either communal law or the consent of the governed?

Also note that Parker’s claim is that a fetus is potentially rational. (Again, this requires us to assent to his idea that rationality is what determines rights—something we’ve already shown above to be flawed.) This comes to fruition when we read:

Individual rights should not and cannot be granted to potentialities because they are metaphysically distinct from actualities. The potential and actual therefore have distinct moral and political implications.

Let us use his reasoning here. If human rights come about because of the humanity of the object, rather than Parker’s invention of “rationality” then we see that the fetus actually satisfies the requirements above at gaining “individual rights.” A fetus is a human being. This is a scientific fact. Human beings have human fetuses. Humans cannot have cat fetuses, humans cannot have walrus fetuses; humans have human fetuses. The fetus is human from conception, and this is scientifically undeniable. Therefore, if rights come about due to the humanity of the fetus rather than due to the rationality of the fetus, we have proven using Parker’s own methodology that the fetus actually has human rights because the fetus actually is human.

Parker then continues:

Another flaw with the anti-abortionist view is the failure to acknowledge the proper metaphysical relationship between mother and the unborn fetus. The fetus is physically within the mother and connected to her via the placenta and umbilical chord. It is directly physically dependent on the mother for all of its life sustaining needs-oxygen, energy and safety from the external environment. The relationship between mother and fetus is not that of two distinct human entities, but rather that of an independent human being (the mother) with rights and a dependent physical appendage, something that is physically within and part of the mother and therefore cannot have individual rights.

Note that Parker is arguing that rights are not just dependent upon rationality (his original claim) but also upon the location of the individual and also the relationship of that individual to another individual. As I did before with his “rationality” argument, I want to examine the outcome of this thinking.

First of all, Parker is flat out wrong when he says “The relationship between mother and fetus is not that of two distinct human entities” because scientifically, it is exactly that. The fetus is a distinct human being and the mother is a distinct human being. It is true that the fetus is dependent upon the mother, but dependency does not affect rights! If it did, parents ought to have the right to kill all their dependants. Infants cannot live on their own. They require nurture. Under Parker’s theory, it ought to remain moral to kill infants.

Furthermore, as a doctor I’m sure that Parker can think of several cases when a person is under anesthesia. That person is now completely dependant upon the doctors for his well-being. Is it morally justifiable for a physician to kill a patient under his care because the patient is now completely dependent upon the doctor? Of course not. A person does not lose his rights simply because he is dependent upon others for his well-being.

Likewise, Parker has determined that the location of a human being can determine whether or not that human being has rights. But what is the rational basis for that argument? This is an ad-hoc claim, completely unsupportable. How does the location of the fetus change the rights of the fetus? How could the fetus have no rights when, if he was moved just a few inches away, he would have full rights? How is such a thing justifiable ethically? Parker cannot simply assert that it is the case that the fetus has no rights based on location: he must prove this claim.
Parker continues:

Individual rights cannot be granted to the parts of human entities-to do so would make a surgeon a murderer when he removes a healthy kidney from a patient for an organ transplant, an internist a murderer when he poisons a tapeworm to achieve its removal from a patient’s intestine, a dermatologist a killer when he removes a mole from a patient’s face.

But of course a fetus is NOT a “part” of the mother. The fetus is a complete human being distinct from the mother. That is the point. If the fetus was a part of the mother, the fetus would remain a part of the mother after birth. Just as the removal of a kidney does not transform it into some other person, so removing a fetus would not transform the fetus into some other person. If Parker wants to play that game, he’s proven himself irrational…which means I can ethically kill him.

Parker continues:

The basis for individual rights lies in man’s nature as a rational animal, as a living being with a volitional consciousness (free will). The concept of individual rights can therefore only be properly understood in the context of a rational independent entity, not in the context of a living thing with rudimentary sensations.

We’ve already addressed this earlier, but note that nowhere does Parker actually argue for this. He merely asserts it as if it were true.

Finally, Parker says:

The metaphysical act of birth, when the unborn makes the transition from mere potential to an actual human being and successfully separates from the mother to become a separate metaphysical entity, an actual living being with a volitional consciousness, confers the moral and political concept of rights.

Birth is a metaphysical act? Moving a few inches down the birth canal changes the metaphysical nature of a fetus?

If one thing is obvious, it’s that Parker has no philosophy degree.

Even if we pretended metaphysics changes at birth, his reasoning is still completely wrong. Before birth, the fetus is distinct from the mother. This is self-evident because you can locate the fetus! The fetus is therefore a separate entity from the mother. That the fetus is connected to the mother does not make the fetus any more equivalent to the mother than the fact that my touching another human being makes us the same person. The fetus is also alive before birth. What is an abortion if not the killing of the fetus? You cannot kill what isn’t alive. Regardless of how you look at it, the fetus is most certainly a living organism, distinct from rocks, gasses, and all other non-living objects. Furthermore, if the fetus has a “volitional consciousness” at birth, it most certainly had it moments before birth too. The act of birth does not create the “volitional consciousness” of the fetus, nor does it animate the fetus. These things were already in place before the birth occurred.

In point of fact, the only thing the act of birth does is confer political rights. But political rights are not the same thing as moral rights. Politically, it was okay to own slaves in 1800. Morally, it was not okay to own slaves. Politically, it may be okay to kill unborn human beings; morally, it is not okay to do so.

Parker says: “This is the reason why I provided this patient with the morning after pill and the reason why I am not a murderer.” But a murder is someone who takes the life of an innocent human being without proper justification. And “because the mother wants to” is not proper justification for taking the life of an unborn human being. Therefore, Parker is a murderer. Not in the legal sense, of course. But not all who are murderers are legally murderers.

I just got back from watching The Happening with my friend Travis. Thankfully, the movie theater provided us with a refund. Because seriously, I’ve had bowel movements that were more creative than this movie.

How shall I sum this up?

I think that was about as subtle as the point M. Night Shyamalaladingdong was trying to make.

It’s difficult to believe this is the same guy that wrote Signs and The Sixth Sense. I don’t know what M. Night was smoking when he thought This is a great idea for a movie!, but for the sake of the universe whatever it was needs to be criminalized.

The Happening was supposed to be a scary movie, one that would thrill you. Instead, it’s so bad you couldn’t even spoof it. We’re treated to an endless montage of the worst dialogue ever penned coming from characters so flat they disappeared when they turned sideways (and Wahlburg had to have what’s got to be the absolute worst delivered “Oh no” ever put on film). To make up for it, however, there was no plot. The motivating force of the movie was simple: “See everyone who’s not Mark Wahlburg, Zooey Deschanel, or Ashyln Sanchez? They’re going to die.”

Normally, that fact would rank up there as a SPOILER ALERT but unless you’re dumber than a package of mislabeled UPS bubble wrap (which, incidentally, would have written a better script than M. Night), you figure this out pretty much 27 seconds into the movie. Ergo, I haven’t ruined anything for you.

This movie is Shyamalan’s first R-rated movie. I agree with Travis, who said it would have worked better as a PG-13 movie. It’s rated R for gore, and the gore just doesn’t fit. There are movies where gore is appropriate (We Were Soliders, When Harry Met Sally), but The Happening is not one of those films. Instead, it’s distracting. The film is set up just so that M. Night can kill each character in more gruesome ways.

The problem is that for a horror movie to work, you actually have to care about the characters who are at risk of death. That’s where the scary part comes in. You empathize with them and you don’t want them to die. In this film, each death scene is so abrupt and so over the top that it’s closer to a comedy than a horror flick. This sets a dangerous precedent.

The film is also so on-the-nose that it’s pathetic. The Earth is dying and we are the problem. It’s so bad, after the guy gets run over by a lawnmower, you see the real estate sign proudly saying, “You got what you deserved!” Yeah, nothing subtle about that, M. Night! Where’s the skill you had when you weaved the threads of Signs together?

Also, this whole notion that everyone from the Midwest is a militia gun nut? Pathetic. Go back to your progressive cave and spawn a stalk of asparagus or something.

To conclude, the only good part of this movie was The X-Files trailer. And I could have watched that on You Tube for free. If I wanted to see something on the caliber of this movie, I’d watch a compost heap for a few hours. For the first time ever, I asked for my money back after watching a film. The theater probably was not surprised. But if this movie is still showing on Friday, I’ll be surprised.

It’s always surprising how drastically the days increase in length. Of course, it’s easier to see this I guess when you’ve had to work lots of overtime and you get used to not seeing the sun when you leave work and suddenly you leave work and there’s lots of sun.

But even without that frame of reference, it’s getting amazing. It’s staying bright outside until nearly 9:00 now, and even then you look outside and the sky’s not black yet. Deep purple, but not black.

And that also brings up another interesting point. You ever notice that the longest day of the year tends to be around June 21 (it changes a bit due to leap year and the like)? Why is it that the hottest month is then August? Likewise, the shortest day is in December; but the coldest month is usually February. It’s like the temperatures are two months behind the sun or something.

Yeah, yeah…I know, it’s like inertia. It takes a while to get going and then it takes a while to slow down again. But I think it’s still just one more weird thing about the world that makes living in it so interesting!

Today, as I walked down to the store to pick up groceries for the upcoming week, I thought some more on the math formula that I worked on yesterday. The end result is that I have no figured out a trick to easily multiply two “teen” numbers together.

Of course, it behooves us to define what a “teen” number is then! I’m defining a “teen” number as any number between (and including) 10 and 19. This can be expressed in the following way as well (which will benefit us shortly):

A “teen” number is any two-digit number in the format 1x, where x is a whole number between 0 and 9.

If we multiply two “teen” numbers together, then it is equivalent to the format 1x x 1y where x and y are both integers between 0 and 9, and where x may or may not equal y.

Now that we have it defined, let me give you an example of the trick first, and then I will demonstrate the reasons why the trick works after that. Suppose you wanted to find out what 17 x 15 is. Here’s how the trick works:

1. Begin with 100. This is your “baseline” and will always be the baseline for teen numbers.
2. Take off the beginning “1”s on your numbers (i.e. 17 becomes 7, 15 becomes 5. This gives us 7 & 5).
3. Add those numbers together (i.e. 7 + 5 = 12).
4. These are our “tens”, so multiply the result by 10 by sticking a 0 at the end (i.e., 12 becomes 120).
5. Add that to the baseline 100 (i.e. 100 + 120 = 220).
6. Now multiply the two numbers we got in step 2 together (i. e. 7 x 5 = 35).
7. Add that result to the number we got in 5. (220 + 35 = 255).

That’s your answer. Now at first glance, the above looks difficult. However, as you practice it, you’ll see it makes mental math quite simple. For instance, to figure out what 15 x 13 is, you only need to calculate 5 + 3 and 5 x 3, which are both simple. The rest follows simply too: since 5 + 3 = 8, then you simply add a zero to the end (equivalent to multiplying by 10) to make 80, and add that to your 100 baseline (180), and then add 5 x 3, or 15 and you’ve got 195.

Thus far, I think the method is easier than doing the multiplication the way we’re all taught to do it. However, where this method really shines is when our x and y variables add up to 10. For example, 18 x 12. 8 + 2 = 10. When you have those variables that add up to 10, you do this:

1. Begin with 200 (instead of 100!)
2. Take off the beginning “1”s on your numbers (same as step 2 in the first method)
3. Multiply those numbers together (i.e. 8 x 2 = 16)
4. Add to our baseline. (200 + 16 = 216).

And you’re done. Yup, that easy. So, 17 x 13. Start with 200, add 7 x 3 = 21. 221 is your answer. This even works if you break out of the single-digit mould. For instance, 10 x 20 = 200. You can take your x as 0 and your y as 10, and find out that 200 + 0 x 10 = 200. But of course it becomes a little more difficult to mentally think of 20 as 1A (where A = 10).

However, if you did continue with that, 21 x 9 (where you think of 21 = 1B, (B = 11), and 9 = 1-A, (-A = -1) in the same format: 9 x 21 = 189. So you have 200 + 11 x – 1, or 200 – 11 = 189. So the method still works, but at this point it becomes difficult to do it mentally.

Now on to the reason why this method works. Let’s look at the equation I used yesterday:

n² = (n – x)(n + x) + x²

The (n –x)(n + x) section of the equation is where we put in our multiplication terms. So what would happen if I wanted to see what (n + a)(n + b) would need?

n² = (n + x)(n + x) + ?

Once again, we factor:

(n + x)(n + x) = n² + nx + xn + x² Or:
(n + x)(n + x) = n² + x² + 2nx.

So the ? would have to get rid of everything except for the n² to satisfy the equation. The ? would therefore be –x² - 2xn. Therefore:

n² = (n + x)(n + x) – x² - 2xn.

But remember last time I made it relative by using (n – a) and (n + b). What would that look like here?

n² = (n + a)(n + b) + ?
(n + a)(n + b) = n² + bn + an + ab.

Therefore, we need to subtract bn, an, and ab:

n² = (n + a)(n + b) – bn – an – ab.

Now let us make these numbers “teen” numbers. In that instance, n = 10:

100 = (10 + a)(10 + b) – 10b – 10a – ab

The formula can be rearranged to show us:

(10 + a)(10 + b) = 100 + 10b + 10a + ab

And there you have the trick I showed above. You start with the baseline of 100. You take the “1” off of the number and get your x and y, which are equivalent to the a & b in the above formula. The rest follows.

The only part that would be tricky to immediately see at this point is the fact that:

10b + 10a = 10(a + b).

However, if you know how to factor, you’ll see that that is the case. And we can demonstrate it by plugging in some values too. For instance, a = 7, b = 9:

(10 x 7) + (10 x 9) = 10(7 + 9)
70 + 90 = 10 x 16
160 = 160.

This also gives us our reason for why, if the digits (a and b, or x and y) add up to 10, we start with 200 instead of 100. If:

(10 x a) + (10 x b) = 10(a + b)

Then if a + b = 10, then we are adding another 100 to the baseline.

Therefore, we can do that from the start and don’t have to worry about adding 100 + 100. We can simply say, if a + b (or x + y in the original formula) = 10, then start with 200 instead of 100.

So there you have it. The general trick to multiplying teen numbers is to start with 100, add the right-hand digits together and put a zero at the end, multiply the right hand digits together, and add all of those together. If a + b = 10, then start with 200 and add the multiple of the right-hand digits to that number.

Just to give a brief detailed explanation for my previous post, while I was at work today I began to think about something that had very little to do with work. This happens all the time, yet somehow my error rate stays fairly low… Anyway, I started with a simple supposition:

I believe that the reason most people hate math is because our schools do such a horrific job of teaching it.

I have personal experience to back this up, although that might just make me biased. (Based on others’ testimony, however, I feel my personal experience is hardly unique.) When I was in elementary school, I loved math. I used to do extra credit problems in the 2nd Grade. I’d get a packet of 100 addition problems and do them all to turn in the next day. I remember how much fun that was. By the time I finished 6th Grade, I had done all the prelim work to prepare for Pre-Algebra for 7th Grade.

But at that time, I moved to a different school district. Instead of getting Pre-Algebra, I got put in remedial math. Why? Because everyone took it in 7th Grade at the new school. 8th Grade…same thing. Remedial math yet again. I was totally bored.

To make up for it, they tossed us all into Algebra I in 9th Grade. It was a sink or swim moment. Some people, my sister for example, couldn’t swim under those conditions. As a result, my sister hates math to this day. She’s probably the smartest person I know who doesn’t do Algebra. I was fortunate enough to love math enough before this happened that, by the time the school made me hate math I was still functional enough to pull myself out. If you look at my grades, you’ll see that I got a C in Algebra I. In Algebra II I had a B. Then, for Geometry and Trig, I was back up to As. I had caught on…but it was far more work than it needed to be. And I only caught on because I happen to love math despite how much they tried to make me hate it.

Separating from my personal experience, one of the biggest problems with math education on the whole is the fact that teachers require students to show their work. This is just a euphemism for: “You have to do it the way that we tell you to do it.” Granted, some of it is to protect against cheating…but if the teacher is halfway decent he or she will already know whether a student is actually learning or not.

But because we require everyone to approach math the same way, people fail. Some of the smartest people in the world can do math equations without being able to show how they know the answer. The answer is right, but they cannot do the “work” to prove it. That’s because they did not solve it in the “correct” manner. As a result, they do not get credit for their answers. The solution is unimportant; following the method is key.

This is a travesty. In math, there are multiple roads to the same answer, and if one road works easier for you…use it!

But enough sermonizing. The above is sufficient for you to get my point of view. As I sat in front of the scanner at work, I thought about mental math tricks. I’ve talked to a couple of coworkers and asked them how they would solve a problem such as: 17 + 23 = ?

Most said the same thing. “You start with 7 + 3 = 10, carry the one…”

I’m thinking, I’m too lazy to carry the freaking 1! Sure, that method will get you the answer, but I look at that and think this:

17 is pretty close to 20. In fact, it’s 3 away. 23 is also close to 20. It’s 3 away as well. The 17 is 3 under, the 23 is 3 over; the 3s cancel each other out. This is the same thing as 20 + 20, which is obviously 40.

And there, I’ve solved the problem without needing to “carry” anything at all. And I do this for everything. What is 19 + 19? Well, add 1 to 19 and you get 20. You have to do that twice, so you end up with 2 left over. 20 + 20 = 40, and 40 – 2 = 38. Problem solved. None of this 9 + 9 = 18, carry the 1 crap at all.

As a result of this, when I see the number 7, for example, I don’t see 7. I see “2 above 5 and 3 below 10.” 5s and 10s are easy to add; I seek to convert everything to them. 6 is 1 above 5; 3 is 2 below 5 (and 3 above 0). Etc.

That works well enough for addition, but I wondered today if there was a way that I could take that similar method and figure out the way it works with multiplication. I thought, if I were to add 19 + 21, I would go 19 + 1 = 20; 21 – 1 = 20; the 1s cancel each other out, and the result is 20 + 20 = 40. But what if I were to multiply instead of add? How would I solve 19 x 21 in a similar manner?

And that’s how I discovered my formula. See, I know 20 x 20 = 400. That’s pretty easy. So what does 19 x 21 equal? 399.

399 = 400 – 1.

I found that to be very interesting. Especially when I then tried 29 x 31, knowing that 30 x 30 = 900. 29 x 31 = 899.

899 = 900 – 1.

Aha! A pattern emerges! I tried it for a few more variables and it continued to work. Without using a calculator, I could instantly know that 49 x 51 = 2500 – 1, or 2499. I then tested it with numbers that weren’t next to multiples of 10. I started easy:

7 x 5 = 35. Well, 6 x 6 = 36, and 36 – 1 = 35! The pattern continued. I tested a few more numbers and found it worked through. (BTW: I should note at this point that you can obviously see that I do math as a scientist. I “test” numbers and make hypothesis and then experiment with them, etc. This is not a rigorous proof…but I felt quite confident in this process given the fact that it’s worked so well—and I should also point out, once I get to the formula, that I can prove it after all.)

Anyway, at this point I then asked the next question. So far I’ve only been subtracting by 1. What happens if I subtract by 2? Let’s start with the ol’ standby, 20.

18 x 22 = 396. 396 = 400 – 4.

Let’s test the next level up!

28 x 32 = 896. 896 = 900 – 4 (!)

Again, the pattern is consistent. If you’re spaced 1 away from a number, then you subtract 1; if you’re 2 away, you subtract 4! But this could still fit several patterns. It was time to test one more:

17 x 23 = 391. 391 = 400 – 9
27 x 33 = 891. 891 = 900 – 9

The pattern was still there! If you were 3 away from a given number, then you subtract 9. This was obviously a sequence of squares: 1, 4, 9 from 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9.

With this in mind, I got the formula:

(n – x)(n + x) = n² - x²

And from that, it was a simple switch:

n² = (n – x)(n + x) + x²

It’s easy enough to prove certain aspects of it. For instance, it’s easy to prove that this formula is true whenever n = x. Since the (n – x)(n + x) term exists, if n = x, then that multiplication would be 0. We then simply have n² = x², which we can take the square root of each side and get back to n = x, which is what we started with. So the equation is proven true under that condition.

Likewise, if x = 0, we see that n² = (n + 0) (n – 0) + 0; or n² = n x n, which is what n² means.

And it even works if n = 0. Under that condition, we have 0 = (0 – x)(0 + x) + x², which is 0 = -x² + x²; or x² – x² = 0, which is true.

I was about to write: “However, since I am publik skewled I lack the ability to prove this for all numbers”…but then I figured out a way to do so when I looked at the above n = 0 part. So, instead I will amend that to: Despite being publik skewled, I can prove this for all numbers:

n² = (n – x)(n + x) + x²
n² = n² + nx – xn – x² + x² [Factoring]
n² = n² + nx – nx – x² + x² [Cancel out like terms]
n² = n²

Thus, I’ve proven it true for all numbers after all!

And because of that relationship, we can immediately generalize further. Instead of limiting ourselves to numbers the same distance from a certain square, we can subtract by a and add by b. Therefore:

n² = (n – a)(n + b) + ?

Let’s figure out what the question mark would be. Obviously, it needs to be something that would cancel out the rest of the factorization:

(n – a)(n + b) = n² + nb – an – ab

Therefore, the ? needs to be –nb + an + ab

Therefore, for any number combination now:

n² = (n – a)(n + b) + an + ab – nb.

Test with n = 10, a = 3, b = 7

100 = 7 x 17 + 30 + 21 – 70
100 = 7 x 17 – 19
119 = 7 x 17

And that can be checked with a calculator to see that it is, indeed, correct.

And just for fun, let’s have negative numbers! n = 10, a = -3, b = 4

100 = 13 x 14 – 30 – 12 – 40
100 = 13 x 14 – 82
182 = 13 x 14

Which is again proven by the calculator.

Now this brings us immediately to an easier way to do math. If you are multiplying two numbers together and you can find the square of a number that is smaller than both the numbers, you can use the following method. It works perfectly well with 10² and multiples of 10, so why not use them?

Suppose we want to find what 16 x 19 is. Well, since I know that 10 x 10 = 100, and I know 6 x 10, 9 x 10, and 6 x 9 because those are all done by rote. 60 + 90 + 54 = 204. Since both 16 and 19 are greater than 10, we add the result to 100. We therefore have 304, which is the correct answer.

Of course, we could use 20 instead, but in this case because the numbers are both lower than the square we’re looking at, we have to do more subtraction. For instance, 16 is 4 less than 20, and 19 is 1 less than 20. We’re looking for 4 x 20 and 1 x 20 and 4 x 1. But what to do with them? Since both numbers are lower than the square, we subtract the numbers that are multiplied by the squared number (i.e. 4 x 20 and 1 x 20) from the squared number, but we add back the product of the other terms. Thus, 400 – (4 x 20) – (1 x 20) + 4 x 1, or 400 – 100 + 4, or 304.

Obviously, the first method is much easier to do in our heads.

n² = (n + x)(n - x) + x²

Try it. It works.

Example: n = 19, x = 3

19² = (19 + 3)(19 - 3) + 3²
361 = (22 x 16) + 9
361 = 352 + 9
361 = 361

More fun. n = 8; x = 50

8² = (8 + 50)(8 - 50) + 50²

64 = (58 x -42) + 2500
64 = -2436 + 2500
64 = 64

See!

Finally, n = 7, x = 7

7² = (7 + 7)(7-7) + 7² (as you can see, we don’t even have to solve 7² to prove this one…):

7² = (49 x 0) + 7²
7² = 7²
49 = 49 (…but we will anyway)

Today, I went to the Pepsi machine at work and found out they were all out of Diet Pepsi. So I picked a Diet Dr Pepper instead. As I drank it, I thought about the advertising that Diet Dr Pepper does: “It tastes more like regular Dr Pepper!”

First, notice that it’s a non-comparison comparison. Yeah, it doesn’t tell you what it tastes more like regular Dr Pepper than… That is, it could be “It tastes more like regular Dr Pepper than dirt.” Or it could be “It tastes more like regulard Dr Pepper than Pepsi tastes like regular Dr Pepper.” There’s so many ways to take that.

But more fundamentally, I noticed a simple fact. Diet Dr Pepper says it tastes more like regular Dr Pepper. But this is a uni-directional comparison. You never hear “Regular Dr Pepper tastes more like Diet Dr Pepper!”

That’s because regular Dr Pepper tastes so much better than Diet Dr Pepper that it would never want to make that comparison.

In the same way, of course, Darwinists will say, “Darwinism is just as proven as Einstein’s theory of relativity.” But you never hear a physicist say, “Einstein’s theory of relativity is just as proven as Darwin’s theory of evolution.” Yeah, that’s another uni-directional comparison.

Great sign that the comparison is bogus.

…than leaving your computer for a few minutes with a web article that you’re reading up on the screen, only to come back an hour later to find it gone. Why? Because Microslop had to update again with an automatic restart.

Grrr!

Some have made the claim that it is irrational to believe in a mind separate from the brain. The materialist argues that there is no real mind because everything reduces to a tangible physical object. Thus, our consciousness is merely a by-product of electrochemical reactions in the brain. Duelists, on the other hand, believe that there is a distinction between the brain and the mind. That is, while the mind most certainly is linked to the brain, the physical attributes of the brain are not the totality of the mind.

This post will not delve deeply into these subjects, nor will it attempt to prove one position over the other. Instead, I want to ask a more basic question: Suppose that we grant the materialist claims as they regard the empirical dimensions that we experience on a daily basis. Is it irrational, under that system, to believe there is a mental aspect that is separate from the empirical brain?

I should point out that I am asking a very narrow question. I am not asking what the likelihood of such a mind would be. I am merely asking whether an immaterial mental realm is actually incompatible with the materialistic worldview. If it is not—if mental existence remains viable even under materialistic concepts—then the materialist’s claim that belief in the separation of mind and brain is irrational is itself irrational, because even granting everything the materialist is forced to concede the possibility of the immaterial mental dimension.

As one might be able to surmise from the use of the term “dimension” I will begin by examining a planiverse. The planiverse is just like our universe, except instead of existing in three dimensions the planiverse exists in only two dimensions (i.e., a plane—hence, the planiverse). Compressing dimensions in this manner helps us to visualize the effects of added dimensions since each of us are able to view two dimensional representations using our three dimensional empirical faculties. If the mental dimension exists, it would be a fourth (or higher) dimension; therefore, if we examine how a three dimensional object would appear to a two dimensional observer, that can yield information as to how an extra-dimensional object would appear to a three dimensional observer such as ourselves.

To think of the planiverse go no further than getting a piece of paper. Let us stipulate that the piece of paper is the entire planiverse. Nothing exists beyond the edge of the paper, just as we believe nothing exists beyond the edge of our universe. Now draw a circle on the paper with a radius of, say, one inch. That is our two-dimensional observer. This circle cannot view depth: it can only view length and width. Therefore, if you had another circle that approached the first circle, it must go around the circle or else through the circle—it cannot go over the circle (i.e. “stacking”) because that requires the third dimension.

Because of that requirement, however, interesting things can occur. Place a coffee cup on your piece of paper. The coffee cup is three dimensional. The circle, however, only sees the portion of the coffee cup that exists in the plane of the piece of paper (for the sake of argument, we will say that the layer of the coffee cup that touches the paper moves into the plane of the circle so that it would become visible to our observer). The circle would view the coffee cup as another circular object rather than as a “cup-shaped” object.

We, however, as three dimensional observers can see that the coffee cup extends beyond what is observable in the two dimensions that the circle can see. Now, if you were to grab the top of the cup and push it from one edge of the planiverse to the other edge (without going through the circle so as to not terrify our observer!), the circle would observe another circular object move through the planiverse. However, the observer would be unable to find what caused the movement. The forces occurred in the third dimension, not in the two dimensions the circle has access to.

With this example in mind, we can extrapolate back to the three dimensions. If a mental dimension exists in, say, the fourth dimension, then immaterial consciousness could be just as much a physical object as a three dimensional coffee cup is physical even if a two dimensional observer cannot see it in its entirety. If the mental object in the higher dimension is really a physical object then it remains a material object. While it exists “above” the three dimensional space so that it cannot be empirically viewed as such, it nevertheless remains just as materialistic as a rock in three dimensions because there is nothing “special” about it. It just happens to exist in a different dimension than what we can observe.

Furthermore, it is easy to imagine that this fourth dimensional physical object is connected to an object that we can view in three dimensional space just as the circle of the coffee cup that broke the plane of the planiverse existed as a full physical object in three dimensions connected to the two dimensional observable existence. A fourth dimensional object therefore can exist fully in three dimensions just as well as it exists in the fourth dimension. But three dimensional observers can only view the portion that occurs in three dimensional space. Nevertheless, the object remains purely materialistic in nature. There is nothing supernatural about it at all. Therefore, no rules of materialism have been violated.

Finally, we can argue that if the portion that exists in the fourth dimension can exert force to cause effects to occur in the three dimensional portion of the object, then we have all that we need to prove the possibility of a materialistic mental realm.

Let us put this in a concrete example then. Take an average human being. Let us stipulate that in addition to the body that we see in three dimensional space there also exists a fourth dimensional aspect to that person which is the mind. This mind is physically attached to the three dimensional body; it cannot be removed from it naturally. Furthermore, this mind is where all the “thoughts” of the individual reside, all the motives and impulses, and dreams.

Because this fourth dimensional object is physically linked this means that the mind can influence the body. It has direct access to it. It cannot be seen in the three dimensional realm (just as hovering an atom’s width above the circle in the planiverse renders you invisible to the circle), yet the connection is there. When you think, therefore, even though this is something that occurs in the fourth dimensional aspect of your being, it manifests itself in your body as well. You brain has certain electrical and chemical changes that result.

Likewise, one can reverse the normal flow. One can stimulate certain portions of the brain and cause changes in the fourth dimensional portion of the being. What the brain “sees” remains locked away in the fourth dimension, yet there is a physical link to the three dimensions that are observable.

This idea would obviously work even under a materialistic universe. It is therefore not accurate to say that an immaterial mental dimension is irrational, even if we grant every single presupposition of the materialist. But there is something else that this theory has to make it even more robust. It explains phenomena that are quite difficult to explain under the usual materialistic theories. Just a few examples would include out of body experiences, near death experiences, astral projection, and the like. While it is obvious that not every claim of such experiences can be substantiated, there is enough evidence of people who have been clinically dead who can describe things that occurred in different areas of the hospital that they had no access to (for example) that not all claims can be easily dismissed as hoaxes, and it stretches credibility to assume voices that no one except the person who was clinically dead could hear bounced through the heating vents!

This is not problematic if the fourth dimensional aspect of a human being (the mind) can survive for even limited amounts of time if “severed” from the three dimensional body (just as severing an arm will not instantly kill the arm, and it can later be reattached).

Given all of this, even if it cannot be proven true (and even if we say it’s not even likely to be true), the materialist cannot claim that the mental dimension is irrational. It could exist even under materialistic premises.

The direct theological implication of this is that we instantly have a possible explanation for the spiritual realm as well. A spiritual realm could exist in the fourth dimension (or any higher dimension) and be rendered invisible to us. But while atheists like to claim that a spiritual entity cannot interact with a physical object, we can see that objects that exist fourth dimensionally can interact with physical objects if the physical objects in the three empirical dimensions also have existence in the fourth dimension (all without violating any rules of materialism). Naturally, I’m not arguing that this actually is how the spiritual realm exists; however, the materialist’s claim that it is irrational to hold to the existence of such a realm is disproven by this possibility alone. It is not irrational at all, even given all the claims of materialism.

The big news of the day is…$4 gas.

Yeah. It’s the end of the world. Everything as we know it will change! No one will be able to go anywhere ever again!!!

Think I’m joking? Then you haven’t been listening to the Noose. Er, the News.

Of course then there’s lil ol’ me who happens to think, “Countries with far worse economies than ours are paying far more for their gas than we are…AND THEY’RE STILL DRIVING AROUND!”

Yup, nothing will change.