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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.

I’ve known this for some time. But it’s been proven even more so today.

It used to be this time of day on a Friday, I was looking forward to the weekend where I could spend all my time trying to defeat Guitar Hero. But now….

…I’m looking forward to viewing the free on-line mathematical lectures provided by MIT.

One never knew matrices could be so kewl.

I realized something today as I rode the bus home. See, today I wrote an article on DNA (genetics, biology, probability, information theory), I read a section from a cosmology book before getting on the bus (it dealt with galaxies, so: astronomy), and then on the bus I watched the clouds (weather) play over the mountains (geology). And it hit me.

I love science.

Perhaps it’s because I just want to know. I want to know how things work, why they work, what they’re there for. I actually enjoy watching natural interactions, like the weather. Or watching how birds fly around chasing after insects. Name a scientific endeavor and I find it fascinating.

And I realized that this means something else. I am my mother’s son. See, I think most of my intellectual reasoning ability has come from the influence of my father. He’s always been the one I could discuss “deep thoughts” with. In fact, when my parents are visiting from Ukraine we often talk a great deal about virtually any theological or philosophical subject. I’ve known for some time that I am my father’s son because of the intellectual aspect of my character.

Don’t get me wrong. My mom’s not stupid. In fact, in any other family that did not have someone like my dad in it, she’d be the intellectual head hands down. But my mom is different from my dad. Her intelligence isn’t as “out there.” Her intelligence is more introverted while my dad’s is extroverted (if that makes any sense).

My mom loves science though. I can remember my mom watching the clouds in the sky on many occasions (she really loves thunderstorms). Growing up, our family spent many a night gazing at the sky, watching the stars in the endless void above…and it was mostly at my mom’s instigation. I remember her stories of the Northern Lights in Alaska. She watches the way animals behave, and even the way Ukranians behave differently than Americans now. She is a keen observer, a watcher.

And I realized that as much as I am my father’s son, I am my mother’s son too. I am definitely blessed to have the family that I have. To have people who love science just as much as I do, and who love intellectual discussion just as much as I do. I wish more people could have families like I’ve got, so that they too can spend an hour watching wind rustle through the grass and not be bored because you’re trying to figure it out. To watch the patterns that rain drops make on the window pane. To see comets in the night sky. To watch the color of the sky change as the sun peeks out over the horizon.

We have such an amazing world God has given us. I thank Him for giving me parents who enabled me to see it.

In my previous post on DNA, I mentioned the following argument:

A) DNA is information.
B) Information cannot arise from a random, non-directed process.
C) Darwinism requires DNA to have arisen from a random, non-directed process.
D) Therefore, Darwinism cannot explain DNA.

In my first post, I demonstrated A) DNA is information. In this post, I will demonstrate B) Information cannot arise from a random, non-directed process.

The first thing to note is an example that Apolonio brought up. He said:

For example, we can conceive of a case where a person knocks over a scrabble box and the letters I Love You comes out with that order.

While this would be a semi-random process creating information, it is not using foundational forces. The specific example requires a person to knock over the Scrabble box. But even if we adjust for that and make it gravity pulling a box off a shelf or something similar, Scrabble tiles are not foundational in nature; they are designed. So the information still requires a non-foundational force (human ingenuity) to create the tiles which are used to create information in the pattern “I love you.”

Even then, the odds that “I Love You” would form are quite rare. Assuming an equal sample of each letter of the alphabet (as well as an infinite supply of them), you have 8 letters, so the odds of pulling these particular letters would be 1/26⁸, or 1 in 208,827,064,576, which is: 4.79 x 10 ^-12. If you include the space as a character, we have 10 characters and 27 possibilities each draw: 1/27¹⁰, or 4.9 x 10^-15.

In reality, however, Scrabble boxes do not contain an equal sampling of each letter. Instead you have 12 Es; 9 As & Is; 8 Os; 6 Ns, Rs, Ts; 4 Ds, Ls, Ss, Us; 3 Gs; 2 Bs, Cs, Fs, Hs, Ms, Ps, Vs, Ws, and Ys; 1 J, K, Q, X, Z. Finally, there are 2 blanks. This yields 100 total pieces. If we use the blanks as spaces, the odds for each letter in “I [blank] Love [blank] you” are:

I = 9/100
Blank = 2/99
L = 4/98
O = 8/97
V = 2/96
E = 12/95
Blank = 1/94
Y = 2/93
O = 7/92
U = 4/91

Because we are not dealing with an infinite number of tiles, we have to reduce how many are available after each selection. Thus, we have a 9/100 chance of pulling an I on the first draw from the box. If we do so, there are now only 99 tiles remaining, 2 of which will be blanks. That means we have a 2/99 shot for the blank, etc. Note that when a letter repeats (for instance, the O), we have to decrease the number remaining too. Thus, the first draw of an O is 8/97 but the second is 7/92 (because the first draw picks one of the Os). Finally, we get the combined odds by the following:

9/100 x 2/99 x 4/98 x 8/97 x 2/96 x 12/95 x 1/94 x 2/93 x 7/92 x 4/91, which is:

774,144 / 62,815,650,955,529,472,000

Or 1.23 x 10^-14

Which is roughly 1 in 81 trillion. So even though the tiles were created by humans, a random arrangement of them to spell out “I love you” is still extremely rare.

The above does, however, help us understand a bit about DNA. As most are already aware, DNA uses 3-base codons to create amino acids. There are four possible DNA bases (ACGT), and that means that means 4³ (64) possible combinations of those letters. However, there are only 20 amino acids. As a result, amino acids are often encoded by multiple numbers of codons. For instance, Leucine (L) can be encoded by CTT, CTC, CTA, CTG, TTA, and TTG. Which means there are 6 possibilities for L. In fact, quickly going through the amino acids (using their single-letter code name) we find:

I = 3
L = 6
V = 4
F = 2
M = 1
C = 2
A = 4
G = 4
P = 4
T = 4
S = 6
Y = 2
W = 1
Q = 2
N = 2
H = 2
E = 2
D = 2
K = 2
R = 6
Stop = 3

As you can see, all 64 possible combinations would be represented in the above. Therefore, we can say that given a random piece of DNA with 3 codons, there is a 3/64 chance that it is I (Isoleucine) and a 2/64 chance that it is N (Asparagine), etc.

Because base pairs are so prevalent, we can treat them as if there is an infinite supply of them. As a result, if we wanted to calculate what the odds would be that six base pairs will code for Isoleucine and then Asparagine, we would simply multiply 3/64 and 2/64 to yield: 6/4096, or about 1 in 683.

Of course, proteins can have hundreds of amino acids chained together in polypeptides. (In fact, by convention, most scientists do not consider a polypeptide chain to be a protein until it has at least 50 amino acids in it, although that is an arbitrary dividing line.) Because of their size, the odds of even a single 50-amino acid polypeptide forming are quite rare. In fact, even if they were simply a chain of L (Leucine), which has a 6/64 chance of forming for each L, the odds of 50 formulating would be 6⁵⁰ / 64⁵⁰, which is roughly 8 x 10³⁸ / 2 x 10⁹⁰ which is approximately 4 x 10^-52, or 1 chance in 3 x 10⁵¹.

Clearly, this method of explaining DNA is insufficient to explain even a basic protein, let alone complex cells and higher organisms.

This brings us to our next point, which is something that Mighty Pile brought up: the definition of information (i.e., something that is non-repeating, non-random, and not based on foundational forces) seems to exclude the ability of random, non-directed processes in the first place. As such, B) seems to be proven by stipulation, which means it relies on a circular argument.

However, when we examine B) carefully we see that it does not rely on circular reasoning when cashed out. To demonstrate how that is possible, I must first point out that the Darwinist must assert the opposite of B). They must assert that information can arise from random, non-directed processes (as evidenced by premise C)). And this is demonstrated by the fact that you are reading this blog post, which is information.

This blog post has an author. The author is not a random, non-directed process. But, if Darwinism is correct, at some point we can link my existence back to a random, non-directed process. Therefore, in a causative sense, the Darwinist would say that a random, non-directed process somehow created a non-random, directed process that was able to create information.

And it is because this option remains open to the Darwinist that B) does not entail circular reasoning. All the Darwinist needs to do is to show that Information can arise from forces that are non-random, non-repetitive (to exclude crystals) and non-foundational if those forces (we will call them meta-forces) are themselves built on random, non-directed forces. In other words, the Darwinist can argue: “Information comes from meta-forces, which are non-foundational; but meta-forces come from foundational forces.” Putting it into this two-step process would avoid the circular reasoning charge, while also giving the Darwinist a possible route to establishing C).

So the question now becomes, can random, non-directed processes create non-random and non-repeating meta-processes that could then create information in the form of DNA? DNA is one of the simplest information processes we can think of (compare it to trying to establish the framework for a spoken language), but even it is vastly complicated. In order for DNA to function, it has to store information that is used to create amino acids that bond together to form proteins that then create the mechanism for storing and reading DNA. In other words, in order for DNA to function biologically, we need to have a loop where DNA is used to create the processes needed to create more DNA. DNA is copied via cellular processes that are created with proteins that are themselves created by DNA. Thus, we have a vicious cycle going on.

But before we get to the loop, is there a simple way to just encode amino acids into DNA? Amino acids, after all, are fairly easy to create in a test tube, as Stanley Miller demonstrated (albeit his experiment does not prove what he thought it proved). Using those same “primitive” conditions, however, it is not possible to create DNA.

DNA also presents a problem because, as you’ve seen above, sometimes as many as six different DNA codons can represent a single amino acid. While moving from a DNA codon to an amino acid is easy, moving from the amino acid to a particular strand of DNA is much harder.

Due to the limitations of DNA, Francis Crick proposed that life began based on RNA instead of DNA. RNA is only single stranded, as opposed to the DNA double helix. RNA can also sometimes function similarly to proteins. DNA, however, is much more stable and less prone to errors (which is why an intelligent being would pick DNA instead of RNA to start life off; and which is why Darwinists claim DNA was “selected for” by Natural Selection).

Which brings up an important point. The “central dogma” (as Crick named it) is DNA to RNA to protein. It doesn’t go in the opposite order. (There are a few exceptions to the strictness of the “central dogma”, most notably RNA viruses (like HIV) which go from a single strand of RNA to DNA before then going through the “central dogma”; but there are no instances that I am aware of where proteins go to RNA then to DNA.) This makes it highly unlikely that amino acids bonded to become proteins and then those proteins created RNA that was then made into DNA and eventually stored in cells.

That means we had to start someway with DNA or RNA and then create proteins from that; but in order to create the proteins, it means we must have the structure in place by which RNA can be converted to a protein. Once again, we’re left with the chicken and the egg problem. And this system cannot have arisen by blind chance, since as you’ve seen even a single protein of 50 of the most common amino acids has astronomically long odds at forming randomly.

Regardless of where we start, we have to have some method of going from a random soup of amino acids to a particular sequence of amino acids being coded in information, be it RNA or DNA. But this will only start to happen if there is a reason for the information of a protein’s make-up to be converted to RNA or DNA.

That DNA is useful for life is not debated. Suppose that the amino acid “soup” manages to create a protein that could be used by a cell later on. It would be useful for the cell to have a way to rapidly create this protein. And the protein is created from amino acids that can be stored in DNA. Obviously, if we have this end in mind, we could design the process by which the DNA code comes about. But this requires teleology, which Darwinism denies. We cannot have the end of a working cell in mind; we have to have completely random processes that somehow create the necessary steps involved.

But suppose that we are left with only the random creation of the system to begin the evolutionary process. According to modern materialistic theory, life first became possible about 3.5 billion years ago. That is, the Earth cooled enough, the atmosphere was in the correct state, water existed, etc. so that life would not be extinguished if it was formed. Amazingly enough, according to these same scientists, the first life on Earth appeared roughly 3.5 billion years ago. In other words, as soon as it was possible for life to exist on Earth, life did exist on Earth. This must mean that the creation of life ought to be an “easy” process, given materialistic claims. If it is easy, then it should not rely on a process that has such poor odds of succeeding. Either life’s occurrence on Earth was a miracle against all odds, or else this cannot be how life began on Earth.

NOTE: This post has been updated since it was originally posted to correct the line: “While this would be a random process creating information, it is not using foundational forces” to “While this would be a semi-random process creating information, it is not using foundational forces.”

I mentioned in my comments with Mighty Pile the Gambler’s Ruin. The GR occurs when a gambler runs completely out of money. There are two aspects of the GR that impact our understanding of Natural Selection. First is the fact that if you are at a numerical disadvantage, then even if you have a statistical advantage in gambling you will often hit GR first simply because the other person can take “more damage” before he reaches it. Thus, just because one individual gains a favorable mutation does not mean that that mutation will be automatically chosen for due to the sheer number of competitors that the individual would have to compete with.

But more importantly is the fact that Natural Selection, in order to work at all, is an All-Or-Nothing proposition. That is, favorable traits must be selected for while unfavorable traits must die out. In one of his comments, Mighty Pile said:

Some traits DO confer an advantage to a particular organism and its progeny. While fit individuals certainly do die sometimes and unfit individuals certainly do live sometimes, the fit organisms would outcompete the unfit ones in large numbers. One antelope’s chance vs another antelope’s chance may be a 49%-51% split. But in a whole herd, the one that gets eaten will almost always be of the slower variety, or of the sick or injured variety. This is, of course, supposition based on logic. I don’t know how I’d prove it right now; it seems obvious in any context I can come up with for it. The difference between fit and unfit would probably be very small most times, setting up a sort of tipping point situation. I don’t have to outrun the bear, I only have to outrun you, right?

In response, I pointed out that one would be foolish to wager everything he owned for a chance to win a billion dollars if he only had a 51% chance of winning it and a 49% chance of losing it. This did get me to thinking a bit further, however, and I developed the following.

Suppose you start with 100 individuals. Each begins with $100. Each wagers $100 in order to gain $100. The odds are 51% win and 49% lose each bet, but with the following stipulation: as soon as you hit $0, you’re out of the game. You cannot continue. This is important to mimic Natural Selection, because as soon as you die you can no longer reproduce. It’s over. So you need a final set point.

How long will it take for a person to reach $1,000 given this structure? And how many people will hit GR before that occurs?

I made up an Excel spreadsheet to show this to me (click here for graphic). It assumes a literal 51% - 49% split for each round (in other words, I don’t randomize the data; this is the “ideal”). The vertical axis is how much money people have; the horizontal axis is the number of rounds. The number plotted in each cell is how many people remain for each row (i.e., how many people have whatever money is in that row). The bottom line beneath the graph simply sums how many people remain (i.e., those who did not hit GR). The cell at the far right of the 0 line is the grand total of those who hit GR.

Thus, we begin with 100 people holding $100. After the first round, 49 people are bankrupt and 51 people have $200. In the second round, 51% of those 51 people (26.01) at $200 will gain another $100 for a total of $300, while 49% (24.99) lose $100 to go back to $100 total. For the third round, we again calculate each group: 51% of the 26.01 (13.27) at $300 will go to $400; simultaneously, 49% of the 26.01 (12.74) drop back to $200. In the meantime, 51% of the 24.99 (12.74) who dropped to $100 will gain $100 and make it back to $200. They combine with the 12.74 who lost $100 to drop down to $200 to make 25.49. Finally, 49% of the 24.99 (12.25) who were at $100 will go bust.

Note that unlike in real life (where a whole number of people either win or lose), these calculations are made with the decimal points from the previous numbers still intact. In fact, I used dependent formulas for each cell. If we were rounding before we did the math, the answers would vary slightly.

And the results: It takes 11 rounds for the first person to hit $1,000 (and that’s only if you round 0.58 up to 1; the line does reach in round 9, but the value would round down to 0). In the meantime, 75.93 people have gone bust. That means that in order to get one person from $100 to $1,000, 76 people have to go bankrupt. And that’s starting with 100 people. A 1% advantage does not provide much of an advantage at all under these circumstances.

Natural Selection falls to the same principal. Just because a favorable mutation may confer a 1% advantage onto an antelope does not mean that the antelope really has that much more of an advantage than other antelope. And I should point out that living systems are actually far more complex than even this illustrates.

The key to why this works this way is because the chart is capped at 0. Once you hit 0, it’s over. That provides a literal line in the sand that has a huge impact. Because in Natural Selection death is such a line in the sand, this demonstrates that even a 1% advantage holds no real benefit to the furtherance of a trait in the species.

In reality, survival rarely comes down to a single trait though. Chance encounters are almost always going to outweigh any mutational advantage of a single trait. Consider all the following that mitigate against the classical view of Natural Selection:

* An antelope is born with 1% more speed than any other antelopes who have been born. However, when the antelope is a newborn, he is not as fast as the adults. As a result, despite being 1% faster than all other newborns, he is still slower than the slowest adult; therefore, he remains a preferential target for predators. If he is near adults at the edge of the herd when lions attack, they will go after him rather than the adults. This brings to mind the second point:

* As Mighty Pile pointed out, there is an oft repeated joke that one need only be faster than the slowest prey when a predator attacks. This, however, ignores the fact that if you are faster than me, but you are five feet away from a hungry bear while I am a quarter mile away from the hungry bear, the bear will catch you before you can run far enough to surpass me and make me a target.

* Sometimes pure dumb luck happens. A ram may be the fittest ram ever, but if he slips and breaks his leg, he’ll be eaten. And accidents happen quite often in nature. And even aside from nature. A highly specialized and advanced snake in Baghdad might happen to get hit by a mortar round fired from an insurgent that was not intended to strike the snake, but did. Or a random lightning strike could kill an elk in the forest who was “superior” to the other elk. When it comes to random events, traits have no bearing on survivability. There is no survivability trait for bad luck.

* For that matter, the strongest bull may be cut down by a viral infection that attacks only strong animals, leaving the weak bulls alive. The weak bulls are “more fit” (by definition, since they survived) but once the infection runs its course the herd would have been better off with the stronger bulls.

* A mutation for greater intelligence might occur in a sheep that’s also the least hearty sheep in the herd. Despite the fact that this intelligence trait would benefit the herd as a whole, the sheep dies of an illness before reproducing.

So survival rarely is about any one trait anyway. Instead, to have the best chance at surviving, organisms need to have a wide range of traits, any one of which may or may not be relevant at any particular time. But some traits are mutually exclusive. Because evolution must be blind (in a materialistic world) it cannot predict which trait will be needed in the future. And because it cannot predict what is needed (after all, it is non-teleological; and furthermore, even intelligent agents like weathermen cannot predict what will happen in the environment tomorrow), the random forces of nature will far outweigh any slight statistical advantage that individuals in a herd have.

So the only way to have beneficial mutations that avoid the GR problem is if they grant a far greater than 1% chance upon the individuals (after all, think of mutations, which convey far more than a 1% disadvantage to the individuals and therefore are seen!), or if they occur more often than random mutations would enable them to occur so that more individuals get the trait (remember, we started the above graph with 100 individuals already having $100, and 76 of them went bankrupt before a single person reached $1,000; if you had 1,000 people to begin with, 760 would go bankrupt…but you’d have 10 make it to the $1,000 mark, so clearly having more individuals get the same mutation would help), or the mutation would have to occur in an individual that is already “more fit” due to other traits to begin with (and that brings up the converse: a detrimental mutation can occur in those who are “more fit” due to other traits and therefore be “selected for” simply because it’s riding along with the system; whereas a “less fit” organism might evolve a wonderful trait that cannot overcome the aspects that make it “less fit” and therefore that trait is not “selected for”).

That’s a lot of front-loading you need before you can get the system going. Living systems are far too complex to be affected greatly by any slight advantage in a single trait.

One strong argument that non-Darwinists have against Darwinism is the simple fact of DNA. Darwinism requires evolution to occur due to random mutations coupled with Natural Selection. DNA, on the other hand, requires some very specific sequences in order for some very specific organisms to exist. As a result, non-Darwinists (be they Creationists, theistic evolutionists, or believers in panspermia) find DNA to be a convincing counter to gradualistic Darwinist claims regarding the origin of life. The basic argument can be summarized thus:

A) DNA is information.
B) Information cannot arise from a random, non-directed process.
C) Darwinism requires DNA to have arisen from a random, non-directed process.
D) Therefore, Darwinism cannot explain DNA.

Since C) is a given under Darwinism, the only thing that a Darwinist can do to reject this proof is to deny either A) or B). In a coming post, I will seek to demonstrate the truth of B). For this post, I will seek to demonstrate the truth of A).

Information is something that is most commonly associated with language. But what separates information theory from linguistics is that information theory moves beyond mere language and incorporates many other things. Information theory really began only recently, after it was discovered language could be transmitted via mechanical devices. Even before it was a science, telegraph operators would have to engage in information theory to distinguish between the pulses of Morse code on the line and random noise (caused, say, by a tree swaying in a breeze with a branch striking the telegraph wire and interrupting the electrical signal). This became more pronounced with radio signals. The need to differentiate between information—the message being sent—and noise—radio interference, random fluctuations, etc.—required the spawning of information theory.

To discuss this, we need a working definition of information. As you can see from the above examples of the genesis of information theory, one way would be to say: Information is non-random.

This, however, is not sufficient. After all, if a telegraph operator received only a constant signal of dot-dash (for A) that would convey no information either. Linguistic meaning is not conveyed in that manner.

So we can start with: Information is non-random and non-repeating.

But non-random and non-repeating…what? If we’re looking at text being written on the page, it’s obvious: non-random and non-repeating letters. Thus, we know that

The quick brown fox jumps over the lazy dog.

is information, whereas

lasdkfjuyqwensd

and

VVVVVVVVVVVVVVVVVVVVVVVVVVVV

are not information.

But if we’re dealing with telegraph signals, we’re not looking at letters on the page. We’re listening to electrical pulses being translated into sounds and visual representations created by the raising and lowering of a pen based on those electrical pulses. And with radio, we have to examine radio waves, using instruments to detect whether or not information is present (which, today, you can do by turning on your radio and listening to the radio pulses transformed to electrical impulses which drive a magnet that creates airwaves that bring sounds to your ears and differentiating it from static).

But why stop there? Why not examine the natural world as well? And it is when we do that that we discover the richness of information in living structures.

Consider rocks for instance. Sandstone is a great example. If you examine a piece of sandstone under the microscope, you will notice that the individual grains that make up that stone appear quite random. While there are certain elements that show up more often (due to their greater abundance on Earth), there is no foundational law governing which grain in the sandstone should be next to another grain in the sandstone. It’s random.

Now look at a diamond, one that has not been cut so as to avoid human interference. It’s crystallized carbon. The atoms of carbon are structured in a specific pattern, and there are no random variations from it (the only random variations in a diamond come from the inclusion of other elements that are not carbon, which will affect the diamond’s color, etc.).

Neither a rock nor a diamond carry information in their structure. However, someone can carve an inscription into a rock and someone can laser designate a diamond. Someone can take sandstone rocks and organize them in such a manner as to build a bungalow, and someone can put a diamond into a ring setting. So consider a bungalow. Is a bungalow information? Is a diamond ring information?

If we use the above starting definition, then they would be. A bungalow and a diamond ring are both non-repeating and non-random.

But this immediately brings to mind the next question. What if someone were to design a bungalow that was repeating. A bungalow on top of another bungalow? Story after story, until you have a repeating-structure: a sky scraper. Now the building would be repeating, and therefore not information.

But sky scrapers do not appear in nature. They have to be built, and that requires work beyond the foundational laws that govern matter. When a diamond is in a crystal shape, it takes no extra effort on the part of the carbon atoms to get there; in fact, that’s the simplest way that the carbon atoms can organize under those circumstances. Likewise, it takes no special effort for a grain of sand in sandstone to sit next to another random grain of sand. That’s the natural state.

Therefore, we can add our final requirement to what determines information. Information isn’t just non-repeating and non-random, but it must be something that is non-repeating and non-random and cannot be explained by only foundational forces. (Note: by “foundation forces” I mean the laws of the universe that materialists consider to be basic, such as the laws of magnetism and the way atoms will bond with each other. For the sake of argument, we will assume these are the basic laws and that they will happen by “default” without any divine guidance needed.)

So a sky scraper may be repetitive and it may mimic a crystallized structure. But sky scrapers are not created using foundational forces of nature. Indeed, the individual units that create the sky scraper themselves are composed of bungalows, and bungalows (in our example, anyway) are composed of sandstone. Sandstone does not form bungalows using foundational forces of nature. It requires something else to organize sandstone into a bungalow. Therefore, sky scrapers exist due to something beyond foundational forces of nature.

And that brings us to DNA. As we know, DNA functions as the blueprint for life. It’s called that because the DNA is used to form all the amino acids that are used for cellular life. And the cellular life must function in order for organs to function. And organs must function for organisms to function. DNA therefore determines many things about the organism, including the means by which that same DNA can be replicated.

Let us therefore ask our questions. Is DNA repetitive like a crystal? If it was, it would mean that Adenine had a proclivity for having Thymine next to it, so you’d have ATATATATATATATAT. Or perhaps Guanine and Thymine would be structured like that.

But the fact is that there is no real proclivity at all between the various bases. Thymine could just as easily follow a Cytosine as an Adenine, or even another Thymine (note that I am not talking about the base pair here, but only which base would be next to another base on the same strand).

Since there is no proclivity, then we would expect natural forces to create random structures of DNA. But is DNA random? Obviously not, because the higher organism depends on the structure of DNA creating the right amino acids to form the right cells to form the right tissues, etc. If the DNA is not exactly like it is, the organism does not exist. But since there is not only one organism, but in many cases there are billions of the same kind, then DNA must have structure; it is not random.

If it is not random, and it is not crystallized, and if it would be one or the other if left only to foundational forces, then DNA is information.

(Click on graphic to have it open in a new browser window if it doesn’t display fully for you.)

Okay, after having worked on the equations for a bit more (and discovering I had left off an important set of parentheses in the previous function formulas), I have found the simplified version of each of them. These equations will once again use two variables, but since the 6n +/- 1 format is already established for primes, I’ve reworked it. For the following, n = the row you’re trying to build on the graph. This is slightly misleading because each row is actually patterned off of the 6n +/- 1 format itself. Therefore, there are two rows for each n. The 6n - 1 and the 6n + 1 value. And for purposes of the chart, a 6n - 1 number is black and a 6n + 1 number is red.

Finally, there is a controlling x value that determines how far to the right you’ll place the cell. Basically, if you were testing for a prime, you could loop x starting at 0 and running the equation, then increasing x by 1 and running the equation, repeating until x equals the n value you’re searching for. If you’re testing a 6n - 1 number, then any black values in the n column will be factors; if you’re testing a 6n + 1 number, then any red values in the n column will be factors.

Now are you ready for the massively complex new equations?

x(6n - 1) + n ; (Use to find black values on the 6n - 1 line.)
x(6n + 1) + n ; (Use to find red values on the 6n + 1 line.)
x(6n + 1) - n ; (Use to find red values on the 6n - 1 line. x must be greater than 0.)
x(6n - 1) - n ; (Use to find black values on the 6n + 1 line. x must be greater than 0.)

And just to demonstrate it, here’s the values for the first couple of rows.
n = 1
x = 0

Black finds black @ 1
Red finds red @ 1
Red finds black @ - 1*
Black find red @ - 1*

n = 1
x = 1

Black finds black @ 6
Red find red @ 8
Red find black @ 6
Black finds red @ 4

n = 2
x = 0

Black finds black @ 2
Red finds red @ 2
Red finds black @ - 2*
Black finds red @ - 2*

n = 2
x = 1

Black finds black @ 13
Red finds red @ 15
Red finds black @ 11
Black finds red @ 9

* = why X must be greater than 0 for the final two equations.

By the way, the first two equations are equivalent to the equations that I came up with before if n = S + 1. The second two would not be due to some misplaced parentheses in my original formulas :-( Oh well. This way is simpler and more “elegant.”

Note: X must be > 0 to work correctly.

F(S, x) = S + (1 + x) + x[(4S + 2) + 1 + (2S + 1)].
F(S, x) = S + x + 1 + x[(3(2s + 1) + 1]
F(S, x) = S + x + 1 + x[(6S + 3) + 1]
F(S, x) = S + x + 1 + (6sx + 3x + x]
F(S, x) = S + 2x + 1 + 6Sx + 3x
F(S, x) = S + 5x + 6Sx + 1

F(S, x) = S + 1 + x(4s + 4) + 1 + (x – 1)(2S + 1)
F(S, x) = S + 1 + 4sx + 4x + 1 + 2sx + x - 2S - 1
F(S, x) = S + 1 + 6Sx + 5x - 2S
F(S, x) = 6Sx + 5x + 1 - S

F(S, x) = S + (1 + x) + x[(4S + 4) + 1 + (2S + 1)]
F(S, x) = S + 1 + x + x(4S + 4) + x + x(2S + 1)
F(S, x) = S + 1 + x + 4Sx + 4x + x + 2Sx + x
F(S, x) = S + 1 + 7x + 6Sx

F(S, x) = S + 1 + x(4S + 2) + 1 + (x-1)(2S + 1)
F(S, x) = S + 1 + 4Sx + 2x + 1 + 2Sx + x - 2S - 1
F(S, x) = -S + 6Sx + 3x + 1
F(S, x) = 6Sx + 3x + 1 - S

(6n - 1) functions:
F(S, x) = S + 5x + 6Sx + 1
F(S, x) = 6Sx + 5x + 1 - S

(6n + 1) functions:
F(S, x) = S + 1 + 7x + 6Sx
F(S, x) = 6Sx + 3x + 1 - S

Rewritten:

(6n - 1) function:
F(S, x) = 6Sx + 5x + S + 1
F(S, x) = 6Sx + 5x - S + 1

(6n + 1) function:
F(S, x) = 6Sx + 7x + S + 1
F(S, x) = 6sx + 3x - S + 1