CalvinDude.com

It is quite obvious that my parents know me well. For my birthday, they got me DVDs from a course on number theory. This meant I was awake far too long last night watching the first set. In the process, I learned a wicked kewl way of converting kilometers to miles using the Fibonacci series.

The Fibonacci sequence starts with 1,1 as the “seeds.” Then it follows the rule, “The next number in the Fibonacci sequence is the sum of the previous two numbers.” So the sequence begins:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

The 2 comes from adding the previous two numbers (1 + 1). The 3 comes from adding the previous two numbers, which now are (1 + 2). The 5 follows the same rule, only now the numbers are (2 + 3). Etc.

Now it happens that the ratio between numbers in this sequence approaches the golden ratio, and at infinity it is equal to the golden ratio. The golden ratio is defined as the Greek letter phi (which doesn’t show up here, so I’ll use x instead) and can be expressed as x = 1 + 1/x. This gives us a recursive equation, one that includes itself within the definition. However, this equation can still be solved by multiplying both sides by x² = x + 1. This gives us a quadratic equation, which means we want all the terms on one side. That gives us x² – x – 1 = 0. Using the binomial theorem, we can solve this to show that x = (1 +/- sqrt(5))/2.

[In the previous equation, “sqrt(5)” stands for the square root of 5.]

Now even without a calculator, we know that the square root of 5 is just a little more than 2, since the square root of 4 is exactly two. So if we subtract the square root of 5 from 1, we will end up with a negative number as our end result. But we only want the positive version, which is x = (1 + sqrt(5))/2 so we can safely ignore the negative version.

In any case, we know that 1 + a number that is a little bigger than 2 gives us a number that is a little bigger than 3. And if we divide that number by 2, we will end up with a number a little bigger than 1.5. And the golden ratio begins 1.608…

Now it just happens that 1.6 is pretty close to the ratio between a kilometer and a mile. In other words, we have about 1.6 km per mile. So if the ratio between the numbers in the Fibonacci series in about 1.6, then we can use the Fibonacci series to convert km to miles. Let’s start easy by reprinting the Fibonacci series we had above:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

If we want to know how many miles are in 13 km, we find 13 on the series and then look for the previous Fibonacci number, which is 8. So there are about 8 miles in 13 km. And if we measure it, we see that 13 km is roughly 8.08 miles.

But what if we want to know how to convert a number that is not part of the Fibonacci series? Well, it turns out that you can add up Fibonacci numbers to make other numbers. So suppose we want to know how many miles are in 20 km. What you do is start with the closest Fibonacci number that is smaller than the number you’re looking for. We see in this case that that would be the number 13.

So keep 13 in mind. Now if you subtract 13 from 20, you’re left with 7. Let’s find the closest Fibonacci number smaller than 7, and that’s 5. So keep 5 in mind too. Finally, if we subtract 5 from 7, we’re left with 2, which is itself a Fibonacci number. So we end with 2.

So we’ve pulled out 13, 5, and 2. And if you’ll notice, 13 + 5 + 2 = 20, our original number. So 20 is composed of those three Fibonacci numbers. What we do to convert it to miles, then, is to find the next lowest Fibonacci number for each of those composite numbers, and add them together. So the next smallest from 13 is 8, the next smallest from 5 is 3, and the next smallest from 2 is 1. 8 + 3 + 1 = 12.

So there are about 12 miles in 20 km. And by measurement, we see that 20 km is actually about 12.4 miles, so we’re pretty close.

Now you may be wondering how the above works. Well, we know that the ratio between Fibonacci numbers is the golden ratio, and the ratio between miles and km is also close to the golden ratio. This means that so long as we can express the ratio of any number as a sum of Fibonacci numbers, we can use the previous “trick” to convert them.

To demonstrate how this works, let’s use a simpler ratio: 1/2. Suppose we wanted to know what half of 20 is. Obviously, we know that 20/2 = 10. But we can express 20 as 8 + 12 too. If we then take half of each of those numbers, we get 4 +6. 4 + 6 = 10, which is identical to 20/2. Or suppose we expressed 20 as 18 + 2. Half of 18 = 9, and half of 2 = 1. 9 + 1 = 10.

Because the ratio is the same, then no matter how you compose 20, dividing each of those numbers by the same ratio before you add them together is equivalent to finding the value of the original number divided by that ratio. So the same thing happens with Fibonacci numbers, except the ratio is the golden ratio instead of a half. Therefore, if we can compose a number as the sums of Fibonacci numbers (and if I am not mistaken, I believe all natural numbers can be expressed as the sums of Fibonacci numbers), then we can use the same technique as shown above to find a conversion between km and miles.

Now I should point out that while there are many things in nature that seem to use the golden ratio, the fact that the relationship between km and miles is close to the golden ratio is actually a matter of serendipity rather than due to some natural law of the golden ratio. Apparently, the mile was defined by the English Parliament in 1592 as being 1760 yards. The survey mile was derived as being 8 furlongs (each furlong being 10 chains, each chain being 4 rods, and each rod being 25 links—yeah, you figure it out). There is no intrinsic pattern or order to any of these gradations, hence the continual demand in science to use the metric system.

A meter, on the other hand, was originally defined as the length of a pendulum with a half-period of 1 second. It was later changed to being 1/1000000 of the distance between the North Pole and the equator. In 1983, the definition was changed so that a meter is now officially the distance light travels through a vacuum in 1/299792458 seconds. This number was formed by using an updated version of the previous definition of a meter and measuring the speed of light as 299792458 meters per second; but it has now become the benchmark itself.

So these two methods, one complete arbitrary and seemingly random, and the other apparently strict measurements of distance covered through time, somehow happened to form a ratio fairly close to the golden ratio.

One of the biggest problems I have with Darwinists is their tendency to take evidence that proves a trivial portion of their theory correct and assume that proves the entire theory correct. As a result, the plethora of evidence for, say, adaptation (e.g., wolves with thicker coats in cold climates, the peppered moths of England, etc.) is used to cover the paucity of evidence for large-scale evolution (i.e., species-to-species evolution, assuming “species” is ever defined by Darwinists, of course). To give an analogy, it is as if Darwinists are attempting to convict a man of first degree murder by proving beyond the shadow of a doubt that he is a jaywalker. But a bunch of adaptation doesn’t lead to evolution of species anymore than a bunch of jaywalking leads to murder.

One of the strongest arguments Darwinists use is based on the fact that many different creatures look similar to each other in some fairly foundational ways, including sometimes in the genome itself. Even Michael Behe (of Darwin’s Black Box fame) believes in common decent in part because of a broken gene that is found in both chimps and humans. The assumption is that if some feature is the same in two different population groups, they must have a common ancestor with that same feature.

It is certainly plausible to assume that common features indicate a common cause, and common decent is one possible way that that could occur (whether likely or not is a different issue). But it is by no means the only way. Indeed, a common environment could just as easily explain certain common traits. That is, suppose that a gene is mutated due to radiation in the environment, and two species have that same gene and share the same environment. There is a good possibility that the gene will be mutated identically in both populations simply because of the environment, and it has nothing to do with lineage.

Naturally, I’m not saying that’s what happened with the broken gene found in both chimps and humans. I haven’t studied that particular issue enough to know either way; but I do know enough to not assume ipso facto that commonality must require common decent. Indeed, there is a specific example of which I am familiar that demonstrates just how dangerous it is for scientists to dogmatically claim decent in such a manner.

It’s called the marsupials of Australia (they also exist here and there in South America and Asia, but they reign in Australia).

Marsupials differ from placental mammals in that marsupials will give birth to their young prematurely, and then the offspring will move into a pouch (called the “marsupium”) in females, and they be raised in that pouch until they are fully developed. In contrast, placental mammals carry their offspring to full term before birth. These differences result in some anatomical differences, mostly in soft tissue, between placental mammals and marsupial mammals.

That said, there are many marsupials that look virtually identical to placental versions of the same animal, as pointed out in this article:

In some cases, placental and marsupial mammals physically resemble each other: the pouched marsupial mouse and the harvest mouse, the marsupial mole and the common mole, the marsupial wombat and the marmot, the tasmanian wolf and the wolf.

The comparison between animals is such that, for instance, in the case of the wolf it is virtually impossible for the untrained eye to tell the difference between an Australian marsupial wolf skeleton and a European placental wolf skeleton.

Let us assume Darwinism is true for this argument. If we see a marsupial wolf that looks almost exactly like a placental wolf, we would immediately argue that this proves that marsupial and placental wolves had a common wolf ancestor that diverged into two lineages: one placental and one marsupial. And indeed, for a time, this is what Darwinists believed. Likewise with the marsupial mouse and the placental mouse: they too would have had a common mouse ancestor that diverged into two lineages.

But Darwinists must also consider the case of the wolf and the mouse together. The assumption is that since both are mammals (regardless of whether marsupial or placental animals are in view) then at some point each had a common ancestor that diverged into different lineages, one of which lead to the mouse line and one of which lead to the wolf line. Thus far, the Darwinist is not in any trouble.

The problem comes when he tries to handle both of these. The Darwinist needs to account for how both the wolf and the mouse diverged into marsupial and placental lines. It seems fairly logical to say that the differences between a marsupial wolf and a placental wolf are not as extreme as the differences between a wolf and a mouse (after all, even the untrained eye can distinguish between the skeleton of a mouse and the skeleton of a wolf despite not being able to distinguish between the marsupial and placental skeletons of a wolf). This would mean that, in order of precedence, the mammal lineage should have split into the mouse lineage and the wolf lineage before each branch then split into placental and marsupial lineages.

Yet that would mean that the marsupial split needed to happen multiple times. Not just twice, but there are about twenty such species that have marsupial members with corresponding placental members, and there are also several marsupial species that only exist as marsupials.

To make matters worse, even if we could stipulate that for some unknown reason, marsupials just happen to arise a lot in the fossil record, we also have to deal with the timeline. Australia and Antarctica broke off from Gondwanaland roughly 45-80 million years ago, according to which modern geological timeline you pick. As most of us have heard repeatedly, dinosaurs ruled the world until about 65 million years ago, and the only mammals alive at the time were small shrew-like creatures. This means if we assume Australia broke off only 45 million years ago, mammals only had 20 million years to co-evolve before those mammals on Australia were isolated from the rest of the world. If Australia broke off closer to 80 million years ago, we’d only have those shrew-like creatures to develop all the species of marsupials in Australia.

Which is it? Well, today most Darwinists on this issue believe all the marsupials in Australia have come from just one species: microbiotheria. In other words, Darwinists today believe that the marsupial/placental split only happened once. After that, placental mammals developed into the wide variety of animals that exist in Europe and North America, and the marsupial mammals developed into the wide variety of animals that exist in Australia and parts of South America. In the meantime, certain lineages just happened to evolve such that the Tasmanian wolf looks exactly like a European wolf to all but the trained observer. And the marsupial mouse looks like the placental mouse. And the placental flying squirrel looks like the marsupial flying squirrel. Etc, etc, etc.

Never fear though. Darwinists already know about this and have proposed an explanation! It’s called convergent evolution. Convergence is the idea that two organisms from separate species follow similar evolutionary paths due to identical environmental pressure. Thus, according to Darwinists, there was one species on Australia that also lived on the rest of the continents with mammal life. Because the environment was similar, the decedents of organisms on either side of the divide both evolved along similar pathways, to the point that the marsupial wolf, mouse, mole, and squirrel look almost identical to the placental wolf, mouse, mole, and squirrel.

Unfortunately, Darwinists don’t see how this undercuts their best evidence for common descent: the similarity of features. For you see, one broken gene that is the same in chimps and humans is proof of common decent, but having an entire skeleton that looks indistinguishable to another organism isn’t proof of common decent—it is proof of convergence. I would think that if the environment is sufficient to explain widespread morphologic similarities between marsupial and placental mammals, it must be sufficient to explain one broken gene.

Yet when you consider the vast difference between a mouse and a wolf, there is really no reason to think that an environment that would so alter the reproductive system of certain types of mammals—such that one becomes marsupial and one becomes placental—that that same environment would somehow “magically” zero in on the exact phenotype of the wolf or mouse. Indeed, on Darwinian principles alone, would this not actually suggest that given a shrew-like mammal on Earth, it was inevitable that wolf-like creatures would come about? Doesn’t all this suggest some kind of teleology? It certainly doesn’t seem to make sense from a process of random mutation followed by natural selection. That may get you the difference between placental and marsupial mammals, but it certainly cannot explain the existence of similar placental and marsupial wolves, given how far along the Darwinian lineage they each are from their shrew-like predecessor.

In my opinion (which therefore makes it infallible truth, seeing as how Jesus said “Thou art Peter and upon this rock” etc.), the most consistently funny television show of all time was Whose Line Is It Anyway? By which I mean the American version, because the British version wasn’t as funny, although it still had its moments of greatness too. Whose Line was all about improv. There was no script, just a bunch of comedians who acted out sketches on the barest of suggestions.

One of the better sketches was called “Newsflash” and consisted of two members pretending to be newscasters while a third (usually Colin Mochrie) was put in front of a green screen. He didn’t know what was being displayed on the green screen behind him, but had to pretend that he did. By the end of the sketch, based on clues given him, he had to guess what it had actually been showing.

Here’s one of my favorite examples:

Now that you’re back from following the linked videos and getting your fill of Whose Line clips, I’ll appear to randomly change the subject…

When most of us try to visualize time, we tend to think of it from the perspective in which we perceive it. That’s to be expected, of course, but if we think about it in detail, we find flaws with our typical concepts. For example, we tend to believe that what we are experiencing as “now” is now for everyone, everywhere. That it’s some kind of “universal now.”

But this treats time as an objective reality. However, modern physics (and many philosophies) reject the objective nature of time. Time is relative to the observer in physics—there is no constant “speed” of time, and there is no objective “now” for any two observers. Indeed, one observer may view two events as simultaneous while another observer views those same two events as one preceding the other. Both views are equally valid, if you take their relative motion into account.

In the end, time is intricately linked to space. Einstein’s method of treating time as a fourth dimension worked well in math, and typically physics still keeps time as an extra dimension. Even in M-theory, where there are eleven physical dimensions, time is seen as an extra dimension too (so it’s common for someone holding to M-theory to say “There are eleven dimensions plus time”). String theory typically states there are ten dimensions plus time, and so on. Additionally, in theistic views, time is usually seen as having been created by God along with the rest of the universe. Therefore, time is intimately linked with space under theistic views too.

It’s easy for us to visualize space (or at least objects in space) as an abstract quantity. We can imagine any object, say, a desk. It exists in space, and the dimensions of the desk define the dimensions of the space the desk exists within. It is far more difficult to picture time in here as well, but we can imagine a desk as it progresses through time. The desk starts new, then gets scratches, coffee spills on it, kids draw on it, until such point as the wood begins to rot and eventually the desk crumbles away.

While it is easy for us to visualize the special aspect of the desk, we can’t visualize the entire time-line of the desk as a whole in spacetime, as that would require us to view something in at least four dimensions. But while it is difficult for us to view it, it is not at all difficult to write mathematical equations about it and understand how the variables interact with each other.

Since we view only the special aspects, we usually think of various objects as special snapshots within time. We mentally compare a start point with an end point, but we cannot see the time dimension itself. I would like to suggest that in order to view the entirety of the object, one must also take into account the timeline of the object, viewing the whole in spacetime rather than just in space. I would suggest that that is how God views the universe. Obviously we cannot do it, but we can come up with analogies to help us better understand certain concepts.

One of the better analogies has come to us from the movie industry. This is the epitome of a series of snapshots in time, usually at the rate of 24 frames per second (for movies) or 30 per second (for TV). What’s interesting is if you film at, say 48 frames per second, and play back at 24 frames per second, time will appear to take twice as long for the actors involved. Or, if you film at 12 frames per second and play it at 24 frames per second, time will appear to take half as long. Varying the speed at which action is filmed varies the appearance of time, and gives us such things as the “slow-motion” shot. Alternatively, you can alter the speed at which the film is played back (such as when you press fast-forward while playing a movie) instead of when the film is shot.

So suppose you watch a scene of a movie and you set your DVD player to play it in slow motion. The events unfold and seem to take much longer than they normally would; but, from the perspective of the characters in the video, time does not take any longer than normal. That’s because, from the character’s perspective, everything has slowed in relation to each other. Put it this way: if it takes 24 frames for the character to reach a certain point, it will always take 24 frames regardless if you play it at 12 frames per second or 48 frames per second. Changing the frame rate in playback doesn’t affect the number of frames used for the action.

Let us extend the analogy. Suppose that there are four scenes in a movie: A, B, C, and D. Suppose that for the characters, the events unfold chronologically. A happens before B, B before C, and C before D. What would happen if you took D and spliced it between A and B? You would have A, D, B, C (this would be similar to old theaters when the rolls of film got mixed up). The characters at point D know things that occurred in B and C, but D is played before B or C are played. From the point of view of the characters involved, B and C both preceded D even if D is played back before B and C. That is, as far as the characters in the movie are concerned, they have a specific history that is related to the story itself that has nothing to do with how the film is played back. You could actually randomize the entire movie so that there are no two consecutive frames. Pick any frame at random, and the characters in it will have knowledge of the history of whatever went before them, and will know nothing of the future that is ahead of them, within the context of that frame.

This means that, again as far as the characters are concerned, you could completely randomize time and they would not know it. Someone who watches the movie would know, but not the characters in it. Techniques like this (although not as extreme) have been used by many non-linear movies. Tarantino’s Pulp Fiction is an example of such a non-linear story, where the things that occur chronologically at the end of the story are shown in the middle of the movie, etc. As far as the characters are concerned, there is no “jumping” in time—but the audience can see it.

Let’s take that analogy and apply it to reality itself: as long as we have a concept of history, time itself could actually be completely randomized and we would not know it. That is, the “now” that we have could have been preceded by a “now” in the middle of next week, but we wouldn’t know it because we have only the experience of our history in mind at our “now.” While it is certainly unlikely that this is the case, what it shows is once again that our experiences in time do not have any bearing on the way that time actually unfolds from the perspective of an outside observer, such as God. God could have arranged time like a movie director, in that as He “views” the movie of the universe, He might see the Flood occur after the Resurrection. For that matter, time could be flowing backwards.

Of course, such assumes a closed future. That is, it views all objects in their entirety in both space and time. If God views the Flood after He views the Resurrection (on His heavenly DVD player), then the characters at the Flood could not do other than they did do. For God has already seen the Resurrection, which occurred after the Flood in chronological time, and required the actions of the Flood to have already been in the history of the universe at that point, even if it hadn’t yet been viewed.

It is important to note that this truth has absolutely nothing to do with what the people existing in time observe. Again, time could be completely randomized and they would not sense it. This is a function of an outside observer having seen that portion of the spacetime existence of an object, not a function of the character who is in time itself.

In the end, this means that if someone can view a complete object in spacetime, then the future is closed for that object. Whatever will happen is what will happen and it is unavoidable because it has been seen. More importantly, it means that if we exist as objects seen fully in spacetime by someone outside of spacetime, that means that the future is fully, 100% determined for us too! This means that an outside observer could “play” history over and over, just like we do a video, and the same exact results will obtain because the object that exists at any particular point in time (from its perspective) exists in the future and the past as that same object. If it were to change, then it would mean that randomizing time would be observable to people within time.

And this brings me back to Whose Line (bet you thought I forgot). Because of the movie analogy, it is tempting for someone to argue that this determinism is due to a feature of characters following a script. Whose Line has no script, yet the same principals apply. Take a frame from the above video, say one that occurs 30 second into the clip. Colin at that point doesn’t know what is on the green screen. You could splice in a frame from 3:40 in. Colin now knows what was on the green screen. It doesn’t matter what order you play those frames in, nor if you play it forwards or backwards. As far as Colin is concerned within the context of the film clip, how you view it does not alter time for him. You can alter the outside perception of time—play it in slow motion or speed it up—but it will not affect his perception of what went on. When you view the clip, the events are fully determined. The ending will be what it will be as you watch it; it cannot be other than what it is.

Additionally, this does NOT require infallible knowledge on the part of the observer. For instance, if you watch the above clip, it requires a certain history to be true for the characters who have been filmed. This means that if you watch them “now,” it necessitates their history so that they get to that point, yet you are not infallible. And this means that if the last “frame of time” has been viewed by any outside observer, the entire scope of spacetime has been determined, because it must be what it is to get to that last frame.

Ultimately, this means that even if God knows our “future” imperfectly—if He simply knows any of it—determinism obtains up to that point. Whatever God knows from our future requires a certain history for the world to get to that future. If God has seen scene D in the movie, then scenes A, B, and C are determined even if we are only in scene A “now.”

The only way to avoid this is to assert that there is no actual future; there is only the present and an eternally unfolding “now.” But this would require an “objective now” that even God must follow. God cannot have seen the ending, because if He has then all the preceding events are determined even if He didn’t want them to be.