21st-century Christian Philosopher

Lamar got back to me, and he raises a good point at first:

[T]his is a truism. There might always be something I don’t know. The clencher is that you have not solved the problem of evil until you give us that reason.

My problem is with the formation. There are two general theories of “truth”. One is the Verification Theory, the other is the Correspondence Theory. What in this formulation is “verifiable”? What is corresponds to anything?

Now it does have a shot at *correspondence. But, if there are things that correspond to these properties, then whatever has them, is close enough to “God” that I suspect that the atheists already don’t believe in it. That’s not a matter, though: correspondence is true regardless of verification; verification just helps us understand it.

The problem comes that this can often be used in a verificationistic manner.

Sure, whatever it is, is not exactly the theists’ God. But as atheist are often at odds with a Creator God as “unnecessary”, in practice, they don’t expose themselves as much more yielding to any deistic ideas either.

Now, the Unmoved Mover (UM) at least had Aristotle fooled into thinking he was standing on bedrock. Because, a God of power has the capability to make whatever seems improbable to us manifest. A universal observer would be even less evident and as result, less necessary. The Divine Couch Potato (DCP) may exist, but it hardly seems more reasonable from the argument of atheists.

At least the UM would manifest itself in the cosmos, or even provide the basis of “Being”. The DCP doesn’t even do that. Now truly, “Creation” is in the realm of the Omnipotent Being. Being the “Necessary Being” also makes sense from that role.

But the more we talk about the guy that can “do everything” the more we get closer to a guy that atheists don’t think is any more reasonable to consider. If such a being does not exist, it is doubtful that there is anything that corresponds to “omnipotence” to observe.

What is “doing everything”? Well, here again, I’m going to throw a little more knowledge and speculation at it: To some degree, we increase our power with the elimination of prior barriers. Rayguns and faster-than-light drives are about as far as I can follow it out around the bend of my world (perhaps Dyson spheres). All “solve problems” all reduce barriers. Further out, we have that conjecture from Arthur C. Clarke that any technology sufficiently advanced will appear as magic. So now, we’re talking “magic” in a phenomenal sense.

But if it appears to us, only a projection that says “it’s technology”. It’s only a belief that only technology can be the proper answer despite knowing of the correct construction that makes it “just technology”. Until we can understand it, it’s hard to “verify”. It would have to just “correspond” until we knew better, if possible.

Quantum-tachyonic, seemingly-magic, egg timers don’t immediately spring to mind as that bit of “sufficiently advanced technology”. No, it makes sense to say that it would do more–i.e. things that cannot be done with spring tension or gravity and friction. So I think I’m consistent.

Now we’re in the territory of titans. Extra-dimensional beings with power to create worlds. You can almost see the Marvel Comic red and purple cosmic fizzing power-streams bristling across the field of stars, if you’re so inclined. Power to retriangulate the variance and modulate the polarity of the very fabric of SPACE! (Or perhaps you could see William Blake’s illustration of his “Four Zoas”.)

From our standpoint, it’s hard to say what stumbling blocks can be cleared away. We might accept that some seeming bedrock of our world is actually contingent in the unseen picture. As such it can be mitigated by sufficient power, unbeknownst to us. From our inkling, it might seem impossible. Thus God can do some of the “impossible”. We might scratch our heads and say, we can’t imagine how a seeming bedrock can be negotiated. But then again, it doesn’t necessarily follow that all frames of knowledge can be intuited from lesser frames.

Given that idea, it might be a hollow academic idea of eliminating the barrier of having any barriers in the first place. What about the barrier between knowing and power? Well then omnipotence and omniscience are the same thing.

But in this Marvel-ous cosmos, any linear projection is doubtful. Let’s look at the phenomal idea of trajectory, an analogy that we’ve been leveraging for a while now. Fire a bullet in space, and the idea is that it continues in a straight line forever. The trajectory won’t change the bullet has mass and inertia. But what happens to the bullet when it passes by the asteroid of these godz? Could they curve space? If it’s possible, yes. Can they anul inertia? Why not! These are godz.

Switching to categorical terms, the matrix gives shape to the trajectory. And to some extent if the matrix can be greatly altered in ways we do not understand, the trajectory is unpredictable. Which is why Clarke’s principle has an absurdist corollary: any sufficiently dependable magic would be “technology”. It means about the same thing.

Next up is “all-loving”.

Lamar from The Philosopher’s Corner stopped by and gave me this poser:

Do you agree that it is better to stop a baby from drowning, if you have the ability to, than to not do so? Obviously the answer is yes. In fact, we’d call anyone who does not stop a baby from drowning, if he could, a very bad person (let alone a not all-good person).

Now, do you believe that God is all-good (i.e., always does the right thing)? Do you believe that God can do anything logically possible? Do you believe that this God exists?

(here)

I have to admit that stumped me, until I realized he was right.

No Drowning at Any Time

But I can do him one better. Don’t babies themselves argue against a “Good God”? You see babies are just people at their most vulnerable. People that God seemingly singled out to be the easiest to abuse or kill.

Since nothing should happen to babies, they shouldn’t be vulnerable. You ought to be able to toss a baby into a pool and know it’s not going to drown. We shouldn’t even be able to think of the two together. We should be able to think. “Whoops! Ran over the baby again…”

Except there’s something odd about that. Obviously since knowledge isn’t a factor, nothing else in what Lamar said suggests that it is insufferable that God created us as “empiric beings”. So we might not know what we’ve never seen. And we wouldn’t know a baby is not going to drown, unless something could drown.

Now, I don’t think we can let God get away with anyone drowning. Thus creatures don’t drown. And water is not dangerous. And it’s curious why someone might think it was. It’s pointless to point out that the baby won’t do what we’ve never seen anything do. Water just doesn’t kill. It’s kind of like thinking about God saving us from “colors that kill.”

But of course, God’s not on the job if a baby should fall from a high window. So were God truly loving, you should be able to throw your baby out of a 15-story window into a pool–or then again, to the pavement if you were going somewhere in a hurry.

Of course, nothing hurts them babies–have you ever heard of a baby getting damaged?!! But wait, there’s more! God’s not going to let his guard down; if you don’t feed them, why should they starve to death, simply because you forgot. Why should they die of exposure, just because you left one out in the driveway for a week?

Let’s say nobody dies. (Sounds like God’s starting to pull his weight, now.) Nobody would say “You’ll live through this,” because…well…(du-uh?).

But that makes me wonder why we need God. The world exists without this imaginary concept called “death” that the religious nuts have tried to explain to me once or twice. I told them that the Flying Spaghetti Monster also doesn’t exist, as does (or “doesn’t”?) his cousin the Divine Teacup. If God exists, perhaps he’s keeping us from “death” (???) or perhaps its non-issue because beings just exist. You can’t by definition see an absence of being, so it might be a contradictory concept–it’s definitely not an observable one.

And why would we say that God is in any sense “benevolent” when it’s not clear he’s done any of this. Would knowledge help?

The God Next Door

But let’s say that a guy named Theo lived down the street from you. He had the best lawn, and gave the best lawncare tips. He impressed you with his constant uncanny knowledge and awareness. You’ve often thought that you couldn’t guess what he might not know.

Surely, in the case, Theo exists. But suppose he let on the idea that someone–perhaps even him–was holding back death and destruction. And you noticed a curious tendency of him preferring to keep conversations simple. If asked about it, he would tell you that there are so many things that would take you endless hours for you to even understand, and that there were so many pitfalls into misunderstandings, that he preferred to avoid talking about the real hairy issues.

Of course, there is this whole curious “non-being” thing he let slip, but absent any proof or direct relation to it, we might just choose to think that Theo is just putting on airs. Beings just are. Sure rocks may crumble and seas rise and recede, but people and animals are just stay around. Sure babies once weren’t, but non-being comes before being. As it can never be that time again, because any time referred to as “past” cannot follow what is called “present”. So which one of these principles do you disagree with:

1. We were babies in the past.
2. All babies were not before they were.
3. The past cannot come after the present
4. We are now, in the present.

Thus, we cannot “cease to be”, otherwise that would suggest that being can precede not being. Theo’s a nice guy–but there really is no proof he’s holding back anything.

What Are We Doing Here?

So what are we doing? Well we’re considering scenarios and interactions and categorizing things. It’s a tough sell that knowledge doesn’t help with categorization, or that it doesn’t help with deciding on the logical implications of scenarios.

If we decide that not saving babies is “wrong”, do we have an absolute or a convention. Wouldn’t an absolute, unfailing view, tell us better? Let’s decide it’s an absolute. Fine. Truly God cannot withstand our logic, so he must take our criticism. We are authorities on the matter, because we agreed. No facts that God could muster can come between our absolute and God’s dereliction.

That’s right, if everything were not as it is, only if we had no knowledge of evil, could we even credit God with having everything under control or knowing what he was doing. Except, it’s a stretch giving him credit unless we know what he did.

No Knowledge Required

Lamar’s right. Knowledge is no part of the Problem of Evil (PoE). We only need to be convinced that God has an amped-up version of the Superfriends’ Trouble Alert to know where the Evil is, then it’s just a cross-section of his Power and his Goodness. It’s only necessary for God to know how to use his cosmic blast and that blasting a planet out of existence is no cure when on the call for a drowning baby, and that you and I agree that we’d save the baby. So God’s got needs the skill of operating his awesome superpower. Aside from that he’d have to know what we know, that neglecting drowning babies is wrong.

Really, the way it is phrased, knowledge played little part. And as I assessed it more and more that what caused me to suspect that it is overly simple.

Still though, let’s get this back to what I was doing: I was assessing the PoE. And my comment on the PoE was an examination of whether God would have to throw up his hands at the PoE and say “You’re right, boys. There’s no way you can be wrong with 5 simple principles. It’s not like I made a complex world in the first place. It’s not like some things in my world are hard to judge and that the most important questions can’t be decided with 5 easy principles of a dozen or so words each. Why you should be able to project outside of your sphere of knowledge with mathematical accuracy, whether or not you know the curve or whether or not the concept is projectable.”

It was a meta-question of could God, while we’re granting his existence, have an argument against it. Would having a wider range and a greater depth of knowledge help him?

So yeah, I misunderstood the simplicity of it. If we keep it simple, there’s almost no way that God can go. We’ve got him between the flat planes of mathematical projections in the Tron world.

A Little Knowledge Now and Then….

Interestingly enough, something just happened with my daughter that I thought related to this concept. She wanted to turn on the TV, but couldn’t manage it. She complained “I keep pressing power!!” (She was pressing the right button too.)

There is no reason in her mind that it shouldn’t turn on. It was the principle of the thing. When you’ve pressed the TV button on the remote, and when you press power afterward, and you know that you’ve pressed the right buttons, with a simple enough model, there is NO reason that the TV shouldn’t eventually come on.

The weird thing was that a little extra knowledge helped(!!) I told her that the TV, for whatever reason, didn’t come on immediately, and she was probably turning it off before it came fully on. When she accepted that there is something that she didn’t know that could interrupt this very simple scheme she laid out. (Is it the power button or isn’t it?!) Then she stopped pressing the power button–imagine the incongruity of not pressing a button to turn on the TV–and the TV eventually came on.

So I’ve got this curious idea–and scientists and skeptics have had it too-that incremental knowledge helps assess a situation and counter a simpler model. Sextus Empiricus so believed that new knowledge invited a reversal of some things that were known that he thought it best not to be overly ardent about any item currently considered “knowledge”.

Most atheists I’ve met have little idea IF there is a universal standard of Good. It would be curious for me to understand how, were such a detail to exist, knowledge of it’s shape–it it had a non-linear shape–it it existed–wouldn’t help.

Knowledge has contents.

You might like me to sharpen the picture of this three-word cipher. But a firmer principle underlies it than the atheists’ nebulous “omniscience” uttered without examination in the Argument From Evil.

First of all atheists, usually adherents of empericism, have no Russell-ian entity that they can point a finger to and say “That is omniscient”. So we’re out of the evidential, the only thing left from an atheistic standpoint is the axiomatic.

This is where the character of knowledge matters. If in fact, my leading premise is true, then we cannot have a “knowledge” that ceases to have contents just because it exceeds our grasp to know what they are. This is why “knowing everything” increases as an inaccurate statement with an unknown bound.

Let me try to illustrate.

Doctors and Aliens

I am not exceptional as a human being. So I don’t think it is outlandish to imagine somebody who knows everything I do, and more. What does he know? If I posit him as a doctor, I kind of know some of that. We’ll give it the technical title of “doctor stuff”. Chances are that if we’re not doctors, though you might know something that falls in this gap, you will not know the contents of this gap.

I accept that there are some contents of “doctor stuff” that I can only guess by their relation to more familiar things. We have “bone stuff” for example. I know about bones. I can name most of them. I’ve heard about doctors setting bones. I know a bit about the role of marrow in producing blood cells. But I also accept that there are facts in bone physiology that I wouldn’t have the slightest inkling of because I don’t know what comprises what I don’t know.

Likewise you can’t guess at what the doctor knows that neither you or I have any clue about. There might be something there. Of course the existence of that set of knowledge doesn’t depend on my ability to theorize it, but the doctors’ ability to know it.

Now, if we can imagine an alien race where the a certain member knows almost everything we do about common phenomena, let’s imagine that on the scale of things he knows a lot more. What does he know? Suppose he knows of a phenomenon on his planet that acts in a totally different way than our planet. What does he know? Is there anything that we would have to find not as invariable as we thought?

But we can dream up as many potential–and hopefully somewhat plausible–scenarios as our imagination can handle. But to illustrate the concept we have to add details. Nothing in particular demonstrates “the state of knowing 60% more than the sum total of human knowledge.” No one concept demonstrates knowing double, triple, quadruple and so on. So what are the contents of omniscience?

We can imagine that it consists of everything we know, plus everything we hope to learn from science. And we can imagine that’s it. But only the omniscient entity would know the contents.

Which is why it is silly to pretend to let God sit in the room while we talk about him, call him characteristically “omniscient” and then telling him what we’ve deduced about his omniscience as authoritative, dismissing him from the room. Once we’ve allowed God to duck his head in the door, he is the authority. Not us.

The athiest has already concluded that he can’t comment on it, because he can’t be a party to the discussion, because he doesn’t exist. It’s strange to then conclude, given a lack of substantive objection on the human level, that he can’t then exist. The atheist has only played at “considering God.”

I do not find it meaningful, given my acquaintance with knowledge that there can ever be an abstract “state of knowing everything” that can ever approximate the likely case of a singular, particular state of knowing all particular states.

Afterward

I’m not trying to leverage human-specifications onto the cosmos. As a result, the vagueness of “omniscience” is not a limiting factor. But I would be more correct to leave up to a posited omniscient being the details of what it implies. Thus the “Problem of Evil” becomes only “A Case for the Non-existence of God provided an intuition of ‘Omniscience’”.

Judging from the sensible ground of facts as one thing and not others, I think it is at least a fair projection in counter to the “Problem of Evil” that omniscience has a lot of particulars. Not only that but there are perhaps more things known not to be the case, then are the case. I think it’s like that I can name more things that I didn’t have for supper, than what I had for supper. (They are arguably facts, though Carnap should object.)

On the subject of Logical Positivism (the undead material philosophy), Russell essentially doesn’t fail in Logical Atomism because there is a manifest lack of atomic positive states. Of course, he doesn’t come close to justifying that there are intelligibly distinct descriptions of all positive states, which would justify them as being “logical” (logos <=> word). But he also doesn’t justify the conjecture that takes up the last third of his essay as meaningful in the narrow sense that he defined as meaningful.

I have to credit William Vallicella (Maverick Philosopher) with getting me started on this. He does an interesting job attacking the “There is evil claim” portion here. (I have to warn you, if your eyes glaze over when I skim formalism here, you’re not going to like his site–but you may get a taste for it.)

In A View to Computation, I tried to lay some ground for Computational theory. I also said at the top that Computational theory contributes to my basic skepticism, as a formal (not fluffy) basis for it. In this post I would like to carry that idea a little further.

Long Streams of Digits

Before we get too far, I wanted to give you one more way to see how numbers represent programs, by taking a look at text in the computer world.

Consider a string of digits. As we add more digits, we get a larger number. In the same way, this post is basically a string of digits:
I=73, n=110, SPACE=32 A=65, SPACE=32, V=86…

Those are the first six characters in this post. Now, because we have 3-digit numbers we can represent each character as 3 digits, creating a number looking something like this: 73,110,032,065,032,086. It should be easy to see that if we continue on in this fashion we have a string of digits that 1) represent this post, and 2) is a number (although large) like any other number.

I should stress here, for those of you who are less familiar with this idea, that this IS how your computer sees it. When it sees a 65, it knows that I intended an “A” and shows you a picture that we both recognize as “A”. There is nothing especially “A-ish” about 65 and nothing especially “65-ish” about an A. It’s just a mapping. It happens to work especially good in Roman-character-based languages, but it’s just a standardized way to get a computer, which only stores numbers, to store text.

Of course, the computer doesn’t see a “6″ and a “5″—and it really doesn’t even see the binary equivalent, which is another string of digits (100001). What it sees is high-current or low current circuits in a pattern that matches then ones and zeros in this one: 100001. If we can imagine that a “1″ represents high-current and a “0″ represents low current, that’s as close as we can come in a brief over view. Since the circuits only have two states, we can think of them as binary digits (where the word b(inary)+(dig)its comes from).

Now, I want to skip ahead, because I’m close to boring myself. We only need 8 bits (a byte) to represent characters, because we have more than enough slots for English letters and punctuation with 255. But, unless 255 is the largest number, we aren’t set with numbers. So we just add a couple of bytes together. When we add 4 of them, we can get a number 4,294,967,295 which we’ll call 4 billion, just for ease. But we can only count this high, when we don’t care or expect negatives. Otherwise, 2,147,483,647 is our limit.

Some other applications have seen a need to count in integers higher than 4 billion. So they string 8-bytes together and get a really large number. Thus any number of bytes with their “ones and zeros” can be considered “a number“. Which means that there is a very large number which represents the Microsoft Word program of a specific release. If any other program had the same number, it would be complete with the identification section that had the characters “Microsoft Word” in them–so for all intents and purposes would be Microsoft Word.

Let’s call this number M. A number is just a number unless a machine knows how to decode it.

Let’s journey back in a time machine: before you read my last piece, if I told you 36 is a program, could you decipher what 36 “did”? Unless you’d seen this scheme, or read the book, you probably wouldn’t. The coupling function is a really neat function—but is it implicit in 36 that it is derived by the coupling function? Not really, because 36 can just be the number of people in a certain room.

To think that a number is an encoded program is kind of backwards. We can, through our cleverness, find ways of making numbers stand for letters or programs. But it all is dependent on what the clever human was trying to do. It can only be interpreted through those means. But it’s not much different than a computer’s inability to take a shape that looks like an “A” and understanding it as an “A”.

I wanted to show yet another thing here: In the last post, I showed you a very simple algorithm. I called it Add_Two. Now since we know that the number system is infinite, we also know that there is an Add_Three, Add_Four, and on up forever.

The weird thing is that doesn’t even begin to scratch the surface. I showed an alternate version of Add_Two as my very last step. It looked like this:

Store X + 1 in X
Store X + 1 in X
Store X + 1 in X
Store X – 1 in X

But there can be any number of Add_Two programs, just as long as I end up adding two more than I subtract. What’s even weirder, is that there are an infinite number of Add_Two programs no more than 3 lines long. Remember when I introduced the mapping of instructions to numbers? Remember when I discussed the variable as V_n? Thus all the following can be Add_Two programs for all n &gt; 1.

Store V_n + 1 in V_n
Store V₀ + 1 in V₀
Store V₀ + 1 in V₀

And I believe that any reasonably intelligent person can realize that the first (or second or third) argument could as well be “Store V_n – 1 in&nbsp;V_n” as well, or even the null op “Store V_n&nbsp;in&nbsp;V_n” so we don’t run out of Add_Two programs. Plus there are&nbsp;three&nbsp; slots to put the triple-fold infinite number of no-effect statements as well. And we can see how this would go for any integer above 2 as well.

So this made our pioneers wonder, is there someway that we can decipher which algorithms do what?&nbsp; First of all it was decided that some poorly-constructed—but no less possible—algorithms would loop forever. In view of that, they wanted to know if there were there anyway to tell what algorithms looped forever and which ones didn’t, just be analyzing the number? And the answer was “No”. As presented in Alan Turing’s famous Halting problem. If there was a way to tell what programs would loop forever—and on what input—certain, cleverly constructed programs would make that impossible.

I’ve done a bit of writing about Turing Machines (TMs) and the Halting Problem. For the most part, I’ve only wanted to cover them in at a high-level. However, it’s become clear to me how basic they are to the form of my philosophy. As such, I want to skim a little deeper.

By exposing some of the detail involved in computability theory, can I best give you a window into what is provable by some explicit process and what is not. The theory comments on all processes that rely on an explicit manipulation of symbols.

In essence, TM theory and the implications of Gödel’s Incompleteness make up a good portion of my skepticism.

The Basics

I like the formulation in Davis, Sigal, and Weyuker’s (DSW) Computability, Complexity, and Languages. So we’ll start there. I will keep mainly to that strategy of presentation. Even though it does not deal with the reading and writing cells in Alan Turing’s machines, it still illustrates the concept of an algorithm reduced to a number.

Basically, the DSW book gives us three elementary instructions as:

1. Store X in X ¹
2. Store X + 1 in X
3. Store X – 1 in X
4. If X ≠ 0 GOTO L (Where L is some label)

With this structure they show that the function *Add_Two” can be constructed as follows:

Store X + 1 in X
Store X + 1 in X

In addition, X + Y can be constructed in this fashion

[A] Store X + 1 in X
     Store Y – 1 in Y
     If Y ≠ 0 GOTO A

Thus we are storing X + Y in X.

So how does this become a number, right?

What’s in a Number?

Well DSW introduce a pairing function, which they write as ⟨ x, y ⟩:

⟨ x, y ⟩ ⇒ 2^x( 2y + 1 ) – 1

Rendering a unique number for a pair of numbers ( x, y ). For example, given ( x = 2, and y = 3 ), we get 2²( 2 * 3 + 1 ) – 1 = 27. And if we are given a number 13, there is only one “decomposition”.

13 + 1 = 14 = 2 * 7 = 2¹( 2 * 3 + 1 ), so x = 1, and y = 3.

After you divide away all the possible 2’s, all that can be left is an odd number. A fundamental definition of odd numbers in higher mathematics is 2n + 1, meaning that there is always a number n, so that the odd number o = 2n + 1.

You can add to that successive pairings. For example, in the previous computation, we were satisfied with the second number being factored to 3, but 3 can be written as ⟨ 2, 0 ⟩, thus creating the possibilities of denoting ⟨ x, ⟨ y, z ⟩⟩ with a single number 13.

I hope that you’ve followed me this far.

Now, to encode a single instruction, they recommend the following:

1. Assign a number to each variable, starting from 0.
2. Assign a number to each label, starting at 1.
3. Given a to represent a label (a = 0 if no label), and c to represent the variable acted upon, we use b to determine the instruction.
   a. b = 0 if we Store V in V
   b. b = 1 if we Store V + 1 in V
   c. b = 2 if we Store V – 1 in V
   d. b = n if we goto Label # n – 2 if V ≠ 0
   

Recall the X + Y program 1. Assign 0 to X 1. Assign 1 to Y 1. Assign 1 to Label A

The first line

[A] Store X + 1 in X

translates to ⟨ 1, ⟨ 1, 0 ⟩⟩ = 5

Store Y – 1 in Y

translates to ⟨ 0, ⟨ 2, 1 ⟩⟩ = 22

If Y ≠ 0 GOTO A

translates to ⟨ 0, ⟨ 3, 1 ⟩⟩ = 46

Now, that shows how an instruction becomes a number, perhaps, but we need Gödel (pronounced “girdle”) Numbers in order to properly capture a sequence of instructions.

Prime Time

Remembering that any number has one–and only one–prime factoring, you might see how we use a prime factoring, we can get a number which can only be one program in this system. For example the program above could be given the number: 2⁵ * 3²² * 5⁴⁶ then we have a number that, in that encoding can only be the X + Y program.

It’s huge, no doubt. In fact, it is out of the range of most computers to casually compute this number. (OpenOffice.org’s Calc Program gives it as 142,704,537,252,030,000,000,000,000,000,000,000,000,000,000). 5⁴⁶ itself is 1.42 * 10³². The standard computer process of computing 5⁴⁶ loses enough accuracy that we lose which number it is.

The standard computer method is to accept that if you have a number this big, your scale of measurement will probably make it impossible to tell 142,000,000,000,000,000,000,000,000,000,000 from 142,000,000,000,000,000,000,000,000,000,001. The computer uses an approximation of a rational number raised to a power, expecting that in a vast majority of cases it will be “close enough”. But in encoding schemes, anything less than dead-on exact, will give us another prime decomposition, and another “program”.

But we’ll put that aside for a time, and discuss decomposition. For this purpose, I’m going to change the terminology of the variables and labels. V_n indicates the variable to which we assign the number n. Thus V₀ is the first variable. Likewise, *L₁ refers to the first label.

Given the number 1 it can only be 2⁰ = ⟨ 1, ⟨ 0, 0 ⟩⟩ and thus the “program”

[L₁] Store *V₀ in V₀

2 can only be 2¹ = ⟨ 0, ⟨ 1, 0 ⟩⟩, or

Store V₀ + 1 in V₀

3 is 2⁰ * 3¹, thus ⟨ 0, ⟨ 0, 0 ⟩⟩, ⟨ 1, ⟨ 0, 0 ⟩⟩ …

Store *V<sub>0</sub>* in *V<sub>0</sub>*

[L₁] Store V₀ in V₀

4 is 2² = ⟨ 0, ⟨ 1, 0 ⟩⟩ …

Store V₀ + 1 in V₀

It’s pretty obvious that the “programs” don’t start to get interesting until we get to larger numbers, so

36 : 2 * 2 * 3 * 3 = 2² * 3².

So it’s instruction 2, followed by instruction 2 or ⟨ 0, ⟨ 1, 0 ⟩⟩ repeated

2 => ⟨ 0, ⟨ 1, 0 ⟩⟩ => Store V₀ + 1 in V₀

2 => ⟨ 0, ⟨ 1, 0 ⟩⟩ => Store V₀ + 1 in V₀

So it’s our old friend “Add_Two”

As the last point we can touch on, this is bascially “Add_Two” as well:

Store X + 1 in X
Store X + 1 in X
Store X + 1 in X
Store X – 1 in X

So that’s 2² * 3² * 5² * 7⁶ … or 105,884,100.

Here’s an interesting tidbit I ran across on the web.

Daniel Dennet says:

“If we don’t understand religion, we’re going to miss our chance to improve the world in the 21st century.” http://www.ted.com/index.php/talks/view/id/94

It’s funny because this is the bio page off of a tape of the talk that Dennett gave at the TED conference (Technology, Entertainment, Design), where he invokes “Orgel’s Second Rule” : “Evolution is cleverer than you are.”

He believes that religion came about through evolution. Apparently, nobody had to understand religion to get us this far. Nobody had to understand it to “create” it, make it “beautiful” (as he relents). But all of a sudden, we have to understand it to do something clever.

Keep in mind that Dennet invests in this “rule”, because he says:

If you understand Orgel’s Second Rule, then you understand why Intelligent Design is basically a hoax.

See, ID is a hoax based on Orgel’s second rule. You can’t understand the real implications of something based on just a precept. A more rational man would say “So you understand why if Orgel’s Second Rule is true, ID is a hoax” if he meant that. No, he means by understanding Orgel, we understand the state of ID. Orgel’s Second Rule (despite being a pretty flimsy ad hoc rule) is a fact in that context.

So Evolution is cleverer than we are. But somehow, not cleverer than Dennett because he thinks he sees what reins have to be siezed to make the evolutionary product of religion run other than its course.

Or do we just have to understand it because we’re going to be graded on it at the end of the 21st century?

I can imagine Evolution showing up and critiquing Dennett about the “flaw” he sees about the state of things.

Who has put wisdom in the innermost being Or given understanding to the mind? Do you give the horse his might? Do you clothe his neck with a mane? Do you make him leap like the locust? His majestic snorting is terrible Is it by your understanding that the hawk soars, Stretching his wings toward the south? Is it at your command that the eagle mounts up And makes his nest on high? Will the faultfinder contend with [Evolution]? Let him who reproves [Evolution] answer it.

You see, I think that if evolution is all that is going on, the reverence for “the Creator’s” being more clever than we are is more faithfully carried out by the worshipper than the smartypants, who thinks its time to jump up and grab the reins now. God’s wisdom or Evolution’s cleverness be damned. We can no more turn Evolution into God than we can turn God into Evolution. It’s out of our hands, the yielding to the greater wisdom of “the plan” is the portion of what remains as a practical matter.

It’s not just something compartmentalized into the slapping-down-opponents mode.

What’s untouched is the question: HOW is Evolution cleverer than we are?

Well, I get tired of explaining the logical implications of their worldview to them, but here goes:

What works survives and theories about what might have worked, what should have worked are discarded. Natural selection is not about deciding what species gets The Best Manifest Idea award, it TESTS every variation so that the animals adapted to survive. Eohippus did not die out because the horses thought they saw a flaw in their logic, or didn’t like what they were doing, or thought that they had a fundamental flaw which would jeopardize the entire world. It’s not about getting ideas into a our overtaxed survival-brains of how we’re going to save the species from extinction. It’s about unproductive patterns adapting or dying.

It’s not about any seeing process coming up with a solution at all, but (as we are consistently told) a blind one grinding away the chaff.

But Dennett, I guess, thinks he has a better idea.

It’s True!

Watch out!! They’re out there!! They look like people; they eat like people; they listen to music; they seem to feel emotion. But don’t let that fool you!

Some scientists, devotees and writers today talk about the “illusion” of free will. The choices that we seem to experience thousands of times a day, are really out of our hands. Perception of what we’re doing comes later. Some how observations that researchers make a couple dozen times a day, are different from our propensity to fool ourselves.

So we have a frequent and commonly agreed perception which as far as I know still continues to work, despite not having been confirmed by Science. Taking both facts and relating them we have ample evidence of the brain fooling itself. Yet a researcher is often spoken of as if they were a disembodied observer, somehow not barraged my the brain’s evident ability to confuse itself about what came first.

Sometimes, I can’t believe they are talking about the same brains that they are trying to convince us have fooled us all along.

The “proof” of this is, as the New York Times puts it (here) “A bevy of experiments in recent years suggest that the conscious mind is like a monkey riding a tiger of subconscious decisions and actions in progress, frantically making up stories about being in control.” Like other agents of this idea, they cite the Libet studies of the 70s and 80s.

Dr. Libet found that brain signals associated with these actions occurred half a second before the subject was conscious of deciding to make them.

The order of brain activities seemed to be perception of motion, and then decision, rather than the other way around. http://www.nytimes.com/2007/01/02/science/02free.html?pagewanted=2

Where was Libet standing? What was his body doing at the time. Was he looking at the monitor? Did his body just decide to point his head toward the monitor and he said, “Hey I want to look at the monitor”? Look how that worked out! He ended up seeing what it was his research to see!

Here’s another representation from Science Week:

Libet’s team measured [how?]two objective parameters: the electrical activity over the motor areas of the brain, and the electrical activity of the muscles involved in the wrist movement.

But Libet also found [any physical actions?] a surprising temporal relation between subjective experience and individual neural events. The actual neural preparation to move (RP) preceded conscious awareness of the intention to move (W) by 300 to 500 milliseconds. Put simply, the brain prepared a movement before a subject consciously decided to move.

You gotta’ wonder if these scientists touch the floor as they are flitting about out of their bodies like this. They just “find”, “measure”, “correlate”, and “conclude”.

It Looks Bad for Our Heroes…

Sometimes, though, if you take a second look, you can spot the absurdity before your eyes. Take a look at the framework: (Again, from Science Week.)

In 1983, Benjamin Libet and his colleagues at the University of California San Francisco [did some stuff]. In this study, participants watched a small clock hand that completed one full revolution in 2.56 seconds. While fixated on the clock, a participant voluntarily flexed his wrist at a time of his choosing. After the movement, the clock hand continued to rotate for a random time and then stopped. Then, a participant reported the position of the clock hand at the time when she first became aware of the will to move.

Now such a things as “voluntarily flexed” and “at the time of his choosing” can’t happen, if it’s just the wrist moving and him deciding that he wanted to move it later. So it’s odd that Libet (provided he was rational) conceived of this experiment. Because the experiment seems to be a figment of his imagination as originally planned.

Why was the subject even conscious of his wrist moving? We can imagine a seen of a participant sitting serenely in a chair staring at the clock that his eyes and neck decided to look at, moving mostly just his wrist.

And, we can imagine the participants sitting serenely in the chair, because Tai-Bo or dancersize would kind of prove a distraction to judging when they decided to move that one part of their body.

So, what’s going on? Apparently his leg didn’t just fly up out of nowhere doing an imitation of John Cleese’s Silly Walks. But somehow his body just decides to do mostly only that which he was instructed to do by the researchers. Somehow his wrist, eyes, and neck decided to obey. As well as whatever firmware it is that tells time.

The experiment would be a joke if the doctors didn’t believe that they could plan (intend) to instruct a subject, that the subject could conceptualize it enough to code intentions to sit quietly and flex his wrist whenever it hit him.

So we have ample evidence of the instructions preceding the event. Instructions in the form of planning the test and explaining to the participant, and the participants odd feeling that he knew how to do all that and avoid his body doing something else.

If this is how the body acts, how could they in the preliminary trial even have trusted that the eyes would be in focus on the clock at the time the decision dialog box popped up? “Ding. You’ve got Movement.” We have to have a collision between the eyes just feeling like being in focus and the brain’s attempt to represent a time on the clock as the time.

He clearly intended to sit there (if he sat). He clearly intended to move his wrist and watch the clock. So what it seems to be the case is that the scientists can’t measure it yet.

So how much is this like “like a monkey riding a tiger of subconscious decisions and actions in progress, frantically making up stories about being in control”? The monkey might shake his head and convey that he’s going to sit still and only move the tiger’s wrist. But we don’t see him as being as effective at that as Libet (assuming he’s rational) saw in designing the experiment. I would suspect that no time-outs were planned for spontaneous Charlestons. The monkey on the other hand, will only say that he was intending the tiger to maul you, and he might decide later to move that wrist, but he’s mauling you now, and that’s kind of how things are going.

Real monkeys on the backs of real tigers (however unlikely that combination) have a connotation that we well recognize in providing the picture of futility. Real people planning, conducting, and complying with experiment plans also have an expected range of outcome. That provides the idea that Libet can even do this in the first place. (Provided he was rational in thinking that he could instruct anyone to move their body.)

In Clunk-clusion

It’s nothing like it at all. And both expectations (assuming Libet was rational) are likely to be highly successful. We can conclude a couple of things:

• Although scientist seldom touch the floor in their disembodied form, they can be very wrong about suggesting that they can pick up a pencil and plan how they are going test in experiments, and I’m guessing that because Science is not prey to brain illusions like I am that it is not a meat-forced error.
• Despite this unforced error, if Science don’t see it, it don’t happen.
• We should always live our lives by “best guess scenarios” which take lesser documented, alternate ideas off the table. Especially, if they don’t sound as “sciencey”.
• The same science that toasts your bread every morning, tells you that your legs have already figured out that your stomach wants toast.
• Wrists apparently listen real good. And even if we are riding around on a raging tiger, it’s wrists that we can expect to buckle down and complete the experiment.
• OR Science has a view that is limited by what has been proved before, but manages to turn that into a conviction that we can only accept what it can and has measured, no matter how much that conclusion ignores.

The Claim to Frame

It’s this last point that really makes it like Zeno’s most famous paradox. I resolve that one, not by playing along with the rules of the micro-game, but by contrasting it to its frame. If Hercules cannot win the race, having to pass through so many lines, then he can’t have gotten to the coliseum to stand at the start of the race just by walking at a slower pace. And nobody would be there to witness it (so there wouldn’t be a coliseum, where nobody goes) and nobody would know of anything called “a race” where movement that can’t happen happens.

Zeno may have had an academic point, but it is almost incontestable that that model was wrong for things known as races. Greeks will move and race, the tiger will eat you, the monkey won’t tell you stories, but people can be expected to execute a planned experiment doing something called “voluntary movement”. And that doesn’t change just because we can’t fit it all into a system or measure it.

This has been a presentation of my fingers.

Did you know the Bible computes the ratio pi wrongly?

Here’s the argument. 1. 1 Kings 7:23 says

[Soloman] made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference.

1. The text says it was round or circular. Thus, the ratio should have been pi and not 30/10 = 3.
2. QED: the Bible misrepresents pi! And the Bible is anti-science or some such.

But that’s ignoring the camel for the gnat. Did you notice that Solomon made a sea 10 cubits across!?!?! A 15-feet (by some measures of a cubit) sea?!?!

Is the Bible telling us that any body of water, about 7 feet deep and 16 feet across should be classified as a sea? How much did it roar? For “roar” is the root meaning of the word yäm, the word in Hebrew. Surely, we can see (or hear) what the ungodly geographers call a “sea” roar, but are we supposed to believe that a large swimming pool roared?

What are we supposed to believe?

That Solomon made a big bowl about 10 cubits across (which gives you an idea how big it is).

Arie Uittenbogaard of Abarim Publications, before he really gets rolling on page 2, deals with some attempted answers and rebuttals (here). One of the attempted answers is worded as so:

The Bible isn’t a science book. It’s more like a story. Like an analogy.

To which he replies:

But if the Bible isn’t a science book, it shouldn’t make a scientific statement. Now that it did, we see that it states a fallacy.

To which I reply, I can’t see one thing that makes this chapter anything more than a description about what was made. I don’t see it as a general statement at all. I can’t see that it qualifies as a “scientific statement” such as “it was 10 cubits across, thus it could not have been other than 30.0 cubits around.”

But that’s okay, Uittenbogaard needs to quickly move past other answers that he finds inadequate. I think he’s hasty here, because he’s on to something better in the next couple of pages. (Which I recommend.)

Still though, it’s not a scientific or mathematical point. The first part of the chapter details what Solomon built for his house, the second part what he built for the temple.

Some people describe this as “The Bible says that pi is 3.0.” Well, not really. Because they did the nose (Monty Python reference). You added a digit of precision that is not necessary meant in the text. From what I can see, it’s rounding to 5 cubits, just as 1 Kings 7:2, describing the dimensions of Solomon’s house seems to round to 10 cubits. And I doubt it’s a “architectural” statement.

1 Kings 7:14 already tells you how you get a “sea” the way described here: You hire someone “filled with wisdom and understanding and skill for doing any work in bronze.” Why doesn’t the Bible “tell the truth” about bronze-working skill right here? Would it help?

But lastly, the word yäm is used in the Bible 300 times as a sea with a shore and ships on it. Likely because the Mediterranean coast was to the west, it also took on the meaning of West, westward, western. The only time it refers to a sea that can fit in a building, is Solomon’s. But sea, skeptics can glide by realizing that language works by metaphoric extensions. Somehow, the idea of the Bible making an oceanographic or geographic definition doesn’t phase them. Just the math does.