Archive for December, 2006

December 20, 2006: 12:42 pm: CalvinDudeEthics, Theology

The first thing to notice when looking at what Scripture says in reference to profanity is that the Bible only gives one instance of any specific word that you ought not misuse.  That is found in the 10 Commandments, where we read: “You shall not take the name of the LORD your God in vain, for the LORD will not hold him guiltless who takes his name in vain” (Exodus 20:7).

Other than that, there is no command not to use a specific word.  And this is with good reason.  Profanities are, as I argued earlier, contextually defined based on cultural considerations.  There is no magic sound that makes any specific word good or evil.  Morality depends on the context in which it is used.

This becomes important because, unlike blasephemy, one cannot appeal directly to Scriptures in regards to a specfic word.  If someone uses the LORD’s name in vain, we can simply point him to Exodus 20:7 and the matter is settled.  There is, however, no specific text that says, “You shall not say the F-bomb or the s-word” etc.

And this is not surprising as the Bible was written to transcend cultures.  Thus, we need to get beyond the simple words that are used and instead look at the intention and meaning that is conveyed by the words.  And this becomes clear when we look at some specific texts used against profanity.

In this post, we shall look at Ephesians 4:29.

Let no corrupting talk come out of your mouths, but only such as is good for building up, as fits the occasion, that it may give grace to those who hear.

Naturally, the first rule of reading a Bible verse is…never read a Bible verse!  That’s right, we need to see what the context of this entire passage is.  So, what is the context of Ephesians 4:29?

Therefore, having put away falsehood, let each one of you speak the truth with his neighbor, for we are members one of another. Be angry and do not sin; do not let the sun go down on your anger, and give no opportunity to the devil. Let the thief no longer steal, but rather let him labor, doing honest work with his own hands, so that he may have something to share with anyone in need. Let no corrupting talk come out of your mouths, but only such as is good for building up, as fits the occasion, that it may give grace to those who hear. And do not grieve the Holy Spirit of God, by whom you were sealed for the day of redemption. Let all bitterness and wrath and anger and clamor and slander be put away from you, along with all malice. Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you (Ephesians 4:25-32).

In this context, it suddenly becomes clear that Paul is not speaking of “profanities” at all.  What he is addressing is something much deeper than that.  Notice verse 25 begins with the distinction between truth and falsehood.  This is the first thing we are commanded: avoid falsehoods.

Paul then tells us that we are not to sin in our anger (thus indicating that anger itself is not sinful, but can certainly lead to sin–a position that I would argue is reflected in the use of profanity as well).  He then speaks of doing honest work, once again emphasizing the matter of truth as opposed to falsehood.

After that, we get the verse in dispute (which we will skip for the moment before looking back on it).  Immediate after the disputed portion, we are told not to grieve the Holy Spirit.  Finally, Paul tells us to avoid bitterness, wrath, anger, clamor, slander, and malice; instead being kind, tenderhearted, and forgiving.

Now let’s look at verse 29 again.  Paul says: “Let no corrupting talk come out of your mouths…”  What is corrupting talk?  It is defined by Paul as “bitterness, wrath, anger, clamor, slander, and malice” in verse 31.  All these are based on falsehoods, as Paul warns us in verse 25.  Paul then says, “but only [speak] such as is good for building up, as fits the occasion, that it may give grace to those who hear.”  What kind of speech does this?  Paul has already defined it as truth in verse 25, and he includes in verse 32 kindness, tenderheartedness, and forgiveness.

One other thing that must be pointed out is the fact that Paul himself states that our language must “fit the occasion” in that passage.  In other words, Paul recognizes that sometimes a rebuke is necessary–and rebukes are generally not considered “kind” by the person receiving the rebuke!  The context determines whether we are to act tenderheartedly toward someone, or if we are to cut him off from fellowship, as Paul did to the sinner in 1 Corinthians 5.

Now, how does this relate to the issue of profanity.  First, I would argue that every time an unbeliever says anything–regardless of whether he uses profanity–he is speaking sinfully.  But the issue is whether a Christian who uses profanity is sinning.  In this case, that is determined not by the word that is used but by the context.  Is the Christian using profanity in anger, malice, or slanderous ways?  If so, then he is sinning.  But if he is using profanity in a way that builds up another person, he is not sinning.  Likewise, if a Christian does not use profanity but is still angery, malicious, or slanderous he is still sinning; and if he does not use profanity but builds another person up, he is not sinning.  The sin or non-sin in the passage remains the same, regardless of whether someone uses a specific word (and therefore, the word itself is irrelevant to the morality of the issue).

Naturally, some may object to the possibility that profanity could ever be used to build up a person.  I can only answer that I have personally benefited from someone rebuking me with strong language in the past, and it was during a time when I probably would not have listened to the “flowery” Christianese that others would use.

What about neutral situations then?  Situations where the Christian uses a profanity but not in a sinful way, but without building anyone up at the time.  This verse does not answer that question.

: 11:58 am: CalvinDudePersonal

This is ironic.  Just a week or two ago, someone on the news said that the way El Niño had set up shop, Colorado wouldn’t get any snow at all until the end of February at the earliest.

Tell that to the blizzard outside my window.

It’s coming down so heavy that they closed shop where I work today and sent everyone home.  With good reason.  As I stood on the corner of Tejon and Platte, I couldn’t even see the statue of General Palmer in the intersection of Platte and Nevada (those who are familiar with downtown Colorado Springs will realize how poor visibility was).  You could only just barely make out headlights of vehicles coming through the intersection.

Anyway, I made it back home safe (where I am currently typing this).  At least this will give me time to post my article looking at the Biblical texts used against profanity!  Look for that in a few…

Lord willing, of course.  After all, in blizzards such as this one, it is not unheard of for the power to get knocked out… :-\

: 9:14 am: CalvinDudePersonal

Since I still get the occasional question as to why I have comment moderation for the first comment people send:

December 19, 2006: 10:45 pm: CalvinDudePersonal

During the end of November and into the beginning of December, my website had had some problems updating the stats for hits, visits, unique vistors, etc.  My log files were still there, but they weren’t being compiled.  Anyway, I finally got that fixed with the lovely folks who host my site (and they are awesome people!).

Anyway, as I looked into the stats I discovered that I could look up year-long stats.  So I figure I’ll share them with you because I can!  Note that these stats try to filter out bots.  Who knows how well that actually works, though? :-P

I started this website in April of 2005.  For the year 2005, my stats looked like:

< = 3,831 unique visitors (estimate)

16,565 actual visits

408,345 page views

423,222 total hits.

Of course, I should point out that these numbers were vastly overinflated due to the insane amount of spammers I got.  Thankfully, I was able to get them under control this year, so the only month where I had any residual spammers was January.  In any case, this year I had (with 11 days still to go!):

< = 4,961 unique visitors (estimate; change of +1,130 over 2005).

20,584 actual visits (change of +4,019)

69,989 page views (change of -338,356)

106,987 hits (change of -316,235)

You can really tell the difference the spammers had in the last two categories!  Thankfully, my spam filter appears to be working just fine now :-)

: 10:13 pm: CalvinDudeEvolution, Philosophy, Science

A book quote for Travis:

“On this fundamentally important question [the age of the Earth], the Natural History Museum and all other modern authorities are in complete agreement.  The Earth is 4,600 million years old.  What is more, different periods of the Earth’s history have been characterized by the formation of different kinds of rock containing the fossil remains of distinctive kinds of creature.  These different periods have also been dated to give what is usually referred to as the Geological Column of the Earth’s history.

…By referring to the geological column anyone can tell the age of a rock or fossile that he or she finds.  For instance, England’s white cliffs consist of chalk dating from the end of the Cretaceous period, which the column tells us, dates from 65 million years ago.

The dates attached to the geological column have been arived at and refined over the past century or so.  The most recent evaluation, and the one quoted in Natural History Museum publications, is that of Van Eysinga published in 1975.  This scheme…is closely similar to that used in most museums and universities since the early decades of century…

When I began to research this question a little more closely I uncovered a puzzle.  Those experts I referred to and the authoritative textbooks I consulted all told me that modern dating has been accomplished by using radioactive methods and hence was an absolute dating method of a far higher order of accuracy than all previous methods–most of which relied on calculations involving one or more relative factors.  These relative dating methods had relied on such factors as the increasing salinity of the oceans, or the Earth’s rate of cooling, and are now considered unreliable.  Radioactive dating, though, is used to date the rocks and the fossils they contained directly and hence was welcomed as an absolute method.

The puzzle arrises because radioactive dating techniques can be applied only to volcanic rocks that contain some radioactive mineral-the primary rocks of the Earth’s crust.  But the geological column consists of sedimentary rocks–rocks formed from sediments laid down on the beds of ancient seas and composed of particles of those primary rocks.  So, of course, any age determination made using these particles will be the same as that of the primary rocks from which they were derived.  In some common sedimentary rocks, such as chalk or limestone, there are not even particles of the primary rocks present and so radioactive dating cannot be used at all.  Happily for English men and women, the white cliffs of Dover are not radioactive.

In The Age of the Earth published by the Institute of Geological Sciences, the position is succinctly explained by John Thackray:

The only sediments which can be dated directly are those in which a radioactive mineral is formed during diagenesis [laying down] of the sediment, such as the rather uncommon illite shales and glauconitic sandstones, other sediments give only the age of the parent rock from which the mineral grains that make them up are derrived.

How then did [scientists] arrive at the dates attached to the sediments of the geological column?

The Institute of Geological Sciences explains:

Where lavas or volcanic ashes are interbedded with a sediment of known stratigraphic age, then a date may be given to that stratigraphic division.  Where an igneous rock intrudes one sedimentary unit and is blanketed by another, then the sediments may be dated from the igneous rock by inference.  The rarity of such cases, together with analytical error inherent in age determination, mean that isotropic ages are unlikely to rival or replace fossils as the most important method of …correlation.

It turns out that what has been dated by radioactive decay methods is not the sedimentary rocks or fossils themselves but the isolated intrusion into them of igneous or primary rocks, usually as volcanic material.  This has been a rare and purely fortuitous process and one that is unreliable–so rare and so unreliable that the Institute of Geological Sciences thinks it unlikely to replace or even rival fossils as a method of dating.  Nor is this all, for the method depends in turn on a further chain of inference.  For the geological column…is nowhere to be found in nature.  It is an imaginary structure that has been synthesized from comparing a stratum of rock in one part of the world with a similar looking stratum in another part of the world.

… [W]hen Darwinists speak of absolute dating of the geological column and the fossils it contains by radioactive methods they are quite mistaken, there is nothing absolute about it.  In fact the method ought to be referred to as “comparative dating,” because it dates the sedimentary rocks by inference alone thorugh their relationship to the rare samples of igneous or primary rocks that are being dated.

When I pursued this question a little further, I found that there is in reality another factor that has been used to arrive at the age of the geological column and the fossils it contains–conjecture.  This process crept into geological dating at a very early stage when Charles Lyell, the nineteeth century’s most prominent geologist and Darwin’s mentor in geological matters, attempted to date the end of the Cretaceous period by reference to how long he thought it would have taken the shellfish (whose fossils are found in later beds) to have evolved into their modern descendants.  Lyell estimated that the Cretaceous ended 80 million years ago–not too far from today’s accepted figure of 65 million, plus or minus 3 million.

According to Harold Levin of Washington University, “By comparing the amount of evolution exhibited by the marine molluscs in the various series of the Tertiary System with the amount that had occurd since the beginning of the Pleistocene Ice Age, Lyell estimated that 80 million years had elapsed since the beginning of the Cenozoic.”

Levin adds that, “He came astonishingly close to the mark.”  In fact, it is not at all astonishing when you know that today’s accepted date has been derived not from an absolute, independent source but from conjectures including Lyell’s [emphasis added].

The kind of surmise used to supplement the relative dates yielded by radioactive dating includes assumptions about the rates at which sediments are laid down on the bottoms of lakes, seashores, and ocean floors; estimates of the rates at which forests are turned into coal deposits; and estimates of the rates at which certain very long-lived families of creatures might have evolved.  But although these conjectures are embodied in the modern view of the age of geological deposits, they are rarely if ever disclosed in geological or biological textbooks, and they are rarely exposed to debate.

Curiously, too, no geologist seems to have checked out the geological column dates with an electronic calculator on a common-sense basis. …[T]here is a remarkable consistency between assigned age and thickness of deposit.  For instance the Cretaceous period is said to have lasted 65 million years and is 15,000 meters thick–an average annual rate of deposition of 0.2 millimeters.  Now look at the Silurian period: this, too, yields an average rate of deposition of about 0.2 milimeters per year–as does the Ordovician, the Devonian, the Carboniferous, and the rest.  It is only when we come to relatively modern times in the Cenozoic era that the rates of deposition very much, and here they appear to speed up slightly.

This is a very remarkable finding.  One naturally expects Uniformitarian geology to favor uniformity, but this is too much of a good thing. Throughout widely changing climactic conditions, advancing and retreating oceans, droughts, and Ice Ages, the rate of sedimentation appears to remain amazing constant regardless–through the thousands of millions of years that are said to have elapsed.  …[I]t is worth pausing in passing to note that such a slow rate would be quite incapable of burying and fossilizing entire forests, dinosaurs, or even a medium-sized tadpole.

Darwin and his supporters realized at an early stage that their theory demanded vast reaches of geological time to support the supposed microscopic changes in form from one generation to antoher.  Equally, evolutionists stood in need of a geological basis for this great antiquity–a mechanism that worked slowly and gradually rather than one that worked suddenly and all at once [catastrophism].  They rejected catastrophism and instead found the mechanism they sought in an idea taking shape among the new generation of secular geologists who asserted that sedimentary rocks (that is, fossil-bearing rocks) were formed slowly by the same processes that can be seen on the ocean bottom today: the deposition of silt and sand that becomes cemented and compacted over millions of years to form successive strata of rock.

Under the reassuring-sounding label of uniformitarianism these ideas were actively promoted by secular geologists like James Hutton and later Charles Lyell…  The uniformitarian doctrine is summed up in the famouse phrase “the present is the key to the past”–a concept eagery accepted by Darwinists as ready-made for their theory and one expounded on at length in Lyell’s Principles of Geology, the primary geological work of the century, published between 1824 and 1833.

The important point to note here is that it was the imperative need for great antiquity that deposed catastrophism, rather than any new scientific discoveries or observations; it was a new way of looking at things, not a new piece of knowledge.  But, superficially, that change in view seemed to be a shift away from naive belief in biblical tales of creation and flood, and toward a newly established scientific viewpoint….

Darwinists needed time, and lots of it: unformitarians had the geological theory that demonstrated great antiquty.  Geologists needed a firm foundation for the relative dating and correlation of the many sediments piled on on another in the past–the many strate of the geological column: Darwinists were able to supply the key to the stratigraphical succession of the rocks by comparative anatomy of the fossils contained in those strata, interpreted along evolutionist lines.  Thus an unusual academic interdependence sprang up between the two sciences that continues to this day.  A geologist wiwshing to date a rock stratum would ask an evolutionist’s opinion on the fossils it contained.  An evolutionist having difficulty dating a fossil species would turn to the geologist for help.  Fossils were used to date rocks: rocks were used to date fossils [emphasis added].

A modern example of paleantologists using fossils to date rocks in a circular way is provided by one of the most famous of all North American dinosaur discovery sites: the rocks at Como Bluffs, Wyoming. …

Of the site, Robert Bakker says:

…We don’t have radioactive beds that can give us a nice hard number [on the age of the deposit].  But by comparing the fossils we get at the bottom of the section and at the top, it’s about 10 million years.  So all of this history is played out roughly over about 2 million dinosaur generations, 10 million chronological years.

Ironically, not only is there no radioactive basis for the dating of Como Bluffs, there is, as Robert Bakker says [elsewhere], not even a complete history of a single dinosaur family at the stie.  Yet we are given the confident assertion concerning the number of dinousaur generations and the number of years to which this sequence is equivalent, with no solid physical basis.  No other scientific discipline would be permitted even to consider such procedures, but when paleontologists date rocks by means of fossils, they do so with the authority of Charles Darwin himself.

Milton, Richard (1992, 1997).  Shattering the Myths of Darwinism, Rochester, Vermont: Park Street Press (pp. 19-23; 27-29)

 
By the way, for other readers (besides Travis, who I already told) it might be worth noting that Milton is not (or at least was not at the time of writing this book) a creationist, nor is he even anti-evolution.  As he explains in his introduction: “[Nature magazine's] editor, John Maddox, ran a leading article that described me as believing science to be a myth (I don’t), evolution to be false (I don’t), and natural selection to be a pack of lies (I don’t)” (ibid, x).  He then adds:

To forestall any repetition of false claims like these, let me make my position clear on both issues from the outset.  I accept that there is persuasive circumstantial evidence for evolution, but I do not accept that there is any significant evidence that the mechanism driving that evolution is the neo-Darwinian mechanism of chance mutation coupled with natural selection.  Second, I do not believe that the Earth is only a few thousand years old.  I present evidence that currently accepted methods of dating are seriously flawed and are supported by Darwinists only because they provide the billions of years required by Darwinist theories.  Because radioactive dating methods are scientifically unreliable, it is at present impossible to say with any confidence how old the Earth is.

(ibid, xi)

By the way, I might add that when it comes to the age of the Earth, I agree with him.  I do not believe the Bible requires only a few thousand years for the age of the Earth; on the other hand, there are some problems with some of the dating methods regarding rocks.  (Note: measurements in astronomy seem more accurate; but that would only give us the age of the universe as a whole and not the Earth in particular.)

: 6:47 pm: CalvinDudePersonal

I know I said that I would address the Biblical issues re: profanity today.  While there still might be time later, some unforseen events have required me to assume I’ll be postponing that until tomorrow!  (And for family members who may read this with concern–this means you, Mom!–it’s not a bad thing!  Just unexpected!) :-D

This is, though, why James makes it clear we should say we will do something if the Lord wills!

December 18, 2006: 10:18 pm: CalvinDudeEthics, Philosophy, Theology

This is a post I’ve been meaning to write for a while but never got around to doing. Tonight, however, I’ve been given my opportunity.That’s because I just had a discussion in #pros about profanity. I even managed to disagree with Dr. White himself on it :-)

In any case, allow me to now present my apology for profanity. First, however, I should note a couple of things. 1) I do not consider this specific issue to be a very important issue at all. I know that many people disagree. However, even if it is the case that profanity turns out to be a symptom of something worse, it is still that—the symptom and not the thing that is worse. 2) I do not mind if people disagree with me on this issue. I have my reasons (obviously, or I would not be writing this post) but because I believe in # 1 above, I’m not going to live or die on this issue. Frankly, it doesn’t mean that much to me. 3) I am not going to speak of blaspheming God in this as there are no exceptions to the sinfulness of blasphemy.

So with those caveats in place, allow me to begin by first giving a brief philosophy of language. This is important because it is necessary to define what a profane word is before we can decide if such a word ought to be used or not. Before we can discover that, the question is more general. How is any word defined?

Words are defined conventionally. That is, the way that a culture uses a word is how the word ends up being defined. There are no “magic” sounds that make certain words special or unique. In point of fact, one culture’s curse word could be another culture’s term of endearment. Often, we have seen foreign names, for instance, that have vulgarities in the midst of them–if they were English names instead of foreign names!

This is key to the entire discussion. If one cannot divorce oneself from the idea that specific sound combinations are not inherently good or evil, one will never truly understand the concepts involved. What is a profanity in English (sound wise) is not a profanity in Spanish, and vice versa.

So what is profane? This is slightly trickier to define because there is a mixture between conventionally defined profanity and objective, transcendent profanity. Unfortunately, it’s easier to explain by going through examples, so let me begin.

Let’s begin with the “crass” profanities. These largely deal with such things as natural bodily functions (typically involving some kind of bodily waste). Firstly, of course, it should be noted that these things are indeed natural and they do indeed have their right and proper place. These bodily functions happen to everyone on a fairly consistent basis. There are indeed appropriate times to talk about these things, and appropriate places.

However, most cultures deem talk about such things as fecal matter to be inappropriate and therefore “profane.” But this is not a necessary conclusion. That is, there is nothing inherently sinful in fecal matter; this is a matter of cultural taste as to whether it is appropriate to speak about it or not. A culture who did not find these sorts of things to be “profane” would not be offended by talk about them.

Going further, even sexual activity (which is often referenced in profanity) has a right and proper place; namely, the marriage bed. This is, in and of itself, amoral. That is, heterosexual sexual activity has no morality within itself (as opposed to homosexuality, which is condemned in all circumstances Biblically). Instead, the morality of the action of heterosexual sex is determined by the state of those engaging in the behavior. If they are married, it is moral; if they are not, it is immoral. Therefore, at times the behavior itself is moral; at other times it is immoral.

A final category of individual behavior that is in view refers to the salvific state of individuals. We speak of people going to “hell” or being “damned”—and this can be done in a correct manner, such as when I say: “Reprobates are damned and will spend eternity in hell.” However, it can also be used incorrectly and profanely such as when I curse someone and state that my desire is that they be damned and placed into hell.

Once again, however, we see that the term itself is only profane in certain contexts. It is appropriate in other contexts. In this case, the context is defined by my motivations and my actions.

These last two points (sexual activity and the concept of “damnation”) are the most important for this discussion, in my opinion. How do we determine if a referent to sexual activity is profane or not? How do we determine if it is sinful to say someone is damned or not?

For the first question, we have a couple of principles in play. If someone uses these terms in a manner that causes another person to sin, then we can judge that it is a sinful use (or at least it is using Christian freedoms to the detriment of one’s brother, which is also condemned). However, this does not require a specific vulgar term (such as the F-bomb) to be used for this to happen. Certain clinical texts may be more than sufficient to cause someone to stumble. On the other hand, many times the F-bomb is used the concept of sexual activity is the last thing on the person’s mind.

Remember that words are defined contextually. For instance, if I asked you to define “lead” you would need to know if I’m talking about a metal or a person who is motivating others forward. The sound is identical, but when someone speaks this sound he does not think the same thing in his mind.

Likewise, when it comes to metaphors, a person who uses a figure of speech does not literally think of that figure. In other words, one thinks of the meaning of the figure. So when I say, “It’s raining cats and dogs outside” I don’t think of felis or canis critters falling from the sky. I think of a downpour.

In the same manner, just because a specific term is used vulgarly to describe a sexual act does not mean that it automatically triggers that thought when it is used by a person. Indeed, most people who drop the F-bomb do so so frequently that the meaning of the term is lost completely. Contextually, they are not thinking of any illicit sexual activity at all.

So we see in such a case that clinical terms (ie “correct, non-vulgar terms”) can be used to cause someone to sin, while the “profanity” can be used without that concept of sin involved. Which of the two actually results in sinful action?

Let us look at the second case, that of the concept of “damning” someone. Again, most of the time this phrase is used, hell is not in view. Instead, it is an expression of anger. For that reason alone, it may very well still be sinful of course! However, the sin is the result of the anger, not necessarily the result of the words used.

On this point, however, I would urge more caution. If someone is really using this term in a proper manner toward another person, it is worse than the flippant use of people who divorce the term from its original meaning. That is, if you know the concept of the term and actually wish to send someone to hell forever, you are in essence saying that you wish you were God so that you could determine someone’s eternal status. You are, therefore, blaspheming God by presuming to take His role.

Ironically, then, it appears that this term is actually more harmful for those who use it properly (but in anger) than those who use it improperly (but in anger). Naturally, there is a third use—properly without anger—that is not sinful at all.

It should be clear by now, then, that profanity is A) dependent upon the context of the culture and B) dependent upon the context in which it is used individually.

With that in mind, I would therefore state the following. 1) Never use profanity in a place where you know someone else is going to be offended. This is a misuse of Christian liberty. 2) In order to communicate as clearly as possible without the possibility of meaning being lost, it is best to stick to culturally defined “proper” words. 3) However, on the same principle, you shouldn’t let other people say you’re sinning when you know you’re not.

Tomorrow, I will look at some specific Biblical texts that have been used against my position.

: 2:42 pm: CalvinDudePersonal

I was talking to a friend at work about this, so figured I’d pass it on:

Here’s how an infinite list of numbers cannot contain every possible number.  It was discovered by Cantor (hence the name “Cantor diagonal”).  In this illustration, the “…” will be for “on to infinity.”  For ease of writing, we’ll use fractions (represented in decimal format): thus, 1/3 = 0.3333…, etc.  Also, I’m using Curier font since the rows need to line up to see the diagonal.  Finally, note that you can’t repeat any of the previous decimals in this list (i.e. in the list, N1 can’t equal N2, etc.)If we were to list out the infinite number of decimals, we could start in the following manner:

N1 = 0.333333…
N2 = 0.123456…
N3 = 0.837741…
N4 = 0.937151…
N5 = 0.999999…

.

.

.

The N series goes on to infinity.  Therefore, this is a list of an infinite number of numbers (of which we only represent the first part above).

Now, what we need to do is create a diagonal on the digits (excluding the 0. prefix), running from upper left to lower right.  So we get (in bold is the diagonal):

N1 = 0.333333…
N2 = 0.123456…
N3 = 0.837741…
N4 = 0.937151…
N5 = 0.999999…

D1 = 0.32719…

Now we construct a NEW diagonal off the original by adding 1 digit to each digit in the original diagonal.  However, this is done modularly where 9 + 1 = 0, not 10.  Thus, the NEW Diagonal (D2) is:

D1 = 0.32719…
    +0.11111…
     ——-
D2 = 0.43820…

Now we know that the first digit in D2 does not match the first digit in N1, so:

D2 <> N1    ( <> is the computer term for “does not equal”; since I don’t have a mathematical font, it will have to do)

We also know that the SECOND digit in D2 does not match the SECOND digit in N2, so:

D2 <> N2

And the third digit in D2 does not match the third digit in N3.

Etc.

Therefore, D2 <> anything in the N series.

This gives us one number that is not in an infinitely long list of numbers.  But there are more numbers not in that list!

We created D2 by adding 1 to the digits in D1.  Instead of doing that, we could add 2, 3, 4…etc. up to 9.  To demonstrate this, let’s make D3 by adding 5 to each of the digits:

D1 = 0.32719…
    +0.55555…
     ——-
D3 = 0.87264…

Again, the first digit in D3 <> the first digit in D1, but it’s ALSO <> the first digit in D2!  This gives us now 9 numbers that are not contained in the original infinitely long list of numbers.

But there’s more!  Why is it that we limit ourselves to adding the same number to each digit?  Why couldn’t we do the following instead?

D1 = 0.32719…
    +0.34971… * (this is just a random number I typed down)
     ——-
D4 = 0.66680…

D4 <> D1, D2 or D3.  And, since these numbers are infinitely long, there are an infinite number of ways you can alter how you add to the numbers (the only stipulation being that you can’t add 0 to any particular digit–it must be at greater than or equal to 1 and less than or equal to 9).

So, this means that in an infinitely long list of numbers, you are missing an infinite number of numbers.  Of course, it’s all a function of the fact that the list is WRITTEN down.  If the list wasn’t actually created, then you would have a set of numbers containing all possible numbers; however, as soon as you list out that set, it is impossible for the list to contain all the numbers.  I’m pretty sure there’s some metaphyical reason to this :-P  I’ll let you figure it out!

 

December 17, 2006: 10:36 pm: CalvinDudePersonal

Man, this weekend went by FAST!

Of course, tomorrow it’ll go slower to compensate.  In the end, it’ll all balance out :-D

December 16, 2006: 2:48 pm: CalvinDudeEthics, Philosophy

The BBC is reporting:

Healthy new-born babies may have been killed in Ukraine to feed a flourishing international trade in stem cells, evidence obtained by the BBC suggests.

Seriously…what’s the ontological difference between a fetus and a new-born baby?  I can’t see the difference.  Apparently, neither can these doctors.  Sadly, I apply my ethics towards human beings in general back to the fetus; these doctors apply their ethicts of “tissue” in general back to the new-born.  This is the kind of slippery slope that will continue until all humans are just tissue.

But don’t say there wasn’t any warning.