Discussions of Mormons and Mormon life, Book of Mormon issues and evidences, and other Latter-day Saint (LDS) topics.

Saturday, April 01, 2006

Benford's Law and Numbers in the Book of Mormon

While listening to conference today, I thumbed through George Reynolds' old book, A Concise Concordance of the Book of Mormon, looking up entries for numbers. My goal was to compile the occurrences of numbers reported for time (mostly years) and also for people (sizes of groups, numbers slain in battle, etc.), the two dominant groups of numbers given in the Book of Mormon. I was hoping to find enough numbers reported to make a crude comparison to what is known as Benford's Law, an empirical observation that the distribution of the first digits in groups of many numbers are not uniformly distributed, but show a tapering distribution heaviest in 1s, followed by 2s, 3s, etc., with 9s being least represented.

Benford's Law is explained in several helpful sources on the Internet. For the mathematically inclined, see Eric W. Weisstein's article, "Benford's Law" at MathWorld--A Wolfram Web Resource, where we read that this law refers to:
A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ∼30%, much greater than the expected 11.1% (i.e., one digit out of 9). Benford's law can be observed, for instance, by examining tables of logarithms and noting that the first pages are much more worn and smudged than later pages (Newcomb 1881). While Benford's law unquestionably applies to many situations in the real world, a satisfactory explanation has been given only recently through the work of Hill (1996).
Another good source is an article by Alexander Bogomolny, who writes:
With the view to the eerie but uniform distribution of digits of randomly selected numbers, it comes as a great surprise that, if the numbers under investigation are not entirely random but somehow socially or naturally related, the distribution of the first digit is not uniform. More accurately, digit D appears as the first digit with the frequency proportional to log10(1 + 1/D). In other words, one may expect 1 to be the first digit of a random number in about 30% of cases, 2 will come up in about 18% of cases, 3 in 12%, 4 in 9%, 5 in 8%, etc. This is known as Benford's Law. . . .

The law was discovered by the American astronomer Simon Newcomb in 1881 who noticed that the first pages of books of logarithms were soiled much more than the remaining pages. In 1938, Frank Benford arrived at the same formula after a comprehensive investigation of listings of data covering a variety of natural phenomena. (Benford's original data table can be found on Eric Weisstein's Treasure Troves of Mathematics - Benford's Law page.) The law applies to budget, income tax or population figures as well as street addresses of people listed in the book American Men of Science.
Benford's law has been used in several cases to detect fraud. See, for example, discussions of Benford's law and cheating by Malcolm W. Browne and another by Jason Kottke. For example, falsified numbers generated by cheaters and frauds will rarely follow Benford's law in situations when real physical data will tend to do so. Careful cheats, unaware of Benford's law, may craft numbers that are relatively uniform in the distribution of leading digits. But when it comes to recorded numbers for populations and other measurements, especially measurements that have dimensions (things like feet, pounds, years, etc.), Benford's Law will often apply, and large unexplained disparities between the data and Benford's law can be a warning sign of possible fraud.

I've known of Benford's law for some time, but only today did I take them time to jot down the numbers given in the Book of Mormon to see how they compare to Benford's Law. I've only spent about a little over an hour on this project, so my findings are preliminary, but here's what I did. From the onset, I recognized that a fair comparison using small numbers like one and two would be problematic, since there a hundreds of references to "a man" or "a person" = do all those count as the number 1? I felt that a fair analysis would require consideration of numbers beginning with 10. Thus, all groups of people of 9 or less are discarded, as well as units of time of 9 or less (a day, a month, etc., are thrown out).

Here are the results, showing the distribution of leading digits for periods of time:

Occurrences of Leading Digits in Measures of Time
1: 69
2: 59
3: 65
4: 33
5: 13
6: 17
7: 15
8: 16
9: 12


I would say that the time-related numbers show reasonable agreement with Benford's Law.

For numbers of people, there were fewer numbers to work with and thus a choppier distribution:

Occurrences of Leading Digits in Counts of People
1: 20
2: 16
3: 8
4: 6
5: 10
6: 6
7: 0
8: 1
9: 0


In these people-related numbers, I have deliberately ignored all references to the 12 Tribes, the 12 Disciples, or the 12 Apostles. There were 19 such references that I have left out, feeling that they were too "non-random" and would inflate the number of 1s as leading digits. On the other hand, the leading 1s include 10 references to groups of 10,000 in Moroni 6, which arguably could be viewed as "inflationary." Perhaps 9 of those could be discarded, in which case the number of leading 1s would be 11. As another downward adjustment, the statistics for the leading digit 2 use only 1 of 12 references to the 2000 stripling warriors and 1 of 3 references to the 2060 of Helaman's expanded army. Several of the other references appear related to the preference of 2000 as a base unit of soldiers in an army (interestingly, I think that all large military groups whose numbers are stated are always multiples of 2000). Note that the large number of leading 5s is due to 8 occurrences of the number 50, 5 of which refer to a military unit, as in "Laban and his fifty." Units of 50 men also played an important role in ancient Jewish systems. Given these considerations and the smaller sample size, the numbers for people still seem reasonably compatible with Benford's Law.

Update (April 2): Please note that this is not necessarily a confirmation of Book of Mormon authenticity, for it is entirely possible for ordinary fiction to have a numerical distribution similar to Benford's law. Numbers in the teens, hundreds, thousands, etc. tend to be more important to us than numbers in the nineties, nine hundreds, and nine thousands, for one thing. It would be interesting to look at distributions of leading digits in several works of fiction and see if any broad generalities might be drawn. At the moment, though, this post is a confirmation of Benford's Law rather than a confirmation of the Book of Mormon, though it may at least suggest that the numbers in the Book of Mormon were not consciously fabricated by someone trying to make them look randomly distributed. But I am sure that you can find Benfordesque distributions in ordinary fiction as well.

As always, do your own due diligence, and don't give too much weight to anything I say, especially since this is preliminary and subject to errors of several kinds. But so far, I think it's interesting. I have not tweaked the numbers to get a desired result, but have tried to be fair. In particular, the choice to start with 10 and higher was made before doing any counting to prevent artificial inflating of the number 1.

32 comments:

Catherine said...

Thanks for the intro to Benford's law. Just for fun, try seeing if your numbers work for a vigesimal (base 20) system! After all, the Mayans used a base 20 system. If the Book of Mormon writers used a base 20 system, I'd say that would certainly help explain why 2 (as in 2000 warriors) occurs more than 1 when you were looking at people.

Mormanity said...
This comment has been removed by a blog administrator.
Anonymous said...

What about the human tendacy to round?

Unless a person is from Utah I tell them I'm from Salt Lake City (where actually I'm 15 miles away).

Likewise when asked about a set, unless acuracy is required I'd say 100 (if the number was from 90..110 or may even 80 to 120).

Also when someone asks the time if it is from 4:21 to 4:39 I'll usually say 4:30

Anonymous said...

I suppose all bets are off for a post from April first.

But I hope Jeff posted this as a confirmation of Benford's Law, not of the Book of Mormon. The unsuspecting reader may not catch the difference, though I'm confident Jeff's motives were completely above board.

Aaron said...

Please let me know this:

If 100% conclusive evidence was found that made it perfectly clear that the BOM is not true, would you still believe in it? I think so. And there is nothing wrong with that. Likewise, I think that if 100% conclusive evidence made it perfectly clear that the BOM was completely true, there would still be people that wouldn't believe it. Given that, why do you think people spend time on trying to determine whether the BOM is true or not? Do the answers, if ever found, really change anyone's opinion? Should they?

Bookslinger said...

Aaron,
Nothing presented so far, for or against the Book of Mormon, proves anything. All evidence so far, for or against, merely tends either for or against plausibility.

Secondly, to add another layer, there's evidence, and there's _interpretation_ of evidence.

Different people can look at the same archeaological artifacts and geological conditions, but interpret them differently and come up with different meanings and conclusions.

Your first hypothetical question is also questionable. Is it really possible to have 100% conclusive evidence to prove a negative?

If the naysayers would only say "there's not a shred of physical evidence that conclusively proves the Book of Mormon to be true" they'd be right.

But their problem is that they say things like "There's not a shread of physical evidence supporting the Book of Mormon," which is incorrect. There are lots of physical evidences that lend credence to the Book of Mormon.

Moreover, there are lots of alternative explanations for evidence that the naysayers claim goes counter to the Book of Mormon.

Aaron said...

Bookslinger,

Thanks for the response. You didn't get at the heart of my questions/comments which is this: would you still believe in the BOM if evidence appeared (in your interpretation) showed it to not be true? I think you would. There is no need to dance around with semantics...

I suppose this gets at the old adage: If God could be proven, there would be no need for God to exist.

Bookslinger said...

Aaron,
Perhaps I just don't or can't accept the premise of the question. If someone presented me with what they called evidence, and claimed that the evidence 100% conclusively proved the BoM wrong, I just wouldn't accept their word for it.

I have my spiritual witness from a known source, the Holy Ghost, that the Book of Mormon is true. That witness came with such convincing power, that I must believe a man to be a liar, or at least mistaken, if he were to demonstrate any evidence that he claimed was 100% conclusive in proving the Book of Mormon false.

For me to deny the Book of Mormon would be like denying the existence of the sun while it shines at mid-day.

The only way I "might" possibly be surer would be if Jesus himself appeared to me, introduced a resurrected Nephi and Moroni; and Nephi then said "Yep, I started it," and Moroni said "Yep, I finished it, put it in the box, and loaned it to Joseph Smith to translate."

Not only would I have to take Jesus' word that those two guys were indeed Nephi and Moroni. But since we are talking "100% conclusively":

how would I know that it was really Jesus, and not some advanced alien life-form imitating a character from one of our planet's religious legends?

My testimony of Jesus, the way that I would know it's him, comes from the Holy Ghost in the first place. I know (a little bit) the Holy Ghost. I have received, on rare occasions, "pure intelligence" from him.

Therefore, if I were to trust the Holy Ghost as to who Jesus is (and I do), and not really the devil appearing as an angel of light, or some alien, or illusion or hallucination, then I can trust the Holy Ghost when he (the Holy Ghost) told me that the Book of Mormon is true. Therefore, I wouldn't really need Jesus, Nephi and Moroni to confirm the truthfullness of the Book of Mormon.

But I realize that *MY* proof is not reproducible outside of myself. It is subjective/internal to me. I can't share my proof with anyone, other than to bear verbal or written testimony, and perhaps testify by my actions as I feebly and unsuccessfully try to live by that book.

Another reason I don't accept the premise, is that I don't believe there can be any firm proof or 100% conclusive evidence of history, because it cannot be repeated or independently verified without taking someone's word for it. You always have to take someone's word if you can't scientifically reproduce something yourself.

A question need not be answered if you reject the premise, such as "Do you still beat your wife, yes or no?" Or a common one from the bullies of yesteryear, "If you were swimming in a lake of _____, and someone threw a bucket of ____ on you, would you duck?"

So I reject the premise, and the above is why.

Aaron said...

Well, Bookslinger, in spite of your attempts not to, I think you have answered the question. Now, going back to one of my original questions - given your steadfastness about the authenticity of the BOM and/or beliefs, (and assuming that others feel as you do) why would folks bother to try and 'prove' the BOM, one way or the other, when it's "rightness" doesn't effect whether people belive or not? If you are not opposed to viewing the Koran - check out verse (or section, I'm not sure what they are called) 109. It is really really short, and very interesting, especially if you have never seen how the Koran is organized. (I'm not a Muslim, BTW).

Walker said...

I'm curious Aaron--are you in favor of critical inquiry in the least? This principle could, after all, be applied to any intellectual endeavor. Will researching Josef Stalin's role in the Cold War change my views about him? They should change, but that doesn't mean they will. And so it goes for the limitless bounds of intellectual inquiry. By applying your principle, we will damming the potential floodwaters of human knowledge. And that's the kind of flood I want to be in.

Your argument just seems too far reaching to be practical--give up learning because we're all going to think as we do anyway? I would think there's more hope for at least some members of the human race.

But if we just write ourselves off as hopeless victims of subjectivity, let's just stop inquiry for truth altogether. We can all live happily together, devoid of questions, but also devoid of intelligence.

Aaron said...

Hardly. I was attempting to get at the "nature of belief". Exploring and learning more about a certain subject in history, science, mathematics, geography, social work, etc. will definitely lead to changes in what one knows and opines on. However, it is the faith and belief parts of religion that make it relatively unique in that people's knowledge of the facts on the ground will NOT generally supersede their beliefs. For example: a billion people believe in the 'miracle of the virgin birth' when in fact such a conception is totally impossible (at that time). Similarly, people continue to 'believe' that flying is an airplane is less dangerous than driving a car, which of course is not true by any stretch of the imagination.

I am attempting to suggest that true believers will ignore these minor inconveniences. Which is fine. Religion makes no attempt to be rational. And that is why is forms an important part of the human consciousness. Don't forget - children are also not rational at times (that is part of the fun of being a child I suppose).

Aaron said...

PS. Great discussion. One can't get this stuff randomly on the street!

Walker said...

Thanks.

No attempt to be rational (???) That, again, is a very broad statement. Were we not given reasoning power with our minds? Must we, as Kierkegard said, be "crucified on the paradox of the absurd"?

I should hope not. Otherwise, we must believe that 95% plus of the world's population are superstitious fools, unable (or unwilling) to use their powers of reason. Furthermore, I think it is unwise to separate entirely one' religious view from intellectual inquiry. Such an approach leads to a compartmentalized life, even a dual life. Reconciliation is important, even necessary, for the disciple-scholar.

Aaron said...

Well then, how do you explain why people believe in a virgin birth? Is that rational? Clearly, these same folks don't think it happened to their mothers...I think some compartimentalization is going on here. There is nothing wrong with agreeing that the nature of much of religious belief is not based on anything provable. In fact, this is what makes humans' ability to hold such dualities so interesting.

Walker said...

Unfortunately, I have learned by sad experience that much of the time when individuals say that something is "interesting," it usually translates into a cynical (or at best, heavily skeptical, attitude) towards religion. Just my little chip on the shoulder (sigh).

Our fundamental difference really doesn't lie in whether or not we believe in the virgin birth--that's peripheral. Rather, it rests in how we approach the seeming lack of rationality. Some individuals, like yourself, simply state that this is a contradiction in rationality. Then they proceed to study the individual with the contradiction, turning the issue into a psychological one rather than a historical/archeological/biological one. Of course, they assume course, that the contradiction is a bonafide one.

However, I prefer a different route (and the correct route, of course :). Take another example, say, horses in the BOM (since we can discuss and still remain within the realms of propriety). There is little evidence to indicate that horses as we know them existed in pre-Columbian times. However, does that mean I then go ask how Mormons can be so duplicitious in their understanding? No, I just see if I am understanding the Mormon belief correctly. Perhaps even THEY don't understand what the BOM is really telling them (Christians haven't understood the Bible fully for two millenia now, certainly the Latter-Day Saints can be afforded the same privilege).

Perhaps the Mormons can tweek an understanding of what the BOM is while still holding true to its veracity as a historical record (the possible reconcilliation here relating to a matter of the translation of animal names, which would have implications for those who maintain a fundamentalist "every syllable is God's syllable" paradigm")

If we assume a fair amount of intellectual humility in acknowledging our lack of knowledge in history, we need to write off the process of intellectual inquiry in the realm of religion. Indeed, if we acknowledge our lack of knowledge, we cut the gordian knot that locks up the healthy relationship that can and should exist between scholarship and religion.

Bookslinger said...

Aaron: "why would folks bother to try and 'prove' the BOM, one way or the other, when it's 'rightness' doesn't effect whether people belive or not?"

I don't know that people are trying to "prove" the BOM. All I've seen so far, from the likes of Jeff Lindsay, FARMS, FAIR, etc, are attempts at illustrating plausibility, not attempts at proof.

If you think those folks are trying to "prove" the BOM, or are trying to get people to believe in it for any reason other than a spiritual witness by the Holy Ghost, then they are giving the wrong impression, or perhaps you are making incorrect inferrences.

I would not want someone to believe in the BofM based on historical, lexicographal (lexicographical?)or archeaological evidences.

What I see from the Mormon apologists are 1) evidences of plausibility, and 2) seemingly logical (to me, at least) counter arguments to the nay-sayers' claims that certain evidences disprove the BofM.

Bookslinger said...

Aaron: "For example: a billion people believe in the 'miracle of the virgin birth' when in fact such a conception is totally impossible (at that time)."

Impossible from what frame of reference? From man's understanding, sure. But what if there is an omnipotent God along the likes which is described in the Bible and Book of Mormon?

If there is such an omnipotent being, would not such a being, who created man kind in the first place, who has power over life and death, who can restore dead people to life, would he not also have the power to cause a virgin to conceive?

You could point to any miracle that can't be explained or duplicated by science as we know it, and label it "impossible." But the real question at the bottom of it all, is whether or not there exists an omnipotent (from our viewpoint, at least) God, or "higher power" or whatever label you want to use.

To deny the possibility of the existence of such an omnipotent being, based on "science" is sophomoric. To deny the possibility of a spiritual realm merely because it cannot be measured and analyzed by present scientific methods is arrogance.

Science has advanced very much over the centuries creating areas of study that were labeled irrational before they were discovered.

Galileo and Copernicus were labeled irrational. Those who speculated about heavier-than-air flight were labeled irrational. Those who speculated about space flight were called irrational.

Many many scientists and engineers see no conflict between their science and religion.

Honest men of science readily admit that spiritual matters are merely an area that human scientific understanding has merely not penetrated. Science does not make religious beliefs "irrational." To assert so is to misunderstand the scientific method and the history of science.

Bookslinger said...

Walker,
I am so disappointed, dejected and crestfallen that you neglected to mention what I consider to be the most logical counter to the seeming anachronism of horses in the Book of Mormon.

It is that either due to nature, or man's interference, horse remains either don't remain, or they aren't allowed to remain when they die.

Similar absence of horse remains has been noted (by non-Mormon scholars, to boot) in the former "Hun" empire of Eurasia. Thus we have an established precedent that an area which was widely documented to have many horses yeilds no archeaological evidence of horse bones.

Thus when the critics shout "Aha! There have been no horse bones found from the time frame of the Book of Mormon" we have a rejoinder in "Same thing happened in the Hun empire too."

By the way, either on Farms or Fair, there is an article somewhere indicating that horse _statuary_ has been found on the western hemisphere that dates from the BofM era.

I tend to believe that if the Book of Mormon says "horses" it means an animal that we would recognize as a horse.

Walker said...

Put on a happy face, Book :)

Thank you, though, for pointing this out in the discussion.

Actually, I am quite aware of the Hun evidence (or lack thereof). Mostly, I did not want to distract from the "mane" issue of reconciliation (I crack myself up). Discussing the possibility of having different animal names fit more neatly into the "reconciliation lens" then did this evidence of absence for the Huns.

And what I said is still true, even considering the Huns. All I claimed was that there was no evidence, which there isn't. Why there isn't is the only real question. And frankly, I could accept your explanation as well--I don't really know.

Aaron said...

Wow. You folks like to run in circles. I know it is sometime difficult to convey ideas in print, without the benefit of the normal back and forth of a conversation. It just seems to me that where I am attempting to illustrate nd discuss some middle ground between a fully religious view on one side and the fully scientific, secular view on the other (I would guess that I know where you stand, and you don't know where I do). And that this middle area is where a lot of scientists come to that are exploring comsmology or even where that question chain of children tends to end up (why A, why B, why C, etc). I wasn't asking for anyone to justify why they think the way the do, I wasn't attacking anyones beliefs or putting them down, I wasn't asking for 'proof' of any document or omnipotent being, I wasn't splitting the human mind in any substantial way. And, I wasn't even necessarily suggesting that people with deep seeded religious beliefs need to think irrationally in order to believe what they do.

In summary, I had hoped (how's that for irrationality?) that religious folks like yourself could see it from the middle, but I'm not sure you're willing (or able?) to. I feel I understand the religious viewpoint - what's not to get? God is omnipotent - that explains everything. The scientific - it can be explained somehow, we just don't know yet. But the middle is where the questions get harder, and the realm of philosophy is opened, and there are no right answers. To me, this unknown, this questioning and discovery for the self is what makes being a human being so cool.

Bookslinger said...

Aaron: "...is what makes being a human being so cool."

If you could be any intelligent life form from the Star Trek Universe what species would it be?

You can choose from The Original Series, Next Generation, or Deep Space Nine. I didn't get to see much of the Voyager or Enterprise series.

Bookslinger said...

Aaron: "In summary, I had hoped (how's that for irrationality?) that religious folks like yourself could see it from the middle, but I'm not sure you're willing (or able?) to."

That's because you're trying to force a contradiction, separation, or gulf, that we, or at least I, don't acknowledge.

I don't seek middle ground because I don't see a conflict between science and religion.

Would not a religion that claims to be in harmony with the divine creator encompass scientific truth as it is found and not deny it?

It is those who deny the existence of the spiritual realm unless it can be scientifically observed and measured who create the apparent gulf in which you are trying to hold a meeting.

Example: the alledged conflicts come in when you, ostensibly the "science guy", claim that the virgin conception is "impossible."

Honest scientists who understand the limitations of man's current understanding don't deny the spiritual. But they can honestly say "We don't understand. We don't know. We haven't gone there yet. Our science doesn't address that."

Honest believers in the spiritual realm also don't deny evidences and appearances.

Gulfs or apparent contadictions can occur when some promoters of science act as if or purport that their understanding of observable evidence is truely complete or accurate.

Similar gulfs are created by some spiritual believers who, just as wrongfully, act as if, or purport that their understanding of spiritual matters or spiritual/Biblical history is truely complete or accurate.

Examples of what I consider to be a comedy of errors are the creationism versus evolution/big-bang debate, and the debate over Noah's flood.

Proponents of evolution and the big-bang theory try to state historical facts based on backwards extrapolation of currently observable conditions and artifacts. To me, that's just laughable.

Neither we, nor anyone else we know, has observed the creation of planets. We have no one's notes or records of what happened or happens. All we have is an "educated guess" of what happened.

Scientifically, we're looking at the last 1/32" inch of a mile long snake, and trying to guess what its head looks like, not having seen its or any other snake's head or body.

The religionists who claim that the Biblical account of creation is complete, or even literal are similarly groping in the dark, and are likewise creating gulfs where none really are.

The Bible is very vague about the creation of this universe, galaxy, solar system and planet, perhaps intentionally vauge.

Honest believers in the spiritual realm must likely say "We don't know the engineering and actual mechanics of how God actually did it."

One of the best reconcilliations I've heard from a Mormon is a guy who said he wanted to study geology for his college degree because he was fascinated with how God creates planets.

That is a good example of a believer who sees no conflict between science and religion.

ujlapana said...

bookslinger said: I don't seek middle ground because I don't see a conflict between science and religion.

If that is true, then I'm not sure I think you have clear definitions of "religion" and "science" as they impact epistemology. Science (or, more specifically, the scientific method) is founded on falsifiable assertions being tested in an objectively repeatable manner. It may not always be applied by scientists (who sometimes really want the next grant), but that is still its nature. Religious epistemology is about subjective experience. It's results are not reliably or objectively repeatable, as the vast disparity in belief systems demonstrates. (Surely you will admit that Mormon's aren't the only people who believe the Spirit, or something like that, has given them "pure knowledge" about their beliefs?)

bookslinger said: Honest scientists who understand the limitations of man's current understanding don't deny the spiritual.

No, they ignore it. They ignore it like you ignore claims about alien abductions, Greek mythology (in a literal sense), and the Flying Spaghetti Monster. They can, however, as can any rational person, hold spiritual assertions to the standard of logic. For God to exist, she must meet the criteria of existence (A=A, A<>B). Thus traits like "omnipotent" become meaningless, even when applied to spiritual measures.

The gulf between scientists and religionists isn't in the current conclusions--it's in the methodology. This is a far more fundamental rift. The big bang theory may be wrong--it's a big extrapolation timewise, as you suggest--but it's based on logical theories built from objective observations of how matter and energy have consistently behaved ever since we watched them. Creationism (be it Judeo-Christian or Hindu, to pick to diametrically opposing ideas) is simply an assertion based on how people feel about things. Hindu's and Christian's will never come to a theological consensus by debating their feelings, but two opposing scientists certainly can by gathering additional evidence.

Walker said...

"No, they ignore it"

Very broad assertion, one that is not supportible by case studies. I could point to whole dep'ts at BYU, but they, unfortunately, are dismissed out of hand as little more than a concourse of driveling Mormon hacks and propagandists.

One has a more difficult time dismissing Henry Eyring Sr. though. Developed the steady theory in chemistry for crying out loud.

They can, however, as can any rational person, hold spiritual assertions to the standard of logic...For God to exist, she must meet the criteria of existence (A=A, A<>B).

Problem here is one of fundamental assumptions. In order to assume such things, you must assume that one's "standard of logic" is infallible. If one knew everything needed to prove whether or not there was a God, that person would him/herself be God. The question of applying logic as we know it to God is thus self-defeating and circular. Not to discourage learning as much about man's logic as we can (it is extremely useful for this life and to an extent, in understanding things spiritual), but we must understand the limits of this logic of which we speak.

Those who divorce secular learning from religious understanding maim themselves in both realms. In my view, secular learning (in general) is always spiritual, in that it should better mankind in someway.

Cutlerite said...

Well I don't know much about benford's law.... but I don't see how it can be applied to the book of mormon....

Wouldn't you want to be consistent with your number system if you were writing a book? Are you saying that if Joseph smith had written the book of mormon, that he would just give random numbers the whole time?

Bookslinger said...

ujlapana:
Any science or engineering that is sufficiently advanced beyond the observer is subject to being called magical or miraculous.

When a believer (in the spiritual realm) calls something miraculous (as I often do) that is not to say that it violates the laws of the universe. It may merely _appear_ to violate _known_ laws of the universe, but in fact be in accordance with higher laws that the Supreme Being (God) or other higher order beings (angels) know how to control or manipulate.

An example of this would be when Europeans brought their 16th century technology to the Western Hemisphere and were thought to be gods by the natives.

Think of how the technology of electricity, electro-magnetism, or radio-waves, could have been made to appear miraculous if the underlying principles were held back from general knowledge of the public, and were not made available to outsiders who wanted to study them.

My assertion that there is no conflict between true science and true religion is based on my belief/assertion that our omnipotent and omniscient God knows all science all scientific laws, and all "rules" of existence. And that he knows everything there is to know about how our 3-dimensional matter acts and reacts.

I believe He knows if there are other planes or dimensions of existence.

I believe the passage in Mormon scripture (DC 131:7) that declares that "spiritual matter" is still matter but is more refined, and is not observable with our physical human eyes or with instruments that we create.

I believe the miracles of the Bible (and Book of Mormon) were not wrought by "godly magic", but by a being, or beings, who operate according to _higher_ laws that we are completely unaware of, just as our knowledge today of radio waves supercedes the wildest dreams of scientists of 500 years ago.

Transmitting voice and pictures through the air was an impossibility at one time. But radio waves and electro-magnetic radiation are the higher technology, along with the scientific laws that govern them, that radio and television works under.

My point is that we don't know the higher laws that God is working under.

One of the things that makes Mormonism different than other Christian denominations is that according to our doctrine, God doesn't use "godly magic", and that he himself operates under the laws of "existence" or "the universe" as opposed to _creating_ or making up rules as he goes.

Bookslinger said...

bookslinger: "Honest scientists who understand the limitations of man's current understanding don't deny the spiritual."

ujlapana: "No, they ignore it."

But they don't _deny_ it, if they are honest.

And not all ignore it, either.

Among the most spiritual men on earth are many scientists, and vice versa.

Walker already pointed out many devout Mormon scientists at BYU.

There are a couple scientists whom we hold to be Apostles of the Lord. Henry B. Eyring Jr, and Richard G. Scott.

Dr. Russell M. Nelson, another Mormon Apostle is a renowned heart surgeon. I remember him claiming that the Holy Ghost taught him a surgical technique in the middle of a heart operation. What a blend that must have been of both the spiritual and the scientific. God could have "miraculously" healed the heart valve of the patient, but instead God said to him "Here's how you do it."

What are the scientific principles of multiplying fishes and loaves, walking on water, restoring sight to the blind, healing leprosy, and raising the dead? We don't really know. But I believe God knows them.

And I believe he knows how spiritual matter and physical/temporal matter interact.

Spiritual principles and scientific principles may be taught in different classes and from different books, but it's all one world.

Mormons, along with most other religions, are among the strongest proponents of education and learning everything we can about our physical realm of existence.

Science and religion, to us, don't compete or contradict. They balance and complete each other.

That's my take

ltbugaf said...

Elder Nelson's example is similar to Nephi's story in the Book of Mormon: God could have simply conjured up a ship, or could have simply transported Lehi's family instantly to their new home. Instead, he taught them how to build the ship on their own and made them sail it.

ujlapana said...

Walker said: One has a more difficult time dismissing Henry Eyring Sr. though. Developed the steady theory in chemistry for crying out loud.

He did not apply the scientific method to his knowledge of God. Scientists, like all people, must make a choice to be rational. They can easily choose to let their emotions guide them in non-professional areas of their lives (such as religion). They will have a hard time putting food on the table if they make arbitrary, non-falsifiable assertions within their scholarly works, however.

Walker said: If one knew everything needed to prove whether or not there was a God, that person would him/herself be God.

I see no basis for this assertion. If God were to appear to hundreds of thousands of people and repeatedly demonstrate his great power (by, say, violating all “known” scientific principles), I think her existence would be proven. (If you believe Jesus will descend to the Earth at some point, do you believe his “existence” will be questioned then? In the pre-Earth life did the spirit children have to be God to know God existed?) As it stands, any “proof” that I have ever come across had readily available non-supernatural alternative explanations. This is the value of Occam’s razor.

bookslinger said:An example of this would be when Europeans brought their 16th century technology to the Western Hemisphere and were thought to be gods by the natives.

If God is merely an advanced techie, then eventually humankind could advance to her level merely through scientific progress. Or find her floating by, on accident. Do you really believe that? What actually happens, of course, is we learn how things really work (such as weather) and then remove God from the equation. True, people sometimes pray for certain weather conditions, but how many faithful Christians really approach weather as something that God is actively attending to? The recent GC focus on addictions is particularly interesting in this light—it’s not just Satan’s persistent influence anymore? Empiricism continually pushes God into the unknown realms of existence (if it can't be explained, it is God's influence).

bookslinger said:Think of how the technology of electricity, electro-magnetism, or radio-waves, could have been made to appear miraculous if the underlying principles were held back from general knowledge of the public, and were not made available to outsiders who wanted to study them.

Held back by whom? Physical laws are omnipresent. Newton didn’t need anybody’s permission to study gravity—it’s influence was everywhere and objectively observable. It’s only the “spiritual universe” that can be consciously withheld from observers. I may not understand all of the principles of quantum mechanics, but I do know that I have the physical potential (if not financial or mental capabilities) to build a particle accelerator and learn about them. The same assertion cannot be made about “spiritual knowledge” because it is painfully obvious that people draw very different metaphysical conclusions from this so-called knowledge.

bookslinger said:Transmitting voice and pictures through the air was an impossibility at one time.

Define “impossible.” As you are well aware, it was quite possible. The problem was that nobody knew how to do it. But the principles behind it were everywhere (lightning and static electricity would have been easily observable, even then). The discovery of electromagnetic fields did not violate natural laws. Supposed miracles, on the other hand, regularly do—-be it conservation of mass/energy, gravity, entropy, etc.

bookslinger said:Dr. Russell M. Nelson, another Mormon Apostle is a renowned heart surgeon. I remember him claiming that the Holy Ghost taught him a surgical technique in the middle of a heart operation. What a blend that must have been of both the spiritual and the scientific.

This is a classic example of where we can apply Occam’s razor. An experienced heart surgeon comes up with a novel way to suture a heart valve. Okay, what’s so miraculous? The fact that it was a new idea? Are airbags a miracle? Walkmen? Toothpicks? Song lyrics? I’m sorry, but people invent things all the time, particularly in their domain of expertise. The fact that Russell Nelson doesn’t think he has an imagination doesn’t mean he’s right.

bookslinger said:What are the scientific principles of multiplying fishes and loaves, walking on water, restoring sight to the blind, healing leprosy, and raising the dead?

That’s easy--there are none. Maybe you meant to say “what are the natural laws that allow for…?” In that case, we don’t know, but we know of a lot of natural laws that would prevent such things from happening. We know of no natural laws that prevent fictional writing, however.

bookslinger said:Spiritual principles and scientific principles may be taught in different classes and from different books, but it's all one world.

It’s one world. The question is, “how do you learn about that world?” By looking at the world, or by contemplating your navel? The fact that “spiritual principles” lead to so many contradictory conclusions about the world, along with the fact that they inherently cannot be reconciled with each other through reason, leads the earnest seeker of truth to discard them as an epistemological tool.

Aaron said...

ujlapana:

Frankly, I'm glad it was you who wrote that last post rather than me. Very well written. I think you've pretty much said it on this topic, as far as I'm concerned. Next?

Bookslinger said...

uj: "If God is merely an advanced techie, then eventually humankind could advance to her level merely through scientific progress."

God has revealed such a plan or a course of study with lab work whereby humankind can advance to his/her/their level. The Mormons call it "The Plan of Salvation" and "Eternal Progression."

And fortunately for collidge dropowts like me, one doesn't need fancy collidge degrees to advance.

One doesn't need sophisticated and expensive instruments to penetrate the veil or wall between the temporal/physical world and the spiritual world and make studies and observations and learn to operate according to the spiritual laws of existence.

One can do so by studying ancient textbooks called the Bible and the Book of Mormon. A more modern textbook called the Doctrine and Covenants is also available. A panel of 15 spiritual experts, based out of Salt Lake City, Utah, oversees the publishing of a monthly supplement called "The Ensign", and they subsize its cost so that subscriptions are only $10/year.

Hundreds of thousands of people, perhaps millions worldwide, attest to beneficial results as a result of following this course of study with its accompanying lab work.

Not all those who participate report positive results. But results have been reproduced among a significant portion of studetns.

Cost of participation in the course is on a sliding scale, that being 10% of the student's income, regardless of their level of income.

So yeah, maybe in a way, God is an advanced techie. He knows how to work within and control both the physical realm and the spiritual realm.

ujlapana said...

Clever bookslinger, I like it.

Used to be registered for that class, but then I realized most students at the university were learning the same stuff in totally different (and cheaper) courses. It didn't help that the course material basically kept repeating itself or that special projects using outside research was frowned on.

Over time I realized that neither this nor any of the similar courses helped with employability post-graduation, so I dropped them all to squeeze in another science class.