B primes are primes where, in binary, any number of digits can be removed from the front and it is still prime or 1. This can work in any base, but I’m doing it in binary. In other bases, there are far fewer B primes. Also, it’s a lot easier in binary.

Here’s an example.

1011 is a B prime. 1011 in binary is 11 in base 10, which is prime.

If the first digit is removed, it becomes 011, which is 3 in base 10.
If the second digit is removed, it becomes 11, which is also 3 in base 10.
If the third digit is removed, it becomes 1, which is 1 in base 10.

I wrote a Java package to calculate B primes. It is currently being edited, and will become available soon.

The highest base ten B primes it was able to find is 17.

I believe I have found all the B primes up to 2^18.

New complete list of every B prime up to 2^20 (1048576):
0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43,
61, 67, 71, 83, 101, 107, 131, 139, 151, 157, 199,
211, 229, 257, 263, 269, 293, 317, 467, 523, 541,
613, 619, 643, 769, 829, 1031, 1061, 1091, 1163, 1181,
1223, 1637, 1667, 2053, 2131, 2179, 2311, 2341, 3079,
3109, 3229, 3271, 4099, 4133, 4139, 4157, 4253, 4637,
8209, 8221, 8263, 8293, 8461, 9283, 9829, 9859, 12829,
16421, 16427, 16451, 17027, 19463, 20483, 24593, 24677,
25667, 32771, 32779, 32797, 32839, 32869, 33037, 33829,
33931, 36901, 37021, 65537, 65539, 65543, 65579, 65687,
66179, 67589, 73757, 98573, 102437, 131101, 131143,
131203, 132103, 132709, 132739, 135211, 233509, 262147,
262151, 262187, 264323, 270407, 270437, 272003, 274973,
294923, 295973, 393287,

The highest B prime so far is 393287.

I have also proved several theorems about B primes:

1. All primes p are B primes in at least one base b where p > b.
2. All primes p are B primes in infinitely many bases b where b > p.
3. There are infinitely many B primes. (follows from 2)
4. If there are infinitely many primes in the form 2^p + 1, then there are infinitely many primes in base 2.

http://www.geocities.com/athens/aegean/8830/mathproofcreat.html

This article, which comes from a non-Christian, by the way, argues that abiogenesis could not have occurred naturally.

“…even today it is often assumed that such “simple” life-forms here on earth originated from non-life (abiogenesis) by natural chemical processes alone, apart from the creative work of any intelligent “chemist,” and that evolution –guided by natural selection– produced all the complexity of life today.”

YES!!!!!! YOU GOT THE DISTINCTION BETWEEN ABIOGENESIS AND EVOLUTION CORRECT!! I’M SO HAPPY!

The gist of this article is that abiogenesis is too improbable. Several points are made to support that.

1. “Since there are 10^84 sub-atomic particles in the known physical cosmos, and
Since there are a maximum of 10^20 interactions (oscillations/cycles) per second between any two of those sub-atomic particles, and
Since there are 10^17 seconds in the supposed age of the cosmos (15 bill. yrs),
. . . if we multiply the above three numbers out, we get the number 10^121. —-So, 10^121 equals the total number of sub-atomic interactions possible since the beginning of the universe (at the “Big Bang”).

We could very reasonably let 10^121 be our “Cosmic Limit” —but just to play it safe and conservative, we’ll make it 10,000 times bigger, and say that according to our “Cosmic Limit Law of Chance,” any chance that is less than one chance out of 10^125 is considered to be a chance of zero. Therefore, we can reasonably say that any event whose chance of occurrence is less than one chance out of 10^125 has been virtually “proven” to be statistically impossible in all of the cosmos ( …actually, in 10,000 such universes as ours).”

Not exactly. It’s still possible for something with a probability of 1 in 10^130, or even 1 in 10^500, to have happened. Something with a likelihood of 10^121 would be reasonably likely to occur exactly once in the entire history of the universe. Something with a likelihood of 10^130 would have a 1 out of a billion (1 out of 10^9) chance of occurring in the entire history of the universe. For an occurrence to be impossible beyond reasonable doubt, I’d say it would have to have at most a 1 in 10^135 chance of occurring.

Even so, the probability of some proteins evolving* is far less than 1 in 10^135.

*Not in the sense of natural selection, but in the sense of random particles moving around and sticking to each other, making proteins.

BUt how do we know that the proteins we see are the only ones that could lead to life? There are practically infinite possible combinations of amino acids; probably, a huge number of them could support life, not just the ones that are already supporting life.

Here is a comparable argument. A deck of cards has 52 cards. If you shuffle the deck thoroughly, the chance of any particular order coming up is 1 in 52 factorial (52 * 51 * 50 * 49 . . . ), which is about 10^68. This is incredibly unlikely. So we can assume beyond reasonable doubt that it is impossible for this hand to come up without the deck being pre-sorted. But at the same time, some order must come up. That order will always be incredibly unlikely, and yet it comes up. It’s the same with proteins.

Why I should finish reading articles: The article had a rebuttal to what I just said.

“Here is where the above criticism fails:

The card-shuffling illustration assumes that basically ANY ordering of the cards is an acceptable outcome –and, comparing it to life-chemistry, this would be the equivalent of saying that almost any ordering of the amino acids would work to build a functional protein. So, whatever one might randomly come up with is basically “easy” to achieve –no matter how “unlikely” the probability calculations might make it seem.

However, the critic unwittingly brings out the correct perspective when he says we are basically looking for one “particular ordering of the cards” –because the research just previously cited in this article (esp. from Behe), points out that –in reality– only about one specific sequence of amino acids out of 1060 possible sequences is adequate to produce a properly folding protein which could be used by actual life. The rest are junk, and useless to life.

Therefore –to more accurately represent the life-chemistry situation– the card-illustration should actually be restricted to say that there are only a few specific orderings of the cards which are the acceptable outcomes of the random shuffles of cards. That is, only about 24 out of the 1068 possible outcomes will do. –For example, the only good outcomes in cards would be: a well-shuffled deck must randomly end up with all four suits in proper numerical order starting with the Ace, then the 2, then the 3, etc., on up through to the King. All four suits must be so ordered. –Specificity is required.

It is the same with the “functional complex specified information” (FCSI) of life.”

This is a good point, but it’s not exactly what I was saying. There are possibly many types of proteins that would work. Not all, but a lot. Maybe 1 out of 10^30. Maybe the proteins don’t have to be folded, but there could be some other way to extract information from them.

When you see a car, you know that it had a designer, right?

Well, yes.

So we must have been designed.

Well, no. The default assumption is that something arose naturally. Why? Because it’s the simplest explanation. If something arises naturally, it happened without any outside interference. That’s about as simple as it gets. So without any prior knowledge, we should assume that a car is natural. But when we look around at the natural world, we don’t see anything that looks like a car, or even anything that looks like car parts. That is why we must conclude that it was designed, not because it’s complicated.

This is an argument made against (idea).

(Person) who is affiliated with (thing) did (something bad) using (idea). Since (thing) endorses (idea), and (person) is affiliated with (thing), therefore (idea) is wrong.

1. (Person) is not a complete representation of (thing), and so if (person) does something or feels a certain way, (thing) does not necessarily endorse the same view.
2. Even if point 1 is false, and (idea) was used to endorse (something bad), that does not make (idea) wrong.
3. It is sometimes not even true that (person) did (something bad) using (idea).
4. It is sometimes not even true that (person) is affiliated with (thing).

You wouldn’t think this would come up a lot, but it does.

EXAMPLE ONE
person: Hitler
thing: atheism
something bad: mass genocide
idea: the theory of evolution
Points one, two, three, and four all apply here.

EXAMPLE TWO
person: Al Gore
thing: theory that global warming is man-made
something bad: influenced the 2000 election
idea: theory that global warming is man-made
Points one, two, and three apply here.

Can you think of any more examples?

12/9/08

Right now I am expanding my corpus. If anyone else has big blocks of text, like a bunch of stuff they typed on their computer, send it to me at MTGandP@gmail.com. Tell me what’s in it (like, emails, computer programs, business letters) so I don’t have to read it. (For confidentiality reasons, and for my convenience.)

12/11/08
I’m trying to get my corpus up to 10,000 pages, because I think that’s enough to have a really good variety of text. Right now I have about 3000.

12/12/08
I have about 11,000 pages in my corpus. However, I only have about 1000 pages of casual text, an I’d like about 3000. I’d also like about 1000 pages of news, and only have about 400. But I’m close to being done. (Collecting news is just so tedious, though.)

I just realized that Carpalx has a good corpus that’s free. It doesn’t have everything that I want, but it has a lot of books and programming code.

VvV from colemak.com wanted to make an evolutionary algorithm for non-latin letters. I don’t have any data for any languages other than English. But if I did, what languages could be done? I’ll look at the world’s most popular languages (from geography.about.com).

1. Mandarin Chinese - 882 million
There are far too many characters in Chinese to make a keyboard layout.
2. Spanish - 325 million
latin
3. English - 312-380 million
latin
4. Arabic - 206-422 million
This could work. http://en.wikipedia.org/wiki/Arabic_alphabet
5. Hindi - 181 million
This alphabet is also probably small enough. http://www.omniglot.com/writing/hindi.htm
6. Portuguese - 178 million
latin
7. Bengali - 173 million
It looks kind of big, but it should work. http://www.omniglot.com/writing/bengali.htm
8. Russian - 146 million
Yep. http://en.wikipedia.org/wiki/Russian_alphabet
9. Japanese - 128 million
Same deal as Chinese.
10. German - 96 million
latin

Any comments you have relating to the NKLP should be posted here.

For English class, I have been reading White Teeth. In the book, the issue of genetic engineering is brought up. It is said that it’s morally wrong to modify the genes of a mouse. That’s playing God; that’s Creation with a capital C, which only God is allowed to do.

So maybe it’s morally wrong to genetically engineer a mouse. That leads to a series of questions.

Is it wrong to engineer a beetle?
Is it wrong to engineer a sunflower?
Is it wrong to engineer a mushroom?
Is it wrong to engineer an amoeba?
Is it wrong to engineer a virus?
Is it wrong to engineer something completely non-living, like a table?

Even if one answers “yes” to the first one or even two or three, you must answer: how complex does a life form have to be for it to be wrong to engineer it?

Since I try to be unbiased, I will now refute my own argument.

I believe that abortion should be legal. But at what point should it become illegal? Let’s say the cutoff point is birth. There is barely a difference between a nine month old baby and a nine month and one day old baby. So why choose birth as a cutoff point? Well, because we have to choose something. The same logic can be applied to my argument.

Here’s another argument, coming from my atheist side.

Supposedly it’s not right to engineer mice because doing so is playing God, i.e., only God gets to do that. But what makes God so much better than us? Why can’t we do it? Also, this argument is assuming that, just because only God has been doing it up until now, no one else is allowed to do it. When the train was invented, did people say that it was morally wrong to play Horse? When the airplane was invented, did people say that it was morally wrong to play Bird? I realize that God is different from Horse or Bird. But in the end, God is just another creature. Even so, where the analogy fails, my original point still holds true: just because only God has been doing it up until now, why does that mean we shouldn’t be allowed to do it?

* * * * * * * * * * * * * * * * * *

Another completely unrelated point about White Teeth:

At the beginning of part four, a woman says, “Excuse me, you’re not going to smoke that, are you?” It is followed with this paragraph:
Marcus closed his eyes. He hated the construction. He always wanted to reply with equal grammatical perversity: Yes, I’m not going to smoke that.

In fact, the original sentence is grammatically correct. The original sentence was originally this:
“Excuse me, but you’re not going to smoke that. Are you[going to smoke that]?”
The bracketed part is redundant, so can be removed. The two sentences are part of the same idea, so when spoken, they are pronounced as one sentence, with a comma.

My brother and I just broke a wishbone. He won. But before he did, I wished to lose. So who really won? It is possible that my wish came true for a reason other than my wishing it. But if both people wish to lose, then no matter who wins, that person’s wish is not coming true. (If I had won, my wish would not have worked.)

Therefore, wishbones do not work. By similar logic, it is possible to disprove any sort of wish.

I am a big fan of YouTube, but they do some strange stuff sometimes.

http://www.youtube.com/watch?v=-RAEWdCz0eY

WEBSITE SIX
6.1. “There is extensive evidence for the layers of strata in the geologic record being laid down very quickly, similar to the processes observed when Mount St. Helens erupted. Rapid global formation of sedimentary rock beds is evidence that the earth is thousands of years old.”
Note a complete lack of cited evidence here. Saying it’s there is not the same as providing it.

6.2. “For example, sandstone is a major feature of the lower part of the Grand Canyon. The same rock layer is found in Utah, Wyoming, Montana, Colorado, South Dakota, the Midwest, the Ozarks, and in northern New York state. Equivalent formations are found across wide portions of Canada, eastern Greenland, and Scotland.”
So sandstone is common. What does this prove?

6.3. “The flood that covered the earth formed the large geological structures that we can observe today.”
So you’re saying 40 days of rain carved out gigantic mountains, when today it takes millions of years to turn rocks into sand on beaches?

Well that one sure was easy.

WEBSITE SEVEN

7.1. “Plants and animals were originally created with large gene pools within created kinds.”
Just because they say “kind” in the Bible doesn’t mean you should use it. “Kind” is not scientific.

7.2. “A large gene pool gives a created kind the genetic potential (the potential to produce a variety of types within a kind) to adapt to a variety of ecosystems and ensure the survival of that kind of organism through natural selection.”
This is correct, but I don’t see how it supports Creationism.

7.3. “Natural selection can only operate on the genetic material already present in a population of organisms. It cannot create new genetic information and subsequently change one kind of organism into another.”
There’s the kicker.

Interestingly, this article is mostly factual. It is, however, misleading. It is possible for a mutation to make the genome larger and to create new information.[a]

We have, in fact, observed one species changing into a different species. See reason 3 on video[c].

WEBSITE TEN
This website has a bunch of articles branching off from it. For the sake of time and saving space, I will not provide quotes on most of them, and will instead rebut the entire article.
10.1. http://www.icr.org/universe-center/
This article made me laugh. The idea is just so silly! But I realized that it wouldn’t seem silly to most people. The ideas here are not very well known. So I will explain it.

The universe is actually 78 billion light years in radius, and only 13 billion years old.[d] This works because of the way the universe is expanding. So we can’t see the entire universe. We can only see 13 billion light-years. The light we see that’s the farthest away has been traveling for the entire existence of the universe. We can see 13 billion light years away in all directions, because that’s how far any photon has gotten, on any side.

Now, why is everything moving away from us? That is because of inertial reference frames.

You’re spinning very rapidly right now, because the earth is spinning. But can you tell? No. It’s because you are in the same inertial reference frame as the earth. It looks like the sun is moving around you.

It’s the same deal with the moving galaxies. If you were on one of those galaxies, you would see earth moving away from you. And everything around you would be moving away, because things that are further out are moving faster than you, and things closer to the center of the universe are moving slower. So it looks as though everything is moving away from you, no matter where you are.

The universe does have a center, but there’s no reason to believe that we are at it.

10.2. http://www.icr.org/universe-power/
“If the laws of nature were just slightly different, the delicate balance would not exist between hydrogen, oxygen, and carbon. Without this balance thousands of critical molecular interactions would not happen. There are only a few elements that can sustain life through their unique properties. Any change would make life impossible.”
That is the only significant portion of this article.

Life as we know it would be impossible. But other sorts of life may be able to exist in many other possible universes. Like life that does not use carbon, and instead uses some other weird element that relies on a different gravitational constant, a different source of energy, etc.

10.3. http://www.icr.org/recent-universe/
We have no direct evidence for the Oort cloud, because if it exists, the comets are just so small and it’s so far away. The comets are separated by about 10 million kilometers on average.[e]

But we have good reason to think it exists. For example, many independent sources confirm that our universe is 13 billion years old, and that earth is 4.6 billion years old. This single lack of evidence is not enough to sway us; it’s just enough to keep us on our toes.

Here is what we think about Oort clouds:
Comets come into the solar system and hit earth when another star disrupts our Oort cloud. Oort clouds are so far out that other stars can significantly affect them.

We also have other evidence for Oort clouds.

There are also other reasons to believe that the Oort cloud exists. The way that comets seem to come from any direction is an indication of a large cloud of comets outside our solar system.

10.4. http://www.icr.org/earth-sun/
“Our solar system is filled with amazing planets, but none are perfect for life except the earth.”
Well obviously the planet that’s perfect for life is the one that life will develop on. Why would life develop on any other planet?
“[tells all the reasons why life wouldn’t work on other planets in our solar system]”

“Each planet in our solar system demonstrates that earth is unique and specially created for life.”
No. Each planet in our solar system demonstrates that life will only develop on planets where it can develop.

10.5. http://www.icr.org/earths-location/
What I said in [10.4] still applies. Life will only develop in places that support the environment of life. If the universe was uniquely created for life, then why are there so many places that are uninhabitable? Like they said, earth is the only planet in the solar system that can support life. Wouldn’t God want there to be more life than just one planet?

10.6. http://www.icr.org/earths-core/
[10.4]

10.7. http://www.icr.org/water-cycle/
[10.4]

10.8. http://www.icr.org/law-conservation/
“Energy cannot be created or destroyed; it can only be changed from one form to another.

Energy is not currently being created. The universe could not have created itself using natural processes because nature did not exist before the universe came into existence. Something beyond nature must have created all the energy and matter that is observed today.”
This is correct.

“The logical conclusion is that our supernatural Creator with infinite power created the universe.”
Something created the universe, yes. It was, by definition, supernatural (at least as we know it). But was it God? There is no evidence for that. (See M Theory.)

10.9. http://www.icr.org/thermodynamics/
“Fortunately for us, the temperature of the universe is not zero. It is moving that way each moment, but it is not there yet.”
It is actually moving away from zero. When energy is expended, it is converted into heat. There is no way (occurring in nature) to convert thermal energy into another form of energy. So eventually, all the energy in the universe will be thermal energy, a.k.a. heat.

“The logical conclusion is that an infinite Creator made the universe a finite time ago.”
See Big Bang Theory and [10.8].

10.10. http://www.icr.org/electromagnetic/
This page states some scientific facts, and then states some religious crap that does not follow from the science. No rebuttal necessary.

10.11. http://www.icr.org/worldwide-flood/
It is possible that there was a global flood. I’m not very familiar with the geology involved. But I think that multiple religions have accounts of a great flood. It is likely that some event triggered a very large flood, and many people across the world saw it as a sign from God.

10.12. http://www.icr.org/geological-strata/
I’m sure that there is evidence for a worldwide flood. But was it a flood created by God to wipe out life on earth? I doubt it.

10.13. http://www.icr.org/fossil-record/
The fossil record is very extensive, and we have accounts of many transitional forms. My first post on this topic has a link to a list.

Not all fossils are expected to have transitional forms. Fossils only form under certain conditions, so we do not see them very often. If every living being ever to exist was fossilized, there would be piles of fossils hundreds of miles high. (I might be off by a few orders of magnitude.)

10.14. http://www.icr.org/creation-dna/
DNA does not, in fact, require intelligence. It’s possible that you randomly throw some rock on the ground, and they spell out a word. (Unlikely, but possible.) Does that mean the rocks are intelligent?

http://godisimaginary.com/i25.htm
http://godisimaginary.com/i37.htm

There are a bunch of articles in the “biological” section that can be explained by evolution, and it’s a waste of time to go over them.

10.15. http://www.icr.org/special-creation/
I like this one because it’s not scientific.

“[Man] is able to imagine and create objects never seen before (art, buildings, etc.).”
Well so is Chimpanzee, Gorilla, Orangutan, Bonobo, Dolphin, Killer Whale, Elephant, Magpie, and possibly Pigeon.[f]

“He is able to ponder his role and fate in creation.”
Other animals (particularly the ones on the above list) may do that. We just have no way to know if they do. (That is, no way to know right now. Someone may discover a way.)

10.16. http://www.icr.org/mitochondrial-eve/
“Variations in mitochondrial DNA between people have conclusively shown that all people have descended from one female, just as it is stated in Scripture.”

Not all people ever. Just all people who are alive. This is called natural selection. That one woman and her descendants were “fittest”, so they survived and eventually all other humans died off. They were probably only a little bit “fitter” in little ways, but it was enough that they eventually were the only humans left.

Fun fact: 1 in 12 people in the world are descendants of Genghis Khan; 1 in 4 in Asia.

WEBSITE ELEVEN
11.1. http://www.icr.org/planet-earth/
The earth is unique, at least among planets that we can effectively study. It can support life. We know that planets that can support life are fairly rare. But how is this evidence of a god? As I said above, God would want there to be humans all over the universe.

Earth’s conditions are very good. But they’re not perfect. Meteors hitting earth kills people. (It helps natural selection move along faster, but according to Creationists, natural selection doesn’t exist.) People dying is bad, from a biblical perspective. And so many places on earth are inhospitable. Antarctica, for example. The Sahara Desert is hospitable, but it sure would be nice if it were not so hot, and if there were, like, trees. So since when is earth “perfect”?

Almost the entire website relies on two arguments: The “earth is perfect” argument, and the “nature is amazing, therefore God exists” argument. The first argument has been refuted, and the second is completely unscientific, appeals to emotion, does not provide any evidence, and does not logically follow.

WEBSITE THIRTEEN
“The claim is sometimes made that Hitler was a Christian - a Roman Catholic until the day he died. In fact, Hitler rejected Christianity.”
Then why does he mention in his journal that the is on a godly mission to kill the Jews?

http://homepages.paradise.net.nz/mischedj/ca_hitler.html

Hitler may have talked about things that were anti-Christianity in order to get more power. But in his personal journal, he clearly states that he is a Christian. He did not always act very Christianly, though. (I’m not going to say he didn’t act atheistish, because there is no such thing as “acting atheistish”.) (What’s the adverb form of “atheist”?)

Whatever his religion, Hitler was not a nice guy, but that doesn’t mean his entire religion is like him. In general, Christians are good people and atheists* are good people. Hitler was not. So let’s stop bickering about whether he was atheist of Christian.

*I am not saying that atheism is a religion. It’s not. It is, however, mutually exclusive with Christianity, because Christianity implies theism. Non-Christian theism is also mutually exclusive with those two groups. For the most part, non-Christian theists are good people, too.

WEBSITE FIFTEEN
I haven’t even read the website yet, and the deception has began. The title is “Darwinian evolution was basis of Nazi legal system”. This is completely irrelevant.

The title has five flaws:

I. It is using the “I don’t like it, so it’s not true” argument about evolution.
II. It is assuming that because evolution was used for evil, that makes evolution evil. I could pull that argument and say that the Bible was the basis of the Crusades, therefore the Bible is evil. But that is clearly not correct. Or here’s a funnier example: box cutters were used to hijack the planes that bombed the World Trade Center, therefore box cutters are evil. This is obviously false.
III. Darwin’s theory is that of NATURAL selection, not selection enforced by humans. It just so happens that human selection works in much the same way.
IV. The Aryan race is not evolutionarily superior to other races. So if Hitler was trying to emulate evolution, he was not doing a very good job. In fact, most characteristics of the Aryan race are recessive, and so less likely to continue. (Dark skin > light skin, brown eyes > blue eyes, dark hair > light hair…)
V. It’s not even true.

At this point, I don’t even need to read the website except to confirm the fifth point. The first four points stand on their own.

“‘Adolf Hitler and the Nazi regime are the perfect illustration of what can occur when a civil government declares itself to be completely independent of God’s law.’”
It can also occur when a civil government declares itself to be sent by God to kill people.[27.14]

a: http://www.don-lindsay-archive.org/creation/new_info.html
b: http://www.youtube.com/watch?v=rtmbcfb_rdc
c: http://www.youtube.com/watch?v=EDFJviGQth4&feature=related
d: http://www.space.com/scienceastronomy/mystery_monday_040524.html
e: http://www.solarviews.com/eng/oort.htm
f: http://en.wikipedia.org/wiki/Mirror_test

Creationists sometimes use the following argument:

The universe is just perfect. If any of the laws of physics were a tiny bit different, life as we know it would not exist.

The primary fallacy here is that life as we know it is the only form of life. But you can find out about that elsewhere. I have a new angle.

Let’s assume for a moment that God created the universe. So why did He create it like this? He could have created it differently, and just changed life so that life was capable of existing in this different universe. But why did He do it like this?

The refutation of the second argument is more obvious than the refutation of the first. But the same logic can be applied to refute either one.

EDIT: Wow. Not ten minutes after I wrote this, I ran into this video, which contains the fallacy mentioned in this post. The video is well done, made by one of the few intelligent Creationists on YouTube. But it’s still wrong.