B Primes

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.

The Best Intelligent Design Article I've Ever Read

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.

You Know It Had a Designer

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.

A Common Type of Argument, and the Rebuttals

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?

The New Keyboard Layout Project (NKLP)

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.

Genetic Alterations and Cloning

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.

Wishbone

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.

YouTube Censorship

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