"If you post on usenet you put things in the public domain,..."
"Public domain" is a legal term that means not just that copies were given to the public but that rights were given to the public. Posting an article to Usenet is not putting it in the public domain.
"If you wrote a letter to
the NY times 20 years ago that was subsequently published it is still available in the archives today and there is nothing to be
done about it!"
Your letter to the Times is available to anybody who wants to look it up and make a copy for personal or other fair use. But if somebody started publishing copies, they would be violating the law.
"So you're running them through an external compressor..."
No, it is not external. The compressor and decompressor are written with an internal copy of the compressor known to be used by the person who generated the file.
"... your decompressor ONLY decompresses 'uncompressable'
files"
That is the point here. This thread is about how one might go about compressing files that had been generated by somebody who filtered out compression-resistant files.
"However, there should be no way for the decompressor to generate compression resistant files in order to enumerate them."
Generating files is easy. You just iterate through them: empty file, all the one-byte files (0x00, 0x01, 0x02,... 0xff), all the two-byte files (0x0000, 0x0001, 0x0002,... 0x00ff, 0x0100, 0x0101,... 0xffff), all the three-byte files (0x000000, 0x000001,...), et cetera. It would take a while, but time isn't the issue.
Of course, the decompressor wants to count compression-resistant files, but it does this by generating each file, as described above, and then running it through the compressor. If it does not come out smaller, it is compression-resistant.
I'll retract my previous comments. Trying to find a 1024-byte block of zeroes requires bits to record where the block is found, which consumes the potential savings. Whether counting compression-resistant files saves space depends on the choice of "compression-resistant."
Sorry, not so. The proportion of compression-resistant files necessarily decreases as file length increases. To see this, consider that if a file had a nice block of 1024 bytes of zeroes somewhere in it, we could easily write a simple program that wrote the bytes before that block, then 1024 bytes of zeroes, then the bytes after that block. This program would easily fit in less than 1024 bytes, plus the bytes before and after the block of zeroes. So such a file is compressible. I will show that the proportion of files that are not compressible like this decreases as file length increases.
To make this easy, I'll count for compressible files just the ones where a block of zeroes begins at a multiple of 1024 bytes from the beginning of a file. The chance that a single 1024-byte block (selected randomly from a uniform distribution) is not all zeroes is (2^8192-1)/2^8192, a very tiny bit less than one. The chance that all n blocks of n 1024-byte blocks are not zeroes is (2^8192-1)/2^8192)^n. Obviously this approaches zero as n increases. Thus the proportion of files that are not compressible decreases as file length increases. Pick a large enough length, and you are virtually guaranteed there is a 1024-byte block of zeroes in it somewhere.
When we open compression up to a wider range of techniques, the same effect occurs; the proportion of files that are not compressible under any given, reasonable technique decreases as file length increases. This makes Goldman's challenge a bad offer for him -- the fact that the average file size change must be positive under any compression technique in the limit does not mean the probability of a positive change in a randomly selected file is large enough to give him a positive return on the challenge.
"... this challenge where the
rules are 'compress this specific file which has been carefully generated to resist compression'."
It's not so easy to generate a file to resist compression. If you had and used a method for determining whether a file could resist compression, then I could compress your generated file simply by counting how many compression-resistant files preceded it in some sort order and writing that number as a binary file. Decompression would proceed by counting that number of compression-resistant files in the same order and writing the file found at the count.
Visualization and "understanding" are all well and good, but visualization and human thinking are prone to certain types of error. There is value in obtaining correct results without those errors, and the only certain way to do that is with rigidity and formalism. Therefore you must have something like Metamath in mathematics. Not for everyday use to be sure, but available when needed.
I don't see where it was suggested Metamath is for newbies, or for newbies to understand math. There are several ways in which something like Metamath can provide value to non-mathematicians. For one thing, they can use it to see that there are links from a theorem all the way down, even if they do not study all those links and comprehend them as a whole.
Some posters have commented that Metamath doesn't make math understandable. That isn't its purpose. You can make something completely verifiable without making it understandable -- and that is the only way to work with the largest structures. A demonstration that a large office building will not fall down depends upon ensuring that each structural component does its job, and a single person might actually check each and every component and thus know the building will not fall down, but that person could still end up not understanding the building as a whole.
While I would not recommend somebody learn C++ by studying the compiler's generated assembly language, I would recommend that an experienced expert in C++ learn more, from time to time, by experiencing the compiler's generated assembly language. I know that studying generated assembly code has occasionally provided a useful insight into the high-level langugage specification. Similarly, studying the details is a useful occasional part of a professional mathematician's experience.
Metamath can (or will be able to) answer questions that are difficult to answer otherwise -- What axioms does (a proof of) such-and-such a theorem use? Do we know of a proof that does not use a certain axiom?
Today's proofs are subject to errors. Occasionally an error slips by an author and the referees. Eventually, papers may be submitted with links to Metaware-verified proofs, essentially eliminating the possibility of error.
Further in the future, databases like Metaware will aid the construction of proofs by supplying already-proven lemmas, so the author does not have to expend time proving something already published or reviewing publications to find it.
Maple and Mathematica are useful tools for some mathematicians, but they are flawed because they have gaps. They sometimes offer deductions that are false, because they make unwarranted assumptions about domains or absences of singularities, or whatnot. E.g., some software engineer may have poured a table of integrals into the software but neglected to make Mathematica prove a table entry is applicable to a particular user's situation before applying the entry. We need something like Metamath that is complete to serve in those times when mathematical proof is desired.
While nobody travels every road that is connected to our highway system, a key characteristic of the system that makes it useful is that it is connected. Thus each user finds a route to their destination, even though they don't understand where every road leads to or comes from.
Casio used to make a watch with an orrery on it, the Cosmo Phase. I don't see it on their web pages now. The display provides a resolution of only 12 positions for each planet. Halley's Comet is shown too, and there's a list of solar eclipses.
Among its other features, you can advance or reverse the planetary motions to future and past dates by pressing a button. As you hold down the button, the motions speed up several steps, until the planets are whizzing around the solar system. Some engineer designed a funny behavior at this point -- if you let go of the button, the planets coast to a stop, as if there were real inertia and friction in the display.
Re:It will affect the wrong people
on
Hash Cash
·
· Score: 2
"I also think that the handshake has to occur on the individual's computer rather than at server level.
It is not clear to me what part of the process you mean. Is it the hash cash generation you mean should occur on the individual's computer (the sending computer) or is it the hash cash verification you mean should occur on the individual's computer (the receiving computer)?
If the former, yes, the calculations should occur on the originating computer or a computer the originator pays for the use of. If the latter, no, the calculations need not occur on the actual recipient's computer. They could occur on the recipient ISP's computer, and at little cost.
Hash cash essentially involves two functions, say MINT and VERIFY. MINT is expensive to compute. VERIFY is cheap. The sender must compute MINT(x), where x is something determined by the recipient -- x could be the recipient's email address, the recipient's email address concatenated with the current time, or a value provided by the recipient upon each request. Note that the former two do not involve a handshake (after initial publication of the specification of x); there does not have to be any exchange, just a one-way transmission. Calculating MINT(x) is expensive, and this is the "hash cash" that the spender is providing.
VERIFICATION is cheap. VERIFICATION(y) returns true or false according to whether y is MINT(x) or not. VERIFICATION is very cheap, cheap enough that ISPs shouldn't mind computing it.
This scheme does not shift the cost of spam to the recipient's ISP. The spammer has to compute a great many very expensive MINT functions. The ISP only has to compute cheap VERIFICATION functions on actually received email -- and the number of email messages received will decrease since this scheme will make spam unprofitable and hence decrease it, so there can be a net saving to the ISP.
Re:It will affect the wrong people
on
Hash Cash
·
· Score: 3
"The next time that happens, y.com's SMTP sees
that there's already been a correspondence, and therefore does not challenge it."
No, it doesn't say that. It only suggests remembering approved mailing list senders. Although a recipient would be free to remember other senders if they wish and offer those senders postage-free receipt. And your calculation of an N^2 bit array is excessive. The N^2 function is extremely sparse. If you communicate with one new person with a 30-character email address per day for your entire life, you need less than a megabyte of memory.
But this still doesn't acknowledge the flexibility of hash cash postage, and it need not impose any burden on the relayers, except to relay the data. I don't see it spelled out on the linked-to page, but there are a variety of ways to implement this. A recipient might merely require that the sender send hash cash that is a function of the recipient's email address. The sender computes it and puts it in the email. The SMTP relays do no computation. The sender can reuse the hash cash since it is an unchanging function of destination address. Each sender has to compute the hash once -- unwieldy for spammers, easy for normal correspondents.
Another implementation could require the sender to send hash cash that is a function of the recipient's email address and the current time. (The sender would send plaintext of the actual time they used, and the recipient would require that be a reasonable approximation of the time the mail was actually sent, estimated from its receipt.) Then each sender would have to spend hash cash each time they transmitted.
"That is, if you ignore the very first sentence in the TOS:"
A person who does not agree to the terms of service is perfectly free to ignore the first sentence of the terms of service, since no sentence in the terms of service is binding on a person who does not agree to the terms of service.
Furthermore, Google does not even ask you to agree to the terms of service as a condition of using their service. I just visited www.google.com and did a search and did not see anything asking me to agree to anything or even a link to their terms of service or other legal information.
So why would you think that a sentence written somewhere is binding upon somebody who perhaps never saw it, never agreed to it, and was never asked to agree to it? What is the rule you are using -- 'Anything a big company writes is law'?
Your comments are consistent with a misintepretation of the question. Specifically, your comments appear consistent with an attempt to demonstrate how the algorithm described in the New York Times article yields a 75% probability of success. However, the question addressed here has been a different problem. The question in this thread is, if you see two hats of the same color, what is the probability your hat is the same color?
That probability is indeed 1/2.
Perhaps you would like to reconsider your assertions that others were in error.
The cases in which you see two hats of the same color are RR-R, RR-B, BB-R, and BB-B, where the last color in each case is your own hat. These cases have equal probability of occurring. The frequency with which your hat is the same color is 1/2 of these equally probable cases, and so the probability is 1/2.
So, the answer to the question "If you see two hats of the same color, what is the probability your hat is the same color?" is 1/2.
However, the answer to the question "If (at least) two hats are the same color, what is the probability all hats are the same color?", the probability is 1/4.
This is because the equally probable cases in which two hats are the same color (as is always the case of course) are RRR, RRB, RBR, RBB, BRR, BRB, BBR, and BBB. Of those, the proportion that have all three the same color is 1/4, and hence the probability is 1/4.
"... existed for no apparent reason.... 'God did it' becomes the best explanation?
Sigh, I should know pointing out the obvious will accomplish little, but "God did it" does not solve the problem you pose. "God did it" does not explain why something exists for no apparent reason, since then you have God existing for no apparent reason.
Baloney. Fear of death does not "make us human." Other animals also fear death, to the extent they understand it, and some do. "Fear of death" is a normal evolutionary development to any species, not just humans, since such a fear naturally has survival benefits. If anything, it is consciousness that makes us human, and that's turning out not to be such a fancy trick as once thought.
"... soon the wonder would fade..."
Science and mathematics show no sign of slowing down and running out of wonders. Nor does the production of entertainment. There will be new experiences to have and new thoughts to think for thousands of years, at least.
"... fear would set in..."
A few individuals might develop pathologies, but most people would not. Already, most people have a poor grasp on things more than a few years in the future. The value they place on future benefits compared to present benefits (as shown in saving money versus spending, eating poorly versus maintaining health, et cetera) shows they do not highly value future benefits. Would the prospect of an infinite future change this? Not really. If a benefit a year from now is worth only 90% of the same benefit today, then the sum of an infinite stream of benefits is worth only ten times the value of the benefit today. An infinite future has a finite value, and hence is only worth a finite amount of effort to protect.
In other words, emotionally people are willing to trade off future benefits for current benefits, and rationally that is the right choice for an appropriate return rate. It would not be reasonable to forego all of today's benefits in exchange for an infinite lifetime if the infinite lifetime contained no benefits. Nor would it be reasonable to take great risks today since they would jeopardize an infinite lifetime of some benefits. Emotionally and logically, the optimal course would be some intermediate path, taking reasonable risks for reasonable pleasures.
"Bit" is the standard unit of memory used by hardware-oriented folks. "Byte" is for software folks, after the memory has been nicely packaged into eight-bit bytes (which was not always the case), error corrected, and so on.
Back when the government first passed laws requiring motorcyclists to wear helmets, I heard about people wearing the helmets on their knees. This bill mandates provision of software that automatically blocks or screens indecent material. It doesn't say anything about necessarily letting anything through. Seems to me an off-button, or equivalent software, satisfies the requirement.
It was more amusing when NASA got entry visas from the US Immigration and Naturalization service to bring back two aliens from space.
Cosmonauts Vladimir Dezurov and Grennady Strekalov were launched from Kazakstan to Mir and destined to land in the United States via Space Shuttle Atlantis.
"The only person who can sign for it is the congressman,..."
Anybody can sign for a certified letter. For an additional fee, around $5, you can send it "restricted delivery." Then only the addressee or their registered agent can sign for it.
Of course, your representative is supposed to live in your district, and their address is public record. If you really want to be sure they get the message, go knock on their door.
"Sure, it does document the legal case, but is there a way to actually find what you did?"
Intel investigative report lays it out pretty well, along with notes from police interrogation. Those appear to tell us he cracked passwords that he should not have and he ran a program on Intel computers that enabled him to access the computers from outside Intel, which he had been previously caught doing and instructed to stop. I don't see what he's complaining about; he committed crimes and was punished proportionately.
"As a molecular biologist . . . . Sure, you let out your
engineered moths, they have sterile offspring, . .."
I am surprised a molecular biologist misunderstood this aspect of the project. Quoting from the article:
the "Terminator"... that is sterile...
That is, the moths to be released do not have offspring. They are sterile, at least by design. Nor does anything in the article suggest the entire population of moths will be eliminated, so what makes you think this would be anything more than local control, just as pesticide is? Maybe this approach is even more controlled. Some pesticides leave resides around for a long time. These moths will die out in one moth lifetime.
"These stats help advertisers market products to you more efficently... So my question
is, why do you care?"
I don't want to be marketed to "efficiently." It is efficient for them, not me. I want to make reasoned, informed choices. Marketing statistics don't provide that to me. They help marketers increased emotional choices based on puffery, at best. I am as analytic as they come, but I can't be on guard all the time. Even if I could, the noise from "marketing" drowns out the signal of useful information about quality products.
"... once the judgement has been reached by due process in a court of law then the judge is allowed to
be predjudiced..."
It is impossible to be prejudiced after a trial. That's postjudice. Seriously, much of our society has come to view almost any opinion as "prejudice." That term is not appropriate for informed, reasoned opinion.
Slashdot Mirror
"If you post on usenet you put things in the public domain, ..."
"Public domain" is a legal term that means not just that copies were given to the public but that rights were given to the public. Posting an article to Usenet is not putting it in the public domain.
"If you wrote a letter to the NY times 20 years ago that was subsequently published it is still available in the archives today and there is nothing to be done about it!"
Your letter to the Times is available to anybody who wants to look it up and make a copy for personal or other fair use. But if somebody started publishing copies, they would be violating the law.
"So you're running them through an external compressor ..."
No, it is not external. The compressor and decompressor are written with an internal copy of the compressor known to be used by the person who generated the file.
"... your decompressor ONLY decompresses 'uncompressable' files"
That is the point here. This thread is about how one might go about compressing files that had been generated by somebody who filtered out compression-resistant files.
"However, there should be no way for the decompressor to generate compression resistant files in order to enumerate them."
Generating files is easy. You just iterate through them: empty file, all the one-byte files (0x00, 0x01, 0x02, ... 0xff), all the two-byte files (0x0000, 0x0001, 0x0002, ... 0x00ff, 0x0100, 0x0101, ... 0xffff), all the three-byte files (0x000000, 0x000001, ...), et cetera. It would take a while, but time isn't the issue.
Of course, the decompressor wants to count compression-resistant files, but it does this by generating each file, as described above, and then running it through the compressor. If it does not come out smaller, it is compression-resistant.
I'll retract my previous comments. Trying to find a 1024-byte block of zeroes requires bits to record where the block is found, which consumes the potential savings. Whether counting compression-resistant files saves space depends on the choice of "compression-resistant."
"Since this is not the case, ..."
Sorry, not so. The proportion of compression-resistant files necessarily decreases as file length increases. To see this, consider that if a file had a nice block of 1024 bytes of zeroes somewhere in it, we could easily write a simple program that wrote the bytes before that block, then 1024 bytes of zeroes, then the bytes after that block. This program would easily fit in less than 1024 bytes, plus the bytes before and after the block of zeroes. So such a file is compressible. I will show that the proportion of files that are not compressible like this decreases as file length increases.
To make this easy, I'll count for compressible files just the ones where a block of zeroes begins at a multiple of 1024 bytes from the beginning of a file. The chance that a single 1024-byte block (selected randomly from a uniform distribution) is not all zeroes is (2^8192-1)/2^8192, a very tiny bit less than one. The chance that all n blocks of n 1024-byte blocks are not zeroes is (2^8192-1)/2^8192)^n. Obviously this approaches zero as n increases. Thus the proportion of files that are not compressible decreases as file length increases. Pick a large enough length, and you are virtually guaranteed there is a 1024-byte block of zeroes in it somewhere.
When we open compression up to a wider range of techniques, the same effect occurs; the proportion of files that are not compressible under any given, reasonable technique decreases as file length increases. This makes Goldman's challenge a bad offer for him -- the fact that the average file size change must be positive under any compression technique in the limit does not mean the probability of a positive change in a randomly selected file is large enough to give him a positive return on the challenge.
"... this challenge where the rules are 'compress this specific file which has been carefully generated to resist compression'."
It's not so easy to generate a file to resist compression. If you had and used a method for determining whether a file could resist compression, then I could compress your generated file simply by counting how many compression-resistant files preceded it in some sort order and writing that number as a binary file. Decompression would proceed by counting that number of compression-resistant files in the same order and writing the file found at the count.
Visualization and "understanding" are all well and good, but visualization and human thinking are prone to certain types of error. There is value in obtaining correct results without those errors, and the only certain way to do that is with rigidity and formalism. Therefore you must have something like Metamath in mathematics. Not for everyday use to be sure, but available when needed.
Replying to various comments here:
I don't see where it was suggested Metamath is for newbies, or for newbies to understand math. There are several ways in which something like Metamath can provide value to non-mathematicians. For one thing, they can use it to see that there are links from a theorem all the way down, even if they do not study all those links and comprehend them as a whole.
Some posters have commented that Metamath doesn't make math understandable. That isn't its purpose. You can make something completely verifiable without making it understandable -- and that is the only way to work with the largest structures. A demonstration that a large office building will not fall down depends upon ensuring that each structural component does its job, and a single person might actually check each and every component and thus know the building will not fall down, but that person could still end up not understanding the building as a whole.
While I would not recommend somebody learn C++ by studying the compiler's generated assembly language, I would recommend that an experienced expert in C++ learn more, from time to time, by experiencing the compiler's generated assembly language. I know that studying generated assembly code has occasionally provided a useful insight into the high-level langugage specification. Similarly, studying the details is a useful occasional part of a professional mathematician's experience.
Metamath can (or will be able to) answer questions that are difficult to answer otherwise -- What axioms does (a proof of) such-and-such a theorem use? Do we know of a proof that does not use a certain axiom?
Today's proofs are subject to errors. Occasionally an error slips by an author and the referees. Eventually, papers may be submitted with links to Metaware-verified proofs, essentially eliminating the possibility of error.
Further in the future, databases like Metaware will aid the construction of proofs by supplying already-proven lemmas, so the author does not have to expend time proving something already published or reviewing publications to find it.
Maple and Mathematica are useful tools for some mathematicians, but they are flawed because they have gaps. They sometimes offer deductions that are false, because they make unwarranted assumptions about domains or absences of singularities, or whatnot. E.g., some software engineer may have poured a table of integrals into the software but neglected to make Mathematica prove a table entry is applicable to a particular user's situation before applying the entry. We need something like Metamath that is complete to serve in those times when mathematical proof is desired.
While nobody travels every road that is connected to our highway system, a key characteristic of the system that makes it useful is that it is connected. Thus each user finds a route to their destination, even though they don't understand where every road leads to or comes from.
Casio used to make a watch with an orrery on it, the Cosmo Phase. I don't see it on their web pages now. The display provides a resolution of only 12 positions for each planet. Halley's Comet is shown too, and there's a list of solar eclipses.
Among its other features, you can advance or reverse the planetary motions to future and past dates by pressing a button. As you hold down the button, the motions speed up several steps, until the planets are whizzing around the solar system. Some engineer designed a funny behavior at this point -- if you let go of the button, the planets coast to a stop, as if there were real inertia and friction in the display.
"I also think that the handshake has to occur on the individual's computer rather than at server level.
It is not clear to me what part of the process you mean. Is it the hash cash generation you mean should occur on the individual's computer (the sending computer) or is it the hash cash verification you mean should occur on the individual's computer (the receiving computer)?
If the former, yes, the calculations should occur on the originating computer or a computer the originator pays for the use of. If the latter, no, the calculations need not occur on the actual recipient's computer. They could occur on the recipient ISP's computer, and at little cost.
Hash cash essentially involves two functions, say MINT and VERIFY. MINT is expensive to compute. VERIFY is cheap. The sender must compute MINT(x), where x is something determined by the recipient -- x could be the recipient's email address, the recipient's email address concatenated with the current time, or a value provided by the recipient upon each request. Note that the former two do not involve a handshake (after initial publication of the specification of x); there does not have to be any exchange, just a one-way transmission. Calculating MINT(x) is expensive, and this is the "hash cash" that the spender is providing.
VERIFICATION is cheap. VERIFICATION(y) returns true or false according to whether y is MINT(x) or not. VERIFICATION is very cheap, cheap enough that ISPs shouldn't mind computing it.
This scheme does not shift the cost of spam to the recipient's ISP. The spammer has to compute a great many very expensive MINT functions. The ISP only has to compute cheap VERIFICATION functions on actually received email -- and the number of email messages received will decrease since this scheme will make spam unprofitable and hence decrease it, so there can be a net saving to the ISP.
"The next time that happens, y.com's SMTP sees that there's already been a correspondence, and therefore does not challenge it."
No, it doesn't say that. It only suggests remembering approved mailing list senders. Although a recipient would be free to remember other senders if they wish and offer those senders postage-free receipt. And your calculation of an N^2 bit array is excessive. The N^2 function is extremely sparse. If you communicate with one new person with a 30-character email address per day for your entire life, you need less than a megabyte of memory.
But this still doesn't acknowledge the flexibility of hash cash postage, and it need not impose any burden on the relayers, except to relay the data. I don't see it spelled out on the linked-to page, but there are a variety of ways to implement this. A recipient might merely require that the sender send hash cash that is a function of the recipient's email address. The sender computes it and puts it in the email. The SMTP relays do no computation. The sender can reuse the hash cash since it is an unchanging function of destination address. Each sender has to compute the hash once -- unwieldy for spammers, easy for normal correspondents.
Another implementation could require the sender to send hash cash that is a function of the recipient's email address and the current time. (The sender would send plaintext of the actual time they used, and the recipient would require that be a reasonable approximation of the time the mail was actually sent, estimated from its receipt.) Then each sender would have to spend hash cash each time they transmitted.
"That is, if you ignore the very first sentence in the TOS:"
A person who does not agree to the terms of service is perfectly free to ignore the first sentence of the terms of service, since no sentence in the terms of service is binding on a person who does not agree to the terms of service.
Furthermore, Google does not even ask you to agree to the terms of service as a condition of using their service. I just visited www.google.com and did a search and did not see anything asking me to agree to anything or even a link to their terms of service or other legal information.
So why would you think that a sentence written somewhere is binding upon somebody who perhaps never saw it, never agreed to it, and was never asked to agree to it? What is the rule you are using -- 'Anything a big company writes is law'?
Your comments are consistent with a misintepretation of the question. Specifically, your comments appear consistent with an attempt to demonstrate how the algorithm described in the New York Times article yields a 75% probability of success. However, the question addressed here has been a different problem. The question in this thread is, if you see two hats of the same color, what is the probability your hat is the same color?
That probability is indeed 1/2.
Perhaps you would like to reconsider your assertions that others were in error.
"It's 0.75."
The cases in which you see two hats of the same color are RR-R, RR-B, BB-R, and BB-B, where the last color in each case is your own hat. These cases have equal probability of occurring. The frequency with which your hat is the same color is 1/2 of these equally probable cases, and so the probability is 1/2.
So, the answer to the question "If you see two hats of the same color, what is the probability your hat is the same color?" is 1/2.
However, the answer to the question "If (at least) two hats are the same color, what is the probability all hats are the same color?", the probability is 1/4.
This is because the equally probable cases in which two hats are the same color (as is always the case of course) are RRR, RRB, RBR, RBB, BRR, BRB, BBR, and BBB. Of those, the proportion that have all three the same color is 1/4, and hence the probability is 1/4.
"... existed for no apparent reason .... 'God did it' becomes the best explanation?
Sigh, I should know pointing out the obvious will accomplish little, but "God did it" does not solve the problem you pose. "God did it" does not explain why something exists for no apparent reason, since then you have God existing for no apparent reason.
Science is finding out the reasons. Be patient.
This Slashdot story reminds me of the restaurants nobody goes to because they are too crowded.
"... this part of what makes us human."
Baloney. Fear of death does not "make us human." Other animals also fear death, to the extent they understand it, and some do. "Fear of death" is a normal evolutionary development to any species, not just humans, since such a fear naturally has survival benefits. If anything, it is consciousness that makes us human, and that's turning out not to be such a fancy trick as once thought.
"... soon the wonder would fade ..."
Science and mathematics show no sign of slowing down and running out of wonders. Nor does the production of entertainment. There will be new experiences to have and new thoughts to think for thousands of years, at least.
"... fear would set in ..."
A few individuals might develop pathologies, but most people would not. Already, most people have a poor grasp on things more than a few years in the future. The value they place on future benefits compared to present benefits (as shown in saving money versus spending, eating poorly versus maintaining health, et cetera) shows they do not highly value future benefits. Would the prospect of an infinite future change this? Not really. If a benefit a year from now is worth only 90% of the same benefit today, then the sum of an infinite stream of benefits is worth only ten times the value of the benefit today. An infinite future has a finite value, and hence is only worth a finite amount of effort to protect.
In other words, emotionally people are willing to trade off future benefits for current benefits, and rationally that is the right choice for an appropriate return rate. It would not be reasonable to forego all of today's benefits in exchange for an infinite lifetime if the infinite lifetime contained no benefits. Nor would it be reasonable to take great risks today since they would jeopardize an infinite lifetime of some benefits. Emotionally and logically, the optimal course would be some intermediate path, taking reasonable risks for reasonable pleasures.
"What is this 'gigabits of RAM' crap?
"Bit" is the standard unit of memory used by hardware-oriented folks. "Byte" is for software folks, after the memory has been nicely packaged into eight-bit bytes (which was not always the case), error corrected, and so on.
Back when the government first passed laws requiring motorcyclists to wear helmets, I heard about people wearing the helmets on their knees. This bill mandates provision of software that automatically blocks or screens indecent material. It doesn't say anything about necessarily letting anything through. Seems to me an off-button, or equivalent software, satisfies the requirement.
It was more amusing when NASA got entry visas from the US Immigration and Naturalization service to bring back two aliens from space.
Cosmonauts Vladimir Dezurov and Grennady Strekalov were launched from Kazakstan to Mir and destined to land in the United States via Space Shuttle Atlantis.
"The only person who can sign for it is the congressman, ..."
Anybody can sign for a certified letter. For an additional fee, around $5, you can send it "restricted delivery." Then only the addressee or their registered agent can sign for it.
Of course, your representative is supposed to live in your district, and their address is public record. If you really want to be sure they get the message, go knock on their door.
"Sure, it does document the legal case, but is there a way to actually find what you did?"
Intel investigative report lays it out pretty well, along with notes from police interrogation. Those appear to tell us he cracked passwords that he should not have and he ran a program on Intel computers that enabled him to access the computers from outside Intel, which he had been previously caught doing and instructed to stop. I don't see what he's complaining about; he committed crimes and was punished proportionately.
"As a molecular biologist . . . . Sure, you let out your engineered moths, they have sterile offspring, . . ."
I am surprised a molecular biologist misunderstood this aspect of the project. Quoting from the article:
That is, the moths to be released do not have offspring. They are sterile, at least by design. Nor does anything in the article suggest the entire population of moths will be eliminated, so what makes you think this would be anything more than local control, just as pesticide is? Maybe this approach is even more controlled. Some pesticides leave resides around for a long time. These moths will die out in one moth lifetime.
"These stats help advertisers market products to you more efficently... So my question is, why do you care?"
I don't want to be marketed to "efficiently." It is efficient for them, not me. I want to make reasoned, informed choices. Marketing statistics don't provide that to me. They help marketers increased emotional choices based on puffery, at best. I am as analytic as they come, but I can't be on guard all the time. Even if I could, the noise from "marketing" drowns out the signal of useful information about quality products.
"... once the judgement has been reached by due process in a court of law then the judge is allowed to be predjudiced ..."
It is impossible to be prejudiced after a trial. That's postjudice. Seriously, much of our society has come to view almost any opinion as "prejudice." That term is not appropriate for informed, reasoned opinion.