Converting Pi to binary: DON'T DO IT!
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Daniel Pfeffer wrote:
... the not-yet-released Pearl Harbor movie ...
Unless they're making another one, that dates this message to May 2001 or earlier. :-D
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
I never said it was new; I just found it funny (but accurate...)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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[The RISKS Digest Volume 21 Issue 42](http://catless.ncl.ac.uk/Risks/21.42.html#subj5.1) Converting Pi to binary: DON'T DO IT! (via Russ Perry Jr.) <"Keith F. Lynch" kfl@KeithLynch.net> [not included] Newsgroup: alt.math.recreational WARNING: Do NOT calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains ALL finite bit strings. If you compute it, you will be guilty of: • Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code) • Trademark infringement • Possession of child pornography • Espionage (unauthorized possession of top secret information) • Possession of DVD-cracking software • Possession of threats to the President • Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords • Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie. • Defaming Scientology. Which IS illegal — just ask Keith Henson. Also, your computer will contain all of the nastiest known computer viruses. In fact, all of the nastiest POSSIBLE computer viruses. Some of the files on my PC are intensely personal, and I for one don't want you snooping through a copy of them. You might get away with computing just a few digits, but why risk it? There's no telling how far into Pi you can go without finding the secret documents about the JFK assassination, a photograph of your neighbor's six year old daughter doing the nasty with the family dog, or a complete copy of the not-yet-released Pearl Harbor movie. So just don't do it. The same warning applies to e, the square root of 2, Euler's constant, Phi, the cosine of any non-zero algebraic number, and the vast majority of all other real numbers. There's a reason why these numbers are always computed and shown in decimal, after all.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
:omg:
Jeremy Falcon
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:omg:
Jeremy Falcon
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:omg:
Jeremy Falcon
No, but the better jokes have been migrated.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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Daniel Pfeffer wrote:
God might equally have said ...
They are in pi somewhere, so he only had to make one statement. God being concise and all...
Our Forgotten Astronomy | Object Oriented Programming with C++ | Wordle solver
Not necessarily. The conjecture is that all finite strings may be found somewhere in Pi; infinite strings are not (and cannot) all be included in Pi. My argument is that assuming we have one infinite string starting at position p1 and another infinite string starting at position p2 > p1, then the second string must be a subset of the first. As not all infinitely long strings can be ordered as substrings, not all infinitely long strings can appear in Pi. For example, 01(01) repeating is not a substring of 001(001) repeating.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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[The RISKS Digest Volume 21 Issue 42](http://catless.ncl.ac.uk/Risks/21.42.html#subj5.1) Converting Pi to binary: DON'T DO IT! (via Russ Perry Jr.) <"Keith F. Lynch" kfl@KeithLynch.net> [not included] Newsgroup: alt.math.recreational WARNING: Do NOT calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains ALL finite bit strings. If you compute it, you will be guilty of: • Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code) • Trademark infringement • Possession of child pornography • Espionage (unauthorized possession of top secret information) • Possession of DVD-cracking software • Possession of threats to the President • Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords • Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie. • Defaming Scientology. Which IS illegal — just ask Keith Henson. Also, your computer will contain all of the nastiest known computer viruses. In fact, all of the nastiest POSSIBLE computer viruses. Some of the files on my PC are intensely personal, and I for one don't want you snooping through a copy of them. You might get away with computing just a few digits, but why risk it? There's no telling how far into Pi you can go without finding the secret documents about the JFK assassination, a photograph of your neighbor's six year old daughter doing the nasty with the family dog, or a complete copy of the not-yet-released Pearl Harbor movie. So just don't do it. The same warning applies to e, the square root of 2, Euler's constant, Phi, the cosine of any non-zero algebraic number, and the vast majority of all other real numbers. There's a reason why these numbers are always computed and shown in decimal, after all.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Not according to IEEE 754 :p
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Not according to IEEE 754 :p
IEEE 754 deals with finite-precision floating-point numbers, so Pi cannot be exactly represented in a manner compatible with it. :-\
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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IEEE 754 deals with finite-precision floating-point numbers, so Pi cannot be exactly represented in a manner compatible with it. :-\
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
I've studied physics and there, we got methods to get right answers from values with finite precision B)
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I've studied physics and there, we got methods to get right answers from values with finite precision B)
Member 9167057 wrote:
've studied physics
By a strange coincidence, so did I. I also studied Numerical Analysis. The issue here is that Pi cannot be represented to adequate accuracy using IEEE 754 types. This has implications for argument reduction, e.g. for the trigonometrical functions. If the closest representation of Pi in IEEE 754 is Pi+dPi, the argument reduction for a value x will calculate x' = x - 2 * N * (Pi + dPi), giving a reduced argument that is in error by at least 2 * N * dPi. This can be significant even for small values of N, e.g. around the zeroes of a function. It is possible that not even the sign of the calculated result is correct! Some mitigations are possible, e.g. representing Pi as a sum of a few parts, but for large N the only fix is to use a highly precise form of Pi. I enclose a link to an article that discusses this issue in more detail than most people will ever need... [https://redirect.cs.umbc.edu/~phatak/645/supl/Ng-ArgReduction.pdf\](https://redirect.cs.umbc.edu/~phatak/645/supl/Ng-ArgReduction.pdf)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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[The RISKS Digest Volume 21 Issue 42](http://catless.ncl.ac.uk/Risks/21.42.html#subj5.1) Converting Pi to binary: DON'T DO IT! (via Russ Perry Jr.) <"Keith F. Lynch" kfl@KeithLynch.net> [not included] Newsgroup: alt.math.recreational WARNING: Do NOT calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains ALL finite bit strings. If you compute it, you will be guilty of: • Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code) • Trademark infringement • Possession of child pornography • Espionage (unauthorized possession of top secret information) • Possession of DVD-cracking software • Possession of threats to the President • Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords • Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie. • Defaming Scientology. Which IS illegal — just ask Keith Henson. Also, your computer will contain all of the nastiest known computer viruses. In fact, all of the nastiest POSSIBLE computer viruses. Some of the files on my PC are intensely personal, and I for one don't want you snooping through a copy of them. You might get away with computing just a few digits, but why risk it? There's no telling how far into Pi you can go without finding the secret documents about the JFK assassination, a photograph of your neighbor's six year old daughter doing the nasty with the family dog, or a complete copy of the not-yet-released Pearl Harbor movie. So just don't do it. The same warning applies to e, the square root of 2, Euler's constant, Phi, the cosine of any non-zero algebraic number, and the vast majority of all other real numbers. There's a reason why these numbers are always computed and shown in decimal, after all.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Actually all copyrights, trademarks, and patents would be invalid, as pi existed since the Big Bang (if not earlier) thus rendering all IP unoriginal. You're still screwed on the malware and defaming scientology fronts though.
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Member 9167057 wrote:
've studied physics
By a strange coincidence, so did I. I also studied Numerical Analysis. The issue here is that Pi cannot be represented to adequate accuracy using IEEE 754 types. This has implications for argument reduction, e.g. for the trigonometrical functions. If the closest representation of Pi in IEEE 754 is Pi+dPi, the argument reduction for a value x will calculate x' = x - 2 * N * (Pi + dPi), giving a reduced argument that is in error by at least 2 * N * dPi. This can be significant even for small values of N, e.g. around the zeroes of a function. It is possible that not even the sign of the calculated result is correct! Some mitigations are possible, e.g. representing Pi as a sum of a few parts, but for large N the only fix is to use a highly precise form of Pi. I enclose a link to an article that discusses this issue in more detail than most people will ever need... [https://redirect.cs.umbc.edu/~phatak/645/supl/Ng-ArgReduction.pdf\](https://redirect.cs.umbc.edu/~phatak/645/supl/Ng-ArgReduction.pdf)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
I'm perfectly aware of the fact that IEE 754 ROUNDS floats as you can't, for obvious reasons, represent them exactly. However, if we really want to hammer details here, how would you represent Pi in binary EXACTLY? The most obvious approach would be a classical LongInt: that is a number array with each number representing a digit. But the Pi digits we're talking about are decimal so now we don't get every possible piece of binary data! Well, sure, you could calculate & represent Pi as hexadecimal digits but what's with the underlying computing system? RAM is, generally, organized in pages (on a system you would calculate Pi anyway and I sure as hell wouldn't do this on an MCU with a raw memory model) and you don't know how those pages are laid out, you don't even know if you can fill those pages! My point is, if you really don't want to take this with a wink, if you really want to go into the details in a pedantic manner, the statement in the OP isn't nearly as clear as if you take the basic idea and run with it. I'm somewhere between a physicist and a software engineer, not only do I need pedantry in my job, I love it! Well, I don't technically need it, I got co-workers proving day after day that you don't need discipline, that clearing up the mess arising from handwaving important details but I'd rather pour effort into fun parts of the job and clearing up a mess I've let lying around isn't fun. However, this is the lounge here, not a specification meeting, and the OP got a fantastic idea in theory. So I'm treating this one with a wink. Without winks, arbitrary precision doesn't make sense. Without winks, you need a precision up to a fixed point. This point depends on the use case, of course, but there's still a finite point to which we need numbers to be precise. Including measurement results, including Pi. So if you really want to get into the practical implications of all this, then Pi is effectively finite.
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Actually all copyrights, trademarks, and patents would be invalid, as pi existed since the Big Bang (if not earlier) thus rendering all IP unoriginal. You're still screwed on the malware and defaming scientology fronts though.
Peter Moore - Chicago wrote:
Actually all copyrights, trademarks, and patents would be invalid, as pi existed since the Big Bang (if not earlier) thus rendering all IP unoriginal.
I beg to differ. Pi has existed as a concept, but it is the expression of the idea that is subject to copyright. One cannot claim copyright just because one has defined a generating function for a book; one must actually write the book.
Peter Moore - Chicago wrote:
You're still screwed on the malware and defaming scientology fronts though.
Wouldn't the defamation of {Paganism, Judaism, Christianity, Islam, Taoism, Hinduism, Scientology, ...} (the order is more-or-less chronological) be countered by the equally present works in support of said religions? :-\
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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Peter Moore - Chicago wrote:
Actually all copyrights, trademarks, and patents would be invalid, as pi existed since the Big Bang (if not earlier) thus rendering all IP unoriginal.
I beg to differ. Pi has existed as a concept, but it is the expression of the idea that is subject to copyright. One cannot claim copyright just because one has defined a generating function for a book; one must actually write the book.
Peter Moore - Chicago wrote:
You're still screwed on the malware and defaming scientology fronts though.
Wouldn't the defamation of {Paganism, Judaism, Christianity, Islam, Taoism, Hinduism, Scientology, ...} (the order is more-or-less chronological) be countered by the equally present works in support of said religions? :-\
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Daniel Pfeffer wrote:
I beg to differ. Pi has existed as a concept, but it is the expression of the idea that is subject to copyright. One cannot claim copyright just because one has defined a generating function for a book; one must actually write the book.
You make it seem as if a concepts must be expressed as a physical text (a digit sequence considered to be text) to be copyrightable. If I tell a story, one that could be a short story or novel, without writing it down, is this story not copyrightable because it only exists as a concept between every time I tell it? If you write my story down, could you claim copyright on it, because you were the one to write it down? Could pi be physically expressed in a non-textual form? E.g. can the relationship between the circumference and the diameter of a circle be expressed graphically? Would you say that a graphical expression of pi still is just "a concept"? We saw a related issue fifty years ago: Ritchie's patent on the setUID mechanism of Unix. His first application specified the mechanism in c code, but software patents were not accepted at the time; they were viewed something like "just a concept". So for the patent application, he had to design an electronic circuit realizing the same logical operation as his source code; that was accepted for the patent. I don't know if the circuit was ever built (I guess lots of soldering iron guys have done so, 'just for the fun of it'), but it was not required for the patent application; a schematic was enough. Graphics was OK, a textual rendition of the logic was not. I certainly know that saying software patents could have some merit is extremely non-PC in most programmer environments. Yet, the setUID circuit makes a fascinating philosophical question. Should we reject the setUID circuit because we reject software patents and the logic of the circuit can easily be expressed in software? Or, are we willing to accept any software patent as long as it is - for the sake of the patent application - expressed as a circuit? (And satisfy other reasonable newness and invention height requirements) Or is a software patent acceptable as long as is can be expressed as a circuit, even if it in the patent application appears as source code? There are nuances between patents and copyrighted works; those are inessential for the philosophical question of when a "concept" turns into something that can be protected. The setUID patent expired long ag
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Daniel Pfeffer wrote:
I beg to differ. Pi has existed as a concept, but it is the expression of the idea that is subject to copyright. One cannot claim copyright just because one has defined a generating function for a book; one must actually write the book.
You make it seem as if a concepts must be expressed as a physical text (a digit sequence considered to be text) to be copyrightable. If I tell a story, one that could be a short story or novel, without writing it down, is this story not copyrightable because it only exists as a concept between every time I tell it? If you write my story down, could you claim copyright on it, because you were the one to write it down? Could pi be physically expressed in a non-textual form? E.g. can the relationship between the circumference and the diameter of a circle be expressed graphically? Would you say that a graphical expression of pi still is just "a concept"? We saw a related issue fifty years ago: Ritchie's patent on the setUID mechanism of Unix. His first application specified the mechanism in c code, but software patents were not accepted at the time; they were viewed something like "just a concept". So for the patent application, he had to design an electronic circuit realizing the same logical operation as his source code; that was accepted for the patent. I don't know if the circuit was ever built (I guess lots of soldering iron guys have done so, 'just for the fun of it'), but it was not required for the patent application; a schematic was enough. Graphics was OK, a textual rendition of the logic was not. I certainly know that saying software patents could have some merit is extremely non-PC in most programmer environments. Yet, the setUID circuit makes a fascinating philosophical question. Should we reject the setUID circuit because we reject software patents and the logic of the circuit can easily be expressed in software? Or, are we willing to accept any software patent as long as it is - for the sake of the patent application - expressed as a circuit? (And satisfy other reasonable newness and invention height requirements) Or is a software patent acceptable as long as is can be expressed as a circuit, even if it in the patent application appears as source code? There are nuances between patents and copyrighted works; those are inessential for the philosophical question of when a "concept" turns into something that can be protected. The setUID patent expired long ag
trønderen wrote:
You make it seem as if a concepts must be expressed as a physical text (a digit sequence considered to be text) to be copyrightable.
Pi is a description of a generating function that can produce any and all finite texts; it is not the text itself. A physical analogy might be between a printing press and a copy of a book. Possession of a printing press does not constitute copyright violation.
trønderen wrote:
I certainly know that saying software patents could have some merit is extremely non-PC in most programmer environments. ...
I take the unpopular view that any description of a "new and non-obvious" mechanism - whether in software, hardware, a detailed description of an algorithm, or a detailed blueprint - should be patentable. The effort to develop a new algorithm is, in many cases, considerable, and there is no reason why this effort should not be encouraged and rewarded. My problem with software patents is that the patent offices are generally not well equipped to determine what is "new and non-obvious" in software. This has led to absurdities such as a patent on XORing a cursor on to a screen, the issue being that this was so obvious to a professional programmer that no one bothered documenting it. IIRC, the patent was eventually revoked because it was shown to have been used in software that predated the patent application.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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I beg to differ; the matter in the visible Universe appears to be finite, but we don't know how large the Universe (visible and non-visible) is. There is good evidence that it is much larger than that, and could be infinite in size. [If the universe is only 14 billion years old, how can it be 92 billion light years wide? - YouTube](https://www.youtube.com/watch?v=vIJTwYOZrGU) [How far is the edge of the universe? - YouTube](https://www.youtube.com/watch?v=u23vZsJbrjE) Given that the visible Universe is expanding, your assumption merely places an upper limit on the rate at which the calculation can proceed. The maximum number of bits calculated per second is the energy density of the newly-visible parts of the Universe, multiplied by the newly-visible volume, and divided by the energy required per bit.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Daniel Pfeffer wrote:
Given that the visible Universe is expanding, your assumption merely places an upper limit on the rate at which the calculation can proceed.
The original comment made it clear that the actual outcome was publishing the result and not the calculation itself.
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jschell wrote:
Since the matter in the universe is finite,
I really hope that it is. And that time is finite, and will end some time. I am very uncomfortable with the idea of infinites. I am hoping for a gnab gib.
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I beg to differ; the matter in the visible Universe appears to be finite, but we don't know how large the Universe (visible and non-visible) is. There is good evidence that it is much larger than that, and could be infinite in size. [If the universe is only 14 billion years old, how can it be 92 billion light years wide? - YouTube](https://www.youtube.com/watch?v=vIJTwYOZrGU) [How far is the edge of the universe? - YouTube](https://www.youtube.com/watch?v=u23vZsJbrjE) Given that the visible Universe is expanding, your assumption merely places an upper limit on the rate at which the calculation can proceed. The maximum number of bits calculated per second is the energy density of the newly-visible parts of the Universe, multiplied by the newly-visible volume, and divided by the energy required per bit.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
In theory, when the "big bang" occurred, the gravity was so intense that the light could not escape. (The gravity was more intense then a big black hole.) At some time later, when the gravity subsided, the pieces left that central point and moved out in all directions. Also, the more intense the gravity, the more time shrinks. Items closer to intense gravity will move faster than items much further away. To us, in our time, it may seem like 14 million years. But, much closer to the high gravity source, it would have been a longer time.
