I can assure you that in most of the EU, you go to your local school and that's that. Wherever it's tried, choice just leads to ghettoisation.
In Belgium, freedom of education is in the constitution. So pupils (or their parents) can choose to which school to go (rightfully so in my opinion), but it does indeed lead to ghettoisation by religion.
Almost all schools are funded by government. The largest school network is the Catholic one. They teach their own programmes, have their own inspection and all that is being paid with state money. The second largest network are the community level schools (we have a Dutch-speaking, a French-speaking and a German-speaking community). Some schools are not state-funded, I think a couple of Steiner, Jewish and Sudburry schools are truly private (and consequently expensive).
My kids, not believing in any god and therefore avoiding Catholic schools, go to a Dutch-speaking-community high school in Brussels. (I insist on my kids making their own choices on what to believe in and what school to go to - their mother tried to convince them on Wiccan nonsense but she has little credibility being in mental hospital for years, my own mother tried to talk them into believing in Jesus.)
About 80% to 90% of the pupils in their school are muslim. The vast amount of them does not believe in evolution - which is a pity because only half a century ago the muslims had no problems with evolution.
There now is discussion on whether it would be a good thing or not if there would be a separate muslim network or not. A very first muslim school has opened recently because muslim girls are not allowed to wear a veil during class in community and Catholic schools.
Most teachers in community schools are atheists, they have to be very creative. My son's French teacher once drew 2 rectangles on the blackboard. The first one was a painting of god by an atheïst, it was emty, since there is no god. The second one was a painting of god by a believer, it also was emty because god forbids making depictions of him. Some students accused the teacher of blasphemy, because he had made a "cartoon of god" (no formal or official accusation, just during the class discussion after him drawing the rectangles).
In the Catholic high schools (which I attended, before going to an atheist university), evolution and big bang are accepted by almost everybody.
Sometimes, they broadcast ZX Spectrum, sometimes it was MSX programs.
The Dutch NOS radio created BASICODE to transmit BASIC binaries over radio. It was used in several countries until the early 90s.
BASICODE could be understood by almost all computers at the time, including Exidy Sorcerer, Colour Genie, Commodore PET, VIC-20, C64, Amiga, Sinclair ZX81, ZX Spectrum, QL, Acorn Atom, Micro, Electron, Tandy TRS-80, MSX, Oric Atmos, Philips P2000T, Grundy NewBrain, Amstrad CPC, IBM PC, Apple II, Texas Instruments TI-99/4A & Mattel Aquarius.
It only used a minimal subset of BASIC command, all system-specific commands were replaced by GOSUB calls, for example GOSUB 100 to clear the screen. The program itself would then start at line 1000.
Also, is oracle really trying to state that they have never heard of clean room design?
When Oracle hired Informix people who had created the Informix online hot backup and shortly after that released hot backups for Oracle, they pleaded that the folks who came over from Informix did not work on that and that Oracle did a clean room design. They could perhaps claim that the _names_ of the Java API calls are the copyrighted material, but if that would stick, no compatibles APIs would be possible anymore at all.
And this is newsworthy.... how? DOS is still Microsoft's property, regardless of how thoroughly reverse engineered it has become. This is like dedicating an article to YouTube making a video unavailable because a record label said take it down.
MS/DOS is Microsoft's "property" (stolen property btw, but that's another story), DOSBox is not. But this is not what this is about: iDOS was taken away not because it would infringe on Microsoft, but probably because it would turn the non-jailbroken iPhone/iTab into a programmable device.
Also the first tank serial # should not be 1.
Try something like 24370239.
Hitler knew this trick: he was member number 555 of the DAP, the first member had number 501. When the DAP changed into the NSDAP, he became member number 1.
My first computer was a Sharp MZ-80K in 1979 - it had the words "Personal Computer" on it, two years before the "IBM PC". Z80 CPU, 48Kb RAM, 4Kb ROM. I also have a Sharp Zaurus.
Both machines were highly innovative. This is a sad day.
We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.
Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s. So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.
Except the people who think they're being cleaver and claim that "pure communism" was supposed to be Libertarian Socialism, aka "Anarchism." it wasn't. Mikhail Bakunin and Karl Marx were arch-rivals in the First Internationale over this issue, and Marxism, slightly refined by Lenin and Trotsky, and established by the Bolsheviks in the Soviet Union was the real McCoy.
Communism is a "social system based on collective ownership". The word is originally French, existing since the 12th century. Victor d’Hupay was in 1785 the first (afaik) to use the word in its modern meaning. Marxism (19th century) is one form of communism, the form which redefines communism as "social/political system based on state ownership". "Pure communism" is the end goal of Marxism, a free state which they tried to reach by installing a dictatorship... (Sorry - as an anarchistic communist I had to try to be "cleaver".)
No I'm not. You are confusing the first and second incompleteness theorems.
OK, you made me read your post again.
(incidentally you forgot the assumptions Godel made for 2), showing that for example, there are consistent maths, we just don't use them, as they're not infinite, and not "generally useful" whatever that means)
There are indeed limited mathematics which are built upon first order logic and which are consistent and complete. They can even be infinite, if you allow for an infinite number of axioms by using an axiom scheme. But they are not strong enough to express arithmetics.
Additionally you forget the followup proofs, there are no consistent theories that can prove the consistency of "meaningful" mathematics (ie. +, -, *,/, n -> n + 1,...). It's not just that the consistency of Peano arithmetic cannot be proved inside Peano arithmetic, it can't be proved, at all (in any meaningfull way : the only way to "prove" it is to accept it's correctness as axiom).
Using nothing but logic, one can build two kinds of mathematics which are strong enough (i.e. being of second order) to express arithmetics:
1) consistent (but incomplete) ones,
2) inconsistent ones - you say that all mathematics is inconsistent, but that is just plain wrong. Unless if one uses a paraconsistent logic to prevent the ex falso sequitur quodlibet, inconsistent mathematics is trivially complete, because all well-formed formulas would be true.
3) Gödel proves that the third kind, mathematics which are complete AND consistent do not exist.
3') One could consider mathematical theories of which we do not know if they are consistent or not as a third kind of mathematics, I don't know if anybody has ever constructed a mathematical system of which it can be proven that it is undecidable wether it is consistent or not (sounds like a nice project actually.)
So really math is not consistent (if something cannot be proved, even if not actually disproved, you cannot reasonably say that it *is*, because it isn't). You can NOT say that math (arithmetic) is consistent, that's WRONG. You *can* say it's inconsistent
You are confusing "consistency" with "completeness".
(if you've proven, correctly, that a plane can never be observed flying, is it really such a stretch to say that it's going to crash when it's haning up in the air and time is frozen ?).
I have no clue what you are talking about.
This is also not the sole problem with numbers. There are all sorts of unsolved paradoxes with even the natural number "infinite". (more general there are paradoxes that apply to any collection with infinite elements)
Yes, that's why there is a movement called finitism in maths.
And this is talking about *just* natural numbers. rational numbers and, God help us, real numbers have much, much worse problems than mere doubts. It is known that rational numbers are inconsistent, and real numbers cannot be proven to even exist. There are no known ways to construct real numbers that are not simple extensions of rational numbers.
Of course the existence of real numbers can be proved: take a triangle with a 90 angle & with both legs on that angle having a length of 1. Then the length of the third leg is a real number, SQR(2). It is easy to proof that SQR(2) is not integer nor rational. Now, defining and constructing real numbers is harder and there are non-standard mathematics which try to address the problems you hint at.
Sorry, the second sentence of my last paragraph should read as "axioms of relativity do not lead to theorems" (in stead of 'theories'.)
The theory of Goldblatt is a "first order theory", logicians like that, because it is decidable. The theory of Schutz in categorical, the mathematician like that, even if it is undecidable.
I agree with m50d that it is not relevant for the reason he gives above.
The Gödel theorems are interesting for the study of the foundation of mathematics and more specifically for the study of the relation between logic and mathematics. Using it outside that field is at least tricky, and more often than not crackpottery.
Out of a set of axioms (or out of a set of hypothesis) you use deductive logic to prove some theorems which are true if the axioms are true. The axioms together with the theorems form a theory. The question of completeness is: can we construct a proof for every true stament in that theory, or do there exist true statements which cannot be proven. The question of (in)consistentcy is: can we construct a proof for a false statement? All this is about the internal properties of a theory.
Now back to your question: relativity theory and quantum mechanics have different sets of axioms. The axioms of relativity do not lead to theories which are in contradiction with other theorems of the same theory (I am not sure about this for general relativity, there are however several sets of axioms for special relativity which have proofs of consistency*). I guess the same holds for QM**. The problem is: theorems of relativity are in contradiction with theorems QM, so this is a problem between two theories. The problem is that both theories are very solid and well-tested on their own right. A theory which tries to combine relativity and QM on a logical level is Branching Space-Time by Nuel Belnap.
Thanks you for supporting my point of view - you should create an account, then I could become a fan:)
However, I disagree with mathematics including physics. I consider mathematics as being a tool or even a language used by physiscs.
Disclaimer: I'm neighter a mathematician nor a physicist (I'm a logician.)
Yes, there is a name for a theory which hasn't yet been tested: hypothesis.
A hypothesis is the starting point. A theory is the hypothesis and everything which follows from it. The hypothesis can be true or false, a theory can also be true or false.
So really math is not consistent (if something cannot be proved, even if not actually disproved, you cannot reasonably say that it *is*, because it isn't).
You are confusing "consistency" with "completeness".
Well, propositional logic can be proven to be consistent (there are no contradictions) AND complete (all true propositions can be proven out of the axioms), so can first order predicate logic (in the PhD dissertation of Gödel, 1929).
To construct arithmetic out of logic, we however need second order predicate logic. Gödel (1930, published 1931) showed that axiomatic systems in second order logic are either incomplete (true non-provable sentences can be constructed) OR they are inconsistent (containing contradictions).
Slashdot Mirror
Couldn't you make a column-based database that uses SQL as a query language?
Sybase IQ is column based and uses SQL.
I can assure you that in most of the EU, you go to your local school and that's that. Wherever it's tried, choice just leads to ghettoisation.
In Belgium, freedom of education is in the constitution. So pupils (or their parents) can choose to which school to go (rightfully so in my opinion), but it does indeed lead to ghettoisation by religion.
Almost all schools are funded by government. The largest school network is the Catholic one. They teach their own programmes, have their own inspection and all that is being paid with state money. The second largest network are the community level schools (we have a Dutch-speaking, a French-speaking and a German-speaking community). Some schools are not state-funded, I think a couple of Steiner, Jewish and Sudburry schools are truly private (and consequently expensive).
My kids, not believing in any god and therefore avoiding Catholic schools, go to a Dutch-speaking-community high school in Brussels. (I insist on my kids making their own choices on what to believe in and what school to go to - their mother tried to convince them on Wiccan nonsense but she has little credibility being in mental hospital for years, my own mother tried to talk them into believing in Jesus.)
About 80% to 90% of the pupils in their school are muslim. The vast amount of them does not believe in evolution - which is a pity because only half a century ago the muslims had no problems with evolution.
There now is discussion on whether it would be a good thing or not if there would be a separate muslim network or not. A very first muslim school has opened recently because muslim girls are not allowed to wear a veil during class in community and Catholic schools.
Most teachers in community schools are atheists, they have to be very creative. My son's French teacher once drew 2 rectangles on the blackboard. The first one was a painting of god by an atheïst, it was emty, since there is no god. The second one was a painting of god by a believer, it also was emty because god forbids making depictions of him. Some students accused the teacher of blasphemy, because he had made a "cartoon of god" (no formal or official accusation, just during the class discussion after him drawing the rectangles).
In the Catholic high schools (which I attended, before going to an atheist university), evolution and big bang are accepted by almost everybody.
Sometimes, they broadcast ZX Spectrum, sometimes it was MSX programs.
The Dutch NOS radio created BASICODE to transmit BASIC binaries over radio. It was used in several countries until the early 90s.
BASICODE could be understood by almost all computers at the time, including Exidy Sorcerer, Colour Genie, Commodore PET, VIC-20, C64, Amiga, Sinclair ZX81, ZX Spectrum, QL, Acorn Atom, Micro, Electron, Tandy TRS-80, MSX, Oric Atmos, Philips P2000T, Grundy NewBrain, Amstrad CPC, IBM PC, Apple II, Texas Instruments TI-99/4A & Mattel Aquarius.
It only used a minimal subset of BASIC command, all system-specific commands were replaced by GOSUB calls, for example GOSUB 100 to clear the screen. The program itself would then start at line 1000.
Nerds know that the number is (6^6)^6 or or 10,314,424,798,490,535,546,171,949,056.
By plugging this hardware in you agree to the terms of the license...........
No: only by signing a license agreement, I agree with the terms of the license.
Python is definitely my script language of choice. Compiled Python with static typing would kick ass.
Except for the use of tab stops over { }... that's just plain stupid...
No, it is just a matter of taste.
I would personally rather like Python to replace "=" by ":=" and "==" by "=" over changing the tabs into braces.
Nothing stupid about having another taste. If you really have a problem with such details, just fork it.
Also, is oracle really trying to state that they have never heard of clean room design?
When Oracle hired Informix people who had created the Informix online hot backup and shortly after that released hot backups for Oracle, they pleaded that the folks who came over from Informix did not work on that and that Oracle did a clean room design. They could perhaps claim that the _names_ of the Java API calls are the copyrighted material, but if that would stick, no compatibles APIs would be possible anymore at all.
Indeed, you're right; my statement above was wrong.
And this is newsworthy.... how? DOS is still Microsoft's property, regardless of how thoroughly reverse engineered it has become. This is like dedicating an article to YouTube making a video unavailable because a record label said take it down.
MS/DOS is Microsoft's "property" (stolen property btw, but that's another story), DOSBox is not. But this is not what this is about: iDOS was taken away not because it would infringe on Microsoft, but probably because it would turn the non-jailbroken iPhone/iTab into a programmable device.
"These days"??? I was 6 when I started using computers in 1975. By the early 80s, all my friends had a computer.
Also the first tank serial # should not be 1. Try something like 24370239.
Hitler knew this trick: he was member number 555 of the DAP, the first member had number 501. When the DAP changed into the NSDAP, he became member number 1.
My thought was "animated tattoos tied to pulse and temperature monitors so the tattoo could display imagery to indicate my current mood."
Minmatar War Tattoos
My first computer was a Sharp MZ-80K in 1979 - it had the words "Personal Computer" on it, two years before the "IBM PC". Z80 CPU, 48Kb RAM, 4Kb ROM.
Yeah, but does it run linux?
Nope, but it did run CP/M.
My first computer was a Sharp MZ-80K in 1979 - it had the words "Personal Computer" on it, two years before the "IBM PC". Z80 CPU, 48Kb RAM, 4Kb ROM. I also have a Sharp Zaurus.
Both machines were highly innovative. This is a sad day.
Just write a little AWK script to replace evey occurence of "48' in the source code by, say, 256 or 1024.
Can you please explain where I went wrong? Thx.
BTW, the link I provided is to an article about Bailey's formula.
We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.
Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s. So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.
Except the people who think they're being cleaver and claim that "pure communism" was supposed to be Libertarian Socialism, aka "Anarchism." it wasn't. Mikhail Bakunin and Karl Marx were arch-rivals in the First Internationale over this issue, and Marxism, slightly refined by Lenin and Trotsky, and established by the Bolsheviks in the Soviet Union was the real McCoy.
Communism is a "social system based on collective ownership". The word is originally French, existing since the 12th century. Victor d’Hupay was in 1785 the first (afaik) to use the word in its modern meaning. Marxism (19th century) is one form of communism, the form which redefines communism as "social/political system based on state ownership". "Pure communism" is the end goal of Marxism, a free state which they tried to reach by installing a dictatorship... (Sorry - as an anarchistic communist I had to try to be "cleaver".)
No I'm not. You are confusing the first and second incompleteness theorems.
OK, you made me read your post again.
(incidentally you forgot the assumptions Godel made for 2), showing that for example, there are consistent maths, we just don't use them, as they're not infinite, and not "generally useful" whatever that means)
There are indeed limited mathematics which are built upon first order logic and which are consistent and complete. They can even be infinite, if you allow for an infinite number of axioms by using an axiom scheme. But they are not strong enough to express arithmetics.
Additionally you forget the followup proofs, there are no consistent theories that can prove the consistency of "meaningful" mathematics (ie. +, -, *, /, n -> n + 1, ...). It's not just that the consistency of Peano arithmetic cannot be proved inside Peano arithmetic, it can't be proved, at all (in any meaningfull way : the only way to "prove" it is to accept it's correctness as axiom).
Using nothing but logic, one can build two kinds of mathematics which are strong enough (i.e. being of second order) to express arithmetics:
1) consistent (but incomplete) ones,
2) inconsistent ones - you say that all mathematics is inconsistent, but that is just plain wrong. Unless if one uses a paraconsistent logic to prevent the ex falso sequitur quodlibet, inconsistent mathematics is trivially complete, because all well-formed formulas would be true.
3) Gödel proves that the third kind, mathematics which are complete AND consistent do not exist.
3') One could consider mathematical theories of which we do not know if they are consistent or not as a third kind of mathematics, I don't know if anybody has ever constructed a mathematical system of which it can be proven that it is undecidable wether it is consistent or not (sounds like a nice project actually.)
So really math is not consistent (if something cannot be proved, even if not actually disproved, you cannot reasonably say that it *is*, because it isn't). You can NOT say that math (arithmetic) is consistent, that's WRONG. You *can* say it's inconsistent
You are confusing "consistency" with "completeness".
(if you've proven, correctly, that a plane can never be observed flying, is it really such a stretch to say that it's going to crash when it's haning up in the air and time is frozen ?).
I have no clue what you are talking about.
This is also not the sole problem with numbers. There are all sorts of unsolved paradoxes with even the natural number "infinite". (more general there are paradoxes that apply to any collection with infinite elements)
Yes, that's why there is a movement called finitism in maths.
And this is talking about *just* natural numbers. rational numbers and, God help us, real numbers have much, much worse problems than mere doubts. It is known that rational numbers are inconsistent, and real numbers cannot be proven to even exist. There are no known ways to construct real numbers that are not simple extensions of rational numbers.
Of course the existence of real numbers can be proved: take a triangle with a 90 angle & with both legs on that angle having a length of 1. Then the length of the third leg is a real number, SQR(2). It is easy to proof that SQR(2) is not integer nor rational. Now, defining and constructing real numbers is harder and there are non-standard mathematics which try to address the problems you hint at.
Sorry, the second sentence of my last paragraph should read as "axioms of relativity do not lead to theorems" (in stead of 'theories'.)
The theory of Goldblatt is a "first order theory", logicians like that, because it is decidable. The theory of Schutz in categorical, the mathematician like that, even if it is undecidable.
I agree with m50d that it is not relevant for the reason he gives above.
The Gödel theorems are interesting for the study of the foundation of mathematics and more specifically for the study of the relation between logic and mathematics. Using it outside that field is at least tricky, and more often than not crackpottery.
Out of a set of axioms (or out of a set of hypothesis) you use deductive logic to prove some theorems which are true if the axioms are true. The axioms together with the theorems form a theory. The question of completeness is: can we construct a proof for every true stament in that theory, or do there exist true statements which cannot be proven. The question of (in)consistentcy is: can we construct a proof for a false statement? All this is about the internal properties of a theory.
Now back to your question: relativity theory and quantum mechanics have different sets of axioms. The axioms of relativity do not lead to theories which are in contradiction with other theorems of the same theory (I am not sure about this for general relativity, there are however several sets of axioms for special relativity which have proofs of consistency*). I guess the same holds for QM**. The problem is: theorems of relativity are in contradiction with theorems QM, so this is a problem between two theories. The problem is that both theories are very solid and well-tested on their own right. A theory which tries to combine relativity and QM on a logical level is Branching Space-Time by Nuel Belnap.
* For axioms of special relativity, check: - Optical geometry of motion, a new view of the theory of relativity by A. A. Robb, 1911
- A theory of time and space by A. A. Robb
- The absolute relations of time and space by A. A. Robb, 1921
- Geometry Of Time And Space by A. A. Robb, 1936
- Orthogonality and Spacetime Geometry by Robert Goldblatt, 1987 (this is a first oder theory, so it is both complete and consistent - however it is not categorical
- Independent axioms for Minkowski space-time by John W. Schutz, 1997. This theory is of second order, so it suffers from the problems caused by the Gödel theorems.
** Check Quantum Logic by J. von Neumann (yes, the guy of the "Von Neumann Concept") and G. Birkhoff.
Thanks you for supporting my point of view - you should create an account, then I could become a fan :)
However, I disagree with mathematics including physics. I consider mathematics as being a tool or even a language used by physiscs.
Disclaimer: I'm neighter a mathematician nor a physicist (I'm a logician.)
Yes, there is a name for a theory which hasn't yet been tested: hypothesis.
A hypothesis is the starting point. A theory is the hypothesis and everything which follows from it. The hypothesis can be true or false, a theory can also be true or false.
So really math is not consistent (if something cannot be proved, even if not actually disproved, you cannot reasonably say that it *is*, because it isn't).
You are confusing "consistency" with "completeness".
Well, propositional logic can be proven to be consistent (there are no contradictions) AND complete (all true propositions can be proven out of the axioms), so can first order predicate logic (in the PhD dissertation of Gödel, 1929).
To construct arithmetic out of logic, we however need second order predicate logic. Gödel (1930, published 1931) showed that axiomatic systems in second order logic are either incomplete (true non-provable sentences can be constructed) OR they are inconsistent (containing contradictions).