It's not an exaflood if there aren't exabytes in transit at any given moment.
And TCP/IP is massively scalable, but it has limits. There are probably a hundred or so major choke points that will get creamed without major hardware upgrades, just as major hardware upgrades were necessary to increase capacity in the mid-late 90s and early 00's.
You don't really think the.com bubble was about pet food and toys, do you?
No, unless they have incorporated as a charitable organization and not just a not-for-profit corporation. I don't believe the Apache Foundation qualifies to be a charitable organization, but that's for lawyers to argue.
Perhaps, but it's just not in the same league. You can say no to Google by just not visiting them. You can only say no to Microsoft (if you're buying a PC class machine in the US) after you've paid them for a license.
Parts of computer science are branches of mathematics. But computer science encompasses fields like computer vision, where notable results are derived from empirical experimentation, and not mathematical reasoning.
Computer science features empirical experimentation as well as mathematical rigor, making it a "true" science. Science and its relation to engineering has nothing to do with it. It's that simple.
By your 'logic' the War in 1776 was also a Civil War. The difference is pretty obvious to anyone with a functioning brain and a basic understanding of the English language.
Uh, it was. It was also a war of independence, by virtue of the fact that we won.
A war between factions or regions of the same country. A state of hostility or conflict between elements within an organization: "The broadcaster is in the midst of a civil war that has brought it to the brink of a complete management overhaul" (Bill Powell). Civil War The war in the United States between the Union and the Confederacy from 1861 to 1865. Also called War Between the States. Civil War The war in England between the Parliamentarians and the Royalists from 1642 to 1648.
I saw no indication that the MPAA was hosting their own apt repositories with source. If you mean that sources.list was pointing at Ubuntu's servers, that's not good enough. That's Ubuntu doing the distribution.
If you want to get a gun for some nefarious purpose, it's not hard at all. And in return for this situation, we create an onerous burden on people who have no criminal intent, and never would use their guns for any illegitimate purpose.
Making people wait 5 days is onerous? What are your thoughts on the conditions at Guantanamo?
Lets start with what Mac has already. It has Java 5, as in a.jnlp will 'just work' on OSX. It kinda has python - unless you want to do GUI stuff. Ruby is in much the same boat as python. However, this is all irrelevant..NET is a new paradigm - learn a decent class library and keep using it from then on, whether that's in J#, IronPython, IronRuby, or whatever language is popular next year. Java claimed much the same thing, which isn't too surprising since.net is basically a java knockoff with some design faults smoothed out.
Python and Ruby development with Cocoa using the PyObjC and Cocoa/Ruby bridges is now officially supported by Xcode. The bridges are installed on all new Leopard installs. They will "just work" for GUI applications.
With the use of bridges to the ObjC runtime environment, Cocoa has the same potential for acting as a platform defining API as.NET.
Ok, I understand: Germans had hard time understanding him. (He wrote in Latin, by the way, not in his "regional variant" of German; in any case, this problem, when it does exist, is solved by the method known as translation.)
Translation of mathematical texts amounts to rewriting it. Why not make it better for a particular purpose at the same time?
What you are essentially saying is that each and every calculus textbook is a worthy read, if you want to learn calculus, even if you have read all other book on this topic.
You evidently have severe difficulties with reading comprehension. That's not what I'm "essentially" saying at all. What I am saying is that you can't know if a book is worth reading until after it has been written. You can't know if a book is worth reading until you know the audience it was written for (in detail) and know whether you are a part of that audience.
You complain because Euler's (of all people) papers aren't used for study by calculus student, and I explained why there are better modern options. I have moved on from learning calculus in my mathematical career, but I usually have 5-10 texts on my desk for any given subject I'm learning. Different authors approach topics differently, and few are consistently ideal. Hell, different authors approach proofs differently -- some use techniques from advanced fields I am ignorant and uninterested in, some use techniques from advanced fields of which I have detailed knowledge. If an author's approach for an idea/theorem/proof/section/chapter works for me, I just continue reading. If it doesn't, I grab another book and try again. Much better than trying to fit a square pedagogical peg in a round hole.
Given %hash, it's called @hash{@keys} when you slice it, and $hash{$key} when you only want one element.
I know you know this, but others don't.
The hash is always called 'hash'. The sigil provides datatype information for the intended return value of your access to the variable -- just about everything in Perl is an expression and has a return value. Program evaluation follows a model remarkably similar to what a functional language might use, evaluating sub-expressions as needed. I'm sure the internals could be better or smarter, but they definitely aren't bad.
Sigils also provide a simple namespacing mechanism, so you can have $hash (say, a reference to a hash) and %hash in the same scope.
And because there's that layer of indirection between the variable's raw values and its return value, you can inject code to make variables act differently than they normally would when accessed, by using the Tie mechanisms. As a result, a fair amount of Perl's OO syntactic sugar can in principle be defined in terms of Perl code instead of having to be a part of the interpreter. This mechanism is obviously open for abuse,
In fact, I'm starting to think that a closure-based object system could be made to replace Perl's "standard" OO system with minimal syntax changes through the use of ties.
Yes, indeed. And if you're developing a new product, you ought to get a clean slate. There's no reason not to pick out the latest (or even legacy but well-tested) Catalyst modules and freeze them on your server. Or put new ones through QA. I know mst and the rest of the Catalyst bunch would have been happy to help the BBC.
Calculus books shouldn't contain any original research. They're textbooks. There are clear pedagogical reasons to use new textbooks:
There are obvious regional variations in spoken and written language. Euler was Swiss.
Notation changes over time as the concepts are hammered down.
More importantly, textbooks are intended to guide students to useful applications, and in advanced texts, possibly fruitful avenues for research, which obviously change as relevant applications change and research progresses.
The approach a textbook takes depends on the intended audience. Euler wrote for mathematicians, not students.
Some of Euler's calculus "proofs" are not rigorous by modern standards.
Authors have different pedagogical approaches. Some are task based. Some are theoretical. Some use examples. Others omit them. Some interpolate results in English text, so that the text reads like "standard" prose. Others use a more structured approach of numbered sections and sub-sections to make finding specific passages easier. And so on. The appropriate approach depends on the student.
If you are unable to think of any reasons one might be motivated to write a modern text other than profit, you aren't qualified to comment on their merits.
It seems that, culturally, we are way behind compared to what we were a hundred years ago. Want to learn geometry? Read Euclid. He wrote his books thousands of years ago. Calculus? Euler is your best teacher, and has been so since 1700s. Fiction? Music? Architecture?... You get the point.
It seems that you aren't exposed to any modern culture.
Euclid's Elements are fine, and fun to read. But I wouldn't read Euclid for differential geometry. Or symplectic geometry. Or dozens of other kinds of geometry borne out in the 20th Century.
Euler was a clever guy, but he is definitely not someone to learn calculus from. Stick with Riemann and Weierstrass if you want to read very old books. Or do the sensible thing and get a modern book, like Marsden's Calculus. That will teach you everything you need to know to move on to fun topics.
Fiction? There's plenty. Find it yourself.
Music? Even more.
Architecture has always been grossly derivative. Except for many interesting experiments in post-modern design in the 20th century.
I just bought a new machine. I'm very happy with it. I'd rather drop the Stacks, I liked having one click access to my Applications folder Finder windows. Spaces are okay -- I never need to use them with a screen this big. No grey screens or "real" panics at all. And I'm glad the machine came with Leopard. I look forward to using the Cocoa/Ruby bridge to write Cocoa applications with Ruby, and brushing up on my Objective C. I'm not currently using the Time Machine, but I will once I get a big enough external drive (or two).
That said, I wouldn't have bought Leopard if it hadn't come with the machine. At least not until an application I was actually interested in running needed it. I do expect those to show up eventually as developers start using Ruby and Python and Objective C 2.0 for development.
Compulsive behavior is by definition uncontrollable.
Re:Python is part of the answer
on
Open Source Math
·
· Score: 1
Sorry it's taken me so long to reply. I hope you see this.
That is a very good question.
Pen and paper proofs have many epistemological weaknesses as you mentioned. But computer assisted proofs have the same ones (since ultimately the reasoning will be put down on paper and read by others), and unfortunately introduce new difficulties.
First, to clarify, I'm going to blur an important distinction. The word proof is overloaded. It can mean empirical proof, such as when a lawyer says he has proof that the defendant is blameless. Or it can mean "formal proof". Or it can mean what I called a pen and paper proof. See the introductory section for http://en.wikipedia.org/wiki/Mathematical_proof for the difference. And immediately forget the difference, since in principle, every valid pen and paper proof can be translated to a formal proof.
In many ways, the use of computer technology in proof is a lot like the use of diagrams in proof, whose use has been rejected as mathematical proof except in very limited circumstances. Among the problems: the diagram is only a representation of the objects you're talking about. The representation may not (usually is not) be provably adequate, which makes it inadmissable in a formal proof.
Diagrams or pictures probably rank among the oldest forms of human communication. They are not only used for representation but can also be used to carry out certain types of reasoning, and hence play a particular role in logic and mathematics. However, sentential representation systems (e.g., first-order logic) have been dominant in the modern history of logic, while diagrams have largely been seen as only of marginal interest. Diagrams are usually adopted as a heuristic tool in exploring a proof, but not as part of a proof.... (http://plato.stanford.edu/entries/diagrams/)
This article goes on to discuss some "diagrammatic logics" that are "sound" and "complete" in the same senses the First-Order Logic is. Obviously, if you know what sound and complete mean in this context, those logics are provably adequate. The article even has some nice examples of places where non-representative diagrams lead to specious conclusions.
Slashdot Mirror
A real guitar has 6 strings. And you have to push down the strings at the right time. And actually use a pick (or finger pick).
It's not an exaflood if there aren't exabytes in transit at any given moment.
.com bubble was about pet food and toys, do you?
And TCP/IP is massively scalable, but it has limits. There are probably a hundred or so major choke points that will get creamed without major hardware upgrades, just as major hardware upgrades were necessary to increase capacity in the mid-late 90s and early 00's.
You don't really think the
No, unless they have incorporated as a charitable organization and not just a not-for-profit corporation. I don't believe the Apache Foundation qualifies to be a charitable organization, but that's for lawyers to argue.
Perhaps, but it's just not in the same league. You can say no to Google by just not visiting them. You can only say no to Microsoft (if you're buying a PC class machine in the US) after you've paid them for a license.
Or you could buy a Dell. Or a Mac.
Parts of computer science are branches of mathematics. But computer science encompasses fields like computer vision, where notable results are derived from empirical experimentation, and not mathematical reasoning.
Computer science features empirical experimentation as well as mathematical rigor, making it a "true" science. Science and its relation to engineering has nothing to do with it. It's that simple.
Thanks for the thought, but I cannot seem to harm my Karma on /....
You're not trying hard enough.
Uh, it was. It was also a war of independence, by virtue of the fact that we won.
What are we trying to do here, compute pi to 14 million decimal paces in 5 minutes or less?
That's not that many digits... It wouldn't take even 5 minutes on a Core 2 Duo.
I saw no indication that the MPAA was hosting their own apt repositories with source. If you mean that sources.list was pointing at Ubuntu's servers, that's not good enough. That's Ubuntu doing the distribution.
Why shouldn't they? Are you some kind of Nazi?
If you want to get a gun for some nefarious purpose, it's not hard at all. And in return for this situation, we create an onerous burden on people who have no criminal intent, and never would use their guns for any illegitimate purpose.
Making people wait 5 days is onerous? What are your thoughts on the conditions at Guantanamo?
Lets start with what Mac has already. It has Java 5, as in a .jnlp will 'just work' on OSX. It kinda has python - unless you want to do GUI stuff. Ruby is in much the same boat as python. However, this is all irrelevant. .NET is a new paradigm - learn a decent class library and keep using it from then on, whether that's in J#, IronPython, IronRuby, or whatever language is popular next year. Java claimed much the same thing, which isn't too surprising since .net is basically a java knockoff with some design faults smoothed out.
.NET.
Python and Ruby development with Cocoa using the PyObjC and Cocoa/Ruby bridges is now officially supported by Xcode. The bridges are installed on all new Leopard installs. They will "just work" for GUI applications.
With the use of bridges to the ObjC runtime environment, Cocoa has the same potential for acting as a platform defining API as
Ok, I understand: Germans had hard time understanding him. (He wrote in Latin, by the way, not in his "regional variant" of German; in any case, this problem, when it does exist, is solved by the method known as translation.)
Translation of mathematical texts amounts to rewriting it. Why not make it better for a particular purpose at the same time?
What you are essentially saying is that each and every calculus textbook is a worthy read, if you want to learn calculus, even if you have read all other book on this topic.
You evidently have severe difficulties with reading comprehension. That's not what I'm "essentially" saying at all. What I am saying is that you can't know if a book is worth reading until after it has been written. You can't know if a book is worth reading until you know the audience it was written for (in detail) and know whether you are a part of that audience.
You complain because Euler's (of all people) papers aren't used for study by calculus student, and I explained why there are better modern options. I have moved on from learning calculus in my mathematical career, but I usually have 5-10 texts on my desk for any given subject I'm learning. Different authors approach topics differently, and few are consistently ideal. Hell, different authors approach proofs differently -- some use techniques from advanced fields I am ignorant and uninterested in, some use techniques from advanced fields of which I have detailed knowledge. If an author's approach for an idea/theorem/proof/section/chapter works for me, I just continue reading. If it doesn't, I grab another book and try again. Much better than trying to fit a square pedagogical peg in a round hole.
Given %hash, it's called @hash{@keys} when you slice it, and $hash{$key} when you only want one element.
I know you know this, but others don't.
The hash is always called 'hash'. The sigil provides datatype information for the intended return value of your access to the variable -- just about everything in Perl is an expression and has a return value. Program evaluation follows a model remarkably similar to what a functional language might use, evaluating sub-expressions as needed. I'm sure the internals could be better or smarter, but they definitely aren't bad.
Sigils also provide a simple namespacing mechanism, so you can have $hash (say, a reference to a hash) and %hash in the same scope.
And because there's that layer of indirection between the variable's raw values and its return value, you can inject code to make variables act differently than they normally would when accessed, by using the Tie mechanisms. As a result, a fair amount of Perl's OO syntactic sugar can in principle be defined in terms of Perl code instead of having to be a part of the interpreter. This mechanism is obviously open for abuse,
In fact, I'm starting to think that a closure-based object system could be made to replace Perl's "standard" OO system with minimal syntax changes through the use of ties.
Hey, didn't/don't you hang out on #catalyst? I'm cidooh. It's been a while, you might not remember me.
(Replying anonymously because you seem to have put me on your enemies list)
Love,
poopdeville
Yes, indeed. And if you're developing a new product, you ought to get a clean slate. There's no reason not to pick out the latest (or even legacy but well-tested) Catalyst modules and freeze them on your server. Or put new ones through QA. I know mst and the rest of the Catalyst bunch would have been happy to help the BBC.
If you are unable to think of any reasons one might be motivated to write a modern text other than profit, you aren't qualified to comment on their merits.
It was sad, and monumentally boring. I wasn't impressed.
It seems that, culturally, we are way behind compared to what we were a hundred years ago. Want to learn geometry? Read Euclid. He wrote his books thousands of years ago. Calculus? Euler is your best teacher, and has been so since 1700s. Fiction? Music? Architecture? ... You get the point.
It seems that you aren't exposed to any modern culture.
Euclid's Elements are fine, and fun to read. But I wouldn't read Euclid for differential geometry. Or symplectic geometry. Or dozens of other kinds of geometry borne out in the 20th Century.
Euler was a clever guy, but he is definitely not someone to learn calculus from. Stick with Riemann and Weierstrass if you want to read very old books. Or do the sensible thing and get a modern book, like Marsden's Calculus. That will teach you everything you need to know to move on to fun topics.
Fiction? There's plenty. Find it yourself.
Music? Even more.
Architecture has always been grossly derivative. Except for many interesting experiments in post-modern design in the 20th century.
I just bought a new machine. I'm very happy with it. I'd rather drop the Stacks, I liked having one click access to my Applications folder Finder windows. Spaces are okay -- I never need to use them with a screen this big. No grey screens or "real" panics at all. And I'm glad the machine came with Leopard. I look forward to using the Cocoa/Ruby bridge to write Cocoa applications with Ruby, and brushing up on my Objective C. I'm not currently using the Time Machine, but I will once I get a big enough external drive (or two).
That said, I wouldn't have bought Leopard if it hadn't come with the machine. At least not until an application I was actually interested in running needed it. I do expect those to show up eventually as developers start using Ruby and Python and Objective C 2.0 for development.
Hey, want to do me a favor? eBay doesn't appeal to me, but I can give you $350 US for a Wii.
Drugs. Sex. Kill. Kill. Kill.
Compulsive behavior is by definition uncontrollable.
That is a very good question.
Pen and paper proofs have many epistemological weaknesses as you mentioned. But computer assisted proofs have the same ones (since ultimately the reasoning will be put down on paper and read by others), and unfortunately introduce new difficulties.
First, to clarify, I'm going to blur an important distinction. The word proof is overloaded. It can mean empirical proof, such as when a lawyer says he has proof that the defendant is blameless. Or it can mean "formal proof". Or it can mean what I called a pen and paper proof. See the introductory section for http://en.wikipedia.org/wiki/Mathematical_proof for the difference. And immediately forget the difference, since in principle, every valid pen and paper proof can be translated to a formal proof.
In many ways, the use of computer technology in proof is a lot like the use of diagrams in proof, whose use has been rejected as mathematical proof except in very limited circumstances. Among the problems: the diagram is only a representation of the objects you're talking about. The representation may not (usually is not) be provably adequate, which makes it inadmissable in a formal proof.
This article goes on to discuss some "diagrammatic logics" that are "sound" and "complete" in the same senses the First-Order Logic is. Obviously, if you know what sound and complete mean in this context, those logics are provably adequate. The article even has some nice examples of places where non-representative diagrams lead to specious conclusions.