As long as a turing machine uses finite memory of length N, there exists a DFA of N^2 length that accomplishes the same in O(1). Essentially, your stick of memory is a finite number (X). Your algorithm, whatever algorithm it is, deterministically translates X into a new finite number (Y). I can avoid running the algorithm by having a static array that maps X to Y. To turn a 16-bit computer into an O(1) DFA, I need 2^32 bits of memory (a 65536-element array where each value is a 65536-bit string).
Anytime O(...) notation is used, it assumes arbitrary length input (a turing machine is never assumed to work on a finite tape, because it would so obviously reduces to a DFA otherwise).
Furthermore, optimal sorting is rarely expressed as O(N lg N), it is O(N lg k) where k is the # of unique elements. Because most textbooks want to use single-variable Big-O notation, they stick with O(N lg N), but more serious analysis uses multi-variable complexity. k is only pseudo-dependent on N, in that it has to obey the relationship k = N. In the worst case, k = N, and hence sorting is N lg N when expressed in terms of a single-variable. If we're serious about sorting it is O(N lg k). When k is finite, it reduces to merely O(N).
Zero doesn't have a sign, but limits to zero _do_ have a sign, plus, or minus, or plus-or-minus. The limits to 0+ and 0- are convergent limits (the + and - at the _end_ of a number, like 2+ or 2- mean the limit is reaching the number from above or below, and in the case of 0+ and 0-, since "above 0" is positive, and "below 0" is negative, we have different signs). The limits to 0 (with the sign unknown) does not converge (meaning there are multiple results). Given lim x -> 0+, then 1/x = +inf and Given lim x -> 0-, then 1/x = -inf Given lim x -> 0 (that is, the sign is "unknown"), then 1/x = { -inf, +inf } -- yes, _two_ answers, just as the sqrt(4) = {+2, -2} whereas |sqrt(4)| = +2
Thus, assuming that 0 = { lim x -> 0+, lim x -> 0- }, yes, we're saying that 0 is of 2 values (one positive, one negative), then 0^0 has 4 possible values, 0+^0-, 0+ ^0+, 0-^0-, 0+^0+. Now, if you work out the limits, you'll see that 0+^0+ converges to 1-, that 0+^0- converges to 1+, that 0-^0+ is... well, I don't have a complex calculator (I'm using perl to plot the curves), but if you work out the math you'll find that it's a complex number which, probably, has a real component that converges to 0 or 1 from above or below and an imaginary component that converges to 0 or 1 from above or below, or a trigonometric function thereof.
I forgot to use < and > instead of < and > Here's a patch:
This is a SIMPLIFIED example of a public-private "key-exchange" protocol:
Let PE = public encryption function/key, aka Public Key Let PD = private decryption function/key, aka Private Key Let S = symmetric encryption/decryption function/key, aka Session Key STEP 1... opening an SSLSocket (handshake, simplified -- no need to go through Cert chains and other nuances in this example!)... Server --> PE --> Client Server <-- PE(S) <-- Client
STEP 2... communicating messages, where the message is concatenated with its MAC (message authentication code: sequence + hash), to prevent replay attacks or malicious noise, before being encrypted by the symmetric session key... Server --> S(foo+MAC) --> Client// note: PE, PD never need to be used once the SSLSocket is successfully opened Server <-- S(bar+MAC) <-- Client
Asymmetric encryption (public-private pairs e.g. RSA, DH, El Gamal) use symmetric encryption (AES, 3DES, etc) for the session. Asymmetric encryption is SLOW. No sane implementation ever uses asymmetric encryption on more than the hash of an email (signing) or the symmetric session key (key-exchange). This is a SIMPLIFIED example of a public-private "key-exchange" protocol:
Let PE = public encryption function/key, aka Public Key Let PD = private decryption function/key, aka Private Key Let S = symmetric encryption/decryption function/key, aka Session Key STEP 1... opening an SSLSocket... Server --> PE --> Client Server S(foo+MAC) --> Client// note: PE, PD never need to be used once the SSLSocket is successfully opened Server -- S(bar+MAC) -- Client
What does this mean? Two things. First, it means that SSL is as fast as symmetric encryption, because it _is_ symmetric encryption beyond the first part of establishing the connection. Secondly, it means that SSL is no stronger than symmetric encryption because the hacker can _EITHER_ solve PD or S, which can never be harder than solving just for S. The advantage of solving for PD is that the hacker would gain access to ALL sessions with the Server. Solving for S, a "throw-away session key", only gains the hacker access to ONE session. But still, assuming there exists no solution better than brute-force exhaustive search across the space of S, it ~almost~ just as likely you will discover the fixed S as you would a variable S. (For a fixed S you have a 1/S chance of being on your first attempt, a 1/(S-1) chance of being right your second attempt, etc., with a 1/1 (100%) chance of being right on your Sth attempt, but that gives you an average of a 1/(0.5*S) = 2/S chance of being right. For a variable S, you always have a 1/S chance of being right on any attempt. So, it's a 2/S chance (on average) vs 1/S chance (on average). Do you know what that means? They're practically identically difficult problems (both are O(S) complexity). If the fixed S had one extra bit than the variable S, then the amortized chance of being right would be identical. This boils down to the conclusion that communication via fixed symmetric keys are NOT in any way more zero-knowledge hackable (i.e. brute force hackable) than communication via asymmetric keys since the real communication past the handshaking uses a symmetric key.
It would be VERY different to say that fixed symmetric keys are less secure than asymmetric private keys, and I would completely agree with you: there's a logistical problem of passing a fixed symmetric key around to trusted members without a "leak", whereas with asymmetric encryption, I don't worry about leaks or rogue members because I only give out the public key and not the private key. But the primary reason fixed symmetric keys are "less secure" is a logistical problem, and NOT a mathematical problem. Mathematically, symmetric keys are as powerful as needed in a non-quantum-computing environment. That's why top-secret communication using 4096Kbit military-grade RSA (asymmetric) keys in the handshake still use 256bit variable AES (symmetric) keys for the session. Don't confuse the logistical issues of _fixed_ symmetric keys from the technical power of a symmetric key.
I translate it into cowboy english as "it is always a high noon somewhere on Earth". You're right that it doesn't imply the Earth is spherical (besides, the Earth is ovuloid anyways, not spherical). Furthermore, you're reading too much sci-fi if you think you need a high-tech instant-communication device to come up with this. And why do you complicate the issue by insisting it's high noon at one spot and not at another? There's no mention of where it isn't high noon, just that it is high noon somewhere. Think low-tech. Think standing atop a tall dune and seeing far away (wow! information retrieval using photons traveling at light-speed, it's called eyesight!). Stand up on a tall dune, and see the shadows at one end of the horizon to the other. You'll see that somewhere in your visible area, it is high noon (the dune without a shadow), and assuming you're not distracted with ADD, ADHD, XBox, an iPod, a homeland security officer asking you move along because you're making others feel uncomfortable, or a girlfriend who wants you to drive her somewhere, you can stand on that tall dune all day, watching for hours the dune shadows as the sun moves across the sky. What you'll notice is that the area where there are no dune shadows (high noon) will move from one end of the horizon to the other end, smoothly. Any bit of inductive reasoning will come up with the idea that this phenomenon doesn't stop at the end of the visible area, and that some surface beyond the horizon is experiencing high noon, even if it's pitch black where you are.
High-tech solutions are not always needed. A little bit of calm, peace, and 12 hours of distraction-free solitude is all that's required for many powerful revelations.
Either your post is +1 Funny or +1 Troll if you had proper education; or, if you don't have proper education, there should be a -1 Uneducated moderation. See here for a complete synposis of the Teleological argument and its scientific refutes so we don't have to replay hundreds of years of history on a Slashdot thread. If you're too lazy to read, here's the summary:
Teleological argument (quotted from wiki): 1. X is too complex to have occurred randomly or naturally. 2. Therefore, X must have been created by an intelligent being. 3. Y is that intelligent being. 4. Therefore, Y exists.
The Eye Argument (quotted from wiki) Many creationists cite the eye as a prime example of this principle; "What use is a partly-developed eye?" they ask. Evolutionists provide an explanation for this and may state that creationists are arguing from ignorance, for scientists have devised working hypotheses on how certain body parts and organs could have evolved.
The explanation by evolution gives major evolutionary steps of: 1. No light sensitivity at all. 2. Cells that can sense the presence of light and send a signal to the brain. 3. Development of multiple, co-ordinated cells. 4. Development of a lens to focus the light. 5. Development of the brain enabling processing of this information, into instructions to muscles which operate the organ to detect light in other places.
Creationists would counter that each step in this process is in reality, a huge leap. However, evolutionists would argue that each step is not completed in one change; rather, these are only the major milestones of development, which itself is going on all the time.
I went to RPI as well, but I guess they've improved on their selection of taped courses since when I was there it was a virtual impossibility to coast through everything from home in PJs. However, I've also attended Stanford through their SITN and online accesses:
Computer Science courses are available through SITN Microwave Broadcast and on the internet through Stanford Online. All remote students must register for Stanford Online. Tapes will not be available.
It is possible via this approach to graduate from Stanford without having step foot on campus. However, the ambition levels of students who never attended class tended to be lower, and hence I joined on-campus project teams and I took time out from work to always attend meetings. Also, TAs and Profs remember faces far better than email/usenet/chat names and tend not to repeat themselves when they remember you (i.e. when they see you), so if you want high signal:noise, show up at their offices. Asking a question on chat or email tends to get an unnecessarily lengthy (and often belated) reply that wreaks of copy & paste.
Another nice thing about SITN is that it's not a "night course" or some secluded class of people who would be distracted by family, work, or other social commitments. Peers are full-time students and the classes are taught in the morning or afternoon (made available as a recording for those for whom only evenings are free). This is very important and I believe the quality is far superior to a program devoted to catering to part-time students or students who have been out of touch with academics. I was a full-time student at the main RPI Troy campus but occasionally I saw middle aged students in Troy who came from the Hartford campus which caters to professionals studying part-time. These students would take some particular courses which are offered solely at the main campus and the one consistent observation I made was that they all complained about how much harder the courses in the main campus were.
For someone who wants to be pushed into excellence and get a degree which marks a level of accomplishment, I'd strongly recommend enrolling only in programs where your peers are dedicated, on-campus, full-time students who are bright and steeped in academic rigor.
I doubt they would have said quantum computers are incapable of ever running Doom or such; they most likely qualified their statement, indicating that they would be slow by some constant time for such tasks, or they would cost too much in the near future to be practical. However, mathematically, it would be unscholarly of them to say without qualification that QCs are incapable of general purpose computing. See here:
Practical quantum computers David DiVincenzo, of IBM, listed the following requirements for a practical quantum computer: scalable physically to increase the number of qubits qubits can be initialized to arbitrary values quantum gates faster than decoherence time Turing-complete gate set qubits can be read easily
It's important to note the inclusion of Turing-complete gate set -- this with O(1) memory access guarantees the ability to run a VMWare-like app and simulate any x86 processor, albeit by some constant time performance penalty.
> Our present understanding of quantum physics tells us that you can't design a quantum computer that can do all the same math problems as a generic Intel/AMD CPU (e.i. run Windows; play Counterstrike; etc.).
I'm going to have to debunk you on that. QCs require the ability to: 1. CPhase (rotate amplitude on the real-imaginary 2D plane) 2. CNot (quantum entanglement) 3. Mix (reset amplitude to random) 4. Measure (collapse of the probability wave) and, importantly, 5. NAND (not-and classical gate, fountainhead for all classical and contemporary logic).
The operations 1-4 allows us to model quantum effects - remember, the whole idea for QCs spawned when Richard Feynman asked his CS buddies to model quantum effects and despite their CS prowess, none could model it efficiently, which Feynman rightly concluded as indicating that the Universe had a faster computer to predict and enact quantum decisions than the computers we built; hence, he reasoned, we're using an inefficient construct and tapping into the Universe's compuations of quantum effects will allow us to build a more powerful (time-complexity-wise and not just boosted by a constant-time coefficient) computer. There is nothing a classical machine can do which a QC cannot. A QC must have NAND, else it's rather pathetic with just CPhase, CNot, Mix and Measure.
And the "Windows/Counterstrike" argument is a bit lame - even Sparc processors can't run Windows/Counterstrike, that hardly makes them inferior to Intel/AMD. Assembly-interoperability and Mapping-reducibility are very different things. Transmeta went for the asm-interop route, but any computer scientist will tell you that as long as you can simulate a NAND and have O(1) random access memory, any functionality of a modern day Opteron is mapping reducible to your simulation.
> That being said, the problems that can be solved by quantum computers tend to be the ones that would take a regular CPU until the end of the universe to perform (break strong encryption, large traveling salesman problems, etc.).
Agreed. But a QC is never worse in complexity than a classical computer. It is always equal or better complexity-wise. It may have a horribly constant coefficient, making it 1/100th as fast for operations a classical computer has equal complexity. However, keep in mind that a mere constant of 1/100 or 1/1,000 or even 1/1,000,000 pales in comparison when a QC can complete in O(n) time what a classical computer requires O(n^1.5) time.
The govt could profit forever if more things were considered property and hence were subject to property tax. If ownership of land gets taxed, why shouldn't ownership of the spectrum, or of a company, or of anything? Of course, I'm equally happy if there was NO property tax at all. Consistency is key.
Part of my cricicism on the school system is their treatment of very smart and highly experienced professionals as "novices". I'd rather have a 68yr old IBM TJ Watson vet with a PhD teaching a class than some 22yr old floozy with a 2yr associate's degree in "education".
The larger pipelines are also in anticipation of most compilers performing inlining and loop unrolling, in which case, many asm instructions will occur in sequence without any branching.
Even though this isn't a "big deal" - that is, no passwords are leaked per se, and accounts with similar passwords as the parent rightly noted are most likely indicative of a single user with multiple accounts, there is a better way to store passwords.
Given H(P1) and H(P2), it's trivial to prove that (probably)P1==P2 or (certainly)P1!=P2, which is leaking information. Thus, storing H(P1) and H(P2) is a poor way to preserve secrecy of P1 and P2. A just-as-easy approach would be to salt the hash: store H(username1||\0||P1) and H(username2||\0||P2) -- where || is the string-concatenation operator. Assuming no two usernames are the same, and \0 is an invalid character for both username and password, then nothing is leaked about P1 and P2. (Note, \0 is essential because if username1 is "tomharrison" with password1 = "city" and username2 is "tom" with password2 = "harrisoncity", then we leak information that user2 has user1's password prepended with "harrison" unless we have \0 dividing user and password strings)
I would actually prefer true salting: H(random1||P1) and H(random2||P2) where random1 & random2 are random (& mathematically non-secret but you shouldn't feel inclined to publicize them) constants stored alongside the username. This avoids the ugly hack of relying on \0 being special. Unfortunately, this relies on change of datastructure instead of a change in the hash function and hence isn't "just-as-easy".
Re:"Negative Energy" a conceptual mistake?
on
Wormholes Unstable (BBC)
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· Score: 2, Interesting
Would the existence of whiteholes and abundance of them suggest that large wormholes are ubiquitous? While there are a lot of measurements supporting blackholes - and rotating blackholes - at the epicenter of galaxies, there seem to be no sound measurements on whiteholes.
Correct me if I'm wrong, but isn't a whitehole a necessary endpoint for a unidirectional wormhole? Also, considering how most blackholes at the epicenter of galaxies lie dormant, their corresponding whiteholes, if any, would be dormant as well, observable only by how they influence ambient light. Since measurements suggesting blackholes are at the center of most all galaxies are relatively new, I need to ask, has there been much study or analysis of observable space to look for corroborating evidence of whiteholes?
You are correct insofar as the approach being similar to the one used for electron scanning microscopes. This project is less about the 'R' and more about the 'D' in R&D. Don't get me wrong, the 'D' is extremely cool, and it's an awesome util, but as you pointed out, the theory has been laid out already.
The 'R' portion of the project is to iron out the wrinkles of providing a/general/ solution instead of a specific one the electron scanning microscope solved. I'm glad an american univ is heading in this direction; europe had in the past been leading in image reconstruction (an old slashdot article from the late '90s mentioned a doctoral research paper&project on reconstructing a monitor display purely from the oily reflection from a person's forehead - unlike with a mirror which doesn't disperse the light, undoing the dispersion of light from oily skin is complicated and the transformation & inverse transformation are lossy).
It's nice to see computers being put to task on simulation and mathematics instead of perpetually emulating typewriters, hyperlinked magazines, and jukeboxes.
crypto signatures are based on signing the hash of the message, not the message itself (this is because signatures are based on loseless decryption, and no one wants to sign a 200KB file with a 200KB signature). Why target P2P when "Verisign-signed" certs can be forged?
In other words, bullshit. They might have found some collisions in weaker hash functions, but if _strong_ hash functions were defeated, the concept of security as we know it ceases to exist.
While it takes less money to entice criminals there, it also takes less money for a victim to pressure the police to "prioritize" the case.
When's the last time you know of someone who had a few thousand stolen being given priority police attention in the US? It generally gets swept under the rug and insurance pays for it, raising everyone's premiums (hence, we all pay for the crime). Whereas, in a poorer country, while insurance stills pays for it, the theft would be considered substantial. Moreover, you can pad the constable another couple thousand and the case will probably be escalated to the federal bureau with the full attention of everyone.
Further, the letter stated that the University doesn't even know the password, so it should be kept safe
Does any organization keep anything of more informational value than just the salted hash of the password? "We can reset your password, but cannot retrieve your password for you." is the typical disclaimer sent out. Hooray for hash pre-images being difficult.
in 2D riemannian geometry, of which the surface of a sphere is the euclidean analog. Say boats depart in a straight line perpindicular to the equator, thereby being parallel; these two boats will meet at both poles if their lines are extended.
in 2D lobachevskian geometry, of which an area-filled asymptotically to the perimeter of a circle whose diameter is negative-infinity and whose perimeter as at distance 0 from the origin of the circle is the euclidean analog. Any two lines in the circle must interesect since they will converge to the perimeter of the circle which is by definition a single point.
what is reachable and un-reachable, beyond the Slashdot Effect, is a question on what topology you're asking the question. Our universe as an observably euclidean manifold is a small region of a lobachevskian topology. In net-speak, the reachable net is quite different as you build proxies and other bridges to escape local topology.
Now, I mentioned DMDs in the subject-- they are digital micromirror devices also called MEMs, micro-electromechanical-systems. These are what the article states the Virtual-Reality lazer-image is based on. I want to note that while DMDs are far better than lcd-projection (not lcd - lcd *projection* -- where light is either shone off a small high-density lcd screen and reflected out, or where light is shone through a translucent high-density lcd screen), and the contrast/brightness abilities of DMDs are amazing (no loss to semi-permeable substances like lcd), the *COST and RESOLUTION* of these DMDs are not fantastic, especially when you're limited to a wearable-sized DMD. Underneath every micro-mirror is a *MECHANICAL* lever, controlled by an electrical pulse (MEMs), these are not simple, these require lots of moving parts, and a polished *MIRROR*. The moment I said mechanical and mirror I hope everyone understands the limits to dpi of the DMD. While we can obtain arbtriarily high resolution VR, it will no longer be wearable. The lazer would need to be backed by a DMD the size of a sheet of a paper if you want a billion pixels, not to mention the high cost of that producing that.
The solution to cost and size is viable, albeit not commercial yet. GLVs (grating light valves) are in research (I believe stanford univ. is ahead more than others in this technology) and deal with thin film hundreds of nanometers apart from each other which can widen or narrow the space thereby controlling the wavelength of light that passes (color) and the trajectory of the light (position). At current tech. levels, GLVs are 1000x faster that DMDs (you don't need to flip a lever and turn a mirror a large amount), and since we don't care about FPS higher than 30, that extra 1000x speed translates into 1000x *less* material, since we can control the trajectory, we can with an array of 1024 GLVs mimick a 1024x1024 matrix of a DMD. And GLVs have the potential to be 1,000,000x faster, which means next to no material while acheiving equivalent resolution of a gigantic DMD. And cost - yes, with next to no material being involved, the manuf. cost will be peanuts (rest assured they won't sell for peanuts.. hey, we R&D folks need a salary to buy toys!)
Although our eyes don't have great resolution (10m 'pixels' total, with more density in the center of our field of vision), we have *TERRIFIC* interpolation, allowing it to not only stabilize a shaking image (blood pulses our eyes, and we don't exactly stand still - keep your hand still and look carefully at it), but also to interpolate missing points through time. Try looking through a screen door standing close - if you're very still, you'll see pixelated trees through the screen door. Once you start walking, your brain adjusts and you can see "through" the screen.. not that hard. Now imagine that the screen is not a metal impasse but just an absence of cones/rods. Same idea.
I don't dispute Hans' rigor in studying the issue, but how can the correlation of the impact and the magnetic field reversing lead to the conclusion the impact caused the reversal?
And why even compare this 780K yr old impact to what might've done the dinosaurs in 65m yrs ago? It just would confuse people with poor reading skills (*cough* slashdot readers) and lead them to associate this 780K yr old impact with the extinction of the dinasaurs.
Also, the article attemps to explain why the 65m yr old impact would've caused climactic change whereas the 780k yr old impact would not -- I didn't quite understand their argument of why the older impact caused dust clouds leading to extinction while the newer impact did not -- was it because of the composition of ice vs rock?
I think what China is doing is extremely bad for me and others alike in the US, but excellent for it. Protection makes sense when mixed with competition. I just hope it finds a suitable 'x' in the x% local-competition and 100%-x% aggressive-open-competition formula.
The best example is my highschool, which had an idiot coach who reserved the tennis courts four and half of the five days to the Varsity team players, giving only 2 hours for JV players, many of whom had never played tennis before.
The end result was that our varsity team improved dramatically, but our JV team was as bad at the end of the year as the start. What did this mean? Kids like me and a *select* few others with parents willing to pay for lessons were able to practice and get into varsity. Those without the money continued in JV and never made varsity. This resulted in our varsity team winning LESS than our varsity team of years past, because we were filled with the affluent JV players and not the talented-yet-latent JV players.
This ties in wonderfully well into economics. Those who have parents/foundations/communities etc. which let them *practice* are the ones who will succeed in a capitalistic, hyper-aggressive, winner-takes-all society (just watch our Reality Shows where all but the best leave in humilation and with $0).
China realizes that the average chinese family cannot compete with "Varsity" teams and is letting their "JV" teams have court time, in the hope that they will one day become "Varsity." Kudos to the brilliant PRC! However, I really wish I could post more kudos to/my/ country... I also wish the democratic populace would lessen their support for flagship varsity teams (MS, IBM, Oracle, etc.) and think of their JV team which may yield a future Varsity player better than any in existence, given the opportunity to train.
This is not to say let -everyone- have equal time. Oh, not at all! Just let the JV have *some more* time than currently given. Dedicate resources to ANALYZE them, spot the rapid achievers, and send them up to the next grade where they're given some more resources. Let the dedicated resources mitigate the leverage affluence provides to the few.
Please note, there's the even simpler matter of Dominos selling pizzas at $3.50 to kill competition in my homecity, locals unable to sell below $6, only to price it up to $22 once colonizing the area. Pizza Hut moved in and the "added competition" has reduced the price to $20. Yay... duopolies..
Side-rant: I wish schools would teach kids who flunk classes Civics instead of that class again.. I rather they graduate knowing how to be a member of a democracy than memorize the A B B C E D A answers to the final they're retaking for the 5th time. The only Civics anyone learns these days is from Rap which teaches the alternative to the status quo is drugs and promiscuity or from advertisement which teaches you should revitalize your hair by giving patron to status-quo brands X, Y and Z. I doubt drugs, promiscuity, or giving patron to brands will improve our Civics.
Slashdot Mirror
As long as a turing machine uses finite memory of length N, there exists a DFA of N^2 length that accomplishes the same in O(1). Essentially, your stick of memory is a finite number (X). Your algorithm, whatever algorithm it is, deterministically translates X into a new finite number (Y). I can avoid running the algorithm by having a static array that maps X to Y. To turn a 16-bit computer into an O(1) DFA, I need 2^32 bits of memory (a 65536-element array where each value is a 65536-bit string).
Anytime O(...) notation is used, it assumes arbitrary length input (a turing machine is never assumed to work on a finite tape, because it would so obviously reduces to a DFA otherwise).
Furthermore, optimal sorting is rarely expressed as O(N lg N), it is O(N lg k) where k is the # of unique elements. Because most textbooks want to use single-variable Big-O notation, they stick with O(N lg N), but more serious analysis uses multi-variable complexity. k is only pseudo-dependent on N, in that it has to obey the relationship k = N. In the worst case, k = N, and hence sorting is N lg N when expressed in terms of a single-variable. If we're serious about sorting it is O(N lg k). When k is finite, it reduces to merely O(N).
Zero doesn't have a sign, but limits to zero _do_ have a sign, plus, or minus, or plus-or-minus. The limits to 0+ and 0- are convergent limits (the + and - at the _end_ of a number, like 2+ or 2- mean the limit is reaching the number from above or below, and in the case of 0+ and 0-, since "above 0" is positive, and "below 0" is negative, we have different signs). The limits to 0 (with the sign unknown) does not converge (meaning there are multiple results).
Given lim x -> 0+, then 1/x = +inf and Given lim x -> 0-, then 1/x = -inf
Given lim x -> 0 (that is, the sign is "unknown"), then 1/x = { -inf, +inf } -- yes, _two_ answers, just as the sqrt(4) = {+2, -2} whereas |sqrt(4)| = +2
Thus, assuming that 0 = { lim x -> 0+, lim x -> 0- }, yes, we're saying that 0 is of 2 values (one positive, one negative), then 0^0 has 4 possible values, 0+^0-, 0+ ^0+, 0-^0-, 0+^0+. Now, if you work out the limits, you'll see that 0+^0+ converges to 1-, that 0+^0- converges to 1+, that 0-^0+ is... well, I don't have a complex calculator (I'm using perl to plot the curves), but if you work out the math you'll find that it's a complex number which, probably, has a real component that converges to 0 or 1 from above or below and an imaginary component that converges to 0 or 1 from above or below, or a trigonometric function thereof.
I forgot to use < and > instead of < and > Here's a patch:
... opening an SSLSocket (handshake, simplified -- no need to go through Cert chains and other nuances in this example!) ...
... communicating messages, where the message is concatenated with its MAC (message authentication code: sequence + hash), to prevent replay attacks or malicious noise, before being encrypted by the symmetric session key ... // note: PE, PD never need to be used once the SSLSocket is successfully opened
This is a SIMPLIFIED example of a public-private "key-exchange" protocol:
Let PE = public encryption function/key, aka Public Key
Let PD = private decryption function/key, aka Private Key
Let S = symmetric encryption/decryption function/key, aka Session Key
STEP 1
Server --> PE --> Client
Server <-- PE(S) <-- Client
STEP 2
Server --> S(foo+MAC) --> Client
Server <-- S(bar+MAC) <-- Client
Asymmetric encryption (public-private pairs e.g. RSA, DH, El Gamal) use symmetric encryption (AES, 3DES, etc) for the session. Asymmetric encryption is SLOW. No sane implementation ever uses asymmetric encryption on more than the hash of an email (signing) or the symmetric session key (key-exchange). This is a SIMPLIFIED example of a public-private "key-exchange" protocol:
... opening an SSLSocket ... // note: PE, PD never need to be used once the SSLSocket is successfully opened
Let PE = public encryption function/key, aka Public Key
Let PD = private decryption function/key, aka Private Key
Let S = symmetric encryption/decryption function/key, aka Session Key
STEP 1
Server --> PE --> Client
Server S(foo+MAC) --> Client
Server -- S(bar+MAC) -- Client
What does this mean? Two things. First, it means that SSL is as fast as symmetric encryption, because it _is_ symmetric encryption beyond the first part of establishing the connection. Secondly, it means that SSL is no stronger than symmetric encryption because the hacker can _EITHER_ solve PD or S, which can never be harder than solving just for S. The advantage of solving for PD is that the hacker would gain access to ALL sessions with the Server. Solving for S, a "throw-away session key", only gains the hacker access to ONE session. But still, assuming there exists no solution better than brute-force exhaustive search across the space of S, it ~almost~ just as likely you will discover the fixed S as you would a variable S. (For a fixed S you have a 1/S chance of being on your first attempt, a 1/(S-1) chance of being right your second attempt, etc., with a 1/1 (100%) chance of being right on your Sth attempt, but that gives you an average of a 1/(0.5*S) = 2/S chance of being right. For a variable S, you always have a 1/S chance of being right on any attempt. So, it's a 2/S chance (on average) vs 1/S chance (on average). Do you know what that means? They're practically identically difficult problems (both are O(S) complexity). If the fixed S had one extra bit than the variable S, then the amortized chance of being right would be identical. This boils down to the conclusion that communication via fixed symmetric keys are NOT in any way more zero-knowledge hackable (i.e. brute force hackable) than communication via asymmetric keys since the real communication past the handshaking uses a symmetric key.
It would be VERY different to say that fixed symmetric keys are less secure than asymmetric private keys, and I would completely agree with you: there's a logistical problem of passing a fixed symmetric key around to trusted members without a "leak", whereas with asymmetric encryption, I don't worry about leaks or rogue members because I only give out the public key and not the private key. But the primary reason fixed symmetric keys are "less secure" is a logistical problem, and NOT a mathematical problem. Mathematically, symmetric keys are as powerful as needed in a non-quantum-computing environment. That's why top-secret communication using 4096Kbit military-grade RSA (asymmetric) keys in the handshake still use 256bit variable AES (symmetric) keys for the session. Don't confuse the logistical issues of _fixed_ symmetric keys from the technical power of a symmetric key.
Har har! You just commented on a comment about a buyer of an autograph! ...
D'Oh!
I translate it into cowboy english as "it is always a high noon somewhere on Earth". You're right that it doesn't imply the Earth is spherical (besides, the Earth is ovuloid anyways, not spherical). Furthermore, you're reading too much sci-fi if you think you need a high-tech instant-communication device to come up with this. And why do you complicate the issue by insisting it's high noon at one spot and not at another? There's no mention of where it isn't high noon, just that it is high noon somewhere. Think low-tech. Think standing atop a tall dune and seeing far away (wow! information retrieval using photons traveling at light-speed, it's called eyesight!). Stand up on a tall dune, and see the shadows at one end of the horizon to the other. You'll see that somewhere in your visible area, it is high noon (the dune without a shadow), and assuming you're not distracted with ADD, ADHD, XBox, an iPod, a homeland security officer asking you move along because you're making others feel uncomfortable, or a girlfriend who wants you to drive her somewhere, you can stand on that tall dune all day, watching for hours the dune shadows as the sun moves across the sky. What you'll notice is that the area where there are no dune shadows (high noon) will move from one end of the horizon to the other end, smoothly. Any bit of inductive reasoning will come up with the idea that this phenomenon doesn't stop at the end of the visible area, and that some surface beyond the horizon is experiencing high noon, even if it's pitch black where you are.
High-tech solutions are not always needed. A little bit of calm, peace, and 12 hours of distraction-free solitude is all that's required for many powerful revelations.
Either your post is +1 Funny or +1 Troll if you had proper education; or, if you don't have proper education, there should be a -1 Uneducated moderation. See here for a complete synposis of the Teleological argument and its scientific refutes so we don't have to replay hundreds of years of history on a Slashdot thread. If you're too lazy to read, here's the summary:
Teleological argument (quotted from wiki):
1. X is too complex to have occurred randomly or naturally.
2. Therefore, X must have been created by an intelligent being.
3. Y is that intelligent being.
4. Therefore, Y exists.
The Eye Argument (quotted from wiki)
Many creationists cite the eye as a prime example of this principle; "What use is a partly-developed eye?" they ask. Evolutionists provide an explanation for this and may state that creationists are arguing from ignorance, for scientists have devised working hypotheses on how certain body parts and organs could have evolved.
The explanation by evolution gives major evolutionary steps of:
1. No light sensitivity at all.
2. Cells that can sense the presence of light and send a signal to the brain.
3. Development of multiple, co-ordinated cells.
4. Development of a lens to focus the light.
5. Development of the brain enabling processing of this information, into instructions to muscles which operate the organ to detect light in other places.
Creationists would counter that each step in this process is in reality, a huge leap. However, evolutionists would argue that each step is not completed in one change; rather, these are only the major milestones of development, which itself is going on all the time.
QED
It is possible via this approach to graduate from Stanford without having step foot on campus. However, the ambition levels of students who never attended class tended to be lower, and hence I joined on-campus project teams and I took time out from work to always attend meetings. Also, TAs and Profs remember faces far better than email/usenet/chat names and tend not to repeat themselves when they remember you (i.e. when they see you), so if you want high signal:noise, show up at their offices. Asking a question on chat or email tends to get an unnecessarily lengthy (and often belated) reply that wreaks of copy & paste.
Another nice thing about SITN is that it's not a "night course" or some secluded class of people who would be distracted by family, work, or other social commitments. Peers are full-time students and the classes are taught in the morning or afternoon (made available as a recording for those for whom only evenings are free). This is very important and I believe the quality is far superior to a program devoted to catering to part-time students or students who have been out of touch with academics. I was a full-time student at the main RPI Troy campus but occasionally I saw middle aged students in Troy who came from the Hartford campus which caters to professionals studying part-time. These students would take some particular courses which are offered solely at the main campus and the one consistent observation I made was that they all complained about how much harder the courses in the main campus were.
For someone who wants to be pushed into excellence and get a degree which marks a level of accomplishment, I'd strongly recommend enrolling only in programs where your peers are dedicated, on-campus, full-time students who are bright and steeped in academic rigor.
It's important to note the inclusion of Turing-complete gate set -- this with O(1) memory access guarantees the ability to run a VMWare-like app and simulate any x86 processor, albeit by some constant time performance penalty.
> Our present understanding of quantum physics tells us that you can't design a quantum computer that can do all the same math problems as a generic Intel/AMD CPU (e.i. run Windows; play Counterstrike; etc.).
I'm going to have to debunk you on that. QCs require the ability to:
1. CPhase (rotate amplitude on the real-imaginary 2D plane)
2. CNot (quantum entanglement)
3. Mix (reset amplitude to random)
4. Measure (collapse of the probability wave)
and, importantly, 5. NAND (not-and classical gate, fountainhead for all classical and contemporary logic).
The operations 1-4 allows us to model quantum effects - remember, the whole idea for QCs spawned when Richard Feynman asked his CS buddies to model quantum effects and despite their CS prowess, none could model it efficiently, which Feynman rightly concluded as indicating that the Universe had a faster computer to predict and enact quantum decisions than the computers we built; hence, he reasoned, we're using an inefficient construct and tapping into the Universe's compuations of quantum effects will allow us to build a more powerful (time-complexity-wise and not just boosted by a constant-time coefficient) computer. There is nothing a classical machine can do which a QC cannot. A QC must have NAND, else it's rather pathetic with just CPhase, CNot, Mix and Measure.
And the "Windows/Counterstrike" argument is a bit lame - even Sparc processors can't run Windows/Counterstrike, that hardly makes them inferior to Intel/AMD. Assembly-interoperability and Mapping-reducibility are very different things. Transmeta went for the asm-interop route, but any computer scientist will tell you that as long as you can simulate a NAND and have O(1) random access memory, any functionality of a modern day Opteron is mapping reducible to your simulation.
> That being said, the problems that can be solved by quantum computers tend to be the ones that would take a regular CPU until the end of the universe to perform (break strong encryption, large traveling salesman problems, etc.).
Agreed. But a QC is never worse in complexity than a classical computer. It is always equal or better complexity-wise. It may have a horribly constant coefficient, making it 1/100th as fast for operations a classical computer has equal complexity. However, keep in mind that a mere constant of 1/100 or 1/1,000 or even 1/1,000,000 pales in comparison when a QC can complete in O(n) time what a classical computer requires O(n^1.5) time.
The govt could profit forever if more things were considered property and hence were subject to property tax. If ownership of land gets taxed, why shouldn't ownership of the spectrum, or of a company, or of anything? Of course, I'm equally happy if there was NO property tax at all. Consistency is key.
Part of my cricicism on the school system is their treatment of very smart and highly experienced professionals as "novices". I'd rather have a 68yr old IBM TJ Watson vet with a PhD teaching a class than some 22yr old floozy with a 2yr associate's degree in "education".
The larger pipelines are also in anticipation of most compilers performing inlining and loop unrolling, in which case, many asm instructions will occur in sequence without any branching.
Even though this isn't a "big deal" - that is, no passwords are leaked per se, and accounts with similar passwords as the parent rightly noted are most likely indicative of a single user with multiple accounts, there is a better way to store passwords. Given H(P1) and H(P2), it's trivial to prove that (probably)P1==P2 or (certainly)P1!=P2, which is leaking information. Thus, storing H(P1) and H(P2) is a poor way to preserve secrecy of P1 and P2. A just-as-easy approach would be to salt the hash: store H(username1||\0||P1) and H(username2||\0||P2) -- where || is the string-concatenation operator. Assuming no two usernames are the same, and \0 is an invalid character for both username and password, then nothing is leaked about P1 and P2. (Note, \0 is essential because if username1 is "tomharrison" with password1 = "city" and username2 is "tom" with password2 = "harrisoncity", then we leak information that user2 has user1's password prepended with "harrison" unless we have \0 dividing user and password strings) I would actually prefer true salting: H(random1||P1) and H(random2||P2) where random1 & random2 are random (& mathematically non-secret but you shouldn't feel inclined to publicize them) constants stored alongside the username. This avoids the ugly hack of relying on \0 being special. Unfortunately, this relies on change of datastructure instead of a change in the hash function and hence isn't "just-as-easy".
Would the existence of whiteholes and abundance of them suggest that large wormholes are ubiquitous? While there are a lot of measurements supporting blackholes - and rotating blackholes - at the epicenter of galaxies, there seem to be no sound measurements on whiteholes.
Correct me if I'm wrong, but isn't a whitehole a necessary endpoint for a unidirectional wormhole? Also, considering how most blackholes at the epicenter of galaxies lie dormant, their corresponding whiteholes, if any, would be dormant as well, observable only by how they influence ambient light. Since measurements suggesting blackholes are at the center of most all galaxies are relatively new, I need to ask, has there been much study or analysis of observable space to look for corroborating evidence of whiteholes?
You are correct insofar as the approach being similar to the one used for electron scanning microscopes. This project is less about the 'R' and more about the 'D' in R&D. Don't get me wrong, the 'D' is extremely cool, and it's an awesome util, but as you pointed out, the theory has been laid out already.
/general/ solution instead of a specific one the electron scanning microscope solved. I'm glad an american univ is heading in this direction; europe had in the past been leading in image reconstruction (an old slashdot article from the late '90s mentioned a doctoral research paper&project on reconstructing a monitor display purely from the oily reflection from a person's forehead - unlike with a mirror which doesn't disperse the light, undoing the dispersion of light from oily skin is complicated and the transformation & inverse transformation are lossy).
The 'R' portion of the project is to iron out the wrinkles of providing a
It's nice to see computers being put to task on simulation and mathematics instead of perpetually emulating typewriters, hyperlinked magazines, and jukeboxes.
or at least a clever title should be used if the Dell articles see-saw between the possibility that AMD may get a new distributor or not.
crypto signatures are based on signing the hash of the message, not the message itself (this is because signatures are based on loseless decryption, and no one wants to sign a 200KB file with a 200KB signature). Why target P2P when "Verisign-signed" certs can be forged? In other words, bullshit. They might have found some collisions in weaker hash functions, but if _strong_ hash functions were defeated, the concept of security as we know it ceases to exist.
While it takes less money to entice criminals there, it also takes less money for a victim to pressure the police to "prioritize" the case.
When's the last time you know of someone who had a few thousand stolen being given priority police attention in the US? It generally gets swept under the rug and insurance pays for it, raising everyone's premiums (hence, we all pay for the crime). Whereas, in a poorer country, while insurance stills pays for it, the theft would be considered substantial. Moreover, you can pad the constable another couple thousand and the case will probably be escalated to the federal bureau with the full attention of everyone.
Further, the letter stated that the University doesn't even know the password, so it should be kept safe Does any organization keep anything of more informational value than just the salted hash of the password? "We can reset your password, but cannot retrieve your password for you." is the typical disclaimer sent out. Hooray for hash pre-images being difficult.
in 2D riemannian geometry, of which the surface of a sphere is the euclidean analog. Say boats depart in a straight line perpindicular to the equator, thereby being parallel; these two boats will meet at both poles if their lines are extended.
in 2D lobachevskian geometry, of which an area-filled asymptotically to the perimeter of a circle whose diameter is negative-infinity and whose perimeter as at distance 0 from the origin of the circle is the euclidean analog. Any two lines in the circle must interesect since they will converge to the perimeter of the circle which is by definition a single point.
what is reachable and un-reachable, beyond the Slashdot Effect, is a question on what topology you're asking the question. Our universe as an observably euclidean manifold is a small region of a lobachevskian topology. In net-speak, the reachable net is quite different as you build proxies and other bridges to escape local topology.
Now, I mentioned DMDs in the subject-- they are digital micromirror devices also called MEMs, micro-electromechanical-systems. These are what the article states the Virtual-Reality lazer-image is based on. I want to note that while DMDs are far better than lcd-projection (not lcd - lcd *projection* -- where light is either shone off a small high-density lcd screen and reflected out, or where light is shone through a translucent high-density lcd screen), and the contrast/brightness abilities of DMDs are amazing (no loss to semi-permeable substances like lcd), the *COST and RESOLUTION* of these DMDs are not fantastic, especially when you're limited to a wearable-sized DMD. Underneath every micro-mirror is a *MECHANICAL* lever, controlled by an electrical pulse (MEMs), these are not simple, these require lots of moving parts, and a polished *MIRROR*. The moment I said mechanical and mirror I hope everyone understands the limits to dpi of the DMD. While we can obtain arbtriarily high resolution VR, it will no longer be wearable. The lazer would need to be backed by a DMD the size of a sheet of a paper if you want a billion pixels, not to mention the high cost of that producing that.
The solution to cost and size is viable, albeit not commercial yet. GLVs (grating light valves) are in research (I believe stanford univ. is ahead more than others in this technology) and deal with thin film hundreds of nanometers apart from each other which can widen or narrow the space thereby controlling the wavelength of light that passes (color) and the trajectory of the light (position). At current tech. levels, GLVs are 1000x faster that DMDs (you don't need to flip a lever and turn a mirror a large amount), and since we don't care about FPS higher than 30, that extra 1000x speed translates into 1000x *less* material, since we can control the trajectory, we can with an array of 1024 GLVs mimick a 1024x1024 matrix of a DMD. And GLVs have the potential to be 1,000,000x faster, which means next to no material while acheiving equivalent resolution of a gigantic DMD. And cost - yes, with next to no material being involved, the manuf. cost will be peanuts (rest assured they won't sell for peanuts.. hey, we R&D folks need a salary to buy toys!)
Although our eyes don't have great resolution (10m 'pixels' total, with more density in the center of our field of vision), we have *TERRIFIC* interpolation, allowing it to not only stabilize a shaking image (blood pulses our eyes, and we don't exactly stand still - keep your hand still and look carefully at it), but also to interpolate missing points through time. Try looking through a screen door standing close - if you're very still, you'll see pixelated trees through the screen door. Once you start walking, your brain adjusts and you can see "through" the screen.. not that hard. Now imagine that the screen is not a metal impasse but just an absence of cones/rods. Same idea.
I don't dispute Hans' rigor in studying the issue, but how can the correlation of the impact and the magnetic field reversing lead to the conclusion the impact caused the reversal?
And why even compare this 780K yr old impact to what might've done the dinosaurs in 65m yrs ago? It just would confuse people with poor reading skills (*cough* slashdot readers) and lead them to associate this 780K yr old impact with the extinction of the dinasaurs.
Also, the article attemps to explain why the 65m yr old impact would've caused climactic change whereas the 780k yr old impact would not -- I didn't quite understand their argument of why the older impact caused dust clouds leading to extinction while the newer impact did not -- was it because of the composition of ice vs rock?
I think what China is doing is extremely bad for me and others alike in the US, but excellent for it. Protection makes sense when mixed with competition. I just hope it finds a suitable 'x' in the x% local-competition and 100%-x% aggressive-open-competition formula.
/my/ country ... I also wish the democratic populace would lessen their support for flagship varsity teams (MS, IBM, Oracle, etc.) and think of their JV team which may yield a future Varsity player better than any in existence, given the opportunity to train.
The best example is my highschool, which had an idiot coach who reserved the tennis courts four and half of the five days to the Varsity team players, giving only 2 hours for JV players, many of whom had never played tennis before.
The end result was that our varsity team improved dramatically, but our JV team was as bad at the end of the year as the start. What did this mean? Kids like me and a *select* few others with parents willing to pay for lessons were able to practice and get into varsity. Those without the money continued in JV and never made varsity. This resulted in our varsity team winning LESS than our varsity team of years past, because we were filled with the affluent JV players and not the talented-yet-latent JV players.
This ties in wonderfully well into economics. Those who have parents/foundations/communities etc. which let them *practice* are the ones who will succeed in a capitalistic, hyper-aggressive, winner-takes-all society (just watch our Reality Shows where all but the best leave in humilation and with $0).
China realizes that the average chinese family cannot compete with "Varsity" teams and is letting their "JV" teams have court time, in the hope that they will one day become "Varsity." Kudos to the brilliant PRC! However, I really wish I could post more kudos to
This is not to say let -everyone- have equal time. Oh, not at all! Just let the JV have *some more* time than currently given. Dedicate resources to ANALYZE them, spot the rapid achievers, and send them up to the next grade where they're given some more resources. Let the dedicated resources mitigate the leverage affluence provides to the few.
Please note, there's the even simpler matter of Dominos selling pizzas at $3.50 to kill competition in my homecity, locals unable to sell below $6, only to price it up to $22 once colonizing the area. Pizza Hut moved in and the "added competition" has reduced the price to $20. Yay... duopolies..
Side-rant: I wish schools would teach kids who flunk classes Civics instead of that class again.. I rather they graduate knowing how to be a member of a democracy than memorize the A B B C E D A answers to the final they're retaking for the 5th time. The only Civics anyone learns these days is from Rap which teaches the alternative to the status quo is drugs and promiscuity or from advertisement which teaches you should revitalize your hair by giving patron to status-quo brands X, Y and Z. I doubt drugs, promiscuity, or giving patron to brands will improve our Civics.