They then go on to say that "In Furey’s model, the symmetries associated with how particles move and rotate in space-time, together known as the Lorentz group, arise from the quaternionic CxH part of the algebra."
I'm no expert, but from the Wikipedia page it sounds like the biquaternions are that CxH part. (That is, they're quaternions where each "value" is actually complex.)
Yup. The biquaternions are indeed CxH. They can also be represented by 2x2 complex matrices where the basis vectors for the three spatial dimensions are represented by the three Pauli spin matrices and the basis vector the time dimension by the 2x2 identity matrix.
True, ordinary quaternions aren't that useful for describing spacetime but biquaternions give a very natural and elegant way to model the space-time of special relativity. In particular, Maxwell's equations can be written as one simple equation which is manifestly covariant. Lorentz transformations in this algebra have the matrix representation SL(2,C), the set of complex 2x2 matrices with determinant one which is the covering group of the 4x4 matrix algebra representing proper, orthochronous Lorentz transformations. In a sense, biquaternions are to Lorentz transformations in special relativity what quaternions are to rotations in three dimensional Euclidean space.
Given that the technology exists today to build passenger planes which require no flight crew at all, I can imagine why someone in their late teens/early twenties deciding on a career path would be hesitant to make the HUGE investment of time and money it requires to become a commercial airline pilot. My guess is within ten years, you will start to see automated commercial flights in which the "pilot" doesn't need to touch anything from pushback at the departing gate to pulling up at the arrival gate, and within twenty, you'll start to see flights with no flight crew on board at all. Why would anyone want to start a career in that field now? I think the pilot shortage problem is only going to get worse in the years to come, before automation takes over, and the shortage may accelerate the trend to automation.
From what I understand, he didn't assert a 5th Amendment right, but rather, he claimed to have "forgotten" his password. The judge found that unlikely and so jailed him for contempt.
Before you guys get excited, this is DRM=Direct Rendering Manager (Linux's graphic driver infrastructure), and it has nothing to do with Digital Rights Managemtn.
Wow! In that case, this could be about the most misleading Slashdot headline ever. And that's really saying something!
This is great news for the school-shooting industry. I expect that the NRA and Second Amendment activists are thrilled at having these new tools to murder children.
Yeah, because the existing AR-15 and similar weapons which are readily available all across the country are no match for these plastic super weapons, which on a good day, may be able to fire one bullet without exploding and killing the shooter!
What if you will be out driving and don't want the police to have access to your phone, but don't want to wait one hour after using it before leaving the house? Is there a way to bypass the one-hour wait feature and tell the phone to immediately disable the USB when you next lock the phone? People should be able to activate maximum device security whenever they please.
It all seemed perfectly clear to me what was happening and nothing I just read in TFA was any sort of revelation to me. Do people really have a hard time understanding what was going on there?
The article didn't provide a link to the SCOTUS opinion, so here it is. It is an interesting split. Thomas wrote for the majority and was joined by Roberts, Kennedy, Ginsburg, Alito, Sotomayor, and Kagen. Gorsuch wrote the dissent, joined by Breyer.
Students take exams in the U.S.A. as well, and I don't think the American government has ever shut down the entire Internet to prevent cheating. Why does Algeria have so much more trouble dealing with cheating than America? Can Algeria learn anything from the American model?
I'm always losing thumb drives. There must be half a dozen of them in my house that I have no idea where they are. If I could hire one of these dogs to come by and find them all for me, that would be great!
Some people will tell you that quantum uncertanties introduce randomness, but my theory discounts that.
Please tell us more about your theory. I'd be interested in reading about it. And if I sound snarky, sorry, but I was predestined by the universe to ask you that question.
Yeah, the headline is a bit misleading. It would have been better to say, "organic compounds" or "organic chemicals" were found on Mars. The phrase "organic matter" is somewhat ambiguous and is suggestive of decomposing Martian bodies.
So where's the quantum hardware to making this all work?
I was confused by this point too, till I did some reading. "Post-quantum cryptography" is NOT the same thing as "Quantum cryptography". The former merely refers to cryptographic algorithms for which there are no known algorithms for quantum computers which can break them. So, RSA would not be considered post-quantum, because Shore's algorithm can break it.
The question of whether or not P=NP is not really relevant in the realm quantum computing, because concepts such as P-space, NP-space, etc. are defined in terms of classical computing, i.e. how many steps would a Turing machine take to solve a problem, and in particular what is the growth law of the number of steps with respect to the size of the input. Quantum computers are completely outside the realm of Turning machines. Talking about P vs. NP in the context of quantum computers would be like talking about the congestion on the Interstate to someone flying a plane.
The problem is that you would need to convert a quark to an antiquark, which is a bit tricky.
You can't turn quarks into anti-quarks, and this is directly related to the conservation of
baryon number. Protons and neutrons have baryon number 1 each, while mesons have baryon number 0, and as far as we can tell, baryon number is a strictly conserved quantity. Since protons and neutrons are the lightest baryons, the "sub-nuclear" fission described is, as far as we know, not possible under the laws of physics as we understand them.
Amazon has profited from the infrastructure that the Seattle taxpayers have provided for them over the years, including an education system that has provided the workers that have been the engine that has driven Amazon's wealth. And now that Seattle is asking Amazon to give a tiny percentage back to help the community that fostered them, they threaten to leave.
This is the kind of selfish short-term thinking that will destroy this country.
Amazon already pays taxes like everyone else. This is a new, special tax which punishes only the most successful companies, i.e. those that are bringing the most wealth into the community. I think its highly counter-productive.
The reasoning behind this tax is the idea that big employers like Amazon are creating high salary jobs in the community which are driving up the price of housing. Therefore, the homelessness is, at least in part, Amazon's fault, and they should pay to "fix" the problem through a special tax, aimed exclusively at those businesses which are bringing so much money into the community.
With this kind of insane logic, the city will doom itself. Companies like Amazon should leave and set up shop elsewhere. We'll see if that fixes the problems in Seattle's economy.
How in the hell is mandatory arbitration for customers legal? That makes zero sense. For any business.
Actually, it makes a lot of sense. Lawsuits in courts can be very expensive to litigate and damage awards are often very high. Arbitration generally results in much more reasonable judgements.
What you're saying is true, but what I think the previous poster was referring to was mens rea vs. actus rea. When the police say they dropped charges because they didn't believe there was intent to commit a crime, they are suggesting there was indeed actus rea, but there was no mens rea. What the GP is suggesting, I think, is that there was neither actus rea nor mens rea, and I agree.
Really? It's the system we've been using for hundreds of years. Phones, computers, audio cassettes don't automatically forget you, so there's digital precedent.
But that's not really a good analogy. If I forget to wipe my computer's hard drive before I sell it to someone else, it's my privacy that's compromised, not the new owner's. In this case, it sounds like the reverse.
Slashdot Mirror
They then go on to say that "In Furey’s model, the symmetries associated with how particles move and rotate in space-time, together known as the Lorentz group, arise from the quaternionic CxH part of the algebra."
I'm no expert, but from the Wikipedia page it sounds like the biquaternions are that CxH part. (That is, they're quaternions where each "value" is actually complex.)
Yup. The biquaternions are indeed CxH. They can also be represented by 2x2 complex matrices where the basis vectors for the three spatial dimensions are represented by the three Pauli spin matrices and the basis vector the time dimension by the 2x2 identity matrix.
True, ordinary quaternions aren't that useful for describing spacetime but biquaternions give a very natural and elegant way to model the space-time of special relativity. In particular, Maxwell's equations can be written as one simple equation which is manifestly covariant. Lorentz transformations in this algebra have the matrix representation SL(2,C), the set of complex 2x2 matrices with determinant one which is the covering group of the 4x4 matrix algebra representing proper, orthochronous Lorentz transformations. In a sense, biquaternions are to Lorentz transformations in special relativity what quaternions are to rotations in three dimensional Euclidean space.
The Q language has nothing to do with quantum computing (other than both their names start with a Q).
And more to the point, Q and Q# have absolutely nothing to do with each other. The similarity in names is purely coincidence: they are unrelated.
Given that the technology exists today to build passenger planes which require no flight crew at all, I can imagine why someone in their late teens/early twenties deciding on a career path would be hesitant to make the HUGE investment of time and money it requires to become a commercial airline pilot. My guess is within ten years, you will start to see automated commercial flights in which the "pilot" doesn't need to touch anything from pushback at the departing gate to pulling up at the arrival gate, and within twenty, you'll start to see flights with no flight crew on board at all. Why would anyone want to start a career in that field now? I think the pilot shortage problem is only going to get worse in the years to come, before automation takes over, and the shortage may accelerate the trend to automation.
From what I understand, he didn't assert a 5th Amendment right, but rather, he claimed to have "forgotten" his password. The judge found that unlikely and so jailed him for contempt.
Before you guys get excited, this is DRM=Direct Rendering Manager (Linux's graphic driver infrastructure), and it has nothing to do with Digital Rights Managemtn.
Wow! In that case, this could be about the most misleading Slashdot headline ever. And that's really saying something!
This is great news for the school-shooting industry. I expect that the NRA and Second Amendment activists are thrilled at having these new tools to murder children.
Yeah, because the existing AR-15 and similar weapons which are readily available all across the country are no match for these plastic super weapons, which on a good day, may be able to fire one bullet without exploding and killing the shooter!
What if you will be out driving and don't want the police to have access to your phone, but don't want to wait one hour after using it before leaving the house? Is there a way to bypass the one-hour wait feature and tell the phone to immediately disable the USB when you next lock the phone? People should be able to activate maximum device security whenever they please.
It all seemed perfectly clear to me what was happening and nothing I just read in TFA was any sort of revelation to me. Do people really have a hard time understanding what was going on there?
Yes.
And here I am, freezing by arse off down here in New Zealand where it's cold, went and windy and I've had a cold for over a month now.
Throw some of that heat down this way guys!
Actually, New Zealand is in the southern hemisphere so it is winter now. It will be warmer in the summer months.
and the threat of three months' jail for those caught repeatedly using single-use plastics.
If people are repeatedly using them, they're not single-use plastics, by definition.
The article didn't provide a link to the SCOTUS opinion, so here it is. It is an interesting split. Thomas wrote for the majority and was joined by Roberts, Kennedy, Ginsburg, Alito, Sotomayor, and Kagen. Gorsuch wrote the dissent, joined by Breyer.
Students take exams in the U.S.A. as well, and I don't think the American government has ever shut down the entire Internet to prevent cheating. Why does Algeria have so much more trouble dealing with cheating than America? Can Algeria learn anything from the American model?
I'm glad I installed Cat 5e ethernet cable in my home 10 years ago!
I'm always losing thumb drives. There must be half a dozen of them in my house that I have no idea where they are. If I could hire one of these dogs to come by and find them all for me, that would be great!
Some people will tell you that quantum uncertanties introduce randomness, but my theory discounts that.
Please tell us more about your theory. I'd be interested in reading about it. And if I sound snarky, sorry, but I was predestined by the universe to ask you that question.
Yeah, the headline is a bit misleading. It would have been better to say, "organic compounds" or "organic chemicals" were found on Mars. The phrase "organic matter" is somewhat ambiguous and is suggestive of decomposing Martian bodies.
So where's the quantum hardware to making this all work?
I was confused by this point too, till I did some reading. "Post-quantum cryptography" is NOT the same thing as "Quantum cryptography". The former merely refers to cryptographic algorithms for which there are no known algorithms for quantum computers which can break them. So, RSA would not be considered post-quantum, because Shore's algorithm can break it.
Quantum computation doesn't guarantee NP = P.
The question of whether or not P=NP is not really relevant in the realm quantum computing, because concepts such as P-space, NP-space, etc. are defined in terms of classical computing, i.e. how many steps would a Turing machine take to solve a problem, and in particular what is the growth law of the number of steps with respect to the size of the input. Quantum computers are completely outside the realm of Turning machines. Talking about P vs. NP in the context of quantum computers would be like talking about the congestion on the Interstate to someone flying a plane.
The problem is that you would need to convert a quark to an antiquark, which is a bit tricky.
You can't turn quarks into anti-quarks, and this is directly related to the conservation of baryon number. Protons and neutrons have baryon number 1 each, while mesons have baryon number 0, and as far as we can tell, baryon number is a strictly conserved quantity. Since protons and neutrons are the lightest baryons, the "sub-nuclear" fission described is, as far as we know, not possible under the laws of physics as we understand them.
Amazon has profited from the infrastructure that the Seattle taxpayers have provided for them over the years, including an education system that has provided the workers that have been the engine that has driven Amazon's wealth. And now that Seattle is asking Amazon to give a tiny percentage back to help the community that fostered them, they threaten to leave.
This is the kind of selfish short-term thinking that will destroy this country.
Amazon already pays taxes like everyone else. This is a new, special tax which punishes only the most successful companies, i.e. those that are bringing the most wealth into the community. I think its highly counter-productive.
The reasoning behind this tax is the idea that big employers like Amazon are creating high salary jobs in the community which are driving up the price of housing. Therefore, the homelessness is, at least in part, Amazon's fault, and they should pay to "fix" the problem through a special tax, aimed exclusively at those businesses which are bringing so much money into the community.
With this kind of insane logic, the city will doom itself. Companies like Amazon should leave and set up shop elsewhere. We'll see if that fixes the problems in Seattle's economy.
How in the hell is mandatory arbitration for customers legal? That makes zero sense. For any business.
Actually, it makes a lot of sense. Lawsuits in courts can be very expensive to litigate and damage awards are often very high. Arbitration generally results in much more reasonable judgements.
What you're saying is true, but what I think the previous poster was referring to was mens rea vs. actus rea . When the police say they dropped charges because they didn't believe there was intent to commit a crime, they are suggesting there was indeed actus rea, but there was no mens rea. What the GP is suggesting, I think, is that there was neither actus rea nor mens rea, and I agree.
Really? It's the system we've been using for hundreds of years. Phones, computers, audio cassettes don't automatically forget you, so there's digital precedent.
But that's not really a good analogy. If I forget to wipe my computer's hard drive before I sell it to someone else, it's my privacy that's compromised, not the new owner's. In this case, it sounds like the reverse.