If people are smart enough to be expected to follow the law, they are smart enough to propose and vote on law.
First, this isn't about intelligence, it's about knowledge. Second, most of us are reasonably good at obeying the law, but that's only because the law was written by educated people so that its letter matched our normal moral behavior. If we had no moral sense, I'm sure we'd be breaking laws left and right. Third, there are many, many laws out there that don't directly apply to me, including the three strikes, frozen property taxes, and Native American casinos initiatives I previously mentioned. And laws have complicated consequences that go beyond their direct effects. It's simply ridiculous to say that the knowledge necessary to write good laws is equal to the knowledge necessary to follow them.
If direct democracy is implemented in any serious manner, people will become familiar enough with the law to do it well. You would study it in civics class in high school. You would talk about it over dinner just like you do other subjects.
It takes a lawyer 3 years of intense study to become familiar with the law. And people who go to law school are typically more interested, intelligent, and hard-working than average. I highly doubt that a semester in high school and a few dinner conversations are going to give the average person an equivalent education.
The California proposition system is essentially direct democracy, and IMO it's a disaster. People aren't lawyers, and they aren't economists -- they simply don't have the skills to determine if a given law is good or not. This means we end up with ridiculous laws that sound good in a 4-word summary, like three strikes (tough on crime -- must be good!) and frozen property taxes (lower taxes -- must be good!). Additionally, as the battle over Native American casinos has shown, the public isn't any harder to buy than a politician.
Direct democracy might work at an extremely local level, but the general public simply does not have the necessary knowledge to participate in large-scale direct democracy.
I understand that the dB scale is logarithmic in intensity. But I think you're confusing changes in dB with changes in perceived volume.
To make it a little more precise, let's do some algebra. Let V(I) be the perceived volume at intensity I. Assuming you agree that every 10 dB increase doubles perceived volume, the equality V(10 * I) = 2 * V(I) should always hold.
Now, you're asserting that volume is logarithmic in intensity; in other words, V(I) = k * log(I). Let's test out the equality:
The decibel scale is logarithmic. So if the ear also used a logarithmic scale, perceived volume would be directly proportional to decibel level. This is clearly not the case: 160 dB sounds far more than twice as loud as 80 dB.
Instead, whenever intensity increases by a factor of 10, volume increases by a factor of 2. This implies that perceived volume is proportional to (intensity) ^ (log10(2)).
Right! These cats are geting all worked up about 1-3dB decreases for each change. Don't they know that the ear is a logarithmic device? It generally takes about 10dB of change to be preceived by most people. -7dB would hardly be noticable!
7 dB is certainly noticeable -- most people describe 1 dB as the smallest audible difference, 3 dB as the smallest significant difference, and 10 dB as about doubling or halving the volume. And technically, if every increase of 10 dB multiplies the intensity by 10 and the perceived volume by 2, then the ear uses a power scale, not a logarithmic scale.
the small states... will likely reject is since it would weaken their power.
In the current winner-take-all system, it's not the small states that have disproportionate power; it's the swing states.
For example, Rhode Island will almost certianly go to Kerry, so neither candidate has an incentive to seek votes there. If the president were elected by popular vote, however, swing voters in Rhode Island would be just as important as swing voters everywhere else. Bush and Kerry would want their votes, so their platforms would be more influenced by Rhode Island's preferences. So even though Rhode Island is a small state, it would gain power if the electoral college were abolished.
Since there aren't very many swing states, I see no reason why the amendment could not pass in the senate and the states.
On the other hand, the Riemann hypothesis is a particular question about a precisely stated function on the precisely defined set of complex numbers. There is only one such function and only one such set of complex numbers, no matter which set theory you are talking about.
I think you're confusing two possible definitions for "the set of complex numbers".
The first is mathematical -- we can call a set S a set of complex numbers if it satisfies certain axioms. With this definition, the set of complex numbers is precisely defined, but there may be many such sets. It may be the case that RH is true in some of these sets and false in others.
The other definition is more philisophical -- you could say that numbers are actual entities, and that there is an actual set of complex numbers that exists in some sense. But while this set is unique, it certainly isn't precisely defined.
Mathematicians use the first definition almost exclusively, because precise definitions are necessary in order to construct valid proofs. So I would say it is possible that RH is neither true nor false.
Say you're a small company competing with Microsoft. They decide that you're infringing on their patent by designing a product that allows double-clicking, and decide to throw a bit of their huge legal budget at you. If you don't have the resources to fight the patent until the case is resolved, you pretty much have no choice but to settle. It's more or less irrelevant that the patent would probably be thrown out if you fought to the end.
I think he's referring to the fact that current gravitational theories don't seem to match observations over extremely small distances (I seem to remember ~10^-30m). So strictly speaking the current theory is "wrong", even though it matches observations extremely well at any reasonable scale.
I also don't have much of a physics background, but I believe we notice protons because they have strong interactions with other particles, not because of their mass. Nuclear forces cause protons and neutrons to cluster together, and electromagnetic forces cause atoms, molecules, and larger objects to form. If WIMPs only interact with (relatively much weaker) gravitational forces, they could easily go unnoticed. Similarly, it's easier to detect electrons than neutrons, even though neutrons are 1000 times as massive.
Re:One thing that's never been clear
on
Hairy Adhesives
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· Score: 5, Informative
From the article:
The total van der Waals force on the spider's feet is very strong, but it is the sum of many very small forces on each molecule. The researchers believe the spider lifts its leg so that the setules are lifted successively, not all at once, and it does not need to be very strong to do this. All you would have to do to lift a future kind of Post-it® note is peel it off slowly.
dt = 1/2*PI*df
If we have a two state device, than this would be teh minimum amount of time we would need to detect a single bit change.
Assuming this is correct, it would seem to imply there is a lower bound on the time it takes to flip a bit using photons of a given frequency. But by increasing the frequency, couldn't this lower bound be made arbitrarily small?
My guess is that the extra power comes from potential energy stored in the magnet. As the motor runs, the magnet becomes weaker and weaker, kind of like draining a battery.
There's an important difference. If I'm given a valid human proof, I can (in principle) study it until I am absolutely 100% sure it is correct. If I accept an invalid human proof, it's my own fault -- I can't blame it on chance. On the other hand, if computer-assisted proofs are allowed, I may accept an invalid proof without making any logical errors. That seems to contradict the concept of a proof.
As an aside, if proofs only need to be probably valid, can a randomized algorithm constitute a proof? Say I write a program that proves P!=NP with 99.99999% probability (assuming the hardware and software works as intended). Does that prove P!=NP?
More accurately, computers usually do what we tell them to. The problem is, sometimes they don't. Chips can be fabricated incorrectly, radiation can corrupt memory -- the list goes on. So even if everything directly human-created, from the code to the hardware specification, were verified to be correct (which ain't gonna happen), we could still only say that the proof is probably valid. And probably isn't good enough for rigorous proof.
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Yep. I made the decision to vote no on any proposition I don't fully understand, and so far that's been all of them.
Direct democracy might work at an extremely local level, but the general public simply does not have the necessary knowledge to participate in large-scale direct democracy.
Your math must be off -- I get 18.4 N.
To make it a little more precise, let's do some algebra. Let V(I) be the perceived volume at intensity I. Assuming you agree that every 10 dB increase doubles perceived volume, the equality V(10 * I) = 2 * V(I) should always hold.
Now, you're asserting that volume is logarithmic in intensity; in other words, V(I) = k * log(I). Let's test out the equality:
which isn't the result we want.On the other hand, I'm asserting that V(I) = k * I^(log_10(2)). Then,
which is exactly what we were looking for.Instead, whenever intensity increases by a factor of 10, volume increases by a factor of 2. This implies that perceived volume is proportional to (intensity) ^ (log10(2)).
For example, Rhode Island will almost certianly go to Kerry, so neither candidate has an incentive to seek votes there. If the president were elected by popular vote, however, swing voters in Rhode Island would be just as important as swing voters everywhere else. Bush and Kerry would want their votes, so their platforms would be more influenced by Rhode Island's preferences. So even though Rhode Island is a small state, it would gain power if the electoral college were abolished.
Since there aren't very many swing states, I see no reason why the amendment could not pass in the senate and the states.
The first is mathematical -- we can call a set S a set of complex numbers if it satisfies certain axioms. With this definition, the set of complex numbers is precisely defined, but there may be many such sets. It may be the case that RH is true in some of these sets and false in others.
The other definition is more philisophical -- you could say that numbers are actual entities, and that there is an actual set of complex numbers that exists in some sense. But while this set is unique, it certainly isn't precisely defined.
Mathematicians use the first definition almost exclusively, because precise definitions are necessary in order to construct valid proofs. So I would say it is possible that RH is neither true nor false.
Say you're a small company competing with Microsoft. They decide that you're infringing on their patent by designing a product that allows double-clicking, and decide to throw a bit of their huge legal budget at you. If you don't have the resources to fight the patent until the case is resolved, you pretty much have no choice but to settle. It's more or less irrelevant that the patent would probably be thrown out if you fought to the end.
I think he's referring to the fact that current gravitational theories don't seem to match observations over extremely small distances (I seem to remember ~10^-30m). So strictly speaking the current theory is "wrong", even though it matches observations extremely well at any reasonable scale.
I also don't have much of a physics background, but I believe we notice protons because they have strong interactions with other particles, not because of their mass. Nuclear forces cause protons and neutrons to cluster together, and electromagnetic forces cause atoms, molecules, and larger objects to form. If WIMPs only interact with (relatively much weaker) gravitational forces, they could easily go unnoticed. Similarly, it's easier to detect electrons than neutrons, even though neutrons are 1000 times as massive.
The total van der Waals force on the spider's feet is very strong, but it is the sum of many very small forces on each molecule. The researchers believe the spider lifts its leg so that the setules are lifted successively, not all at once, and it does not need to be very strong to do this. All you would have to do to lift a future kind of Post-it® note is peel it off slowly.
My guess is that the extra power comes from potential energy stored in the magnet. As the motor runs, the magnet becomes weaker and weaker, kind of like draining a battery.
As an aside, if proofs only need to be probably valid, can a randomized algorithm constitute a proof? Say I write a program that proves P!=NP with 99.99999% probability (assuming the hardware and software works as intended). Does that prove P!=NP?