Yup, I can see that there's easily enough wildlife out there to support the entire US population by hunting. Must have been by accident we practically wiped out buffaloes last time it was a common occupation.
And I don't see how you can describe hunting with modern firearms to be an "awesome skill". Bringing down a charging wild boar with a spear, now that would be impressive.
What's intuitive? It all depends on your experience, education and intelligence. For most people, intuition is the same as common sense. But science only advances when somebody intuits that common sense is wrong.
Think about the great scientific advances. The earth being round. The earth going around the sun. Heavy and light things falling at the same rate. Evolution. Plate techtonics. Wave-particle duality. Nothing going faster than light.
None of these comply with common sense. But when you've understood the arguments behind them, all completely intuitive. And anyway, there are plenty of physical quantities that can only be positive. Absolute temperature. Probabilities. Entropy. Why not mass.
Moreover, consider the basic attributes ("quantum numbers") of fundamental particles and how intuitive they are. OK, so they can have electric charge -- that's positive or negative, i.e. two types of electric charge. Spin -- well that can be "up" or "down", so yes, two types there. But you have to spin an electron 720 degrees to get it back to the orientation you started -- 360 turns it upside down. Is that intuitive? Then there's "colour" (the thing that interacts with the strong nuclear force). That comes in six different types.
If we relied on common-sense intuition to understand science, we'd be stuck in the Middle Ages.
Re:Spamming != bulk mailings
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I, Spammer
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· Score: 4, Interesting
To go wildly offtopic...
Postage stamps were first introduced in Britain, in 1840. As you say, before then it was the recipient who paid for the mail, not the sender.
Now in those days that was sensible, since there was no mail system as such anyway. Cash on delivery was the only way you could be fairly sure that the messenger would actually deliver your letter -- since if he didn't, he wouldn't get paid.
Problem was, people cheated the system. Early hackers, shall we call them, figured out that they didn't need to have their letters actually delivered & paid for to communicate. For instance, if someone wanted the answer to a simple yes-no question (remember, all long-distance communication was by letter then, so this happened a lot), they could set up a code for the response to be communicated by the colour of the envelope. So: messenger arrives with a letter -- but the recipient, having seen the colour of the envelope, says he doesn't want it and refuses to pay.
Solution: set up a national postal system that people trust, so they're willing to prepay for delivery.
Of course, 150 years later and US phone companies make the same mistake with cellphones. Charge people to receive calls + caller id -> don't answer, just call back on a land line.
Let's assume you're right about this powers-of-two thing (I have no idea).
2^64 is more or less equivalent to 10^20. That's over a billion times as much memory as a gigabyte. Since the late 1970s we've gone from having several Kb to several Gb RAM for your average computer. That's a factor of a million. So at the same exponential rate of growth growth, it would take us about 30 years before we'd have that much RAM in a desktop.
That would also mean, to get that much memory in the same size box, that we'd need to reduce the size of each memory element by about a thousand in each linear direction (volume scales as cube of length).
Now at the moment we're down to about 100nm fabrication lengths for memory chips. 1000th of this is 0.1nm, which is about the diameter of a hydrogen atom. That means there's no way we could achieve these memory densities with exiting silicon-based technology.
However there's no reason why it should be impossible. Suppose you've got 10cm^3 of space in a laptop for your memory chips, i.e. a bit more than a cube 2cm each side. To fit in 10^20 bits, you'd need each memory element to have a volume of 10^-25 cubic metres -- that's about 10nm each side, or about a million atoms.
All we need to do is work out how to power, address and cool a functioning chip at that density.
BTW, anyone have any idea about the memory capacity of a human brain? I wonder if you'd need more than 64 bits to address that...
Re:Simple... it's antiwater
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Water Flows Uphill
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· Score: 5, Informative
There can be no doubt, for solid physical reasons, that antiparticles behave identically to regular particles when it comes to gravity.
First of all, the only relevant physical quantity to determine how something is affected by gravity is its mass (and equivalently, in relativity, energy). That's practically the definition of gravity -- the force one body exerts on another by virtue of its mass. In physicist speak, the gravitational field "couples" to mass/energy. Any force having an origin in some other physical quantity is by definition not gravity.
Now we have plenty of experimental evidence -- eg from particle accelerators that antimatter has positive mass, just like regular matter. Indeed, antiparticles have IDENTICAL masses to their corresponding real particles. Therefore they must be affected in the same way as regular matter by gravity.
Secondly, in both relativistic and quantum frameworks, gravity can only be understood if it is always attractive. In other words, mass can only be positive. In quantum terms, this comes out of the fact that gravity must be "spin 2" field. (There's a nice book by Feynman on his attempts to come up with a quantum theory of gravity that explains why it has to be spin 2).
Thirdly, according to quantum field theory the vacuum is filled with "virtual" particles and antiparticles -- that's the zero-point energy of the vacuum. Now the whole point about the vacuum is that it's the lowest possible energy state. If anti particles had negative mass-energy, they'd be in a lower energy state than the vacuum, which means that they'd be stable compared to the vacuum and would not decay back into the vacuum. If that were true, the universe would long ago have filled up with antiparticles...
For this luxury, I'm quite willing to sacrifice some environmental aspect
Sorry, I didn't realise the environment was _yours_ to sacrifice. Sure, global warming, rising sea levels and famines in africa are a perfectly reasonable price to pay for _your_ convenience.
If such "convenience" is all you care about, well, stay in your traffic jam.
I live in central London. Personally I find it more convenient (and a lot more fun) to walk the 2 miles to work everyday, rather than spending the same 30 minutes stuck in a car. I know how long it will take, the route is pleasant, and it's good exercise. Plus if it's raining (or I oversleep), I can be there in 10 minutes by tube (the London subway).
I find it convenient to have have a cinema, a theatre and dozens of great bars, restaurants and nightclubs within 10 minutes walk of my apartment. No need to worry about drinking and driving!
Shopping? Well, I could choose from 4 supermarkets that will deliver to my doorstep, but actually I prefer making the 15 minute walk to the local farmers market. For non-grocery items, if it's too big for public transport, and I don't want to wait for delivery, it's a 10 minute taxi ride to the main shopping district.
People say to me, how can you afford to live in central London -- I reply that I couldn't afford to live anywhere else. What I save on transport alone more than makes up for the increased price of property in the city centre. What I save in real convenience -- the convenience of having everything you need on your doorstep -- is priceless.
No, diamond is very difficult to burn (that's why diamond-tiupped drills don't burst into flame). And in fact, so is pure graphite. One reason for this is that diamond (& pure graphite) is non porous, so any burning can only take place on the surface. (Charcoal briquettes are extremely porous by comparison.)
Another reason is that the carbons in diamond are so tightly bound, you don't get any "diamond dust" lying around that could kick-start the burning. Again, with charcoal, there's tiny bits of carbon everywhere -- and the more you burn, the more carbon dust you create. A lot of what's burning is this surface dust rather than the core briquette.
It's true that if you heat diamond to a very high temperature, the surface will slowly oxidise and "evaporate" to form CO2. But it's practically impossible to persuade diamond to combust fast enough to create a self-sustaining fire. Certainly not in a an 80% nitrogen atmosphere.
I have heard that diamond can combust in liquid oxygen, but that's not a problem in most applications...
Diamond is one of the most remarkable materials known to exist.
Yes we all know it's the hardest material in existence. But it's also the stiffest, the least compressible and the best conductor of heat and sound, and one of the best electrical resistors. And it's not brittle either -- it has a tensile strength equivalent to steel.
In fact one of the potentially biggest uses of diamond coatings is nothing to do with its strength. The combination of electrical resistances and heat conductivity makes diamond coatings ideal for coating electronic components -- it means you can pack components closer together and still have them effectively cooled.
For more info on diamon, go here (free registration required).
The main problem with diamond-tipped tools is that diamond is soluble in iron at high temperatures -- and cutting tools generally get very hot at least in industrial applications.
That means that (a) you can't use a diamond-tipped tool to cut iron or steel, since the diamond tip will just dissolve away, and (b) for the same reason, you don't want to use a diamond coating on steel.
Of course this isn't a problem at low Ts. In fact I use diamond-coated razor blades to shave.
As a Brit what totally shocks me is that Americans have virtually elevated to the status of holy scripture a 220-year-old document written largely by a bunch of slave-owning farmers, and don't imagine that it should ever be changed.
To be fair to the drafters, I don't think they envisaged their constitution as being flawless and unchanging. That's why they ratified the first 12 amendments at the same time as the constitution itself -- to set a precedent.
I'm not saying the constitution is a bad document. It's survived longer than any other written constitution (France got through 5 democratic ones in the same period, not to mention all those dictatorial and monarchical interludes). It's a model for many countries. But it should be regarded as a flexible document that must be adapted as times change, in order that its underlying spirit remains intact. Otherwise constitutionalism becomes another fundamentalism.
No because slavery is illegal. You can't make an enforceable contract to do anything illegal.
But you could very easily put up a sign by your door that anyone entering the premises has to pay you money. That's what happens at most museums.
Of course, unless you've got something to show them, you wouldn't get many visitors that way.
Non-decimal systems have advantages
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Making Change
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· Score: 4, Interesting
First, can't you tell a joke when you see one? (By joke I don't mean the maths is wrong, just that obviously the writer wasn't intending that we move to 18c coins).
Second, what is easy is what comes with practice. Currencies, like most other measurement systems, were not originally decimal, but duodecimal (i.e. using base 12) and various multiples thereof. Right up to the 1970s, the UK used a currency system which had 12 pennies to a shilling and 20 shillings to a pound. The US and UK still use duodecimal for weights and measures (think pounds and feet) and the whole world uses it for time (12/24 hour systems) and angles (360 degrees is 30 times 12).
Why were systems based on numbers like 6, 12, 24, 360 etc. so common, given that we tend to count in decimal? Well, they have large numbers of factors. In other words, while they might be harder to add and subtract in your head than decimal systems, they're much easier to do division with. And since division is much harder to do in mental arithmetic than addition, that's a big advantage.
For example, with 12 ounces in a pound, I can take a half, a third, a quarter, a sixth or a twelth of a pound and still be dealing in whole ounces. With a decimal system, 10 has only 2 factors: 2 and 5. So to buy a quarter of something devised in a decimal system you end up with 2.5.
Now that also has a knock-on effect when making change. Because of the limited factorisation of 10, most decimal systems divide things into 100s or 1000s.
Result: in a decimal currency, you end up not with 10 cents per dollar, but with 100 cents. And that's the real reason you have so much change in your pocket. If we had 12 cents to the dollar (or euro), then by copying the old british system -- with a 1c, 2c, 3c and 6c coin -- you'd never need more than 4 coins to make change from a shilling.
And would the cashier at WalMart be able to handle it? Well first off, maybe if as a result they had to think more as kids they'd be better off at maths to start with. And secondly, since they have to use a calculator now anyway, what would be the difference?
And even the best division of responsibility (whether elections are run by the federal government, the states or a third party) can't stop interference when the person in charge of whoever's running the election is the elder brother of one of the top candidates...
What we really need to do is clamp down on people who actually _sing_ those songs, out loud, without paying a royalty. And I'm not talking just street musicians -- what about those immoral folks who sing in the shower? And the even more wicked ones -- since they try to conceal their crimes -- yes, people who hum along in their heads.
Let's face it. It's wrong. The original artist (via the record company) has complete control over how the music is to be experienced. Any performance not sanctioned by them is clearly illegal. And worse, all those folks who heard you sing would otherwise have bought the CD, so you're losing sales -- stealing from the artist. Not only that, but someone could record you singing the song, even if the original CD was copy protected, which would clearly be a breach of the DMCA.
What doubters need to understand about evolution is that it is not the basis of what we know about biology, but the inevitable consequence of fundamental genetics -- about which we have plenty of proof -- and the mathematics of population growth.
So long as you accept that organisms are subject to mutations, and that these mutations can be inherited -- two things that cannot be denied without throwing out pretty much all basic biology, not to mention the everyday evidence of your own eyes -- evolution must take place.
Inevitably, some individuals will, because of their inherited characteristics, be better suited to their environments than others, and their offspring will eventually dominate the environment. Thus you have evolution within a species.
Inevitably populations in different environments will develop in different directions, depending on what mutations confer an advantage in that environment. That gives you evolution of different species.
Anybody who doesn't believe in evolution, can't believe in dogs -- if humans could breed so many different types of dog from a wolf in a few thousand years, it's obviously possible that far larger changes can take over billions of years.
Of course if you're going to claim the earth is only 6000 years old, there's no hope of persuading you of anything scientific. Though if it were, what interest would God have in making everything look as if it were billions of years old? Some practical joke.
What do you do if you don't have a bat handy (and don't you know they're a protected species?)
Just another advantage of having a power switch on the socket (as we do in the UK)... if you've got a faulty appliance, don't fret about how to unplug it without electrocuting yourself, just switch off the juice at the socket.
Of course if the socket is faulty, you'd better find that bat.
also bathroom outlets in the UK -- even for hard-wired appliances such as heaters -- must be connected via an RCD, which will trip as soon as it detects a current leak. Not to mention that any switches need to be of a pull-cord variety with a double-pole switch. You're more likely to be struck by lightning than electrocuted in a properly wired British bathroom.
Also did you know that the reason most British bathrooms & kitchens have separate hot and cold taps was safety legislation to prevent any chance of the hot water being siphoned back into the cold-water supply. They've only change the rules since the introduction of check-return valves (one-way water valves).
Re:Everything can be related to math.
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Origami and Math
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· Score: 1
Think about what maths is. You start with a limited set of axioms; you choose the axioms, not God. You then apply logical rules to those axioms; again, you choose the rules to apply. Each branch of mathematics is just the consequence of applying the rules you chose to the axioms you chose. Divine intervention doesn't come into it.
For example, consider the proof that there are an infinite number of prime numbers. It's simple: if there were a finite number of primes, you could generate a new one by multiplying them all together, and adding one to the result. Therefore there can't be a finite number of primes.
Now what is needed for that? A concept of number and addition (this gives me multiplication and so division, and so the concept of a prime number). The rest is pure logical deduction -- as is most of the rest of algebra (with a few more axioms).
Now you could say that God created numbers, or God created addition, or God created logical deduction. Maybe she did; but I could easily create the concepts independently. It's not like creating a particle; if you're saying that God must have invented mathematics, you're saying God has a monopoly on ideas, and no-one could have thought of these concepts if God hadn't let you do so. Personally I find the idea of a divine DMCA quite unattractive.
Does that mean that mathematics is a human creation? No; what mathematics is, is the sum total of all possible deductions of self-consistent axioms using self-consistent rules. It therefore has an independent logical existence. A mathematical truth would not cease to be true if the real universe was any different, since mathematics describes its own self-contained universe.
It is true that most of what non-mathematicians consider to be mathematics appears to be grounded in reality; thus take one orange, and another orange, and you have two oranges, so 1+1=2. Indeed until the 19th century almost all mathematics was based on "obvious" axioms, i.e. those you could see were true from everyday experience. For example, euclidean geometry is based on the basic way in which lines seem to behave in the real world.
But as it turned out, the world isn't Euclidean; Einstein showed otherwise. Does that mean that Euclidean geometry is wrong? Of course not; just that it doesn't describe our universe. Pure mathematics is full of concepts and ideas that have no relation to the "real" world -- though it is a tribute to human (not divine) ingenuity that we find applications for them nonetheless.
There are many things that might be considered evidence of a divine being; that the universe obeys mathematical laws is one -- or perhaps more importantly, that the laws that govern the universe tend to be simple, elegant and minimal.
But the fact that mathematical truths exist at all is not evidence of anything, except that it's possible to get a long ay with logic alone.
Re:Everything can be related to math.
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Origami and Math
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· Score: 1
Mathematics is merely an expression of pure logic; it was not created, it simply is. That 2+2=4, or that e^(i*pi)+1=0, are entirely independent of the universe; they are simply logical assertions of the consequences of a set of axioms.
That the universe can be described mathematically might, in some people's opinions, be evidence of the existence of God; but mathematics itself has an independent existence.
Indeed, that something as incredibly beautiful and full of structure can exist independently of any creator, whether human or divine, is perhaps one of the strongest arguments for the non-existence of God.
From a physics point of view, I'd be very wary about baking tapes. Certainly don't do it at home.
Let's not forget that tapes are a magnetic medium. All magnetic media have a temperature (the Curie point) at which they will suddenly demagnetize. Now I don't know what that temperature is for tapes, but it's often not that high.
Additionally information on magnetic media degrades faster at a higher temperature. This is because the way information is stored is basically as an alternating sequence of magnetic domains (areas of the same polarity). With time, large domains grow at the expense of small domains, basically smoothing out the information. Turning up the heat just makes this happen faster.
Yup, but a projector, a decent sound system and a decent screen together will set you back at least $1500. That's 150 movies at the theater already. Let's say the system lasts you three years. That means you have to watch at least one movie per week -- at massively lower sound and video quality than in a real movie theater -- before you start saving money. And that's without figuring in the cost of DVD rentals, which makes a big difference.
I was thinking about getting a projector but worked out that it would end up much more expensive than seeing all the movies I want at the cinema. (Of course I can still watch movies on my small screen if I really want to stay home). Plus my local cinema is closer than my local DVD rental...
Slashdot Mirror
Head up displays? I prefer to use the force...
Yup, I can see that there's easily enough wildlife out there to support the entire US population by hunting. Must have been by accident we practically wiped out buffaloes last time it was a common occupation.
And I don't see how you can describe hunting with modern firearms to be an "awesome skill". Bringing down a charging wild boar with a spear, now that would be impressive.
Also, I think growing food on your land is somehow quintessentially American
Sure, the rest of the world never got past hunter-gathering, right?
What's intuitive? It all depends on your experience, education and intelligence. For most people, intuition is the same as common sense. But science only advances when somebody intuits that common sense is wrong.
Think about the great scientific advances. The earth being round. The earth going around the sun. Heavy and light things falling at the same rate. Evolution. Plate techtonics. Wave-particle duality. Nothing going faster than light.
None of these comply with common sense. But when you've understood the arguments behind them, all completely intuitive. And anyway, there are plenty of physical quantities that can only be positive. Absolute temperature. Probabilities. Entropy. Why not mass.
Moreover, consider the basic attributes ("quantum numbers") of fundamental particles and how intuitive they are. OK, so they can have electric charge -- that's positive or negative, i.e. two types of electric charge. Spin -- well that can be "up" or "down", so yes, two types there. But you have to spin an electron 720 degrees to get it back to the orientation you started -- 360 turns it upside down. Is that intuitive? Then there's "colour" (the thing that interacts with the strong nuclear force). That comes in six different types.
If we relied on common-sense intuition to understand science, we'd be stuck in the Middle Ages.
To go wildly offtopic...
Postage stamps were first introduced in Britain, in 1840. As you say, before then it was the recipient who paid for the mail, not the sender.
Now in those days that was sensible, since there was no mail system as such anyway. Cash on delivery was the only way you could be fairly sure that the messenger would actually deliver your letter -- since if he didn't, he wouldn't get paid.
Problem was, people cheated the system. Early hackers, shall we call them, figured out that they didn't need to have their letters actually delivered & paid for to communicate. For instance, if someone wanted the answer to a simple yes-no question (remember, all long-distance communication was by letter then, so this happened a lot), they could set up a code for the response to be communicated by the colour of the envelope. So: messenger arrives with a letter -- but the recipient, having seen the colour of the envelope, says he doesn't want it and refuses to pay.
Solution: set up a national postal system that people trust, so they're willing to prepay for delivery.
Of course, 150 years later and US phone companies make the same mistake with cellphones. Charge people to receive calls + caller id -> don't answer, just call back on a land line.
Let's assume you're right about this powers-of-two thing (I have no idea).
2^64 is more or less equivalent to 10^20. That's over a billion times as much memory as a gigabyte. Since the late 1970s we've gone from having several Kb to several Gb RAM for your average computer. That's a factor of a million. So at the same exponential rate of growth growth, it would take us about 30 years before we'd have that much RAM in a desktop.
That would also mean, to get that much memory in the same size box, that we'd need to reduce the size of each memory element by about a thousand in each linear direction (volume scales as cube of length).
Now at the moment we're down to about 100nm fabrication lengths for memory chips. 1000th of this is 0.1nm, which is about the diameter of a hydrogen atom. That means there's no way we could achieve these memory densities with exiting silicon-based technology.
However there's no reason why it should be impossible. Suppose you've got 10cm^3 of space in a laptop for your memory chips, i.e. a bit more than a cube 2cm each side. To fit in 10^20 bits, you'd need each memory element to have a volume of 10^-25 cubic metres -- that's about 10nm each side, or about a million atoms.
All we need to do is work out how to power, address and cool a functioning chip at that density.
BTW, anyone have any idea about the memory capacity of a human brain? I wonder if you'd need more than 64 bits to address that...
There can be no doubt, for solid physical reasons, that antiparticles behave identically to regular particles when it comes to gravity.
First of all, the only relevant physical quantity to determine how something is affected by gravity is its mass (and equivalently, in relativity, energy). That's practically the definition of gravity -- the force one body exerts on another by virtue of its mass. In physicist speak, the gravitational field "couples" to mass/energy. Any force having an origin in some other physical quantity is by definition not gravity.
Now we have plenty of experimental evidence -- eg from particle accelerators that antimatter has positive mass, just like regular matter. Indeed, antiparticles have IDENTICAL masses to their corresponding real particles. Therefore they must be affected in the same way as regular matter by gravity.
Secondly, in both relativistic and quantum frameworks, gravity can only be understood if it is always attractive. In other words, mass can only be positive. In quantum terms, this comes out of the fact that gravity must be "spin 2" field. (There's a nice book by Feynman on his attempts to come up with a quantum theory of gravity that explains why it has to be spin 2).
Thirdly, according to quantum field theory the vacuum is filled with "virtual" particles and antiparticles -- that's the zero-point energy of the vacuum. Now the whole point about the vacuum is that it's the lowest possible energy state. If anti particles had negative mass-energy, they'd be in a lower energy state than the vacuum, which means that they'd be stable compared to the vacuum and would not decay back into the vacuum.
If that were true, the universe would long ago have filled up with antiparticles...
For this luxury, I'm quite willing to sacrifice some environmental aspect
Sorry, I didn't realise the environment was _yours_ to sacrifice. Sure, global warming, rising sea levels and famines in africa are a perfectly reasonable price to pay for _your_ convenience.
If such "convenience" is all you care about, well, stay in your traffic jam.
I live in central London. Personally I find it more convenient (and a lot more fun) to walk the 2 miles to work everyday, rather than spending the same 30 minutes stuck in a car. I know how long it will take, the route is pleasant, and it's good exercise. Plus if it's raining (or I oversleep), I can be there in 10 minutes by tube (the London subway).
I find it convenient to have have a cinema, a theatre and dozens of great bars, restaurants and nightclubs within 10 minutes walk of my apartment. No need to worry about drinking and driving!
Shopping? Well, I could choose from 4 supermarkets that will deliver to my doorstep, but actually I prefer making the 15 minute walk to the local farmers market. For non-grocery items, if it's too big for public transport, and I don't want to wait for delivery, it's a 10 minute taxi ride to the main shopping district.
People say to me, how can you afford to live in central London -- I reply that I couldn't afford to live anywhere else. What I save on transport alone more than makes up for the increased price of property in the city centre. What I save in real convenience -- the convenience of having everything you need on your doorstep -- is priceless.
No, diamond is very difficult to burn (that's why diamond-tiupped drills don't burst into flame). And in fact, so is pure graphite. One reason for this is that diamond (& pure graphite) is non porous, so any burning can only take place on the surface. (Charcoal briquettes are extremely porous by comparison.)
Another reason is that the carbons in diamond are so tightly bound, you don't get any "diamond dust" lying around that could kick-start the burning. Again, with charcoal, there's tiny bits of carbon everywhere -- and the more you burn, the more carbon dust you create. A lot of what's burning is this surface dust rather than the core briquette.
It's true that if you heat diamond to a very high temperature, the surface will slowly oxidise and "evaporate" to form CO2. But it's practically impossible to persuade diamond to combust fast enough to create a self-sustaining fire. Certainly not in a an 80% nitrogen atmosphere.
I have heard that diamond can combust in liquid oxygen, but that's not a problem in most applications...
Diamond is one of the most remarkable materials known to exist.
Yes we all know it's the hardest material in existence. But it's also the stiffest, the least compressible and the best conductor of heat and sound, and one of the best electrical resistors. And it's not brittle either -- it has a tensile strength equivalent to steel.
In fact one of the potentially biggest uses of diamond coatings is nothing to do with its strength. The combination of electrical resistances and heat conductivity makes diamond coatings ideal for coating electronic components -- it means you can pack components closer together and still have them effectively cooled.
For more info on diamon, go here (free registration required).
Actually you can by these in Europe now: the Wilkinson Sword FX Diamond
The main problem with diamond-tipped tools is that diamond is soluble in iron at high temperatures -- and cutting tools generally get very hot at least in industrial applications.
That means that (a) you can't use a diamond-tipped tool to cut iron or steel, since the diamond tip will just dissolve away, and (b) for the same reason, you don't want to use a diamond coating on steel.
Of course this isn't a problem at low Ts. In fact I use diamond-coated razor blades to shave.
As a Brit what totally shocks me is that Americans have virtually elevated to the status of holy scripture a 220-year-old document written largely by a bunch of slave-owning farmers, and don't imagine that it should ever be changed.
To be fair to the drafters, I don't think they envisaged their constitution as being flawless and unchanging. That's why they ratified the first 12 amendments at the same time as the constitution itself -- to set a precedent.
I'm not saying the constitution is a bad document. It's survived longer than any other written constitution (France got through 5 democratic ones in the same period, not to mention all those dictatorial and monarchical interludes). It's a model for many countries. But it should be regarded as a flexible document that must be adapted as times change, in order that its underlying spirit remains intact. Otherwise constitutionalism becomes another fundamentalism.
No because slavery is illegal. You can't make an enforceable contract to do anything illegal.
But you could very easily put up a sign by your door that anyone entering the premises has to pay you money. That's what happens at most museums.
Of course, unless you've got something to show them, you wouldn't get many visitors that way.
First, can't you tell a joke when you see one? (By joke I don't mean the maths is wrong, just that obviously the writer wasn't intending that we move to 18c coins).
Second, what is easy is what comes with practice. Currencies, like most other measurement systems, were not originally decimal, but duodecimal (i.e. using base 12) and various multiples thereof. Right up to the 1970s, the UK used a currency system which had 12 pennies to a shilling and 20 shillings to a pound. The US and UK still use duodecimal for weights and measures (think pounds and feet) and the whole world uses it for time (12/24 hour systems) and angles (360 degrees is 30 times 12).
Why were systems based on numbers like 6, 12, 24, 360 etc. so common, given that we tend to count in decimal? Well, they have large numbers of factors. In other words, while they might be harder to add and subtract in your head than decimal systems, they're much easier to do division with. And since division is much harder to do in mental arithmetic than addition, that's a big advantage.
For example, with 12 ounces in a pound, I can take a half, a third, a quarter, a sixth or a twelth of a pound and still be dealing in whole ounces. With a decimal system, 10 has only 2 factors: 2 and 5. So to buy a quarter of something devised in a decimal system you end up with 2.5.
Now that also has a knock-on effect when making change. Because of the limited factorisation of 10, most decimal systems divide things into 100s or 1000s.
Result: in a decimal currency, you end up not with 10 cents per dollar, but with 100 cents. And that's the real reason you have so much change in your pocket. If we had 12 cents to the dollar (or euro), then by copying the old british system -- with a 1c, 2c, 3c and 6c coin -- you'd never need more than 4 coins to make change from a shilling.
And would the cashier at WalMart be able to handle it? Well first off, maybe if as a result they had to think more as kids they'd be better off at maths to start with. And secondly, since they have to use a calculator now anyway, what would be the difference?
And even the best division of responsibility (whether elections are run by the federal government, the states or a third party) can't stop interference when the person in charge of whoever's running the election is the elder brother of one of the top candidates...
Why stop at banning reproduction of song lyrics?
What we really need to do is clamp down on people who actually _sing_ those songs, out loud, without paying a royalty. And I'm not talking just street musicians -- what about those immoral folks who sing in the shower? And the even more wicked ones -- since they try to conceal their crimes -- yes, people who hum along in their heads.
Let's face it. It's wrong. The original artist (via the record company) has complete control over how the music is to be experienced. Any performance not sanctioned by them is clearly illegal. And worse, all those folks who heard you sing would otherwise have bought the CD, so you're losing sales -- stealing from the artist.
Not only that, but someone could record you singing the song, even if the original CD was copy protected, which would clearly be a breach of the DMCA.
I know theft when I see it.
What doubters need to understand about evolution is that it is not the basis of what we know about biology, but the inevitable consequence of fundamental genetics -- about which we have plenty of proof -- and the mathematics of population growth.
So long as you accept that organisms are subject to mutations, and that these mutations can be inherited -- two things that cannot be denied without throwing out pretty much all basic biology, not to mention the everyday evidence of your own eyes -- evolution must take place.
Inevitably, some individuals will, because of their inherited characteristics, be better suited to their environments than others, and their offspring will eventually dominate the environment. Thus you have evolution within a species.
Inevitably populations in different environments will develop in different directions, depending on what mutations confer an advantage in that environment. That gives you evolution of different species.
Anybody who doesn't believe in evolution, can't believe in dogs -- if humans could breed so many different types of dog from a wolf in a few thousand years, it's obviously possible that far larger changes can take over billions of years.
Of course if you're going to claim the earth is only 6000 years old, there's no hope of persuading you of anything scientific. Though if it were, what interest would God have in making everything look as if it were billions of years old? Some practical joke.
What do you do if you don't have a bat handy (and don't you know they're a protected species?)
Just another advantage of having a power switch on the socket (as we do in the UK)... if you've got a faulty appliance, don't fret about how to unplug it without electrocuting yourself, just switch off the juice at the socket.
Of course if the socket is faulty, you'd better find that bat.
also bathroom outlets in the UK -- even for hard-wired appliances such as heaters -- must be connected via an RCD, which will trip as soon as it detects a current leak. Not to mention that any switches need to be of a pull-cord variety with a double-pole switch. You're more likely to be struck by lightning than electrocuted in a properly wired British bathroom.
Also did you know that the reason most British bathrooms & kitchens have separate hot and cold taps was safety legislation to prevent any chance of the hot water being siphoned back into the cold-water supply. They've only change the rules since the introduction of check-return valves (one-way water valves).
Think about what maths is. You start with a limited set of axioms; you choose the axioms, not God. You then apply logical rules to those axioms; again, you choose the rules to apply. Each branch of mathematics is just the consequence of applying the rules you chose to the axioms you chose. Divine intervention doesn't come into it.
For example, consider the proof that there are an infinite number of prime numbers. It's simple: if there were a finite number of primes, you could generate a new one by multiplying them all together, and adding one to the result. Therefore there can't be a finite number of primes.
Now what is needed for that? A concept of number and addition (this gives me multiplication and so division, and so the concept of a prime number). The rest is pure logical deduction -- as is most of the rest of algebra (with a few more axioms).
Now you could say that God created numbers, or God created addition, or God created logical deduction. Maybe she did; but I could easily create the concepts independently. It's not like creating a particle; if you're saying that God must have invented mathematics, you're saying God has a monopoly on ideas, and no-one could have thought of these concepts if God hadn't let you do so. Personally I find the idea of a divine DMCA quite unattractive.
Does that mean that mathematics is a human creation? No; what mathematics is, is the sum total of all possible deductions of self-consistent axioms using self-consistent rules. It therefore has an independent logical existence. A mathematical truth would not cease to be true if the real universe was any different, since mathematics describes its own self-contained universe.
It is true that most of what non-mathematicians consider to be mathematics appears to be grounded in reality; thus take one orange, and another orange, and you have two oranges, so 1+1=2. Indeed until the 19th century almost all mathematics was based on "obvious" axioms, i.e. those you could see were true from everyday experience. For example, euclidean geometry is based on the basic way in which lines seem to behave in the real world.
But as it turned out, the world isn't Euclidean; Einstein showed otherwise. Does that mean that Euclidean geometry is wrong? Of course not; just that it doesn't describe our universe. Pure mathematics is full of concepts and ideas that have no relation to the "real" world -- though it is a tribute to human (not divine) ingenuity that we find applications for them nonetheless.
There are many things that might be considered evidence of a divine being; that the universe obeys mathematical laws is one -- or perhaps more importantly, that the laws that govern the universe tend to be simple, elegant and minimal.
But the fact that mathematical truths exist at all is not evidence of anything, except that it's possible to get a long ay with logic alone.
Mathematics is merely an expression of pure logic; it was not created, it simply is. That 2+2=4, or that e^(i*pi)+1=0, are entirely independent of the universe; they are simply logical assertions of the consequences of a set of axioms.
That the universe can be described mathematically might, in some people's opinions, be evidence of the existence of God; but mathematics itself has an independent existence.
Indeed, that something as incredibly beautiful and full of structure can exist independently of any creator, whether human or divine, is perhaps one of the strongest arguments for the non-existence of God.
From a physics point of view, I'd be very wary about baking tapes. Certainly don't do it at home.
Let's not forget that tapes are a magnetic medium. All magnetic media have a temperature (the Curie point) at which they will suddenly demagnetize. Now I don't know what that temperature is for tapes, but it's often not that high.
Additionally information on magnetic media degrades faster at a higher temperature. This is because the way information is stored is basically as an alternating sequence of magnetic domains (areas of the same polarity). With time, large domains grow at the expense of small domains, basically smoothing out the information. Turning up the heat just makes this happen faster.
You can't beat entropy.
Yup, but a projector, a decent sound system and a decent screen together will set you back at least $1500. That's 150 movies at the theater already. Let's say the system lasts you three years. That means you have to watch at least one movie per week -- at massively lower sound and video quality than in a real movie theater -- before you start saving money. And that's without figuring in the cost of DVD rentals, which makes a big difference.
I was thinking about getting a projector but worked out that it would end up much more expensive than seeing all the movies I want at the cinema. (Of course I can still watch movies on my small screen if I really want to stay home). Plus my local cinema is closer than my local DVD rental...