The essence of understanding math is being able to use it to solve problems. Math problems are like chess problems: they both have a start state and an end state and a solution consists of a sequence of legal moves. Routine problems are easy, like mate-in-1 or a simple application of a single mathematical rule. Non-routine problems require you to think a few moves ahead, but if you can't do that, you don't really understand the moves/material.
It's important to become proficient at non-routine applications of basic material before moving on to more advanced material like calculus. As the author of The Calculus Trap writes: Rather than learning more and more tools, students are better off learning how to take tools they have and apply them to complex problems.
To this end, I recommend The Art of Problem Solving Volume 1: the basics & The Art of Problem Solving Volume 2: and beyond. They are the best math textbooks I have ever seen. The intuitive explanations really sink in, so no memorization is required. But the key is that each section is followed by a bunch of non-routine problems from middle-school and high-school math contests like MATHCOUNTS and AMC. These are a fun way to make the material second nature, and besides, it's pretty motivating to know that a bunch of middle- or high-school kids solved the problem you're struggling with. (I want a shirt that says I'm as good as a middle schooler on the front, and on the back says MATHCOUNTS.)
After studying the first few chapters of Volume 1, you will be able to solve problems such as these:
The formula N = 8 * 10^8 * x-3/2 gives, for a certain group, the number of individuals whose income exceeds x dollars. What is the smallest possible value of the lowest income of the wealthiest 800 individuals? (AHSME 1960)
Find Sqrt[53 - 8 Sqrt[15]]. (MATHCOUNTS 1990)
If for three distinct positive numbers x, y, and z: y/(x-z) = (x+y)/z = x/y,
then find the numerical value of x/y. (AHSME 1992)
For each of n = 84 and n = 88, find the smallest integer multiple of n whose base 10 representation consists entirely of 6's and 7's. (USAMTS 1)
There can be a surprising amount of depth to these "middle-school math" problems. The concepts they cover are the fundamental building blocks upon which calculus is built.
This post is based in part upon similar posts of mine at Reddit and MathNotations.
Agreed. I couldn't stand Rainbow's End, though I read it through to the end because it was written by Vinge, and I loved his other work. This frankly makes me lose faith in the Hugo as a guidepost to what to read.
A free-market economics think tank published an interesting article a few days ago on this very subject, called The Coming Second Life Business Cycle.
Second Life's economy could reasonably be compared to that of a small foreign country dependent on tourism. Consumers are inhabitants of the real world who take what are essentially pleasure trips to Second Life. However, it appears very likely that Second Life will experience at least some form of economic recession.
The fact that he will beat you up if you refuse is the immoral part, not the offer.
Yet the government will beat up tax resistors (who haven't left the country). Does that make its offer immoral?
How is the Mafia example any different than the police?
Couldn't have said it better myself.:)
The point that the quote addressed was whether or not taking money from everyone (taxes) and redistributing it to the poor could be moral... of course it is.
"If someone can recognize an act of unjust aggression when it is perpetrated
by one individual against another, but not when the same act is
perpetrated by an organized group of individuals, such a person must be
confused about right and wrong."
-- Lao Tzu
[R]eaching into one's own pocket to assist his fellow man is noble and worthy of praise. Reaching into another person's pocket to assist one's fellow man is despicable and worthy of condemnation.
For the Christians among us, socialism and the welfare state must be seen as sinful. When God gave Moses the commandment "Thou shalt not steal", I'm sure He didn't mean thou shalt not steal unless there's a majority vote. And, I'm sure that if you asked God if it's okay just being a recipient of stolen property, He would deem that a sin as well.
If gold made a decent currency, then it would've been flat across that period.
Due to advances in technology, the real prices of many consumer goods should actually drop over time. Why would a "decent currency" freeze the price of a cell phone (for example) at $3000 just because that's what they cost years ago?
Brackett's Data Resource Quality is the definitive tome on organizing data. From creating a sytematic data naming taxonomy with comprehensive field definitions to specifying precise data integrity rules, this book tells you everything you need to know to manage data collections of any size.
That said, this is probably overkill for your stated purpose of categorizing email messages. A good email search engine would probably serve you better.
By following these easy instructions, you too can encrypt your data and swap partitions with Loop-AES.
(The instructions are for Linux From Scratch, but they worked fine on my Debian box.) This way, no unencrypted data ever touches the disk; even if your computer is stolen, the thief can't read your data.
Local IPv6 addresses don't offer any advantages over 10.* IPv4 addresses.
they do, though. having true end-to-end communication means that peer to
peer applications like voice over IP or BitTorrent actually work.
Clearly, Bernstein is referring to IPv6 addresses as presently implemented on the Internet at large.
Most client computers around the
Internet can't talk to a server on a global IPv6 address
of course they do. every host in my home network has a globally routable
ipv6 address (thanks to hurricane electric's tunnelbroker.net) and i can
reach hosts at my colo provider that are set up via freenet6
Your motley island of connectivity notwithstanding, Bernstein's claim
remains true (as stated) for the vast majority of computers on the
Internet.
But they still require manual action by the system administrator
before they can talk to IPv6 addresses.
no they don't. if your hosts are ipv6 capable, start up radvd on your
ipv6 connected router
Um, that's what he was referring to as "manual action".
this page basically says two (false) things.
1) you can't use ipv6 and ipv4 at the same time, so if you switch to
ipv6 now you can't reach 99.9% of the internet.
Where did you get that? In fact, His transition plan is based
on using IPv4 and IPv6 at the same time: "There will be a transition
period from old clients, which can connect only to IPv4 addresses, to
new clients, which can connect to both IPv4 addresses and IPv6
addresses. Servers will have to be reachable through IPv4 addresses
until the old clients are gone. "
2) it takes a massive amount of work to convert all applications over to
ipv6 and no one has even started on such a task.
[...] i've got ipv6 enabled apache, ipv6
enabled qmail, ipv6 enabled djbdns, ipv6 enabled mozilla/phoenix, ipv6
enabled xchat, ipv6 enabled internet explorer, etc. all of these
applications on every modern OS have all been written to use ipv6 first,
then fall back on ipv4.
Great. 5 down, how many thousands to go? What do you want for that, a junior G man badge? IPv6 compatibility doesn't come
for free. Why do you think Stevens' Unix Network
Programming Vol 1 (2nd Ed.) spends so much space on how to achieve
IPv6 compatibility?
johncompanies "linux virtual hosting" service gives you root on a virtual
server with 4Gbyte of disk, 40Gbyte transfer/month, and up to 10 IP addresses.
I've had my account for almost two months now, and overall I've been quite
happy with it. Although they are coy about the software used to multiplex the
server, I'm pretty sure they use SWsoft's Virtuozzo.
My "virtual server" has been rebooted twice; once it didn't come back up,
and they never did find out why. They were able to get it running within a few
hours of my emailing them about it. (They said if I had sent my message to the right address and put URGENT in the subject the response time, they would have responded within minutes.)
Performance is good; it usually takes about 4 seconds to un-tar and compile
djb's checkpassword package. The worst I've seen was when it took 20 seconds
(which is how long it normally takes my home machine, an AMD K6-2 "334 MHz"
with 32 Mbyte of RAM.)
Support is also good, but not particularly fast. They will work on a problem
until it is resolved to your satisfaction; they really want to make you happy.
But it might take some time, because they offer "unlimited tech support" to all
their customers.
One potential weak point is their authentication for support requests, since
they seem to just accept email from my address as being "from me", without
asking for a password or anything.
With the appearance of usermode linux and vserver,
Linux virtual hosting is becoming common, so if I ever become unhappy here, it shouldn't be too much
trouble to move my system elsewhere.
Pay cash for an anonymous prepaid Visa account. For example, you can buy CashX at your local 7-11 or elsewhere. Not available in your state? Get one over the web; they accept money orders.
I guess my point is that we should recognize that one of the functions
of government is to take some money from those that have it, and give it
to those that don't.
Well stated. This seems to be the crux of your position.
Assume that government represents the people,
it's constituents. If a majority of the
people have an innate desire (or believe, as you say, that it is in
their self interest) to help the needy, then why do they need government
to force them to do so? If they don't, then government isn't
representing them by forcing them to do so.
The question is how much of it should be done, and as frequently
happens, I don't like either of the extremes, i.e. communism or
libertarianism.
This is what I call the Limited Government Fallacy: the idea that you
can have just a little government, and that it can be limited to "good"
functions. History and theory show that beauracracies (goverments and
companies) inevitably grow more bloated and inefficient with time; eventually
they fail to provide the services people want.
Some organizations are more succesful in adapting, but nothing lasts forever. In the market, these
companies fail. Governments fail too, eventually; it just takes a lot
longer and it usually involves a lot of unnecessary bloodshed.
What counts as our "minds" are simply far too tied into the physical instantiation of our bodies. (Not that "mind" is too abstract, but that it's not abstract enough for separation from our bodies.) If I make a computer-based simulation of myself, will it get tired? Hungry? Thirsty? Itchy? Horny? Sick? If not, can it then get excited? Scared? Concerned? Bored? Will it have any emotional reactions at all, if all the standard physical stimuli are removed?
As Kurzweil points out in his response to Rodney Brooks: these experiences are delivered via systems such as neurotransmitters and endocrine glands, which are "relatively low bandwidth phenomena and are more easily modeled than neurons".
Even if all the "human" inputs are replaced or simulated -- you've still got an added problem of a new level of "hardware breakdowns" on whatever platform is running the simulation. Suddenly you've also got to deal with the various downtimes, pauses, glitches, etc., that will break the illusion of it being the same "mind" as in the original person.
And your point is what, exactly? Our biological "hardware" breaks down and suffers from down time on a regular basis, yet people's self-images don't seem to have suffered too badly as a result.
Kurzweil argues that strong AI will preceed the ability to download minds, which does not seem logical.
On the contrary, as he states explicitly in
the first paragraph of The Virtual Thomas Edison and elsewhere, downloading minds will come first, and will lead to strong AI.
The capacity for thought we have is an intensely complex combination of the neural processes of survival and reproduction, with all those billions of years behind it, plus the geologically recent development of a whole lot of extra cognitive juice in the frontal lobe department, plus a couple of million years of tweaking this wetware system in the context of social, tool-using behavior, plus several tens of thousands years of social behavior combined with the meta-social instruction of language, art, text and such...
Nevertheless, the processing speed of the human nervous system is effectively fixed. CPU processing speed is increasing exponentially. The lines on the graph will cross sooner than you think. As to what happens next, Vernor Vinge said it best: "Will there ever be a computer as smart as a human?" I think the correct answer is, "Well, yes. . . very briefly."
So where in hell do we get an estimate like "Strong AI by...?"
By estimating the processing power of the human nervous system, and extrapolating from trends in computer hardware. No matter where you estimate the first, it is effectively fixed, while the second is growing exponentially.
As far as I'm concerned science has barely framed the question of what that would mean... and only in qualitative terms at that.
I take it you don't accept repeatedly passing the Turing Test as a valid, objective indicator if intelligence?
extrapolate based on some law of technological development with far less than a century of statistical evidence
The trend underlying Moore's Law has remained constant for well over a century. Computing devices have been consistently multiplying in power (per unit of time) from the mechanical calculating devices used in the 1890 U.S. Census, to Turing's relay-based "Robinson" machine that cracked the Nazi enigma code...
ANd how do you get from there to the process of downloading consciousness, despite the fact that there is not even an inkling of a glimmer of the slightest valid theory about how an active and continuously shifting neourochemical proccess of personality and intellectual template, stored memory and present cognition (not to even touch the primal, the emotional, the glandular, the spiritual) gets translated to something that can be interpreted by a machine or stored in a meaningful sense or caused to be active outside of a biological framework?
What evidence do you have for the claim that only biological systems can support consciousness in principle? We have cochlear implants and bionic eyes that let the deaf hear and the blind see.
The technology to interface with the nervous system is here today. Where exactly do you think the ever-accelerating trend of replacing biological components with nonbiological ones will stop, and why?
[Kurzweil] infers that because they predict that massive CPU power and network bandwidth will be available, that the software to match it will naturally come along, too.
Kurzweil is right. The faster your hardware, the dumber your software can be.
If you give my little sister a fast computer from the year 2029, she could probably write a Kasparov-beating chess program for it in under 100 lines of C.
Read up on Las Vegas. Note how the corporations involved were never involved with private armies and never used violence. Or Shell's involvement in Nigeria. Or copper mining companies in the South Pacific.
Companies don't use violence because they can't get away with it in most of the world you appear to be familiar with.
Those exceptions do not refute the general principle that "companies don't use tanks; goverments do."
Which type of entity has killed more civilians since, say, 1900: companies or governments? During World War II alone, 35 million civilians were murdered by (a) governments (b) companies.
Clearly, the organizations claiming a territorial monopoly on the use of violence pose the greater threat.
Slashdot Mirror
Oops, the [sup] tags didn't work. That's supposed to be x^(-3/2). Good catch.
The essence of understanding math is being able to use it to solve problems. Math problems are like chess problems: they both have a start state and an end state and a solution consists of a sequence of legal moves. Routine problems are easy, like mate-in-1 or a simple application of a single mathematical rule. Non-routine problems require you to think a few moves ahead, but if you can't do that, you don't really understand the moves/material.
It's important to become proficient at non-routine applications of basic material before moving on to more advanced material like calculus. As the author of The Calculus Trap writes: Rather than learning more and more tools, students are better off learning how to take tools they have and apply them to complex problems.
To this end, I recommend The Art of Problem Solving Volume 1: the basics & The Art of Problem Solving Volume 2: and beyond. They are the best math textbooks I have ever seen. The intuitive explanations really sink in, so no memorization is required. But the key is that each section is followed by a bunch of non-routine problems from middle-school and high-school math contests like MATHCOUNTS and AMC. These are a fun way to make the material second nature, and besides, it's pretty motivating to know that a bunch of middle- or high-school kids solved the problem you're struggling with. (I want a shirt that says I'm as good as a middle schooler on the front, and on the back says MATHCOUNTS.)
After studying the first few chapters of Volume 1, you will be able to solve problems such as these:
- The formula N = 8 * 10^8 * x-3/2 gives, for a certain group, the number of individuals whose income exceeds x dollars. What is the smallest possible value of the lowest income of the wealthiest 800 individuals? (AHSME 1960)
- Find Sqrt[53 - 8 Sqrt[15]]. (MATHCOUNTS 1990)
- If for three distinct positive numbers x, y, and z: y/(x-z) = (x+y)/z = x/y,
then find the numerical value of x/y. (AHSME 1992)
- For each of n = 84 and n = 88, find the smallest integer multiple of n whose base 10 representation consists entirely of 6's and 7's. (USAMTS 1)
There can be a surprising amount of depth to these "middle-school math" problems. The concepts they cover are the fundamental building blocks upon which calculus is built.This post is based in part upon similar posts of mine at Reddit and MathNotations.
Agreed. I couldn't stand Rainbow's End, though I read it through to the end because it was written by Vinge, and I loved his other work. This frankly makes me lose faith in the Hugo as a guidepost to what to read.
Inflation is essentially a tax on net worth. And governments are the sole cause of inflation in their fiat currencies.
The owner of a good (including an IP network) should be allowed to decide how much to charge for the use of it.
Right! Because his Word (the Bible) gives us a glimpse into His thoughts.
"Let this mind be in you, which was also in Christ Jesus" -- Philippians 2:5
Yet the government will beat up tax resistors (who haven't left the country). Does that make its offer immoral?
How is the Mafia example any different than the police?
Couldn't have said it better myself. :)
The point that the quote addressed was whether or not taking money from everyone (taxes) and redistributing it to the poor could be moral... of course it is.
"If someone can recognize an act of unjust aggression when it is perpetrated by one individual against another, but not when the same act is perpetrated by an organized group of individuals, such a person must be confused about right and wrong." -- Lao Tzu
When the Mafioso offers to "protect" your store, he may also give you the option of moving. Does that make his offer moral?
Walter Williams said it best:
Due to advances in technology, the real prices of many consumer goods should actually drop over time. Why would a "decent currency" freeze the price of a cell phone (for example) at $3000 just because that's what they cost years ago?
No. A 10-word diceware passphrase can be typed in about 6 seconds and gives you 128 bits of entropy.
That said, this is probably overkill for your stated purpose of categorizing email messages. A good email search engine would probably serve you better.
By following these easy instructions, you too can encrypt your data and swap partitions with Loop-AES. (The instructions are for Linux From Scratch, but they worked fine on my Debian box.) This way, no unencrypted data ever touches the disk; even if your computer is stolen, the thief can't read your data.
they do, though. having true end-to-end communication means that peer to peer applications like voice over IP or BitTorrent actually work.
Clearly, Bernstein is referring to IPv6 addresses as presently implemented on the Internet at large.
of course they do. every host in my home network has a globally routable ipv6 address (thanks to hurricane electric's tunnelbroker.net) and i can reach hosts at my colo provider that are set up via freenet6
Your motley island of connectivity notwithstanding, Bernstein's claim remains true (as stated) for the vast majority of computers on the Internet.
no they don't. if your hosts are ipv6 capable, start up radvd on your ipv6 connected router
Um, that's what he was referring to as "manual action".
this page basically says two (false) things.
1) you can't use ipv6 and ipv4 at the same time, so if you switch to ipv6 now you can't reach 99.9% of the internet.
Where did you get that? In fact, His transition plan is based on using IPv4 and IPv6 at the same time: "There will be a transition period from old clients, which can connect only to IPv4 addresses, to new clients, which can connect to both IPv4 addresses and IPv6 addresses. Servers will have to be reachable through IPv4 addresses until the old clients are gone. "
2) it takes a massive amount of work to convert all applications over to ipv6 and no one has even started on such a task.
[...] i've got ipv6 enabled apache, ipv6 enabled qmail, ipv6 enabled djbdns, ipv6 enabled mozilla/phoenix, ipv6 enabled xchat, ipv6 enabled internet explorer, etc. all of these applications on every modern OS have all been written to use ipv6 first, then fall back on ipv4.
Great. 5 down, how many thousands to go? What do you want for that, a junior G man badge? IPv6 compatibility doesn't come for free. Why do you think Stevens' Unix Network Programming Vol 1 (2nd Ed.) spends so much space on how to achieve IPv6 compatibility?
johncompanies "linux virtual hosting" service gives you root on a virtual server with 4Gbyte of disk, 40Gbyte transfer/month, and up to 10 IP addresses. I've had my account for almost two months now, and overall I've been quite happy with it. Although they are coy about the software used to multiplex the server, I'm pretty sure they use SWsoft's Virtuozzo.
My "virtual server" has been rebooted twice; once it didn't come back up, and they never did find out why. They were able to get it running within a few hours of my emailing them about it. (They said if I had sent my message to the right address and put URGENT in the subject the response time, they would have responded within minutes.)
Performance is good; it usually takes about 4 seconds to un-tar and compile djb's checkpassword package. The worst I've seen was when it took 20 seconds (which is how long it normally takes my home machine, an AMD K6-2 "334 MHz" with 32 Mbyte of RAM.)
Support is also good, but not particularly fast. They will work on a problem until it is resolved to your satisfaction; they really want to make you happy. But it might take some time, because they offer "unlimited tech support" to all their customers.
One potential weak point is their authentication for support requests, since they seem to just accept email from my address as being "from me", without asking for a password or anything.
With the appearance of usermode linux and vserver, Linux virtual hosting is becoming common, so if I ever become unhappy here, it shouldn't be too much trouble to move my system elsewhere.
"Fuck you, that's my name. You know why, mister? 'Cause you drove a Hyundai to get here tonight; I drove an $80,000 BMW -- that's my name."
Pay cash for an anonymous prepaid Visa account. For example, you can buy CashX at your local 7-11 or elsewhere. Not available in your state? Get one over the web; they accept money orders.
I guess my point is that we should recognize that one of the functions of government is to take some money from those that have it, and give it to those that don't.
Well stated. This seems to be the crux of your position.
Assume that government represents the people, it's constituents. If a majority of the people have an innate desire (or believe, as you say, that it is in their self interest) to help the needy, then why do they need government to force them to do so? If they don't, then government isn't representing them by forcing them to do so.
The question is how much of it should be done, and as frequently happens, I don't like either of the extremes, i.e. communism or libertarianism.
This is what I call the Limited Government Fallacy: the idea that you can have just a little government, and that it can be limited to "good" functions. History and theory show that beauracracies (goverments and companies) inevitably grow more bloated and inefficient with time; eventually they fail to provide the services people want. Some organizations are more succesful in adapting, but nothing lasts forever. In the market, these companies fail. Governments fail too, eventually; it just takes a lot longer and it usually involves a lot of unnecessary bloodshed.
The ways he tries to achieve this goal are, by the most, static. It will be harder to modify a detail or change a component of such organism.
Where did you get this idea? Digitizing information is the key to making it easy to manipulate.
Besides, such technologies are by too weak to external factors and demand much more energy inputs than a usual organic carbon-rich body.
Wrong again. See how many people you can keep alive for a year in a 1U rack with minimal power and cooling expenses.
[snip all the mistakes in the middle]
Besides, this mind will have the big need to reproduce itself. Alone in the Universe does not give good chances for eternity...
Has it escaped you that digital systems reproduce ("copy") vastly more quickly and easily than biological systems?
As Kurzweil points out in his response to Rodney Brooks: these experiences are delivered via systems such as neurotransmitters and endocrine glands, which are "relatively low bandwidth phenomena and are more easily modeled than neurons".
Even if all the "human" inputs are replaced or simulated -- you've still got an added problem of a new level of "hardware breakdowns" on whatever platform is running the simulation. Suddenly you've also got to deal with the various downtimes, pauses, glitches, etc., that will break the illusion of it being the same "mind" as in the original person.
And your point is what, exactly? Our biological "hardware" breaks down and suffers from down time on a regular basis, yet people's self-images don't seem to have suffered too badly as a result.
On the contrary, as he states explicitly in the first paragraph of The Virtual Thomas Edison and elsewhere, downloading minds will come first, and will lead to strong AI.
The capacity for thought we have is an intensely complex combination of the neural processes of survival and reproduction, with all those billions of years behind it, plus the geologically recent development of a whole lot of extra cognitive juice in the frontal lobe department, plus a couple of million years of tweaking this wetware system in the context of social, tool-using behavior, plus several tens of thousands years of social behavior combined with the meta-social instruction of language, art, text and such...
Nevertheless, the processing speed of the human nervous system is effectively fixed. CPU processing speed is increasing exponentially. The lines on the graph will cross sooner than you think. As to what happens next, Vernor Vinge said it best: "Will there ever be a computer as smart as a human?" I think the correct answer is, "Well, yes. . . very briefly."
So where in hell do we get an estimate like "Strong AI by...?"
By estimating the processing power of the human nervous system, and extrapolating from trends in computer hardware. No matter where you estimate the first, it is effectively fixed, while the second is growing exponentially.
As far as I'm concerned science has barely framed the question of what that would mean... and only in qualitative terms at that.
I take it you don't accept repeatedly passing the Turing Test as a valid, objective indicator if intelligence?
extrapolate based on some law of technological development with far less than a century of statistical evidence
The trend underlying Moore's Law has remained constant for well over a century. Computing devices have been consistently multiplying in power (per unit of time) from the mechanical calculating devices used in the 1890 U.S. Census, to Turing's relay-based "Robinson" machine that cracked the Nazi enigma code ...
ANd how do you get from there to the process of downloading consciousness, despite the fact that there is not even an inkling of a glimmer of the slightest valid theory about how an active and continuously shifting neourochemical proccess of personality and intellectual template, stored memory and present cognition (not to even touch the primal, the emotional, the glandular, the spiritual) gets translated to something that can be interpreted by a machine or stored in a meaningful sense or caused to be active outside of a biological framework?
What evidence do you have for the claim that only biological systems can support consciousness in principle? We have cochlear implants and bionic eyes that let the deaf hear and the blind see.
The technology to interface with the nervous system is here today. Where exactly do you think the ever-accelerating trend of replacing biological components with nonbiological ones will stop, and why?
[Kurzweil] infers that because they predict that massive CPU power and network bandwidth will be available, that the software to match it will naturally come along, too.
Kurzweil is right. The faster your hardware, the dumber your software can be.
If you give my little sister a fast computer from the year 2029, she could probably write a Kasparov-beating chess program for it in under 100 lines of C.
Read up on Las Vegas. Note how the corporations involved were never involved with private armies and never used violence. Or Shell's involvement in Nigeria. Or copper mining companies in the South Pacific.
Companies don't use violence because they can't get away with it in most of the world you appear to be familiar with.
Those exceptions do not refute the general principle that "companies don't use tanks; goverments do."
Which type of entity has killed more civilians since, say, 1900: companies or governments? During World War II alone, 35 million civilians were murdered by (a) governments (b) companies. Clearly, the organizations claiming a territorial monopoly on the use of violence pose the greater threat.