Archive for the Mathematics Category

Search engine terms & less frequent posting

Posted in College life, computer science, Mathematics, Myself with tags , , , , , , , , on April 1, 2008 by chthenos

All right, this post is about 2 things: (1) The search engine terms that have led to my blog so far and (2) the fact that I am not going to be posting quite as frequently for a little while, and why.

(1) Okay, so nothing lewd has led to my blog yet, which I guess I should be proud of. But some funny searches have led people here. I wonder if they found what they were looking for? Numbers mean frequency. I am putting these in order of hilarity (in my opinion):

“credit card debt”
credit
coins (2)
quotes from the perfect woman: jokes
transhumanism
technology (2)
things a person can do before they die
curiosity short story
mental math
“identifying natural images from”
can learn chinese casually
awesome
he sits at my table
cultural awkward situations
— and, to me, the most bizarre and hilarious…
awkward asian cultural situations

It’s quite possible that the last two were the same person. I didn’t check, and I don’t know if it’s possible to check. Also, I’m quite proud that I was high enough up in page rank for the word “awesome” that someone found my blog by searching for that. Sweet!

Now for the other point: I won’t be posting quite as often anymore. I came to a sudden realization today that I’ve been dicking around way too much this semester. I’ve been reading about news, reading about AI, playing silly games, reading random blogs, etc. I’ve been avoiding my research and my coursework and I haven’t been exercising. This is causing me to be unhealthy and it’s risking bad grades and missing out on the learning opportunities that I’ll never have again in my life. So I’m going to have to stop messing around and get back to work.

I’ll still post here, of course. Probably, I’ll be more stressed, and therefore be inclined to write more of my short story posts. I’ll probably not post about technology or transhumanism for a while. We’ll see. But I’m probably not going to keep up the ~1 post per day average that I’ve had going lately. If there’s actually anyone who was interested in my posts and already a regular reader, I’m quite sorry to disappoint. At least, if my content is less frequent, it will hopefully be of higher quality!

Now it’s time to create a web page, arrange a meeting with my research advisor, talk to another professor about research next year, do some other research for a final project, write to the guy I’m working with for that project, go through 50 unread emails that are actually important, attempt to cancel or rescue an event I was planning, actually do some work so I have something to say to my advisor when I meet him, and then try to remember what else I have been putting off for the past month! (I just remembered going to the bank, and sending 4 letters including tax returns, and filing another document for next year’s grant from the university.)

Also:  Bernard Host & Bryna Kra, if either of you happen to Google your names and find this page, your paper Nonconventional Ergodic Averages and Nilmanifolds is hard to read! It’s taking me forever to get used to the notation! If you found this page looking for that paper, you can email me. I have a PDF of it. I also have lots of other related literature. But that stuff is mostly easily available online…

A fun explanation of quantum uncertainty

Posted in computer science, Humor, Mathematics, technology with tags , , , , , , , on March 31, 2008 by chthenos

Suppose that we lived in a Matrix-like world. A computer-simulated world. It doesn’t have to be exactly like the Matrix — we (as entities) could be entirely within the system, we could be programs. Anyway, imagine that we are all part of a huge computer program.

Think about how complex this system is. According to Wikipedia, the universe contains about 10^80 atoms. Each of those atoms has a number of physical parameters (energy, velocity, angular momentum, etc.) and is also made up of a number of smaller particles (electrons, protons, neutrons) which also have those sorts of parameters. There are also a large quantity of free particles in the universe, mostly photons and neutrinos (and gluons?). I would guess that there are a lot more of those than there are atoms, but I’m honestly not sure. So anyway, even assuming that there’s nothing at a smaller scale than quarks (i.e. quarks and leptons really are the fundamental particles) and that atoms dominate, there are well over 10^80 parameters in the system. Furthermore, we are able to make observations at very small time scales. According to Wikipedia again, the smallest time scale we have been able to measure is on the order of 10^-18 (quantum theory says that the smallest measurable time scale should be on the order of Planck time, or 10^-44 seconds). So that means that a simulation of our universe requires the updating of 10^100 parameters per second in order in order to be consistent with our observations! That’s a googol!

Not only is the number of parameters huge, but the size of the universe is huge, and our ability to measure scale is pretty fine, so very large and high precision numbers would be needed to specify positions and velocities. This results in space requirements on the order of 10^120 or something. (I’m getting a bit lazy with the computations.) “Astronomical” hardly even describes this.

What’s the point? My fun little thought is that you could view quantum uncertainty as computational efficiency. When we’re not observing something, the computer can just remember approximately where it was. This saves a LOT of storage space. Additionally, when we observe one parameter of a particle too closely, the computer sacrifices some of the space used to store other parameters for that particle, which is where the Heisenberg uncertainty principle comes from. It makes a lot of sense from a computer science perspective!

I hereby propose this theory as an alternative to string theory. You’ll have to give me a bit more time to figure out how to use it to create a complete and consistent theory of quantum gravity, though.

Another awesome game!

Posted in computer science, Mathematics, technology with tags , , , , , , on March 28, 2008 by chthenos

This one isn’t quite as addictive as the previous one, but it’s also really interesting. (If you like this kind of stuff, make sure you read the post below, too!)

Somebody made a game where you have to try to outsmart their program. Basically, it predicts your next move based on what you’ve done so far, and if it predicts right then it advances and if it predicts wrong then you advance. I think the algorithm is fairly sophisticated; they provide their code, but I didn’t look at it. If you look at the code, you could probably come up with a technique to beat it, but I wonder if you could consistently beat it just by trying to trick it with your own cleverness!

Anyway, here’s the link. If you can consistently beat it, post here and let me know what you did! I’d be interested.

Fun, challenging, (addictive!) game

Posted in Mathematics with tags , , , , , , , on March 28, 2008 by chthenos

This is the coolest online game I’ve seen in a LONG time. Warning: suitable mainly for nerds.

Planarity!

This makes a puzzle game out of graph theory. A graph is just a bunch of points and a bunch of lines between the points. A graph is called planar if you can draw it on a piece of paper so that none of the lines cross each other (except at the points). If you’re still confused about what this means, go to the game and play around with the points. The graph that you start out with probably won’t be planar.

A graph is uniquely determined by how many points it has and which points are connected. But there are plenty of different-looking ways to draw a graph on paper. This is the point of the game — you’re given a graph which is planar, but it’s not drawn in a planar fashion. You’re supposed to rearrange the points so that it is planar.

I do wonder about the computational complexity of the game. My strategy right now is to move each vertex near to the other ones it’s connected to, and after I’ve done that with a number of the vertices, I can kind of visualize the graph as a planar graph that is folded over itself a few times, and then I just have to “unfold” it. I’ve gotten up to level 37 using this strategy.

However, I don’t think that strategy is the mathematically optimal one. It just makes sense considering the way I process information visually. I bet that one could write an algorithm to solve this problem in O(nlog(n)) “moves” (a “move” is a geometric move of a single point). Maybe even O(n). I think when I don’t make mistakes, my algorithm is about O(nlog(n)) moves. But the total complexity of the algorithm might be much higher — geometric problems are typically not very easy. I’m not really sure how you would program an algorithm to solve this (I certainly wouldn’t be able to code up my technique!); I am fairly sure that any strategy that always reduces the number of crossings on each step will not always work.

Any ideas?

Some cool mental math tricks

Posted in Mathematics with tags , , , on March 16, 2008 by chthenos

I don’t want to go to sleep, and I am too tired to write, so I’m just going to post some random cool tricks I know for doing mental math.

Subtraction: do it one step at a time from the left. This is the opposite of how it’s usually taught in school, but it’s way easier to do mentally, because instead of doing the whole computation at once, you do it step by step, slowly reducing the amount of information you’re storing until you get the answer. Example: 3327 – 483. First do 3327 – 400 = 2927. Then do 2927 – 80 = 2847. Then do 2847 – 3 = 2844. As you go, all you have to do is remember the current “temporary answer” and what’s left of the thing you’re subtracting. On the other hand, if you did that the standard way, you have do do 7-3 = 4 and remember the 4. Then you have to do 2-8 = 4, and borrow a 1 from the next number. Then you have to do 2 – 4 = 8, and borrow a 1 from the next number. Then you just have a 3 that lost a 1 so it’s 2. Putting this together, you get 2844. Try it yourself with 1144 – 877!

Addition: There are lots of ways to speed up your addition.  My strategy depends on what kind of thing I’m adding. The only one I’m going to describe here is grouping. The idea of this strategy is that instead of adding everything at once, you take “pieces” of some of the numbers that add up to something nice and easy to remember. So, for example, say I have to add up four paychecks, 327.44 + 89.07 + 161.53 + 491.28. Notice that 9 + 491 = 500, so you can group this as 500 + 327.44 + 80.07 + 161.53 + 0.28. Also, 320 + 80 + 100 = 500, so you can group again as 1000 + 7.44 + .07 + 61.53 + 0.28. Now, .07 + .28 + .44 = .79 (nothing special about this but it reduces the number of terms), so we have 1000 + 7.79 + 61.53, and this is pretty easy now: 1069.32.

Multiplication: This is definitely the coolest operation. There are lots of interesting multiplication tricks. Impress your friends with your ability to do quick calculations using these!

(1) Difference of squares. A really useful thing from algebra! This is the factorization x^2 – y^2 = (x + y)(x-y). So for example, 19 = 100 – 81 = 10^2 – 9^2 = (10-9)(10+9) = 1 * 19 = 19. Neat, huh? So, if you have to multiply two numbers, say 27 * 23, you might notice that these are actually 2 above and 2 below 25, so you can write that as (25 + 2)(25 – 2) = 25^2 – 2^2. Then you change your 2×2 multiplication problem into an easy subtraction: 625 – 4 = 621. Of course, this only works if you know the relevant perfect squares, so it’s easiest to use on examples like 82 * 78 or whatever.

(2) Rounding. This is an extension of the previous idea. Suppose that you have to multiply two numbers that are both close to “nice” numbers, such as 89 * 68. You can write that as (90 – 1)(70 – 2) and expand: 90 * 70 – 2 * 90 – 1 * 70 + 1 * 2 = 6300 – 180 – 70 + 2 = 6052. As before, this changes a hard multiplication problem into a less-hard subtraction problem. This trick generally works pretty well for numbers ending in 9, 8, 1, or 2. If you are rounding more than that, then the subtraction problem starts to get harder.

(3) Taking advantage of 5s. This uses the fact that numbers ending in 5 don’t gain more digits (besides the ending 0) if you multiply by 2. You can simplify any multiplication problem that’s a product of an even number and a number ending in 5 this way. For example, 26 * 75 = 13 * (2 * 75) = 13 * 150. But 13*15 is way easier than 26 * 75!

All right, now I’m really tired so I’m going to go to sleep. But one of these days I’ll explain some of my more sophisticated mental math tricks, like how to estimate complicated things quickly and accurately, or my general multiplication algorithm.

Things I’d like to do before I die

Posted in College life, Mathematics, Music, Myself, Philosophy with tags , , , , , , , , on March 9, 2008 by chthenos

I think it’s important for a person to have minor long-term goals in life. Of course people will have major goals, like “achieve some level of success in a particular career” or “get married” or whatever. But if you don’t have minor goals that you can strive towards on the side, you will spend your entire life just working towards a few major goals (or intermediate goals whose true purpose is to get you to those larger goals) and you will have very few achievements to look back upon when you are old.

So I thought I’d list out a few things that I want to do.  Some of these I’m actually doing, or close to doing, right now. Others are way out of the question at the moment but could be quite doable later on. Mostly they are trivial in the sense that they aren’t aimed at helping society or shaping the course of my life; they’re just minor things I’d like to do, goals I have alongside “prove a landmark theorem”, “become extremely rich”, and “actually fall in love (and have something come of it)” that I can actually accomplish and thus will keep me sane.

1) Learn to play the theremin. I’ve always regretted that my parents didn’t make me learn an instrument when I was little, and now that I am older I am free to choose what instrument to teach myself. As the theremin is the coolest instrument ever, there’s no question here. All I need to do now is buy a theremin. I can actually afford it now (a decent one is only $350 or something), but I don’t think I have much free time for it now so I am waiting. I’ll probably buy one before I get my degree, though.

2) Learn another language. I have studied a lot of different languages before (Spanish, Latin, Japanese, Hebrew), but I have never become proficient at any of them. I would like to be fluent in a second language. Of course, this would be a long process, hopefully involving living in a country where the primary language is the one I’m learning. I haven’t decided what language yet. I’m interested in German and Chinese right now primarily, but I’d also be pretty willing to learn Hebrew (I’d have a head start, because I still remember some stuff from middle school), French, Russian, or Japanese. One of my Vietnamese friends offered to teach me Vietnamese, but I don’t know what use I would have for speaking that language.

3) Travel the world. In particular, I’d like to visit rural Ireland, Iceland, Greece (anywhere), Rome, and some places in China. There are some other “lower priority” places that I’d visit too if I had the opportunity. It would be cool to see Mt Fuji in Japan, anywhere in Australia or the Pacific islands, Germany, Israel, Russia (especially St. Petersburg), and lots of other places that I’m not inclined to name right now.

4) Own an aureus of the emperor Augustus. I collect coins, but an aureus is a gold coin and Augustus coins are pretty popular, so that would be something like $2500+ probably. Well out of my price range right now. Actually, I’m more interested in generally expanding my coin, stamp, and currency collections, but I feel like having an Augustus aureus would be a good landmark. By the time I had that, I would surely have bought all kinds of other cool things too.

5) Build cool lighting and sound systems into my house, using awesome technology like X10 combined with a computer program that I could remotely access, so that I could control all of the electronics in my house using (say) my phone or a remote control. This would be excellent. I don’t think it’s excessively expensive, and I do think I have the technical abilities to install and program it. It would also be cool to build my own workstation which was designed for efficiency and had half of the keyboard on each arm of the chair, mouse immediately to the right of the right half of the keyboard, screen suspended above the chair, etc. It would be so comfortable and efficient! Also interesting would be a completely wireless system with 3D motion sensing gloves, as well as wall screens throughout the house, so that I could move around the house while working on the same thing, carrying nothing and just wearing the gloves. This is seriously not too far in the future in terms of technology.

6)  Experiment with drugs. I’m not talking about illegal drugs in particular. I mean mind-influencing drugs, especially ones that are supposed to improve mental capacity. I’d like to test “brain-boosting” type drugs and see if they actually work. (Test them on myself, of course!) I’d also be willing to experiment with implantation of electronics into my body for performance enhancement purposes, and energy or activity boosting drugs, but I’m very wary of causing permanent physical or mental damage by doing these kinds of things, so I’m not going to go crazy with this stuff. I would also be willing to do the traditional “experimenting with drugs”, although I’d really prefer to stay away from anything that’s potentially addictive or that can have negative long-term mental side effects. I’d probably try shrooms or LSD at least once or twice to see what it’s like. My brain is the most interesting thing that I have access to, besides mathematical ideas, so I’m very interested in experimenting with it and seeing how it works and what it can do.

I could probably come up with a lot more stuff, but I am hungry so I’m going to go to dinner. (There’s another thing — I’d like to learn to cook interesting dishes from various cuisines and nations.) Anyway this is already a lot to do…

a couple of points about transhumanism

Posted in Mathematics, Myself, Philosophy with tags , , , , , , on March 5, 2008 by chthenos

I’m not planning to make any kind of thorough treatment of my views on the morality of technological advancement or human enhancement.  I’m just going to post a few thoughts that I have. My views on this matter are very extreme. I believe that pretty much any technology that enhances the capacity of humans to cope with environmental pressures or to better understand the world (even artistically) are inherently good. I also believe that evolution transcends genetics and it is not even necessarily bad if the human race is destroyed by some superior intelligence of our own creation.

So what are the points I’d like to make? Let’s see:

1) There’s no such thing as “unnatural” human performance enhancement.

2) We are subject to an evolutionary imperative to seek more and better methods for human performance enhancement.

3) Humanity as we know it today will cease to be the dominant living things on the planet some time in the near future (if this has not yet already happened).
4) The risk of human extinction (without replacement by superior beings) due to research and experimentation in this direction is much smaller than our sensationalist media would like us to think.

Now, these are all fairly controversial stances, as I said before. I’m not going to defend these to the full extent of my abilities (although if you object, feel free to comment and I’ll explain my position more thoroughly); I just want to give some basic explanation.

1)  A lot of people seem to believe that it’s unnatural to create things that help us achieve our goals in interacting with the environment. Most people only apply this belief to specific categories of things; other people believe that it’s categorically bad. (At least two of my friends think that pretty much all technology, even as far down as basic agriculture, is overall bad.) I do not think that this view is consistent with observational evidence about evolution. Even if there are some negative effects from these things, obviously evolutionary pressures selected for the technological advancement. Even outside of the human race, we can find things like chimpanzees using sticks as tools to get termites out of rotten tree stumps, and we can also find social structure in all kinds of different species which help them deal with environmental pressures.

So, then there’s this question of whether certain kinds of things are “natural” or otherwise acceptable, and other things are not okay. In particular, most people seem to believe that things like eugenics, genetic enhancement, and direct physical enhancement are wrong. I find these beliefs to be highly inconsistent with accepted behavior. Why is it fine to apply the principles of eugenics and genetic engineering to plant crops and domesticated animals, but not to humans? Why is it acceptable to consume highly structured and artificial “health food” products, but not to take performance-enhancing drugs like steroids and nootropic drugs, acceptable to have artificial limb replacements after a limb is lost but not acceptable to voluntarily have a limb replaced by a prosthetic, acceptable to have a chip inserted in a blind person’s retina to enable them to see but not acceptable for a healthy person to have a chip inserted in his brain to enhance his ability to do computations, etc.?

My personal opinion is that these people are just jealous that other people will be able to benefit from these things but they won’t. I know when I was in 9th grade, I saw a video about people who selected for good traits when choosing sperm or egg donors, and I was mad about it because I thought that these genetically engineered “super-children” would have an unfair advantage over me.  My math skills and suchlike were hard-earned, not bestowed upon me magically by my parents’ decision to pick sperm and eggs from very smart people. But now that my worldview has developed into a more sophisticated thing, I no longer think that complaint is justified. In fact, I think we have a moral responsibility to encourage the kind of behavior that I once spurned. This brings me to point (2).

(2) Not only is there nothing wrong with the stuff I just discussed, but we actually should be doing it. Now, this isn’t unconditional. We do need to be careful. I’m not going to take some “mind-enhancing” drug just because some dodgy dudes in some commercial lab said that it influences your acetylcholine activity to make you think more clearly. But I think if there’s substantial evidence that one of these nootropic drugs works with relatively negligible side effects (and I can afford it), I’m going to go for it. What reason is there against it? I think I should try to realize as much of my potential as possible.

It’s also important (in fact, even more so) to take actions that will have long term effects for human society. That’s why I’m in favor of eugenics and general technological advancement. I think that evolution has transcended the physical. It’s no longer true that physical environmental pressures result in selection of traits and it’s no longer true that all (or even most) of human advancement occurs in the realm of genetics. When we upgrade our computers every two years, we are perpetuating a societal selection pressure which encourages the development of superior computational technologies. In my opinion, the collective societal judgment that this stuff is desirable is sufficient justification for people to put their energy into developing it. Even if society changes and decides it doesn’t like technology (on average), and I still do like technology, I am evolutionarily obligated to apply that selection pressure in our society (unless that conflicts with more immediate goals, such as acquiring other things that I care more about than a better computer). This is what selection means.

I suppose I should clarify that by “evolutionary obligation”, I mean that if we believe that the Darwinian system of evolution (introduction of variation, selection of traits, retention of traits, and competitive pressure) is “right” (in some sense; maybe “natural” is a better word), then the only rational action when we want a particular thing is to try to contribute to the selection for that thing (or situations that would encourage the creation of that thing) and to the competitive pressure that will result in the success of that thing or situation. Personally, I think that change in our world is in fact governed by Darwinian evolutionary processes, and I think that increasing intelligence, capacity for abstract thought and understanding, computational ability, precision in measurement and construction, etc. are good, so I should take whatever actions I can to perpetuate these things. I also think that most of my views about what we should work to increase (the things I just listed) are generally accepted, and when people refuse to take the actions (the views I described in the beginning as controversial), they are doing something wrong.

Unfortunately, I didn’t make a very good transition into (3). Basically, I think that technology and society are advancing at an ever increasing pace, and people do not realize how fast this pace actually is. People don’t think that technology is advancing that quickly because they don’t see the details of what’s going on. They don’t see how much innovation is happening, and many of the new ideas and creations don’t appear before their very eyes. They only notice the things that are really revolutionary. However, when you are on the cutting edge of a field, you see how fast that field is really moving. Of course, I’m not on the cutting edge of any field of technology, but I know some people who are and I am on (in the sense of observation, not participation) the cutting edge of an academic field.  Anyway, my point is that I believe in the “technological singularity” ideas put forth by certain scientists and science fiction authors in the past few decades.

Allow me to briefly explain this concept. Basically, the idea is that the ever-increasing rate of technological advancement will eventually (some say soon) outpace human comprehension.  This requires the development of devices which can accomplish superhuman feats. Of course, we are pretty close in terms of computation (machines are much better than we are at many kinds of computation already, although not higher order processing), and we are well into the realm of superhuman capacity in terms of physical activity and information transmission. The only major gap is “intelligence”, or “creativity”. Once we create artificial intelligence, the last piece will be in place, and a new era will be ushered in.

Some people think that AI will run rampant and destroy the human race. I don’t think this is necessarily bad. The new beings will have to be alive in some reasonably concrete sense, or they would not be able to destroy humans; they would in some sense have evolved from us and replaced us.

But I think less drastic situations are much more likely. Personally, I’m hoping for technology that will allow the lossless imprinting of all of the information stored in a human mind into a computer. Then our consciousnesses can be placed in machines, and we can reap the benefits of the superior transmission of information, physical strength and efficiency, etc. of machines. At this point there will be no use for human bodies any more; but can we really say that the human race is destroyed, as long as all of the living humans are transplanted in this way, and our “species” still has a mechanism by which it can survive indefinitely?

Another (more radical) idea I have is that organizations will become the dominant sentient life forms some time in the near future. Since organizations do not exist in the same framework as humans, it’s hard for us to evaluate where they are (in terms of overtaking us) right now. But I think that already an argument can be made that organizations are alive, and an argument can be made that organizations are intelligent (perhaps even more intelligent than humans). It may even be the case that organizations have been the dominant life forms on this planet for decades (or centuries). But this will become much more pronounced as technology advances, because organizations are able to incorporate technology into themselves much more effectively than humans, so organizations can cope with the advancement of technology much better than humans can. I am very interested in this idea of organizations as living things, and I’ll post about it in much more detail some other time.

The last, and possibly least repulsive to most other people, option that I think is worth mentioning is just vast human enhancement. In order to cope with increasing demands on our minds and bodies, we (as a society) acquiesce and actually make the sort of modifications that I’m advocating; in the not-too-distant future, the typical human is physically and mentally superior to even the most brilliant or physically fit human today. Furthermore, human appearance will probably be somewhat different, due to side effects of the modifications and inclusion of mechanical (cyborg) modifications…

I’m getting really tired, which is why my writing is getting much less organized already. I’m just going to briefly mention point (4). There are lots of essays and articles already written about how we are about to destroy ourselves and about how the previous dude who wrote about how we’re going to destroy ourselves is an idiot. I just wanted to briefly mention some key points.

(a) The “reproducing machine” problem. Everyone’s so paranoid about this that it’s definitely not going to happen. This apocalypse is so old that von Neumann thought of it. Basically, the fear is that a machine that can reproduce in the natural environment may end up consuming all available resources just to make more copies of itself. Personally, I think that as this kind of technology develops, people will be very careful to make sure that self-reproducing machines will not be able to copy themselves in any general environment. In nanotechnology, the general idea is usually that you’ll put your nano constructors into a vat of specialized chemicals, and only if these chemicals are all available in the appropriate states will the constructor be able to make things.

(b) Military or medical disaster. If this hasn’t happened already, why do we think it will? Some people think that point (a) could be a subset of this: someone makes a “doomsday machine” which will unleash this kind of machine on the world. Even if someone could make these self-copying machines that could function in the natural environment, who’s to say that it wouldn’t be easy to destroy them? Also, I don’t think that human medical experimentation or weapons technology is even close to capable of wiping us out right now, and our ability to protect ourselves from these things continues to advance along with our ability to harm ourselves with these things, so there’s no reason to expect this to change.

(c) Robots destroy us but then cannot sustain themselves, resulting in apocalypse. This is absurd. If robots could destroy us, they could surely sustain themselves too. This is because they must have been able to take control of pretty much all electronics and they are also physically articulate enough to do the things we do, and therefore they can turn all of our current energy-generating capacity to their uses, build new generators, repair themselves, etc.  The only concern is that there might not be a very effective variation mechanism built into the machines, so they may not be subject to the same evolutionary process that currently governs the world. However, I don’t know if this is bad. It’s an interesting question.

I should point out that I don’t want to be killed by machines of superior intelligence. Some of my earlier statements make it sound like I wouldn’t mind if this happens. My point is actually that I don’t think this is bad from a global perspective. I think it’s only natural that humans (as we know ourselves today) will develop into or be replaced by something markedly different and in certain ways superior. If there’s a human-machine war, I’m going to do what I can to survive (if I think I can side with the machines and survive after they won, I’d certainly consider it).