If you want to look at the p+/e- collision as the electron reversing in time, then what happens is that the e- emits a gamma photon and reverses its "direction" in time. Its charge reverses, so it turns into a positron. Its velocity doesn't necessarily do a 180, because we need to account for the momentum of the emitted photon. The velocity changes in such a way that the momentum of the new positron after the event plus the momentum of the gamma photon equals the momentum of the electron before the event. You can look at this as the electron needing to "fire off" a photon to reverse its motion in time, somewhat as a rocket might fire its engines ahead in order to reverse its velocity.
There's one case in which the electron doesn't need to fire off a gamma to reverse, however: if the electron/positron pair were a "virtual" pair created out of nothing, a vacuum fluctuation. In this case, since the electron and positron's energy has been "borrowed" from the vacuum, then when they collide their energy is "paid back" and no gamma photon results.
In fact, from the point of someone traveling straight forward in time, there are two watches to explain: the watch you are wearing after you pick it up, and the watch that you were wearing while you were traveling backward in time. A person moving forward in time would see both watches.
Where did they come from? I don't know. You wrote the story, so you need to explain it. You didn't feel the need to explain where the watch came from before you added in the time-travel business. That is, if the story was just "I found a watch and picked it up" you wouldn't feel the need to explain where the watch came from. Clearly, it was manufactured, sometime, somewhere, and left there somehow.
Well, the same must be true of the other watch, the anti-watch that annihilates with the real watch at some point in the future. Who made it? How did it get there? I don't know. It's your story!
Well, if you want to cause Marty to go back in time for real (and not just think you do), then of course you need to start at the point "back in time" where he arrives (say 1955). At that point, you duplicate Marty. That requires E = mc^2, where m is Marty's mass, plus the mass of his skateboard, clothes, and assorted paraphernalia, plus some trivial amount of energy to give him the right momentum.
Note that you'll need to create a slightly different Marty than the original, because Marty #2 must be identical to Marty #1 when he started time traveling (say 1985). He's physically older, and needs to have different memories -- he needs to "remember" the future. He's not remembering it in the usual sense we remember things, of course, because these events are in his future, not his past. But from the point of relativity, events in our future are no less real than events in our past, and there's no reason in principle we can't run off a few quick calculations on our superdupercomputer, and predict the relative handful of events in his "future" that Marty will need to "remember." (We're assuming for the purposes of argument that quantum uncertainty is not so important that it fundamentally fouls up this calculation.)
Now we create an anti-Marty. He is just like Marty #2, but with the charge, parity, and velocity of every single particle in him reversed. He is actually Marty #1, traveling backwards in time. This, too, takes E = mc^2.
Now, Marty #2 (the one who believes he has come "back in time", because he "remembers" the future) does whatever he's going to do. Meets Marty #1, picks a fight with him, puts him in the hospital with a broken arm, and then impregnates his mother. Whatever.
And time goes on. When we reach the point where we want Marty to go back in time (say 1985), we arrange for Marty #1 and anti-Marty to meet. They annihilate each other, of course, releasing all the energy we put into creating Marty #2 and anti-Marty 30 years ago. Now we're left with only Marty #2, the time traveler, who keeps on going forward.
To sum up, to us the observers, merely traveling along forward as we do, it looks like Marty #2 and anti-Marty were created out of pure energy in 1955. Marty #2 had weird memories of the future which turned out to be accurate in every respect. Marty #1 had the odd property of getting physically younger and forgetting stuff as he got "older." At some point, Marty #1 was born and grew up. As he got older, we began to see that anti-Marty was beginning to look more and more like Marty #1, except for the fact of being made of anti-matter and getting "younger" with time, while Marty #1 was getting older. We begin to see that Marty #1 and anti-Marty are converging, becoming more and more similar. Indeed, they probably start converging physically, too, spending more and more time closer to each other.
Anyway, around about 1985, Marty #1 gets the idea of going time traveling. But alas, at the exact moment when he gets in the time machine and pulls the switch, as bad luck would have it, he comes into contact with anti-Marty and both are utterly destroyed with a huge bang and flash. (We can forgive anti-Marty for not warning Marty #1, because it was at this exact moment that anti-Marty finally forgot everything about his experience of time travel.)
Marty #2, bemused, just takes of his protective goggles and keeps going. He remembers it all differently, of course. He "remembers" being Marty #1, and being anti-Marty, and being himself.
Nooo, I don't quite agree. Firstly, I think there is a big difference between the Everett "many worlds" interpretation and the far more ordinary Feynman "sum over histories" decomposition of the propagator. The first is pretty much a purely philosophical or metaphysical point, untestable, while the latter is firmly rooted in good mathematics.
Let's assume you mean Everett. In that case, no, my believing the universe is deterministic doesn't mean I fail to subscribe to the methods of QM. It does mean I refuse to accept that before a measurement is made, the universe is in some weird state in which all possibilities latent in the wavefunction can be said to really exist, somehow. If an electron's wavefunction has a finite amplitude here and also there, with there being 200 million light-years distant, then I flatly refuse to believe that when the position of the electron is actually measured, and it's found to be here, then something real has changed, instantly, 200 million light years away. Even leaving aside relativity, that's just insane -- logic error -- must sterilize.
Hence I do not believe that the universe decides, only at the point of measurement, which eigenstate of the measurement operator to fall in to. I suppose that makes me a believer in some kind of hidden-variable theory. Yes, I know all about Bell's Inequality and Aspect's experiments. Very interesting and all that, but there are a number of ways other than the nonexistence of hidden variables in which these experiments could be explained.
By the way, I accept the possibility -- no, the probability -- that even if we know electrons or whatever are doing something definite when we do not measure them, we will still be unable to measure it, even in principle. This isn't hard to accept. After all, we know (or believe) that events outside of our light cone exist, and obey the normal rules of physics. But we'll never be able to observe them, even in principle.
Fair enough, but I prefer to believe that energy et cetera is conserved, and your interpretation wildly violates conservation laws. I'd rather preserve conservation of energy than forbid closed loops in world-lines.
If "time travel" just means the usual physics definition of "tracing a trajectory backward" then of course you can regard it as happening all the time. Positrons (anti-electrons) can easily be regarded as electrons traveling "backwards" in time, so that a positron-electron annihilation event is nothing more than an electron traveling "forward" in time, then reversing itself and traveling "backward" in time. Obviously we (traveling steadily forward in time) see two particles with opposite properties converge and disappear. Whoopee.
However, I think what most people mean by "time travel" is something different, a causality loop. That is, they mean you do something (which they call "time travel") and this something lets you become your own grandpa, or influence the outcome of the Civil War, and so forth. Since, of course, those things influence the you that's influencing them (otherwise the story is not interesting), this makes a nice little loop of cause and effect: you influence x which influences you who influences x, and around and around.
Whether or not the physics of the universe allows such a thing, I can't see any obvious reason why it would cause big problems -- or even be interesting. Certainly it could not manifest itself the way it's shown in the movies, in which you see the loop first one way (Marty McFly's parents marry and produce him), and then another way (Marty's parents fail to marry, because McFly travels back in time and interferes with their meeting). That's logically impossible. If the loop exists at all, it must have one unchanging form.
That is, if Marty McFly does go "back in time" he obviously can't (or rather doesn't) prevent his parents from marrying and having him, because they actually did. Whatever he does "back in time" is already part of history. His "changes" already exist, and have always existed. Indeed, they can't even logically be regarded as "changes" because nothing really changed. Although...it's possible McFly, with his imperfect knowledge of the past, could have assumed something about the past was different than it actually was (e.g. he thought his parents met at the dance, instead of afterward, when some strangely-dressed clown introduced them). Therefore, when he "changes" history (by interfering with his parents meeting during the dance, and then "fixing" things up by introducing them afterward), he might be under the illusion that he is really "changing" history instead of simply causing it to happen as it actually did.
I suppose we could now argue about whether Marty's sense of free will (as well as our own) is therefore just a big fat self-delusion, but, ugh, not before a pint or two.
Actually the easy part is doing the output. You're right, I could put it out as TeX without much trouble. The tricky bit would be parsing the input, or really, parsing the bits of output recycled as input. This happens because of the conditionality of much of the output page. That is, some parts of the page have different content depending on what other parts of the page have turned out to be. The way this is done now is to recycle bits of the output (which are XML) to the input parser (which expects XML).
You're absolutely right in the end I don't want to be doing this on the server! So far this is no trouble, because as alpha (or less) product it's only used on a company intranet anyway. When I think about exposing it to the public, it will need to be done on the client side. But in this case, I have bigger problems than the parsing issue; there is some heavy processing that goes on beween parse and output, e.g. solving algebra equations, balancing chemical equations, calculating the graph of functions. This needs to be wrapped up in some kind of downloadable plug-in.
I haven't tried the Design Science plug-in for IE that displays MathML, but they say it's nice. I would hope that works. Myself, since I'm a Linux geek, I just use FF anyway.
Well...I could do that, I suppose, yes. Only problem is, the input to the applications is pretty solidly XML, since I don't know any way to do it in TeX, and I don't see a point, actually, since the input isn't really text as such but more or less a collection of descriptions of objects. Since at present I (sloppily) use the output to communicate back to the input, it's helpful to have this be XML at both ends. Otherwise, I'd need both a parser and a writer for TeX and XML.
But in the end I shouldn't be feeding back XML this way anyway, because it's very slow. I'll be abandoning this crutch sooner or later, and at that point, sure, I could consider doing the output in TeX. Might even be a good idea, to let people get printed pages...
I did look at the link. Thank you. Not much of it worked for me, and lots was inappropriately sized. Not sure why, as I know all the CM fonts and such are available {shrug}.
I dunno if parsing XML is a hog or not, compared to parsing TeX. I do know, however, that I can just plug in a library for parsing XML. I use libxml2, which is very fast, but alas sports random bugs and bizarre behaviour from time to time because the designer (an arrogant yoyo) doesn't give a f*** about breaking the thing to introduce Kool New Featurez. Would I need to roll my own TeX parser? That would be the pits.
I use the XML as a high-level encoding of a fairly complex document. It's complex not so much because of the math and figure content, but because much of the content is randomly variable and conditional. For example, a particular number or phrase is chosen randomly at the top of the document, or in response to user action, and then all the rest of the document changes in response (a trivial example being that if a proper name is picked, like Joe or Mary, the pronouns further down adjust to reflect the sex, he or she, him or her, and so forth).
I don't know any way to encode this kind of complexity as TeX, but I can do it with XML. Something like this:
The application figures out from internal rules that the correct pronoun for "Joe" is "he", and so forth.
Similar stuff happens with the math. For example, at the top I might have an equation. Further down the page, I might want to substitute a randomly generated number for a variable in the equation, then evaluate it, keeping track of whether the substituted number was an integer, decimal, or fraction and writing the output accordingly.
Assuming we can extrapolate back from their behaviour after birth, that is. At least, I spend about 86% of my time preventing one child from trying to kill the other...
Ah, I wondered about that. Whether the RNA just floated around or whether its reverse-transcribed DNA got inserted into the genome. Interesting.
Looks like a job for an antisense DNA enzyme, then! Get that baby into the nucleus -- don't ask me how, I'm the big-picture guy, not the details man -- let it bind to the HIV genome, snip it out, presto.
Ah well. The existence of these deadly little bastards gives one new insight into why so much of our genome is ignored by our own cellular apparatus. It's like most of our own DNA consists of spam, trojans, and phishing attacks "downloaded" over the millenia from invading viruses, and we need to apply a huge filter to make sure only our own genes get transcribed.
Oh, aye, if I was writing a nice static document, of course I'd use TeX. And then if I wanted to serve it on the Web, I'd probably just serve the DVI or PS file. Or PDF, if I wanted a wider audience.
The problem is that I'm writing dynamic Web documents, which are constructed "on the fly" by the server, and which have a rich mathematical and figure content. Furthermore, these pages may be dynamic at the user end, too. That is, I sometimes serve some Javascript that allows the user to mess with the page a bit.
It's not hard to write programs that read and write XML in all its flavors (that being the point of XML, after all), so I can easily compute and serve a document of mixed XHTML,MathML and SVG. Unfortunately, at this point, only FF can render it natively.
The previous solution was to extract the math bits from the stream, construct a GIF/PNG image on the fly, and serve that. But this is a pain, and a server bottleneck, and anyway the GIFs occupy far more bandwidth than the equivalent MathML or SVG, "bloated" though those XML dialects may seem.
Sigh. If only Opera would render MathML native, I'd use it. What's a mathematically-inclined geek who wants both pretty math (MathML) and graphs and stuff (SVG) to do?
I dunno. So the compound destroys HIV in the test tube. AFAIK, this is underwhelming, because the problem with HIV is that it hides out inside cells where blood-borne drugs can't get to it. (I don't even think it's in there as a complete viral particle, probably just the RNA.)
You could hope that if you kept your bloodstream flooded with the drug you could nail each new virus as it emerged, but I seem to recall HIV can go directly from cell to cell, without entering the bloodstream at all.
I think our natural immune system kills off viral infections in substantial part by recognizing which of our cells are infected and killing them. That is, it's not just a question of wiping out the free virus, I think.
Ah...well...depending on your point of view, the fact that user-created data might end up secure against even the owner of the hardware on which it is processed is either a problem or a feature.
I take it you want an "object-oriented" operating system, wherein user data is precious and locked up tight, with access rigidly controlled by public and semi-public methods (the methods doing the job the present OS does).
Eh, it may be a plausible vision for the future. Basically a thumb-print lock on every bit of data you create, and you can only get to it via a few, limited methods. But your OS will still have to be secure, perhaps more so. You'll need your locks and keys to be functioning perfectly if you expect to get access to your data in the way you expect. God help you if you "lose" (or someone "steals") your "key" to data that's locked up in a truly impregnable vault.
That doesn't...seem...quite...right. Now, granted it's been 11 years since I started using Linux and 19 years since I started using Unix, and the ol' memory isn't what it used to be --- but I seem to recall there being a bit of an activation barrier there, a steepish bit of learning curve right at the beginning, where you have to sweat and curse through a bit of figuring out how to set the damn thing up. WTF does everything important live in "/etc"? What the hell is a "root" password and why do I need one? And so forth. So it doesn't seem to me like most people who take it into their heads to repartition the disk, download 4 gigs of RPMs (or whatever), and fire up Linux on the home machine are going to be the uberlazy types who just robotically hit "OK" and "Next" buttons on install script dialogues without bothering to read all the interesting messages that come with them...
Analogy's. Dontcha just love 'em.
Well, they're like guns. They can be highly effective or bloody dangerous, depending on the skill of the user.
I think the superfine stuff on Earth gets picked up by our ubiquitous flowing water and turned into mud, which over geological time gets turned into shale, sandstone, and other sedimentary rock. That is, what we call "sand" on Earth consists of grains too large to be suspended in water. There's a lower limit on the size of "sand" on Earth that doesn't apply to "sand" on the Moon.
The guy skips lightly over the fact that it's the system that mediates interactions between the Big Bad World (a/k/a the Internet) and the user and his precious files, so that if the system is well-designed and set up properly, it will do a great deal to protect the user even from his own actions.
An analogy one might usefully make is to the highway: good system-level security is like a well-designed, well-lit highway. Sure, the user (driver) can still kill himself, but he has to behave unusually recklessly. On the other hand, poor system-level security is like a rutty, unexpectedly curving dark country road. Even reasonably careful drivers at moderate speeds can get in trouble.
The guy is focussing on the fact that in both cases the driver can get himself killed. But that isn't the whole story. One "road" (system) makes it easier for a moderately careful "driver" (user) to survive. The other puts even careful "drivers" at risk. And, of course, there's the obvious fact that no "road" (system) can possibly protect the completely reckless "driver" (user).
I would have thought its temperature would have had to be much lower than that of normal matter. After all, it's only in equilibrium with the translational degrees of freedom of ordinary matter, because those are the only degrees of freedom that can couple gravitationally. I'm hard pressed to believe the average translational temperature of matter in the galaxy is that high -- it implies the average speed is at least several km/s. That seems very high.
Maybe the dark matter has some kind of weird internal degree of freedom, like the electronic degrees of freedom inside ordinary atoms, and there's a lot of energy in these. I suppose since these internal modes can't couple to ordinary matter, they wouldn't be in thermal equilibrium with ordinary matter. That would let the dark matter have a temp very different from that of ordinary matter.
But I'm just guessing wildly. Really, I'm just as...erm...in the dark here as anybody else.
Slashdot Mirror
If you want to look at the p+/e- collision as the electron reversing in time, then what happens is that the e- emits a gamma photon and reverses its "direction" in time. Its charge reverses, so it turns into a positron. Its velocity doesn't necessarily do a 180, because we need to account for the momentum of the emitted photon. The velocity changes in such a way that the momentum of the new positron after the event plus the momentum of the gamma photon equals the momentum of the electron before the event. You can look at this as the electron needing to "fire off" a photon to reverse its motion in time, somewhat as a rocket might fire its engines ahead in order to reverse its velocity.
There's one case in which the electron doesn't need to fire off a gamma to reverse, however: if the electron/positron pair were a "virtual" pair created out of nothing, a vacuum fluctuation. In this case, since the electron and positron's energy has been "borrowed" from the vacuum, then when they collide their energy is "paid back" and no gamma photon results.
In fact, from the point of someone traveling straight forward in time, there are two watches to explain: the watch you are wearing after you pick it up, and the watch that you were wearing while you were traveling backward in time. A person moving forward in time would see both watches.
Where did they come from? I don't know. You wrote the story, so you need to explain it. You didn't feel the need to explain where the watch came from before you added in the time-travel business. That is, if the story was just "I found a watch and picked it up" you wouldn't feel the need to explain where the watch came from. Clearly, it was manufactured, sometime, somewhere, and left there somehow.
Well, the same must be true of the other watch, the anti-watch that annihilates with the real watch at some point in the future. Who made it? How did it get there? I don't know. It's your story!
No. And I'm definite about that.
oops, right here....
Marty #1 had the odd property of getting physically younger and forgetting stuff as he got "older."
I mean to say:
Anti-Marty has the odd property of...
Well, if you want to cause Marty to go back in time for real (and not just think you do), then of course you need to start at the point "back in time" where he arrives (say 1955). At that point, you duplicate Marty. That requires E = mc^2, where m is Marty's mass, plus the mass of his skateboard, clothes, and assorted paraphernalia, plus some trivial amount of energy to give him the right momentum.
Note that you'll need to create a slightly different Marty than the original, because Marty #2 must be identical to Marty #1 when he started time traveling (say 1985). He's physically older, and needs to have different memories -- he needs to "remember" the future. He's not remembering it in the usual sense we remember things, of course, because these events are in his future, not his past. But from the point of relativity, events in our future are no less real than events in our past, and there's no reason in principle we can't run off a few quick calculations on our superdupercomputer, and predict the relative handful of events in his "future" that Marty will need to "remember." (We're assuming for the purposes of argument that quantum uncertainty is not so important that it fundamentally fouls up this calculation.)
Now we create an anti-Marty. He is just like Marty #2, but with the charge, parity, and velocity of every single particle in him reversed. He is actually Marty #1, traveling backwards in time. This, too, takes E = mc^2.
Now, Marty #2 (the one who believes he has come "back in time", because he "remembers" the future) does whatever he's going to do. Meets Marty #1, picks a fight with him, puts him in the hospital with a broken arm, and then impregnates his mother. Whatever.
And time goes on. When we reach the point where we want Marty to go back in time (say 1985), we arrange for Marty #1 and anti-Marty to meet. They annihilate each other, of course, releasing all the energy we put into creating Marty #2 and anti-Marty 30 years ago. Now we're left with only Marty #2, the time traveler, who keeps on going forward.
To sum up, to us the observers, merely traveling along forward as we do, it looks like Marty #2 and anti-Marty were created out of pure energy in 1955. Marty #2 had weird memories of the future which turned out to be accurate in every respect. Marty #1 had the odd property of getting physically younger and forgetting stuff as he got "older." At some point, Marty #1 was born and grew up. As he got older, we began to see that anti-Marty was beginning to look more and more like Marty #1, except for the fact of being made of anti-matter and getting "younger" with time, while Marty #1 was getting older. We begin to see that Marty #1 and anti-Marty are converging, becoming more and more similar. Indeed, they probably start converging physically, too, spending more and more time closer to each other.
Anyway, around about 1985, Marty #1 gets the idea of going time traveling. But alas, at the exact moment when he gets in the time machine and pulls the switch, as bad luck would have it, he comes into contact with anti-Marty and both are utterly destroyed with a huge bang and flash. (We can forgive anti-Marty for not warning Marty #1, because it was at this exact moment that anti-Marty finally forgot everything about his experience of time travel.)
Marty #2, bemused, just takes of his protective goggles and keeps going. He remembers it all differently, of course. He "remembers" being Marty #1, and being anti-Marty, and being himself.
Nooo, I don't quite agree. Firstly, I think there is a big difference between the Everett "many worlds" interpretation and the far more ordinary Feynman "sum over histories" decomposition of the propagator. The first is pretty much a purely philosophical or metaphysical point, untestable, while the latter is firmly rooted in good mathematics.
Let's assume you mean Everett. In that case, no, my believing the universe is deterministic doesn't mean I fail to subscribe to the methods of QM. It does mean I refuse to accept that before a measurement is made, the universe is in some weird state in which all possibilities latent in the wavefunction can be said to really exist, somehow. If an electron's wavefunction has a finite amplitude here and also there, with there being 200 million light-years distant, then I flatly refuse to believe that when the position of the electron is actually measured, and it's found to be here, then something real has changed, instantly, 200 million light years away. Even leaving aside relativity, that's just insane -- logic error -- must sterilize .
Hence I do not believe that the universe decides, only at the point of measurement, which eigenstate of the measurement operator to fall in to. I suppose that makes me a believer in some kind of hidden-variable theory. Yes, I know all about Bell's Inequality and Aspect's experiments. Very interesting and all that, but there are a number of ways other than the nonexistence of hidden variables in which these experiments could be explained.
By the way, I accept the possibility -- no, the probability -- that even if we know electrons or whatever are doing something definite when we do not measure them, we will still be unable to measure it, even in principle. This isn't hard to accept. After all, we know (or believe) that events outside of our light cone exist, and obey the normal rules of physics. But we'll never be able to observe them, even in principle.
I'm uncertain about my position on this...
Right. And in fact I don't believe in non-determinism, so I'm OK.
Fair enough, but I prefer to believe that energy et cetera is conserved, and your interpretation wildly violates conservation laws. I'd rather preserve conservation of energy than forbid closed loops in world-lines.
However, as a quantum mechanic, I happen to think the "many worlds" interpretation is nonsense. So I gotta part ways with you on this. Sorry.
If "time travel" just means the usual physics definition of "tracing a trajectory backward" then of course you can regard it as happening all the time. Positrons (anti-electrons) can easily be regarded as electrons traveling "backwards" in time, so that a positron-electron annihilation event is nothing more than an electron traveling "forward" in time, then reversing itself and traveling "backward" in time. Obviously we (traveling steadily forward in time) see two particles with opposite properties converge and disappear. Whoopee.
However, I think what most people mean by "time travel" is something different, a causality loop. That is, they mean you do something (which they call "time travel") and this something lets you become your own grandpa, or influence the outcome of the Civil War, and so forth. Since, of course, those things influence the you that's influencing them (otherwise the story is not interesting), this makes a nice little loop of cause and effect: you influence x which influences you who influences x, and around and around.
Whether or not the physics of the universe allows such a thing, I can't see any obvious reason why it would cause big problems -- or even be interesting. Certainly it could not manifest itself the way it's shown in the movies, in which you see the loop first one way (Marty McFly's parents marry and produce him), and then another way (Marty's parents fail to marry, because McFly travels back in time and interferes with their meeting). That's logically impossible. If the loop exists at all, it must have one unchanging form.
That is, if Marty McFly does go "back in time" he obviously can't (or rather doesn't) prevent his parents from marrying and having him, because they actually did. Whatever he does "back in time" is already part of history. His "changes" already exist, and have always existed. Indeed, they can't even logically be regarded as "changes" because nothing really changed. Although...it's possible McFly, with his imperfect knowledge of the past, could have assumed something about the past was different than it actually was (e.g. he thought his parents met at the dance, instead of afterward, when some strangely-dressed clown introduced them). Therefore, when he "changes" history (by interfering with his parents meeting during the dance, and then "fixing" things up by introducing them afterward), he might be under the illusion that he is really "changing" history instead of simply causing it to happen as it actually did.
I suppose we could now argue about whether Marty's sense of free will (as well as our own) is therefore just a big fat self-delusion, but, ugh, not before a pint or two.
Actually the easy part is doing the output. You're right, I could put it out as TeX without much trouble. The tricky bit would be parsing the input, or really, parsing the bits of output recycled as input. This happens because of the conditionality of much of the output page. That is, some parts of the page have different content depending on what other parts of the page have turned out to be. The way this is done now is to recycle bits of the output (which are XML) to the input parser (which expects XML).
You're absolutely right in the end I don't want to be doing this on the server! So far this is no trouble, because as alpha (or less) product it's only used on a company intranet anyway. When I think about exposing it to the public, it will need to be done on the client side. But in this case, I have bigger problems than the parsing issue; there is some heavy processing that goes on beween parse and output, e.g. solving algebra equations, balancing chemical equations, calculating the graph of functions. This needs to be wrapped up in some kind of downloadable plug-in.
I haven't tried the Design Science plug-in for IE that displays MathML, but they say it's nice. I would hope that works. Myself, since I'm a Linux geek, I just use FF anyway.
Well...I could do that, I suppose, yes. Only problem is, the input to the applications is pretty solidly XML, since I don't know any way to do it in TeX, and I don't see a point, actually, since the input isn't really text as such but more or less a collection of descriptions of objects. Since at present I (sloppily) use the output to communicate back to the input, it's helpful to have this be XML at both ends. Otherwise, I'd need both a parser and a writer for TeX and XML.
But in the end I shouldn't be feeding back XML this way anyway, because it's very slow. I'll be abandoning this crutch sooner or later, and at that point, sure, I could consider doing the output in TeX. Might even be a good idea, to let people get printed pages...
I did look at the link. Thank you. Not much of it worked for me, and lots was inappropriately sized. Not sure why, as I know all the CM fonts and such are available {shrug}.
I dunno if parsing XML is a hog or not, compared to parsing TeX. I do know, however, that I can just plug in a library for parsing XML. I use libxml2, which is very fast, but alas sports random bugs and bizarre behaviour from time to time because the designer (an arrogant yoyo) doesn't give a f*** about breaking the thing to introduce Kool New Featurez. Would I need to roll my own TeX parser? That would be the pits.
I use the XML as a high-level encoding of a fairly complex document. It's complex not so much because of the math and figure content, but because much of the content is randomly variable and conditional. For example, a particular number or phrase is chosen randomly at the top of the document, or in response to user action, and then all the rest of the document changes in response (a trivial example being that if a proper name is picked, like Joe or Mary, the pronouns further down adjust to reflect the sex, he or she, him or her, and so forth).
I don't know any way to encode this kind of complexity as TeX, but I can do it with XML. Something like this:
<noun name="person">
<option>Mary</option>
<option>Joe</option>
</noun>
Then further down:
<noun name="person">
<pronoun/>
</noun>
The application figures out from internal rules that the correct pronoun for "Joe" is "he", and so forth.
Similar stuff happens with the math. For example, at the top I might have an equation. Further down the page, I might want to substitute a randomly generated number for a variable in the equation, then evaluate it, keeping track of whether the substituted number was an integer, decimal, or fraction and writing the output accordingly.
Anyway, thanks for the info.
Assuming we can extrapolate back from their behaviour after birth, that is. At least, I spend about 86% of my time preventing one child from trying to kill the other...
Ah, I wondered about that. Whether the RNA just floated around or whether its reverse-transcribed DNA got inserted into the genome. Interesting.
Looks like a job for an antisense DNA enzyme, then! Get that baby into the nucleus -- don't ask me how, I'm the big-picture guy, not the details man -- let it bind to the HIV genome, snip it out, presto.
Ah well. The existence of these deadly little bastards gives one new insight into why so much of our genome is ignored by our own cellular apparatus. It's like most of our own DNA consists of spam, trojans, and phishing attacks "downloaded" over the millenia from invading viruses, and we need to apply a huge filter to make sure only our own genes get transcribed.
Oh, aye, if I was writing a nice static document, of course I'd use TeX. And then if I wanted to serve it on the Web, I'd probably just serve the DVI or PS file. Or PDF, if I wanted a wider audience.
The problem is that I'm writing dynamic Web documents, which are constructed "on the fly" by the server, and which have a rich mathematical and figure content. Furthermore, these pages may be dynamic at the user end, too. That is, I sometimes serve some Javascript that allows the user to mess with the page a bit.
It's not hard to write programs that read and write XML in all its flavors (that being the point of XML, after all), so I can easily compute and serve a document of mixed XHTML,MathML and SVG. Unfortunately, at this point, only FF can render it natively.
The previous solution was to extract the math bits from the stream, construct a GIF/PNG image on the fly, and serve that. But this is a pain, and a server bottleneck, and anyway the GIFs occupy far more bandwidth than the equivalent MathML or SVG, "bloated" though those XML dialects may seem.
Sigh. If only Opera would render MathML native, I'd use it. What's a mathematically-inclined geek who wants both pretty math (MathML) and graphs and stuff (SVG) to do?
I dunno. So the compound destroys HIV in the test tube. AFAIK, this is underwhelming, because the problem with HIV is that it hides out inside cells where blood-borne drugs can't get to it. (I don't even think it's in there as a complete viral particle, probably just the RNA.)
You could hope that if you kept your bloodstream flooded with the drug you could nail each new virus as it emerged, but I seem to recall HIV can go directly from cell to cell, without entering the bloodstream at all.
I think our natural immune system kills off viral infections in substantial part by recognizing which of our cells are infected and killing them. That is, it's not just a question of wiping out the free virus, I think.
Ah...well...depending on your point of view, the fact that user-created data might end up secure against even the owner of the hardware on which it is processed is either a problem or a feature.
I take it you want an "object-oriented" operating system, wherein user data is precious and locked up tight, with access rigidly controlled by public and semi-public methods (the methods doing the job the present OS does).
Eh, it may be a plausible vision for the future. Basically a thumb-print lock on every bit of data you create, and you can only get to it via a few, limited methods. But your OS will still have to be secure, perhaps more so. You'll need your locks and keys to be functioning perfectly if you expect to get access to your data in the way you expect. God help you if you "lose" (or someone "steals") your "key" to data that's locked up in a truly impregnable vault.
Linux user - install and go.
That doesn't...seem...quite...right. Now, granted it's been 11 years since I started using Linux and 19 years since I started using Unix, and the ol' memory isn't what it used to be --- but I seem to recall there being a bit of an activation barrier there, a steepish bit of learning curve right at the beginning, where you have to sweat and curse through a bit of figuring out how to set the damn thing up. WTF does everything important live in "/etc"? What the hell is a "root" password and why do I need one? And so forth. So it doesn't seem to me like most people who take it into their heads to repartition the disk, download 4 gigs of RPMs (or whatever), and fire up Linux on the home machine are going to be the uberlazy types who just robotically hit "OK" and "Next" buttons on install script dialogues without bothering to read all the interesting messages that come with them...
Analogy's. Dontcha just love 'em.
Well, they're like guns. They can be highly effective or bloody dangerous, depending on the skill of the user.
I think the superfine stuff on Earth gets picked up by our ubiquitous flowing water and turned into mud, which over geological time gets turned into shale, sandstone, and other sedimentary rock. That is, what we call "sand" on Earth consists of grains too large to be suspended in water. There's a lower limit on the size of "sand" on Earth that doesn't apply to "sand" on the Moon.
The guy skips lightly over the fact that it's the system that mediates interactions between the Big Bad World (a/k/a the Internet) and the user and his precious files, so that if the system is well-designed and set up properly, it will do a great deal to protect the user even from his own actions.
An analogy one might usefully make is to the highway: good system-level security is like a well-designed, well-lit highway. Sure, the user (driver) can still kill himself, but he has to behave unusually recklessly. On the other hand, poor system-level security is like a rutty, unexpectedly curving dark country road. Even reasonably careful drivers at moderate speeds can get in trouble.
The guy is focussing on the fact that in both cases the driver can get himself killed. But that isn't the whole story. One "road" (system) makes it easier for a moderately careful "driver" (user) to survive. The other puts even careful "drivers" at risk. And, of course, there's the obvious fact that no "road" (system) can possibly protect the completely reckless "driver" (user).
I would have thought its temperature would have had to be much lower than that of normal matter. After all, it's only in equilibrium with the translational degrees of freedom of ordinary matter, because those are the only degrees of freedom that can couple gravitationally. I'm hard pressed to believe the average translational temperature of matter in the galaxy is that high -- it implies the average speed is at least several km/s. That seems very high.
Maybe the dark matter has some kind of weird internal degree of freedom, like the electronic degrees of freedom inside ordinary atoms, and there's a lot of energy in these. I suppose since these internal modes can't couple to ordinary matter, they wouldn't be in thermal equilibrium with ordinary matter. That would let the dark matter have a temp very different from that of ordinary matter.
But I'm just guessing wildly. Really, I'm just as...erm...in the dark here as anybody else.