The way that we tell if a theory is broken is by experimentation. That is not entirely true. A theory which also gives infinite answers to certain questions, or answers which contract results from other (accepted) theories must be broken as well. That is not entirely true. Take for example the quantum electrodynamics: it's broken beyond repair
and still very accurate in many experiments, but not all of them. Physics is also an experimental science.
The problem is that as stated, the Standard Model and General Relativity are mutually exclusive. As they stand, both imply the invalidity of the other. But General Relativity is great for analyzing big things, and the standard model for extremely tiny things. Both make predictions with surprising accuracy. But as stated, they're incompatible. I'm happy then to inform you that there is the black hole radiation.
This isn't exactly what most scientist would consider "good news". We already know that both the standard model and the general relativity are wrong or at least incomplete, but they continue to pass every experiment, including this one... If you bothered to read the post you would have noticed:
The experiment ruled out the simple neutrino oscillation interpretation of the 1990s LSND experiment. Neutrinos have a tiny amount of mass, required by their oscillations, as observed in solar, atmospheric, and reactor neutrino experiments. Combining this mass with the LSND experiment's results required the presence of a fourth but 'sterile' neutrino, breaking the 3-fold symmetry of particle families in the standard model. Let me translate this to you: there was an experiment that implied that there must be an additional neutrino
not currently accounted by the Standard Model, but the new experiment ruled out this possibility. Okay?
Neither of the two has much (if anything at all) to do with the general theory of relativity, they neither prove nor disprove it, just with the Standard Model of particle physics.
Lets say that I write some hand writing recognition software using a neural-net. In order to train my software, I use a large database of handwriting samples that I have found on the web. However, the person that compiled this database made the mistake of labeling all of the sample images of the letter 'n' as the letter 'q', and all of the images of the letter 'q' are labeled as the letter 'n'. Person B comes along and uses the same data set to train a naïve-Bayes classifier. Guess what? Both algorithms will make the same mistakes when it comes to the letters 'n' and 'q'. Not because I stole code from Person B, but because we used the same training data. According to this example, both algorithms behave pretty much the same way because they've been trained on the same set of data, no? That is, algorithms that need to be trained in order to be functional at all only depend in an even more crucial way on the training set than, say, a key-based search of a phone book.
I'm appalled, too. I'm also surprised. Why?
What I'm not is a Google apologist. So naturally you go on to provide some apologies for Google:
The dictionary could've been indexed via the spiders. It could've been indexed via the desktop search app. There are lots of ways that Google could've got the information. Anyone who works for Google, knows the deep ins and outs of their data handling, and who reads and posts on this site ain't gonna tell. And then, well, some more apologies:
Google is information. Well, thanks for this explanation, I always thought of Google as being a corporation.
They get it from everywhere, and they know how to store, sort and use it. This must be some very deep secret knowledge that only Google possesses:
Anyone who works for Google, knows the deep ins and outs of their data handling, and who reads and posts on this site ain't gonna tell. Google is information... Google is corporation... information... corporation... brain in pain:
It may well have been intentional theft, but I don't think Google the corporation has reached the point where they actually believe "All Data Are Belong To Us".
[Google is] going to have a hard time enforcing [in China] western style ideas about copyright and what constitutes "doing no evil" What do you mean? Are you saying that the responsibility of Google is to enforce the Western values upon "natives" (to borrow your word) of the non-Western world?
Recognition of authorship, among free(beer) work at least, is a courtesy we have no need to abandon. nor, strictly speaking, to follow. For example:
If all of maathematics was written down in nameless books with mystery authors, we would live in a crappy world indeed. How come? Would mathematics be different?
I submit that there is no originality in the character -- Pinyin pairing, though perhaps there is in the use of the engineers' names. So then after the removal of these names, the originality of the database is gone?
Philosophical argument, I suppose, but "equality" doesn't mean the same thing as "sameness." For example, in Z_5, 2 and 7 are "equal" (in the same equivalence class), but it would be hard to argue that 2 is the "same" as 7. Similarly, the digit string "3.999999...." and "4.0000000" are clearly not "the same", although they are in the same equivalence class. There is a similar but different thing in LISP: one can check both for a certain kind of "sameness"
as well as "equality". For example, (eq 4.0 4.0) is False, but (= 4.0 4.0) is True. Of course,
(= 4.0 3.99999999999999999999999999999999999999) is True, and so is (= 4 4.0).
"[H]earing only one side of a conversation makes it more noticeable and intrusive."[...]
I agree with researcher;s conclusions. What if this is only because people are not used to listening to one-side conversations?
Then, as such conversation become more common, they would also become less "noticeable and intrusive".
Hmm... I don't quite follow what that would prove. Conventional logic says that that is just "False". Yes, you're right. It was my mistake: I wanted to define x==y as x>=y & x<=y, but wrote instead
what you show to be false.
I'm not sure if you're therefore supporting me or refuting me. I'm just wondering how far one can get without == for floats.
From a practical viewpoint, I just never do == on floats, because it's meaningless.
Actually, I challenge people to come up with a practical and valid use for == on floats. I also can't remember using == on floats, but, ok, since you've posed the
chalange, two examples that come to mind would be: using x==x+y as a check for
underflows or end of iteration; also expression x=y/(b-a+epsilon) used for
avoiding overflows or divisions by zero could be in some cases semantically
viewed as x=y/epsilon when b==a, or x=y/(b-a) otherwise. Of course, one can
use in both cases <= just as well.
In fact, saying 4.0 equals 4.0 is folly as well - in general it isn't really safe to do equality comparisons on floats - only greater or less than comparisons. How about defining x == y of two floating-point numbers x and y as (x >= y)&&!(x >= y)?
As a mathematician (or at least, an ex-mathematician) I am always amazed by mathematicians who forget that 'equality' between distinct domains is introduced (in standard developments) as a mere abuse of notation. Just because there is a canonical injection of Z into (say) Q does not mean that any element of Z is equal to any element of Q in any normal sense.
There exists natural injective maps from N -> Z -> Q-> R -> C, but they are actually different domains, and not strictly, subsets (as people like to presume for convenience). To see this clearly (and simply), consider the formal defintions for a natural number 4, and the rational number 4, in set theoretic foundations: the first is finite set, the second is an infinite equivalence class. Clearly they are different objects. No, the rational number 4 and the integer number 4 can be considered to be "the same object"
by noticing that the infinite equivalence class representing 4/1 is equivalent to the integer 4.
I won't bother you with mathematics, just give you an example from programming language LISP:
$ clisp -q
[1]> (eql 4 4.0)
NIL
[2]> (eql 4 4/1)
T
[3]> (eql 4 8/2)
T
[4]> (equalp(type-of 4)(type-of 8/2))
T
[5]> (equalp(type-of 4/3)(type-of 8/2))
NIL
[6]>
As a mathematician (or at least, an ex-mathematician) I am always amazed by mathematicians who forget that 'equality' between distinct domains is introduced (in standard developments) as a mere abuse of notation. Just because there is a canonical injection of Z into (say) Q does not mean that any element of Z is equal to any element of Q in any normal sense. Here is one normal sense: take the union of Z and all integers in Q, and, bang!, you can introduce =, >, *, + and = naturally.
Moreover, since 4.0 is a floating point number, it's not even a very helpful abuse of notation to allow 4 and 4.0 to be 'mathematically' equal, since you can demonstrate that mathematically all floats are equal to each other: there's some nonzero epsilon small enough that epsilon + x is 'equal' to x. It is not helpful to then apply normal mathematical reasoning and conclude that all integers are equal - that is, it's nice to maintain some part of a programming language that is actually consistent,[...] Well, not quite. Here is the counter-example to your claim that all floats are equal to each
other based on the fact that there is eps, such that 1.0+eps=1.0
1.0+eps=1.0, (1.0+eps)+eps=1.0; (1.+eps)+eps)+eps=1.0,...
but
1.0+(eps+eps)=1.0+2*eps; 1.0+(eps+(eps+eps))=1.0+3*eps;
where n*eps, n is integer, is defined as eps+eps+...+eps (n times)
Now, we can prove that 1.0 is not equal 2.0 using eps:
2.0=1.0+(eps+(eps+(eps+...))), with eps repeating 1/eps times. Since the r.h.s.
is different from 1.0, so is the l.h.s., i.e 2.0 is not equal to 1.0
Of course, this only shows that associativity is not working, so the care is needed
to get results right, and mathematician surely has the right to be appalled by this
(there are of course also overflows and underflows, etc).
Really, any programming language for the mathematically savvy would issue a warning whenever you used a floating point type for anything; floating point support is a somewhat lame compromise for hardware compatibility. Not really. They are used because they can be efficiently implemented to imitate reals. It is then
up to programmer to be a bit careful in order to maintain the accuracy when imitating the
"true" reals, be they constructively defined or not.
AI in an FPS would be if the computer received a matrix of pixels of what would be on their screen if they were human, and then discerning from the pixels where the enemies were and how they were moving. Well, then you would have to add also mechanical arm to move the mouse, also pipe in mics
to analyze sounds etc... computer games of this type would come in a big box.
A properly coded AI bot would not have access to the location of every player. Think about OOP for a sec: Player would be an interface (not a class) implemented by either ComputerPlayer or NoncomputerPlayer. The perfect class Map would be an element of Game, not of ComputerPlayer. If it was an element of ComputerPlayer, it would have to be an element of Player, which means it would be an element of NoncomputerPlayer, and as we all know, humans do not have a perfect map to use. There are many games where computer players are already supposed to know the place where the game is taking place, so your perfect class Map would already exclude one common type of games...
Of course, games probably aren't designed this way simply because COMPUTER AI COULD NOT WIN EVER if it had to play this way. Which way?
Hell, computers have a hard enough time picking certain shapes out of static images, and definitely not in real time! The same is true for human players looking at the screen during FPS games.
The only reason you think a computer can miss is because the AI of past games have built in flaws and limitations so that you can actually get a shot off. Try playing any first person shooter on the highest difficulty and you'll get a taste of the "facts". Then ask yourself why the computer missed you at all if it doesn't have to think about where to aim, since it knows your exact position at all times. Well dude, even if computer knows player's exact position at all times, it still does not now where the player is gonna go next,... you get the drift: as long as there is some delay before computer actions affect the player's, the player still has a chance.
It seems simple at first:
It's ironik that you swear in the process of advising upon how to be taken seriously, in that your argument is subjekt to being automatikally adjudged wanting for it's (unnecessary) inklusion of a low-grade shok taktik. but then...
Please, bestow more sagacity upon us, I know I'm primed to receive after your first offering... I think you're onto something here! Maybe "I gnow I'm primed..."?
There is something very unhealthy about aspects of the anoymnity that people assume and/or require when they sit down and are typing at a keyboard. Would you mind sharing some thoughts on what would be this unhealthiness?
Approved articles (even those written by experts) will be subject to peer review before being approved. That doesn't mean that people can't prank the system on unapproved articles, but if an article has the approved sticker on it, we have at least one expert (and usually 2-3) who have gone over it and gone on record as saying "This is a good article". Will then every approved article have also the link to the referee(s) reports, or will these reports be secret?
"Appeal to authority" is listed among "logical fallacies" for a reason. Let's see then this reason:
If your point is good, if you're correct and you have the background to argue your point well, then a know-nothing shouldn't be able to stand against you in a debate. But should not PhD provide exactly these qualities: "to be correct", "to have a good point", "to have the background to argue your point well", etc? Let me ask this differently: Is it not that when you prefer these qualities over credentials, you also appeal to authority, where the authority in
your case is that of "good point", "background", "arguing well", etc?
If you can't debate your point, and you need to fall back on, "I'm a professor at [such-and-such] College!" then you probably don't really know what you're talking about anyway. Or maybe that person is appealing to authority? Which does not imply that the
person does not know what he or she is talking about.
Slashdot Mirror
You've just written a sentence.
Neither of the two has much (if anything at all) to do with the general theory of relativity, they neither prove nor disprove it, just with the Standard Model of particle physics.
Now we just need some clean explanation for the "any well-meaning company" term...
I agree with researcher;s conclusions. What if this is only because people are not used to listening to one-side conversations? Then, as such conversation become more common, they would also become less "noticeable and intrusive".
the way you put it, it sounds kind of interesting,...
You're welcome!
[1]> (eql 4 4.0)
NIL
[2]> (eql 4 4/1)
T
[3]> (eql 4 8/2)
T
[4]> (equalp(type-of 4)(type-of 8/2))
T
[5]> (equalp(type-of 4/3)(type-of 8/2))
NIL
[6]>
Moreover, since 4.0 is a floating point number, it's not even a very helpful abuse of notation to allow 4 and 4.0 to be 'mathematically' equal, since you can demonstrate that mathematically all floats are equal to each other: there's some nonzero epsilon small enough that epsilon + x is 'equal' to x. It is not helpful to then apply normal mathematical reasoning and conclude that all integers are equal - that is, it's nice to maintain some part of a programming language that is actually consistent,[...] Well, not quite. Here is the counter-example to your claim that all floats are equal to each other based on the fact that there is eps, such that 1.0+eps=1.0
1.0+eps=1.0, (1.0+eps)+eps=1.0; (1.+eps)+eps)+eps=1.0,
but
1.0+(eps+eps)=1.0+2*eps; 1.0+(eps+(eps+eps))=1.0+3*eps;
where n*eps, n is integer, is defined as eps+eps+...+eps (n times)
Now, we can prove that 1.0 is not equal 2.0 using eps:
2.0=1.0+(eps+(eps+(eps+...))), with eps repeating 1/eps times. Since the r.h.s. is different from 1.0, so is the l.h.s., i.e 2.0 is not equal to 1.0
Of course, this only shows that associativity is not working, so the care is needed to get results right, and mathematician surely has the right to be appalled by this (there are of course also overflows and underflows, etc). Really, any programming language for the mathematically savvy would issue a warning whenever you used a floating point type for anything; floating point support is a somewhat lame compromise for hardware compatibility. Not really. They are used because they can be efficiently implemented to imitate reals. It is then up to programmer to be a bit careful in order to maintain the accuracy when imitating the "true" reals, be they constructively defined or not.