Well, what else can it be? It is not April 1st, so my only explanation is that it is an Onion article that somehow was picked up by the BBC. What do you think? It reads exactly like one, right down to the picture of the pleasant bearded academic at the board, the well-scrubbed English schoolchildren, and the quotes from the children. The only thing missing is the page with the three heads (whose names and occupations change every week) making comments on the story. (Be sure to watch the video links of the demo too!)
This is the sort of science/mathematics reporting that I usually expect to read in the Guardian. All about someone “solving” the “problem” of dividing by zero by inventing a new number called “nullity”. I should be annoyed, but I woke up in a strange mood today and so I’m finding that it’s just funny. For appropriately angry comment, see Mark Chu-Carroll.
-cvj
(Before anyone claims that I’ve just defined renormalization as dividing by infinity, I haven’t. I’m well aware it is a case of taking different values for charge and mass to avoid infinities in the result, rather than just cancelling the infinity out of the result. In a mathematical sense – when you ignore the polarization of the vacuum dynamics as Dr Oakley does – renormalization does look like a trick to just get rid of an infinity and make the result give the right answer. This shows that you need physical understanding of the dynamics, not just mathematical equations which physically are so vague and abstract it could be compatible with many different, contradicting models. The fact that there are no loops in the vacuum beyond the 1 fm range of the IR cutoff should dispose of the idea that dark energy is justified by the vacuum. However, the crackpots who believe in the ad hoc lambda-CDM cosmology and who probably censored me out from publishing in the right journals in 1996, two years before Perlmutter confirmed that there is no empirical evidence of gravitation slowing down expansion, don’t care whether their physical model has validity. They’re just showmen.)
His argument is no better than 0/x = 0 hence with x = 0 you get 0/0 = 0, which is his “nullity”. He just ignores the contradicting x/x = 1 argument, which would imply 0/0 = 1. Until he resolves this conflict here that 0/0 = 0/x = 0 = x/x = 1, the value of 0/0 is undefined except where you know physically what you are doing and say say it is 0 or 1. Example, if you have dx/dx you can cancel to give 1, where dx ~ 0. Another example is that you can cancel infinities (where 1/infinity = 0) if you know physically that each infinity is the same thing, see Dr Oakley’s page on quantum field theory for silly objections to this: http://www.cgoakley.demon.co.uk/qft/
Infinity/infinity is only undefined (like 0/0) if you don’t know physically how you have arrived at them. As long as you haven’t in the process absorbed other factors into one of those infinities (like assuming that x * infinity = infinity), you shouldn’t get errors. The absence of an IR cutoff would physically make the observed electronic charge zero, because it would allow the vacuum to polarize without any radial limit, until the core charge was entirely cancelled by the polarization field (which points the opposite direction to the core charge field). The absence of a UV cutoff would allow vacuum loops at the electron centre to have infinite energy and momentum. Disposing of the infinities and zeroes in these cases is physically justified: http://nige.wordpress.com
Division by zero is absurd, but triviality is quite useful.
http://sciphysicsopenmanuscript.blogspot.com/
There are 3 existential types, not just 2.
1) That which exists.
2) That which does not exist.
3) That for which existence is indeterminate.
Any trivial is of the third type because “The Existence of a Trivial is Indeterminate”.
This last statement can be proved quite easily. It says that given any unique object, there is no way to determine if the object is really itself, or if it is in fact a trivial clone of itself. This is indeterminate.
One can exploit this existential indeterminacy of the trivials to make all kinds of unusual models.
http://sciphysicsopenmanuscript.blogspot.com/
But division by zero ? I dont think that this will ever work.
Huang
The Grad — Hahaha, wow! Snort retracted! ^_^
I did watch the video. Sure, I thought it was basic as there were several ways to extend the number system already and several ways in hardware, software and programming technique to get around the problem of division by zero. But like Carl Brennan, I thought there were a lot of metaphors that sound silly at first hearing, when one is ignorant of the mathematical formalism the speaker is using. I expect this sort of pop science piece to be filled with metaphor and gross simplifications. So in general I do not consider it a fair hearing of the mathematical ideas of the academic involved.
I do agree that this issue has probably generated more discussion than necessary and I think I have pretty much covered my point. Please enjoy the following cartoon, gotten from Steven Hsu’s blog, which illustrates what I think is going on in these pop science news pieces:
http://photos1.blogger.com/blogger/8109/2153/1600/dilbert2006081526805.gif
TheGraduate:- The issue of extending numbers systems is just an irrelevance at the level we talking about here. You can bring in increasingly high levels of mathematics and say that any mathematical discussion at high school involves those, and point to all sorts of Wikipedia articles. That’s just silly…. I don’t know what high school you went to, but I would *hope* that you’d have been able to smell a bit of a rat, and that would make you willing to make a call to someone.. do a bit of research. (Have you actually *looked* at the site and the video? Are you just deliberately being contraarian here to waste time? You honestly believe that the arithmetic you did in high school would not have equipped you with enough knowledge to try to learn a bit more? Come on.)
Nobody suggested that you need to be (as a journalist) the world expert on a topic in order to make a report on it… But you ought to know enough to be able to know when to get another opinion, read a bit more, etc. This is why journalists are supposed to be able to do research, why they have editors, fact-checkers, etc.
And the stuff about string theory is just over the top and irrelevant to the heart of the issue. You can continue to bring it up, and it does not change the fact that journalists should do a little bit of research, and it does not change the fact that a little bit of science education *can* be obtained in high school – enough to help your average reporter (perhaps with the aid of his/her editorial team) decide to pick up the phone and do a bit of checking. At least get another person along to say something cautionary.
Feel free to go on and on about how this is ok because science in other fields has sometimes been covered indifferently (in fact, poor coverage is often pointed out on this blog and others -whether about string theory or particle physics or whatever, so I am not even sure what you’re complaining about- perhaps read what I’ve written a bit more before moaning about balance of treatment on this issue)
So keep going on and on about coverage of string theory or whatever. All you are saying is that two wrongs make a right (another interesting form of mathematics), and that it all does not matter anyway. That would be *wrong*. But sure… please go on saying it.
Best,
-cvj
Wakalixes makes it go!
Aaron F.
This is a situation that happened with the USS Yorktown:
“In September 21, 1997 while on maneuvers off the coast of Cape Charles, Virginia, a crew member entered a zero into a database field causing a divide by zero error in the ships Remote Data Base Manager which brought down all the machines on the network, causing the ship’s propulsion system to fail.”
http://en.wikipedia.org/wiki/USS_Yorktown_(CG-48)
I am not sure how big a problem this kind of thing is in practical applications but it does seem to happen occasionally. There are already numerous ways of avoiding a messy shut down when this kind of thing happens.
There is some interesting stuff on this here: http://en.wikipedia.org/wiki/Division_by_zero
Dr. Johnson,
I am not sure why you think this is high school mathematics. Understanding that division by zero is simply undefined in the standard number system is standard high school mathematics. I agree. But I have never really heard of a high school that taught abstract algebra and ways of extending the number system (surreals, hyperreals etc) as a part of the standard school curriculum, taught to everybody.
I frankly consider it HIGHLY unlikely that they would cover this in the basic high school math curriculum that your average reporter can be expected to have taken. It’s not that the math is particularly complicated, just not standard.
If people are curious about the possible extensions, they can read about them here:
http://en.wikipedia.org/wiki/Division_by_zero#Other_number_systems
I suppose we could make a rule that reporters shouldn’t cover math they don’t understand but then where would all the wonderful articles about string theory be? And of course by definition, a new discovery in science, is going to be something at the periphery of the field that a novice or even a professional scientist in a neighboring field, might not be likely to understand.
You said, “What subtle point am I missing here?”
I think discussing this issue without acknowledging the context of yourself being part of a community and perhaps even an individual who has benefited from media’s typically gentle coverage of science, leaves out a critical part of the analysis of how reporters cover science in general.
Anyway, since I am not Dr. Anderson’s lawyer, for further amusement and perhaps clarification of what he is doing, one may look at an article on Wikipedia concerning his work. It is apparently being challenged as shameless self promotion:
http://en.wikipedia.org/wiki/Nullity_%28transreal%29
Hehehe… I’m sure everybody’s toyed with the idea of an imaginary-ish number defined as 1/0. But what’s it good for? Any attempt to work with it quickly lands you in indeterminate hell. Maybe someone smarter than me will need it someday, but til then…
“Imagine you’re landing on an aeroplane and the automatic pilot’s working,” he suggests. “If it divides by zero and the computer stops working – you’re in big trouble. If your heart pacemaker divides by zero, you’re dead.”
*SNORT.* I mean, I guess it’s possible that an autopilot could crash on an unhandled divide-by-zero, but we already have a “nullity” for that situation — floating point infinity. And do pacemakers even DO floating point math?
Right then…. Thanks.
-cvj
Everybody (who’s any good) has a solution to the various Zen koans that litter physics, but not that many people agree on the solutions. I forgot to mention that the proponents of WMI claim that >50% of physicists believe in multiple universes which split off every time a measurement exists.
The reason the military wants recruits at roughly the same age when they should be learning physics is because humans are easier to indoctrinate at that age. And once humans get a principle in their head, whether it is epicycles, aether or string theory, it is very hard for them to get it back out. A good book to read is Hesse’s “The Glass Bead Game”, or Collins’ “Gravity’s Shadow”.
The problem with the foundations of particle physics is precisely that it is “backed up with laboratory evidence”. Experimenters observe an approximate symmetry (no experiment can be exact), and then the theoreticians assume that the symmetry is exact (or “broken”), and look for the simplest model that fits the symmetry. This is doing physics from the bottom up, experimental guidance is at the foundation. But our pitiful experiments are at minuscule energies compared to the Planck energy.
Nature is a hall of mirrors. You cannot easily distinguish between the reflections on the truth and the truth. There are many possible models that give the same symmetry, therefore symmetry cannot distinguish between them. So you end up with a standard model with 10^2 arbitrary constants.
Rather than basing the foundations of physics on symmetry, you should be looking for a foundation based on a simple (noncommutative) geometry. You will know that you have the right geometry because it will allow you to derive the symmetries from first principles. And then you will be able to compute the arbitrary constants.
And the arbitrary constants are not at all arbitrary (see hep-ph/0505220 ), so you have every hope that a simple geometry will allow you to derive the complicated observed symmetries.
at best are zen koans … “Electrons are both waves and particles.â€
That’s the first zen koan I’ve encountered that’s backed up with laboratory evidence!
Carl Brannen (11):
Would you give me some examples of this “shot through” state of affairs? I am not aware of the situation you’re talking about. If you’re complaining about the usual naive approaches to renormalisation that are taught in older books and courses, I suggest you read a good modern introduction to quantum field theory. And are you worried about asymptotic series vs convergent ones? There’s no mathemaical problem there either…
Best,
-cvj
TheGraduate (10) – I’m still not geting your point… are you saying that is ok then… it just does not matter? Anything goes? Just give it all up an print any old nonsense? I don’t agree with this.
-cvj
I don’t see how we can expect reporters to avoid obvious nonsense mathematics like this when we our students learn at least as much stuff that is patent nonsense on first sight, and at best are zen koans:
“Space and time are the same thing.” “Electrons are both waves and particles.” “If you rotate a fermion by 360 degrees it gets multiplied by -1.”
That’s just what the public is exposed to. If you study the stuff at a higher level the mathematics just gets worse. Quantum field theory is shot through with divisions by zero, and divergent series that are approximated in perturbation theory. At one time these sorts of niceties bothered the leading theorists, but the present generation seems to accept them with little complaint.
Dr. Johnson,
What I said is not the argument to which you are responding. The point is the same standard probably gets applied quite often to other scientific fields including string theory, lqg and those who oppose them. Something to think about …
Oh gosh….
(1) If the reporter did not do high school mathematics, then the reporter has no business reporting on a story -with no checking- in mathematics…. What subtle point am I missing here? The issue here is whether the same standard is applied to reporting on other topics… politics… economic stories… etc. I have got the impression that less care is given to checking science stories because it is considered less crucial to get the basic facts right. This is not a good thing. This is what I’m talking about…
(2) The reporter was not reporting on string theory or any other subject beyond high school arithmetic. I am just not getting your point here. What on earth does string theory have to do with this?
And furthermore…. are you saying that because reporters have been sloppy in their journalism elsewhere that it means that all reporters everywhere are allowed to by sloppy, for all time?
Further… credentials have nothing to do with this.
Further… the term “group think” .. why is it that there is a specific group who always thinks to use that term?
Best,
-cvj
“the reporter either knows some high school mathematics to at least report this a little more skeptically”
1. The issue is one of abstract algebra at least. Most high schools wouldn’t cover that. But regardless, there are alternative algebras, surreal numbers etc.
“have the sense to call someone at a local university mathematics department for a quote”
2. Dr. Anderson has a PhD in Computer Science. (Some consider Computer Science a branch of applied mathematics.) But obviously, the reporter had no reason to question this guys credentials. I put a link to his publication list. He seems like an established academic to me.
http://www.cs.reading.ac.uk/people/J.Anderson.htm?publications
But in general I was talking about people that interface with the media from a position of knowing much, much more mathematics than the reporter does and the fact that reporters usually don’t know what that expert is talking about. And usually this is fine except when they make science in general or someone’s subfield look bad or they quote a ‘crank’ making him seem ‘legitimate’. Then there is usually a big argument about it.
I do think not everybody has mastered highschool math and while it might have made a difference here in this instance, I think it would be of no help if the reporter was covering string theory or something like that. So I find it interesting to compare the reactions to this incident with things going on in general with theoretical physics and the media.
I suppose I could just agree how bad it is that reporters are so stupid but I don’t like group think. It would be boring if this whole thread was just about how terrible the schools are and how silly that reporter is. I think he was probably doing his job in a way that is characteristic of how reporters cover string theory.
Huh? I don’t know what you’re talking about.
The issue is simple. I think all we are asking is that the reporter either knows some high school mathematics to at least report this a little more skeptically, or at least have the sense to call someone at a local university mathematics department for a quote, or to ask the opinion of someone else. It would take ten or fifteen minutes of their time.
-cvj
I would be curious to know what people think went wrong in this situation.
I think the scientific community often enjoys the ignorant adoration of reporters. Then there is hypocritical outrage when the reporter does the same favor to others whom we don’t put on a pedestal. I think encouraging a more investigative attitude on the part of reporters starts at home, with encouraging say, every reporter that reports a string theorist to then go and make sure they interview parties critical to string theory.
In this particular debate, I’ve heard parties on both sides claim that there is no way to decide the issues other than understanding the physics. Is it then not unethical or at the very least contradictory to give interviews to the media knowing they are doomed to report inaccuracies and to propagate ignorant decision making?
I find myself very annoyed by the way certain members of the scientific community use the media for self promotion and promotion of their research. But it’s a very old game I know. It goes back centures so perhaps this is the nature of the beast. But if we are to accept that it is fair game to dupe reporters into ignorantly supporting our research programs wherever possible, then it’s probably hypocritical to get mad when another colleague or subfield does so also.
With no indications that this is a joke/parody , I suppose we will have to assume that this is really happening. While, I am aghast that BBC does not point out anything disturbing, I am somewhat thankful to them for bringing it to their readers’ attention. It is ridiculous that people can be allowed to walk into school and teach what they like to school children. What is an appropriate place to express outrage that would have some effect? I suppose enough slamming comments on the BBC article will prompt them to take care of that?
Yes the Onion is such a site. No, there is no such link since -sadly- there is no such original article… it seems to be the BBC’s idea of a real science news article.
-cvj
Is the Onion a parody news website? Is there a link to the original Onion article?
Of all the people in the world, this person from a com.sci dept. is demostrating it to some school children who think that this is “cool.”
Think of the children! Poor kids…