# Nullity and Perspex Machines

December 7, 2006 12:07 PM Subscribe

Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even taught it to high school students [via Digg]. You just have to work with a new number he calls Nullity (RealPlayer video). According to Anderson's site The Book of Paragon, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of transreal arithmetic (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies? identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.

The comments section below the BBC article makes me want to stab myself in the face.

posted by Tlogmer at 12:18 PM on December 7, 2006

posted by Tlogmer at 12:18 PM on December 7, 2006

My head asplode.

posted by ZenMasterThis at 12:26 PM on December 7, 2006

posted by ZenMasterThis at 12:26 PM on December 7, 2006

What a loon. (Besides which, differential calculus is

posted by Steven C. Den Beste at 12:29 PM on December 7, 2006

*already*based on division by zero.)posted by Steven C. Den Beste at 12:29 PM on December 7, 2006

OK, great, Doctor. You've attached a name to an artificial construct in mathematics and computer science, with tales of woe about pacemakers failing on divide-by-zero (if it were me designing the artificial heart, I might, y'know, change the behavior of divide-by-zero from 'cataclysmic system failure' to 'return 0', but sure, why not). You still haven't told us how you're going to store 'nullity' as a bit pattern, or how you're going to enforce its acceptance across the same legacy systems that cause landing gear to fail, or whatever the hell else trouble you're ascribing to a problem NOT BASED IN TANGIBLE REALITY.

*mutters*

He may have a point in the mathematical need for a definition of n/0 (which already exists, but sure, why not), but it's not like the CS community needs a savior.

Also, I'll second the part about the comments from the peanut gallery... sweet christ, I take back any mean words I ever said about the circle jerks around here, the pile-on at the Beeb blows it out of the water.

posted by Mayor West at 12:29 PM on December 7, 2006

*mutters*

He may have a point in the mathematical need for a definition of n/0 (which already exists, but sure, why not), but it's not like the CS community needs a savior.

Also, I'll second the part about the comments from the peanut gallery... sweet christ, I take back any mean words I ever said about the circle jerks around here, the pile-on at the Beeb blows it out of the water.

posted by Mayor West at 12:29 PM on December 7, 2006

Bah... the BBC didn't print my politely-worded and short rebuttal.

Basically, it's all crap. There's no way to define a value for 0/0 such that it's consistent with the regular definition of +, -, * and /. 0/0 has to be undefined. Now, you can try to rename this value as "nullity" but you might as well call it "put down your pencils" because the moment you get this number the rest of your calculation is invalid.

As for defining 1/0 and -1/0 as infinity, it can be done -- but not in the way this bozo does it. Abraham Robinson did a very cool job on this with his non-standard analysis, which is (very informally) a way of doing calculus so that dy and dx are actually numbers, albeit special new infinitesimals that are less than every positive number but greater than zero.

(I have a degree in mathematics so I'm not just talking out of some non-oral orifice, even though I studied non-standard analysis more than 20 years ago...)

posted by lupus_yonderboy at 12:33 PM on December 7, 2006

Basically, it's all crap. There's no way to define a value for 0/0 such that it's consistent with the regular definition of +, -, * and /. 0/0 has to be undefined. Now, you can try to rename this value as "nullity" but you might as well call it "put down your pencils" because the moment you get this number the rest of your calculation is invalid.

As for defining 1/0 and -1/0 as infinity, it can be done -- but not in the way this bozo does it. Abraham Robinson did a very cool job on this with his non-standard analysis, which is (very informally) a way of doing calculus so that dy and dx are actually numbers, albeit special new infinitesimals that are less than every positive number but greater than zero.

(I have a degree in mathematics so I'm not just talking out of some non-oral orifice, even though I studied non-standard analysis more than 20 years ago...)

posted by lupus_yonderboy at 12:33 PM on December 7, 2006

When I left the BBC Comments Section in December, I was in awe and a little depressed, as if someone or something had told me to go fuck myself, and had told me with a kind of meticulous exactitude that was overwhelming and irrefutable.

Boum indeed.

posted by cytherea at 12:36 PM on December 7, 2006

Boum indeed.

posted by cytherea at 12:36 PM on December 7, 2006

Extending the real number line to include plus and minus infinity is hardly a new idea. I learned about it in my 600-level real analysis class. One important thing about adding these things to the real number is that basic arithmetic operations on them are often undefined. For example, what is ∞+∞? ∞-∞? If ∞+∞=∞, and ∞-∞=0, then we have:

(∞+∞) + -∞ = ∞ + -∞ = 0, but

∞ + (∞ + -∞) = ∞ + 0 = ∞.

Trying to do so much as add two of these things together kills something as basic as associativity of addition.

Now, it is possible to do arithmetic on infinities in non-standard analysis (a.k.a. infinitesimal analysis). This adds not just plus and minus ∞ to the number line, but many infinite numbers and many infinitesimal (i.e. infinitely small) numbers. Something resembling this approach was used (clumsily) by Newton and Leibniz, whose infinitesimal "ghosts of departed quantities" were criticized by many.

Non-standard analysis is not often taught for two major reasons:

1) Non-standard calculus is less powerful than the usual limit-based calculus, and

2) Learning about infinitesimals is much more burdensome than learning limits.

By the way, his comments about mathematics sometimes requiring human intervention should come as a bit of a shock to those who, like me, are inclined to believe that mathematics is man-made, and wouldn't exist at all without human intervention.

posted by CrunchyFrog at 12:37 PM on December 7, 2006

(∞+∞) + -∞ = ∞ + -∞ = 0, but

∞ + (∞ + -∞) = ∞ + 0 = ∞.

Trying to do so much as add two of these things together kills something as basic as associativity of addition.

Now, it is possible to do arithmetic on infinities in non-standard analysis (a.k.a. infinitesimal analysis). This adds not just plus and minus ∞ to the number line, but many infinite numbers and many infinitesimal (i.e. infinitely small) numbers. Something resembling this approach was used (clumsily) by Newton and Leibniz, whose infinitesimal "ghosts of departed quantities" were criticized by many.

Non-standard analysis is not often taught for two major reasons:

1) Non-standard calculus is less powerful than the usual limit-based calculus, and

2) Learning about infinitesimals is much more burdensome than learning limits.

By the way, his comments about mathematics sometimes requiring human intervention should come as a bit of a shock to those who, like me, are inclined to believe that mathematics is man-made, and wouldn't exist at all without human intervention.

posted by CrunchyFrog at 12:37 PM on December 7, 2006

i don't know about the math but let me make two side observations:

- terrible name for a new number, i mean come on

- it's symbol should not look like green latern's ring

posted by poppo at 12:39 PM on December 7, 2006

- terrible name for a new number, i mean come on

- it's symbol should not look like green latern's ring

posted by poppo at 12:39 PM on December 7, 2006

It's not my fault.

posted by homunculus at 12:45 PM on December 7, 2006 [1 favorite]

posted by homunculus at 12:45 PM on December 7, 2006 [1 favorite]

Poppo: or, as someone in the BBC comments pointed out, his symbol should not look like phi.

posted by spaceman_spiff at 12:51 PM on December 7, 2006

posted by spaceman_spiff at 12:51 PM on December 7, 2006

Here's a hint:

If a guy claims to have a fabulous mathematical result, but he chooses to take it to a) the BBC, and b) a classroom full of high school kids, well, you should assume he is a quack until proven otherwise.

I haven't examined this guy's claim, but everything about it screams 'NONSENSE!' So much so, that I really don't think it is worth my time to even investigate (and I have a degree in math, so I'd be at least minimally qualified to do so).

The guy is claiming to "solve" a "problem" I have never heard of, in getting that degree in math. I've yet to see any links to journals or articles, either. You know, the kind of stuff where peers with PhDs in math might examine his claims? (Which the folks at the BBC and the high school kids certainly aren't in a position to do).

Probability of Qauckery: Very, very high. Best case: self-agrandizing bozo that's rediscovered the wheel and renamed it, hoping it gets him great fame. Extremely unlikely case: that there actually turns out to be any "here" here.

posted by teece at 12:55 PM on December 7, 2006

If a guy claims to have a fabulous mathematical result, but he chooses to take it to a) the BBC, and b) a classroom full of high school kids, well, you should assume he is a quack until proven otherwise.

I haven't examined this guy's claim, but everything about it screams 'NONSENSE!' So much so, that I really don't think it is worth my time to even investigate (and I have a degree in math, so I'd be at least minimally qualified to do so).

The guy is claiming to "solve" a "problem" I have never heard of, in getting that degree in math. I've yet to see any links to journals or articles, either. You know, the kind of stuff where peers with PhDs in math might examine his claims? (Which the folks at the BBC and the high school kids certainly aren't in a position to do).

Probability of Qauckery: Very, very high. Best case: self-agrandizing bozo that's rediscovered the wheel and renamed it, hoping it gets him great fame. Extremely unlikely case: that there actually turns out to be any "here" here.

posted by teece at 12:55 PM on December 7, 2006

*phi is not a superhero I have heard of*

Here you go, then.

posted by luftmensch at 1:06 PM on December 7, 2006

Chuck Norris divides by zero.

posted by cptnrandy at 1:07 PM on December 7, 2006 [2 favorites]

posted by cptnrandy at 1:07 PM on December 7, 2006 [2 favorites]

*For example, what is ∞+∞?*

Every school child knows, e.g.:

"I double dog dare you!"

"I triple dog dare you!"

"I dare you infinity!"

"I dare you infinity plus infinity!"

Although more often infinity plus one is used.

posted by TheOnlyCoolTim at 1:08 PM on December 7, 2006

Commentary from Good Math, Bad Math.

*** SPOILER ALERT ***

It's bad math.

posted by mhum at 1:09 PM on December 7, 2006

*** SPOILER ALERT ***

It's bad math.

posted by mhum at 1:09 PM on December 7, 2006

*It's not my fault.*

posted by homunculus at 3:45 PM EST on December 7

posted by homunculus at 3:45 PM EST on December 7

roffle!

posted by cowbellemoo at 1:10 PM on December 7, 2006

There you go then, cptnrandy. James Anderson should have called it a Norrity.

posted by Sparx at 1:13 PM on December 7, 2006

posted by Sparx at 1:13 PM on December 7, 2006

*...claims to have defined what it means to divide by zero.*

Anyone can define what it means to divide by zero. I can define five divided by zero to be feta cheese if I want to. Whether the definition is a mathematically useful one is a different question entirely. Mine is not, and I suspect Anderson's is not either.

posted by DevilsAdvocate at 1:15 PM on December 7, 2006

*Although more often infinity plus one is used.*

I was the smart kid. I dared them ℵ

_{1}times.

I got beat up a lot too.

posted by alby at 1:18 PM on December 7, 2006

Dr. Anderson. It seems that you've been living two lives. One life, you're James Anderson, program writer for a respectable computer science department. You have a social security number, pay your taxes, and you... help your landlady carry out her garbage. The other life is lived in computers, where you go by the alias "Nullity" and are guilty of virtually every mathematical crime we have an axiom for. One of these lives has a future, and one of them does not. We’re willing to wipe the slate clear...

posted by Smedleyman at 1:22 PM on December 7, 2006 [2 favorites]

posted by Smedleyman at 1:22 PM on December 7, 2006 [2 favorites]

DIVIDE BY ZERO ERROR, POST TERMINATED

posted by IronLizard at 1:25 PM on December 7, 2006

posted by IronLizard at 1:25 PM on December 7, 2006

TheOnlyCoolTim:

The infinities of schoolchildren (i.e. where infinity+1 > infinity), are well established in mathematics. Look up "ordinal numbers" (as opposed to cardinal numbers) if you're interested.

posted by ErWenn at 1:33 PM on December 7, 2006

The infinities of schoolchildren (i.e. where infinity+1 > infinity), are well established in mathematics. Look up "ordinal numbers" (as opposed to cardinal numbers) if you're interested.

posted by ErWenn at 1:33 PM on December 7, 2006

That poor fool. I wonder if they'll fire him. I suppose high school students must be protected from this kind of nonsense, but I do pity him.

posted by jamjam at 1:36 PM on December 7, 2006

posted by jamjam at 1:36 PM on December 7, 2006

Having myself invented a new letter of the alphabet I feel compelled to sympathize with Dr. Anderson.

posted by Chuckly at 1:56 PM on December 7, 2006

posted by Chuckly at 1:56 PM on December 7, 2006

Interesting post on Slashdot that points out this "solution" creates other problems, and which kind of undermines his (misguided) ragging on the IEEE standard for floating point numbers.

c.f. his other work...

posted by ny_scotsman at 2:13 PM on December 7, 2006

c.f. his other work...

posted by ny_scotsman at 2:13 PM on December 7, 2006

*Can we get a batshitinsane tag on this?*

Ah. I knew I'd left something off the tag list.

posted by treepour at 2:15 PM on December 7, 2006

From the Wikipedia entry on his proposed perspex machine:

Hehe. I love Wikipedia sometimes.

posted by Bugg at 2:16 PM on December 7, 2006

*Original research. Citation from http://www.bookofparagon.com is authors own home page which publishes non-peer reviewed math articles. This article is also complete 100% nonsense from a mathematical point of view and like all articles on http://www.bookofparagon.com***borders on Timecube levels of crank silliness**.Hehe. I love Wikipedia sometimes.

posted by Bugg at 2:16 PM on December 7, 2006

Has Anderson never heard of exception handling? A good programmer always tries to find a way to recover from errors. Windows doesn't crash if I try to access the floppy drive while it's empty, it returns an error, and returns to safe state. Programmers do make errors, sometimes fatal, sometimes just expensive, but the tools to handle divide by zero errs already exist.

posted by nomisxid at 2:22 PM on December 7, 2006

posted by nomisxid at 2:22 PM on December 7, 2006

His university is the one getting ready to close it's physics department, and yet they have someone like this on the faculty.

I think some accrediting board or other had better be taking a closer look at the University of Reading.

posted by jamjam at 2:33 PM on December 7, 2006

I think some accrediting board or other had better be taking a closer look at the University of Reading.

posted by jamjam at 2:33 PM on December 7, 2006

chuckly:

I recently heard there might be a previously undiscovered weekday somewhere between Thursday and Friday.

posted by sour cream at 2:35 PM on December 7, 2006

*Having myself invented a new letter of the alphabet I feel compelled to sympathize with Dr. Anderson.*

I recently heard there might be a previously undiscovered weekday somewhere between Thursday and Friday.

posted by sour cream at 2:35 PM on December 7, 2006

*"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."*

What the hell? A divide by zero exception is thrown, presumably mission critical systems would handle the error. This guy is a computer science professor?

There's bad science writing, and then there's bad science writing caused by scientist spouting idiotic garbage like this.

UGH

posted by delmoi at 2:39 PM on December 7, 2006

sour cream : That's actually Grunday, sometimes encountered between Friday and Saturday that gives the illusion of only having one good day off before work on Monday. You in fact have two, but because Grunday isn't a generally visible day, you have to go back to work on Sunday and pretend it's Monday. In fact, Grunday accumulation means that it's actually Tuesday today.

posted by ny_scotsman at 2:39 PM on December 7, 2006 [1 favorite]

posted by ny_scotsman at 2:39 PM on December 7, 2006 [1 favorite]

*I think some accrediting board or other had better be taking a closer look at the University of Reading.*

Well there's the problem. We could trust him if only he were from the University of 'Rithmatic.

posted by The Bellman at 2:45 PM on December 7, 2006 [1 favorite]

*. You still haven't told us how you're going to store 'nullity' as a bit pattern,*

This isn't a big deal, currently "NaN' and "Infinity" have bit-patterns defined for floating point numbers. If you divide by zero, you get NaN currently.

posted by delmoi at 2:47 PM on December 7, 2006

*If you divide by zero, you get NaN currently.*

Well, sometimes you get Inf or -Inf:

`R version 2.4.0 (2006-10-03)`

Copyright (C) 2006 The R Foundation for Statistical Computing...

> 1/0

[1] Inf

> -1/0

[1] -Inf

> 0/0

[1] NaN

Copyright (C) 2006 The R Foundation for Statistical Computing...

> 1/0

[1] Inf

> -1/0

[1] -Inf

> 0/0

[1] NaN

For any non-computery people out there, we have been doing this for

*years*. Anyone who starts calling NaN "nullity" should be called a nullo.

posted by grouse at 3:09 PM on December 7, 2006

!

I've developed a new method of prioritisation: self-interest, absent empathy.

I think I'll call it 'pragmatism'!

posted by The Confessor at 3:14 PM on December 7, 2006

I've developed a new method of prioritisation: self-interest, absent empathy.

I think I'll call it 'pragmatism'!

posted by The Confessor at 3:14 PM on December 7, 2006

*Having myself invented a new letter of the alphabet I feel compelled to sympathize with Dr. Anderson.*

LIAR! I came up with it first. You haven't heard of it because it's silent.

posted by Sparx at 4:13 PM on December 7, 2006

While we're wikilinking, the wikipedia page on cranks is quite thorough, and in the bibliography you can find Underwood Dudley's entertaining and rather touching Mathematical Cranks, the definitive study of the subject; the BBC coverage will have served a good purpose if it sends people to Dudley's book.

posted by escabeche at 4:22 PM on December 7, 2006

posted by escabeche at 4:22 PM on December 7, 2006

*- it's symbol should not look like green la[n]tern's ring*

we may have escaped the problem of dividing by zero, but now what happens if we try to divide by yellow?

posted by spiderwire at 4:36 PM on December 7, 2006 [1 favorite]

spiderwire, then you get bleu cheese instead of feta.

posted by hattifattener at 4:56 PM on December 7, 2006

posted by hattifattener at 4:56 PM on December 7, 2006

*Interesting post on Slashdot that points out this "solution" creates other problems,*

I'm not a real mathematician, I just studied math at university for a few years, and never considered myself a standout in the discipline, so my judgement could be off, but that post on slashdot seems to me to be the best (and fairest) commentary on the theory in a sea of rather unmeasured evaluations.

posted by weston at 6:55 PM on December 7, 2006

Inspired by this, and Homer Simpson's discovery of a meal between breakfast and brunch, I hereby unveil

The middle day in a three-day weekend.

posted by Joseph Gurl at 7:06 PM on December 7, 2006

**CHUNDAY**The middle day in a three-day weekend.

posted by Joseph Gurl at 7:06 PM on December 7, 2006

*(Besides which, differential calculus is already based on division by zero.)*

No, it's not. Conventional calculus has been based on limits since its invention.

posted by Blazecock Pileon at 7:47 PM on December 7, 2006

Someone should create an Incorrect Statement's by SCDB blog.

posted by delmoi at 7:55 PM on December 7, 2006

posted by delmoi at 7:55 PM on December 7, 2006

Or a mistaken comments by delmoi blog. it would be a catalog of misspellings, random crossposts, HIPPA [sic], and general stream-of-conciousness inanity.

posted by blasdelf at 11:04 PM on December 7, 2006

posted by blasdelf at 11:04 PM on December 7, 2006

Correct me if i'm wrong on this, but you don't have the computer land a plane. Not with passengers or expensive cargo, or outside of military drones. You still need humans for landing.

But yes, return 0, please. Gah.

posted by jam_pony at 11:21 PM on December 7, 2006

But yes, return 0, please. Gah.

posted by jam_pony at 11:21 PM on December 7, 2006

On a related note, what does the crowd think about the square root of minus one? That's always struck me as nullity-level nonsense on stilts, personally. Anyone else?

posted by imperium at 2:11 AM on December 8, 2006

posted by imperium at 2:11 AM on December 8, 2006

I saw James Anderson talk once. That's half an hour of my life I'll never get back. The audience were entertaining though. Watching the facial expressions of twenty academics transition from "This is novel, and could be interesting" through "WTF?" to "Batshitinsane" is really quite funny.

And yeah, Reading University. Physics? Nah, don't need that. Perspex machines? Give the man tenure! They also employ Kevin Warwick, who is

posted by handee at 2:35 AM on December 8, 2006

And yeah, Reading University. Physics? Nah, don't need that. Perspex machines? Give the man tenure! They also employ Kevin Warwick, who is

*at least*as entertaining as he is crackpot.posted by handee at 2:35 AM on December 8, 2006

*They also employ Kevin Warwick, who is at least as entertaining as he is crackpot.*

When it says "not for reproduction without permission", are they talking about the image or are they disbarring you from producing cyborg replicants of Warwick?

posted by vbfg at 5:57 AM on December 8, 2006 [1 favorite]

When I sent this link to a friend last night, I used the standard New Yorker cartoon caption: "Christ, what an asshole." Ok, so we have the extended complex plane if you really want to play with infinity, but it doesn't work the way he's going on about it.

This sort of shit just pisses me off. We have fantastic books like Inumeracy out there, which go about explaining how we mess up in math and how it can be fixed and we have asshole's like this destroying the public's understanding of how math works.

It's a useless artifact. i, being sqrt{-1} is actually useful in solving several real life problems. (A lot of stuff to do with electricity and magnetism suddenly works a lot better on the complex plane)

I'm disappointed in the BBC for not bringing in anyone nto show how he was wrong. Hell, a second year mathematics student in college should be able to refute this formally and completely.

Things like this pain me. At least when NPR had a guy on ATC claiming that he had squared the circle, they brought on a mathematician to show where he was wrong. (He ended up using 3.55 for pi.)

The fact that this man is looking at employment in anything beyond the creative writing department makes the baby jesus cry.

posted by Hactar at 5:59 AM on December 8, 2006

This sort of shit just pisses me off. We have fantastic books like Inumeracy out there, which go about explaining how we mess up in math and how it can be fixed and we have asshole's like this destroying the public's understanding of how math works.

It's a useless artifact. i, being sqrt{-1} is actually useful in solving several real life problems. (A lot of stuff to do with electricity and magnetism suddenly works a lot better on the complex plane)

I'm disappointed in the BBC for not bringing in anyone nto show how he was wrong. Hell, a second year mathematics student in college should be able to refute this formally and completely.

Things like this pain me. At least when NPR had a guy on ATC claiming that he had squared the circle, they brought on a mathematician to show where he was wrong. (He ended up using 3.55 for pi.)

The fact that this man is looking at employment in anything beyond the creative writing department makes the baby jesus cry.

posted by Hactar at 5:59 AM on December 8, 2006

*No, it's not. Conventional calculus has been based on limits since its invention.*

No, when Leibniz and Newton invented (or developed or whatever they did with) calculus, it was based on infinitesimals, which led to the criticisms mentioned by CrunchyFrog early in this thread. Limits weren't brought into the picture until the 1800s.

posted by noahpoah at 7:23 AM on December 8, 2006

*Some helicopters can do automatic landings too. I've seen helicopters land in well over 20 kts of wind in what seems like zero visibility, in order to pick up emergency medical patients from football fields. In some urban areas, that is the only place a helicopter can land. When conditions are clear, the pilots visit the field and program in the landing parameters. When someone gets a heart attack at rush hour in the middle of a storm, the helicopter can still magically appear on the field. Kind of spooky to see a giant helicopter materialize a few dozen feet in front of you.*

Rest of the thread aside, that's pretty fucking awesome.

w/r/t the flying thing, I know that lots of modern fighter planes are fly-by-wire; I remember reading that the vectored-thrust planes like the Su-37 pretty much have to have a computer mediating between the pilot and the navigation systems.

posted by spiderwire at 3:56 PM on December 8, 2006

**noahpoah**writes

*"No, when Leibniz and Newton invented (or developed or whatever they did with) calculus, it was based on infinitesimals, which led to the criticisms mentioned by CrunchyFrog early in this thread. Limits weren't brought into the picture until the 1800s."*

Early on, Newton gave a few ways of thinking about calculus. One way, the way he thought was correct, was in terms of infinitesimals. But another way he mentioned was in terms of "ulitimate ratios", which we would recognize as limits. So the idea was out there. Of course, everyone else talked about infinitesimals. Also, it's hard to talk about limits precisely without a good understanding of the real numbers. This understanding did not come until later. It is a testament to the power of calculus that so much was acheived before the foundations of the subject were sorted out.

posted by samw at 9:16 PM on December 9, 2006

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Remember, just say no to James Anderson.

posted by owenkun at 12:10 PM on December 7, 2006