## New Comic Book About Logic, Math, and Madness 99

areYouAHypnotist writes to tell us the New York Times has the scoop on a new comic book about the quest for logical certainty in mathematics.

*"The story spans the decades from the late 19th century to World War II, a period when the nature of mathematical truth was being furiously debated. The stellar cast, headed up by Bertrand Russell, includes the greatest philosophers, logicians and mathematicians of the era, along with sundry wives and mistresses, plus a couple of homicidal maniacs, an apocryphal barber, and Adolf Hitler."*
## Too hard? (Score:2, Funny)

Reading all those words...turning all those pages. I don't suppose they're going to do a cartoon version? 90..no, make that 60 minutes long, with explosions. Plenty of explosions.

## As a troll... (Score:1)

You are one dimension short of being a cartoon yourself.

## Re: (Score:2)

## It's like dinosaur comics (Score:1)

Without the humor.

## Re:It's like dinosaur comics (Score:4, Interesting)

No, it's more like these two Dresden Codak strips:

Dungeons and Discourse [dresdencodak.com]

Advanced Dungeons and Discourse [dresdencodak.com]

## Re: (Score:2)

But hopefully with a little more variety in the art...

## Math: The Musical! (Score:1)

## Yeah... (Score:2, Funny)

## Lovelace and Babbage (Score:5, Informative)

## Re: (Score:1)

This is the greatest comic I have ever read! A few pages into the comic and I am already a fan. There's just so many excellent insights.

"As an initial tactic, I've had some bankers shot this morning to keep up confidence."

The Duke of Wellington for the new Federal Reserve Chairman!

## Re: (Score:2)

It looks good, but I really wish web-comic authors would choose reasonable web-interfaces. Blog software makes for irritating comics, and having to scroll down to see the most important part of the page is ridiculous, let alone having to scroll to see a three-panel comic.

## Re:Spoiler requested... (Score:5, Funny)

## Re: (Score:1, Offtopic)

## Missed opportunities (Score:2)

From the article:

So there's that, and from what I could tell there is no mention of Gödel's incompleteness theorems, either. Meh.

## Re:Missed opportunities (Score:5, Interesting)

So there's that, and from what I could tell there is no mention of Gödel's incompleteness theorems, either. Meh.

It does. Even Von Neumann's reaction to it is included. I had the chance to read the Greek version in august, and it is pretty awesome. Both for computer scientists and mathematicians, it is pure win. I'm so glad that it gets published in English as well now, I would HIGHLY recommend this comic book to any geek.

## Re: (Score:2)

If you can spot the error, I would call you a winner. If you cannot, I would call you a loser. As is that page, which is anything but win/win.

(Hint: what is actually informing what?)

## Re: (Score:3, Informative)

Godel is mentioned on the second page of TFA.

## Um... (Score:2, Insightful)

That follows only if you think that the logicist system for the foundation of mathematics proposed in the

Principiais something "similar" to Fortran and the calculus.## wrong similarity (Score:1)

I meant the use of "non-standard"/"non-textbook" approaches to teaching things.

## Re: (Score:1, Insightful)

Except that this is a historical drama (and perhaps comedy), not an instructional text.

## Re: (Score:1)

## The ending of the strip is rather disappointing (Score:1)

Math (all useful mathematical theories, and therefore all science based on them) is one of 2 things, but not both :

-> logically inconsistent

-> not logically consistent*

* this is not the same as the first thing. The difference is that it might very well be logically consistent, but you can't prove it one way or the other. This means that while God might know it to be logically consistent, you can't say it *is* logically consistent since there is no procedure to verify this. Not even in infinite time. S

## Re: (Score:2)

That's completely wrong on so many counts that it doesn't even deserve the criticism. Have you got a copy of the book?

## Re: (Score:2)

This means that while God might

knowit to be logically consistent, you can't say it *is* logically consistent since there is no procedure to verify this. Not even in infinite time. So nobody will ever know for sure, no matter how far in the future.How could "God"

knowsomething to be true if there was no way to know it?Reminds me of Catholic-school catechism tales of the Holy Trinity "mystery:" There is one God who is three Gods. Believe that and you're on your way to believing just about anything.

## Wishfull thinking. (Score:1, Interesting)

"How could "God" know something to be true if there was no way to know it?"Same way that the GP

knowsgod exists - wishfull thinking. Wishfull thinking allows you to create whatever universe takes your fancy. A univesre created from wishfull thinking does not have to be consistent, it can be anything you want.I'm not sure why so many people use wishfull thinking to create a universe were every detail of life is watched and controlled by a celestial dungeon daddy. However it does fit nicely with using

## You should deride religion knowingly. (Score:2)

I was raised as a Catholic, and am now an atheist by reasoned conviction.

What you say about the Catholic religion is factually incorrect. If you commit a sin and are not truly repentant then your confession is yet another sin and your initial sinning is not considered forgiven, in other words you are only adding to the burden by which you will be judged at the end of times.

it is also untrue that if you actually repent you are given carte blanche to sin again, since sinning again would demonstrate that you

## Re: (Score:2)

It may not accurately reflect all the idioms found in your previous christian cult, but it does describe my skeptical/cynical attitude to the message I have been hearing from "Christians" for the last 50yrs (ie: morals come from god). More importantly your description does not reflect the behaviour of the Catholic c

## Re: (Score:3, Informative)

Infinite Godby definition is not restricted to a subjective point of observation.The GP is playing the subjective/objective game.

## Re: (Score:2)

In the end it doesn't matter whether math is complete or incomplete, consistent or inconsistent. We know math works as a tool to understand our universe because we have used that understanding to make technology that works.

## Re: (Score:3, Insightful)

## Re: (Score:1)

And there are several problems in the natural numbers system that all of science uses that might turn out to be sources of inconsistency.

Just for an example : have they solved the barber's paradox yet ?

In an infinitely large village, there's 1 barber. He shaves all the people that do not shave themselves. The question to be answered is : does the barber shave himself ? You can prove that he does, and you can prove that he doesn't, both entirely correctly reasoned.

Either someone must make a convincing case t

## Maths MUST be consistent.... (Score:2)

## Re: (Score:1)

And for designing buildings we use simulations that describe a world that resembles the discworld (building stands on a disc floating in space and gravity is just a dead simple straight down, also known as the "it's turtles all the way down" argument) and only contains springs, all described by VERY newtonian physics, which we *know* to be inconsistent.

So your point is ? Every last event that any human will ever be confronted with, and the inner workings of said human, with can be explained perfectly well e

## Re: (Score:1)

(and the point being : just because "it works" does not mean it's consistent. Lots of things work. When it comes to women, according to hollywood the "either they're ugly, or they want to sleep with me" way of thinking seems to work. Yet I'm told it's not all that consistent)

## Re: (Score:2)

Transistors can not be accurately described by Newtonian physics.

## Re: (Score:2)

## Re: (Score:1)

Why not ? I've even seen a professor construct a "water based" transistor. What specific formula do you need to describe a transistor ?

Yes we've all been taught to think about them in terms of Bohr's model of the atom, which, btw, is still (although not perfectly) Newtonian.

Transistor radios were constructed long before anything resembling quantum physics existed. I suppose you think they were just shooting blind ?

You most certainly do not require quantum physics to describe the workings of a transistor. Th

## Re: (Score:2)

"The only place to find quantum mechanics, for any human being, is in said human's imagination."The macro effects of quantum mechanics [wikipedia.org] can be observed in the viscosity of mayonnasie [physicsworld.com] and similar liquids.

"The only place to find relativity theory in action is off the planet."Time dialation [google.com.au] has been repeatedly observed on the surface of Earth and is important for navigation.

## Re: (Score:1)

Time dilation is important for navigation because we're using off-world devices to do it (stars, sattelites).

They matter for accuracy, but navigation can work perfectly well without compensating for time dilation.

## Re: (Score:3, Interesting)

Your arguments intrigue me and I'd like to subscribe to your....

Nah, just kidding. I'm a graduate mathematics student, and I can't make any sense at all of what you said. Does that mean I've already been conditioned by The Man (TM), and that it's too late for me to understand The Truth (TM)?

## Re:The ending of the strip is rather disappointing (Score:5, Insightful)

Agreed. The problem is you get philosophers that write books about mathematics and physics. They almost always get everything wrong or blow things out of proportion. Things philosophers love to talk about without actually knowing anything about them: quantum physics, logic (

especiallyGodel's Theorems), set theory.## Re: (Score:2)

Basically he means, everything he knows is obvious human's science. Everything he doesn't know is magically Gods realm.

## Re: (Score:2, Informative)

Actually I mean this [wikipedia.org].

Literally I mean "For any formal effectively generated theory T including basic arithmetical truths* and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent."

* he means the peano axioms (to be exact a small subset of them). In general you could say he means any "reasonable" axiom set that contains a sucessor function, as that's the essential part.

## Re: (Score:2, Interesting)

Actually it means you might want to lookup, say "incompleteness theory". Or the subject of this strip, "Bertrand Rusell". His philosophy's more than worthless but he did some actual work in mathematical logic that you really ought to have seen by now.

And by the way, in this argument the person making it (math is inconsistent) is generally considered "the man", as it's the academic and unassailable viewpoint.

Generally the "radical" viewpoint is the one where "every theory is correct" in some way or another.

## Re: (Score:2)

Math (all useful mathematical theories, and therefore all science based on them) is one of 2 things, but not both : -> logically inconsistent -> not logically consistent*

While I am mathematician I am not a logician, but do you mean that math is either logically inconsistent or not complete? (That is just the statement of the First Incompleteness theorem). By definition, a theory is logically consistent if it does not contain a contradiction. A theory is therefor not consistent (or inconsistent) if it contains a contradiction.

Your remarks about there being no hope of proving a theory inconsistent also makes me wonder what theorem you are referencing. Certainly not the

## Oh boy this will look like a 2nd grade text book. (Score:1)

## Cryptonomicon (Score:2)

schnapps, and talk math).## Bipolar = Art; Schizophrenia = Math/Science (Score:3, Interesting)

## Re: (Score:2)

A

bit(over)simplified, wouldn't you say?## Where are your stats? (Score:2)

There are thousands of artists, many of them very notable, that have no problems whatsoever.

Ditto for mathematicians and scientists.

So unless you show concrete eveidence regarding this (good luck) I think you are oversimplifying for nefarious purposes only known to your own good self.

## I've read the first chapter (Score:2, Informative)

This page [volkskrant.nl] (Dutch) has a link to the PDF (bottom of the article) of the Dutch translation of the first chapter. (I would have linked to an English translation, but I am not aware of any preview releases.)

I read the first chapter, and found it pretty cool, but also awkward to read it in Dutch, since the characters (in ch. 1) are all Britons or Americans.

Anyway, if you're interested, have a look at it.

## Mmmmm hmmmmm. (Score:2, Funny)

It's my understanding Superman can hold a black hole in his hand while simultaneously writing the formula to prove anything on a blackboard with his other hand.

The Hulk, however, could only hold a black hole in his hand.

## It's the axioms... (Score:5, Insightful)

All (correct) mathematical proofs are true, if the axioms are true. However, there's an infinite set of axioms and the only reason you have to believe any of them correspond to the system you are trying to predict is through observation. If you don't have any observations, if you're trying to make a priori knowledge, then your prediction power is thus infintesimal. Or in English, you don't know shit. As for pure mathematics, imagine it a little bit like infinite quantum universes in sci-fi. For every mathmatical result there are other sets of axioms leading to all other possible results. Without excluding axioms you can not exclude any results, so you're only going in circles defining your own results. In English, anything's possible.

Of course in practice you would have to create insane and arbtrary axioms to do this. But "logical" axioms like the set of real numbers or three dimensional space only appear so because of observation and how it reflects the real world. A priori you have no basis to say why one set of axioms should better reflect reality than the other. So I would say the answer is simply false, you can not have meaningful mathematics without context. However, once you do have meaningful axioms through observation you can get many results through mathematics that are non-obvious through observation. Honestly though, you're more heading into philsophy than mathematics once you go that deep.

## Re:It's the axioms... (Score:5, Informative)

If a conjecture can neither be proven nor disproved given a set of axioms, then either the conjecture or the axioms were wrongly chosen. If your ultimate goal is to prove or disprove that conjecture, you must pick a set of axioms that allows that goal to be achieved. If your ultimate goal is to prove or disprove every conjecture possible given a specific set of axioms, then you must ignore the conjectures that can neither be proven nor disproved with that set of axioms.

It isn't that math doesn't work. Given a set of axioms, you can find absolute truths. However, not all absolute truths can be discovered with a single set of axioms.

## Re: (Score:2)

But the really, really great bit is that you can never "prove" the core axioms; your "absolute truths" will therefore always be dependent on a set of unprovable assumptions.

And people think I work in a "soft science."

## Re: (Score:2)

## Maybe it's just an unfortunate quote, but... (Score:2, Flamebait)

...includes the greatest philosophers, logicians and mathematicians of the era, along with sundry wives and mistresses...

Maybe I'm seeing omission where there is none, but I find it unlikely that there were no contributions to this subject from female philosophers, logicians and mathematicians. Please tell me they've not been left out of the story in the comic.

## Re:Maybe it's just an unfortunate quote, but... (Score:5, Interesting)

Are you really so feminist that you assume women MUST HAVE contributed somehow, and if they are not mentioned, it must have been because they were unfairly left out of the story? Just why do you find it so unlikely?

## Re: (Score:2, Insightful)

## Re: (Score:1, Insightful)

Ask anybody on the street to name even one mathematician of either sex.

## Re: (Score:3, Informative)

## What do these have to do with mathematical truth ? (Score:1)

Which is great, and I don't doubt they're very smart women, worthy of recognition in informatics (and especially Ada is never denied that) ...

But none of them has any bearing on the issue of the connection between mathematics and truth.

## Re: (Score:2)

## Re: (Score:1)

the connection between mathematics and truth

Which is not what I was responding to, but never mind. Mathematics has nothing to do with truth or otherwise: it is simply the logical consequences that arise from given axioms. It so happens that if you pick the right axioms then there are many correspondences with the real world, but truth? Nowt to do with it.

Yes, but the point is that any inconsistency can be translated into 1=2. So if math were to be inconsistent there would be ZERO consequences of said inconsistent axioms.

Suppose the peano axioms were inconsistent, then there is no reason why a car travelling at a constant speed 10km/h would travel 20 km in 2 hours. It might as well be 100, or 2, or 5 cm. All would be correct answers. In other words, inconsistent mathematical theories get us nowhere.

So obviously math and truth are related concepts. And there

## Re: (Score:2)

Emmy Noether, Fotini Markopoulos, and Lisa Randall.

Anyone who says these women are physicists will be smacked. They are all extremely theoretical physicists. Noether is a legendary mathematician in her own right; Markopoulos and Randall are both such theoretical physicists that their work is essentially indistinguishable from pure math. The latter two could easily receive appointments to the math departments of their choice; Emmy Noether couldn't, but only on account of being dead.

Come to think of it, so

## OK, educate us. (Score:2)

What is so important about them.

Being brilliant does not mean you are unique or revolutionary.

## Re: (Score:2)

You must be kidding.

I am not going to save you the trouble of three Wikipedia searches. (Except, I will tell you that Fotini Markopoulou has gotten married recently, and is now Fotini Markopoulou-Kalamara. That might help you find information on her.)

The question was to name three famous women mathematicians. Those three definitely qualify.

## Re: (Score:2)

> Please tell me they've not been left out of the story in the comic.

They've not been. Just their husbands and boyfriends.

## Oh boy! (Score:2)

I've always wanted to see Bertrand Russell in tights.

## Re: (Score:2)

Thanks much, AC. You just made Slashdot illegal in Germany.

## I must get hold of this... (Score:2)

It'll make those long winter nights coming up really whistle past!

## Mathematical truths? More like tools (Score:1)

Mathematics is not recognized in the natural universe. What mathematics is is a tool used by humans to manage the important human-given properties of the natural world we care about

Treating mathematics as something that the natural world created is like saying that the natural world created the game of chess.

## Re: (Score:2)

## Barber of Seville (Score:2)

(Think of the barber of Seville, who shaves all men, and only those men, who do not shave themselves. Does this barber shave himself or not? Either possibility yields a contradiction.)The answer is obvious, and has been obvious to me since I was a teenager (in the 1960's):

If he has not shaved himself, he shaves himself. Else he does not. (cos he does not need to if shaved)

Disclosure: my mother was a Fortran programmer. The original philosophers saw the world as static. I, as someone who had grown up wi

## Re: (Score:2)

The answer is obvious, and has been obvious to me since I was a teenager (in the 1960's)Well, the way I heard the paradox, the question was phrased 'Who shaves the barber?', not 'Does the barber shave himself?'. A subtle but important difference, for when phrased the first way, it's quite possible that the barber does not shave herself.

## The barber does not shave herself? (Score:2)

If there ever was a place where the word "himself" could be used with impunity is in the above sentence.