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Comments: 99 +- Science: New Comic Book About Logic, Math, and Madness on Friday October 02, @04:39PM
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ScuttleMonkey
on Friday October 02, @04:39PM
from the only-math-some-kids-are-likely-to-get-these-days dept.
from the only-math-some-kids-are-likely-to-get-these-days dept.
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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."
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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.
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Yeah... (Score:2, Funny)
Lovelace and Babbage (Score:5, Informative)
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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.
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.
Parent
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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?)
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Godel is mentioned on the second page of TFA.
Cryptonomicon (Score:2)
Bipolar = Art; Schizophrenia = Math/Science (Score:3, Interesting)
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A bit (over)simplified, wouldn't you say?
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.
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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.
Parent
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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."
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?
Parent
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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
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> 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.
I must get hold of this... (Score:2)
It'll make those long winter nights coming up really whistle past!
Barber of Seville (Score:2)
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
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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.
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]
Parent
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But hopefully with a little more variety in the art...
Re:Spoiler requested... (Score:5, Funny)
Parent
Um... (Score:2, Insightful)
That follows only if you think that the logicist system for the foundation of mathematics proposed in the Principia is something "similar" to Fortran and the calculus.
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That's completely wrong on so many counts that it doesn't even deserve the criticism. Have you got a copy of the book?
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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. So nobody will ever know for sure, no matter how far in the future.
How could "God" know something 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.
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Infinite God by definition is not restricted to a subjective point of observation.
The GP is playing the subjective/objective game.
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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.
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Maths MUST be consistent.... (Score:2)
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Transistors can not be accurately described by Newtonian physics.
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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.
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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 (especially Godel's Theorems), set theory.
Parent
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Basically he means, everything he knows is obvious human's science. Everything he doesn't know is magically Gods realm.
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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.
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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.
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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
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Thanks much, AC. You just made Slashdot illegal in Germany.