Things Of Interest Blog

Pseudomathematics

2009-11-28 by qntm

Oh. No. You. Di'int.

Pseudoscience is something I don't really have the social skills to fight head on. I'm not a practical, working research scientist. "But that's obviously nonsensical" isn't a sufficient counterargument for, say, homeopaths.

Speaking of which, let's take a brief detour to cover that. Homeopathic remedies "work" for a suitably relaxed definition of "work". By "work", what homeopaths mean is that homeopathic remedies do have measurable beneficial effects on those who receive them; and, as scientific studies have routinely and eternally confirmed, those beneficial effects are precisely equal to the beneficial effects experienced by patients administered a placebo instead. In other words homeopathic remedies work precisely as well as "nothing-disguised-as-a-pill". Or, to put that in black and white: if your remedy works precisely as well as "nothing at all", then your remedy does nothing. It is possible that there might be other remedies - let's call them null-remedies - out there, which, when administered to one group of patients while the others are given a placebo, actually have literally no effect on the health of the patient, while those with the placebo actually do cheer up and feel a little better, as we might expect. In that situation we would have to conclude that the null-remedies, since they do not even cause the patient to cheer up a little, are actually counter-acting the placebo effect. If a pill does literally nothing, not even a placebo effect, then we know it is actually harmful. That's negative. Remember this: placebo is zero. Placebo is zero. To simply have "no effect" is less than zero. For a medicine to attain the status of "actually viable as a legitimate medicine" requires measurably more than just the placebo effect, which homeopathic remedies do not and, if the slightest logic is applied, cannot provide.

The real question, then, is: should it be medically acceptable to sell a placebo? My answer is: only if it's labelled, in black and white, as a warning from the Department of Health: "PLACEBO". "Dimextrothin - proven weight loss through psychological (placebo-effect) appetite suppression." "Take an unlimited quantity at will for strictly illusory light to moderate pain relief." "100% pure water. No active ingredients." Anyway.

So yes: there's junk science. But it's not often you run into actual junk mathematics. Here's the thing about junk mathematics. Science is up for debate. With a law, a theory, a paper, a data source or a single datum, you can dispute the author, the source, the motivation, the politics, the data gathering methods and the spelling. You can fight over this stuff. That which is "true" is what stays standing after the fight is over. That's how science works. Science is what fits the universe better than anything else, all brute force statistical manipulation and personal biases removed.

Mathematics? Not so much.

When you're wrong in maths, you're wrong. You're wholly, one hundred percent wrong. Exactly as wrong as it's possible to get. Boolean false. Zero points out of a possible one. When you're wrong in mathematics, you're claiming a falsehood is true. That means that the statement you just made - regardless of its other ramifications - results in one equalling zero and the destruction of all mathematics. When someone proves you wrong in mathematics and you raise protest, the person who proved you wrong will turn around with condescending amusement and go, "I'm sorry. Did you just argue back? Perhaps you mistook mathematics for one of your airy-fairy grey-area subjects? Literary analysis? Philosophy, maybe?" And that person can be anybody. It can be a high school upstart who spotted a typo in your long division. It can be the Lucasian Professor of Mathematics undermining your life's work in two lines. There are no points for experience here. There are no "mainstream" and "alternative" mathematicses. There are no "fringe theorems".

That which is "true" is that which makes the universe easiest to understand, model, explain, predict and generally deal with. Climate change is real because this is the option (as opposed to the "climate change isn't real" option) which best explains accumulated climate data. Solipsism is obviously complete horsebull, because assuming that other people are real is a much more efficacious way to deal with real life than behaving as if they don't exist. No, there is no Matrix, because pretending there is a Matrix doesn't help us with anything or explain anything or predict anything.

Point nine recurring equals one because the people who operate under the assumption that point nine recurring equals one are real mathematicians who accomplish real maths, and the people who believe otherwise are to a man gawking, wrong-headed bystanders who have no business playing with concepts they don't understand, and who have accomplished no significant mathematics. At all. The people who are right are the people whose beliefs haven't led to the undermining and collapse of all mathematics. The people who are wrong do not matter. Be quiet. Adults are working.

You can't say things like "it is not possible to represent all real numbers in any given radix system". You can't say "the real numbers aren't well defined" and argue for the countability of the real numbers if you don't accept the well-formed and logical existence of infinite decimal expansions as real numbers. You can't use "Cantor was ridiculed again and again" as an argument against his mathematics or say that Cantor's enumeration of the rationals being technically a surjection, not a bijection, invalidates it. Well, you can, in as much as humans have the right to be wrong. But you're not a plucky underdog challenging the status quo. You're not a breath of fresh innovative air to a stiff-collared, staid establishment grown complacent, creaky, stale and irrelevant. If you've come up with something which directly contradicts established mathematics, you're just wrong. And if you don't stop talking (and start disabling comments) when a mathematician who knows anything about anything tells you that, then you're more than wrong, you're out of your depth and self-evidently mucking with forces you don't understand.

This guy's filling (polluting) Knol with his dubious junk. If Knol was relevant, I'd bother to campaign against it.

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Discussion (76)

2009-11-29 01:54:16 by Baughn:

Bravo!

2009-11-29 04:23:39 by MsJaye:

An excellent rant, however, I would like to point out the following: "Take an unlimited quantity at will for strictly illusory light to moderate pain relief." Your bias is showing. It's the word "illusory" that's getting my goat in the above. Pain is subjective. The very idea of illusory pain relief is a nonsense: you can't think you have had your pain relieved, and yet still be in pain.

2009-11-29 04:31:19 by dankuck:

Next don't campaign against Deepak Chopra's misuse of quantum mechanics.

2009-11-29 05:10:49 by Dwight:

Are you a redditor, by any chance?

2009-11-29 06:58:45 by Ryan:

To be clear, placebos work because people don't *know* that they're placebos. And yes, by "work" I mean "have real, measurable physiological effects on the body and not just the mind". http://www.wired.com/medtech/drugs/magazine/17-09/ff_placebo_effect Labeling them as placebos would eliminate this. Other than that, spot on :).

2009-11-29 07:12:58 by kabu:

I once had the experience of a classmate try to tell the math teacher that he was, and had been for years, wrong about a certain interesting problem. It was funny as hell. Which is why literary analysis can sometimes be refreshing -- even if you're completely off the mark, if you argue loud enough people will still listen to your perfectly valid opinion :P.

2009-11-29 07:56:42 by Ricecake:

Ryan, you can get around that whole "knowing-it's-a-placebo-makes-it-useless" thing by making sure to get an extra strength placebo, then you should be fine.

2009-11-29 09:16:22 by Idran:

"There are no points for experience here. There are no "mainstream" and "alternative" mathematicses. There are no "fringe theorems"." This seems to ignore much of the debate in philosophy of mathematics. It might not be a major aspect of the field, but it exists, constructivism vs. nonconstructivism, mathematical objects existing before our deduction of them vs. mathematical objects only existing based on our deduction of them, and ZFC vs. ZF!C being three of the biggest examples (even if the last pretty much no longer exists as a divide, it must be admitted that it was certainly one for years not all that long ago). There's certainly no debate that given certain axioms and certain rules of deduction, certain results follow, but there's ample room for debate on what axioms and rules to accept, and whether or not it's valid to accept certain axioms or rules. That said, that article you linked is full of dumb, and no one would consider it valid. I just wanted to make a statement here because it's often ignored that philosophical divides do exist in mathematics.

2009-11-29 10:54:00 by Val:

Hm, what about Bolyai, for example? He discovered that there is something fishy about euclidean geometry, and discovered a new geometry because of this. However, you are right, and sometimes I think how ridiculously the minds of some people can work: take a scientific theory, which is a very good and usable model, but still has some minor problems or some small areas not 100% understood (which one doesn't?). Then you will surely find pseudoscientists, that point out that small problem, and claim not only that the whole theory is bogus, but that their completely different theory, no matter how stupid, must be correct. The strange thing is how they can get followers, and how their minds work: there is this well-established theory, with lots of experiments and some practical applications proving that it's working, but as it has some minor inaccuracies, so this MUST mean that another theory, just because it describes something completely contrary, must be true. Even if a lot less evidence supports it. Or no evidence at all. Take a look at cryptozoologists, for example. If there were one single mythical animal which some cryptozoologists would believe in, and would try to find it or prove its existence, it would be ok. But what they do is that they claim that each and every such creature must exist. You can even make fun of them to tell them about some crazy creature you just made up, and they will assure you, that it must exist.

2009-11-29 11:24:22 by ffoobbar:

As a side note, homeopathy has been shown effective (that is, effective significantly over and above placebo effects) in a number of professional clinical trials, with results published in peer-reviewed medical journals. For a selection see http://www.vitalforceconsulting.com/Homeopathy/research-in-homeopathy.html (no, I'm not affiliated with the site, nor am I a homeopath). It is remarkable how much the loudest defenders of rationality resist rational evidence when it doesn't point their way. (This has nothing to do with the guy publishing the knol, who is obviously a fool.)

2009-11-29 12:20:17 by qntm:

Ryan: but selling a placebo which isn't labelled as a placebo is dishonest, unethical and potentially dangerous.

2009-11-29 12:27:01 by qntm:

Idran: I did actually know that there is room for a certain amount of wiggle room in terms of how one chooses one's axioms, and that some collections of axioms are less popular fields of study than others - these are your "fringe mathematicses". (As for which of them is "true", that's a matter of philosophy rather than mathematics.) It's true that on occasion you even get theorems which have been proven true, but which nobody will accept - although I like to think that we're advanced and dispassionate enough in these modern times that this doesn't happen anymore. What you never get, though, is a theorem which has been proven false but its creator continues to push it, which is what we have here. If something is inconsistent, it just goes, no argument. Or maybe, *maybe* it gets retracted, fixed and resubmitted.

2009-11-29 12:31:56 by qntm:

Ffoobbar: that's a homeopathy website. Here's a NPOV one: http://en.wikipedia.org/wiki/Homeopathy "Claims of homeopathy's efficacy beyond the placebo effect are unsupported by the collective weight of scientific and clinical evidence.[8][9][10][11][12] While some studies have positive results, systematic reviews of all the published trials fail to conclusively demonstrate efficacy.[13][14][15][16][17] Furthermore, higher quality trials tend to report less positive results,[15][18] and most positive studies have not been replicated or show methodological problems that prevent them from being considered unambiguous evidence of homeopathy's efficacy.[8][11][19][20]"

2009-11-29 14:53:44 by Eric:

Great article! Now, entirely orthogonal to the point of the argument; I'm curious how your argument handles the existence of Godel's incompleteness theorem.

2009-11-29 17:38:17 by Rowboat:

Does it have to? I don't see what there is to handle. Unless you're referring to the fact that there are people who like to go around namedropping Gödel in support of their nonmathematical ideas, or their pseudomathematics. In which case you could ask them to tell you exactly what Gödel's two incompleteness theorems state. The response will be floundering, or perhaps an incomplete Wikipedia quote or something if it's an online conversation. It probably won't help you convince them that they don't know what they're talking about, but it'll increase your own certainty (and that of at least some observers) that this is so, I suppose.

2009-11-29 21:07:55 by Parmenides:

If I'm not greatly mistaken, the author of the article that you are criticizing quotes himself making an ad hominem comment about Cantor. That's bad form anywhere, not just mathematics. Consider a dialogue in which one party said, "As I have often said, 'Supporters of Eleatic Monism are dumb', quod erat demonstrandum", presumably the other party would have nothing substantial to refute (in terms of Philosophy, perhaps Psychoanalysis could help party one determine that he or she doesn't really think that, but, in fact, has some sort of problem with his or her parents). Is it at all possible that the "kmol" was brilliantly disguised satire? A light spirited treatise on how not to argue, or on how to avoid being taken seriously?

2009-11-29 21:44:26 by Graham:

In one of the knols: "... real numbers are not well-defined." I almost fell out of my chair laughing. The article seemed a bit rantish at times, but -certainly- has a point.

2009-11-29 21:49:24 by Graham:

Sorry for the double post, but to clarify: "...The article seemed a bit rantish, but -certainly- has a point" I meant Sam's article, not the rantee.

2009-11-29 21:59:15 by Fjord:

Parmenides: If the Knol were a troll, it's a 10/10. Given the fact that Google's Knol is trying to eat into Wikipedia's market by providing theoretically "scholarly" articles on the topics that it discusses, any average user (like me) who was looking for information on this particular subject could stumble across this article and find themselves a week later failing their math class, or causing their major programming project to go up in smoke because they tried to use the misinformation in this article in a practical manner, or something similar. This is the major problem with Knol, from what I can tell. It doesn't really seem to be peer-edited. A "Comments" section at the end of an article - especially one that the article's author has admin privledges on - is not nearly as effective a tool for spreading correct information as is everyone having admin privledges on the article itself.

2009-11-30 00:12:04 by doesntmatter:

Just wanted to say one thing. "Knol" is supposed to be a unit of KNOWLEDGE. This guy, John Gabriel, posts tons of garbage, very little of which is true knowledge. Most of it is his opinions of how one should teach math, which is respectable. For some reason though, instead of saying "one should teach this and that concept in this and that way", he attacks well-established and useful mathematical concepts, for which I personally can see only one reason and it is that he just doesn't understand them himself, and it interferes with his ego/whatever it is. P.S. What is this "the square root of minus one" question at the bottom of New comment page? There are two roots of minus one, plus and minus i! :-/

2009-11-30 00:13:50 by Knut:

Haha, from his "About me" page: "I am aware of some minor errors in my Knols [...] Finally, some errors are intentional" I guess this article is one of his intentional errors then.

2009-11-30 01:24:18 by Vetaeir:

doesntmatter, it depends on how you define "square root". In one of my math classes, it was formally defined in a way that required it to be nonnegative. I prefer that definition because it makes the notation much neater. I'm not sure which definition is in more common use among mathematicians, though.

2009-11-30 01:38:28 by miles:

http://knol.google.com/k/calculus-without-the-use-of-limits# fun!

2009-11-30 05:27:45 by DanielLC:

-i is non-negative. It isn't less than zero. Less than doesn't mean anything on the real number line. While we're at it, there is an infinite number of square roots of minus one. Quaternions alone has ai+bj+ck where a^2+b^2+c^2=1. In math it isn't so much a deep philosophical question what set of axioms are true as whether or not that even means anything. My philosophy is that none of mathematics is true. It's just a tool. I wonder if the guy that wrote that article knows that the diagonal argument was actually the second proof that real numbers are uncountably infinite. There is sometimes difficulty telling if a given proof is valid, though now there are proof-checkers so if you can get your proof formatted right you know it's valid.

2009-11-30 06:57:16 by AnonymousCoward:

This is a bit of a tangent so you'll have to excuse me but I think it's important. "Solipsism is obviously complete horsebull, because assuming that other people are real is a much more efficacious way to deal with real life than behaving as if they don't exist. No, there is no Matrix, because pretending there is a Matrix doesn't help us with anything or explain anything or predict anything." Reality is kind of an odd thing. There is a lot of potential for the universe not really existing how we understand it to. An unscientific mind pretending there is a Matrix is of course of no use - but a scientific one, even taking this concept to the extreme, a scientific one lost in it's own world of crazy, can find new science that works in their world - as well as ours. I think some people "pretending" that the world is not what it seems is immensely useful because their minds have different bias as to what makes logical sense. Making them not necessarily less, but differently restricted as to what dots they connect.

2009-11-30 09:57:28 by Val:

doesntmatter: this can, in extreme cases, even lead to the downfall of our civilization. The current trend is to attack and try to break well-established societal and cultural norms without first understanding why they even existed in the first place, and without thinking about the possible consequences.

2009-11-30 22:18:24 by Ross:

First, I fully agree with the thrust of your post, Sam. There is math done right and math done wrong, and vanishingly little in between the two. However, I am confused by your denial that "it is not possible to represent all real numbers in any given radix system". Certainly, repeating decimals close the gap on representing all *rationals* in any given radix system. But there are uncountable irrationals, not representable by repeating decimals, nearly all of them not even representable by repeating continued fractions.

2009-11-30 22:43:40 by qntm:

Well, you are allowed to have infinite non-repeating decimal expansions, you know. By "allowed" I mean that mathematics with such expansions is well-defined, doesn't lead to inconsistencies, and universally acceptable.

2009-11-30 22:44:47 by Cory:

Ross: A radix system is a representation of the reals as a formal sum of powers of the base. That is, for a radix r, a real number is: sum a_n*r^(-n) where each a_n is some integer, and the sum is over all natural numbers (n=0,1,2,...) A series is just a sequence of partial sums, and a sequence is a function from N->(the set of interest). In this case, the sequence is uniquely determined by the a_n's so it is a function from N->N. This can be proven (in a myriad of ways) to have the same cardinality as the reals. Using some analysis, we can prove that every one of these sums converges to some real number (not necessarily distinct from other sums)... and most math students have had to sit or work their way through the tedious construction which establishes that. In other words, every real number can be represented as a formal sum of negative powers of some fixed radix. For a whole proof, take an analysis or set theory course. On the other hand, only a countable number of programs exist, so only countably many reals *can be computed*, but this is a different matter entirely. Cheers.

2009-11-30 22:49:38 by Cory:

Ugh... I lied in there somewhere... The function is from N->R. But the number of function from N to R is |R|^|N| which is also provable (in a number of ways) to be |R|. I'm too lazy to fix the sloppy thinking that led to that mistake, but the rest is correct modulo a whole lot of rigour.

2009-11-30 23:13:00 by AnotherMathJunkie:

This guy just sounds like he's angry that he can't understand it and therefore it must be false. From the article "It is a crime that any student should have to learn Cantor's nonsense, much less try to understand it." I can't count (pun fully intended) the number of times I've heard the same argument in my classes.

2009-12-01 23:40:51 by CI:

Sam, I found a homeopathy website I think you'd approve of: http://www.fdhom.co.uk/ Also, I've had some personal experience with John Gabriel. Well, not personal, but I've debated with him on the xkcd forums. He doesn't listen to logic, he just keeps saying that you're misunderstanding his precious work. I think he got lost on his way out of the computational linguistics department.

2009-12-01 23:53:33 by CI:

I stand corrected. The topic title was changed and the thread ID was different from my bookmark, which threw me off. Take a look at his defenses of his "work" here: http://forums.xkcd.com/viewtopic.php?p=1902817

2009-12-02 03:34:50 by Supergrunch:

CI: I don't care what xkcd 114 says, I'll have none of this computational linguist bashing. :p In my experience, many linguists have a decent understanding of maths, although there are of course some hilarious exceptions - recently I found the following in a paper: "There is some question why [the investigation of ungrammatical sentences] should be such a tour de force of the T[ransformational]G[rammar] movement because, if the set of grammatical sentences in a language is infinite (Chomsky 1957:23, 1965), the set of ungrammatical sentences is even larger (if that is philosophically possible) since there are no limitations on the way in which these sentences can be produced." I still fail to see how this got through peer review... Anyway, this Gabriel guy is completely crazy. I fail to see why he puts so much... effort in, given he clearly has no idea what he's on about half the time.

2009-12-02 05:11:54 by Fjord:

CI: After reading that thread you linked, I am totally convinced that this guy is nothing but a troll. A Knol troll. I know, usually trolls know that they're wrong and just do it for the reactions - but this guy is so good, he convinced himself. 10/10.

2009-12-02 06:26:03 by gonk:

well that simplifies things

2009-12-07 02:37:23 by cryforhelp:

What people were wondering about in the xkcd thread, and me too, is why is knols are so highly rated. They're all four stars, is knols rating system so dumb, or are there people who think what he's saying makes sense?

2009-12-07 03:35:29 by Fjord:

Whether he be a troll or just someone with an ego larger than this sector of the galaxy, it would certainly be in character for him to plus-vote his own articles. He might even be a script kiddie. But I must admit: Your thought is scarier. There might -actually- be people who think he's right.

2009-12-07 10:49:47 by William:

"Hm, what about Bolyai, for example? He discovered that there is something fishy about euclidean geometry, and discovered a new geometry because of this." Well, yes and no. He discovered that the parallel postulate has to be assumed to derive Euclidean geometry.

2009-12-09 00:19:46 by Lucas:

Anyone want to submit to him a mathematical proof that he is wrong? That his tree only contains rational numbers, even by his own definition? Hehe. Assume (the fractional part of) Pi is in the tree. This implies that Pi can be expressed as a sum of fractions. This implies that [Pi] can be written in the form p/q, where p and q are integers. Cue all the proofs that Pi is irrational. Anything wrong with that logic?

2009-12-09 08:24:45 by qntm:

Lucas, that's been done. The problem with your logic is that he'd just accept that pi is rational.

2009-12-09 12:20:45 by Lucas:

Heh,if he doesn't accept mathematical proofs then how the hell can he call himself a mathematician :P

2009-12-09 15:27:30 by ASmt:

What is kind of surprising is that all the comments on this site are negative. I read a few of Gabriel's Knols and find them to be extremely well-written and informative. He has a unique perspective on quite a few topics. Someone mentioned he might be rating his own Knols. This is not possible given that Google checks the IP addresses of those who vote. Duplicate votes are disqualified. If he was rating his own knols, he obviously has access to hundreds of different computers. This seems a bit of a strecth don't you think?

2009-12-09 17:19:52 by qntm:

That's the whole problem. His "unique perspective" on the field of mathematics is wrong. People are reading it, and they think they're finding his knols informative, and upvote them. In fact the knols are incorrect, and the readers are being misled, not to say lied to.

2009-12-10 11:25:44 by ASmt:

Sam: From your comment it is evident you know very little mathematics. I am a mathematician. It seems to me the problem might lie with you and others of similar opinion on this site? Knol is open to anyone. If you all feel so strongly, why don't you write a Knol or more exposing Gabriel's errors and "lies" as you call them? Attacking one's character is hardly the right thing to do. Last I checked, his ratings just keep getting better. If indeed he is publishing "pure garbage" as this site claims, what better way is there than to expose the errors in his arguments?

2009-12-10 18:51:18 by Lucas:

Not once did Sam say anything at all about his personal character... I've seen a few of his knols that make a little sense. However a large portion of it is mathematically incorrect. Plus I doubt Google would let you make a knol simply displaying how wrong a different knol is anyway.

2009-12-10 19:47:26 by qntm:

* My previous comment reveals nothing about how much mathematics I know, beyond a certain basic level * If you're siding with the individual in question, you are probably not a professional mathematician * If one guy is wrong, and everybody else is right, the "problem" does not lie with everybody else who is right * I already said I'd campaign against his knol... if I thought Knol was relevant * The guy admits that people have already shown him holes in his proofs, and even lists quite a lot of them in his own knol, but he sticks to his flawed arguments * I never attacked the man's character * Knol rating is not a measure of mathematical correctness * I never used the phrase "pure garbage" * Pushing errors in the original author's direction is evidently not a good way to expose them, because, as previously mentioned, he's listed quite a lot of them in his own knol, but sticks to his flawed arguments His knol already contains almost all of the arguments that I would offer. He offers counterarguments for all of them, but all of his counterarguments are wrong. It is difficult to nail down the precise point of disagreement, but at the time of writing the very last argument/response pair is the most telling. Argument: "[A]ll real numbers can be thought of as infinite paths along your tree. The problem is that your enumeration scheme [does not enumerate] these infinite paths or limits." Response: "I DO NOT think of real numbers in terms of limits. Never have and never shall. The concept of limit is ill-defined." This is it, in a nutshell. Limits are exceptionally, extraordinarily well-defined; but if one does not comprehend and accept their definition, then naturally one will find that the concept of real numbers as an uncountably infinite set of countably infinite decimal expansions is unfathomable.

2009-12-10 23:05:14 by Fjord:

ASmt: "Someone mentioned he might be rating his own Knols. This is not possible given that Google checks the IP addresses of those who vote. Duplicate votes are disqualified. If he was rating his own knols, he obviously has access to hundreds of different computers. This seems a bit of a strecth don't you think?" No, I don't. Not if he uses a few good proxies, requests a new IP via DHCP after each vote, drops a vote-script on any computer he accesses, or any number of other methods. Also, as there are obviously other people on the Internet who believe his posts to be factual (like yourself), it is not inconceivable that some of them may be vote-trolls as well.

2009-12-11 02:19:43 by Parmenides:

Sam, while a Knol rating may not be a measure of mathematical correctness, I think you overlooked a key element in Mr. Gabriel's argument... WORDS IN BOLD SPELLED OUT IN ALL CAPITAL LETTERS FOLLOWED BY EXCLAMATION MARKS! He doesn't merely reject counterarguments, he cleverly refutes them by saying he personally disagrees and is therefore correct. Furthermore, he demonstrates that he is truly ahead of his time, by not bothering with the mundane, banal, quotidian task of providing support or grounding for his arguments, instead, he insightfully insults people who question him. Insert ad hominem here. So if he applies for a job teaching mathematics, think his work in ("in"?) that field will come up in the vetting process?

2009-12-11 11:52:05 by ASmt:

Again, I find it hard to believe that he could vote for himself despite your proxy objections. All I see on this site is a group of individuals who are attacking Gabriel and his character and then denying it. Sam, you made those remarks about Pure Garbage because I recall reading them on your site. A mathematician shows correctness by demonstrating the flaw or flaws in an argument. How much mathematics is actually present on this page? I am sad to say, none.

2009-12-11 23:20:48 by Supergrunch:

ASmt: Other arguments aside, searching for the string "pure garbage" on this page only brings up your comment, Sam's response to it, and your further response, so unless Gabriel is discussed elsewhere on this site, Sam didn't describe his knols using that phrase.

2009-12-11 23:42:02 by Lucas:

"A mathematician shows correctness by demonstrating the flaw or flaws in an argument." How many times have we done this already? Ten? Twenty? I've lost count. Seriously, FIND ONE EXAMPLE OF SAM INSULTING HIM PERSONALLY. Anywhere. Every comment here displays good reasoning for everything said. We are attacking HIS MATHEMATICS and his misleading of anyone who reads those knols. That is all. It is extremely closed-minded of you to assume that since we disagree with what he says then we must be attacking him as a person. He may well be a very kind-hearted person if you meet him for real. Lastly, the last two paragraphs of Sam's previous comment display mathematics, namely what he is trying to invoke and why it is wrong. It CAN be shown to be wrong absolutely mathematically, but we don't want to go into huge amounts of boring detail here.

2009-12-12 11:25:40 by Asmt:

Lucas: I have not seen anyone do it here even once. And you talk about 10, 20, countless times.

2009-12-12 17:24:43 by Lucas:

Examples: "...Limits are exceptionally, extraordinarily well-defined; but if one does not comprehend and accept their definition, then naturally one will find that the concept of real numbers as an uncountably infinite set of countably infinite decimal expansions is unfathomable." The entirety of post: 2009-12-11 23:20:48 by Supergrunch - Sam never used the phrase "pure garbage" anywhere. The entirety of post: 2009-12-10 23:05:14 by Fjord - You CAN rate yourself multiple times. Lastly, the entirety of Sam's last post, which is essentially a list of demonstrations of flaws in your arguments. These are all examples of demonstration of flaws, all in just the last ten comments. You don't seem to be listening to us, though. We have said (and backed up) that his personal character has not been attacked, yet you still keep trying to call us out on it.

2009-12-13 10:46:33 by Fjord:

ASmt: "Sam, you made those remarks about Pure Garbage because I recall reading them on your site." Ad hominem. I lol'd. So much. But seriously. The only use of the word "garbage" prior to your arrival was in comment 2009-11-30 00:12:04 by doesntmatter. Not Sam. And he was referring to the "mathematical" content of Gabriel's Knols, not Gabriel's character, attitude, socks, or anything else. You believe it impossible to vote on a Knol multiple times? I just downvoted it three times. Each time when I refreshed, the vote-count went up, so my votes -did- get counted. This is what I did: 1. Turn on Firefox. Navigate to this particular Knol. Downvote it (one star). Note current vote-count, refresh. Vote got counted. 2. Downvote again, note current vote count, refresh. This was to make sure that my IP had been noted. It had, my second vote was dropped. 3. Enable TOR browsing using the TORbutton extension for Firefox. Refresh page, vote. Take note of vote count, refresh. This vote was retained. At this point, I have now successfully voted twice. 4. Downvote again, refresh. This vote was not counted; the IP of the TOR endnode had been logged. 5. Disable TORbutton. 6. Re-enable TORbutton. 7. Refresh, vote, refresh. This vote was counted. So, in the space of about 90 seconds, I successfully voted 3 times. I did that with just a bit of thought and a mouse. If someone really wanted to, they could write an autovoter program to do basically the same thing, only faster. Although, given the fact that as of this post there are only 366 votes on this Knol, I think it unlikely that an autovoter is in use. Still don't believe it's possible? Try it yourself.

2009-12-14 13:35:39 by ASmt:

Fjord: I tried multiple votes on the knols and it would not work. "Pure garbage": Yes, you are correct. I must have read it on his site. This said, anyone can see this site is intended to smear Gabriel. I read several of his knols and whilst I do not agree with everything, they contain a lot of useful information. His ideas on limits are not necessarily wrong. They (ideas) are his perspective of limits.

2009-12-14 19:15:51 by Lucas:

... definitely a troll. I did wonder.

2009-12-14 21:43:38 by Typhon:

Asmt, this is not philosophy, where nothing means anything, and anything means something, we're talking about. It's math. Talking about having a personal view of math makes no sense. If you fail to understand it, i see little point for you to continue this discussion. Typhon

2009-12-15 07:33:19 by Parmenides:

ASmt, are you familiar with the distinction between "site" and page"? I can see how someone could misconstrue this page as being a smear on the good name of Gabriel, but saying the site, id est, this entire collection of pages on many widely varied topics, most of which predate Gabriel's contribution to Knol (and Knol itself?) is a smear seems erroneous. Could it be that you're looking at a different site and inadvertently commenting on this one. That would explain why you thought Sam had written that the work was "pure garbage" (I'd hate to see impure garbage *pause of laughter*), when in fact the first mention of that phrase on this page was yours. Or perhaps you are simply mistaken in regards to what words mean? And yes, clearly you are trolling (I had secretly hoped that at some point you would reveal that you are Gabriel himself, but that is probably just not meant to be), but don't you think this site deserves a better class of troll? Rather than lying about what was said, and objecting to things you've imagined, take a bold stance, claim that all mathematics is subject or something, make outlandish claims based in improbably anecdotes, tell us that Homeopathic remedies helped your father regrow his legs after he lost them in World War One (they're good for longevity too), be creative, combine ad hominem with red herring, metaphorically speaking, of course.

2009-12-16 04:54:32 by Grylva:

Since somebody brought up XKCD, I think it's quite funny that the comic from a couple of days ago is so relevant. http://xkcd.com/675/

2009-12-18 19:48:11 by JohnDoe:

How much credibility can you give somebody that writes this: 'I think of this book as my opus magnus' (google it and you will find it's writer) Opus magnus. Seriously, was there ever this much irony in one sentence?

2010-01-03 22:27:54 by Scully:

Good way to say this Sam. I mean mathematics requires unique thought at time, but not when it's this incorrect.

2010-01-26 15:48:57 by Azrael:

Re: 2009-12-14 13:35:39 by ASmt: Fjord: I tried multiple votes on the knols and it would not work. Do a little research on anonymizing proxies, or even on a system called Tor, evading IP/cookie checks is a trivial task.

2010-02-14 11:25:36 by Ranbir:

I was always unsure about homeopathy and the alternative medicine thing because I thought it was just exploitation of working traditional treatments that just managed to now get druggified. You know, like a certain herb is good for you and suggested for your diet. But it turns out it is all about water having memory and random flowers being grown in a mystical way. As for this Knol stuff, it is just amazing. Talking about challenging proofs with his own "belief" yet warning off those to have belief in a religion to not bother with his knols.

2010-02-23 23:27:09 by CI:

Oh look, he ended up on Good Math, Bad Math http://scienceblogs.com/goodmath/2010/02/_so_remember_back_in.php

2010-03-31 13:23:42 by WanLee:

A lot of uninformed comments by many claiming to know mathematics. I have seen Gabriel's work and frankly do not believe any of the commentors on this amusing site have what it takes to understand his publications.

2010-03-31 15:15:24 by qntm:

Nor does Gabriel, or he'd retract 'em

2013-02-10 18:13:56 by JohnGabriel:

I haven't visited your crappy site in almost 2 years. You are all still around O morons? Ha, ha. http://thenewcalculus.weebly.com Too funny that a bunch of pathetic losers like yourselves are so angry at me. Could it have anything to do with your jealousy? Your stupidity? Or are you all just bored and having a little amusement at small things, given you all have such small brains? Dead dogs. Go on, I dare you to publish this comment. You have nothing to lose. Really. You never had. Ha, ha.

2013-03-01 05:52:42 by hE:

Someone said that placebo effects are removed if the person knows that it is a placebo. iirc, this is not entirely correct. The effect is reduced, but I think I remember something that said that there was still SOME positive effect. (though buying placebo pills for this purpose would probably not be worth the money) (but that does remind me of something where more expensive placebos were more effective?)

2013-10-16 06:28:41 by JohnGabriel:

In the following comment, I prove conclusively that “real” numbers do not exist: http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-317.html My final proof that 0.999… is not equal to 1 can be found here: http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-372.html#post23252

2013-11-12 14:44:56 by Beber:

John Gabriel is the best entertainer in mathematics, shame on his detractors !

2013-12-01 10:51:07 by JohnGabriel:

The best way to get the truth across is in a form of entertainment. I think it would be quite boring otherwise. Thanks for your support Berber! Ha, ha.

2022-08-12 15:37:39 by John Gabriel:

It's pretty obvious Cantor was a crank and the father of all mathematical cranks in today's mainstream math academia: https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks

2022-08-12 15:38:57 by John Gabriel:

Of course, I can say there is no such thing as an irrational or real number. I still do! https://www.academia.edu/45471258/Is_the_real_number_line_real https://www.academia.edu/44820487/Discovering_the_concept_of_number_a_personal_journey

2022-08-12 16:51:59 by qntm:

Don't post here again.

2022-10-13 21:49:52 by qntm:

Closing this thread now.

This discussion is closed.

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