Logical difficulties in modern mathematics (2012) - <AUTHOR> https://njwildberger.com/2012/10/13/the-problem-of-rigour-in-modern-mathematics/ <comment><USER4> Did the guy ever deliver on his promise to create a better system? I thought the problems he was pointing out was motivation for a better system (that united the naive understanding and rigor better?), but the further into the article I got, the more it just seemed like a list of complaints.

Having 1) studied "naive statistics" when I was young and 2) learning the full-on measure-theory version a la Bourbaki, and now 3) using applied statistics every day, I can say the naive version is the most useful by far. Yes, there is hand waving, but the hand waving works, and you really don't get into that much trouble unless you try to be pathological.

I admit, it would be great to have a version where the naive intuition (many of which are motivated by empirics, physics, and real world situations) and the theoretical definition matched better. Even still, I don't think the formal treatment is appropriate as an introduction -- it's an unnecessary hazing on learning minds when they can get most of the value with a bit of hand waving.

<comment><USER5> "Measure theory a la Bourbaki" is probably not what you meant if you did probability theory and statistics. Bourbaki famously sidestepped classical measure theory with sigma algebras by constructing Radon measures as functionals via functional analysis. This is sufficient for many purposes but not for probability theory. First and foremost, sigma algebras in probability theory are not just a technical device to avoid paradoxes with unmeasurable sets. Sigma algebras play a starring role in conditional expectation, stochastic processes and martingale theory.

The best way to appreciate the information-theoretic role of sigma algebras is to look at them in the simplest case, where you have a discrete-time, finite- valued process. Then a sigma algebra is equivalent to a partition of the state space and it represents the information that can be gained from an observation; it's like a random variable without specific values, just the discriminating information from different outcomes. To say that a random variable is measurable with respect to the sigma algebra is to say that its value may only depend on information that can be gained from an observation. A filtration of sigma algebras corresponds to a causal series of observations where the observer learns more information over time.

The conditional expectation of a random variable with respect to a sigma algebra (or partition or other random variable) is another random variable that tells you the expectation over the states consistent with a given observation; this new random variable is measurable with respect to the sigma algebra you conditioned on, which as mentioned earlier means it only depends on the information gained from an observation. The conditional expectation is the best least-squares estimator given the information from an observation in the same way that the usual expectation is the best least-squares estimator given no information.

<comment><USER6> As someone who moved from pure mathematics -> applied mathematics -> machine learning, perhaps I can offer a similar perspective to GP that explains why the measure theory stuff might not seem so useful to some people. Basically, in application you never need to worry about anything _but_ your simplest case - that of a discrete-time, finite-valued process. All of the subtleties of measure theory, which occupy most of what mathematical measure theorists/analysts work on, are introduced when you assume you've got an infinity or a continuum somewhere in a model, and that assumption is never borne out in practice. Unless you really want to do theoretical math, you're better off learning only the aspects that relate to finite functions, i.e. almost none of what a real mathematician would consider to be "math". And that's not just out of laziness or disinterest - once you've restricted yourself to finite functions for empirical applications, you encounter a whole new realm of engineering difficulties to deal with, that theoretical mathematics doesn't touch. You've got to learn how to solve a different class of problems that aren't as purely logical, but are every bit as challenging.

To put it another way - think about all the pathologies you may encounter working with even a "nice" function space like L^2(R). You'll never deal with those pathologies in reality, because every empirical function is much better behaved - finite domain, finite range, and even if you assume a continuous domain, you can choose a model that only has a finite number of discontinuities, is Lipschitz continuous in between them, has finite total variation, etc. And that's why the hand-wavey, "intuitive" approach works so well if you're not a theorist, at least in my opinion.

<comment><USER7> You're right. Classical measure theory lives in a model divorced from physical reality. You can show that all of the fancy counterexamples which necessitate the complicated constructions of measure theory are artificial (e.g., the characteristic function of a non-measurable set is uncomputable).

There are better approaches to measure theory which live in different "foundations". For example, you can build measure and probability theory based on the locale of valuations on a locale instead of a sigma-algebra on a topological space. You can do even better by starting in a constructive metatheory and adding some anti-classical assumptions which are modeled by all computable functions.

The reason we are teaching classical measure theory as the foundation of probability theory is historical and because there are no good expositions available for most alternative approaches. It is really not the most straightforward approach.

\---

Before you accuse me of being overly negative: classical measure theory offers a consistent approach to probability theory which is well understood and for which carefully written textbooks are available. If you really need to go back to the definitions to derive something then you need to know at least one consistent set of definitions. So it is useful to teach measure theory, even if it is more complicated than it has to be...

<comment><USER5> >Classical measure theory lives in a model divorced from physical reality.

Everything in mathematics is divorced from reality. Unbounded integers are divorced from reality. (Once you move beyond naive realism, bounded integers are divorced from reality, but that's a deeper philosophical debate.) The only question is whether these models are more or less effective for their various theoretical and applied purposes.

> There are better approaches to measure theory which live in different > "foundations". For example, you can build measure and probability theory > based on the locale of valuations on a locale instead of a sigma-algebra on > a topological space.

Better by what definition? According to the practical needs of students, pure and applied mathematicians, etc? I've studied some topos theory and know a little bit about locales from the Topology Via Logic book, but it's hard for me to see that as anything more than a fun curiosity when considering the practical needs of mathematics as a whole. In my mind that kind of thing is much closer to navel-gazing than something like measure theory.

> It is really not the most straightforward approach.

The onus is on critics to do better. Dieudonne/Bourbaki made a valiant and elegant attempt even if they intentionally snubbed the needs of probability theory. And "better" will obviously be judged by the broader community.

<comment><USER7> > Everything in mathematics is divorced from reality.

Mathematics is an abstraction, but it is still useful for talking about concrete problems. Your mathematical assumptions can be either close or far away from your problem domain. Sometimes we introduce idealized objects, such as unbounded integers, in order to abstract further and simplify our reasoning.

These ideal objects can then either be "compiled away" in specific instances, or really do ignore corner cases which might invalidate your results.

For an example of the former, you can assume that there is an algebraically closed field containing a specific field, give an argument in terms of this closure and then translate this argument to one which does not construct the closure explicitly. The translation is mechanical and does not represent additional assumptions you made.

The second kind of ideal object is something like the real numbers applied to physics. We can think of a real number as an arbitrarily good approximate result. In practice we can only ever work with finite approximations. At the scales we are operating on the difference is usually not relevant, but there might, for example, be unstable equilibria in your solutions which are not physically realizable.

> Better by what definition?

Informally, better because it is "simpler". There are fewer corner cases to consider, theorems are more inclusive, constructions are more direct.

Formally, the theory has more models and is therefore more widely applicable. Theorems have fewer assumptions (but talk about a different and incompatible type of objects).

> The onus is on critics to do better. Dieudonne/Bourbaki made a valiant and > elegant attempt even if they intentionally snubbed the needs of probability > theory. And "better" will obviously be judged by the broader community.

Oh, sure, but that's not what I want to argue about.

I can tell you with certainty that classical measure theory is complicated by the interplay of excluded middle and the axiom of choice. This is a technical result. You can see this yourself in textbooks every time the author presents an intuitive "proof idea" which then has to be refined because of problems with the definitions. In alternative models, or in a metatheory with alternative assumptions, the simple proof idea usually works out fine.

</comment></comment></comment></comment></comment></comment><comment><USER8> I know Norman; not personally.

His real complaint as far as I've ever been able to determine is that he is a highly symbolic thinker; and because of that won't accept certain assumptions that everyone else takes as a given - usually what the Reals are. I'm very happy to accept than any length in geometry is a number by definition (hence sqrt(2), constructed by a 1-1-sqrt(2) triangle, is clearly a number corresponding to that length). He won't accept sqrt(2) as a number because it can't be represented in Hindu-Arabic notation. This isn't really a logical issue, he just won't use everyone else's definitions.

He's worth listening too because he is good at maths despite that handicap and his perspective is interesting to provoke a bit of reflection on what your assumptions are and what does infinity really mean anyway. His complaints are otherwise unlikely to catch on.

<comment><USER9> >He won't accept sqrt(2) as a number because it can't be represented in Hindu- Arabic notation.

You sure of that? Based on another of his other blog posts [1], his objection seems to be about _uncomputable_ real numbers. Very roughly, a real number _R_ is computable iff there exists a Turing machine that, given a natural number _n_ on its initial tape, terminates with the _n_ th digit of _R_. See [2] for a formal definition. Sqrt(2) and all familiar real numbers are computable. Of course, since there is only a countable infinity of Turing machines, but an uncountable infinity of reals, some reals must be uncomputable. Some versions of constructivist mathematics do differ from standard mathematics by rejecting the uncomputable reals and instead defining "real numbers" in such a way that they are essentially the computable reals.

[1] [https://njwildberger.com/2016/01/01/uncomputable-decimals- an...](https://njwildberger.com/2016/01/01/uncomputable-decimals-and-measure- theory-is-it-nonsense/)

[2] [https://en.wikipedia.org/wiki/Computable_number#Formal_defin...](https://en.wikipedia.org/wiki/Computable_number#Formal_definition)

<comment><USER8> Yeah, pretty confident. He doesn't like the computable or uncomputable reals; although I suspect he would like the uncomputables less.

Eg, "These phoney real numbers that most of my colleagues pretend to deal with on a daily basis ... such as sqrt(2), and pi, and Euler's number e." [0]

Even in the article you cite, the irony of a _pure mathematician_ of all people complaining that a concept has no tangible link to reality is a bit of a give away that he is speaking from the heart rather than the head. That isn't a valid complaint about pure mathematics; the point is patterns for patterns sake. So what if there are no known examples of your pattern? Study it anyway!

Great case of the flaw maketh the masterpiece; apart from that one little quirk with infinite things he is a lovely character and a force to be reckoned with. And I expect his personality motivates a lot of interesting research from him regardless.

[0] [https://njwildberger.com/2014/10/06/the-infinitely-real- delu...](https://njwildberger.com/2014/10/06/the-infinitely-real-delusion-and- my-recent-debate-with-james-franklin/)

</comment></comment></comment><comment><USER10> After listening to Wildberger's rants – some of which are very educational and some of which are just rants, I keep thinking that his actual problem is that he doesn't seem to believe in the implications of the axiom of the excluded middle. He goes on about infinities and such, but the deeper issue seems to be that he thinks in a constructive, intuitionistic way whereas the majority of mathematics uses classical logic and even accept the axiom of choice.

I wonder why he never talks about this – surely as a mathematician he should be aware of intuitionistic logic? (Or is it that as a computer science and linguistics wannabe, I am aware of it but many mathematicians aren't bothered to take a look?)

If you stop thinking of axioms as value judgements and instead as definitions of formal systems (or adopt a more general system that encompasses others, such as Gentzen style sequent calculus with the only axiom being modus ponens), you achieve a piece of mind. But obviously his beef is not only that; he would like other people to admit the value of the thinking he prefers. And I agree with that.

<comment><USER11> > I keep thinking that his actual problem is that he doesn't seem to believe > in the implications of the axiom of the excluded middle. [...] I wonder why > he never talks about this – surely as a mathematician he should be aware of > intuitionistic logic? (Or is it that as a computer science and linguistics > wannabe, I am aware of it but many mathematicians aren't bothered to take a > look?)

Heck, I know professional logicians (mostly model theorists) who have never seen intuitionistic logic, in any context, ever. That said, Norman does know a fair bit about intuitionistic logic and constructive mathematics, and even some type theory. He does not like the underlying philosophy any more than he likes classical mathematics.

> Gentzen style sequent calculus with the only axiom being modus ponens

Sidenote: a calculus where modus ponens is an axiom is definitely not a Gentzen-style sequent calculus.

</comment></comment><comment><USER12> There is a distinction between analytically correct expositions, and ones which build on naive intuition to teach students. It is inappropriate to expect beginning students to follow a logically rigorous exposition.

That said, there are philosophical questions about truth, infinity, unknowable statements and the like. Mathematicians have by and large settled on a set of answers to these. Every statement is true or false, regardless of whether we know the answer, or even whether we can know the answer. Infinite sets exist, and are described by a known set of axioms called ZFC. Almost all real numbers that exist can never, even in principle, be written down or described in any meaningful way. (In what sense do they exist again?)

All of these statements are part of classical mathematics. Almost every elementary exposition will implicitly assume that they are try. Yet they can all be questioned, and their truth can never be settled in any absolute sense. However woe betide the student who dares question these in a math class.

<comment><USER13> > _Infinite sets exist, and are described by a known set of axioms called ZFC_

This is the assertion of many mathematicians, but the justification for it is "this is convenient" and/or "we take this as an article of faith" (or often "I never really thought about it, but it doesn't much affect my work day to day one way or the other").

There is no way to prove that infinite sets "exist" by reasonable definitions of "exist". Indeed, by a conventional definition of "exist" infinite sets pretty clearly don't qualify.

Instead, mathematicians have redefined the words "exist" and "true". In mathematics it now means something like "if we accept a particular set of non- obvious and rather handwavey premises, we will also accept any conclusions that result from symbolic manipulations thereof following our established formal rules." [This is not a full or precise definition of mathematical existence; folks interested can do a search for those keywords and find piles of material.]

* * *

Personally I am happy to accept ZFC or the like because it is convenient and I can't be bothered to work up an alternative system from scratch and carefully examine all of the conclusions that might follow from that, and whether ZFC is "true" or not doesn't really affect me. It seems intuitively wrong to me, but I remain agnostic.

<comment><USER7> > "I never really thought about it, but it doesn't much affect my work day to > day one way or the other"

In my experience, people won't come out and say it, but this seems to be what everyone is thinking. :)

The problem with this is that it is wrong.

Classical ZFC in particular is a very strong and specific set of assumptions* with a very tenuous link to any practical application. If you actually want to develop a useful bit of mathematics it makes sense to consider the "foundations" as a moving piece. It's a part of the design space for modeling your problem domain, not some god-given notion of truth.

You can translate between different logical theories by building a model of one in another, so it's not like you loose anything. But it's cooky to insist that we should start with ZFC of all things.

\---

*) I mean that second-order ZFC has basically no non-trivial models, so there is no real way of extending ZFC to talk about domain specific aspects of your problems.

<comment><USER14> > The problem with this is that it is wrong.

> You can translate between different logical theories by building a model of > one in another, so it's not like you loose anything. But it's cooky to > insist that we should start with ZFC of all things.

I don't see how these two are consistent. Almost everything most mathematicians do can be done both in ZFC and your favourite non-kooky axiom system. Certain Powers That Be seem to have decided that ZFC is _the_ foundation of mathematics, so they say that what they're doing follows from ZFC even if they have a very hazy idea of what it is, but why does it matter? Most mathematics probably won't be formalized in their lifetime anyway, so whether it ends up being formalized on top of ZFC or something else doesn't affect them.

<comment><USER7> Slightly tongue in cheek, but the analogy to programming is this:

> "Almost everything most programmers do can be done both in x86 assembly and > your favorite non-kooky programming language. Certain Powers That Be seem to > have decided that x86 is _the_ foundation of computer science. [...] Why > does it matter?"

The problem is that it is difficult to translate results in a theory built in ZFC to other "architectures". In mathematics, the architectures in question are not different axiom systems, they are different branches of mathematics.

Let me give you an example. There is a large body of work on differential geometry with many useful constructions. Classical differential geometry works directly in a model where manifolds are certain subspaces of (countable products of) R^n. These constructions have been successfully imported into many different areas of mathematics. In most cases people just had to tweak the definitions slightly and adapt the proofs by keeping the basic strategy and changing all the details.

What is happening here is that the underlying ideas of differential geometry are not specific to this particular model.

When faced with such a concrete model, our first instinct should be to abstract from it and ask which assumptions are required. This is difficult in ZFC, because in the end you have to encode _everything_ into sets. It's not possible to reason about "abstract datatypes" directly, without literally building a notion of logic (generalized algebraic theory) and models of it _within ZFC_. Even then, the existence of choice means that you usually have to exclude unwanted models of your theory.

Coming back to differential geometry: You can generalize a lot of it by working in a differentially cohesive (infinity-)topos. This is terribly indirect (in my opinion) and looses a lot of the intuitions. A topos is literally a model of a certain logic. Alternatively you can work directly in this logic (the "internal language" of the topos), where the differential geometric structure is available in the form of additional logical connectives. You are now talking in a language where it makes sense to talk about two points being "infinitesimally close" and where you can separate the topological from the infinitesimal structure.

At the same time you reap the benefits that there are many more models of differential cohesion than there are models of "R^n modeled in classical set theory". You can easily identify new applications, which might in turn suggest looking into different aspects of your theory. It's a virtuous cycle. :)

This approach is deeply unnatural when working in set theory or arithmetic. You have to encode _everything_ into sets or numbers and then these sets or numbers become the thing you are studying.

<comment><USER14> I only studied mathematics, never actually been a professional mathematician, and I feel like a big difference might be in what we see as "most mathematicians" (if you're working in this area you're probably more right than I am! but it's also possible your view is focussed on people working in areas related to yours).

I'd make the following alternative analogy: I code in Python on an x86, because that happens to be the machine on my desk. If you told me I should be using POWER instead of x86, I'd probably just shrug: I _could_ do that - <USER2> work is portable - but it's also completely irrelevant to my work. I think this would be how most people in say analysis, algorithms or combinatorics feel, for example.

</comment></comment></comment></comment></comment></comment><comment><USER15> I'm not sure if he's a finitist or ultrafinitist [1] but the uncountable reals are clearly a problem for him. I'd like to argue for their usage from a "soft" point of view as opposed to just giving axioms.

Mathematics and physics both began with the advent of astronomy: Babylonians and others were curious to trace star patterns and from there both physics and math developed in tandem and influenced each other greatly. Really, neither would have developed without the other.

Calculus was invented for calculations in physics. This gave rise to differential equations which we use to model so many nontrivial things. The differential eqns describe flow and continuity and arguably reality. Differentiation and smoothness can't be defined over finite sets in the same way. My philosophical counter-argument to finitists is that clearly we're on the right path to understanding the universe and nature when using the reals. It seems foolish to shy from this because computers have trouble computing some functions. Statements like "there are only finitely many atoms in the universe" don't improve our understanding of much but PDEs explain.

[1] [https://en.wikipedia.org/wiki/Ultrafinitism](https://en.wikipedia.org/wiki/Ultrafinitism)

<comment><USER13> > _Mathematics and physics both began with the advent of astronomy_

Arguably mathematics began with accounting and surveying and trade, and more generally with counting and measurement.

<comment><USER16> Never underestimate the power of taxes. On land, especially, for Geometry.

</comment></comment></comment><comment><USER17> If real numbers get this guy's goat, I think he will go ballistic when he hears about bra-ket formalism that quantum theory instructors foist upon students of physics.

<comment><USER12> According to classical mathematics, only a countable number of finite definitions of numbers exist. And an uncountable number of real numbers exist. Therefore almost all real numbers that exist do not correspond to any possible finite definition of a number.

Tell me. In what sense does an abstract concept exist that has no possible definition or unique description?

<comment><USER18> The amount of paper in the universe is finite, not countably infinite, which means almost all natural numbers can't be written down either. But despite its philosophical dubiousness, the set of natural numbers is still useful. If we can prove things about all natural numbers, it doesn't matter how much paper we have; the things we prove will still be true for any individual natural number we can write.

It's the same idea for the reals; we don't actually care about the vast majority of the real numbers, but since it's hard to know ahead of time which ones we will care about, we might as well prove things about all of them!

<comment><USER12> The thing is that the useful things that we can prove about natural numbers are ones that can be proven about practical ones. We can, at least in principle, follow the construction and wind up with whatever exists.

Now compare with the kinds of results that classical mathematics gives us. The Robertson-Seymour theorem (see [https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theo...](https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theorem) for the theorem) says that certain classes of graphs are characterized by a finite forbidden set. This means that membership can be tested by a polynomial time algorithm. However the construction provides no way to actually find that finite set. It also provides no way to find how many members it has. It not only provides no way to prove that you actually have all of them for a given class of graphs, but there are classes of graphs which it is impossible for us to prove that we actually have a complete list. Not only in practice, but in principle.

So the theorem asserts the existence of a finite set. But in what meaningful way does it exist, or is it finite?

</comment></comment></comment></comment><comment><USER19> He is obviously a well trained mathematician so reading his pieces (of which there are many) is akin to watching a tsunami come to shore---you cannot look away yet you know that this is a tragedy unfolding.

This said, his complaints about set theory would have been (probably) more convincing if he stated the axioms correctly. The Infinite Set axiom does not simply say that some nebulous infinite set exists it states the existence of a set with some very specific properties. His complaints about the undefined nature of a 'property' are also not above criticism: GB theory (equivalent to ZF) eliminates it completely.

<comment><USER20> In general his complaints regarding logic are incoherent. A function is not a messy weird object in mathematics; it's a possibly infinite set of ordered pairs where there are no duplicates of the first element of the ordered pair. That's it all it is, formally. Or "class" is a concept that has highly specific meaning in NBG theory—in ZFC it's not a formal distinction and so there's a transformation that must be obeyed where "x \in Class" means "{ x | x satisfies class definition}"; which due to Foundation must be the subset of some other, preexisting, class (and thus is Russell's paradox defeated). Almost all of these things _exist_ and _are present_ and _are extremely well defined_ in the theory, he just doesn't _like_ them for some reason.

</comment></comment><comment><USER21> When discussing a certain discipline, be it mathematics or any other, the issue of rigor and foundation are completely separate. Rigor is established if you are careful to always follow the axioms determined by the foundation. But the foundation, i.e. the _choice_ of the axioms can only be established in another, lower level, discipline, which, in the case of mathematics is philosophy.

In the early decades of the 20th century there were furious philosophical debates about the philosophy of the foundation of mathematics (between Brouwer's Intuitionism and Russell's Logicism, and also Hilbert's compromise of Formalism), but they all stemmed from an underlying assumption that mathematics gains its validity from some notion of philosophical truth. One could argue to no end on how the truth of mathematics is established, but a different perspective later emerged that avoids this debate altogether: that mathematics takes its validity not from truth but from utility (which is always relative to a specific task). We cannot say that one of those views is unacceptable, and if your position is that mathematical validity stems from utility, we cannot tell you that your foundation is shaky if its utility is established.

<comment><USER22> But axioms aren't assertions of truth. They're not declarations from on high about universal truths, they're how mathematicians ensure they're talking about the same things.

Mathematics is about exploring the consequences of your axioms. Axioms are chosen, not dictated by the universe. If your axioms turn out to be inconsistent, well, congratulations on successfully showing that consequence of those axioms.

Case in point: the axiom of choice. There is no objective truth value to it. The physical world gives us no 'answer'. Mathematicians can choose to adopt it, or not, and then explore the consequences. ( [https://en.wikipedia.org/wiki/Axiom_of_choice#Statements_con...](https://en.wikipedia.org/wiki/Axiom_of_choice#Statements_consistent_with_the_negation_of_AC) )

<comment><USER21> Well, that certainly was not the common perception in the philosophy of mathematics in the first half of the 20th century. Sure, they believed mathematics is an exploration of the axioms, but also that the axioms must be true in some deep philosophical sense. Brouwer wrote: _[A]n incorrect theory, even if it cannot be inhibited by any contradiction that would refute it, is none the less incorrect_ ,[1] and Russell believed that all of mathematics could be deduced from laws of logic that are true in the most absolute sense.

It is also doubtful that this is the perception today. If we want to use mathematics to derive any result about the physical world -- and we most certainly do -- our axioms must be consistent with it. How do you ensure that that is the case?

But such questions are not part of mathematics itself, just as the scientific method is not part of physics, but rather belong in a more fundamental discipline, called foundations of mathematics, or the philosophy of mathematics, which is usually studied by philosophers/logicians.[2]

[1]: On the Significance of the Principle of Excluded Middle in Mathematics, 1923

[2]: [https://plato.stanford.edu/entries/philosophy- mathematics/](https://plato.stanford.edu/entries/philosophy-mathematics/)

<comment><USER22> > they believed mathematics is an exploration of the axioms, but also that the > axioms must be true in some deep philosophical sense

That's a contradiction, and it's easy enough to show it: a mathematician can research the consequences of the axiom of choice, _and_ can research the consequences of its negation. It would be silly to deny that such research is legitimate mathematics.

Brouwer's statement strikes me as circular. Beyond that, it seems to me that the law of excluded middle, is patently false. I already gave a counterexample: the axiom of choice. Neither the axiom, nor its negation, has a derivable truth value to settle upon.

Ah, I see I'm behind the times [0]

As to Russell, he of course turned out to be wrong. I refer of course to Gödel. I'm not sure I see your point in mentioning him, or for that matter Brouwer - do explain.

> our axioms must be consistent with it

They don't. We hope that we have the mathematics to advance physics, but we needn't hope that _all_ mathematics is applicable to physics.

It's perfectly legitimate for a mathematician to explore the consequences of denying the axiom of choice. (I already linked to such.) Such work would presumably _never_ have application in physics, but it's still legitimate mathematics.

> How do you ensure that that is the case?

As you later allude to, that isn't a question of mathematics, it's a question of how and why mathematical discoveries map onto observable realities like physics and statistics. This is a completely legitimate line of question. The canonical article about how remarkable this is: Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".

> such questions are not part of mathematics itself

Agreed.

[0] [https://en.wikipedia.org/wiki/Law_of_excluded_middle#In_math...](https://en.wikipedia.org/wiki/Law_of_excluded_middle#In_mathematical_logic)

<comment><USER21> It's not a matter of legitimacy (which is a social construct) but of foundation. Russell, Brouwer and Hilbert believed that mathematics must be based on a solid philosophical foundation so that it leads to some "Truth." I am not saying this is the only way to think about the philosophy of mathematics -- in fact, my original comment said just the opposite -- but it was very much at the center of the mathematical world in the early decades of the 20th century, and is still a matter of debate among logicians. The philosophy of mathematics is a deep and complex subject. It does not seek to mathematically derive theorems from mathematical axioms, but to derive mathematical axioms from philosophical underpinnings -- whether they are physical reality, some Platonic reality, or even common sense. Logicians don't think the subject is silly at all, and if you're interested in learning more about it, the SEP link I provided above is a great place to start.

<comment><USER22> > it was very much at the center of the mathematical world in the early > decades of the 20th century

Ok, but those pre-Gödel mathematicians were profoundly mistaken about the nature of mathematics. To put it bluntly: they were wrong, so why should I care what they thought?

> It does not seek to mathematically derive theorems from mathematical axioms, > but to derive mathematical axioms from philosophical underpinnings

I don't agree. If you _don 't_ add new axioms, then you _are_ 'merely' deriving theorems. If you _do_ add new axioms, fine, you're just adopting a new set of axioms to explore through derivation.

If some set of axioms gives rise to interesting mathematical consequences, does that mean these axioms must have philosophical underpinnings? No. Does the 'validity' of the mathematics depend on the philosophical underpinnings of the axioms? No: it counts as mathematics either way.

It would be pure silliness to dismiss non-Euclidean geometry on the grounds that _Hey, you just made that up!_

Perhaps there's a gap somewhere in my account of things, but I'm not seeing one so far.

> to derive mathematical axioms from philosophical underpinnings -- whether > they are physical reality, some Platonic reality, or even common sense

Which of these underpins non-Euclidean geometry? How about fields with no practical applications? How about, as I've mentioned several times, research into what happens when you deny the axiom of choice?

They're all still valid fields of mathematics. The 'underpinnings' of the chosen axioms are of no consequence: it's valid mathematics either way.

The miracle is that we're able to be so successful with fields like physics and statistics. Picking the right special sets of axioms, we've been able to derive huge amounts.

> the SEP link I provided above is a great place to start

Looks it - will read when I get a moment.

<comment><USER21> > Ok, but those pre-Gödel mathematicians were profoundly mistaken about the > nature of mathematics. To put it bluntly: they were wrong, so why should I > care what they thought?

How do you know they were wrong? Has there been some breakthrough discovery in philosophy? And if they were, Gödel was wrongest of them all. He was the most extreme Platonist of them all.

> If some set of axioms gives rise to interesting mathematical consequences, > does that mean these axioms must have philosophical underpinnings? No. Does > the 'validity' of the mathematics depend on the philosophical underpinnings > of the axioms? No: it counts as mathematics either way.

Again, the points you are raising have been discussed by logicians as part of the philosophy of mathematics. As usual, things are not as simple as you may think.

> Perhaps there's a gap somewhere in my account of things, but I'm not seeing > one so far.

Perhaps that's because you've been thinking about this issue for a little bit, while logicians have been grappling with it for over a century. I may have confused you with the reference to physics. It is not the reason for the problem of foundation, but I used it as an example for a situation where something external to mathematics determines our choice of axioms.

The Wikipedia entry is also a good overview, but as usual, contains a few (sometimes serious) inaccuracies: [https://en.wikipedia.org/wiki/Philosophy_of_mathematics](https://en.wikipedia.org/wiki/Philosophy_of_mathematics)

<comment><USER21> BTW, if you want just a teaser to what it is that you may be missing, here's one:

That mathematics explores the theorems derivable from axioms tells us little. Is mathematics about the formal manipulation of the symbolic expression of those axioms, some (nondeterministic) Turing machine, chewing up and spitting out strings of symbols? Nearly all mathematicians would say not (including Hilbert's Formalism, which some gravely mistake for saying mathematics is just what I described). But if not, this means that the linguistic symbols _mean_ something, and in analytical philosophy, meaning is a sort of a mapping from linguistic terms to something outside the language. But if mathematical formulas mean something -- i.e. refer to something outside them -- what is the nature of that thing, and, more importantly, how do we learn about it?

<comment><USER22> > How do you know they were wrong? Has there been some breakthrough discovery > in philosophy?

Of course there has! Gödel! As you said, _Russell believed that all of mathematics could be deduced from laws of logic that are true in the most absolute sense_. Gödel showed that this is impossible, and his discovery ended Russell's project overnight. Russell was fundamentally mistaken about the nature of mathematics. No two ways about it.

I already linked to the Wikipedia discussion of why Brouwer's idea about the law of the excluded middle, seems no longer to be taken seriously.

> Gödel was wrongest of them all. He was the most extreme Platonist of them > all.

Maybe so, I'm afraid I really don't know his philosophy.

> if mathematical formulas mean something -- i.e. refer to something outside > them -- what is the nature of that thing, and, more importantly, how do we > learn about it?

But the mathematics derives the same with or without associating real-world meaning. Seems to me that this is enough to demonstrate that the mapping to something beyond the mathematics, is something that should be treated as quite separate from the mathematics itself (which is 'merely' axioms + consequences).

Indeed, we see this in action with fields of mathematics that find real-world applications only years after the discovery of the mathematics itself.

Suppose a field of mathematics is found to have _several_ applications. Again, the mathematics is unchanged: the discovered applications are a different beast entirely.

Doubtless I'm not the first to take this line of thought.

> including Hilbert's Formalism, which some gravely mistake for saying > mathematics is just what I described

I'm afraid you're ahead of me again here -- that's still on my reading list.

Also, perhaps just a nitpick: nondeterministic Turing machines might differ from deterministic ones in terms of space/time complexity (that's an open problem), but they're just as impotent against non-computable problems. Were you thinking of some kind of _probabilistic_ machine?

<comment><USER21> You seem to think that philosophy is about settling issues. It's more about understanding the question better.

I also think you're confusing Russell with Hilbert, and it is not accurate that Gödel destroyed Hilbert's project, just changed its nature (or, rather, destroyed the original understanding but not subsequent ones). But Hilbert's idea was actually much more in line with yours -- he also believed that mathematics is about the process rather than some absolute truth, but in order to show that the process can lead _anywhere_ it was important for him to prove consistency. After all, if our mathematics can prove _any_ proposition (including, say, 1=0) then it's rather useless, whether or not it's "valid" in some sense.

> I already linked to the Wikipedia discussion of why Brouwer's idea about the > law of the excluded middle, seems no longer to be taken seriously.

I think that neither Brouwer nor that Wikipedia article says what you think they do. :) There's a whole branch of logic, intuitionistic logic, and mathematics, constructive mathematics, that are largely based on Brouwer's ideas and rejection of LEM. They are particularly popular among some kind of computer scientists, BTW.

> But the mathematics derives the same with or without associating real-world > meaning. Seems to me that this is enough to demonstrate that the mapping to > something beyond the mathematics, is something that should be treated as > quite separate from the mathematics itself

I'm not talking about _real world_ meaning, nor "beyond mathematics", but beyond the formula (as a string). If the _strings_ refer to anything, what is the nature of the things they refer to?

> Also, perhaps just a nitpick: nondeterministic Turing machines might differ > from deterministic ones in terms of space/time complexity (that's an open > problem), but they're just as impotent against non-computable problems. Were > you thinking of some kind of probabilistic machine?

No, I simply meant that deduction in a formal system (like first-order logic) is a nondeterministic computation, and to emphasize the perspective that math is just a manipulation of symbols without meaning I referred to Turing machines. That they cannot settle non-computable problems is irrelevant, because neither can mathematicians, and whatever mathematicians can do, so can a TM.

<comment><USER22> > You seem to think that philosophy is about settling issues. It's more about > understanding the question better.

I'm not sure that's the whole story. The decline of logical positivism was a process of philosophers discovering fatal flaws with it and discarding it, no?

> I also think you're confusing Russell with Hilbert

Oops! Absolutely right!

> it is not accurate that Gödel destroyed Hilbert's project, just changed its > nature (or, rather, destroyed the original understanding but not subsequent > ones)

Perhaps you're right - I'm not qualified to discuss things like proof theory I'm afraid.

> if our mathematics can prove any proposition (including, say, 1=0) then it's > rather useless, whether or not it's "valid" in some sense.

Sure, provided we can maintain the distinction between a situation where the 'principle of explosion' applies, and situations where we're merely adopting exotic axioms like in non-Euclidean geometry. I imagine this distinction is fairly straightforward in practice: either there's contradiction and inconsistency, or there's not. (Ignoring of course the question of how we could know.)

> I think that neither Brouwer nor that Wikipedia article says what you think > they do.

Perhaps so, but doesn't the existence of something like the axiom of choice, disprove the law of excluded middle? (At least when it's applied universally.)

> beyond the formula (as a string). If the strings refer to anything, what is > the nature of the things they refer to?

Ah, right. Well I'm not arguing against 'notions not notations'. The maths derives the same whether we use conventional symbolic representations, or not.

So sure, there's a correspondence to something beyond the string itself (and not merely in the sense that you can substitute each symbol for an alternative, a la alpha equivalence). Presumably the correspondence is between the formula, and some space of facts.

I see a 'problem of interpretation' here - some amount of 'you have to know what it means', such as with clumsy ambiguous mathematical notations [0]. I don't know if that's a serious problem though.

> deduction in a formal system (like first-order logic) is a nondeterministic > computation

I'm afraid I don't follow. You can perform a derivation as many times as you like, you'll always get the same result, no?

> That they cannot settle non-computable problems is irrelevant, because > neither can mathematicians, and whatever mathematicians can do, so can a TM.

Agree -- there's no good reason to assume brains cannot be simulated by computers (which is what that question boils down to, roughly speaking), at least in principle.

A surprising number of people disagree on that point though. Wishful thinking, I suspect. The same patterns arises in discussions of free will.

...and we're back to philosophy :P

[0] This particular bit of indefensibly brain-dead notation never ceases to bother me. [https://math.stackexchange.com/a/932916/](https://math.stackexchange.com/a/932916/)

<comment><USER21> > The decline of logical positivism was a process of philosophers discovering > fatal flaws with it and discarding it, no?

Few things in philosophy are definitively discarded (and if they are, they can come back in some revised form); they may fall out of fashion.

> Ignoring of course the question of how we could know.

But that was precisely Hilbert's point. The problem was this: either you took Brouwer's intuitionism, which has no inconsistencies but is inconvenient, or you take classical mathematics because it's useful. But if you do, you need to know that it's consistent, but you can't.

> but doesn't the existence of something like the axiom of choice, disprove > the law of excluded middle?

No. LEM is an axiom that you either include (in classical mathematics) or not (in constructive mathematics).

> I don't know if that's a serious problem though.

The problem is not exactly that of interpretation, but a more basic one: if the formulas refer to something, what kind of thing is that thing, and if that thing exists independently of the formulas, how do we know that the formulas tell us the truth about those things? Again, there is no definitive answer to this question, just different philosophies.

> You can perform a derivation as many times as you like, you'll always get > the same result, no?

If you start with a set of axioms, you can apply any inference rule in any order to any subset of them. There's an infinity of possible derivations, that yield all the theorems in the theory. We can look at that as a form of nondeterministic computation (that nondeterministically chooses an inference) .

> A surprising number of people disagree on that point though.

Gödel did.

<comment><USER22> > Few things in philosophy are definitively discarded (and if they are, they > can come back in some revised form); they may fall out of fashion.

Disagree.

Some philosophical ideas seem increasingly unsustainable in the face of mounting scientific knowledge. Vitalism, for instance.

In a similar vein, I'd say we're seeing an ongoing erosion of dualism in philosophy of mind, which will be unlikely to recover. Like with vitalism, the more we learn from science, the less magic we need to explain ourselves, be it 'life', or consciousness.

In the case of logical positivism, it was a case of showing the position to be unsustainable on its own terms. That's analogous to disproving a scientific hypothesis - I don't see it coming back.

> either you took Brouwer's intuitionism, which has no inconsistencies but is > inconvenient, or you take classical mathematics because it's useful. But if > you do, you need to know that it's consistent, but you can't.

Neat. I see I'll have to do my homework.

> LEM is an axiom that you either include (in classical mathematics) or not > (in constructive mathematics).

But if you _do_ include it, don't you have to commit arbitrarily to either AC or ¬AC?

> if the formulas refer to something, what kind of thing is that thing, and if > that thing exists independently of the formulas, how do we know that the > formulas tell us the truth about those things?

Isn't this 'just' a question of knowing that the correspondence is valid?

> There's an infinity of possible derivations, that yield all the theorems in > the theory. We can look at that as a form of nondeterministic computation > (that nondeterministically chooses an inference) .

Right, I'm with you. Infinite graph traversal.

> Gödel did.

Roger Penrose too. Honestly I find his position to be almost risibly weak. It's plain old quantum mysticism and wishful thinking, as far as I can tell. Microtubules are meant to be essentially magical? Seriously? Here he is explaining his position (takes about 10 minutes) [https://youtu.be/GEw0ePZUMHA?t=660](https://youtu.be/GEw0ePZUMHA?t=660) and here's the Wikipedia article on his book about it: [https://en.wikipedia.org/wiki/The_Emperor%27s_New_Mind](https://en.wikipedia.org/wiki/The_Emperor%27s_New_Mind)

<comment><USER21> > Some philosophical ideas seem increasingly unsustainable in the face of > mounting scientific knowledge. Vitalism, for instance.

OK, but the philosophy of mathematics is a more slippery beast.

> But if you do include it, don't you have to commit arbitrarily to either AC > or ¬AC?

No. You can have a theory that's consistent with either.

> Isn't this 'just' a question of knowing that the correspondence is valid?

Correspondence to _what_? Are those objects platonic ideals? Are they abstractions of physical reality? You can answer this question in many ways. But whichever way, this question of soundness (formal provability corresponds to semantic truth) rests on us knowing what is true.

Some philosophies of mathematics say that the question is unimportant: it doesn't matter if we get the "truth" part right, all that matters is that mathematics is a useful tool for whatever we choose to apply it to (this doesn't even mean applied mathematics; one valid "use" is intellectual amusement).

<comment><USER22> > No. You can have a theory that's consistent with either.

I think I see your point. If your theory has no way to express the question _Is the AC true?_ then the LEM is no issue, as there's no 'proposition' to worry about at all.

> Are those objects platonic ideals? Are they abstractions of physical > reality?

My intuition is to favour the former, as the latter seems a much stronger claim.

It seems reasonable to say that _any_ mathematical system exists as a platonic ideal, but it's plain that not all mathematical systems abstract physical systems, and we shouldn't be quick to say that we know that _any_ mathematical system does so. That's an empirical question that - true to Popper - can never be positively proved.

<comment><USER21> > If your theory has no way to express the question Is the AC true? then the > LEM is no issue, as there's no 'proposition' to worry about at all.

That's not what I meant. I meant that choice can be neither proven nor disproven. The philosophical fact that, due to LEM, it must either be true or not is irrelevant, because you cannot rely on it being true or on it being false.

> My intuition is to favour the former, as the latter seems a much stronger > claim.

Well, Platonism is a popular philosophy of mathematics among mathematicians, but many strongly reject it.

<comment><USER22> > can be neither proven nor disproven. The philosophical fact that, due to > LEM, it must either be true or not is irrelevant, because you cannot rely on > it being true or on it being false

So it's _similar_ to, but not the same thing as, modifying the LEM to permit _Unknowable_ as a third category (beyond _the proposition is true_ and _its negation is true_ ). Instead we maintain that it has a truth value one way or the other, but that it happens to be both unknowable and of no consequence.

<comment><USER21> > modifying the LEM to permit Unknowable as a third category

LEM doesn't need to be modified, and it's not a third category. In classical logic (with LEM), unlike in constructive/intuitionistic logic (no LEM), truth and provability are simply not the same -- in fact, it is LEM that creates that difference.

> Instead we maintain that it has a truth value one way or the other, but that > it happens to be both unknowable and of no consequence.

Precisely! That is the difference between classical and constructive logic. In constructive logic truth and provability are the same, and something is neither true nor false until it has been proven or refuted. But before you conclude that this kind of logic, without LEM, is obviously better (philosophically), you should know that any logic has weirdnesses. What happens without LEM, for example, is that it is not true that every subset of a finite set is necessarily finite. ¯\\_(ツ)_/¯

</comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment><comment><USER23> Did anyone understand this bit?

> The approaches using equivalence classes of Cauchy sequences ... suffer from > an inability to identify when two "real numbers" are the same

Perhaps there's no _computable_ general method, but it seems like it highlights an even bigger problem which remained unspoken. There is an inability to tell when a sequence of numbers approaches zero!

<comment><USER24> Yup, you can define _distinctness_ of constructive real numbers as two algorithms returning rationals that will differ by more than the approximation error ε they were given as input, for some arbitrarily small ε - but equality involves proving that two algorithms will _never_ be apart in this way - <USER3> this cannot be done in general. As you say, even comparison with zero is problematic. So instead of equivalence relations, you need to define the _apartness_ relation - the notion that a supposed equivalence between two such numerical algorithms can be constructively refuted. This is nothing new - it's a well-known part of constructive math, and is also the sensible way to formalize numerical analysis.

</comment></comment><comment><USER25> A large part of his article seems concerned with the deficiencies and the lack of rigor in first year calculus textbooks. But I think, pedagogically, isn't it appropriate to introduce a subject intuitively and hand-wavingly, before proceeding to a more rigorous treatment? There's a reason students learn calculus before analysis.

</comment><comment><USER26> There are MANY foundations for set theory, some of them very different from each other. It's completely pointless to treat the subject as briefly as this post does.

</comment><comment><USER27> I'm curious to hear what this guy thinks of the esoteric math in higher level economics... how base assumptions there are built and extrapolated on to ultimately guide economic policy. He would have a field day with the assumptions used in DSGE (which there are empirics to contradict those assumptions, and economists keep using those assumptions anyway).

</comment><comment><USER28> Tried watching his video on limit ... but what was said prevented me from wasting my time further. Contrary to the claim of math foundation, it is apparent that the guy does not understand math despite being a stats professor. It is not even wrong.

</comment><comment><USER29> I would start with identity, that's all everything boils down to, and that math is as much a language, a shorthand to express ideas and communicate across the world like some state department, as it is computational.

Then I would explain that imaginary numbers mean harmonics. exponential functions give you a derivative, one function can serve as input to another, PID control, ... ... and that's about it.</comment>


Android App: Cyber Security News Hub - <AUTHOR> https://play.google.com/store/apps/details?id=cyber.security.news <comment><USER2> Looks pretty awesome for cybersecurity professional. My primary device iOS.. Please let me know if there's anything for the iOS.

<comment><AUTHOR> As of it's only for the android. Will share once if they release for the iOS.</comment></comment>


Javascript on the GPU - <AUTHOR> http://ajaxian.com/archives/javascript-running-on-the-gpu?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed:+ajaxian+(Ajaxian+Blog)&utm_content=Google+Reader

<comment><USER2> Too bad this doesn't actually run JavaScript on the GPU.

<comment><USER3> This gives computational access of the GPU to JavaScript.

See: <http://groups.google.com/group/jetpack-to-cuda/?pli=1>

<comment><USER2> Even that is a very generous description. The guy hand-coded a lot of boilerplate to expose one CUDA kernel to JavaScript.

</comment></comment></comment><comment><USER4> It would be frickin' awesome if GPU access became standard for Javascript through a standard API (OpenCL?). A COMPLETE Flash-killer.</comment>


The Failure of iMessages - <AUTHOR> http://nuncamind.com/blog/2011/12/28/the-failure-of-imessages/

<comment><USER2> > Sending a text to either contact would get to her iPhone 4S, but the phone > number contact would send an SMS, and the e-mail address would send as an > iMessage.

Nope. Phone numbers also receive iMessages just fine.

<comment><AUTHOR> Yes, that's how it works with the rest of my contacts, but for this one for some reason she had an exclusive SMS contact and a separate iMessage contact. The iMessage contact was associated with an email address and SMS contact was associated with a phone number.

<comment><USER3> That's quite possible (and not a bug) if she has more than one device - iMessage disabled on the phone (which would force phone number messages to be SMS) but the email address turned on for iMessage on another device. I had my iPhone/iPad set this way for a while to allow me to send messages from either device without getting replies back to both devices.

<comment><AUTHOR> That actually sort of makes sense, although I also have an iPad and used to use it for iMessages occasionally. But no one has had a similar issue with me as a contact (I've checked).

Edit: also I've checked with her and she has iMessages enabled on every iDevice she owns.

</comment></comment></comment></comment><comment><USER4> to be fair, distributed consensus is essentially impossible. iMessage is definitely an improvement on SMS, though.

read up on the 'two generals problem'

<http://en.wikipedia.org/wiki/Two_Generals%27_Problem>

"Because acknowledgement of message receipt can be lost as easily as the original message, a potentially infinite series of messages is required to come to consensus."

<comment><AUTHOR> This is very true, but my main issue was my phone receiving a delivery confirmation when the recipient never actually received the message. That seems like unacceptable behavior to me. Assuming the messages are IDed in some way, why can't phone A just keep sending message 1 to phone B until it receives a confirmation for message 1 from phone B? And phone B can just ignore any duplicate message 1's and send back confirmations for them anyway.

Obviously this becomes a very complex problem over a large scale, but I feel like Apple can do better than this.

<comment><USER4> I would be very disappointed to be able to recreate the scenario you describe.

'Delivered' should mean that the distributed transaction was 'committed', aka Alice has committed Bob's message :)</comment></comment></comment>


Rapere Intercept Drone - <AUTHOR> http://rapere.io/ <comment><USER2> I wonder if projects like this will trigger the development of drone countermeasures, leading to an interesting arms race and regular battles in the skies above us.

<comment><USER3> If you're legally allowed to destroy a drone on your property, then instead of using another drone why not just use a shotgun?

Right now you can't : [http://www.slate.com/blogs/future_tense/2014/10/03/new_jerse...](http://www.slate.com/blogs/future_tense/2014/10/03/new_jersey_man_shoots_down_drone_over_his_property_gets_arrested.html)

<comment><USER4> The issue is that there is no defined elevation above land you own that is designated part of your property.

<comment><USER5> My understanding (from an undergraduate US law class) is that you actually own the column defined by your property lines up into the heavens (and down into the Earth). You implicitly grant an easement (a formalized privilege allowing someone else do something with your property) to aircraft and other things like that. I imagine that this easement doesn't extend to drones doing something they're not supposed to.

<comment><USER6> Slate: How much of the airspace above your home do you own? [http://www.slate.com/articles/news_and_politics/explainer/20...](http://www.slate.com/articles/news_and_politics/explainer/2013/07/photographer_george_steinmetz_arrest_how_much_airspace_do_you_own.html)

</comment></comment></comment></comment></comment><comment><USER7> Destruction of property is destruction of property. The logic behind this seems to imply that you could legally take steps to crash a manned helicopter merely because it was flying over your property. That is almost certainly not the case.

Another example: Some of the wealthiest people in California live on a street called La Jolla Farms Rd. (supermarket magnate Ron Burkle owns a 58,000 sq ft home there). One of the hallmarks of living on this street is that hang and paragliders taking off from the La Jolla Gliderport fly over these homes constantly during the day - many with cameras. Would it be legal to take any of them down? My guess is you would be charged with attempted murder.

<comment><USER8> Hot air balloons frequently fly over Rancho Santa Fe nearby, as well. Local ordinances are such that most if not all of them are doing so illegally, if I recall correctly, but that still doesn't mean shooting them down would be legal.

<comment><USER9> Private property owners generally only have airspace rights in so far as "enjoyment". That, is they can shoot fireworks, have balloons, loft their own drones, etc.

Unless a pilot of an aircaft (including balloons, etc) is somehow being intentionally disruptive (e.g., hovering their helicopter over an ex- girlfriend's birthday party), they have a higher obligation to safe flight. And if that means overflying Coral Reef Ranch, Gwendolyn Sontheim Meyer's show ponies are just going to have to deal with it.

</comment></comment></comment><comment><USER10> Is this a joke? There have to easier ways than physically dropping a string into a rotor.

They are radio controlled. A handful of parts from radioshack, or even just an injection-capable wifi dongle, and they will drop from the sky without you leaving the ground.

<comment><USER11> _> A handful of parts from radioshack, or even just an injection-capable wifi dongle, and they will drop from the sky without you leaving the ground._

Jamming RC control is not that straightforward, and for good reasons: it's common for several pilots to operate RC-controlled vehicles from single airfield simultaneously, thus RC radios evolved to avoid interference with one another.

While modern RC radios indeed usually operate on 2.4GHz band common with WiFi, they typically employ frequency-hopping spread-spectrum communications[1] that has nothing to do with WiFi and is designed with degree of robustness against interference.

Secondly, many `drones' (in this context, quad-rotors and multi-rotors) are catable of semi-autonomous operations, such as position holding, following a pre-planned flight path, and automatic return-to-base, as both aide to pilot and a natural protection against losing radio contact with the remote control.

To combat those capabilities you would have to jam GPS signal too, and most probably the end result would be drone simply drifting with wind and slowly changing altitude, instead of dropping out of the sky right away. Not to mention jamming nearby neighbours and motorists, and illegality of such jamming [2].

[1] [https://en.wikipedia.org/wiki/Radio- controlled_aircraft#Freq...](https://en.wikipedia.org/wiki/Radio- controlled_aircraft#Frequencies_and_sub-channels)

[2] [http://www.gps.gov/spectrum/jamming/](http://www.gps.gov/spectrum/jamming/)

<comment><USER12> Indeed, my Parrot has a preprogrammed behaviour in case of loss of signal: cease lateral movement and descend to hover until signal is reacquired (or the battery runs low, in which case land). If it were flying waypoints, it'd ignore the jamming as it ignores signal loss - and part of the fun flying waypoints is sending Mr Crashy out of direct control for a short time.

Jamming's a fantasy attack just like shotguns are.

</comment></comment></comment><comment><USER13> I thought about making an anti-drone drone that would basically fly in front of another drone and release a fine spray of some sort of air-hardening resin which should foul control surfaces and mechanical parts.

Haven't done it yet.

</comment><comment><USER14> I'm curious if a microwave's magnetron strapped to the pursuit drone could act as a poor man's Active Denial System and fry the other drone.

<comment><USER15> Serious practical problems:

1\. Weight of the magetron, battery, and power supply to power the magnetron.

2\. Shielding required on the aggressor drone to prevent it from frying itself.

</comment></comment><comment><USER16> Whoa, that's an unfortunate name.

<comment><USER17> That's the same strange attitude that got a man fired from DC gov't for using the word "niggardly."

If your sensitivity is such that you can't handle similarities in word sounds I recommend you lock yourself indoors cause it's a tough world out there.

<comment><USER16> To be perfectly clear, I did a double-take because I mis-read it the first time, I'm probably not alone on this, and I'd consider it an ill-advised name.

You could consider me oversensitive, but would you choose Niggardly for a brand name?

<comment><USER18> Niggard Systems: a company devoted to conserving capital resources through a proactive approach towards analytics and trends in money markets.</comment></comment></comment></comment>


GSM codes for replacing iPhone VM with Google Voice - <AUTHOR> http://www.geckobeach.com/cellular/secrets/gsmcodes.php

<comment><USER2> Or this: [http://www.google.com/support/forum/p/voice/thread?tid=56a63...](http://www.google.com/support/forum/p/voice/thread?tid=56a6385ce48d6e5d&hl=en)

</comment><comment><USER3> Before you change to Google Voice for voicemail, please note there is no way to make GV pick up on the first ring. If a call 'times out' from your cellphone it will then ring another few times on GV EVEN IF YOU HAVE DO NOT DISTURB ENABLED. With my phone the wait is so long it's impractical to expect callers to hold on for it.

Please understand, I think GV is primarily good but for many of us this 'lack of feature' is a deal breaker.

</comment><comment><AUTHOR> Dial this: * 002 * 6175551212 # ... replacing the second string of numbers with your own. That should direct your caller to Google Voice messaging for busy/unreachable/no-answer on your iPhone (or other GSM network) but will still give you plenty of time to answer the call as usual.

<comment><USER2> So ##002# will cancel and return to AT&T VM?

<comment><USER4> No, it will cancel voicemail altogether. The phone will ring indefinitely, or eventually disconnect.

To return to AT&T VM, you'll need the phonenumber for that, which should be possible to obtain with _#002#, then re-set with_ 002*(AT&T VM number)#

</comment></comment></comment><comment><USER5> Phones normally have these configuration features built in, in my experience. That is, you go into the configuration menus, and you can query and reassign your call forwarding settings.</comment>


What problem did your first script solve? - <AUTHOR>

Today I wrote my first (trivial, but "real") bash script... 10 years after studying linux scripting in university: https://gist.github.com/3714934<p>Do you remember what was the first problem you scripted your way out of or how long after you learnt your first scripting language? <comment><USER2> I don't remember my first script. Though I _do_ remember the most value I've ever gotten out of a script.

To set the scene, I had a high school science class, and in it you were supposed to do journal entries. (Read: Notes.) You kept track of all your notes and put them in a table of contents. The instructor kept all the notes on his website. It was the night before the last day of school. Or the night before that. I hadn't turned in my organized notes, and thus had a C in the class. I needed them turned in yesterday.

So what I did was:

1\. Download the powerpoint of all the notes.

2\. Use libreoffice to convert it to pdf.

3\. Used less to read the data from the pdf into text.

4\. Used sed to remove the garbage characters from the text.

5\. The file had uniform formatting, so I went over it with sed again to turn it into an HTML file.

6\. Went over the HTML file by hand to correct anomalies and fill in answers to questions. (This was the 'real' assignment, fill in various questions throughout the notes.)

7\. Wrote out an table of contents. (Which in retrospect could have been done with a sed script.)

8\. Turned the whole thing in.

He never actually read it (As it was quite apparent from a glance that I had done it.), but I got an A in the class; and a night of no sleep.

</comment><comment><USER3> It was a script for invoking a C program stored in all of the machines forming a cluster of 16: the whole point of the thing was to generate traffic between the PCs in a structured fashion, measuring the bandwidth and latency results.</comment>


Evolutionary algorithms and analog electronic circuits - <AUTHOR> http://www.hforsten.com/evolutionary-algorithms-and-analog-electronic-circuits.html <comment><USER2> One thing stands out when you try playing with evolutionary systems.

Evolution is _really_ good at gaming the system. Unless you are very careful at specifying all of the constraints that you care about you can end up with a solution that is very clever but not quite what you had in mind. Here power consumption is the issue. If you tried to evolve a sturdy chair you might end up with something that is 1mm tall. or maybe a fuel efficient car that exploits continental drift.

For circuit simulation there are a bunch of potential pitfalls beyond power consumption. I think you would probably need to do multiple runs with components of varying values within their specified precision. I can see evolution getting some sort of benefit by exploiting the fact that two identically specced components behave _exactly_ the same way. Something that would not happen in real life.

<comment><USER3> > I think you would probably need to do multiple runs with components of > varying values within their specified precision.

That's called Monte Carlo analysis. It's important for standard simulation applications as well because most components are specified with certain tolerances. Your amplifier might look stable at the expected component values, but if all of your resistors are at the bottom or top of their tolerance range, it might become unstable!

Commercial SPICE simulators (like HSPICE, for example) come with the option to perform this built-in. You can do Monte Carlo analysis with NGSPICE, but you have to organize the input and output yourself.

> I can see evolution getting some sort of benefit by exploiting the fact that > two identically specced components behave _exactly_ the same way. Something > that would not happen in real life.

You get pretty close with matched transistors, especially when they're on the same die. But yeah, Monte Carlo.

<comment><USER4> Another advantage of this, is that it'll smoothen the fitness landscape somewhat, creating better convergence.

Another advantage of using simulated annealing instead of evolutionary algorithms is that you can add this sort of noise in pretty much for free (instead of doing multiple runs, you basically just lower the cooling rate).

</comment></comment></comment><comment><USER5> Reminds me of this: [http://www.damninteresting.com/on-the-origin-of- circuits/](http://www.damninteresting.com/on-the-origin-of-circuits/)

>The plucky chip was utilizing only thirty-seven of its one hundred logic gates, and most of them were arranged in a curious collection of feedback loops. Five individual logic cells were functionally disconnected from the rest-- with no pathways that would allow them to influence the output-- yet when the researcher disabled any one of them the chip lost its ability to discriminate the tones. Furthermore, the final program did not work reliably when it was loaded onto other FPGAs of the same type.

<comment><USER6> Robustness could have been added as one extra constraint. I.e. the fitness function would also value the ability of the circuit to work on many instances of the FPGA.

This reminds me of Physically Unclonable Functions (PUFs) that tries to utilize differences in manufactured devices as a method of distinquishing unique devices. This is used for identification and authentication. There are for example PUFs that use differences in delays between logic blocks in FPGAs to generate unique responses to applied patterns/challenges.

See for example: [http://en.wikipedia.org/wiki/Physical_unclonable_function](http://en.wikipedia.org/wiki/Physical_unclonable_function)

<comment><USER7> Even with that setup you end up with overfitting after a point. I.e. instead of getting something that works on every FPGA of that type, you start getting things that work on the specific FPGAs you provide. The same thing happens in machine learning for things like recognizing photos: after a while your algorithm stops recognizing cars and starts just recognizing those specific photos of cars.

Ideally, you want to take a bunch of FPGAs, pull out a random subsample of them only for acceptance testing, and stop evolving the circuit when the performance on the acceptance testing subset starts getting worse.

<comment><USER5> Even if it worked on the specific FPGAs you provide, it might not work reliably in different temperatures like the one in the article, or if the noise is slightly further away, etc.

There is no way to stop overfitting because it's difficult if not impossible to test it in every possible environment we want it to work under.

<comment><USER7> There are ways to catch overfitting: [https://en.wikipedia.org/wiki/Cross- validation_%28statistics...](https://en.wikipedia.org/wiki/Cross- validation_%28statistics%29)

<comment><USER5> That's not really relevant to this. That is for selecting hyper-parameters for statistical models.

<comment><USER7> I know the article doesn't mention it, but you can use the exact same techniques for preventing overfitting in machine learning.

<comment><USER5> That's basically what I said, and this is optimization not machine learning. The problem is the genetic algorithm fits the the specifics of the FPGA and the environment it is optimized in, and doesn't work reliably in other environments or FPGAs.

</comment></comment></comment></comment></comment></comment></comment></comment><comment><USER8> This made me think of an article I read years ago about evolving circuits (albeit digital ones) on FPGAs: [http://discovermagazine.com/1998/jun/evolvingaconscio1453](http://discovermagazine.com/1998/jun/evolvingaconscio1453)

<comment><USER9> There's also evolved antennas.

[http://en.wikipedia.org/wiki/Evolved_antenna](http://en.wikipedia.org/wiki/Evolved_antenna)

</comment></comment><comment><USER10> This reminded me of interesting work Cornell has done in evolving circuits that have no single points of failure [1].

One thing to notice is the emphasis on comparing the GA performance to other search methods (like hill climbing). It would be nice to see that more in blog posts like this.

[1]: [http://creativemachines.cornell.edu/sites/default/files/GPEM...](http://creativemachines.cornell.edu/sites/default/files/GPEM09_Kim.pdf)

</comment><comment><USER11> Previous: [https://news.ycombinator.com/item?id=4214476](https://news.ycombinator.com/item?id=4214476)

</comment><comment><USER12> If you like that then you will love this project I have been working on.

[https://github.com/polysome/evolvable_motherboard](https://github.com/polysome/evolvable_motherboard)

</comment><comment><USER13> This is cool. I actually sat down just today to start coding something that would help me automate my exploration of a tunable band-pass filter (or set of tunable filters which could be switched).

In my degree programme I did computer systems, not RF - but even this involved designing/building microwave amplifiers, playing with network analyzers and learning transmission line theory. I wish I could say that this work ~10 years ago has properly prepared me for the task but it seems I have many months of weekend study ahead of me...

In any case, even back then the RF students were generating pretty funky antenna designs out of modeling tools that ran for days sweeping through physical dimensions, numbers & types & topologies of elements, etc. to optimize toward some goal.

<comment><USER3> Analog Devices has a filter wizard[0] on their site, which can help to create filters using their components. It might fit your needs, or at least give you some idea of what might be required.

[0] [http://www.analog.com/designtools/en/filterwizard](http://www.analog.com/designtools/en/filterwizard)

<comment><USER13> It's a cool tool of course, but I have an interesting set of spurs to filter out, and they're quite close to the carrier in some places, over quite a large frequency range. I have a set of fixed filters that mostly works, but the next design will need to more completely suppress these spurs over the entire range.

</comment></comment></comment><comment><USER14> A bandgap circuit subtracts log(A.x) and log(B.x) to get a ratio log(A/B) that is independent of x (x>0), and to achieve this topology by evolution is a striking result. The question is whether one would trust the resultant topology in the absence of a known pattern. This is not casting a doubt on the evolutionary algorithm, it is more about the quality of the device compact models and the ability of the circuit equation solver to capture subtle instabilities and starting problems.

My guess is that today's compact models _and_ solvers are both good enough for us to contemplate a 'Turing test' for analog circuit design.

</comment><comment><USER15> My old tutor at Reading Uni did this in the 1990s. Might be worth checking out his work:

[http://www.personal.rdg.ac.uk/~stsgrimb/publications.htm](http://www.personal.rdg.ac.uk/~stsgrimb/publications.htm)

</comment><comment><USER16> This kind of work was published on scientific american about ~10 years ago.

Anyway this post was more detailed than the introductory on scientific america. This kind idea did not expolode over the past ten years. Something in detail might be wrong.

<comment><USER17> Most genetic algorithms break when you try to make them solve too complicated problems. They do not scale really well. Mother Nature has actually a lot of hacks to scale well. Evolution is a process that evolved by itself. If you want a genetic algorithm to solve complex problems, at one point you have to let the reproduction algorithm itself to evolve.

To give you an idea, only recently have we discovered that totally different species can exchange genetic sequences through virus (it is called horizontal gene transfer) and we are not really sure why sexual reproduction is a good idea when you can already mutate, have horizontal transfers and clone yourself.

"Make random mutations, select the best" is really not how nature works.

<comment><USER18> Interesting. Do you have any good links for learning more about the evolution of evolution? Thanks!

<comment><USER13> It's interesting to read about hypothesized age of plant (and I guess animal) species based on their molecular "clock rate" (rate of mutations) in different parts of the genome.

The mutations indeed are far from random. More important regions which fundamentally affect the viability of the organism evolve incredibly slowly and conservatively. The less important bits are less restricted and mutate more readily.

Additionally it's interesting to consider an individual in the context of its lineage. Some branches are extremely rich in diversity but mightn't have the population numbers of more "boring" clades.

It's easy to mistake success at population size as the end-game, the winner if you will, of evolution. Population size helps but at the end of the day it might be the smaller population, more diverse clades that are more adaptable to environment changes and survivability into the future in general.

</comment></comment></comment></comment><comment><USER4> First important question to ask about any evolutionary algorithm experiment:

Did you check your experiment against a simulated annealing process?

It's simpler to implement, converges faster and gives better results. So far I am unaware of any optimizing problem that was solved better with an evolutionary/genetic algorithm than simulated annealing. That is, unless the evolution part (crossover, mainly) is inextricably connected to the problem at hand and therefore other algorithms are simply not suitable to even try.

</comment><comment><USER19> One thing to watch out with these sorts of approaches is you are actually improving on an exhaustive search of all possibilities (perhaps with some smart pruning).

<comment><USER20> What do you mean watch out? Isn't "improving on an exhaustive search of all possibilities (perhaps with some smart pruning)" a way of saying global optimization? Unrelated, great job with JuliaOpt, if that is you.

<comment><USER19> I guess what I'm getting at is a GA with 100% mutation is basically randomly generating solutions and evaluating them. Now, no one does that, but if your GA eventually explores a large amount of the search space in order to get a good solution then it suggests that its not the right approach. So yes, some sort of "global optimization" where you acknowledge you are basically going to look at the whole domain but avoid the silly cases/provably worse cases would be the alternative.

And yes it is, thanks!

</comment></comment></comment><comment><USER21> Very interesting, could you use this to build a good analog amplifier?

[http://nwavguy.blogspot.com/2011/07/o2-headphone- amp.html](http://nwavguy.blogspot.com/2011/07/o2-headphone-amp.html)

Is there any way from genetic algorithms to learn from good human designs as starting points and breed the together?

What about genetic algorithms for battery and solar cell design?

<comment><USER22> You can use it to build anything given enough time, and a proper full detailed and correct list. This includes things like: reaction when the input voltage goes dead, preventing poping, output resistance, harmonic distortion, ... If you would use this I recommend you try to use it on a small subsystem of the circuits, not the entire circuit, unless you are looking for something neat. I however don't know how practical this all is :)

</comment></comment><comment><USER23> One question to bear in mind when doing this sort of thing: just because it works in SPICE doesn't mean it's going to work as intended when you build it. SPICE is _very_ ideal world. That may or may not invalidate this approach.

Source: several years of arguing with SPICE in a professional capacity.

<comment><USER24> Unfortunately using SPICE pretty much requires knowing exactly how it works so that you understand it's limitations. In turn, this makes it hard to learn, especially for students.

</comment></comment><comment><USER25> At the github repo, it is mentioned to have a Linux machine to get started. What is a recent, decent Linux stack on a laptop to look at? I wanted to buy again a laptop for linux for some time already, and maybe someone here as some buying advice?

<comment><USER13> I've just started using it with Debian but I'd say the dependencies are readily available on any mainstream distro. Many Linux laptop users seem pretty happy with Lenovo, I'm typing this on an x230 - Lenovo tend to fairly consistently use well-supported chipsets.

Having said that you could use VirtualBox to get a Linux environment up fairly painlessly from Windows, if that's what you're on now.

</comment></comment><comment><USER26> This is a really cool way of tackling circuit design! Being able to compare the significant changes between similar designs is something I used to wish I was able to do with ease.</comment>


Pinterest Blocks Vaccination Searches in Move to Control the Conversation - <AUTHOR> https://www.wsj.com/articles/next-front-in-tech-firms-war-on-misinformation-bad-medical-advice-11550658601 <comment><USER2> This is incredibly worrying. I understand that anti-vax conspiracy theories are dangerous, but I can think of a ton of ways banning "bad medical advice", as determined by a $10/hr contractor at Pinterest, Facebook, etc. could end up hurting people with health problems by preventing them from sharing useful information. I have gender dysphoria and at one point considered getting on testosterone, but thanks to conversations with transmen and detransitioned women on social media, I learned about less-commonly discussed side effects and decided against taking testosterone. This is an area where research is still developing and there aren't a ton of long-term studies, so it's incredibly helpful to be able to learn from other people's experiences, even if they aren't yet confirmed by research.

Likewise, I know people who've had a post or comment removed by Facebook because it was erroneously interpreted as racist or sexist. Off the top of my head, I know a friend who was sharing information on ICE raids with friends who were immigrants and they got banned from Facebook for a couple of hours (he was unbanned after appealing). I know someone else who was sharing statistics on domestic violence that was interpreted as discriminatory. The corporations making these policies don't have a good enough understanding of political issues to determine whether a statement is hate speech - and hell, even people who are knowledgeable about politics and history disagree in a lot of areas.

<comment><USER3> > I have gender dysphoria and at one point considered getting on testosterone, > but thanks to conversations with transmen and detransitioned women on social > media, I learned about less-commonly discussed side effects and decided > against taking testosterone. This is an area where research is still > developing and there aren't a ton of long-term studies, so it's incredibly > helpful to be able to learn from other people's experiences, even if they > aren't yet confirmed by research.

I'm sorry for using your actual problem as a jumping-off point, but this is a real issue:

There are people called TERFs, or Trans-Exclusionary Radical Feminists, who think "being trans" doesn't exist, that trans people are all mentally ill and/or (in the case of transwomen) men trying to invade female spaces to cause havoc, and who are organized enough to turn being trans into a huge political clusterfuck.

More than it already is, I mean.

My point is, the project of cleaning up "Bad Medical Information" runs into politics even quicker than most would imagine, and TERFs are very, very good at playing the "You're misogynistic!" card early, often, and loudly. How much courage would a tech company have in the face of _that_ these days?

(They're also good at playing the "TERF is a slur! Cis is a slur!" card.)

<comment><USER4> TERF is most definitely a slur, and cis is often used as one as well. E.g. "cis white males!"

<comment><USER5> _> TERF is most definitely a slur_

Really? What else should we call self-professed radical feminists whose definition of a woman excludes trans women?

<comment><USER4> Radfem. You wouldn't go around calling pro-choice and pro-life people "anti- life" and "anti-choice" would you?

<comment><USER5> Not all radical feminists are trans-exclusionary, hence the need for the term.

[https://en.wikipedia.org/wiki/Radical_feminism#Views_on_tran...](https://en.wikipedia.org/wiki/Radical_feminism#Views_on_transgender_topics)

</comment></comment></comment></comment></comment></comment><comment><USER6> This is a really, really, really thorny issue.

On the one hand, it seems noble/responsible to suppress anti-vax, Russian influence, conspiracy theories, etc.

On the other hand, for centuries it's been recognized that the best antidote to "bad speech" isn't censorship, it's _more speech_. Don't ban, convince.

But on the other other hand, that's been exclusively argued in the domain of _government_ action, that government censorship is ultimately worse than what it purports to cure.

In this case, tech firms/platforms like Facebook, YouTube and Pinterest _aren 't_ the government or society, they're private actors just like newspapers and members of the free press in general. Just like it could be irresponsible of the NYT to publish letters to the editor supporting anti-vax, you can argue it's equally irresponsible for tech firms to allow the same on their platforms.

Yet on the other other other hand, we're reaching a point where a great deal of discourse is concentrated on a few user-content-driven sites, so censorship on them feels like it's inching closer in spirit to government censorship.

But on the other x 4 hand, mainstream public conversation has always been driven mainly by merely a handful of newspapers and then news programs with their own editorial agendas, so a handful of tech actors exercising their own "responsible" (as self-interpreted) curation and promotion doesn't seem to be anything new.

In the end, free speech has never been an absolute right (e.g. yelling fire in a crowded theater, libel, etc.) and it's ultimately a question of finding the right balance between harms.

<comment><USER7> Thanks to AI, it's possible to algorithmically generate almost unlimited amounts of false or meaningless speech to drown out accurate information.

<comment><USER6> Thanks to AI can't we also do the opposite?

E.g. detect conspiracy theory speech and automatically provide relevant links/warnings to relevant curated sources?

<comment><USER5> The list of things that are true is orders of magnitude smaller than the list of things that appear true. Randomly generating plausible-looking bullshit is a thing we can do now, but ascertaining the validity of a factual statement is tantamount to solving the AGI problem.

</comment></comment></comment></comment><comment><USER8> This isn't their first rodeo. In 2008 Google launched Knol, which was a fairly major initiative to provide a service like Wikipedia, but without Wikipedia's problems around unattributed content. The idea was that authors would post with their professional affiliation, and get compensated with ad revenue. They hoped to attract actual medical professionals, as medicine was one of the areas where you want to be able to rely on the information.

It failed miserably. The incentives were favorable to spammers but not to actual professionals. No real expert would invest their time into the platform, putting their reputation on the line, for a few paltry ad dollars. But there were some people who mastered cranking out low quality content.

I'm not making any claims about the new effort, just pointing out that identifying a problem and putting resources behind a solution is often not enough.

</comment><comment><USER9> I still feel like large tech companies don't understand the amount of power they wield beyond it's capacity to influence buying decisions. I personally believe that YouTube (pre-2009) was the early breeding ground for conspiracy theorists, and Facebook groups/pages was the enriched gasoline added to the fire.

<comment><USER10> My father in law is a conspiracy theorist and it came a lot more from Fox News and talk radio than YouTube. They were pretty mainstream well before YouTube

<comment><USER11> The difference was that 1990s conspiracies were all about secret government agencies doing secret stuff in secret places. Modern conspiracies are out in public. Pizzagate, still belived by many, is different than area 51. This visibility means belief is constantly reenforced.

<comment><USER10> Most of the people I've talked to aren't crazy alien conspiracy theorists so I can't really comment on that brand of conspiracy theorist. Honestly my main experience is the standard 9/11, global warming, and Obama conspiracy theories (which were incredibly racist) from the early to mid 2000s and those were all pretty similar to modern theories and at least for my father in law and his friends were definitely from Fox News and talk radio.

Edit: a good example to me was the start of the birther movement, which is a quinessential modern conspiracy theory to me, and I remember that as talk radio and Fox News.

<comment><USER11> Global warming and birtherism were a turning point. It was then than condpiracy theories were directly applicable to politics. Managing them then became a practical political weapon.

<comment><USER12> The John Birch Society predates both, and was a similar movement by similar people towards similar ends.

</comment></comment></comment></comment></comment></comment><comment><USER13> Some firms are more on top of it than others.

Netflix's deal with Goop is not encouraging, Goop just a "lifestyle brand" that is selling snake oil.

<comment><USER14> In the end they will always go for more money despite all the talk about values.

<comment><USER15> Well, I feel like it is also worth pointing out that all money starts to be a lot more persuasive when your business model is "lose other people's money until a miracle occurs". Honestly, if we have a system which permits/encourages sky-high valuations and seemingly interesting businesses to expand well beyond their user's desires or ability to pay, this is precisely what we get.

If you monetize on ads, you need damn expensive ads. If you want to have expensive ads, you gotta do something to actually make them work.

if sustainability vs valuation was a goal, then there might be more incentive to avoid these kinds of odd, consumer hostile behaviors. Users may not be the product, but, they're not the direct revenue source either. As long as ads can trick people into clicking, there is an incentive to charge for those ads.

</comment></comment></comment><comment><USER16> The cure for bad information is usually more information.

<comment><USER16> Expanding on my own post... why is it any tech company's responsibility to protect people from their own bad decisions?

<comment><USER17> Are you serious? Because as of so far, in the US, the law demands it. Look at every product you buy "Don't do X dangerous thing with said device". We regulate countless things that can be physically harmful to individuals. I can't go to the store and by dynamite because I can harm myself and others with it.

So should information be regulated if it can cause physical harm to oneself and others. This is not an easy question to answer.

<comment><USER16> So law should dictate what we're able to say? There was a time when that was counter to the entire point.

</comment></comment></comment></comment><comment><USER18> When the medical system actually starts curing people then they can claim their advice is the best. Otherwise it's just opinion. If you can't cure a disease you don't understand it.

</comment><comment><USER19> Can they finish their other wars first?</comment>