The current observed universe does not include things that correspond to mathematical incompleteness. If you want to claim otherwise, the burden is on you to demonstrate it: the burden is not on me to believe it simply because you'd like it if I did.
Considering that Godel showed that all but the most trivial mathematical systems exhibited incompleteness, if you believe that nature is describable in terms of mathematics it is pretty much an unavoidable conclusion.
Carl Sagan's credited with a quote about extraordinary claims requiring extraordinary evidence. The claim that the universe includes things corresponding to mathematical incompleteness is extraordinary.
What is so extraordinary about the universe exhibiting properties that are found in all but the most trivial mathematical systems?
Oh -- also, scientists don't use the phrase "null hypothesis" in the way statisticians do
As a scientist, I can assure you that we do. The term has no scientific meaning whatsoever outside of statistics. I invite you to cite any scientific text that says otherwise. And the way in which you were trying to use it is invalid even in statistics. Failure to reject the null hypothesis does not constitute evidence in favor of the null hypothesis.
Ask Richard Feynman, who seriously proposed a Journal of the Null Hypothesis which would publish good ideas that have been shown not to be the way the world works, in order to help keep other scientists from going down those same blind alleys.
I am not aware of any case in which Feynman ever defended his own hypothesis on the grounds that it was the null hypothesis and there was no evidence against it. If he ever did this, please provide a citation.
It is not logically valid to equate absence of evidence with evidence of absence.
Correct, but you'll note that's not what we're talking about here. I'm not saying I believe there does not/cannot exist physical analogues of the Incompleteness Theorem: I'm saying that such things have not been established, and for that reason I accept the null hypothesis -- being that they do not.
Here, you are falling into a fallacy that unfortunately seems to be becoming more common: the mistaken notion that the "null hypothesis," which in actuality has a very limited and well defined statistical meaning--namely that a particular measure has a true value of null (i.e. zero)--has some kind of broader philosophical meaning, and that by declaring one's own view as the "null hypothesis," one is then entitled to take absence of evidence against one's favored view as a reason to accept it. Ironically, this is an error of reasoning even within the field of statistics, where the null hypothesis actually has a real meaning--one cannot take failure to exclude the null hypothesis as a reason to accept it.
Correct, but we've also not seen any evidence of such things in physical reality. There's a lot of work going on in the axiomization of physics, but so far no one has been able to demonstrate the existence of things that are true but not testable by experiment. In the absence of that, I take the same attitude that I do towards string theory: it's an interesting idea, and I'll be very interested in reading about empirical results if/when they come in, but for now I'm not signing on to it.
It is not logically valid to equate absence of evidence with evidence of absence. Gödel showed that the mathematical requirements for a system to contain true statements that are not provably true are not particularly stringent.
I have a theory that God created the cosmos in its current form, with photons created in mid-flight towards the Earth, and all of the cosmos assembled in such a way to make it appear to be billions of years old even though it was only created last Thursday. Young-earth Creationists have the right idea, you see, they just don't take it far enough: Last Thursdayism is my theory.
If you specify that in all respects the "Last Thursday" universe is indistinguishable from one that originated billions of years ago, then I would say that the two theories are equivalent--i.e. they are the same theory. It is certainly not implausible that the universe originated billions of years ago. Therefore, your theory is not implausible.
The fact you called MWI "scientifically plausible" should be the first sign you don't have the first clue what you're going on about.
For MWI to be "scientifically plausible" it would have to make predictions which could be confirmed or falsified via experiment. That is, in essence, what science is: the subjecting of ideas to experimental test. (Go ask Zombie Feynman [xkcd.com] if you don't believe me.)
A theory that does not make testable predictions is not well formulated, but that does not make it "implausible." There is no law of nature that guarantees that everything that is true must be testable by experiment. After all, mathematics allows for the existence of true statements that cannot be shown to be true. There is no reason why this could not be the case for physical reality.
It is reasonable to say that two theories that are reducible to the same mathematical description (in which case there is provably no experimental test than can distinguish them) should be regarded as the same theory, however different their verbal description might sound. And it can also be argued that a "theory" that has been proved mathematically to make no predictions at all (i.e. to be consistent with every possible outcome of every possible experiment) is meaningless (which is still not quite the same thing as implausible). On the other hand, it is important to distinguish between a theory that provably makes no testable predictions and one for which you have not yet managed to think of an experimental test.
I imagine the incremental risk is negligible next to the radiation I've voluntarily exposed myself to over the years. But the benefit is pretty negligible too, because I don't mind a pat-down. So when I see the square x-ray boxes, I opt out--but I'll take a microwave scan (curved box)
Apple brainwash has worked again. Whatever goes wrong, it's always the user's fault. Always.
I find it revealing that whereas several possible causes of the complaints were listed (manufacturing defect, software problem, different usage patterns, or unrealistic expectations of a few users), you only seemed to notice the one that fit your prejudice. It seems that whatever somebody says, it's always evidence of "Apple brainwash." Always.
I found the antenna problem on the iPhone 4 quite hard to reproduce. I had to clutch it uncomfortably hard to see anything, and I saw about the same degree of attenuation if I clutched my 3gs tightly near the bottom. My suspicion is the iPhone 4 didn't actually have unusually bad attenuation, and that the true problem was that the visible antenna gave people an idea of exactly where to clutch it to kill the reception.
When should Apple acknowledge the issue? When some users are saying they have a problem, when others are saying they don't? (Many people, myself included, have not encountered this issue). Such problems can be very difficult to track down. How does Apple know if it is a real issue? Maybe the people who are complaining have unrealistic expectations, or are using their phones in a different way. After all, the iPhone 4s has new features, which might cause some people to place a heavier demand on the battery. How many people are encountering the problem? is it 10%? 1%? 0.001% (which would still be quite a few phones). Is it a manufacturing defect, or a software problem? Is there any point in acknowledging the issue if all that you are able to honestly say is something noncommittal like, "Well, we've had some reports, but we haven't yet been able to reproduce them, and we really have no idea at all what's going on or how many people are having this problem, but we're investigating the issue"? Or is it better to wait until there is something substantive to say?
I actually had the same problem with my first-generation iPhone. I didn't even bother reporting it to Apple until I had it figured out, because a bug report that just says "Sometimes my battery runs down really fast" is virtually useless. I eventually figured out that the battery died if I left the Clock application in the foreground while the phone was asleep. I filed a bug report with Apple, and after the next system update, I got an email message that said, "We believe that the bug that you reported has been fixed. Can you verify?"
I think the term "denier" can reasonably be applied to people who are in denial about any well established fact. The psychological concept of being in denial dates back at least to the work of Sigmund Freud and predates the not only holocaust denial but the holocaust itself.
Many people who are in denial would prefer to be called "skeptics," but what distinguishes them from true skeptics is that while they are doubtful of every detail of evidence that is unfavorable to their preferred view (and the history of the temperature record is an excellent challenge, with people continuing to reject the evidence for warming even though it has been independently replicated over and over), they become absolutely credulous with respect to any claim that seems to prop up what they wish to believe (for example, the same people who are so "skeptical" of the extensive evidence of warming here on earth will turn around and assert that Mars or Pluto is warming, even though the evidence for that is far, far more tenuous).
No, it's not the definition of heat capacity can be found here. The greenhouse properties of CO2 are distinct from its heat capacity, and relate to its absorption and emission properties. An explanation can be found here. Who told you this nonsense?
One has to wonder about the gullibility of people who are so willing to believe that climate scientists (most of whom were originally trained in physics) simply forgot to consider the effects of water vapor in calculating the impact of CO2 on the radiative equilibrium of the earth.
That's neither here nor there, since it has been widely demonstrated that if you actually plot his data, you will find that there has been no warming for the last ten years, contrary to the statements he has made to the press
Where, specifically, has he stated that he can still detect warming if he throws out all of his data except for the last 10 years? You can't detect warming if you only look at data for the last 10 seconds. So what?
Nobody cares if there has been warming over the past 10 years; they care whether there is a long-term warming trend that will continue into the future, as predicted based upon the known effect of atmospheric CO2 on the radiative equilibrium of the earth.
Yes, if you throw out enough of your data, you can always find a period short enough that you can't detect the predicted warming trend even if it is there. So what? Absence of evidence is not evidence of absence. Climate models even tell you how much data you need to be able to reliably detect the predicted warming trend, which turns out to be about 15 years.
In this case, it wasn't even about that... All the data we needed was there... But kept from anyone outside their group... And then modified, and the original data deleted.
This is a widely believed falsehood (you might want to consider who profits from propagating this canard). In fact, the data has always been available. The groups that analyzed the data previously never owned the data, and never had control over it, so they couldn't have kept it from anybody else or changed or deleted it even if they wanted to do so. This is not even the first independent analysis of climate data. This group got the data from the same sources as everybody else.
Yes, those who live in regions where the weather is pleasant for a substantial portion of the year, and where the climate is compatible with highly productive agriculture, as well as those who live close to the ocean where they have ready access to fishing and ocean transport.
Which, oddly enough, turns out to be most of them.
There are other voice control apps that do pretty much what the original version of Siri did, so it's hardly a big loss. What Apple offers with the iPhone 4s is extensive integration of voice into the phone's function at a very basic level--which means that it will get a lot more use, and the server load (and Apple's costs for supporting it) will be substantially greater if they'd kept it an app like the original Siri.
I doubt if Apple will roll it out to older iPhones. Siri is not just an application, it is a service, which Apple has chosen to charge for as part of the purchase price of the iPhone 4s. I suppose Apple could offer it as an extra-cost option for older devices, but I suspect that this would not win them any points with owners of those devices. So it makes more sense for Apple to treat it simply as a feature of the iPhone 4s. I suppose Apple might consider adding it to the iPad 2, which was released not long before the iPhone 4s, but it wouldn't surprise me if they decided to reserve it for their phone line.
And it's not as if owners of older devices are not getting new features with iOS 5--just not this one.
Certainly, if this were the first report to reach this conclusion, or if it flew in the face of a large body of research, one might insist on reserving judgement until it was peer-reviewed by experts in the field. However, even before this study, there was already a large body of extensively peer reviewed research that reached the same conclusions. So the interest is not so much in the data or the analysis, but that an outspoken skeptic from a field of science outside climate science field has carried out an independent analysis--and confirmed what the climate scientists have been saying all along.
By the way, making data and/or drafts of submitted publications public prior to peer-reviewed publication is not particularly unusual, although some journals don't like it (since it leaves less incentive to pay for a subscription). It is widely done in many fields of science--and ironically, has been done by many of the "skeptics" who are now criticizing Muller for doing the same thing.
Except of course, that he didn't collect any data at all--he analyzed data that was already collected. And how does analyzing more data and reaching the same conclusion as previous investigators demonstrate that the previous investigators did not have enough evidence, anyway?
It sounds as if you are unclear on the concept of a patent. It is not some sort of software award given for difficult coding.
It is notoriously difficult to judge innovation in hindsight. The most brilliant accomplishments can seem trivial in retrospect. Einstein's theory of Special Relativity can be derived with simple algebra. Anybody with high school math could have done it. Yet prior to Einstein, nobody did.
Sliding a box along a line with your finger to unlock a screen is no Theory of Relativity, to be sure. Yet it is another example of something that anybody could have done--but Apple saw a benefit and did it. There are a lot of ways that a touch screen could be unlocked. There are many possible gestures, as well as many other physical things that could be simulated. The user could trace a figure, or swipe back and forth, or touch a particular spot for some length of time, or "flip" a virtual switch. Many of these are doubtless nearly as good as what Apple came up with; perhaps some are better. The particular method that Apple came up with has little value to anybody other than Apple, because it is one of a large number of small but distinctive features that are combined to create a look and feel that is a critical part of Apple's branding, to identify a device as an Apple.
It is hard to see a negative to allowing a company like Apple to patent a user-interface element like this. Other screen unlock methods are available. And if Apple's really is the best, the patent will eventually expire and anybody will be free to use it. Indeed, it seems like the only guys who lose are those who hope to capitalize on the user good-will that Apple has built up over the years by imitating these "look and feel" elements to create a superficial resemblance to an Apple product in the hope of hitching a ride through the marketplace on Apple's coattails.
This is semantic quibbling and rather foolish quibbling at that. The word "lock" has been used for many years to refer to limiting access to virtual resources of many types.
The publisher of Angry Birds might or might not be able to "patent sliding your finger across the screen to simulate a bird being pulled backwards on a catapult." It is possible that the patent office would consider that sufficiently specific to be distinct from prior art and patentable. It would not seem particularly unreasonable to me for them to be awarded such a patent.
The first company to get rid of most buttons on a mobile phone would have been IBM. Try the IBM Simon Personal Communicator (1993) on for size and tell me why IBM doesnt get the credit for a keyless touch screen phone?
And yet for some odd reason, it was not a huge success, and did not lead to an industry-wide transformation in the way phones work.
Why is that, do you suppose?
Could it be that Apple did indeed create something, perhaps not a single feature, but a combination of features, software, and design that consumers find uniquely appealing? Why shouldn't a company that makes a contribution like that to the industry be rewarded with a limited-term monopoly? So if current patent laws do not protect what Apple created, then maybe they should be changed to provide greater protection to advances in design.
It is clear that there are other ways to do things than Apple's. There are lots and lots of ways to unlock a screen. So let's make other manufacturers develop their own interfaces. And in the unlikely event that ultimately turns out that Apple really did come up with the very best design for a phone that could ever be...well, in a relatively short time, those patents will expire.
Certainly, if your only tool to evaluate toxicity is retrospective epidemiology, you are poorly equipped. But toxicity is not magical. For a substance to be neurotoxic, it needs to do something harmful to neurons, and it has to do it at concentrations that are biologically realistic. These are fundamental requirements of biological plausibility that are readily testable in the laboratory before you consider embarking upon an expensively massive epidemiological study
Slashdot Mirror
Considering that Godel showed that all but the most trivial mathematical systems exhibited incompleteness, if you believe that nature is describable in terms of mathematics it is pretty much an unavoidable conclusion.
What is so extraordinary about the universe exhibiting properties that are found in all but the most trivial mathematical systems?
As a scientist, I can assure you that we do. The term has no scientific meaning whatsoever outside of statistics. I invite you to cite any scientific text that says otherwise. And the way in which you were trying to use it is invalid even in statistics. Failure to reject the null hypothesis does not constitute evidence in favor of the null hypothesis.
I am not aware of any case in which Feynman ever defended his own hypothesis on the grounds that it was the null hypothesis and there was no evidence against it. If he ever did this, please provide a citation.
Here, you are falling into a fallacy that unfortunately seems to be becoming more common: the mistaken notion that the "null hypothesis," which in actuality has a very limited and well defined statistical meaning--namely that a particular measure has a true value of null (i.e. zero)--has some kind of broader philosophical meaning, and that by declaring one's own view as the "null hypothesis," one is then entitled to take absence of evidence against one's favored view as a reason to accept it. Ironically, this is an error of reasoning even within the field of statistics, where the null hypothesis actually has a real meaning--one cannot take failure to exclude the null hypothesis as a reason to accept it.
It is not logically valid to equate absence of evidence with evidence of absence. Gödel showed that the mathematical requirements for a system to contain true statements that are not provably true are not particularly stringent.
If you specify that in all respects the "Last Thursday" universe is indistinguishable from one that originated billions of years ago, then I would say that the two theories are equivalent--i.e. they are the same theory. It is certainly not implausible that the universe originated billions of years ago. Therefore, your theory is not implausible.
A theory that does not make testable predictions is not well formulated, but that does not make it "implausible." There is no law of nature that guarantees that everything that is true must be testable by experiment. After all, mathematics allows for the existence of true statements that cannot be shown to be true. There is no reason why this could not be the case for physical reality.
It is reasonable to say that two theories that are reducible to the same mathematical description (in which case there is provably no experimental test than can distinguish them) should be regarded as the same theory, however different their verbal description might sound. And it can also be argued that a "theory" that has been proved mathematically to make no predictions at all (i.e. to be consistent with every possible outcome of every possible experiment) is meaningless (which is still not quite the same thing as implausible). On the other hand, it is important to distinguish between a theory that provably makes no testable predictions and one for which you have not yet managed to think of an experimental test.
I imagine the incremental risk is negligible next to the radiation I've voluntarily exposed myself to over the years. But the benefit is pretty negligible too, because I don't mind a pat-down. So when I see the square x-ray boxes, I opt out--but I'll take a microwave scan (curved box)
I find it revealing that whereas several possible causes of the complaints were listed (manufacturing defect, software problem, different usage patterns, or unrealistic expectations of a few users), you only seemed to notice the one that fit your prejudice. It seems that whatever somebody says, it's always evidence of "Apple brainwash." Always.
I have location services turned on and I am not experiencing the problem.
I found the antenna problem on the iPhone 4 quite hard to reproduce. I had to clutch it uncomfortably hard to see anything, and I saw about the same degree of attenuation if I clutched my 3gs tightly near the bottom. My suspicion is the iPhone 4 didn't actually have unusually bad attenuation, and that the true problem was that the visible antenna gave people an idea of exactly where to clutch it to kill the reception.
When should Apple acknowledge the issue? When some users are saying they have a problem, when others are saying they don't? (Many people, myself included, have not encountered this issue). Such problems can be very difficult to track down. How does Apple know if it is a real issue? Maybe the people who are complaining have unrealistic expectations, or are using their phones in a different way. After all, the iPhone 4s has new features, which might cause some people to place a heavier demand on the battery. How many people are encountering the problem? is it 10%? 1%? 0.001% (which would still be quite a few phones). Is it a manufacturing defect, or a software problem? Is there any point in acknowledging the issue if all that you are able to honestly say is something noncommittal like, "Well, we've had some reports, but we haven't yet been able to reproduce them, and we really have no idea at all what's going on or how many people are having this problem, but we're investigating the issue"? Or is it better to wait until there is something substantive to say?
I actually had the same problem with my first-generation iPhone. I didn't even bother reporting it to Apple until I had it figured out, because a bug report that just says "Sometimes my battery runs down really fast" is virtually useless. I eventually figured out that the battery died if I left the Clock application in the foreground while the phone was asleep. I filed a bug report with Apple, and after the next system update, I got an email message that said, "We believe that the bug that you reported has been fixed. Can you verify?"
I think the term "denier" can reasonably be applied to people who are in denial about any well established fact. The psychological concept of being in denial dates back at least to the work of Sigmund Freud and predates the not only holocaust denial but the holocaust itself.
Many people who are in denial would prefer to be called "skeptics," but what distinguishes them from true skeptics is that while they are doubtful of every detail of evidence that is unfavorable to their preferred view (and the history of the temperature record is an excellent challenge, with people continuing to reject the evidence for warming even though it has been independently replicated over and over), they become absolutely credulous with respect to any claim that seems to prop up what they wish to believe (for example, the same people who are so "skeptical" of the extensive evidence of warming here on earth will turn around and assert that Mars or Pluto is warming, even though the evidence for that is far, far more tenuous).
No, it's not the definition of heat capacity can be found here. The greenhouse properties of CO2 are distinct from its heat capacity, and relate to its absorption and emission properties. An explanation can be found here. Who told you this nonsense?
One has to wonder about the gullibility of people who are so willing to believe that climate scientists (most of whom were originally trained in physics) simply forgot to consider the effects of water vapor in calculating the impact of CO2 on the radiative equilibrium of the earth.
Where, specifically, has he stated that he can still detect warming if he throws out all of his data except for the last 10 years?
You can't detect warming if you only look at data for the last 10 seconds. So what?
Nobody cares if there has been warming over the past 10 years; they care whether there is a long-term warming trend that will continue into the future, as predicted based upon the known effect of atmospheric CO2 on the radiative equilibrium of the earth.
Yes, if you throw out enough of your data, you can always find a period short enough that you can't detect the predicted warming trend even if it is there. So what? Absence of evidence is not evidence of absence. Climate models even tell you how much data you need to be able to reliably detect the predicted warming trend, which turns out to be about 15 years.
This is a widely believed falsehood (you might want to consider who profits from propagating this canard).
In fact, the data has always been available. The groups that analyzed the data previously never owned the data, and never had control over it, so they couldn't have kept it from anybody else or changed or deleted it even if they wanted to do so. This is not even the first independent analysis of climate data. This group got the data from the same sources as everybody else.
Yes, those who live in regions where the weather is pleasant for a substantial portion of the year, and where the climate is compatible with highly productive agriculture, as well as those who live close to the ocean where they have ready access to fishing and ocean transport.
Which, oddly enough, turns out to be most of them.
There are other voice control apps that do pretty much what the original version of Siri did, so it's hardly a big loss. What Apple offers with the iPhone 4s is extensive integration of voice into the phone's function at a very basic level--which means that it will get a lot more use, and the server load (and Apple's costs for supporting it) will be substantially greater if they'd kept it an app like the original Siri.
I doubt if Apple will roll it out to older iPhones. Siri is not just an application, it is a service, which Apple has chosen to charge for as part of the purchase price of the iPhone 4s. I suppose Apple could offer it as an extra-cost option for older devices, but I suspect that this would not win them any points with owners of those devices. So it makes more sense for Apple to treat it simply as a feature of the iPhone 4s. I suppose Apple might consider adding it to the iPad 2, which was released not long before the iPhone 4s, but it wouldn't surprise me if they decided to reserve it for their phone line.
And it's not as if owners of older devices are not getting new features with iOS 5--just not this one.
Certainly, if this were the first report to reach this conclusion, or if it flew in the face of a large body of research, one might insist on reserving judgement until it was peer-reviewed by experts in the field. However, even before this study, there was already a large body of extensively peer reviewed research that reached the same conclusions. So the interest is not so much in the data or the analysis, but that an outspoken skeptic from a field of science outside climate science field has carried out an independent analysis--and confirmed what the climate scientists have been saying all along.
By the way, making data and/or drafts of submitted publications public prior to peer-reviewed publication is not particularly unusual, although some journals don't like it (since it leaves less incentive to pay for a subscription). It is widely done in many fields of science--and ironically, has been done by many of the "skeptics" who are now criticizing Muller for doing the same thing.
Except of course, that he didn't collect any data at all--he analyzed data that was already collected.
And how does analyzing more data and reaching the same conclusion as previous investigators demonstrate that the previous investigators did not have enough evidence, anyway?
Oh, what a dreadful hardship! How long does it take to learn how to unlock your phone? 5 minutes? Two?
It sounds as if you are unclear on the concept of a patent. It is not some sort of software award given for difficult coding.
It is notoriously difficult to judge innovation in hindsight. The most brilliant accomplishments can seem trivial in retrospect. Einstein's theory of Special Relativity can be derived with simple algebra. Anybody with high school math could have done it. Yet prior to Einstein, nobody did.
Sliding a box along a line with your finger to unlock a screen is no Theory of Relativity, to be sure. Yet it is another example of something that anybody could have done--but Apple saw a benefit and did it. There are a lot of ways that a touch screen could be unlocked. There are many possible gestures, as well as many other physical things that could be simulated. The user could trace a figure, or swipe back and forth, or touch a particular spot for some length of time, or "flip" a virtual switch. Many of these are doubtless nearly as good as what Apple came up with; perhaps some are better. The particular method that Apple came up with has little value to anybody other than Apple, because it is one of a large number of small but distinctive features that are combined to create a look and feel that is a critical part of Apple's branding, to identify a device as an Apple.
It is hard to see a negative to allowing a company like Apple to patent a user-interface element like this. Other screen unlock methods are available. And if Apple's really is the best, the patent will eventually expire and anybody will be free to use it. Indeed, it seems like the only guys who lose are those who hope to capitalize on the user good-will that Apple has built up over the years by imitating these "look and feel" elements to create a superficial resemblance to an Apple product in the hope of hitching a ride through the marketplace on Apple's coattails.
This is semantic quibbling and rather foolish quibbling at that. The word "lock" has been used for many years to refer to limiting access to virtual resources of many types.
The publisher of Angry Birds might or might not be able to "patent sliding your finger across the screen to simulate a bird being pulled backwards on a catapult." It is possible that the patent office would consider that sufficiently specific to be distinct from prior art and patentable. It would not seem particularly unreasonable to me for them to be awarded such a patent.
Not on a touch screen, not a way to unlock a touch screen.
And yet for some odd reason, it was not a huge success, and did not lead to an industry-wide transformation in the way phones work.
Why is that, do you suppose?
Could it be that Apple did indeed create something, perhaps not a single feature, but a combination of features, software, and design that consumers find uniquely appealing? Why shouldn't a company that makes a contribution like that to the industry be rewarded with a limited-term monopoly? So if current patent laws do not protect what Apple created, then maybe they should be changed to provide greater protection to advances in design.
It is clear that there are other ways to do things than Apple's. There are lots and lots of ways to unlock a screen. So let's make other manufacturers develop their own interfaces. And in the unlikely event that ultimately turns out that Apple really did come up with the very best design for a phone that could ever be...well, in a relatively short time, those patents will expire.
Certainly, if your only tool to evaluate toxicity is retrospective epidemiology, you are poorly equipped. But toxicity is not magical. For a substance to be neurotoxic, it needs to do something harmful to neurons, and it has to do it at concentrations that are biologically realistic. These are fundamental requirements of biological plausibility that are readily testable in the laboratory before you consider embarking upon an expensively massive epidemiological study