Re: Prime numbers

John, On 26 May 2013, at 00:54, John Mikes wrote: Bruno and others: did you read http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html the information about prof. Zhang's discovery (U of New Ha

Re: Prime numbers

http://www.newscientist.com/article/dn23595-weinsteins-theory-of-everything-is-probably-nothing.html Brent On 5/25/2013 3:54 PM, John Mikes wrote: Bruno and others: did you read http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_dis

Re: Prime Numbers

On 27 Sep 2012, at 18:46, meekerdb wrote: On 9/27/2012 1:19 AM, Bruno Marchal wrote: On 26 Sep 2012, at 19:29, meekerdb wrote: On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: So you mean if some mathematical object implies a contradictio

Re: Prime Numbers

On 9/27/2012 1:19 AM, Bruno Marchal wrote: On 26 Sep 2012, at 19:29, meekerdb wrote: On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: So you mean if some mathematical object implies a contradiction it doesn't exist, e.g. the largest prime numb

Re: Prime Numbers

On 26 Sep 2012, at 19:29, meekerdb wrote: On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: So you mean if some mathematical object implies a contradiction it doesn't exist, e.g. the largest prime number. But then of course the proof of contr

Re: Prime Numbers

On Wed, Sep 26, 2012 at 5:01 PM, meekerdb wrote: > On 9/26/2012 2:53 PM, Jason Resch wrote: > > > > On Wed, Sep 26, 2012 at 2:33 PM, meekerdb wrote: > >> On 9/26/2012 12:11 PM, Jason Resch wrote: >> >>> >>> >>> On Sep 26, 2012, at 12:29 PM, meekerdb wrote: >>> >>> On 9/25/2012 9:51 PM, Jason

Re: Prime Numbers

On 9/26/2012 2:53 PM, Jason Resch wrote: On Wed, Sep 26, 2012 at 2:33 PM, meekerdb > wrote: On 9/26/2012 12:11 PM, Jason Resch wrote: On Sep 26, 2012, at 12:29 PM, meekerdb mailto:meeke...@verizon.net>> wrote: On 9/25/2012 9:51 PM, Jaso

Re: Prime Numbers

On Wed, Sep 26, 2012 at 2:33 PM, meekerdb wrote: > On 9/26/2012 12:11 PM, Jason Resch wrote: > >> >> >> On Sep 26, 2012, at 12:29 PM, meekerdb wrote: >> >> On 9/25/2012 9:51 PM, Jason Resch wrote: >>> On Sep 25, 2012, at 11:05 PM, meekerdb wrote: On 9/25/2012 8:54 PM,

Re: Prime Numbers

On 9/26/2012 12:11 PM, Jason Resch wrote: On Sep 26, 2012, at 12:29 PM, meekerdb wrote: On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: On 9/25/2012 8:54 PM, Jason Resch wrote: On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07

Re: Prime Numbers

On Sep 26, 2012, at 12:29 PM, meekerdb wrote: On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: On 9/25/2012 8:54 PM, Jason Resch wrote: On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot

Re: Prime Numbers

On 9/25/2012 9:51 PM, Jason Resch wrote: On Sep 25, 2012, at 11:05 PM, meekerdb wrote: On 9/25/2012 8:54 PM, Jason Resch wrote: On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot prove that their existence is self-contradictory

Re: Prime Numbers

On Sep 25, 2012, at 11:05 PM, meekerdb wrote: On 9/25/2012 8:54 PM, Jason Resch wrote: On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot prove that their existence is self-contradictory Propositions can be self contradictory, bu

Re: Prime Numbers

On 9/25/2012 8:54 PM, Jason Resch wrote: On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot prove that their existence is self-contradictory Propositions can be self contradictory, but how can existence of something be self-contradi

Re: Prime Numbers

On Sep 25, 2012, at 10:27 PM, meekerdb wrote: On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot prove that their existence is self-contradictory Propositions can be self contradictory, but how can existence of something be self-contradictory? Brent Brent, it was roger, not

Re: Prime Numbers

On 9/25/2012 4:07 PM, Jason Resch wrote: Yes. If we cannot prove that their existence is self-contradictory Propositions can be self contradictory, but how can existence of something be self-contradictory? Brent then we should consider them as "possible". Just because I cannot experience

Re: Prime Numbers

On 9/25/2012 7:07 PM, Jason Resch wrote: On Tue, Sep 25, 2012 at 5:37 PM, Stephen P. King mailto:stephe...@charter.net>> wrote: On 9/25/2012 10:24 AM, Jason Resch wrote: On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough mailto:rclo...@verizon.net>> wrote: Hi Stephen P. Ki

Re: Prime Numbers

On Tue, Sep 25, 2012 at 5:37 PM, Stephen P. King wrote: > On 9/25/2012 10:24 AM, Jason Resch wrote: > > > > On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough wrote: > >> Hi Stephen P. King >> >> Yes, I think that the structures and >> attributes of matter are provided >> by a creator (the All, the s

Re: Prime Numbers

On 9/25/2012 10:24 AM, Jason Resch wrote: On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough > wrote: Hi Stephen P. King Yes, I think that the structures and attributes of matter are provided by a creator (the All, the supreme monad, or God). Plato

Re: Re: Prime Numbers

On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough wrote: > Hi Stephen P. King > > Yes, I think that the structures and > attributes of matter are provided > by a creator (the All, the supreme > monad, or God). Plato used the analogy > of geometrical shapes for his structures. > > But if you believe i

Re: Re: Prime Numbers

near the end." -Woody Allen - Receiving the following content - From: Stephen P. King Receiver: everything-list Time: 2012-09-24, 10:42:12 Subject: Re: Prime Numbers On 9/24/2012 9:46 AM, Roger Clough wrote: > God's ideas is fine. The numbers and arithmetic

Re: Prime Numbers

On 9/24/2012 9:46 AM, Roger Clough wrote: God's ideas is fine. The numbers and arithmetic etc. can inhere in some mind. The numbers are (idealistically) real, as I think all arithmetic must be. For it is true whether known or not. At least as you stay with common numbers and arithmetic. Pretty

Re: Re: Prime Numbers

Roger Clough, rclo...@verizon.net 9/24/2012 "Forever is a long time, especially near the end." -Woody Allen - Receiving the following content - From: Bruno Marchal Receiver: everything-list Time: 2012-09-24, 09:12:29 Subject: Re: Prime Numbers On 24 Sep 2012, at 12:3

Re: Prime Numbers

On 24 Sep 2012, at 12:39, Roger Clough wrote: Hi Bruno Marchal Numbers are not in spacetime, that is, are not at location r at time t. So they are ideas, God's ideas? Then I am OK. The comp God is arithmetical truth, so this works. they are not physical. OK. To be physical you

Re: Re: Prime Numbers

her always true or always false. Roger Clough, rclo...@verizon.net 9/24/2012 "Forever is a long time, especially near the end." -Woody Allen - Receiving the following content - From: Stephen P. King Receiver: everything-list Time: 2012-09-22, 16:10:38 Subject: Re: Pr

Re: Re: Prime Numbers

s are always real (in the philosophical sense). Roger Clough, rclo...@verizon.net 9/24/2012 "Forever is a long time, especially near the end." -Woody Allen - Receiving the following content - From: Bruno Marchal Receiver: everything-list Time: 2012-09-23, 03:42:03 Sub

Re: Re: Prime Numbers

following content - From: Bruno Marchal Receiver: everything-list Time: 2012-09-23, 03:42:03 Subject: Re: Prime Numbers On 22 Sep 2012, at 22:10, Stephen P. King wrote: > On 9/22/2012 7:32 AM, Roger Clough wrote: >> How could mathematics be fiction ? >> If so, then w

Re: Prime Numbers

On 9/23/2012 3:42 AM, Bruno Marchal wrote: On 22 Sep 2012, at 22:10, Stephen P. King wrote: On 9/22/2012 7:32 AM, Roger Clough wrote: How could mathematics be fiction ? If so, then we could simply say that 2+2=5 because it's saturday. How could we have a world we many minds can, on rare occas

Re: Prime Numbers

On 22 Sep 2012, at 22:10, Stephen P. King wrote: On 9/22/2012 7:32 AM, Roger Clough wrote: How could mathematics be fiction ? If so, then we could simply say that 2+2=5 because it's saturday. How could we have a world we many minds can, on rare occasions, come to complete agreement if that w

Re: Prime Numbers

On 9/22/2012 7:32 AM, Roger Clough wrote: How could mathematics be fiction ? If so, then we could simply say that 2+2=5 because it's saturday. How could we have a world we many minds can, on rare occasions, come to complete agreement if that where the case? Perhaps it is true that 2+2=4 because

Re: Prime Numbers

On 21 Sep 2012, at 19:17, meekerdb wrote: On 9/21/2012 1:22 AM, Bruno Marchal wrote: On 20 Sep 2012, at 20:14, meekerdb wrote: On 9/20/2012 10:31 AM, Bruno Marchal wrote: On 20 Sep 2012, at 18:14, meekerdb wrote: On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is

Re: Re: Prime Numbers

oody Allen - Receiving the following content - From: meekerdb Receiver: everything-list Time: 2012-09-21, 13:30:03 Subject: Re: Prime Numbers On 9/21/2012 5:40 AM, Rex Allen wrote: On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam wrote: On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen wrote:

Re: Re: Prime Numbers

that there's no way to get from "is" to "ought" or vice versa. Roger Clough, rclo...@verizon.net 9/22/2012 "Forever is a long time, especially near the end." -Woody Allen - Receiving the following content - From: Terren Suydam Receiver: everything-l

Re: Re: Prime Numbers

From: Rex Allen Receiver: everything-list Time: 2012-09-21, 09:20:41 Subject: Re: Prime Numbers Just to avoid confusion, this sentence: I would say that mathematics is just very tightly plotted fiction where so many details of the story are known up front that the plot can only progress in

Re: Prime Numbers

On 9/21/2012 12:56 PM, Jason Resch wrote: On Fri, Sep 21, 2012 at 1:55 PM, meekerdb > wrote: On 9/21/2012 8:59 AM, Jason Resch wrote: On Sep 21, 2012, at 8:13 AM, Rex Allen mailto:rexallen31...@gmail.com>> wrote: On Wed, Sep 19, 2012 at 12:27 AM,

Re: Prime Numbers

On Fri, Sep 21, 2012 at 1:55 PM, meekerdb wrote: > On 9/21/2012 8:59 AM, Jason Resch wrote: > > > > On Sep 21, 2012, at 8:13 AM, Rex Allen wrote: > > On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch wrote: > >> On Sep 18, 2012, at 9:19 PM, Rex Allen wrote: >> >> On Mon, Sep 17, 2012 at 1:36 PM

Re: Prime Numbers

Just to avoid confusion, this sentence: *I would say that mathematics is just very tightly plotted fiction where so many details of the story are known up front that the plot can only progress in very specific ways if it is to remain consistent and believable to the "reader".* Should probably be

Re: Prime Numbers

On 9/21/2012 8:59 AM, Jason Resch wrote: On Sep 21, 2012, at 8:13 AM, Rex Allen > wrote: On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch > wrote: On Sep 18, 2012, at 9:19 PM, Rex Allen mailto:rexallen31...@gmail.com>> wrote:

Re: Prime Numbers

On 9/21/2012 5:40 AM, Rex Allen wrote: On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam > wrote: On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen mailto:rexallen31...@gmail.com>> wrote: > > On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam mailto:terren.suy...@

Re: Prime Numbers

On 9/21/2012 1:22 AM, Bruno Marchal wrote: On 20 Sep 2012, at 20:14, meekerdb wrote: On 9/20/2012 10:31 AM, Bruno Marchal wrote: On 20 Sep 2012, at 18:14, meekerdb wrote: On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is given by the behavior of the "probability on

Re: Prime Numbers

On Fri, Sep 21, 2012 at 8:40 AM, Rex Allen wrote: > On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam > wrote: >> >> I'm curious about what a plausible "fictionalist" account of the >> Mandelbrot set could be. Is fictionalism the same as constructivism, >> or the idea that knowledge doesn't exist o

Re: Prime Numbers

On Sep 21, 2012, at 8:13 AM, Rex Allen wrote: On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch wrote: On Sep 18, 2012, at 9:19 PM, Rex Allen wrote: On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam > wrote: Rex, Do you have a non-platonist explanation for the "discovery" of the Mandelbrot se

Re: Prime Numbers

On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch wrote: > On Sep 18, 2012, at 9:19 PM, Rex Allen wrote: > > On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam < > terren.suy...@gmail.com> wrote: > >> Rex, >> >> Do you have a non-platonist explanation for the "discovery" of the >> Mandelbrot set and th

Re: Prime Numbers

On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam wrote: > On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen > wrote: > > > > On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam > > wrote: > >> > >> Rex, > >> > >> Do you have a non-platonist explanation for the "discovery" of the > >> Mandelbrot set and the

Re: Prime Numbers

On 20 Sep 2012, at 20:14, meekerdb wrote: On 9/20/2012 10:31 AM, Bruno Marchal wrote: On 20 Sep 2012, at 18:14, meekerdb wrote: On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is given by the behavior of the "probability one". In Kripke terms, P(x) = 1 in world alp

Re: Prime Numbers

On 9/20/2012 10:31 AM, Bruno Marchal wrote: On 20 Sep 2012, at 18:14, meekerdb wrote: On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is given by the behavior of the "probability one". In Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds acc

Re: Prime Numbers

On 20 Sep 2012, at 18:14, meekerdb wrote: On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is given by the behavior of the "probability one". In Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds accessible from alpha, and (key point) that

Re: Prime Numbers

On 9/20/2012 2:05 AM, Bruno Marchal wrote: A modal logic of probability is given by the behavior of the "probability one". In Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds accessible from alpha, and (key point) that we are not in a cul-de-sac world. What does 'a

Re: Prime Numbers

On 19 Sep 2012, at 21:51, Stephen P. King wrote: On 9/19/2012 2:39 PM, Bruno Marchal wrote: Dear Bruno, Your remarks raise an interesting question: Could it be that both the object and the means to generate (or perceive) it are of equal importance ontologically? Yes. It comes from the

Re: Prime Numbers

On 9/19/2012 2:39 PM, Bruno Marchal wrote: Dear Bruno, Your remarks raise an interesting question: Could it be that both the object and the means to generate (or perceive) it are of equal importance ontologically? Yes. It comes from the embedding of the subject in the objects, that any m

Re: Prime Numbers

On 19 Sep 2012, at 17:03, Stephen P. King wrote: On 9/19/2012 8:39 AM, Bruno Marchal wrote: On 18 Sep 2012, at 18:02, meekerdb wrote: On 9/18/2012 8:13 AM, Bruno Marchal wrote: On 17 Sep 2012, at 22:25, meekerdb wrote: But did anybody think z' = z^2 + c was interesting before that? Y

Re: Prime Numbers

On 9/19/2012 8:39 AM, Bruno Marchal wrote: On 18 Sep 2012, at 18:02, meekerdb wrote: On 9/18/2012 8:13 AM, Bruno Marchal wrote: On 17 Sep 2012, at 22:25, meekerdb wrote: But did anybody think z' = z^2 + c was interesting before that? Yes. This was known by people like Fatou and Julia, i

Re: Prime Numbers

On 18 Sep 2012, at 18:02, meekerdb wrote: On 9/18/2012 8:13 AM, Bruno Marchal wrote: On 17 Sep 2012, at 22:25, meekerdb wrote: But did anybody think z' = z^2 + c was interesting before that? Yes. This was known by people like Fatou and Julia, in the early 1900. I knew they considered

Re: Prime Numbers

On 9/18/2012 9:27 PM, Jason Resch wrote: The unreasonable effectiveness of math in the physical sciences is yet further support if Platonism. I don't see that this follows. If we invent language, including mathematics, to describe our theories of the world that explains their effectiveness.

Re: Prime Numbers

On Sep 18, 2012, at 9:19 PM, Rex Allen wrote: On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam > wrote: Rex, Do you have a non-platonist explanation for the "discovery" of the Mandelbrot set and the infinite complexity therein? I find fictionalism to be the most plausible view of mathematic

Re: Prime Numbers

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen wrote: > > On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam > wrote: >> >> Rex, >> >> Do you have a non-platonist explanation for the "discovery" of the >> Mandelbrot set and the infinite complexity therein? > > > I find fictionalism to be the most plausi

Re: Prime Numbers

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam wrote: > Rex, > > Do you have a non-platonist explanation for the "discovery" of the > Mandelbrot set and the infinite complexity therein? I find fictionalism to be the most plausible view of mathematics, with all that implies for the Mandelbrot set

Re: Prime Numbers

On 9/18/2012 8:13 AM, Bruno Marchal wrote: On 17 Sep 2012, at 22:25, meekerdb wrote: But did anybody think z' = z^2 + c was interesting before that? Yes. This was known by people like Fatou and Julia, in the early 1900. I knew they considered what are now called fractal sets, but not tha

Re: Prime Numbers

On 17 Sep 2012, at 22:25, meekerdb wrote: But did anybody think z' = z^2 + c was interesting before that? Yes. This was known by people like Fatou and Julia, in the early 1900. Iterating analytical complex functions leads to the Mandelbrot fractal sets, or similar. The computer has mad

Re: Prime Numbers

On Mon, Sep 17, 2012 at 6:52 PM, meekerdb wrote: > On 9/17/2012 2:45 PM, Terren Suydam wrote: >> >> Benoit Mandelbrot did. > > > I wasn't aware of that. Did he have a proof of the fractal nature of the > set before he calculated it? > > Brent I don't know. I doubt it, I'm not even sure he had ev

Re: Prime Numbers

On 9/17/2012 2:45 PM, Terren Suydam wrote: Benoit Mandelbrot did. I wasn't aware of that. Did he have a proof of the fractal nature of the set before he calculated it? Brent But what does "interesting" have to do with it? Did anyone think that empty patch of sky was interesting before H

Re: Prime Numbers

Benoit Mandelbrot did. But what does "interesting" have to do with it? Did anyone think that empty patch of sky was interesting before Hubble turned it into one of the most amazing photos ever taken? On Mon, Sep 17, 2012 at 4:25 PM, meekerdb wrote: > But did anybody think z' = z^2 + c was intere

Re: Prime Numbers

But did anybody think z' = z^2 + c was interesting before that? Bretn On 9/17/2012 1:17 PM, Terren Suydam wrote: I would say computers were the tool that allowed us to see it, like a microscope allowed us to see bacteria, and a telescope stars. On Mon, Sep 17, 2012 at 3:14 PM, meekerdb wrote:

Re: Prime Numbers

I would say computers were the tool that allowed us to see it, like a microscope allowed us to see bacteria, and a telescope stars. On Mon, Sep 17, 2012 at 3:14 PM, meekerdb wrote: > On 9/17/2012 10:36 AM, Terren Suydam wrote: > > Rex, > > Do you have a non-platonist explanation for the "discover

Re: Prime Numbers

On 9/17/2012 10:36 AM, Terren Suydam wrote: Rex, Do you have a non-platonist explanation for the "discovery" of the Mandelbrot set and the infinite complexity therein? How can you make sense of that in terms of the constructivist point of view How can you make sense of it otherwise. The Mand

Re: Prime Numbers

Rex, Do you have a non-platonist explanation for the "discovery" of the Mandelbrot set and the infinite complexity therein? How can you make sense of that in terms of the constructivist point of view that you are (I think) compelled to take if you argue against arithmetical platonism? It seems o

Re: Prime Numbers

On Mon, Sep 17, 2012 at 2:05 AM, Jason Resch wrote: > > I think an easier way to intuit prime numbers that can't be represented as > rectangles, only a 1-wide "lines". > > While the concept of primes is straight forward, there is an unending set > of not-so-obvious facts that we continue to disco

Re: Prime Numbers

On Mon, Sep 17, 2012 at 12:27 AM, Rex Allen wrote: > > On Sun, Sep 16, 2012 at 6:10 PM, Stephen P. King wrote: >> >> HI Rex, >> >> Nice post! Could you riff a bit on what the number PHI tells us about >> this characteristic. How is it that it seems that our perceptions of the >> world find an

Re: Prime Numbers

On Sun, Sep 16, 2012 at 6:10 PM, Stephen P. King wrote: > > HI Rex, > > Nice post! Could you riff a bit on what the number PHI tells us about > this characteristic. How is it that it seems that our perceptions of the > world find anything that is close to a PHI valued relationship to be > "beau

Re: Prime Numbers

On 9/16/2012 3:43 PM, Rex Allen wrote: It seems to me that numbers are based on our ability to judge relative magnitudes: "Which is bigger, which is closer, which is heavier, etc." Many animals have this ability - called numeracy. Humans differ only in the degree to which it is developed, and

Re: prime numbers etc

Touche. But I don't believe (in?) it - I am agnostic. Nonbeliever. (SONG: I lost my turf in San Francisco) J On Thu, Sep 6, 2012 at 10:36 PM, Stathis Papaioannou wrote: > On Fri, Sep 7, 2012 at 8:07 AM, John Mikes wrote: > > Stathis wrote (to Craig): > > > > "But you believe that the neurochemi

Re: prime numbers etc

On Fri, Sep 7, 2012 at 8:07 AM, John Mikes wrote: > Stathis wrote (to Craig): > > "But you believe that the neurochemicals do things contrary to what > chemists would predict, for example an ion channel opening or closing > without any cause such as a change in transmembrane potential or > ligand