[hist-analytic] Materialism and mass as a unit of measurement
Scott Holbrook
scott.holbrook at gmail.com
Sun Jan 30 20:52:57 EST 2011
I know you wanted to defer comments, but here are some things you may want
to consider when getting this clearer.
I think the your using the epsilon-delta definition. It does have
inequalities and I'm not aware of any other defitnions using inequalities.
But, it should be noted that epsilon-delta defitnion IS the defintion that
says we can get as close as we like to some number (viz. the limit). (For
any epsilon there exists a delta such that, for all x, if 0 < |x - c| <
delta, then |f(x) - L| < epsilon). So, that's why it seems that the element
of choice is* also* in the "inequality defintion"...because the two are the
same.
But, what I want to point out is that in the now accepted non-standard
treatment doesn't use any inequalities which, I think , would eliminate the
choice that Steve is talking about. The reson that "Steve's choice" is
there has, I think, more to do with inequalities than some intrinsic feature
of Calculus. Inequality solution sets have, most often, more than one
element. So, in effect, we could choose any element in the solution set and
get a right answer. I think the Reimann sums are more of the same. The
choosing of the rectangle width is more less "geting as close as you want."
(the inequality business has actually been the standard for about 200 years
or so, with the work of Bolzano and Cauchy being "arithmetized (i.e.,
formalized) by Weistress)
However, non-standard analysis defines a system of hyper-reals and then sets
the limit EQUAL to the function evaluated with a "non-standard" part. So,
if it's plausible that the "choice" in Steve's post is an artifact of the
inequalities (as opposed to intrinsic to Calculus), then I'm not sure how
this "choice" is different from the conventionalist's "choice of system."
But, if it is something differnt, something connected with that particulr
way of defining limits, then something needs to be said for the apparent
lack of a similar choice in the non-Standard analysis.
I think there are actually 2 levels of choice here. One would be the choice
of a system. I can choose either "epsilon-delta" or "non-standard"
approaches to resolving my Calculus homework. But this doens't seem to have
much to do with the math itself. Then there would be choices within a
system which would be constrained by the math itself. I think Steve's
choice might fall here. Once I decide to use epsilon-delta calculus, then
the inequalities give rise to this "choice." But If I choose to use
non-standard analysis, then it's gone (and I don't, at present, see where it
may be hidden).
Scott
P.S. Incidentally, I think there may be some relation here and to his
earlier posts about indeterminacy (the stuff about arrows and not being able
to know where you started). But I'll need to re-read those posts to make
the connection more lucid to myself.
On Mon, Jan 31, 2011 at 2:27 AM, <Baynesr at comcast.net> wrote:
> I agree with most, if not all, that Scott says here. Let me just add one
> thing on 'E=MC^2'. It has many equivalents; but even if you don't "monkey"
> with other considerations such as introducing Plank's constant, frequency,
> waver length, etc. your choice of units can make it look different. So, if
> instead of miles per hour or kilometers you create a unit for 'C' you can
> see it in different ways. So, e.g., if you take the unit of 'C' to be
> distant traveled in one unit of time equal to 1, then the formula will come
> out 'E=M'. In this case, if you take 'M' to be rest mass (the natural and
> right thing to do) then given that a photon has no rest mass E becomes 0,
> right off, whence 'MC^2=0' *in this case*; in fact 'MC^2=M' (Tautologically
> 'M=M' iff 'E=MC^2') where M is greater than 0 and the unit for 'C' is 1). In
> other words, there are a lot of things you can do algebraically.
>
> Let me "core dump" my immediate and, so far, hidden agenda. I think that
> minds are not in the head; to this extent I am a Cartesian, that is, minds
> are like meaning (vide Putnam, Burge, et al). I think that choice and
> probability are very different notions and relate differently to causation.
> The former, not the latter, is embedded even in the mathematics concerned
> with distance. Choice is involved in the concept of a limit in a certain
> way: recall 'as close as you like' in the df. of a limit? If, for example,
> you use the Fundamental Theorem of Calculus to calculate the area under a
> function using antiderivatives, all derivatives are limits and there is an
> element of choice, something like choice of units. In my opinion this holds
> even on the now accepted definition of limits in terms of inequalities. But
> if you don't use the Fundamental Theorem and, for simple problems, employ a
> Riemann sum where no limit is involved, STILL there is an element of choice,
> given that you can get accuracy "as close as you like" depending on how you
> partition the interval over which the sum is made. So there is what I have
> in the past called a "norm" even in describing mathematically the laws of
> classical mechanics etc. I've actually barely begun to examine the role of
> choice in math and logic. In logic the notion of a domain of interpretation
> is what might be called a "choice point." I didn't want to bring this up
> until later. I had better defer comment until I get this clearer.
>
> Regards
>
> Steve Bayne
>
>
>
>
> ----- Original Message -----
> From: "Scott Holbrook" <scott.holbrook at gmail.com>
> To: Baynesr at comcast.net
> Cc: "hist-analytic" <hist-analytic at simplelists.co.uk>
> Sent: Sunday, January 30, 2011 9:38:14 AM
> Subject: Re: Materialism and mass as a unit of measurement
>
> This is all pretty interesting and a lot of it still hasn't really been
> decided by physicists. But I think we can side-step most of it.
>
> First, I would just like to point out that E=mc^2 isn't really the whole
> equation. The whole equation is:
>
> E=sqrt((pc)^2 + (mc^2)^2) ; where p="rest mass" x "speed of light"
>
> But, since photons are never at rest, they never have "rest mass," it just
> doesn't make any more sense that "round squares." (This term is actually
> just an unfortunate relic from science of yester-years particle vs. wave
> debate. It was figured that if light had a massive particle component, then
> there should be longitudinal waves, but there aren't. The smaller the mass,
> the harder the waves would be to detect and no longitudinal waves have ever
> been discovered. So, if there were a particle, it'd have to be
> "massless."). So, "zero rest mass" really just means "never at rest."
>
> If that's unsatisfying, then it should be remembered that there is a
> conversion factor to go between "rest mass" and "relativistic mass." So, it
> depends on what you mean by "the same units," whether or not they are so the
> same. But it should also be kept in mind that E=mc^2 is a conversion as
> well. So any ambiguity in the units on the rhs quantity would be in the lhs
> as well.
>
> Confessedly, and as Steve pointed out to me, it's not really clear what
> exactly the comment on units amounts to. I was actually interested in units
> in my younger days, but physicists tend not to be bothered with such things
> and I didn't know any philosophers at the time, so it just sort faded into
> the background.
>
> I think I'd like to add one more interesting comment regarding physics and
> ontology. The Bose-Einstein Condensate was speculated upon by Einstein on
> account of a mathematical oddity in B-E Statistics...namely division by 0.
> So, this is a pretty glaring example of...tension?...between what the math
> can describe (legally) and what physically obtains. According to math,
> zeros in denominators don't happen...in nature, B-E condensates do happen.
>
> So, it almost seems like a real physical thing (the condensate) has no
> mathematical expression...or at least not one that is allowed by
> mathematicians.
>
> Scott
>
> P.S. I think I'll give Jammer's book a read then jump back into the foray.
> (*Concepts of Mass in Contemporary Physics and Philosophy* (Princeton,
> 2000))
>
> On Sat, Jan 29, 2011 at 4:19 AM, <Baynesr at comcast.net> wrote:
>
>>
>> "...physicalism...concerns the ontology of the world. It claims that the
>> content of the world is wholly exhausted by matter. Material things are all
>> the things there are." (Kim [2005] 150)
>>
>> Now consider an argument proposed by Block and Stalnaker as described by
>> Kim.
>>
>>
>> Neurophysiology
>> Neural State N1 causes neural state N2
>> Pain = N1
>> Sense of distress = N2
>> Therefore, pain causes a sense of distress.
>>
>> Note the identities. They play no real role in the explanation on Kim's
>> account. He remarks:
>>
>> "True, these identities do have a role in the derivation of 'Pain causes
>> distres,' but this is not an explanatory derivation; rather, it is a
>> dervivation in which 'equals for equals'." (Kim [2005] p. 146. Elsewhere,
>> and repeatedly, he describes identities as "rewrite rules." But is this
>> correct? Suppose it is. If so, the Block-Stalnaker case of explanation
>> appears to fall short. Suppose on Block-Stalnaker all that exists is matter,
>> although we could reconstruct the argument I will propose as directed agains
>> Kim, alone.
>>
>> Kim is, definitely, committed to two things. First, that matter and matter
>> alone exists; and second, matter provides the subvenient basis for
>> supervenience. Physicalists like to get technical with dualists,
>> particularly when "peddling" their physicalism. Let's see how literal their
>> "materialism" actually is.
>>
>> We are told that only matter exists. Well, what about a beam of light? It
>> has no mass, and so we might want to say that it is not physical. Is this
>> right? More importantly is the sense in which it is right consistent with
>> Block-Stalnaker on the role of identity statements? I think not. Suppose we
>> begin by saying
>>
>> 1. A photon is massless
>>
>> This is a given of physics. Another given of physics is the momentum of a
>> photon can be expressed this way, where 'P' is momentum:
>>
>> 2. P = E/C (where 'C' is the speed of light; and 'E' is (rest) energy)
>>
>> Now we, also, have it as a given that
>>
>> 3. E = MC^2 (Yippee!) And so, from (2) and (3) we get
>>
>> 4. P = MC^2/C
>>
>> Leaving us with
>>
>> 5. P = MC
>>
>> But wait! Doesn't (5) contradict (1), since 'M' means 'mass'? David
>> Susskind once raised the question whether the "units" associated with the
>> momentum of a photon are the same as those for massed particles
>>
>> 6. P = MV (for picky people assume we are dealing with vector properties
>> where applicable).
>>
>> That is: does 'M' in both (5) and (6) get indicated by the same units of
>> measure? He sees no problem. I do, one brought on by accepting
>> Block-Stalnaker. If we suppose that these identities are "rewrite rules"
>> then there is no force to the claim that the identity is ontological; it
>> becomes a matter of choice of convention. But if this is so, then neither
>> Block-Stalnaker nor Kim's materialism can be sustained as a ontological
>> claim, particularly in the case of things like photons. By the way, Kim has
>> not committed to "ontological relativity." The photon is interesting in
>> another way relevant to discussions of physicalism.
>>
>> I am concerned with Kim's belief that subvenient bases of supervient
>> properties must be material. Here we have a massless oscillatory field
>> phenomenon consisting of two waves wedded in geometrical symmetry: the
>> magnetic wave at a 90 degree angle to the electric. Now these two are not
>> identical. First, either the magnetic or the electrical properties of the
>> beam of light satisfies being the subvenient basis of the other; so we
>> appear to have mutual supervenience in the absence of a material subvenient
>> base. I would add, as an interesting aside, that we have here a symmetry
>> dependent periodicity which will become significant as I examine issues
>> raised by Mele's discussion and dualism generally.
>>
>> The main point: we cannot use Block-Stalnaker identities in explanation
>> since they allow idntifying a photon as possessing mass. Once we isolate the
>> sense in which this IS allowed we forfeit the idea that explanation can be
>> transferred from talk of one thing, such as c-fibers to another, pain.
>>
>> I haven't edited this darn thing. I may revise it as I usually do pending
>> a reread at some point.
>>
>> Steven Bayne
>>
>>
>>
>>
>>
>>
>>
>> 45000
>
>
>
>
> --
> "Conventional people are roused to fury by departures from convention,
> largely because they regard such departures as a criticism of themselves."
> -- Bertrand Russell
>
> Listen to tracks from my most recent album at:
> www.myspace.com/propheticvyzion
>
--
"Conventional people are roused to fury by departures from convention,
largely because they regard such departures as a criticism of themselves."
-- Bertrand Russell
Listen to tracks from my most recent album at:
www.myspace.com/propheticvyzion
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