Re: Fitness Requires A Constant Frame Of Reference.
John Edser
>> JE:-
>> What differentiates mathematics from
>> non mathematics is the proposal of at least one constant. Note that this
>> is only possible OUTSIDE of mathematics. Mathematics remains incapable
>> of defining a single constant.
> I'm pretty sure it can define one.
JE:-
Hi Jim,
I would be very interested in an example:-) My understanding is that a
constant term within mathematics can only be defined *outside* of
mathematics. I contend this has everything to do with what Godel
discovered: mathematics remains 100% dependent on at least one
proposition which is not of mathematics. All mathematics can do is
logically process algebraic terms no matter if they are constants or
variables. For example, mathematics alone cannot define the maximal
velocity of light in a vacuum as a constant. Science is required to do
that. Mathematics can only treat c mathematically (which is not at all
the same thing as treating c scientifically). If c fails to remain
constant then it can just as easily be processed mathematically as a
variable. Variables and constants have little to do with mathematics but
everything to do with the sciences. If c stands empirically falsified
this must refute Einstein's Special Theory. If c within e=mc^2 was just
a variable then a theory is not now being provided, just mathematics.
Without at least one defined constant all you are left with is a bunch
of variables. These remain meaningless to the sciences (but not to
mathematics) only because no frame of reference has been provided to be
able to measure the variables e and m against. Without this critical
frame the mathematics can only repeat Zeno's Paradox: the hare cannot
mathematically catch up and overtake the tortoise only because one
variable is being compared to another. This paradox of mathematics can
easily be solved by re-including the proposed start and end of the race
as constants to which the proposed variables (the position of the hare
and the tortoise) remain relative.
The maximal velocity of light in a vacuum represents a maximand
velocity, i.e. c is allowed to be reduced when light is traveling in a
dense medium. However, without a single exception, light must travel as
fast as possible within the medium it is traveling to remain a valid
maximand velocity of Special Relativity. In the same way TDF represents
a maximand fitness. Like the maximand velocity of light TDF cannot be
reduced to anything less than a maximum per selectee per the environment
it finds itself within. IOW fitness altruism remains prohibited as a
critical falsification because TDF cannot be selected to be reduced and
remain a maximand fitness within falsifiable Darwinism. K, representing
TDF within Hamilton's rule (rb>K-c) provides a necessary frame of
reference for Hamilton et al be able to _empirically_ distinguish
fitness selfishness from fitness altruism and both of these from fitness
mutualism. Note that true fitness mutualism requires K to be mutually
maximized allowing TDF to remain a fitness maximand.
Regards,
John Edser
Independent Researcher
Perplexed in Peoria
> "Perplexed in Peoria" <jimme...@sbcglobal.net> wrote:-
>>> JE:-
>>> What differentiates mathematics from
>>> non mathematics is the proposal of at least one constant. Note that this
>>> is only possible OUTSIDE of mathematics. Mathematics remains incapable
>>> of defining a single constant.
>
>> I'm pretty sure it can define one.
>
> JE:-
> Hi Jim,
>
> I would be very interested in an example:-)
The one I had in mind is the constant number one (1).
> My understanding is that a
> constant term within mathematics can only be defined *outside* of
> mathematics.
I have no idea where you got that understanding. Though if you are
talking about 'physical constants' like c or h - constants with physical
dimensions - then maybe what you say is correct. But constants like
one or e or pi can be defined within mathematics - I'm not sure what it
would mean to define them outside mathematics.
> I contend this has everything to do with what Godel
> discovered: mathematics remains 100% dependent on at least one
> proposition which is not of mathematics.
I contend that you have no understanding of what Godel discovered.
And I know that it is not my job to rectify that. But I will try to improve
your formulation just a little. "Godel showed that mathematics cannot
be 100% complete without the help of at least one proposition which
is not of mathematics." But then who needs mathematics to be 100%
complete? No one uses more than a tiny fraction of it anyways.
HAND.
John Edser
>>> I'm pretty sure it can define one.
>> JE:- Hi Jim,
>>
>> I would be very interested in an example:-)
> The one I had in mind is the constant number one (1).
But 1 as an _integer_ is not constant because it is infinitely
divisible. Also, an integer can exist as either a positive or a
negative. My point is that a constant must designate some critical NON
reversible state. A classic example is the non reversibility of time. If
time could be reversed this can allow just about anything e.g. the
resurrection of the dead. Integers are not constant because they
disintegrate into an infinity of parts which can independently reverse
backwards and forwards across the equals sign. An empirical example: two
halves of a sheep are not equal to one sheep simply because both halves
are dead. The fact that we can only imagine each half to be alive proves
my point. For this reason we cannot empirically divide one sheep into
two or more independent in fitness halves and make biological sense. The
mathematical division of one Darwinian fertile form into a number of
additive in fitness parts via Hamilton et al, i.e. r representing the
gene level, b an organism group level and c a part of the donor's Total
Darwinian Fitness (the adult organism level) expressed as a cost,
was and remains just a mathematically based fantasy.
The pure _natural number_ 1 does represent an indivisible and strictly
positive number. However, this most pure of natural numbers cannot be
defined within mathematics. Number 1 remains an unfathomable notion
within mathematics even though mathematics remains based on it. Outside
of mathematics this most basic of numbers was predicated on empirically
based things such as "one sheep". Mathematically this became represented
using an algebraic term e.g. s allowing a sheep to be represented by 1s.
This represents 1*s (1 multiplied by s). Note that within mathematics
the reverse s*1 remains equally valid via the commutative law which
allows the logical reversibility of multiplication. Note that this law
only defines a tautology (any 100% self referencing proposition). An
example within evolutionary theory is Herbert Spencer's destructive
tautology "the survival of the fittest" only because the fittest
survive better. IOW, the critical relationship between 1 and S, within
mathematics was and remains NON additive binding 1 and s together in a
critical and non reversible way. Empirically, any non additive
relationship remains logically NON reversible in contradiction to the
commutative law of mathematics. For example, one sheep predicates the
natural number 1 excluding the reverse. In short, the natural number one
represents an abstraction from reality and not the reverse. The net
result of this is that the natural number 1 as a constant _can only be
defined outside of mathematics_ by whatever predicates it.
>> My understanding is that a constant term within mathematics can
>> only be defined *outside* of mathematics.
> I have no idea where you got that understanding.
JE:-
See above. Any proposition is either inside or outside of mathematics.
If all propositions are of mathematics only because propositions outside
of mathematics remain equal to propositions inside mathematics then
separating mathematics from non mathematics becomes reduced to just a
meaningless tautology.
> Though if you are talking about 'physical constants' like c or h -
> constants with physical dimensions - then maybe what you say is
> correct.
JE:-
My argument makes the following point: ALL proposed constants
are predicated on what you term "physical constants" which remain
propositions of science not of mathematics.
> But constants like one or e or pi can be defined within mathematics -
> I'm not sure what it would mean to define them outside mathematics.
JE:-
The constant pi is empirically based because a circle is not just a
mathematical concept. Like the natural number one, the circle within
mathematics is predicated on an empirically based object outside of
mathematics. Note that pi cannot be expressed exactly using integers but
it can be expressed exactly as a finite form outside of mathematics.
>> I contend this has everything to do with what Godel discovered:
>> mathematics remains 100% dependent on at least one proposition
>> which is not of mathematics.
>
> I contend that you have no understanding of what Godel discovered.
> And I know that it is not my job to rectify that. But I will try to
> improve your formulation just a little. "Godel showed that
> mathematics cannot be 100% complete without the help of at least one
> proposition which is not of mathematics." But then who needs
> mathematics to be 100% complete? No one uses more than a tiny
> fraction of it anyways.
JE:-
Incompleteness in mathematics refers to inconsistency. Godel discovered
that the propositions of mathematics are NOT consistent. The problem
with mathematics is one of critical inconsistency. IOW, within a list
of the propositions of mathematics can a contradiction be found? The
short answer: yes it can. Godel described it. The term "inconsistent" is
just a nice way of saying that a fatal contradiction exists within
mathematics. If a system can be demonstrated not to remain consistent
then it fails entirely, i.e. is invalid. The only way to solve this is
to import a proposition which is NOT of mathematics into mathematics.
The problem: my understanding is that Godel et al never defined what
proposition of non mathematics needed to be imported into mathematics in
order to render mathematics consistent.
I previously proposed within sbe that my solution to Zeno's Paradox
characterized the type imported proposition required to make mathematics
consistent: a constant. The only way Zeno's Paradox can be solved is to
re-include the artificially deleted constants representing the start and
the end of the race allowing a measure of the variable positions of the
tortoise and the hare relative to at least one defined constant which
can act as a critical frame of reference, i.e. NOT JUST RELATIVE TO EACH
OTHER. Just measuring variables relative to each other created the
paradox. IOW, at least one constant has to be imported into mathematics
from non mathematics in order to remove inconsistency from within
mathematics (and solve Zeno's Paradox).
Mathematicians have not solved Zeno's Paradox simply because the
solution is outside of mathematics. The net result for Neo Darwinism is
that at least one fitness constant remains to be defined within Neo
Darwinism before that paradigm can make scientific sense.
Earle Jones
John Edser <ed...@ozemail.com.au> wrote:
> >>> I'm pretty sure it can define one.
>
> >> JE:- Hi Jim,
> >>
> >> I would be very interested in an example:-)
>
> > The one I had in mind is the constant number one (1).
>
> But 1 as an _integer_ is not constant because it is infinitely
> divisible....
*
John Edser:
Sorry to break in here.
If you believe that 1 (integer one) is not constant because it is
infinitely divisible, then I ask you this:
What are your qualifications as an "independent researcher"? What is
your educational background? Are you qualified to discuss these things?
Thanks,
earle
*
John Edser
>>>>> PP:-
>>>>> I'm pretty sure it can define one.
>>>> JE:- Hi Jim,
>>>> I would be very interested in an example:-)
>>> PP:-
>>> The one I had in mind is the constant number one (1).
>> JE:-
>> But 1 as an _integer_ is not constant because it is infinitely
>> divisible....
> John Edser:
> Sorry to break in here.
> If you believe that 1 (integer one) is not constant because it is
> infinitely divisible, then I ask you this:
> What are your qualifications as an "independent researcher"? What is
> your educational background? Are you qualified to discuss these things?
JE:-
Hi Earl,
I contend that the integer 1 is not a constant because
1) it remains infinitely divisible.
AND
2) Each infinite part can independently reverse across the equals sign
of mathematics allowing it to change from positive to negative.
In contrast to this the natural number 1 (which is not equivalent to the
integer 1) does represent a constant because it remains indivisible and
always positive. This most critical number remains undefined within
mathematics, i.e. it is only assumed.
These points matter to evolutionary theory for the following reason:
a constant i.e. not just a variable fitness is absolutely required per
selectee per population in order to provider a valid frame of reference
for an evolutionary science. This is because only a single constant can
represent a maximand fitness. It isn't rationally possible to propose
more than just a single maximand fitness per selectee per population.
Note that mathematics has no constant frame of reference so it cannot
constitute a science. This can be easily be proven using Zeno's Paradox
and the solution to it that I have provided.
Any argument from authority (including mine or your qualifications) have
nothing to do with these propositions. If you have a valid criticism
then quite simply, provide it.
John Edser
<ei_spam...@ozemail.com.au> wrote:
> I see no value in "fitness" being counted (not according to any criteria for
> countability) just for the sake of counting.
JE:-
Hi Peter,
A fitness which cannot be measured (because not a single constant frame
of reference has been provided to measure it against) remains 100%
subjective. IOW, evolutionary science 100% depends on an objective
fitness. Science was and remains based on things which can be
empirically measured, i.e. objective things. Thankfully, this excludes
"fairies at the bottom of the garden" and horrors such as racial witch
hunts. Note that just being able to be measured empirically was and
remains critical for falsifiability. Without even a possible refutation
all that remains is the argument from authority. Combining this with our
tribal psychology provides a recipe for yet another authoritarian
disaster. Science, which I define as empirically applied reason,
requires a theory to provide a verification, non verification and a
falsification. The best any subjective notion of fitness can provide is
a verification/non verification neither of which are definitive. IOW,
subjectivity is a good diagnostic for critical incompleteness. In simple
terms, providing just a subjective fitness proves that the theory been
insufficiently thought out, e.g. Hamilton's inclusive fitness which was
and remains only mathematically valid. Only a single fitness maximand
per selectee per population is empirically possible.
> The word (concept) fitness may allow us to more realistically reflect on, or
> to better focus on the fact, that from single-celled to complex
> multicellular biological systems of functures (functional structures)
> sometimes function in ways that more or less directly or indirectly promote
> their procreative potential to the point of reproductive success.
JE:-
But any "proceative potential" remains entirely subjective. What TDF
measures is an empirically realized reproductive maximand per selectee
per population, i.e. not just a potential. In Darwinism TDF can alone
present a falsifiable fitness. This has NOT been realized within Neo
Darwinism because, like many other modern concepts, it has become Post
Modern. An illustration of such a tragic transformation is the current
financial meltdown provided by trendy Post Modern Economics, i.e. a so
called economics without any valid (constant) frame of reference, i.e.
an economics based entirely on mathematics. In a nutshell, the US banks
had a few trillion dollars but they ended up providing loans for about
40 trillion. IOW, the current meltdown was fueled (this time) by massive
private inflation (which is just a technical term for attempting to
obtain "something for nothing"). The dollar represents a critical
financial frame of reference, i.e. increasing (or decreasing) the money
supply publicly (simply printing more money) or privately (allowing
banks to lend out massively in excess of what they hold in deposits) is
only valid if altering the money supply holds the value of the dollar
_as close to a constant as is possible_. As productivity increases the
dollar will increase in value. In order to hold the value of the dollar
constant (so that the relative worth of things can be measured) the
money supply does need to be increased. However Post Modern economics
allowed an increase which was NOT subject to holding the value of the
dollar within the limits set by productivity increases. This was because
within Post Modern Economics, like Post Modern Neo Darwinism, all frames
of reference have been discarded leaving just, mathematics.
> Or, more specifically, it might funnel our attention onto facets of our and
> our ancestors' existence from where there is self-insights and
> social-insights to be had by indentifying traits that have promoted, and
> still promote, the reproductive survival of individual cellular systems'
> such as - not least importantly ;-) - us *human* individuals.
JE:-
The oneness of fitness was and remains dictated by that fact that
fitness represents a maximand within any science of evolutionary theory.
It was and remains empirically absurd to suppose that more than one
fitness maximand can validly represent a defined unit of selection.
This is why the adult human individual was and remains the common sense
mono-centric unit of selection within Darwinism. It's disintegration
within polycentric Neo Darwinism is only allowed via the misuse of
mathematics as a science, i.e. Neo Darwinism has been reduced to non
falsifiable via its embrace of Post Modernism.
Regards,
John Edser
Independent Researcher
Darwin123
> >>> I'm pretty sure it can define one.
> >> JE:- Hi Jim,
>
> >> I would be very interested in an example:-)
>
> negative.
literate. What do you mean by infinitely divisible, anyway? What do
you mean by constant?
Any number divided by 1 is the same number. The number +1 is an
integer, the number -1 is a different integer. By mathematical
convention, the number +1 is sometimes designate simply as 1.
An integer can exist as either a positive or negative number.
With the exception of 0, all integers are either positive or negative.
The integer named 0 is both positive and negative. Zero (i.e., 0)
divided by any number is still 0. I suspect that you really meant 0
instead of 1 as being infinitely divisible, but I can't be sure. I
can't even be sure what you mean by a constant.
Among physicists, the word "constant" almost always refers to
something that has to be calculated from measurements. It is constant
because it doesn't change in time. If you are talking about integers,
you are not talking about something that is determined from
measurements. Integers are often defined by Peano's postulates, and
are objects that are fully defined within mathematics. The fact that
they are useful in describing the physical world doesn't make integers
into constants. Integers are perhaps useful concepts for describing
physical constants.
Physical constants usually have either or standard or a protocol
for measuring them. NIST, for example, does not have a standardized
set of two objects. It doesn't have a standardized set of one object.
Little children are shown pictures of 1, 2 or 3 objects. However,
there is no unique physical object out there that I can say is two,
and only two, objects. Nor is there something out there that I can say
for sure is one object, and can't be broken down into other objects or
put together with other objects to form a still larger object.
Glibly making illogical statements like that are a sign of
illiteracy. You have not made a really good counterexample. I thought
you knew better than that.
Earle Jones
Earle Jones <earle...@comcast.net> wrote:
*
John Edser: You haven't answered my questions.
earle
*
Earle Jones
John Edser <ed...@ozemail.com.au> wrote:
> mathematics, i.e. it is only assumed....
*
John: It is not possible for me, or for anyone educated in science or
mathematics, to argue with you. You lack the discipline of education
and seem to feel free to make up definitions ("natural number 1" and
"integer 1" for example) to suit your rambling arguments.
Study. Learn first; teach later.
earle
*