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Science Forum Index » Bio Evolution Forum » Did prime numbers evolve?
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| John W Edser |
 Posted: Fri Apr 18, 2008 7:34 am |
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dk@no.email.thankstospam.net (DK)wrote:-
Quote: Lots of mathematicians disagree.
Alternative point of view is that
math/logic merely reflect the way
our brains work and have nothing
to do with the "objective"
reality
JE:-
The short answer is that mathematics is *NOT*
a science.
Mathematics may very well not be considered a
"science"(an arbitrary decision in itself)..
JE:-
No, a _strictly empirically based "decision"_. Unless
what we only imagine remains separated from what we
propose _on a contestable basis_ this universe is,
then "anything goes" within a Post Modern epistemology.
Mathematics misused is the basis of Post Modernism. It is
this destructive epistemology which continues to dominate
evolutionary theory almost entirely e.g. Hamilton's Rule.
Within mathematics time CAN be reversed reviving the dead,
but not empirically. What mathematics singularly lacks is
a frame of refernce_. You have to provide one from OUTSIDE
of mathematics just allow mathematics to make any empirical
sense. For example without a falsifiable frame of reference
provided by a constant, "up" cannot be differentiated from
"down", i.e. opposing sides of ANY relative relationship
cannot be differentiated. This was Galileo's great
contribution to the sciences (not mathematics). He
correctly argued that without a falsifiable frame of
reference provided by a fixed star, the sun centric
theory of the solar system cannot be differentiated
from the earth centric theory favored by the then
Catholic church. Einstein went on to use Galileo's
absolutely required falsifiable frame of reference to
refute Newton.
Because of chronic mathematical misuse evolutionary
theory has descended into a dark age dominated by
polycentric reasoning which cannot be tested
to refutation because no falsifiable frame of refernce
can now be supplied. The sense these propositions make
is just, mathematical.
Regards,
John Edser
Independent Researcher
edser@ozemail.com.au |
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| Alan Meyer |
| Posted: Fri Apr 18, 2008 7:34 am |
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On Apr 16, 1:25 pm, d...@no.email.thankstospam.net (DK) wrote:
Quote: ...
Bottom line is, prime numbers "exist" no more than
such things as negative or complex numbers or infinity
do. All are inseparable from the way our mind functions.
I was with you, at least in part, until the last sentence.
I think I can easily separate numbers from the way our minds
function.
We don't have access to other minds and can't compare our
concepts to theirs. But we do know about electronic computers.
A calculator, for example, peforms arithmetic in a totally
different way from the way our minds function. We can understand
it. After all, we designed it. But how many people perform
subtraction by addition of two's complements, or perform floating
point operations with separate operations on fixed length
mantissa and exponent, or determine signs by "extending" the most
significant binary digit to the left for up to 16, 32 or 64
binary places, or perform any mathematical operation by first
converting numbers to binary representation?
And yet calculators not only do all that, they come up with the
same exact answers that humans do - and faster and more reliably
too.
A computer program may find prime numbers in a completely
different way from the way we do. It might use the sieve of
Eratosthenes, or might use trial and error, or might use a
different algorithm. But again, it gets the same set of prime
numbers that we do. And that's not an accident of evolution.
I argue that the electronic calculator produces the same answers
that the human calculator does, not because it mimics the way our
minds function, or because it "thinks" of or represents numbers
the way we do, but because both we and the calculators execute
functions derived from the fundamental properties of numbers.
I argue that the notion of cardinal numbers is central to the
understanding of reality, and that any intelligent mind, human or
not, would develop a notion of cardinal numbers and would see the
same set of properties and derive the same set of prime numbers
that we do. They might speak of un deux trois, uno dos tres, ein
zwei drei, ee er san, or one two three. They might use base 2,
10, 16, or the funny Roman system. But the properties of the
numbers are identical. They might use calculators, abacuses, or
pencil and paper for performing calculations, but the end results
are the same. II + II = IV no matter how the mind functions or
what tricks it uses to perform the addition.
I argue that, although number is an abstraction, it is an
accurate and non-arbitrary abstraction from material existence.
I argue that humans have not evolved an arbitrary notion of
numbers that is idiosyncratic to us. Rather we have evolved to
the point that we can understand the actually existent objective
realities of which numbers are accurate abstractions.
So I think we can argue about your first sentence. We can argue
that "material existence" and "abstraction" mean two different
things. But I don't think we can argue that numbers and their
properties are inseparable from the way that our minds function.
They seem completely separable and non-subjective to me.
Alan |
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| DK |
| Posted: Sat Apr 19, 2008 8:13 pm |
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In article <fuam3f$2ttc$1@darwin.ediacara.org>, Alan Meyer <ameyer2@yahoo.com> wrote:
Quote:
On Apr 16, 1:25 pm, d...@no.email.thankstospam.net (DK) wrote:
...
Bottom line is, prime numbers "exist" no more than
such things as negative or complex numbers or infinity
do. All are inseparable from the way our mind functions.
I was with you, at least in part, until the last sentence.
I think I can easily separate numbers from the way our minds
function.
I don't think you can.
[snip calculator analogy for brevity]
Quote: I argue that the electronic calculator produces the same answers
that the human calculator does, not because it mimics the way our
minds function, or because it "thinks" of or represents numbers
the way we do, but because both we and the calculators execute
functions derived from the fundamental properties of numbers.
You can argue that, sure, but you can't prove it (and the proof is
likely impossible), and so I can, with the same strength, on a gut
level feeling, argue that no, calculators are merely devices designed
to deliver the same answers we do by means we are capable of.
Quote: I argue that the notion of cardinal numbers is central to the
understanding of reality, and that any intelligent mind, human or
not, would develop a notion of cardinal numbers and would see the
same set of properties and derive the same set of prime numbers
that we do. They might speak of un deux trois, uno dos tres, ein
zwei drei, ee er san, or one two three. They might use base 2,
10, 16, or the funny Roman system. But the properties of the
numbers are identical. They might use calculators, abacuses, or
pencil and paper for performing calculations, but the end results
are the same. II + II = IV no matter how the mind functions or
what tricks it uses to perform the addition.
I am with you. I agree that this is entirely reasonable point of view.
All I am pointing to is that it is nothing but a *belief*. There is
nothing in what we know that affirmatively shows that numbers
exist any more than color "green". (Which we know does not exist
because we "know" it is just an electromagnetic wave of ~ 500 nm).
Quote: I argue that, although number is an abstraction, it is an
accurate and non-arbitrary abstraction from material existence.
Maybe. Equally, maybe not.
Quote: I argue that humans have not evolved an arbitrary notion of
numbers that is idiosyncratic to us. Rather we have evolved to
the point that we can understand the actually existent objective
realities of which numbers are accurate abstractions.
Well, you know that we have evolved just enough to survive and
propagate well. If that involves understanding reality to the point
of "cheating" by way of inventing things that don't exist but help
us predict the reality (e.g. negatives), that's fine, says evolution.
Quote: They seem completely separable and non-subjective to me.
Could be only because our minds are so limited that they can't
fathom any alternative. Does not mean one(s) exist(s).
DK |
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| Alan Meyer |
| Posted: Mon Apr 21, 2008 7:50 am |
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On Apr 20, 6:13 am, d...@no.email.thankstospam.net (DK) wrote:
Quote: ...
You can argue that, sure, but you can't prove it (and the proof
is likely impossible), and so I can, with the same strength, on
a gut level feeling, argue that no, calculators are merely
devices designed to deliver the same answers we do by means we
are capable of.
I agree that "proof" is not the right word to apply to this
problem.
Quote: ... II + II = IV no matter how the mind functions or
what tricks it uses to perform the addition.
I am with you. I agree that this is entirely reasonable point
of view. All I am pointing to is that it is nothing but a
*belief*. There is nothing in what we know that affirmatively
shows that numbers exist any more than color "green". (Which we
know does not exist because we "know" it is just an
electromagnetic wave of ~ 500 nm).
<... additional arguments elided ...>
Philosophers have debated these questions for millenia and yet
today, 2,300 years after Plato and Aristotle, there is still no
agreed upon resolution.
One problem is that the very terms of the debate, "existence"
and "reality" are subject to alternate definitions.
Let's consider a number of candidates for existence:
myself
---
people
stones
trees
houses
---
stars
---
electrons
quarks
waves
photons
neutrinos
---
gravity
electromagnetism
nuclear forces
---
colors
tastes
sounds
---
minds
---
numbers
functions
lines
points
---
sentences
facts
propositions
theories
ideas
concepts
I've places dashed lines between groups that might possibly be
accepted or rejected together, but other people might put the
dashed lines elsewhere.
There have been philosophers taking different stances on all of
these things. Even the very first one, "myself", which seemed so
solidly established by Descartes' famous "I think therefore I
am", has been argued against by a few.
My personal view follows the "pragmatic" school. I think that
the concepts of "existence" and "reality" should be defined
"instrumentally". That means that if some entity is required for
some particular theory, and that theory accurately predicts our
experience in a very wide range of cases, with no known
countervailing cases, then the entity exists. I am hard
pressed to come up with a better definition of existence.
By that definition, things like electrons, photons, stars and
gravity clearly exist. Quarks probably do.
Numbers don't exist in the same sense. No one claims that they
are material objects or natural forces. But they are
instrumental in our explanation of the world. The explanations
we have in physics, chemistry, and every other science, depend on
the number system working the way it does.
So while I don't want to claim that numbers are "real" in the
material sense of having mass or energy or taking up space, I
would hold that they are objective, not subjective. We can't
explain things without them.
But, as I said above, there is still no consensus in the
philosophical community about these issues. The view that I have
just presented seems persuasive to me. Your mileage may vary.
Alan |
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