Did prime numbers evolve?

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dkomo

Posted: Fri Apr 11, 2008 7:28 am

Guest

Yes, of course they did. Prime numbers are concepts in human brains,
and human brains obviously evolved. Prime numbers have no independent
existence outside of human minds. If humans went extinct, prime numbers
would go extinct along with them.

Prime numbers went through a two-step evolution process. First the
brain of modern humans evovled from the brains of more primitive
hominids. This stage was completed roughly 100,000 years ago.

Next, cultural evolution took over. This produced language, then
civilization, then mathematics. Prime numbers were in existence as
concepts by the time Euclid came along.

You could try to argue that primes are integers and integers are part of
the fabric of the universe ("God created the integers, all else is the
work of man"). I don't think so. Integers are as much a creation of
the mind as primes are. You can point to three rocks, or five trees,
but these are simply mappings from the world of perception to the ideas
of "three" or "five". And primes depend on the ideas of multiplication
and division, which are clearly human inventions.

The ultimate origin of all prime numbers is the process of evolution.

--dkomo@cris.com

Lorentz

Posted: Sat Apr 12, 2008 8:14 am

Guest

On Apr 11, 1:28 pm, dkomo <dkomo...@comcast.net> wrote:

Quote:

the insects that use them go extinct. Certain insects reach maturity
and swarm periodically. Concsider the seven year locust. Almost all of
them use a period of time equal to a prime number of years.
Why a prime number? Well, if they reach maturity at the same
time there will be too many of them available for predators to eat.
That is unless the predator swarms with a period equal to the number
of years divided by an integer. By swarming with a prime number
period, an insect minimizes it chance of being eaten.
Well, here we see prime numbers being a product of insect
evolution. The insects evolved a prime number before the humans did.
Therefore, the prime number will exist until the insects go extinct.

Guy A Hoelzer

Posted: Sat Apr 12, 2008 8:14 am

Guest

dkomo,

I disagree because I think that discrete entities, including systems that
act as agents of causation, emerged in the universe. This is, I think, the
same as saying that continua gave rise to integers (countable entities).
Once discrete entities emerged, the quantitative features of the prime
numbers were also manifested. The evolution of the human mind and culture
eventually led to a mathematical appreciation of prime number qualities, but
those qualities existed whether or not they were appreciated.

Cheers,

Guy

in article fto73e$2b53$1@darwin.ediacara.org, dkomo at dkomo871@comcast.net
wrote on 4/11/08 10:28 AM:

Quote:

dkomo

Posted: Sun Apr 13, 2008 11:48 am

Guest

Lorentz wrote:

Quote:

On Apr 11, 1:28 pm, dkomo <dkomo...@comcast.net> wrote:

Yes, of course they did. Prime numbers are concepts in human brains,
and human brains obviously evolved. Prime numbers have no independent
existence outside of human minds. If humans went extinct, prime numbers

To expand on your thesis, the prime numbers would go extinct when
the insects that use them go extinct. Certain insects reach maturity
and swarm periodically. Concsider the seven year locust. Almost all of
them use a period of time equal to a prime number of years.
Why a prime number? Well, if they reach maturity at the same
time there will be too many of them available for predators to eat.
That is unless the predator swarms with a period equal to the number
of years divided by an integer. By swarming with a prime number
period, an insect minimizes it chance of being eaten.

This theory is a bit of a reach. Why doesn't the seven year locust
swarm with a period of three, five or eleven years? These are prime
numbers as well. And why don't the predators just swarm with a period
of one year, or of seven years if their existence is central to being
able to prey upon the locust. With a period of one year, the predators
could feast upon any insect species no matter what the prey species
period was.

Quote:

Well, here we see prime numbers being a product of insect
evolution. The insects evolved a prime number before the humans did.
Therefore, the prime number will exist until the insects go extinct.

The insects have absolutely no awareness that they are swarming with a
prime number period, let alone that that prime number is part of an
infinite set of prime numbers with a common property. That's what makes
this different from the concept of "prime number" in the case of humans.
Besides, if there were no humans to observe that the insect swarm period
is a prime number, then who would? The insects themselves wouldn't be
cognizant of it.

--dkomo@cris.com

Paul Ciszek

Posted: Sun Apr 13, 2008 11:48 am

Guest

In article <fto73e$2b53$1@darwin.ediacara.org>,
dkomo <dkomo871@comcast.net> wrote:

Quote:

Not true. Mathematics is based on pure logic, on things that must
be true regardless of whether or not their are any sentients to
discover or use them. The ancient greeks recognized the five
platonic solids and realized that their could not be a sixth long
before examples of all five were found in nature--and no sixth
has been found in nature. If humans went extinct, and some other
species later developed the ability to think about solid geometery,
they would know the same five platonic solids.

Closer to your prime number example, some attempts have been made
to broadcast messages into space that could be understood by non-
human recipients. When trying to represent a "rastered" image,
these messages contain a number of pulses that is the product of
two prime numbers, on the assumption that the recipients, like us,
will only be able to find one combination of rows and columns that
contains that number of pulses.

Prime numbers also play a role in natural phenomenon such as orbital
resonances.

--
Please reply to: | "Evolution is a theory that accounts
pciszek at panix dot com | for variety, not superiority."
Autoreply has been disabled | -- Joan Pontius

dkomo

Posted: Mon Apr 14, 2008 7:17 am

Guest

Guy A Hoelzer wrote:

Quote:

This sounds like Herbert Spencer's idea that "all structures in the
universe develop from a simple, undifferentiated, homogeneity to a
complex, differentiated, heterogeneity, while being accompanied by a
process of greater integration of the differentiated parts."

http://en.wikipedia.org/wiki/Herbert_Spencer

Also, you sound like a mathematical realist, defined like this:

"Mathematical realism, like realism in general, holds that mathematical
entities exist independently of the human mind. Thus humans do not
invent mathematics, but rather discover it, and any other intelligent
beings in the universe would presumably do the same. In this point of
view, there is really one sort of mathematics that can be discovered:
Triangles, for example, are real entities, not the creations of the
human mind."

http://en.wikipedia.org/wiki/Mathematical_realism#Mathematical_realism

The Wiki article describes a number of different schools of mathematical
philosophy. I jokingly replied to another post that I'm a
constructivist on weekdays, a mathematical realist on Saturdays, and a
Platonist on Sundays, especially when I'm inside a cathedral. That
way I've got all the bases covered.

I think one's opinion whether mathematical entities have an independent
existence outside of human minds is similar to having a political
opinion. One can be either a conservative or liberal and make a good
argument either way. It is the dynamic opposition between mathematical
realism and constructivism that is important, not whether one position
is correct and the other isn't.

I chose to focus on whether prime numbers evolved because the numbers
are in a borderline area between having an independent existence in the
natural world and being pure mental ideas. I expected to get some good
arguments either way, and got them, both here and on talk.origins.

Had I asked the question "Did Hilbert spaces evolve?" I would have
gotten far fewer people arguing that Hilbert spaces have an independent
existence outside human minds. Hilbert spaces are infinite dimensional
vector spaces where the vectors are functions, but Hilbert spaces are
the underlying mathematical foundation for quantum mechanics, and
quantum mechanics certainly deals with the physical world. Moreover,
there is a continuum of mathematical ideas starting with integers and
prime numbers, and leading to abstractions like Hilbert spaces. I'd say
this progression is part of the general process of evolution. How is it
possible to put a dividing line between prime numbers and Hilbert spaces
and say prime numbers exist in the real world, but Hilbert spaces don't?

--dkomo@cris.com

Paul Ciszek

Posted: Mon Apr 14, 2008 7:17 am

Guest

In article <fttv49$23op$1@darwin.ediacara.org>,
dkomo <dkomo871@comcast.net> wrote:

Quote:

This theory is a bit of a reach. Why doesn't the seven year locust
swarm with a period of three, five or eleven years? These are prime
numbers as well.

There are all different prime number periods, including 13 and 17 years
for cicaidas. A few years ago, the 13 year and 17 year cicaidas
swarmed at the same time, and entomologists were trying to see if the
13 year ones mated with the 17 year ones when they had the chance to.
(They only see each other every 221 years.)

Quote:

And why don't the predators just swarm with a period
of one year, or of seven years if their existence is central to being
able to prey upon the locust. With a period of one year, the predators
could feast upon any insect species no matter what the prey species
period was.

The predators, being mostly birds, have a totally different life cycle.
The whole point of the cicaida's strategy, though, is for there to be
so many out at one time that even as the predators chomp away to their
heart's content, the odds are it favor of any one cicaida surviving.

Quote:

The insects have absolutely no awareness that they are swarming with a
prime number period, let alone that that prime number is part of an
infinite set of prime numbers with a common property.

Sure, no more than the Chambered Nautilus knows anything about logarithms.

Quote:

That's what makes
this different from the concept of "prime number" in the case of humans.
Besides, if there were no humans to observe that the insect swarm period
is a prime number, then who would? The insects themselves wouldn't be
cognizant of it.

No, but it would still be true that this swarming strategy works
because of the properties of prime numbers, whether or not their
are any humans around to do the factoring.

Or do you claim that trees falling in forests only began making noise
some 100,000 years ago?

--
Please reply to: | "One of the hardest parts of my job is to
pciszek at panix dot com | connect Iraq to the War on Terror."
Autoreply is disabled | -- G. W. Bush, 9/7/2006

Posted: Mon Apr 14, 2008 7:17 am

Guest

In article <fttv4a$23pb$1@darwin.ediacara.org>, nospam@nospam.com (Paul Ciszek) wrote:

Quote:

In article <fto73e$2b53$1@darwin.ediacara.org>,
dkomo <dkomo871@comcast.net> wrote:
Yes, of course they did. Prime numbers are concepts in human brains,
and human brains obviously evolved. Prime numbers have no independent
existence outside of human minds. If humans went extinct, prime numbers
would go extinct along with them.

Not true. Mathematics is based on pure logic, on things that must
be true regardless of whether or not their are any sentients to
discover or use them.

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.

The ancient greeks recognized the five

Quote:

platonic solids and realized that their could not be a sixth long
before examples of all five were found in nature--and no sixth
has been found in nature. If humans went extinct, and some other
species later developed the ability to think about solid geometery,
they would know the same five platonic solids.

Closer to your prime number example, some attempts have been made
to broadcast messages into space that could be understood by non-
human recipients. When trying to represent a "rastered" image,
these messages contain a number of pulses that is the product of
two prime numbers, on the assumption that the recipients, like us,
will only be able to find one combination of rows and columns that
contains that number of pulses.

Merely a hypothesis. Or, a wishful thinking :-)

DK

Lorentz

Posted: Mon Apr 14, 2008 7:17 am

Guest

On Apr 13, 5:48 pm, dkomo <dkomo...@comcast.net> wrote:

Quote:

Lorentz wrote:
On Apr 11, 1:28 pm, dkomo <dkomo...@comcast.net> wrote:

Yes, of course they did. Prime numbers are concepts in human brains,
and human brains obviously evolved. Prime numbers have no independent
existence outside of human minds. If humans went extinct, prime numbers

To expand on your thesis, the prime numbers would go extinct when
the insects that use them go extinct. Certain insects reach maturity
and swarm periodically. Concsider the seven year locust. Almost all of
them use a period of time equal to a prime number of years.
Why a prime number? Well, if they reach maturity at the same
time there will be too many of them available for predators to eat.
That is unless the predator swarms with a period equal to the number
of years divided by an integer. By swarming with a prime number
period, an insect minimizes it chance of being eaten.

This theory is a bit of a reach. Why doesn't the seven year locust
swarm with a period of three, five or eleven years?
http://www.wisegeek.com/what-are-cicadas.htm

"In fact, scientists have observed that the life cycle of cicadas
seems uniquely designed to ensure survival. Both annuals and
periodicals tend to hatch and grow to maturity in prime numbers, 2, 3,
5, 7, and up to 17."
The prime number behavior has more than one fitness advantage. For
alternate explanations of this well studied correlation, read:
http://www.sciencenewsforkids.org/articles/20040519/Feature1.asp
http://en.wikipedia.org/wiki/Magicicada
I first read about this correlation in a book by Dawkins, which I
forgot.

Quote:

These are prime
numbers as well. And why don't the predators just swarm with a period
of one year, or of seven years if their existence is central to being
able to prey upon the locust.
For the individual predator, swarming only increases the

competition for food. If the predator swarms at the same time, there
are more of that species around at that year to compete for resources.
The individual prey, on the other hand, has safety in numbers.
A similar mechanism explains why many prey animals travel in
groups. For example, fish often travel in schools. When a predator
comes, it can only attack so many fish. The individual fish has a
better chance to escape if it is surrounded by alternative targets.

Quote:

With a period of one year, the predators
could feast upon any insect species no matter what the prey >species period was.
Which is why few predators have such long cycles. Of course, most

predators are prey to something else. I am sure the cicadas prey on
something, if only on a plant. Their genome would love to reproduce
every year, munching that poor defenseless plant. Their main problem
is that they are the prey of something else. So it is in the
individual cicadas advantage to defer maturity until all the other
cicadas are out. This way, the cicada has the best chance of surviving
to make other cicadas.

Quote:

assumption is that something only exists if a human being thinks of
its existence in words. I can not believe that a word, even from such
a smart species such as ourselves, can bring something into existence.
You can't build a cat out of a poem.
You are assuming that only human beings, in fact only human beings
that know mathematics, actually perceive the existence of prime
numbers. This may be or may not be true. However, the only way we know
that human mathematicians perceive prime numbers is by their behavior.
They say so verbally and in writing. If everyone forgets math, but an
artist nonverbally learns to use prime numbers in his paintings, does
that still mean he doesn't perceive of prime numbers? How about an
animal.
More than 90% of our minds work on a nonverbal levels. I do not
wish to say "unconscious level," as I think our use of pictures and
words are conscious in a sense. Just because an animal doesn't talk
doesn't mean it doesn't have a clear image of the physical feature of
the world that stimulates its behavior.
I'll sum it up in three points:
1) I don't know how you can be so sure that behavior and perception
are totally separate.
2) I don't see how you can be sure that only human beings, and no
other organism, have any sort of perception.
3) I don't see why you can be so sure that perception is necessary for
the existence of a physical universe.

If perception is physically real, then it can probably evolve
like every other physically real quantity. Physical reality comes
first.

You are right in saying the insect probably has no perception of
using prime numbersA behavior does not always imply perception. On the
other hand, you are making an implicit assumption which is just as
bad. You are implying that behavior and perception are totally
uncorrelated.

Lorentz

Posted: Tue Apr 15, 2008 1:46 pm

Guest

n Apr 14, 1:17 pm, dkomo <dkomo...@comcast.net> wrote:

Quote:

Guy A Hoelzer wrote:
dkomo,

Had I asked the question "Did Hilbert spaces evolve?" I would have
gotten far fewer people arguing that Hilbert spaces have an independent
existence outside human minds. Hilbert spaces are infinite dimensional
vector spaces where the vectors are functions, but Hilbert spaces are
the underlying mathematical foundation for quantum mechanics, and
quantum mechanics certainly deals with the physical world. Moreover,
there is a continuum of mathematical ideas starting with integers and
prime numbers, and leading to abstractions like Hilbert spaces. I'd say
this progression is part of the general process of evolution. How is it
possible to put a dividing line between prime numbers and Hilbert spaces
and say prime numbers exist in the real world, but Hilbert spaces don't?

How is it possible to present without proof the idea that Hilbert

spaces don't exist, then claim without proof that fewer people claim
Hilbert spaces exist, and then ask how it was possible for most people
to believe Hilbert spaces and not prime numbers exist?
The logical contradictions are yours, not mine.

John W Edser

Posted: Tue Apr 15, 2008 1:46 pm

Guest

dk@no.email.thankstospam.net (DK) wrote:-

Quote:

Not true. Mathematics is based
on pure logic, on things that
must be true regardless of
whether or not their are any
sentients to
discover or use them.

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. This is only
because mathematics cannot be falsified so we can never know if prime
numbers evolved or not _until they become predicated by a falsifiable NON
number_. Just numbers alone, like the non predicated number 3 represent an
uncorrected, oversimplification of exactly the same number so predicated
e.g. three APPLES. In mathematics these three apples can be written in two
very different ways _additive_ and _non additive_. Three as a prime number
represents three ENTIRE (additive) apples as just 1 apple + 2 apples or 1
apple + 1 apple + one more apple forming the one, same _population_ of
apples. Non additively this is written as 3*Apple which is shortened in
algebra to 3A such that 3*A =A*3 _critically reversing subject and
predicate in the process because A represents a critical predicate for the
number 3 but not the reverse_. Empirically, addition and non addition are
NOT AT ALL the same because any non addition represents proper subsets
(nested sets) of numbers where the proper set configuration cannot be
reversed and the same meaning maintained. In fact this nested set reversal
always provides a refutation for the original. However, in just mathematics
multiplicative proper so-they-always-remain-non-reversible sets have become
oversimplified to mean additive so-they-always-remain-reversible
intersecting sets allowing the commutative law (without which mathematics
cannot function).

A strictly non additive (in this case multiplicative) association between
the number three and "apples" does not indicate one population but the very
opposite: a single discrete unit such that the number three represents a
_dependent part of the predicate "apple" such that three cannot be
independently selected_. Many times over the last ten years I have argued
that empirically, "multiplicative" indicates parts-to-a-whole while
"additive" indicates a population of independent wholes _which cannot be
selected as a single unit of selection_ as it is within uncorrected,
polycentric mathematical models ranging from dicentric classical group
selection to _minimally_ tricentric Hamilton's Inclusive Fitness. Darwinian
theory remains strictly monocentric but only because this alone can provide
a falsifiable theory of evolution using TDF (total Darwinian fitness). The
polycentric theories of Neo Darwinism were and remain, uncorrected
oversimplifications of monocentric Darwinism which have been misused to
replace/compete against, the one theory all of them were oversimplified
from.

One way of providing a falsifiable theory as to what prime numbers are
empirically is to hypothesise that prime numbers are more likely to
represent NON additive wholes, i.e. not just parts of some (other) whole.
This has interesting ramifications for evolutionary theory because it may
help to provide a mathematical way of modelling the unit of selection
problem which has reduced Neo Darwinism to just irrefutable mathematics. The
view that the prime numbers of 5 or more are empirically important can
verified by the two Goldbach conjectures:

1) Strong Goldbach conjecture: Every even integer greater than 2 can be
written as a SUM of two primes.
2) Weak Goldbach conjecture: Every odd integer greater than 5 can be written
as a SUM of three primes.

IOW prime things which remain greater than 5 are more likely to represent
populations of FITNESS INDEPENDENT (additive) UNITS OF SELECTION. This can
be tested to refutation if the fitness of one population is NOT just the
additive fitness of each unit which comprises that population (no matter how
fitness is defined). How might this work in practice? For gene centric Neo
Darwinism, when gene fitness epistasis is included, it should involve 5 or
more loci. For example within Hamilton's rule (within which all gene fitness
epistasis remains deleted ) becomes: (r^e)b > c where e = 5 minimally when
gene fitness epistasis becomes undeleted while at the same time proposing
independent (selfish) genes.

Quote:

The ancient greeks recognized
the five
platonic solids and realized
that their could not be a sixth
long before examples of all five
were found in nature--and no sixth
has been found in nature.

Regards,

John Edser
Independent Researcher

edser@ozemail.com.au

Alan Meyer

Posted: Wed Apr 16, 2008 7:25 am

Guest

On Apr 11, 1:28 pm, dkomo <dkomo...@comcast.net> wrote:

Quote:

Your conversation piece here is indeed intriguing. I can't help
but take the bait and join in.

Unfortunately, I am not versed in the philosophy of mathematics.
I know that some truly heavyweight thinkers have weighed in on
this topic and anyone attempting to add anything to the
discussion should read them and understand them before voicing
arguments that have, in fact, been demolished hundreds or
thousands of years ago.

But, after all, we are discussing this on the Internet where
ignorance is _de rigeur_. So I'll plow right ahead.

I incline towards the realist school (that numbers exist without
our having to entertain them in our minds.) There is more about
"inclination" at the end.

I will begin by asserting, in blissful ignorance, that material
objects are one category of reality, but not the only one.

Consider such objects as "facts", "propositions", "scientific
laws", "physical relationships", "properties", and possibly some
others.

We can say A is above B meaning that B is closer to the center of
the earth and A is along the same radius line, but further from
the center of the earth. I don't think we have any trouble
saying that the relationship exists even though it itself, i.e.,
the relationship, is not a physical object.

Or consider properties. We can give reasonable physical
interpretations to properties like "heavy", "red", "dense",
"loud", and many others. Although living beings have specific
perceptions of those properties that may be somewhat
idiosyncratic to the the species or even the individuals, the
properties themselves have a demonstrably independent existence
and can be described in terms that don't necessarily appeal to
particular sensations.

Now if "red" is a property, what about "circular", a mathematical
property, or at least a property whose description is
mathematical?

If that's admitted, it seems to me a short step to talk about
numbers as physical properties of collections of objects. Water
is a collection of 3 atoms. Carbon has 6 protons and 6
electrons. If we grant that the protons and electrons are real,
then why not admit the 3's and 6's. After all, there were 3
atoms in water and 6 protons and electrons in carbon long before
humans arrived on the scene - which can be demonstrated by
examining ancient water in the earth and ancient carbon in coal
or wherever. If we admit the numbers, again, there are very
short steps to admitting the properties of numbers, such as
primeness.

I think maybe we're on a slippery slope. Tilt it one way and we
slide towards admitting the reality of all sorts of abstract
objects. Tilt it the other way and we wind up denying the
reality of a lot more than we meant to.

Personally, I'm tilting towards realism rather than the
alternative ("nominalism"?, "subjectivism"?) Tomorrow, I might
incline the other way.

Alan

Posted: Wed Apr 16, 2008 7:25 am

Guest

In article <fu3epc$202e$1@darwin.ediacara.org>, "John W Edser" <edser@ozemail.com.au> wrote:

Quote:

dk@no.email.thankstospam.net (DK) wrote:-

Not true. Mathematics is based
on pure logic, on things that
must be true regardless of
whether or not their are any
sentients to
discover or use them.

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) but that's not the answer.
Only a tangentially related observation.

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.

DK

dkomo

Posted: Wed Apr 16, 2008 7:18 pm

Guest

Lorentz wrote:

Quote:

n Apr 14, 1:17 pm, dkomo <dkomo...@comcast.net> wrote:

Guy A Hoelzer wrote:

dkomo,

Had I asked the question "Did Hilbert spaces evolve?" I would have
gotten far fewer people arguing that Hilbert spaces have an independent
existence outside human minds. Hilbert spaces are infinite dimensional
vector spaces where the vectors are functions, but Hilbert spaces are
the underlying mathematical foundation for quantum mechanics, and
quantum mechanics certainly deals with the physical world. Moreover,
there is a continuum of mathematical ideas starting with integers and
prime numbers, and leading to abstractions like Hilbert spaces. I'd say
this progression is part of the general process of evolution. How is it
possible to put a dividing line between prime numbers and Hilbert spaces
and say prime numbers exist in the real world, but Hilbert spaces don't?

How is it possible to present without proof the idea that Hilbert
spaces don't exist, then claim without proof that fewer people claim
Hilbert spaces exist, and then ask how it was possible for most people
to believe Hilbert spaces and not prime numbers exist?
The logical contradictions are yours, not mine.

I wasn't presenting without proof the idea that Hilbert spaces don't
exist. I simply stated my opinion that most people don't think "that
Hilbert spaces have an independent existence outside human minds." Do
you disagree? If they don't have an independent existence, then I
think they evolved -- as *ideas*.

As for asking "how it was possible for most people to believe Hilbert
spaces and not prime numbers exist", I don't know where you got this.
It certainly wasn't a question of mine.

Rather, I asked where is the dividing line between believing in the
*actual* existence of prime numbers and believing that Hilbert spaces
exist only in the mind, since there is a continuous development of
mathematical ideas between them.

If you believe they *both* exist in the real world, that's fine by me,
although I think that's a belief that is weird as hell.

--dkomo@cris.com

prk via NatScience.com

Posted: Wed Apr 16, 2008 8:23 pm

Guest

Quote:

Prime numbers went through a two-step evolution process. First the
brain of modern humans evovled from the brains of more primitive
hominids. This stage was completed roughly 100,000 years ago.

Next, cultural evolution took over. This produced language, then
civilization, then mathematics. Prime numbers were in existence as
concepts by the time Euclid came along.

You could try to argue that primes are integers and integers are part of
the fabric of the universe ("God created the integers, all else is the
work of man"). I don't think so. Integers are as much a creation of
the mind as primes are. You can point to three rocks, or five trees,
but these are simply mappings from the world of perception to the ideas
of "three" or "five". And primes depend on the ideas of multiplication
and division, which are clearly human inventions.

The ultimate origin of all prime numbers is the process of evolution.

--dkomo@cris.com

I say no. Everything existed before we did, then we came along. Everything
mentioned, it seems to me, from development of language to math and the
sciences, is a construct. They're all useless without a common lexicon, like
we have to agree what a double yellow line in the middle of the road means if
this automobile thing is going to work out. So it's handy in terms of passing
it on to be sure, but it's all nomenclature. Now constructs can be handy, and
our knowledge increases thanks to people keeping track, but what we know and
how fast we learn it is independent of how much there is to know. So our
knowledge evolves through a given milestone rather than to it. M theory comes
to mind; cool if true, but if it is, it was long before we came to Newton's
apple or E=mc2. Indeed, since the beginning.

--
Message posted via http://www.natscience.com

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