Okay, okay, they exist.  But it is not a pre-existing phenomena "discovered" by human beings; it is a construction of human thought, like language.  Allow me to elaborate:

In another thread today, someone asked why we haven't heard communication from aliens.  I suggested that intelligent life need not speak a language, or even use mathematics.  Someone then responded that these creatures wouldn't be intelligent, and that all intelligent creatures would use math, etc. etc.

I disagree with this.  Here is how we "found" math:  Math is an extension of the concept of time.  Time is an abstract concept designed by humanity in order to measure change.  Because of our foreknowledge of death, we felt the need to "measure" our lives against something.  So we took days, months, years, minutes, seconds, milliseconds, decades, millennia, and "created" them.  There really is no such thing as a "day"!  It all depends on where you are!  But we set up generally unbreakable rules and set them as guideposts to measure days against.  Days don't begin and end, we just say they do.  If I'm in Botwsana, and you are in New York, when do the days begin and end?  Time is a matter of perspective, a perspective which doesn't particularly hold up to drastic changes in setting, like supersonic air travel (or lightspeed travel).  

Then we began to count other things.  Two of this, twenty of that, 4,000,000 of this.  But the truth of the matter is that there really is not two of anything:  THERE IS ONLY ONE OF EVERYTHING!!  Everything is unique and individual; nothing is exactly like anything else.  And then we set out to find geometric truths; Pi R squared; A squared plus B squared equals C squared, etc.  But the truth of the matter is that no perfect circles exist in nature!  And PERFECT geometric shapes are fundamentally human objects.  We have taken the world around us and FORCED IT INTO MATHEMATICAL PERFECTION!!!

So here is my point:  Math is not bad; it is useful!  But it is like the brother of language.  Language is a tool we constructed and use to communicate thought; since our thoughts are constantly changing, language changes to fit people.  But we needed another system, a constant and unchangeable system to communicate ideas which are unlike humanity; unchanging ideas.  So we invented math; it always remains the same, it is unchanging, it is constant.  But it is a fundamentally artificial concept, used only by human beings in an attempt to organize and quantify a fundamentally disorganized and unquantifiable existence.

Please discuss.

Quoted: Then we began to count other things.  Two of this, twenty of that, 4,000,000 of this.  But the truth of the matter is that there really is not two of anything:  THERE IS ONLY ONE OF EVERYTHING!!  Everything is unique and individual; nothing is exactly like anything else.   Please discuss.

I think chemists would beg to differ.  There can be two carbon atoms, 6.02x10^23 carbon atoms, etc. All exactly the same

Time is pretty much a constant. I know that it technically isn't (so says Einstein anyway), but for the most part time moves at the same pace throughout the universe. Granted our time units may not be the same as other beings, but time is itself would.

Math is also somewhat unviversal. There are mathematical constants, such as pi, that will also exist everywhere throughout the unvierse.

2 + 2 always equalled 4 even before there was a mind to comprehend it.

Laws of physics can be explained using math.  For example, a revolving body will sweep out equal areas in equal amounts of time.  That is universal.  That did not suddenly begin happening when people found out that 1+1 is 2.

Gravitational force decreases at the square of the distance.  That is universal.  It didn't suddenly begin happening when someone figured out how to count.

Man DISCOVERED math, and then figured out how to use and manipulate it to our ends.

Even if there were "only one of everthing" (and I know what you're getting at), it doesn't matter.  If I have two of ANYTHING in my hands, and then I put two of ANYTHING ELSE in my hand, I have FOUR things in my hand.

time and math are both real.

time is the change of entropy in the universe.

math is simply the language used to describe things, and the relationships between things. Whether you have one, uno, une, ichi, I, or 1 apple, it is still 1 apple. If aliens exist, they would probably describe 1 apple in the same way, unless their perception of the universe is significantly different then our own.

Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it.

Define "2"

Define "+"

Define "4"

Define "Always"

Define "equalled"

Quoted: Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it. Define "2" Define "+" Define "4" Define "Always" Define "equalled"

Define "define"

Quoted: Define "define"

"define":  The removal of a issued fine.

Officer Dan gave Jim a ticket for exposing himself.  But after Jim gave Dan a reach around, Dan thought it prudent to define him.

Quoted: Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it. Define "2" Define "+" Define "4" Define "Always" Define "equalled"

Those are words we use to describe what we are doing.  Put simply, if you have two of something, and you put two more with the first two, you have a total of four.  Simple enough?

you're gonna hate it if your employer gets ahold of this and pays you  $1.00 because math does not exist, for your 80 hours of work, which do not exist.

TXL

Quoted: Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it. Define "2" Define "+" Define "4" Define "Always" Define "equalled"

For what purpose?

Consider the last half of my original statement. To need to define those terms is to miss the point of my statement.

Interesting article from a few days ago:

Science News Online

Week of March 4, 2006; Vol. 169, No. 9
The Limits of Mathematics

Ivars Peterson

At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all mathematics, from basic arithmetic to advanced calculus. His dream was to codify the methods of mathematical reasoning and put them within a single framework.

Hilbert insisted that such a formal system of axioms and rules should be consistent, meaning that you can't prove an assertion and its opposite at the same time. He also wanted a scheme that is complete, meaning that you can always prove a given assertion either true or false. He argued that there had to be a clear-cut mechanical procedure for deciding whether a certain proposition follows from a given set of axioms.

Hence, it would be possible, though not actually practical, to run through all possible propositions, starting with the shortest sequences of symbols, and check which ones are valid. In principle, such a decision procedure would automatically generate all possible theorems in mathematics.

f7065_1367.jpg

Gregory Chaitin.

What Hilbert was saying is that "we can solve a problem if we are clever enough and work at it long enough," mathematician Gregory J. Chaitin of the IBM Thomas J. Watson Research Center wrote in his 1998 book The Limits of Mathematics. "He didn't believe that in principle there was any limit to what mathematics could achieve."

In the 1930s, Kurt Gödel (1906–1978), followed by Alan Turing (1912–1954) and others, proved that no such decision procedure is possible for any system of logic made up of axioms and propositions sufficiently sophisticated to encompass the kinds of problems that mathematicians work on every day.

"More precisely, what Gödel discovered was that the plan fails even if you just try to deal with elementary arithmetic, with the numbers 0, 1, 2, 3, . . . and with multiplication and addition," Chaitin wrote in his 2005 book Meta Math! The Quest for Omega. "Any formal system that tries to contain the whole truth and nothing but the truth about addition, multiplication, and the numbers 0, 1, 2, 3, . . . will have to be incomplete."

In Gödel's realm, no matter what the system of axioms or rules is, there will always be some assertion that can be neither proved nor invalidated within the system. Indeed, mathematics is full of conjectures–assertions awaiting proof–with no assurance that definitive answers even exist.

Turing's argument involved mathematical entities known as real numbers. Suppose you happen upon the number 1.6180339887. It looks vaguely familiar, but you can't quite place it. You would like to find out whether this particular sequence of digits is special in some way, perhaps as the output of a specific formula or the value of a familiar mathematical constant.

It turns out that the given number is the value, rounded off, of the so-called golden ratio, which can also be written as (1 + SQRT 5)/2, an example of a real number. Given that expression, which represents an infinite number of decimal digits, you can compute its value to any number of decimal places. Going in the opposite direction from the given rounded-off number to the expression, however, is much more difficult and problematic.

For example, it's possible that if the mystery number were available to an extra decimal place, the final digit would no longer match the decimal digits of the golden ratio. You would have to conclude that the given number is not an approximation of the golden ratio. Indeed, the extended string of digits could represent the output of a completely different expression or formula, or even part of a random sequence. It's impossible to tell for sure. There isn't enough information available.

To sort through the relationship between random sequences and the types of numbers that mathematicians and scientists use in their work, Chaitin defined the "complexity" of a number as the length of the shortest computer program (or set of instructions) that would spew out the number.

"The minimum number of bits—what size string of zeros and ones—needed to store the program is called the algorithmic information content of the data," Chaitin writes in the March Scientific American. "Thus, the infinite sequence of numbers 1, 2, 3, . . . has very little algorithmic information; a very short computer program can generate all those numbers."

"It does not matter how long the program must take to do the computation or how much memory it must use—just the length of the program in bits counts," he adds.

Similarly, suppose a given number consists of 100 1s. The instruction to the computer would be simply "print 1, 100 times." Because the program is substantially shorter than the sequence of 100 1s that it generates, the sequence is not considered random. If a sequence is disorderly enough that any program for printing it out cannot be shorter than the sequence itself, the sequence counts as algorithmically random. Hence, an algorithmically random sequence is one for which there is no compact description.

Interestingly, the number pi (the ratio of a circle's circumference to its diameter), which is expressed by an infinite number of digits, has little algorithmic information content because a computer can use a relatively small program to generate the number, digit by digit: 3.14159 . . . . On the other hand, a random number with merely 1 million digits has a much larger amount of algorithmic information.

Chaitin proved that no program can generate a number more complex than itself. In other words, "a 1-pound theory can no more produce a 10-pound theorem than a 100-pound pregnant woman can birth a 200-pound child," he likes to say.

Conversely, Chaitin also showed that it is impossible for a program to prove that a number more complex than the program is random. Hence, to the extent that the human mind is a kind of computer, there may be a type of complexity so deep and subtle that the intellect could never grasp it. Whatever order may lie in the depths would be inaccessible, and it would always appear to us as random.

At the same time, proving that a sequence is random presents insurmountable difficulties. There's no way to be sure that we haven't overlooked a hint of order that would allow even a small compression in the computer program that produces the sequence.

From a mathematical point of view, Chaitin's result suggests that we are far more likely to find randomness than order within certain domains of mathematics. Indeed, his complexity version of Gödel's theorem states: Although almost all numbers are random, there is no formal axiomatic system that will allow us to prove this fact.

Chaitin's work indicates that there is an infinite number of mathematical statements that one can make about, say, arithmetic that can't be reduced to the axioms of arithmetic. So there's no way to prove whether the statements are true or false by using arithmetic. In Chaitin's view, that's practically the same as saying that the structure of arithmetic is random.

"What I've constructed and exhibited are mathematical facts that are true . . . by accident," he says. "They're mathematical facts which are analogous to the outcome of a coin toss. . . . You can never actually prove logically whether they're true."

This doesn't mean that anarchy reigns in mathematics, only that mathematical laws of a different kind might apply in certain situations. In such cases, statistical laws hold sway and probabilities describe the answers that come out of equations. Such problems arise when one asks whether an equation involving only whole numbers has an infinite number of whole-number solutions, a finite number, or none at all.

"In the same way that it is impossible to predict the exact moment at which an individual atom undergoes radioactive decay, mathematics is powerless to answer particular questions," Chaitin states. "Nevertheless, physicists can still make reliable predictions about averages over large ensembles of atoms. Mathematicians may in some cases be limited to a similar approach."

That makes mathematics much more of an experimental science than many mathematicians would like to admit.

Chaitin goes further. Human creativity is absolutely necessary for mathematical work, he argues, and "intuition cannot be eliminated from mathematics."

Originally posted: Feb. 21, 1998
Updated: March 4, 2006

Check out Ivars Peterson's MathTrek blog at http://blog.sciencenews.org/.

References:

Chaitin, G.J. 2006. The limits of reason. Scientific American 294(March):74-81. See http://www.umcs.maine.edu/~chaitin/sciamer3.html.

______. 2005. Omega and why maths has no TOEs. Plus (December). Available at http://plus.maths.org/issue37/features/omega/index.html.

______. 2005. Meta Math! The Quest for Omega. New York: Pantheon.

______. 1998. The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning. Singapore: Springer-Verlag.

Kleiner, I., and N. Movshovitz-Hadar. 1997. Proof: A many-splendored thing. Mathematical Intelligencer 19(No. 3):16-26.

Peterson, I. 1998. The Jungles of Randomness: A Mathematical Safari. New York: Wiley.

______. 1990. Islands of Truth: A Mathematical Mystery Cruise. New York: W.H. Freeman.

Velleman, D.J. 1997. Fermat's last theorem and Hilbert's program. Mathematical Intelligencer 19(No. 1):64-67.

Additional information about Gregory Chaitin and his writings is available at http://www.umcs.maine.edu/~chaitin/.

Quoted: Okay, okay, they exist.  But it is not a pre-existing phenomena "discovered" by human beings; it is a construction of human thought, like language.

Not true at all.  The ratio of the circumference of a circle to its diameter is a universal truth, independently of any human being "discovering it".

I disagree with this.  Here is how we "found" math:  Math is an extension of the concept of time.  Time is an abstract concept designed by humanity in order to measure change.  Because of our foreknowledge of death, we felt the need to "measure" our lives against something.  So we took days, months, years, minutes, seconds, milliseconds, decades, millennia, and "created" them.  There really is no such thing as a "day"!  It all depends on where you are!  But we set up generally unbreakable rules and set them as guideposts to measure days against.  Days don't begin and end, we just say they do.  If I'm in Botwsana, and you are in New York, when do the days begin and end?  Time is a matter of perspective, a perspective which doesn't particularly hold up to drastic changes in setting, like supersonic air travel (or lightspeed travel).

You are confusing the units that we use with the underlying mathematics.

"Today a young man on acid realized that all of matter is merely energy condensed to a slow vibration, that we are all of one consciousness experimenting itself sub-objectively, there is no such thing as death, life is but a dream and we are the imagination of ourselves... Here's Tom with the weather."

I think that you are looking into this too far.

you can find perfect geometric shapes in nature....
in.....

CRYSTALS!

I'm down with the guys who say that math exists outside and independent of the human brain.

The stuff we write down and say, yeah that was invented by us, but the things we are tryint to describe/explain ... weren't.

Quoted: Quoted: Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it. Define "2" Define "+" Define "4" Define "Always" Define "equalled" For what purpose? Consider the last half of my original statement. To need to define those terms is to miss the point of my statement.

I was just trying to be a dickhead.

Quoted: Quoted: Okay, okay, they exist.  But it is not a pre-existing phenomena "discovered" by human beings; it is a construction of human thought, like language. Not true at all.  The ratio of the circumference of a circle to its diameter is a universal truth, independently of any human being "discovering it". I disagree; my contention is that there are no PERFECT circles; we invented perfect circles, which do not exist in nature. I disagree with this.  Here is how we "found" math:  Math is an extension of the concept of time.  Time is an abstract concept designed by humanity in order to measure change.  Because of our foreknowledge of death, we felt the need to "measure" our lives against something.  So we took days, months, years, minutes, seconds, milliseconds, decades, millennia, and "created" them.  There really is no such thing as a "day"!  It all depends on where you are!  But we set up generally unbreakable rules and set them as guideposts to measure days against.  Days don't begin and end, we just say they do.  If I'm in Botwsana, and you are in New York, when do the days begin and end?  Time is a matter of perspective, a perspective which doesn't particularly hold up to drastic changes in setting, like supersonic air travel (or lightspeed travel).   You are confusing the units that we use with the underlying mathematics.

No, I am saying one cannot exist without the other; our manufacture of the units in math are the same as math itself; it works only so far as we can MAKE it work.

Quoted: Quoted: Quoted: Quoted: 2 + 2 always equalled 4 even before there was a mind to comprehend it. Define "2" Define "+" Define "4" Define "Always" Define "equalled" For what purpose? Consider the last half of my original statement. To need to define those terms is to miss the point of my statement. I was just trying to be a dickhead.

Oh. Well you do a pretty good job of that. Carry on.

Quoted: No, I am saying one cannot exist without the other; our manufacture of the units in math are the same as math itself; it works only so far as we can MAKE it work.

Certainly the "laws" of nature existed before we ever "discovered" them because nature (space/time) existed and adhered to those "laws" long before we came along.

I like pie

Math is universal.

2 aliens, or fingers, or claws, or eyes,  will be "two" no matter what language, or symbol is used to describe them.

These concepts WILL be universal.

4 Earth Quadrants simultaneously rotate
inside 4 Time Cube Quarters to create 4
- 24 hour days within one Earth rotation.
This simple ignored math indicts you evil.
Demand evil educators explain Cubicism,
or allow me to come teach Cube Creation.

Brain........Hurts........

Imagine the following, at least until you get to the incomprehensible part:

What if there were an intelligent species that was so smart that they destroyed death?  They figured out the key to repairing any injury, and genetically can conquer all diseases and congenital conditions.  Would time continue to have meaning to this species, especially if they were constantly traveling between planets?  And if they had no concept of time, would they have a concept of mathematics?  Would one exist without the other?  What if they only knew of change?  

What if they came to a completely metaphysical understanding of the universe, and could bend space and light?  What if the distance between two planets meant nothing to them, because they could remove that distance using bent space?  Would they still feel the need to measure?  What if they had no reason to ever measure anything?  Would they have math?  

I personally think that math, like language, is a fundamentally HUMAN concept, and we should not think that we share these concepts with anything or anyone else.  In fact, the very urge to MEASURE something, to assign it a quantitative value, may be a uniquely human trait, a way for our mortal brains to organize the disorganized.  

It doesn't mean that I don't use math, or that my paycheck can be less.  My outlook is purely philosophical, not practical.  Math is certainly a useful tool.  That doesn't mean that it isn't a human construct.  I just am mildly annoyed by the engineer-types who feel like math is some sort of universal truth.  I DON'T BELIEVE IT!  We came up with it, and it doesn't work to explain a lot of things.  When you get to quantum physics, time and math start to fall apart.  

Please tell me this isn't the basis for your thesis or something.

Quoted: Math is universal. 2 aliens, or fingers, or claws, or eyes,  will be "two" no matter what language, or symbol is used to describe them. These concepts WILL be universal.

What if they have no word for "two"?  What if there is only one of everything for them?  There will be right and left, and north and south, and up and down, but no "two".    Everything with its own name, and an intellect capable of knowing it all, or a shared intellect?  What if they never thought to measure or count anything, but still have found a way to make things work?

This seems odd, but when you think about it, no other animals on this planet count, but they still can make things happen.  Beavers build dams, bees build hives, geese migrate, but none of them count.  

Quoted: Imagine the following, at least until you get to the incomprehensible part: What if there were an intelligent species that was so smart that they destroyed death?  They figured out the key to repairing any injury, and genetically can conquer all diseases and congenital conditions.  Would time continue to have meaning to this species, especially if they were constantly traveling between planets?  And if they had no concept of time, would they have a concept of mathematics?  Would one exist without the other?  What if they only knew of change?   What if they came to a completely metaphysical understanding of the universe, and could bend space and light?  What if the distance between two planets meant nothing to them, because they could remove that distance using bent space?  Would they still feel the need to measure?  What if they had no reason to ever measure anything?  Would they have math?

Their perception of time and math has changed, not the existance of it.

Quoted: Please tell me this isn't the basis for your thesis or something.

No, I probably don't even believe it; I just think that it is interesting to examine the way that humans examine things.

Quoted: Quoted: Imagine the following, at least until you get to the incomprehensible part: What if there were an intelligent species that was so smart that they destroyed death?  They figured out the key to repairing any injury, and genetically can conquer all diseases and congenital conditions.  Would time continue to have meaning to this species, especially if they were constantly traveling between planets?  And if they had no concept of time, would they have a concept of mathematics?  Would one exist without the other?  What if they only knew of change?   What if they came to a completely metaphysical understanding of the universe, and could bend space and light?  What if the distance between two planets meant nothing to them, because they could remove that distance using bent space?  Would they still feel the need to measure?  What if they had no reason to ever measure anything?  Would they have math?   Their perception of time and math has changed, not the existance of it.

This is my whole point:  our perception of time and math IS the existence of it.

I see what you are saying. Math and time itself could be just ways that our brain interprets/makes sense of its environment. Just the same way what we see colors. Colors really don't exist, they are simply a way our brain has learned to read electromagnetic radiation of different wavelengths. Maybe time is just a way our brain has made sense of changes, and math is just a way to quantify our continous universe into discrete objects. [Morpheus] Do you think that's air you're breathing?[/Morpheus]

Quoted: I see what you are saying. Math and time itself could be just ways that our brain interprets/makes sense of its environment. Just the same way what we see colors. Colors really don't exist, they are simply a way our brain has learned to read electromagnetic radiation of different wavelengths. Maybe time is just a way our brain has made sense of changes, and math is just a way to quantify our continous universe into discrete objects. [Morpheus] Do you think that's air you're breathing?[/Morpheus]

Yep.  And some others species' brains may have developed an entirely different system to come to similar conclusions.  Humans see and measure, dogs smell and seek, bats hear and navigate, aliens marklar and klaatu barada nikto!

Beleg,
Reference the formalist philosophy of mathematics.  You're about a century or so late with this idea...maybe more.  Sorry to burst your bubble.

Duuuuude.  That's deep.  And stuff.  hematics
Similarly, a "rock" is a rock, regardless of the name used in a particular language.  Without a type of language (including the subset of that language devoted to mathematics), a culture cannot effectively cooperate and share knowledge.  Without such sharing, they will never develop technology.

THERE IS ONLY ONE OF EVERYTHING!! Everything is unique and individual; nothing is exactly like anything else.

Nonsense.  Electrons have no hair.  Quarks have no hair.  We live in a quantum world.

Language is a universal concept.  English, and perhaps math, is not a universal concept.  English and math being examples of languages constructed by the human brain.

Now go read about Goedel and the power of formal systems.  That is your next step.

So can you make hamburgers out of ground beef? That is the real question everybody should be asking here.

Oh yeah.  Goedel kind of raped Hilbert when he rolled out his incompleteness stuff.

Anyway, intuition is necessary in mathematics because no one has figured out how to encode intuition in a formal system.

Bah!  This thread is overrun by filthy platonists!

Somebody's been watching the Star Trek marathon again.

I am with Beleg.
Consider geometry for an example.
Mathematics are used to define a circle in Euclidean geometry.  In another geometry invented by someone else, the definition of an Euclidean geometry circle might be the definition of a point or line in this other geometry.  You are taught Euclidean geometry in high school (at least I was) and you believe that is the only way to define shapes, lines, points, planes, etc.  In reality several other lesser used and known geometries exist and the definitions of things in each geometry are different.  So you cannot say that a circle or line or point is universal and has just existed.  These things were defined (invented if you will) by a persousing mathematics.  This is just a further extension of Beleg's thinking.

Quoted: Oh yeah.  Goedel kind of raped Hilbert when he rolled out his incompleteness stuff. Anyway, intuition is necessary in mathematics because no one has figured out how to encode intuition in a formal system. Bah!  This thread is overrun by filthy platonists!

check out the article I posted earlier

Quoted: I am with Beleg. Consider geometry for an example. Mathematics are used to define a circle in Euclidean geometry.  In another geometry invented by someone else, the definition of an Euclidean geometry circle might be the definition of a point or line in this other geometry.  You are taught Euclidean geometry in high school (at least I was) and you believe that is the only way to define shapes, lines, points, planes, etc.  In reality several other lesser used and known geometries exist and the definitions of things in each geometry are different.  So you cannot say that a circle or line or point is universal and has just existed.  These things were defined (invented if you will) by a persousing mathematics.  This is just a further extension of Beleg's thinking.

outside of any math or human rationale, a spherical shape, like a star, will still have a ratio between its radius and volume. This is based on how the universe works, not how we decide to arbitrarily describe it.

Quoted: Quoted: I am with Beleg. Consider geometry for an example. Mathematics are used to define a circle in Euclidean geometry.  In another geometry invented by someone else, the definition of an Euclidean geometry circle might be the definition of a point or line in this other geometry.  You are taught Euclidean geometry in high school (at least I was) and you believe that is the only way to define shapes, lines, points, planes, etc.  In reality several other lesser used and known geometries exist and the definitions of things in each geometry are different.  So you cannot say that a circle or line or point is universal and has just existed.  These things were defined (invented if you will) by a persousing mathematics.  This is just a further extension of Beleg's thinking. outside of any math or human rationale, a spherical shape, like a star, will still have a ratio between its radius and volume. This is based on how the universe works, not how we decide to arbitrarily describe it.

If a tree falls in the woods and no one is around to hear, does it make sound?  

Quoted: What if they have no word for "two"?

Won't matter....words are not important. A rose by any other name is still a rose. An object or idea or sum, is the same no matter the names attached.

What if there is only one of everything for them?  There will be right and left, and north and south, and up and down, but no "two".    Everything with its own name, and an intellect capable of knowing it all, or a shared intellect?  What if they never thought to measure or count anything, but still have found a way to make things work?

Won't matter, if there is one of everything and there is 10 of everything....it will be 10 no matter what symbol is used. If they have never thought to count them....that doesn't matter.....there will still be the same number whether they are counted or not.

This seems odd, but when you think about it, no other animals on this planet count, but they still can make things happen.  Beavers build dams, bees build hives, geese migrate, but none of them count.

It doesn't matter if they count them or not....if some exist, there there is a number that descrbes it

I find it hard to believe that Napoleon_Tanerite hasn't posted in this thread yet.

Time is relative.

Quoted: Beleg, Reference the formalist philosophy of mathematics.  You're about a century or so late with this idea...maybe more.  Sorry to burst your bubble.

Much later than that.  Beleg's proposal is a concept usually introduced by some arm waving freshman , then thoroughly dismissed in Intro to Philosophy.

No offense, beleg. but many ratios and mathematic concepts exist independently of the human mind.  

The ratio Phi, for instance, exists in the chambers of a Nautilus, the growth pattern of flowers and plants, and even in the spirals of galaxies.

1 + 1 = 2 everywhere in the universe.  We may use different symbols for the number and for the mathematical operators, nonetheless, 1 + 1 = 2.

If this hypothetical, super-intelligent, immortal species has any physical technology at all they will need to know mathematics.

Time is also a reality.  We measure it in seconds, minutes, days and years for relatively arbitrary reasons deriving from the orbital characteristics of the planet we happen to inhabit.  Nonetheless, time is real.

If this hypothetical, super-intelligent, immortal species has any physical technology at all they will need to know about time.