# Cosmic Distances

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### #161 Scanman

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Posted 14 March 2010 - 07:02 AM

Sun>>>>>>>You don't know this distance>>>>>Earth

There are a number of ways to make this calculation.

Here is the way the Greeks did it:
Around the 7th of the lunar month, you will notice that exactly 1/2 of the
Moon is lit.  That means that a path from you to the Moon makes a right
angle with the path from the Moon to the Sun.  Now measure the apparent
angle between the Moon and the Sun.  This gives you a trigonometry problem
that let us you calculate the Earth-Sun distance in terms of the Earth-Moon
distance.
The Earth-Moon distance can be obtained in terms of the Earth's radius by
observing the apparent angle traveled by the Moon when it has traveled, say,
four hours (60 degrees as measured from the center of the Earth).
Another way to get the Earth's radius is to note the distance from a
mountain or tower of a given height when it first appears on the horizon.

Another way is to use Parallax during a 'transit of Venus' eclipse.

Another way is to use radar to determine the distance to Venus during it's greatest elongation and then use the angle of Venus/Earth/Sun to calculate the distance to the Sun.

There is yet another way...using parallax to determine the distance from Earth to Mars and then using Kepler's Thrid Law of Planetary Motion...a bit more complicated.

Peace

### #162 Ron

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Posted 14 March 2010 - 10:31 AM

So you are saying that addition, subtraction, division and multiplication are 'metaphysical'?...

Yes, they are. And, until you provide physicality for addition, subtraction, division and multiplication (i.e. three oranges plus two oranges equals five oranges) they remain metaphysical.

and the use of mathematics employed with the gathering of data using the physical senses, nullifies the empirical method?

No, you are attempting to misconstrue what I said with your deductive dalliances scanman. The use of mathematics assists in the gathering of data, but that data is not empirically proven until the physicality of experimentation provides the validation or invalidation.

So the act of physically measuring two things with a tape measure and then adding (mathematics) them together...is not empirical?

And physically being there to verify the validity of the measurement; otherwise you are simply presupposing validity.

Are you saying that Euclidean Geometry is not empirical?

Without physically testing the hypothesis (within the conditions of the experiment), Euclidean Geometry by itself is not empirical Scanman.

I can understand saying that 'mathematics' as a whole (which includes theoretical math) is not empirical...but geometry was born out of empiricism.
Peace

All of mathematics is borne out of empiricism scanman. You needed the oranges, or the tick marks on the paper, or the fingers and toes to count on, in order to give validity to mathematics. Until then, it was just theoretical (and therefore metaphysical).

### #163 Guest_tharock220_*

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Posted 14 March 2010 - 11:26 AM

Hey tharock,
I never took trig, but geometry and algebra.  At any rate I understand in trig you can find the lengths for a triangle if you have one length and the angle measurements.  That's great when you put a triangle on paper, but you have to get it on paper first.

We are taking what amounts to be a 2D image on the night sky and translating that onto paper to do the triangulation.  I'm waiting for Ikester now for my diagram put in regular parallax format like you see in the books.  It will show two different distances for the exact same night sky view and the exact same AU distance for the Earth's orbit.  I did it using my geometry and mechanical drawing knowledge.  I know it sounds like I'm ranting like a lunatic, but when you see it I think things might change.

I look forward to seeing your drawing. I'm guessing your issue is with how the parallax angle is calculated. Do you agree that the base of the triangle using the Earth's orbit around the Sun is correct???

And, until you provide physicality for addition, subtraction, division and multiplication (i.e. three oranges plus two oranges equals five oranges) they remain metaphysical.

There is nothing abstract about arithmetic.

### #164 Scanman

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Posted 14 March 2010 - 04:41 PM

No, you are attempting to misconstrue what I said with your deductive dalliances scanman. The use of mathematics assists in the gathering of data, but that data is not empirically proven until the physicality of experimentation provides the validation or invalidation.

This is where we will have to agree to disagree...I read the definition as saying 'observation or experimentation'...you see it as 'observation and experimentation'

The word "empirical" denotes information gained by means of observation, experience, or experiment.

I know that you have found sources that use the word 'and'...

And physically being there to verify the validity of the measurement; otherwise you are simply presupposing validity.

Where is the predetermined limit on physicality?

It seems that you are saying that any form of indirect mesurement is invalid.

If I look up in the sky and count the number of geese in a formation...is that empirical?...I can only observe them visually, I am unable to touch them.

Is using the reticle on a microscope valid for gathering observed empirical data about how big something is microscopically?

Without physically testing the hypothesis (within the conditions of the experiment), Euclidean Geometry by itself is not empirical...

Geometry is made up of theorems and axioms...all of which have withstood the test of time. Geometry was built upon empirical experimentation.

We have sent men to the moon and back, based on the validity of geometry...and guess what?...Geometry was correct.

Yet when it comes to determining distances that throw a monkey wrench into your concept of the age of the universe, all of a sudden, geometry is not good enough.

I will admit that from my research into the use of the term 'empirical', as it is applied to the sciences and mathematics, there is a fair amount of heated debate...crossing sometimes into the realm of philosophy.

Do you doubt the measured distance from the Earth to the Moon?...once it was only known by 'metaphysical' geometry...now it has been proven out as a fact. The same can be said for every satellite and probe that has been sent to other planets and even outside of our solar system...all validate geometry.

Do you believe that AU (Astronomical Unit) is now a validated term?

If not...then I'M beating a dead horse...if so, then it is valid for determining Parallax measurments.

Peace

### #165 Guest_martemius_*

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Posted 15 March 2010 - 12:55 AM

Without physically testing the hypothesis (within the conditions of the experiment), Euclidean Geometry by itself is not empirical Scanman.

All of mathematics is borne out of empiricism scanman. You needed the oranges, or the tick marks on the paper, or the fingers and toes to count on, in order to give validity to mathematics. Until then, it was just theoretical (and therefore metaphysical).

This simply isn't true -- fingers or oranges or what have you are just a handy way to do things that turn out to match the more rigorous definitions of numbers, addition, subtraction, etc. You can google it if you're interested in how precisely they're defined (you should be warned that there's some heady mathematics involved, though). There is no empiricism in mathematics, but that's because mathematics is better than empiricism -- it's based in proof.

Likewise, the same is true for Euclidean geometry, or whichever type of geometry you choose. There's no way you can test or observe Euclidean geometry -- but you can conclusively prove it beyond a shadow of a doubt.

### #166 Ron

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Posted 15 March 2010 - 03:40 AM

There is nothing abstract about arithmetic.

Really? The proof is in the pudding... Without using anything physical, show me an arithmetic!

### #167 Ron

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Posted 15 March 2010 - 04:06 AM

This simply isn't true -- fingers or oranges or what have you are just a handy way to do things that turn out to match the more rigorous definitions of numbers, addition, subtraction, etc.

That is incorrect martimus; fingers and oranges (or what have you) are THE physical examples we use to provide substance for the metaphysical laws of mathematics.

You can google it if you're interested in how precisely they're defined (you should be warned that there's some heady mathematics involved, though).  There is no empiricism in mathematics, but that's because mathematics is better than empiricism -- it's based in proof.

Once again, you are incorrect martimus. Or, I should say; you are only partially correct. Your attempts to belittle others on the material versus transcendental correlations with statements like Ã¢â‚¬Å“you should be warned that there's some heady mathematics involved, thoughÃ¢â‚¬Â as if those you are talking to have no concept of mathematical laws and theory. And yet you are either totally disregarding the fact that mathematics relies on physicality (i.e. empirical actions)to evidence its empiricism, or you donÃ¢â‚¬â„¢t understand that mathematics relies on physicality to evidence its empiricism.

Nonetheless, you cannot prove mathematics even exists without a physical manifestation (by saying it, writing it, producing physical items to show how it works etceteraÃ¢â‚¬Â¦ etceteraÃ¢â‚¬Â¦)

Mathematics is not better than empiricism, because mathematics requires empiricism to prove it exists.

Likewise, the same is true for Euclidean geometry, or whichever type of geometry you choose.  There's no way you can test or observe Euclidean geometry -- but you can conclusively prove it beyond a shadow of a doubt.

Once again, you are incorrect martimus; you cannot prove Euclidean geometry even exists without a physical manifestation (by saying it, writing it, via producing physical items to show how it works etceteraÃ¢â‚¬Â¦ etceteraÃ¢â‚¬Â¦).

Therefore, without using anything physical, you cannot show me an arithmetic, a mathematic or a geometry!

### #168 Ron

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Posted 15 March 2010 - 04:46 AM

This is where we will have to agree to disagree...I read the definition as saying 'observation or experimentation'...you see it as 'observation and experimentation'

It always has been 'observation and experimentation'. It is only as of late (the last few decades or so) that the attempt to push (promulgate)'observation or experimentation'. But, you and I both know that nothing has been proven (or disproved) by the validation of physical experimentation. Whether we agree to disagree or not.

I know that you have found sources that use the word 'and'...
Where is the predetermined limit on physicality?

See the above.

It seems that you are saying that any form of indirect mesurement is invalid.

That is absolutely correct scanman. Until the measurement has been validated by physical testing, it is nothing more than a working model, presupposition and/or best-guess scenario.

If I look up in the sky and count the number of geese in a formation...is that empirical?...I can only observe them visually, I am unable to touch them.

Absolutely scanman, it can be empirical Ã¢â‚¬Â¦ Why? Because you have seen touched, smelt tasted and/or otherwise measured a goose previously (or have reliable witnesses who have done so). But can you physically transverse the distances youÃ¢â‚¬â„¢ve observed in the telescope as you Ã¢â‚¬Å“pass through the foci of a hyperbolaÃ¢â‚¬Â thus providing substance to your hypothesis? Do you have reliable witnesses who have done so?

Until youÃ¢â‚¬â„¢ve been there, its presupposition!

Is using the reticle on a microscope valid for gathering observed empirical data about how big something is microscopically?

Absolutely, but, until youÃ¢â‚¬â„¢ve proven (empirically via physical experimentation) the hypothesis is nothing more than a hypothesis scanman.

### #169 Ron

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Posted 15 March 2010 - 04:47 AM

Geometry is made up of theorems and axioms...all of which have withstood the test of time. Geometry was built upon empirical experimentation.

Absolutely! No argument there. But it still doesnÃ¢â‚¬â„¢t prove (empirically) what you hypothesize through a telescope, because you havenÃ¢â‚¬â„¢t physically proven it.

We have sent men to the moon and back, based on the validity of geometry...and guess what?...Geometry was correct.

Absolutely! And made all the corrections needed along the way. But, until we did so, everything was hypothesized, theorized and modeled. It wasnÃ¢â‚¬â„¢t empirically proven until we did the physical experimentation.

Yet when it comes to determining distances that throw a monkey wrench into your concept of the age of the universe, all of a sudden, geometry is not good enough.

Nope, unproven theories (i.e. not empirically proven) even with geometrical hypotheses is nothing more than a guess, a presupposition, a model.

I will admit that from my research into the use of the term 'empirical', as it is applied to the sciences and mathematics, there is a fair amount of heated debate...crossing sometimes into the realm of philosophy.

We are all only philosophizing when it comes to the transcendental scanman. And, if it hasnÃ¢â‚¬â„¢t been empirically verified, it is transcendental.

Do you doubt the measured distance from the Earth to the Moon?...once it was only known by 'metaphysical' geometry...now it has been proven out as a fact.  The same can be said for every satellite and probe that has been sent to other planets and even outside of our solar system...all validate geometry.

AS I said scanman, until it was physically measured, it was not proven. When we get beyond that fact (this is where most of you are having a problem) we can move on.

Do you believe that AU (Astronomical Unit) is now a validated term?

I donÃ¢â‚¬â„¢t have a problem with an AU within the parameters of what we have (so far) observed.

If not...then I'M beating a dead horse...if so, then it is valid for determining Parallax measurments.

I donÃ¢â‚¬â„¢t have a problem with Parallax measurements within the parameters of what we have (so far) observed.

Peace

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### #170 Guest_Tommy_*

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Posted 15 March 2010 - 06:47 AM

My understanding is that experiment allows functional relationship to be induced. A hypothesis could be falsified by observations alone should they not match the predictions of the hypothesis.

### #171 Ron

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Posted 15 March 2010 - 09:23 AM

My understanding is that experiment allows functional relationship to be induced.  A hypothesis could be falsified by observations alone should they not match the predictions of the hypothesis.

A hypothesis that is falsified by observation alone, is a weak hypothesis indeed!

### #172 Guest_Tommy_*

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Posted 15 March 2010 - 11:04 AM

A hypothesis that is falsified by observation alone, is a weak hypothesis indeed!

With hindsight a hypothesis subsequently observed to be invalid may seem to have been a weak conception. A hypothesis may be formulated before technological development allows us to ascertain whether its predictions match observation.

### #173 Ron

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Posted 15 March 2010 - 11:27 AM

With hindsight a hypothesis subsequently observed to be invalid may seem to have been a weak conception.Ã‚Â

Most usually, a hypothesis found to be invalid by observation alone is much weaker than one disproved by observation and rigorous empirical testing. Come to think of it, I cannot think of an instance where this hasn't proven itself out.

There again, observation in hindsight is still 20/20...

A hypothesis may be formulated before technological development allows us to ascertain whether its predictions match observation.

This is absolutely true and should be noted as such.

### #174 Guest_martemius_*

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Posted 15 March 2010 - 01:00 PM

That is incorrect martimus; fingers and oranges (or what have you) are THE physical examples we use to provide substance for the metaphysical laws of mathematics.
Once again, you are incorrect martimus. Or, I should say; you are only partially correct. Your attempts to belittle others on the material versus transcendental correlations with statements like Ã¢â‚¬Å“you should be warned that there's some heady mathematics involved, thoughÃ¢â‚¬Â as if those you are talking to have no concept of mathematical laws and theory. And yet you are either totally disregarding the fact that mathematics relies on physicality (i.e. empirical actions)to evidence its empiricism, or you donÃ¢â‚¬â„¢t understand that mathematics relies on physicality to evidence its empiricism.

Nonetheless, you cannot prove mathematics even exists without a physical manifestation (by saying it, writing it, producing physical items to show how it works etceteraÃ¢â‚¬Â¦ etceteraÃ¢â‚¬Â¦)

Mathematics is not better than empiricism, because mathematics requires empiricism to prove it exists.
Once again, you are incorrect martimus; you cannot prove Euclidean geometry even exists without a physical manifestation (by saying it, writing it, via producing physical items to show how it works etceteraÃ¢â‚¬Â¦ etceteraÃ¢â‚¬Â¦).

Therefore, without using anything physical, you cannot show me an arithmetic, a mathematic or a geometry!

You didn't google anything I mentioned, did you?

### #175 Guest_tharock220_*

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Posted 15 March 2010 - 11:25 PM

Really? The proof is in the pudding... Without using anything physical, show me an arithmetic!

6/3=2
2*3=6
2+2+2=6

I don't know how much math you've learned in your life, but arithmetic is the complete opposite of abstract. When you give something a concrete value it is no longer abstract. Abstract is something like

x relates to y by abs(x) = abs(y). Prove it is an equivalence relation.

### #176 Guest_martemius_*

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Posted 15 March 2010 - 11:54 PM

6/3=2
2*3=6
2+2+2=6

I don't know how much math you've learned in your life, but arithmetic is the complete opposite of abstract.  When you give something a concrete value it is no longer abstract.  Abstract is something like

x relates to y by abs(x) = abs(y).  Prove it is an equivalence relation.

Arithmetic is in essence completely abstract (its very basis [a pun? maybe..] lies, more or less, in abstract algebra)! I mean, if you define the natural numbers via the set-theoretic definition (http://en.wikipedia....natural_numbers) so that 0={}, 1={0}, 2={0,1} and so on, and if you then define addition by the definition with cardinalities of the corresponding sets of the added numbers, then in order to say something as simple as 2+2, you need to say that the union of {0,1} and {2,3} (ensuring that the sets are disjoint) is {0,1,2,3}, which is the definition of 4, and so 2+2=4. Math is essentially a complete abstraction, something completely based on arbitrarily defined axioms (after all, why shouldn't we define addition to correspond to be the cardinality of the intersection of sets as opposed to the union?), but it remains something that can be conclusively, non-empirically, proved based on those axioms.

### #177 Ron

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Posted 16 March 2010 - 03:30 AM

You didn't google anything I mentioned, did you?

No need to because you cannot answer the simple question:

Without using anything physical, you cannot show me an arithmetic, a mathematic or a geometry?

Thus shooting major holes in your "There is no empiricism in mathematics, but that's because mathematics is better than empiricism -- it's based in proof" fallacy...

Arithmetic is in essence completely abstract (its very basis [a pun?Ã‚Â  maybe..]

That is in essence completely incorrect unless you fail to physically express the mathematical equation. But, you cannot do that can you? You cannot express any mathematical thoughts without a physical medium,can you...

I mean, if you define the natural numbers via the set-theoretic definition (http://en.wikipedia....natural_numbers) so that 0={}, 1={0}, 2={0,1} and so on, and if you then define addition by the definition with cardinalities of the corresponding sets of the added numbers, then in order to say something as simple as 2+2, you need to say that the union of {0,1} and {2,3} (ensuring that the sets are disjoint) is {0,1,2,3}, which is the definition of 4, and so 2+2=4.  Math is essentially a complete abstraction, something completely based on arbitrarily defined axioms (after all, why shouldn't we define addition to correspond to be the cardinality of the intersection of sets as opposed to the union?), but it remains something that can be conclusively, non-empirically, proved based on those axioms.

You cannot define anything without physicality, and you cannot have empiricism without physicality. Your entire post above proves that point.

Which brings us right back to: without using anything physical, you cannot show me an arithmetic, a mathematic or a geometry?

### #178 Ron

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Posted 16 March 2010 - 03:33 AM

6/3=2
2*3=6
2+2+2=6

I don't know how much math you've learned in your life, but arithmetic is the complete opposite of abstract.Ã‚Â  When you give something a concrete value it is no longer abstract.Ã‚Â  Abstract is something like

x relates to y by abs(x) = abs(y).Ã‚Â  Prove it is an equivalence relation.

Again, you've proven my point... Without using anything physical, you cannot show me an arithmetic!

In your post above, you HAD to use the physical to provide the example. Mathematics are an abstract until you provide the physical experimentation thus showing the empirical validation of the equations. Therefore, you need to validate a hypothesis with physical experimentation for empiricism. If you'll notice; Martimus is the one attempting to say mathematics is abstract, not me:

Arithmetic is in essence completely abstract (its very basis [a pun?  maybe..]

What I am asserting is that you cannot "prove" mathematics until you use a physical form to either validate or invalidate the mathematics you are attempting to express.Therefore, when you falsely stated:

There is nothing abstract about arithmetic.

You were incorrect, unless you don't attempt to formulate your equation by providing a "physical" medium to express it (i.e.oranges, toes or pen and paper etc...), because; until you attempt to express it (a mathematical equation or any other thought for that matter) it is still incorporeal, metaphysical and or "not of physical substance.

Oh,and by the way; I appreciate your Argumentum ad Hominem attack :

6/3=2
I don't know how much math you've learned in your life

martimus did the same earlier. And that is no way to win an argument.

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Posted 16 March 2010 - 06:12 AM

Ron, so if I asked you to imagine what 4+4 equals you would say 8, right? You just did arithmetic in your head, without using any physical visual medium to describe the process to your conclusion.

### #180 Guest_martemius_*

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Posted 16 March 2010 - 07:06 AM

Ron, I know you like making up words, but if you're going to ask someone to show you something, it's common courtesy to stick to words that are actually defined. Once you rephrase your question about "an arithmetic, a mathematic, or a geometry" accordingly, I'll get back to you.

martimus did the same earlier. And that is no way to win an argument.

With all due respect [or maybe not], it's a grade school concept to say that numbers have to be represented physically. Given that you perpetuate such claims, it really doesn't seem too likely that you've had much math. But by all means, feel free to prove me wrong: have you ever taken abstract algebra or real analysis?

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