... on Zeno's Paradox: not necessitating limes, nor a valid reduction of Prima Via's impossibility of infinite regress

youtube : numberphile : Zeno's Paradox
http://www.youtube.com/watch?v=u7Z9UnWOJNY

[Hans-Georg Lundahl:]

You can actually solve both problems in diagrams, without "limits".

Horizontal=distance, vertical=time.

In Achilles and tortoise you get two lines differently slanted, in hand clap (if hands meet) you can actually use "negative distance" for distance covered the other direction, so slant will be same but crossing like a St Andrew's cross, and in arrow paradox the target will be a verticla line.

Then you analyse the paradox part of it: in tortoise example you need to draw lines horizontally and vertically between the two slants, and they will be smaller and smaller and divide it less and less, in arrow example you subdivide the arrow's slant into one half, into a quarter and so on.

But they will not be infinite equal parts added together making a rally infinite process, they will only be shamming an infinite subdivision of a movement.

Which is where St Thomas' Prima Via on impossibility of infinite regress differs from the Zeno paradox.

Bergson thought he had refuted Prima Via thereby, but he was wrong to reduce it to a Zeno paradox. He started out as a fan of infinitesimal calculus before he became concerned with philosophy.

You see, divisibility of a continuum and addibility of separate steps are two different things.

Commented on in Friday 7-VI-2013,
Feast of the Most Sacred Heart of Jesus,
from Library Georges Pompidou/HGL

... on Geocentrism being arrogant or disproven

Commenting on video:

youtube : SecularAstronomer : Arrogance of the theistically geocentric/biocentric mindset
http://www.youtube.com/watch?v=F1PUjrcNCDw

ChipArgyle

[Ce commentaire a reçu trop de votes négatifs.]

Yeah, if I was God, that's where I'd put Earth too: right in the geometric center of the universe.

Oh, it's not there? It's tucked off to the side but not the edge, orbiting a star that by comparison to other stars can only be said to be wanting? Well that makes sense. If He'd put it in the middle, He wouldn't have plausible deniability working to His advantage, would he? Checkmate.

Hans-Georg Lundahl

What do you mean "Oh it's not there"? How do you know?

ChipArgyle

Astronomy. Big honking telescopes. There are numerous videos about Earth's location in the known universe right here on YouTube.

Besides, we know that everything in the universe is moving. If something was by happenstance ever at the geometric center of the universe, it would only be there for a fraction of a second.

Hans-Georg Lundahl

Right. Telescopes are a means of looking at things in better resolution. Between what is seen on the telescopes (big and honking or otherwise) and what is shown as computer simulations on videos, between again what is seen in the telescopes and your position that "we know everything is moving", do have the courtesy to trace the logic connection. If there is one, that is.

ChipArgyle

"My" position that everything is moving? It's not "my" position. It's what we know about the universe thanks to hundreds of years of study by all of the participants in an entire field of science. Trace the logic connection? You've lost me. What's your point?

Perhaps you have your own, unique idea about the universe, where Earth is in it, and relative motion of its contents. Could you enlighten us with your unique insights?

Hans-Georg Lundahl

You could have talked about "our" position. As for Geocentrism it is not my unique position either, it is our position among geocentrics - from Tycho Brahe to Robert Sungenis.

OK, geocentrics before Tycho Brahe were wrong or at least unprecise in being right (Ptolemy was in some places wrong) about detail. But it is the older and more usual position. I simply asked you to prove us wrong. The fact that telescopes exist doess not prove us wrong. That is where thou lostest me.

ChipArgyle

Geocentrism: Everything rotates about Earth, including stars that are millions of light years away. They rotate around Earth once a day, because we see them in the same place in the sky at night, meaning they travel at speeds of millions of light years...per hour. Even Neptune would have to orbit us faster than the speed of light. Which means relativity is incorrect and the speed of light is highly variable. That's what proves you wrong. The telescopes just help with the process.

Hans-Georg Lundahl

That leaves you a task to prove the light years and the constant finite speed of light. Or to give up if you cannot. Since those are things that you use as proof, but which the telescopes are in no position to reveal directly.

ChipArgyle

The light years of distance are known and not up for debate. In a geocentrist universe, the two Mars landers we have on that planet couldn't possibly be there. And your GPS wouldn't work either.

Geocentrism is the most easily debunked of the science frauds. Even geocentrist websites are going the way of the dodo due to lack of funding because only fools believe in such bunk.

We have the Internet now. Try learning about something backed by evidence and research. It's fun!

Hans-Georg Lundahl

"Are known" and "not up for debate" are not arguments. Neither is poverty of geocentric websites, neither is "only fools believe in such bunk".

You did try something rational: refer to Mars landers and to GPS.

Now, four tasks: prove light years, prove finite speed of light over all of universe, prove that Mars landings and GPS (two different things to prove) could not have worked in a Geocentric Universe.

Try using rational argument for once instead of rhetoric. It's fun.

[ChipArgyle did not answer this one, as far as I can recall and now a year later:]

Justwantahover

You have to prove that the stars are smaller than the asteroids. Why don you talk with SUCH FUCKING CERTAINTY??? I'll give you certainty. You are certainly retarded. And by-the-way fuck-head, ALL the things you mentioned are proven. Why ask for proof when you have absolutely no intention of listening at all. You are just totally BLOCKED off from reality. Just talk to Hugh Ross, he's a creationists, but he's NOT geocentric. He's an astro-physicist. He knows, YOU DON'T!

Hans-Georg Lundahl

I do not have to prove stars are smaller than asteroids. You have to prove they are bigger than asteroids.

"And by-the-way fuck-head, ALL the things you mentioned are proven."

According to the best satisfaction of astronomers believing the modern cosmology.

I am challenging their take on what constitutes proof.

I actually did contact Hugh Ross, as you mention it, a while ago, but got no answer.

[He also answered another one of my comments, which I repeat:]

Hans-Georg Lundahl

That leaves you a task to prove the light years and the constant finite speed of light. Or to give up if you cannot. Since those are things that you use as proof, but which the telescopes are in no position to reveal directly.

Justwantahover

The only way your story could be true is that all the stars and galaxies out there are just tiny fragments that are not actually very far out and have very little mass, so earth could hold the mass with it's gravity. You are saying the stars are just very tiny things (smaller than asteroids). Can you prove that?

You are a fucking lying fuck-head, so blatant and so OBVIOUSLY WRONG, that I have no hope for you. You are fucked-in-the-head, that's all I can say>

Hans-Georg Lundahl

"The only way your story could be true is that all the stars and galaxies out there ... are not actually very far out and have very little mass,"

That I am indeed saying is a distinct possibility. The contrary has not been proven so far. The proofs I have seen for contrary do not hold water.

"so earth could hold the mass with it's gravity."

Hold on a minute, I am NOT saying gravity is all that is causing all orbits.

I do believe in God and I do believe in angels.

Earth is not "holding in".

I recalled wrong about ChipArgyle:

ChipArgyle

I don't have to prove it. The math has already been done. All you have to do is research it like I did. It takes very little time.

Geocentrists are funny. Usually rooted in some form of theism, clinging to myths, a tiny little group of people denying what science has known for centuries as conspiracy theory. Tinfoil hats with crosses on them as decoration.

sadly to say

I seem not to have had the time to answer that one. On the other hand, claiming that the math having been done is equivalent to a proof having been proven, or claiming I have only to research it, and adding that "it takes very little time," does not exactly absolutely require an answer. Nor does his final quip on Geocentrics, except insofar as he is quite right that we are usually theists, that we do cling to religions he calls myths, and that, at present, we can be described as a tiny group. The rest is pretty much spoof. Even the insults of "Justwantahover" were interspersed with an argument or two, where ChipArgyle had given that up.

Arguing is less taught in school than the supposed facts. Why don't they teach logic in these schools?/HGL

Actually found a few more of Justwantahover, first connecting them to previous discussion:

Hans-Georg Lundahl

That leaves you a task to prove the light years and the constant finite speed of light. Or to give up if you cannot. Since those are things that you use as proof, but which the telescopes are in no position to reveal directly.

Justwantahover

Hey fucktard, yec fuck-head. Swing a bucket of water around you (with a hole in it) and the water flings out at the same speed as the remaining water in the bucket. So if the galaxies were all orbiting the earth at that speed, they would have all disappeared in one day (and flung out by billions of light years and we would no longer see anything). Earth does not have enough gravity to hold all that mass. Size of earth is proof of that.

Hans-Georg Lundahl

As said in the other answer, I believe there is a God and I believe there are angels.

I believe that not the gravity of earth but either God or angels is doing the "holding in" in this connection.

and:

ChipArgyle

Geocentrism: Everything rotates about Earth, including stars that are millions of light years away. They rotate around Earth once a day, because we see them in the same place in the sky at night, meaning they travel at speeds of millions of light years...per hour. Even Neptune would have to orbit us faster than the speed of light. Which means relativity is incorrect and the speed of light is highly variable. That's what proves you wrong. The telescopes just help with the process.

Justwantahover

Evidence does not mean a thing to them, cos they KNOW! If they are not going to believe the obvious (like that) what's the use? They won't come to the party. The obviousness of proof is proof they won't listen. I reckon there are very few young earth creationists who would totally rule out the geocentalist model.

Hans-Georg Lundahl

"I reckon there are very few young earth creationists who would totally rule out the geocentalist model."

Oh, shucks ... CMI are "very few"? Or they are not like deliberately ignoring me because I am a geocentric and that does not square with their solution to the distant starlight problem or their take on what the words in Joshua chapter ten mean?

Not totally rule out the geocentric model, they could have fooled me!

... on "Science Works" quote (c/o Dawkins)

Dawkins made a challenge, on knowing the past.
On Reading The Greatest Show by Dawkins - Parts of it!
Overlooked in Previous, about Dawkins' The Greatest Show on Earth
Medieval Matters for Richard Dawkins
Do evolutionists ever make unfalsifiable claims?
Two bishop Richards in dialogue (tongue in cheek)
Dawkins said Edgar Andrews had his book "well written" and that is one true word from him
Assortedretorts : ... on "Science Works" quote c/o Dawkins
... on Side issue to "Science Works"

LeCaNANDian: Richard Dawkins - Science works [2013]
http://www.youtube.com/watch?v=eob371ZgGoY

Hans-Georg Lundahl

[Ce commentaire a reçu trop de votes négatifs.]

Medicine cured people back when the four temperaments was a scientific model.

The wheel was invented possibly by "Babylonians" in Sumeria - whose model of reality was very far from that of modern science.

If I must believe evolution every time I use a computer, will you feel obliged to believe in demons everytime you use a wheel?

LeCaNANDian

You don't 'believe' in evolution, you either understand it or you don't.

Hans-Georg Lundahl

That was not the argument that Dawkins made and that I answered, Sir.

Is it according to you evolution believers like Dawkins or evolution disbelievers like Hovind who do not understand it?

Retracted comments have been answered by me before they were retracted, up to you to guess how they looked like:

NN

x

Hans-Georg Lundahl

Computer and wheel I can see or touch.

Demons might be easier to prove than evolution.

NN

y

Hans-Georg Lundahl

then prove me so: prove evolution occurred and demons are fictional (not meaning that they occur in fiction too, since that is obviously true of evolution as well)

as opposed to Dawkins right before, wheel and computer will not do as arguments for either of above positions

NN

z

Hans-Georg Lundahl

that is an ad hominem and even a threat of argumentum baculinum

so, once more: if you use the wheel, does that mean you are a parasite on the honest and hard working demon believers in Sumeria who might have invented it?

Pouya02

i mean its sort of like cooking, yes it is called cooking but what you're really doing is using the chemical reaction that different kinds of ingredients have towards eachother to create a final product that otherwise wouldnt be there, wether or not youre a babelonian or the achamaids in ancient persia. the point is you use science, wether or not youre a scientist to bend the laws of physics towards your favor in creating things that make your life easier, wheels, fire, AC, etc....

Hans-Georg Lundahl

No shit, Sherlock!

But if a person who is a total ignorant about Mendeleyev's Table nevertheless succeeds in cooking, why should not a person who is succeeding in building computers be a total dimwit about recent creation?

Wolfgang Zerobliss

The current scientific explanation of how and why a wheel is useful has nothing to do with demons. And evolution has nothing to do with the workings of a computer (a separate point).

Hans-Georg Lundahl

And evolution has nothing to do with the workings of a computer.

Thank you.

Wolfgang Zerobliss

Evolution isn't true because we have technologies that are based on it; it is true because it's proven to be correct by evidence, and many technologies that we have today are based on that idea. If you don't believe in evolution (which is the same as saying you reject science, which is nothing except the rigorous use of logic) then you must have your own theory why these technologies work.

If you reject logic and science this conversation is over as no one will be able to make an argument.

Hans-Georg Lundahl

I do neither reject logic nor science.

My theory of why wheels and computers work is logically connected to sciences like mechanics and electronics.

When I rigorously use my logic I do not conclude that either evolution or heliocentrism are true theories. They are like Sherlock's "enumerate all possibilities, eliminate all impossibilities, what is left is true however improbable" but with possibilities left out in first enumeration (a k a atheist methodology).

Martin Willett

Enumerating all possibilities is practically impossible. Eliminating impossibilities cannot be done reliably. This method only works for fictional characters in imaginary universes in the mind of the author who knows the solution.

Hans-Georg Lundahl

X seems to exist.

I enumerate as possible explanations:

• it has always been there
• it has emerged from something that was there before it
• it has been consciously made or created
• it is an illusion (dream, hallucination, untrue rumour, optic illusion, misunderstanding ...)

I think this is for instance one of the nodes were a complete enumeration of possibilities is quite possible. For any X it may further be possible to eliminate certain of these.

Martin Willett

How can you ever know that you have listed all possibilities rather than that you have merely exhausted the limits of your own limited imagination?

Hans-Georg Lundahl

There is such a thing as certain choices being binary, for instance.

There is also such a thing as certain combinations of binary choices being self contradicting.

Martin Willett

So in some circumstances that technique might work. But when choices and possibilities are not binary and when you cannot be certain about every deduction the possibilities proliferate and you cannot with any integrity say that you could have considered all possibilities.

Hans-Georg Lundahl

If in a certain case I do consider myself to have considered all the possibilities and ruled out what should be ruled out, it is up to the other guy to point out what I left out from my list of possibilities.

Which is what I was doing about those who left out God from possible explanations, if you care to recall the comment of mine you took issue with in the first place.

sabin97

it was the medical practices that cured people, not the incorrect parts of their knowledge. the part of their model that they used to invent the wheel was most likely correct.

you seem to be implying that the invention of the wheel was caused by a belief in demons.

you dont need to accept evolution in order to understand how computers work, however you do need to accept quantum theory. better examples would be modern medicine and modern agriculture.

Hans-Georg Lundahl

1) "the part of their model that they used to invent the wheel was most likely correct."

Exactly my point about evolution and:

2) "modern medicine and modern agriculture."

or 3) quantum physics (unless say Bolzmann managed a coherent and non-paradoxal version of it) and computers.

4) "you seem to be implying that the invention of the wheel was caused by a belief in demons."

Not by disbelief at any rate. Btw, I think there are angels and demons, so this is ad hominem (vs Dawkin's point).

sabin97

1) glad we agree that it works.

2,3,) glad we agree on those too

"Not by disbelief at any rate" nope, by science.

his point was that science works.

there's a very simple test you can do. next time your children get a very fever you could try taking them to a hospital(or another medical facility) and not pray, or you can try praying and not going to any medical facilities.

my hypothesis is that medical science without prayer will work significantly better than prayer without medical science.

Hans-Georg Lundahl

I agree wheel, medicine and agriculture do work.

I do not agree it is highly contested ideas in their inventors or more recent perfectors that make them work.

Whether demons or evolution/heliocentrism.

Not going to the doctor for sth sufficiently grave or untreatable at home would not be a plus while praying. Unless one were forced to do without the doctor.

As I have in recent years been as to dentists.

Valquill

The four temperaments didn't work, hence why we don't apply leeches when we have a fever anymore; the wheel was "discovered" by Babylonians, but not through their faith, but through their design. You don't have to believe in evolution when you use a computer, but don't pretend that you can understand something as complicated as a computer if you can't understand something as simple evolution.

Hans-Georg Lundahl

The four temperaments did work in many cases.

The theories replacing them do not work in all cases.

Medicine is also a kind of design, and errors in the background may not be affecting its efficiency in a given case. Truth in the background does not guarantee complete success either.

There are computer designers who do not believe in evolution.

And if evolution is simple, how do you explain growing chromosome numbers in mammals? Small changes added to one big cannot apply to whole numbers.

Hans-Georg Lundahl

...

If I must believe evolution every time I use a computer, will you feel obliged to believe in demons everytime you use a wheel? (etc before it)

bossmonkeykj

what a ridiculously stupid statement.the science that explains the idea of why the wheel works doesn'thinge upon the idea of demons.that's what the scientificmethod is for - to destroy as manyassumptions and leaps of logic as possible.unless you think we've accidentally stumbled upon relativitywhich is the only reason our GPS works,or that quantumphysics is completelywrong,and we've just been accidentallypredicting measurements equivalent to measuring the width of the US to within a hair's width

Hans-Georg Lundahl

One theory may be correct in one dimension which is checkable and not in another which either is not so or not in the way the checkers will check it.

It is you who claim that demons are an assumption and a leap of logic, not I.

One real leap of logic you just destroyed for Dawkins when detecting same one in me: it is quite as ridiculous to assume computers and medicine work because modern scientists believe in long term and big change evolution (=macroevolution) and more un-christian stuff .

GPS could work because of relativity - or because Geocentrism is true.

Guess which one I take on that?

I am not sure US can be measured in its width to within a hair's width, and if it can, I do not think "quantum weirdness" is the correct explanation for it.

Some versions of QP might be doing without QW:ness.

bossmonkeykj

that's because you're willfully ignorant of the facts. GPS would not work if we did not take into account the time differences due to relativity. so no, GPS working couldn't possibly be explained by geocentrism

and I didn't say the US could be measured to within a hair's width. I said quantum physics allows us to make predictions that are as accurate as measuring the US to within a hair's width. work on your reading comprehension.

Hans-Georg Lundahl

Are the time differences really due to relativity now?

There is a difference about being "wilfully" ignorant, and ignorant because one has not studied a particular question. GPS falls, if anything, into the latter category for me.

Sorry for missing "equivalent to".

I am not at all sure the measurements you refer so indirectly to are really accurate. But if they are, there might be versions of Quantum Physics that conceptually are not suspect due to Quantum Weirdness.

bossmonkeykj [also added an answer to above "One theory may be correct in one dimension" etc.]

I don't think you understand what a dimension is.

yes, it IS a leap in logic to assume the existence of demons.

and what does evolution have to do with computers? and in what way are you saying that medicine is not related to evolution?

Hans-Georg Lundahl

[voted against]

patphilosopher

You know that the Babylonians were very scientific , had a lot of knowledge about the stars , seasons and constructions.

Stars and Seasons = Astronomy

Construction = Mathematics

(And im just pointing out those 2 because im gonna lack space to write this)

They werent very far from modern science you fool, they are some of the first to use science back then.

You barely know anything about history and science , go educate yourself before making a fool of yourself in public.

Hans-Georg Lundahl

The Hebrews who accepted Genesis had most or all of the science that the ancient Babylonians had.

This was a new turn, but again one which favours my argument.

And yes, if you believe Mathematics, Astronomy OR use the wheel, do you feel obliged to believe the earth is flat (as Babylonians pretty explicitly stated) or that there are demons (which I agree with them on)?

Salafrance

Did people use gene therapy back when the four temperaments was a scientific model? Did people build integrated circuits predicated on semiconductor physics and the quantum theory back when the four temperaments was a scientific model? Did people eradicate entire diseases using vaccination back when the four temperaments was a scientific model. Could people *fly* back when the four temperaments was a scientific model model?

Can you pony up a demon such that I will believe in your delusion?

Hans-Georg Lundahl

OK, that means we might get even more technological advance the day we abandon delusions like Darwinism, right?

As for demons, I guard myself very well from ponying them up, but there is a real background to certain films about exorcism.

Check up exorcist Gabriele Amorth, will you. [continued below answer to phorse]

Salafrance (1/3 to above)

What, no demon, just a reference to some other obscure,delusional theist?

Would you care to comment on the probabilistic advantage of the operation of a genetic algorithm as compared with, oh, say, random chance? Note that links to Conservapedia will be laughed at.

You can actually do you own research in this domain, just as you can perform simple astronomical observations to establish a minimum, *personally established* age for the universe.

Or you can just parrot other deluded souls.

Hans-Georg Lundahl

Gabriele Amorth delusional?

What about checking yourself what his evidence is?

Minimum personally established age of universe: older (at least some) than first men.

Minimum personally established age of first men: older than or coeval with recorded history.

According to Genesis it is the latter.

Salafrance (2/3 to above)

Did people solve engineering problems predicated on the use of genetic algorithms back when the four temperaments was a scientific theory?

Did people *really* conjure demons back when the four temperaments was a scientific theory, or were they just a bunch of schizophrenics with interesting dreams and their associated clutches of the just plain gullible and stupid?

Hans-Georg Lundahl

Engineering problems solved on basis of GENETIC algorithm?

Are you serious? Are you talking about some weird Genetic Manipulation stuff? Or is "genetic algorithm" unconnected to genetics?

Check out the fact that demons speaking through the mouth of the possessed at Gadara asked Jesus not to order them into the abyss.

He ordered them into a herd of swine, which then threw itself into lake Gadara.

Had the man had a purely natural schizophrenia, there would have been nothing to force the swine to do that.

Salafrance (3/3 to above)

Can you describe your personal experience with demons?

Hans-Georg Lundahl

No.

Salafrance (to earlier as cited)

The Hebrews who accepted Genesis had most or all of the science that the ancient Babylonians had.

Did they have most, or all, of the science that *we* have?

Hans-Georg Lundahl

Now you are repeating the argument of Dawkins.

No, they did not have computers (though binary number multiplication was one technique of their which has been used in them).

Nor did the Babylonians.

The point is: our paleontology is as little testable in our daily use of tecdhnology as the Genesis was in daily use of Ancient Hebrew technology.

We use wheels invented by Sumerians or residents among them (Abraham was such in youth), does that oblige YOU to believe in Flood (Ziasudra or Noah)?

[continued

from above

phorse

Demons? On no planet in the universe do demons wander. Evolution is a fact, Brah. Sorry to disappoint. The irony of it is that you would believe it if it were in the bible. I just think it's funny how theists claim evolution is unbelievable nonsense, and the only cause for this is that it's not in the bible.

Hans-Georg Lundahl

Well, how do you explain a madman going sane after babbling he "is" many, after someone orders the many to get out of him ALONG WITH the fact that a herd of swine went suicidal? Saint Matthew witnessed the scene, he was among the original twelve. Chapter 8 of his Gospel. I was six years old and an evolution believer when I wondered how on earth a fish could by however so many degrees and generations in between develop into some kind of non-frog amphibian. And then there is the question of Mammalian Chromosome numbers. ppt d o t li/7m is a short link to a post collecting three other ones.

For her challenge (that of Salafrance) about astronomic observations at home for determining age of earth, check out my responses to:

... on Young Earth Creationism Denying Gravity (with a certain levity towards the matter, thank God!)
http://assortedretorts.blogspot.com/2013/05/on-young-earth-creationism-denying.html

... on Mathematics and Semantics

Continued from a previous one:

... on reality of existence of numbers (and on Pythagoreans and Bruno)
http://assortedretorts.blogspot.fr/2013/04/on-reality-of-existence-of-numbers.html

I) Christopher K

And in any case, I think this whole discussion is really just a matter of semantics. You want number to mean countables, and from what you said earlier, "quantity" to mean "number", though personally, I think that's quite backwards because when I hear "quantity", I think "the amount of things I have". But really, I think we're just arguing over terminology. Would you have these objections if I wasn't trying to label complex and irrational numbers as numbers?

Hans-Georg Lundahl

As soon as you agree that "irrational numbers" are really things like size to size ratios rather than answers to "how many", and as soon as you agree that "complex numbers" or for that matter already "negative numbers" and "zero" (as one number) are the sci fi of maths, that is more important than the terminology you chose.

Christopher K

You say "sci fi" as if those don't have very real, very very useful applications in real life. And the whole definition of irrational number is that it isn't a real ratio of anything to anything. Asking me to agree that irrational numbers are size to size ratios, where both sizes are real numbers is like asking me to agree that orange is purple.

Hans-Georg Lundahl

Having a real, useful, application or more than one in real life does not preclude sth being scifi or fantasy. Denethor and Saruman, Weston and Devine have real useful applications in real lifen nevertheless Lord of the Rings remains fantasy and Out of the Silent Planet remains scifi.

"Asking me to agree that irrational numbers are size to size ratios, where both sizes are real numbers is like asking me to agree that orange is purple."

The phrase "where both sizes are real numbers" is your interpolation.

They are size to size ratios or relations as can be proven in any case:

1) pi = circumference:diameter (any perfect circle)

2) sqrt(2) = diagonal:side (any perfect square)

3) sine x = opposite side (angle x) : hypothenuse (any rectangular triangle with angle x)

II) Christopher K

what's the difference between "minus: 1" and -1? And yes, the solution to x² = -1 is both i and -i, but it's perfectly valid for those sorts of equations to have two solutions. x² - 3x + 2 = 0 clearly has both x = 1 and x = 2 as valid solutions.

Hans-Georg Lundahl

Ah, I thought that the feeble for "negative roots" was sth like related to algebra due to equations!

The difference between operation subtraction with subtrahend 1 and number negative one is how you view subtraction. View it the right way and only the first works. Unless you deal not with numbers as such, what you are primarily counting, but in relative numbers, i e what operations you do, then sth can be simplified algebraically.

Christopher K

I think you're missing the point of my question there. You're saying that -1 isn't a number and you define it to be an operation (ie, the inverse operation, which is defined by x + (-x) = 0, where -x is the inverse of x) on 1 and that you define that as "minus: 1" and I'm asking "how is that different to just saying -1?" They're functionally identical.

Hans-Georg Lundahl

It is among other things your concept of "functional identity" that I am precisely attacking.

There is naturally a science of "how many", called arithmetic, and of "how big", called geometry. They are very empiric disciplines even.

Algebra deals with functionnaly identical ways of stating operations, which is of course useful for complex ones, as in simplifying them, but which is quite as obviously not the rational basis for arithmetic or geometry.

Christopher K

But algebra and geometry have overlaps. We can write geometric formulae as algebraic ones and vice versa. They're really just two sides of the same coin. Well, to a point. Algebra can describe things that can't be described geometrically.

Hans-Georg Lundahl

I do not deny that algebra and geometry have overlaps.

I am saying that geometry is a science in its own right, with an empiric basis of knowledge, and that algebra is an applied art.

III) Christopher K

i is usually defined to be the positive root for -1. And why isn't it valid if all the maths works out? If you don't get contradictions, there's no reason to say "Noooo it isn't valid!", because you're just throwing away a valid answer because you don't like it, and that's terrible science, or terrible anything in general.

Hans-Georg Lundahl

A square root is the obverse of a square number or the side of a square, and neither numbers nor sizes come in negatives.

Negatives don't come in until you ask "how many / much less than previous" and is obviously not a special kind of number but a relation of lessness measured by either number or numericalised magnitudes.

Confusing the two is terrible science and terrible logic and terrible anything (intellectual) in general.

Christopher K

A square root is something raised to the power of a half. Exponents are valid arithmetic operations, and you don't need to have square roots as the inverse function of the square function to use them.

And I'm not sure what the difference is, apart from excluding negative numbers from the set of numbers means that subtraction is no longer a valid function because you can now perform subtraction and get something that isn't a number.

Hans-Georg Lundahl

Whole number exponents certainly are valid arithmetic operations in themselves:

"x to exponent 1/2 = y" MEANS "x to 1 = y to 2"

Subtraction is a form of division. You can divide a whole several ways, but if one is dividing it into two, three or any other number of equal parts giving possibly a remainder less than the number of parts, the other is dividing it into two parts of which one has a determined size.

Which means that "1-2= -1" is not a valid subtraction per se.

Christopher K

Subtraction using only natural numbers doesn't work in general, because subtraction is simply the inverse of addition. In other words, x - y is the same as x + (-y), and (-y) isn't a part of ℕ.

Hans-Georg Lundahl

"x - y is the same as x + (-y),"

On the contrary, it is "x + (-y)," which is a backward way of writing "x - y"

Naturally speaking subtraction as much as division means separating parts of a whole, and multiplication as well as addition means taking separate items and making them part of a whole.

Christopher K

Mathematically though, subtraction is defined as the inverse operation to addition.

Hans-Georg Lundahl

Not traditionally in pre-modern maths.

IV) Hans-Georg Lundahl

calculating pi is sth else than defining it.

pi is not a ratio of two numbers ever, though certain ratios come close (314:100 for instance) but of magnitudes

Christopher K

The way you generate it doesn't matter if you still get the exact same result. 2/4 and 1/2 are both exactly the same number, just generated in a different way.

Hans-Georg Lundahl

Point is you cannot generate an exact value for pi.

If 314:100 (=31400:10000) is an inexact nether approximation, you can generate an upper such by 31416:10000 or by 22:7 or many other ways.

Pi itself is never properly speaking generated arithmetically. Nor is sqrt of 2. And so on for other "purely geometric ratios" ak by misnomer "irrational numbers".

Christopher K

You still miss my point. I'm not saying "generate pi by keeping on adding more decimals places", I'm saying "generate pi by the limit of this infinite sum".

Hans-Georg Lundahl

That is not a generation, that is an infinitely varied approximation depending on how many times you carry out whatever the sum is that is potentially infinite. And yes, I am aware there is a so called infinite sum (which never becomes actually infinite) of incomplete operation, related to those that generate e. I recall it was related to another one as well, but have forgotten which one, was it phi?

Christopher K

Yeah, you can use Taylor series's to produce an infinite sum with the limit of pretty much any irrational number you want.

Hans-Georg Lundahl

But you can only execute a Taylor series in a finite number of steps, meaning that the "infinite sum" of it never actually exists.

Christopher K

Only if you happen to not like infinite sums. Which is possibly an issue, because they can do funny things, but they happen to work pretty well and they make good approximations.

Hans-Georg Lundahl

"infinity" in mathematics is never real infinity

that is my FIRST issue with modern mathematic terminology, and it is an old issue between theology/philosophy and mathematicians: St Thomas, when talking about the infinity of God excludes the mathematic concept (and argues only God is infinite) insofar as when geometers say "take an infinite line" they only draw out the line as far as needed, never actually to infinity

same of course with "infinite sums"

Christopher K

Well of course, we can only approximate infinite lines to however far we can draw. Clearly, nothing in the universe is infinite. That doesn't mean we can't deal with things like infinite sums, by extrapolation or other methods.

Hans-Georg Lundahl

Dealing with an infinite sum by extrapolation or other methods involves not dealing with it directly, because - in this case - it does not exist as such.

I am not saying it has no useful applications in real life, I am just saying it is sth other than real arithmetic, real music, real geometry.

Appendix, on logarithms:

I said that "irrational numbers are size to size ratios or relations", but does this quite apply to logarithms?

I would tend to say, logarithms are a very special case, they are a ratio of number to ratio, of addition to multiplication (and of multiplication to exponents).

Like size to size ratios, they are however geometric in nature. They are the geometric basis of a slide rule.

Like any other purely geometric thing, it cannot be exactly parallelled in arithmetic, but it can be simulated in arithmetic.

If you want the base ten-logarithm for two, you are feigning to ask "ten to the power of how much equals two?" which does not make sense, since the answer cannot be a whole number and since a power must be a whole number. But that in turn can be translated to the somewhat inexact equality "ten to the power of how many equals two to the power of how many?" since "x^a/b=y" means x^a=y^b. One obvious, rough, inadequate answer is 3/10. 10³ = 1000, 2¹⁰ = 1024, "1000=1024". If you know that the logarithm of two on base ten is given in tables with first three decimals as 0.³⁰¹ you will see that this is not far wrong.

10^{approx. 3/10} = 2
10^3/10 = approx. 2
2^10/3 = approx. 10

And reason for the "approx" in each of these is that a logarithm like a size to size ratio is a non-numeric ratio.

At least it is non-numeric on the one side. It would not be useful unless it also had a numeric side.

lg 2 + lg 2 = lg 4
lg 2 + lg 3 = lg 6
lg 3 + lg 3 = lg 9
lg 3 + lg 4 = lg 12

And so on. And the letters lg, which are abbreviation for logarithm, could in English equally be abbreviation for length./HGL

Update on above appendix:

If there had been no logarithms say between lg2 and lg3, of course one side of the logarithmic relation would really have been numbers as such. However, there is a logarithm for the so called "irrational numbers" - like sqrt of two (half lg2) or sqrt 3 (half lg3) and of π and of φ and therefore the "number" side of the logarithmic relation must itself be a magnitude relation. Logarithm "of three" is really logarithm of 3:1. Though that would be harder to write out each time you use it and though the results of what actually amounts to lg(3:1)+lg(2:1)=lg(6:1) work well for application on the arithmetic numbers as well./HGL

Update:

I) Hans-Georg Lundahl

Dealing with an infinite sum by extrapolation or other methods involves not dealing with it directly, because - in this case - it does not exist as such.

I am not saying it has no useful applications in real life, I am just saying it is sth other than real arithmetic, real music, real geometry.

Christopher K

If it gives real results, then what's the problem? Look at, say mathematical demonstrations of solving Zeno's Paradox, where you use a sum to infinity. Sure, sometimes we need to invent funny ways to deal with these things, but if we can show these methods to actually work, then there shouldn't be a problem.

Hans-Georg Lundahl

A method working does not mean it is without conceptual flaw.

In Zeno's paradox about Achilles and the Turtle, you need a time by distance grid with two lines, Achilles' line and the turtle's line, and you can see there is a crossing and also that Zeno was just slowing down the conceptual coverage of the space before the coverage, and neither of the lines needs to be infinite.

II) Hans-Georg Lundahl

"x - y is the same as x + (-y),"

On the contrary, it is "x + (-y)" which is a backward way of writing "x - y"

[it is "x + (-y)" that is the same as "x - y"]

Naturally speaking subtraction as much as division means separating parts of a whole, and multiplication as well as addition means taking separate items and making them part of a whole.

Christopher K

Mathematically though, subtraction is defined as the inverse operation to addition

Hans-Georg Lundahl

Not traditionally in pre-modern maths.

Christopher K

Which, I think, is a lot of where our disagreement comes from. You seem to be under the idea that the Greeks and older maths was the absolute truth and couldn't ever be replaced. Personally, I think this world-view is horribly boring. The world is an ever-changing place and we're learning new stuff all the time and we need to update our world-view to adapt to this. Yes, we've changed the definitions of some things, but this isn't a bad thing. It helps us grow as people.

Hans-Georg Lundahl

It does not.

III) Hans-Georg Lundahl

Having a real, useful, application or more than one in real life does not preclude sth being scifi or fantasy. Denethor and Saruman, Weston and Devine have real useful applications in real life nevertheless Lord of the Rings remains fantasy and Out of the Silent Planet remains scifi.

Christopher K

Fantasy isn't sci-fi. When you call something sci-fi, you imply that it's something that might maybe exist in the future and you try to justify with reasons why it could work or maybe just technobabble. We might develop a Warp Drive some day. We won't develop the Five Wizards of Middle-Earth ever. By saying that zero and negatives are sci-fi, you're saying that they're not anything that exists in reality. The computer you're using disagrees.

Hans-Georg Lundahl

fantasy and sci fi imply you make thought experiments about what could be possible, even if clearly it is not real

wizards in LotR come very much closer to being really possible than "infinite improbability generator" of HHGG

zero and negative how-manys* do not exist in reality, and a computer is not in a position either to agree or to disagree

they have applications, so does - on your saying - i, but so have Saruman and Denethor: they apply to certain attitudes about tradition and politics.

tekhiun

complex numbers don't exist, the concept of them exist same thing with any number, some you can map to the real wolrd, others you cant.

Hans-Georg Lundahl

numbers like 3 exist

size to size ratios like pi exist

i does not exist

* footnote

If zero and negatives do not exist as "how-manys", they do exist as "how-many-more-or-less-than" in relation to "how-manys", and they do exist as "how-much-more-or-less-than" in relation to "how-muches".

Updating again:

Hans-Georg Lundahl

fantasy and sci fi imply you make thought experiments about what could be possible, even if clearly it is not real

wizards in LotR come very much closer to being really possible than "infinite improbability generator" of HHGG

zero and negative how-manys do not exist in reality, and a computer is not in a position either to agree or to disagree

they have applications, so does - on your saying - i, but so have Saruman and Denethor: they apply to certain attitudes about tradition and politics.

Christopher K

The problem is that negative numbers do exist in reality, or do the electrons in your computer not carry a negative charge that aren't floating around freely because they're being attracted to the positively charged protons in the nuclei of the atoms of the metals used?

Hans-Georg Lundahl

positive and negative in electric charges or for that matter credit and debt (which also cancel if brought in contact) are not really

"electric charge times minus one"

but

"negative electric charge times one"

meaning that this is no example of negative numbers existing

Christopher K

And while you're technically correct about credit and debt, pretending that negative numbers don't exist makes the maths more difficult. Allowing negatives makes everything flow much more easily.

Hans-Georg Lundahl

I do not think so.

In the example of credit and debt, do the sums of each account side, then subtract lesser sum from greater sum is a very good and useful and practical and easy way of dealing with it

Christopher K

Well sure, if you ignore all the evidence that says that electrons have the exact same charge as a proton, but multiplied by -1, Coulomb's law which relies on that fact and requires negative numbers, not to mention anti-particles, such as positrons which are identical to electrons except having the opposite charge (ie, multiplied by -1), then yes, there is no examples of negative numbers. Well, apart from all the others.

Hans-Georg Lundahl

Oppositeness of charge is a physical concept rather than a mathematic one.

It can of course be described as "multiply by -1", but if there is no such number that is clearly not what it really means.

Coulomb's law could certainly be restated using no negative numbers. In a more correct fashion.

Just as one can restate

(a-b)^2

=a^2-2ab+b^2

in a more correct but less useful way as:

= a^2 - ab - b(a-b).

Exactitude of concept is as useful for its purposes as ease of calculation for calculating

Hans-Georg Lundahl

numbers like 3 exist

size to size ratios like pi exist

i does not exist

Christopher K

i is as real as any other number. Just because it doesn't exist on the real plane doesn't make it any less real. Wikipedia has a nice section on real-life applications of complex numbers, which it might be a good idea to look at.

And again. You can say "pi is just a ratio" but it needs to be a ratio of at least one irrational number to another number. Look at the ratio diameter:circumference. One of those numbers is an irrational number.

Hans-Georg Lundahl

I never ever said of either pi or sqrt of two that it was a ratio of two natural numbers, I said it was a ratio of not numbers, but lengths - have you forgotten that?

Now, number has a discrete range of values, meaning there is nothing between 1 and 2, nothing between 3 and 4.

In lengths or any other quantities with continuous ranges this is not so. In any of these number is only assigned through ratio.

"3 cm" = "3:1 in relation to the cm"

"4 cm" = "4:1 in relation to the cm"*(continued again below)*

and of course:

"pi cm" = "circumference:diameter in relation to the cm"

"sqrt of two cm" = "diagonal:side (of perfect sqr) in relation to the cm"

Christopher K

And you don't see how that makes doing maths with either of those numbers, both of which have a number of applications outside geometry, more difficult and tedious?

Hans-Georg Lundahl

Writing it out as a ratio would certainly make it more tedious and difficult. REGARDING IT AS ESSENTIALLY a ratio does not.

And admitting that a certain part of say physics uses the same constant as was known from geometry is not in any way demeaning to physics, indeed, it poses physicians the question "why is it exactly the same"? Can it be because movement is in geometry, for instance?

*(continued from further up)* Christopher K

And we represent those lengths by numbers, exactly as you're doing there.

Hans-Georg Lundahl

Representing a length by a number does not make it a number.

"3 cm" does not MEAN "3 pieces, one centimetre each, glued to each other", what it means is "3:1 in relation to length known as cm".

It is very practical to forget what a certain set up of numerals mean when you are counting with them, but generalising the forgetfulness to total amnesia of real mathematical semantics does not add to that kind of usefulness.

Christopher K

Which, I think, is a lot of where our disagreement comes from. You seem to be under the idea that the Greeks and older maths was the absolute truth and couldn't ever be replaced. Personally, I think this world-view is horribly boring. The world is an ever-changing place and we're learning new stuff all the time and we need to update our world-view to adapt to this. Yes, we've changed the definitions of some things, but this isn't a bad thing. It helps us grow as people.

Hans-Georg Lundahl

It does not.

Christopher K

A very well thought out reply there. Mind elaborating on that?

Hans-Georg Lundahl

Growth does not mean leaving qualities behind but adding to them.

If number has a valid definition, changing it will not make us grow.

However, discovering that despite examples like 3-4-5 triangle, lengths are not really numbers and that there is beside the discrete range of values known as number also a continuous range of values in other types of quantity (bigness, weight, etc) is real growth.

This step was taken between Hipparcus and Aristotle/Euclid. Not by Cantor, Gauss etc.

Christopher K

This is why I still get the feeling we're arguing semantics here. You like the word "number" to mean "natural number" and I think it should be any form of quantity. But I don't see it as leaving qualities of numbers behind. Everything you can do with natural numbers, you can still do with complex numbers. What's being left? We're just adding to it so that every mathematical operation will work and give a valid answer (with the exception of division by 0) and we don't get bogged down in semantics

Hans-Georg Lundahl

"You like the word 'number' to mean 'natural number' and I think it should be any form of quantity."

Why not use "quantity" as the general concept then?

"Everything you can do with natural numbers, you can still do with complex numbers. What's being left?"

The fact of being a real multiple, conceived by one being added to one.

Hans-Georg Lundahl

Dealing with an infinite sum by extrapolation or other methods involves not dealing with it directly, because - in this case - it does not exist as such.

I am not saying it has no useful applications in real life, I am just saying it is sth other than real arithmetic, real music, real geometry.

Christopher K

If it gives real results, then what's the problem? Look at, say mathematical demonstrations of solving Zeno's Paradox, where you use a sum to infinity. Sure, sometimes we need to invent funny ways to deal with these things, but if we can show these methods to actually work, then there shouldn't be a problem.

Hans-Georg Lundahl

A method working does not mean it is without conceptual flaw.

In Zeno's paradox about Achilles and the Turtle, you need a time by distance grid with two lines, Achilles' line and the turtle's line, and you can see there is a crossing and also that Zeno was just slowing down the conceptual coverage of the space before the coverage, and neither of the lines needs to be infinite.

Christopher K

I was more thinking of the other paradox, of the arrow going to a target because I find it's an easier one to visualise. And yes, I do realise the flaw in his thinking but it doesn't make it less of an interesting paradox.

Hans-Georg Lundahl

I had only heard Achilles and the turtle in any elaboration.

Mind elucidating?

Christopher K

It's more-or-less the same paradox, but instead, you shoot an arrow at a target. After some time, it halves the distance to the target, then after some more time, it halves it again, and so on, never reaching the target. I think Numberphile's done a video on both versions of the paradox.

Hans-Georg Lundahl

That version can be solved with a diagram of distance and time, and the paradox can be shown to be a mental retarding before delays artificially put up.

http://assortedretorts.blogspot.fr/2013/06/on-zenos-paradox-not-necessitating.html

Update with Christopher again:

I) Christopher K

And while you're technically correct about credit and debt, pretending that negative numbers don't exist makes the maths more difficult. Allowing negatives makes everything flow much more easily.

Hans-Georg Lundahl

I do not think so.

In the example of credit and debt, do the sums of each account side, then subtract lesser sum from greater sum is a very good and useful and practical and easy way of dealing with it.

Christopher K

That's still longer than one subtraction.

Hans-Georg Lundahl

You still have to add up before you subtract one from other, exactly same length, wizeacre.

Christopher K

Depends on what exactly you're trying to do. Say, I've got $6 in my bank account and I buy something for $10. I've now got -$4 in my bank account (Plus some ridiculous bank fee for going into overdraft). It's much more simple than having to deal with two separate accounts.

Hans-Georg Lundahl

Whether it is that for the computer system or not, it is surely by doing:

- $10
+ $6
____
= -$4

same as would have been done with opposite signs, a simple subtraction of lesser amount from greater amount only that the subtraction meaning cancelling of opposite "account forces" you end up with a result carrying opposite "account force". Precisely as with two accounts measuring their forces.

II) Hans-Georg Lundahl

Representing a length by a number does not make it a number.

"3 cm" does not MEAN "3 pieces, one centimetre each, glued to each other", what it means is "3:1 in relation to length known as cm".

It is very practical to forget what a certain set up of numerals mean when you are counting with them, but generalising the forgetfulness to total amnesia of real mathematical semantics does not add to that kind of usefulness.

Christopher K

I never said the length is a number, I said length is represented by a number and then we perform maths on those numbers.

Hans-Georg Lundahl

There are geometric facts that are salient enough even without the numbers attached to it.

Christopher K

I know that. Numbers just make various operations easier, and applicable to more situations.

Hans-Georg Lundahl

Some of them yes.

That is why assigning numbers to length (via arbitrary length unit) is done at all.

But if I have an A7 paper held horizontally to text in, I do not measure either height units or parts of height, I make letters a certain height in a certain height of the height, without bothering to assigne number to the height.

III) Hans-Georg Lundahl

You are assuming today's professional mathematicians are all that count.

Euler did not use number for any mathematic quantity. He used the Latin word quantitas, which means quantity.

You cannot translate quantity with number, since Latin for number is numerus. And while we are at Latin, you cannot bypass the distinction Boethius made about quantitas subdividing into numerus, which is the subject of arithmetic and magnitudo which is the subject of geometry.

Christopher K

You're assuming that classical mathematicians are all that count. Yes, they did use those words back then, but since then, people have decided for whatever reasons that the more modern descriptions are more accurate, or at the very least, they just used the word "number" until it stuck. Meaning of words change over centuries. Awful no longer means "filled with awe".

Hans-Georg Lundahl

Awful probably never meant "filled with awe" but "filled with what is awe inspiring" [or filling with awe] , and that awful still means.

The modern words are not more accurate, and they take more syllables (unlike in German, where Zahl for quantity or number is short and Anzahl for number precise meaning is also short).

Number - Quantity (1 less in modern)

Natural number - number (3 more in modern)

Real number - magnitude (equal).

Modern usage makes it much more awkward to speak of "natural" number.

IV) Christopher K

This is why I still get the feeling we're arguing semantics here. You like the word "number" to mean "natural number" and I think it should be any form of quantity. But I don't see it as leaving qualities of numbers behind. Everything you can do with natural numbers, you can still do with complex numbers. What's being left? We're just adding to it so that every mathematical operation will work and give a valid answer (with the exception of division by 0) and we don't get bogged down in semantics

Hans-Georg Lundahl

"You like the word 'number' to mean 'natural number' and I think it should be any form of quantity."

Why not use "quantity" as the general concept then?

"Everything you can do with natural numbers, you can still do with complex numbers. What's being left?"

The fact of being a real multiple, conceived by one being added to one.

Christopher K

For one thing, because there's no reason to use a different word when number is working just fine and it's what every mathematician uses. [answered above in III]

"The fact of being a real multiple, conceived by one being added to one."

I'm not entirely sure what you mean by that.

Hans-Georg Lundahl

One is the metaphysic ground for both arithmetic and geometry.

In arithmetic its integrity is assumed and you add another to get two, another yet to get three and so on. Those are the definitions of numbers.

Christopher K

Ahh, I get you now. But again, you don't lose that quantity by expanding number to include irrationals and complex numbers. Every arithmetic operation can be brought back to the successor operation (ie, increasing by 1). Addition is just repeated successors. Subtraction is just the inverse of addition. Multiplication is repeated addition. Exponentiation is repeated multiplication, and each of those has a well-defined inverse.

Hans-Georg Lundahl

If this "inverse" of successor operation is limited by "one by one" it stays within arithmetic.

Whenever it includes dividing wholes into parts, we are already dealing with geometry or at least music.

And reversing successor operation of number building will not take one down to zero nor into negatives. Each item added to one can be taken away leaving one.

When a net result can be zero or negative, we deal with cancelling forces rather than with subtraction. One arbitrarily dubbed minus.

... on Young Earth Creationism Denying Gravity (with a certain levity towards the matter, thank God!)

The levity involved is really about angels, but I am thankful for the levity of the music in the videos as well.

http://www.youtube.com/watch?v=8bRvt0InhYk

Now you are presuming that taking a picture jan. 1 and another 6 months later is equivalent to shifting view point like opening and closing the eye.

It would of course be if heliocentrism were true.

Trigonometry works perfectly with two angles and one distance known. Not with one angle and no distance known which is the case for a Geocentric universe where it is the stars that shift place.

This means Magellanic cloud need not be very much further away than alpha Centauri. Which means that its lesser brightness may be due to be really less bright in its own place.

Which means that Main Sequence too has another meaning than supposed and that calibrating Cepheids by it is worthless as to determine a stars own luminosity.

Red Shift has possibly a meaning as Doppler effect which may be wrongly calibrated by errors in previous due to heliocentrism.

Or it is possibly so that we know there is a doppler effect by the car because we know it sounds differently, having heard same car siren before and after it passed, but with redder luminosity we cannot be sure it is because stars further away are distancing from us faster or because the stars thought to be further away are simply redder.

I suppose your part two will involve saying geocentrism entails a denial of gravity?

Let's take that under part two then.

You did not state exactly that under part II, so let's take it here:

You can of course SOH-CAH-TOA your way from largest distance on Earth viewing Moon to distance to Moon, then from there to distance to Sun which is reflected by Moon at an angle presumably measurable through telescopes from Earth. Then measure any other distance to any other body reflecting the sun.

But that works for geocentrism as well as for heliocentrism.

However, a purely gravitational model of what happens (each body moving according to both its own previous motion and the attraction it suffers at the mercy of the other body in each two body problem) will involve heliocentrism and will involve Sun being most massive and Jupiter next most massive and so on.

But with angels moving whatever moves, masses of the bodies are far less interesting. Since inferior to the power of an angel trusted with a heavenly body anyway.

http://www.youtube.com/watch?v=sEW1oQBZu-I

Your minimum mass measure for a star supposes:

1) you know what started the star going

2) and that it would have started Jupiter going too as a star unless Jupiter had been too small.

There is a piece of Atheist Methodology involved too: you assume that if stars did start burning, they did so due to a sufficient mass for self ignition.

Not due to the God you don't believe in, not due to the angels you don't believe in either.

But such self ignition is not absolutely necessary for fusion to work, or people researching fusion in labs at CERN are wasting their times with masses of hydrogen vastly inferior to mass of Jupiter as it is presumed to be.*

You then conclude that a closer but not smaller Magellanic Cloud would hoover away the planets from the sun, if I get it right.

But that may be wrong if stars are much smaller as well as much closer.

Also, things falling to the ground need not absolutely depend on gravity, Aristotle had another option.

Aristotle's option depends on certain substances being in themselves heavy, others light.

Now, whether Aristotle or Newton is right on it, position of stars and planets need not depend on gravity, but may depend - indeed if St Thomas Aquinas is right in Summa Theologiae, Prima Pars, Q 70, A 3 DOES depend - on angels holding them in right place for each moment and bringing them along their orbits.

Update, St Augustine of Hippo (May 27th, 2013):

part III
http://www.youtube.com/watch?v=EAUxQjylzc8

Was summarily refuted like this:

You forgot that Young Earth Creationism has at least yet another option, that one being a small universe, that one being feasible optically with "parallax" not being such (i e with Earth in centre, immovable, giving to each star one known angle, no known distance and hence no triangulation), and physically with stars smaller than Jupiter in mass that needed no self ignition because they were lit by God or by their angels.

part IV
http://www.youtube.com/watch?v=KSEBR_6lnT4

posed no extra problem about that, and I thankfully accept evidence against rival schools of Young Earth Creationism that deny Geocentrism.

part V
http://www.youtube.com/watch?v=j07Y4IirWZ4

merited two extra comments:

Re your reason 5 against white hole cosmology - which I do not agree with anyway - you say that earth is old according to every relevant dating method, but forget that these are calibrated among other things - nowadays at least when the debate has started - around a "distant starlight problem".

I became a geocentric after one evolutionist brought up distant starlight problem in support of those dating methods, which I had attacked same way as any other YEC would.

[re his final challenge:]

God cannot lie.

But God can make the universe so that people getting at it the wrong way can go on deceiving themselves for quite a while. Like heliocentrics claiming we have trigonometric evidence alpha Centauri is four light years away, because its annual wiggle of 0.76 arch seconds (that was proxima Centauri btw) is seen as still star observed from moving earth. Or dendrochronologists who are willing to accept fittings with too little fitting the sequences

Any one giving any other challenge hereon?/HGL

*footnote:

Following commentator missed part of above discussion, I had to spell it out for him:

lxmach1

so basically god placed a time bomb right next to us called Jupiter, just waiting to be lit up? nice god.

Hans-Georg Lundahl

I did not say Jupiter was going to self ignite.

I said Jupiter has enough mass to do fusion IF lit up by divine or angelic action, and IF it had been pure hydrogen, since otherwise researchers at CERN are wasting their time, but I do not concede that therefore God or its angel will light it up.

However one or other did light up Sirius, and it can therefore be smaller than Jupiter, and closer.* Universe can be pretty small and cosy, without absurdity.

[*Not closer than Jupiter, but closer than we have been taught, obviously.]

Antonpreis

Jupiter is sub-critical, so unless it acquires sufficient extra mass, it will remain so: it is mass causing compression - like a bicycle pump - which causes fusion, not angels, and Sirius is not smaller than Jupiter, it's spectrum denotes a star far more massive than our sun, will burn out much more quickly, and as with other massive stars, will seed the local area with elements more massive than our own sun is producing. Your comment below about geocentric universe below is a fairy story.

Hans-Georg Lundahl

I was very well aware that that is how your theory works.

Presuming there are no angels, presuming Sirius is so far away as to be much larger than Jupiter, presuming such sizes have been correctly realted to spectrums and a few other presuppositions presumed to be true.

Only question: how do you know all that?

Simple answer, so far: you do not.

I was not saying Jupiter would self ignite, but I am not saying Sirius or Sun did self ignite either, see. You do, but why?

Antonpreis

Gravity: the moon goes round the earth, because it has less mass than the earth, the planets goes round the sun, for the same reason- less gravity than the central body. The gravity of the sun attracted matter, mainly hydrogen, gravity increased to the point where pressure increased temperature - like the pump - and fusion commenced. Temperature and pressure on earth change the form of materials, same principle but hugely greater occurs in suns, so they "self ignite", but it is not a fire!

Hans-Georg Lundahl

I was totally aware of that explanation.

But explaining is not proving your explanation is the right one.

So, why do you exclude the older explanation? Because you find the new one tastier?

I stop holding a pen, and gravity takes care of it. I keep on holding it, my will takes care of it (excepting my sometimes clumsiness).

Which is the better parallel to the situation of heavenly bodies and WHY SO?

Antonpreis

I can similarly counter, that when predictability in physical events according to mathematical calculations occurs, it would either mean that the angels are boringly predictable - all 200 billion of them - or that the modern understanding of the universe is correct. If i can regularly use spectrum analysis to tell me what metals are present in a sample, and prove that analysis chemically, then it's probably going to work for stars - unless your angels are devious little beggars. Are they?

Hans-Georg Lundahl

I do not see where presence or absence of a metal according to spectral analysis for a star's light would mean anything for our dispute.

UNLESS you add, what I do not grant, that density of star and so on depend solely on initial mass affected by same centre of gravity. I do not grant, for we do not know that. Theism suggests something other.

Predictability of a mathematical sort can be seen in voluntary activites too, like dancing.

I believe angels are good dancers.

Antonpreis

You don't understand predictability based on scientific observation then. If you want to believe fables written by people who had no instruments for observation, but just came up with any unprovable, non-verifiable notion that's fine by me, but I advise you to use science if you get ill, not a witch doctor using chicken entrails to diagnose you. Or fairies, angels, gnomes, goblins, unicorns, trolls, talking goats or bears. Happy dreams.

Hans-Georg Lundahl

Not so fast.

My point is that the instruments of observation we do have - and I have checked up what it is we directly observe with them - do not decide which explanation is the right one.

As for illness, a microscope can study bacteria from every side and angle. Electronic microscopy can study viruses that way - via "translation" to light and ultimately via human sight.

A telescope on or near earth cannot study any star from all angles nor from close up.

"Predictability" is a moot point.

Antonpreis (new start)

The more material available, the greater the mass/ gravity, more bright the star, the spectrum going towards blue, (spectra, not spectrums, it's latin) shorter life-cycle, immense temperatures and pressure producing heavier elements. Like a fire, if you pile all the fuel on at once, you get a short-lived, very hot fire, or you can feed it with small amounts of fuel, keep it going longer. No presuppositions, just observations, known physics, calculations by eg parallax, so no angels with a match.

Hans-Georg Lundahl

Calculations by parallax precisely presuppose the observation known as parallax is caused by our movement around sun and that (often seen as) caused by gravitation.

If stars are moved by angels, where do the parallactic calculations lead us as far as distance and size are concerned?

As said, as long as I hold a pen, its movement is not decided (mainly) by gravitation.

Can you prove the stars are like pens dropping to ground rather than as pens held?

Antonpreis

Actually, the pen's position is decided within the limits of your arm reach, entirely by gravity, as that is determining your own position; in the same way, the solar system moves in concert within the galaxy. Extrapolation - provable by experiment - can indicate other gravitational effects, including the deviation of a pendulum near a cliff face. We can go on like this ad infinitum, but your angels are boring, your arguments just plain silly. goodbye.

Hans-Georg Lundahl

I was not talking about the pen's geographic location. I was talking about its exact position decided by the will of the one holding it - which, as you say, with humans, happens to be as far as the arm reaches. Whether it writes an A or a B on a paper is however not decided by gravity.

My point is, how do you know angels have no similar power on stars?

Because they bore you? Because it is silly?

Well, that is a taste in world views. Mine in blue and your in grey, perhaps?

Antonpreis

Wrong. The pen's spatial position is defined by yours as long as you are holding it, within boundaries of uncertainty: your arm length in any possible direction, but it is still defined by you, just as the earth's position is defined by the sun, wherever in the galaxy it might have moved to. Galaxies define the positions of the stars within them according to gravity, angular velocity, variations according to nearby stars etc. Still no angels - 3 year old girl next door believes in them though.

Hans-Georg Lundahl

Congrats, your neighbour next door is at age three wiser than you as an adult.

That the pen is defined by me, we agree.

That "earth's position is defined by the sun" rather than by an angel holding it or God deciding for it, you prove if you can.

So far you have asserted only.

[Got an appendix to above essay commenting, a little "debate skirmish"]

robertwc82

so in other words you abandoned reality when ever you realise it contradicts your fantasies? lol and you admit it? hahahaahhahahaha

Hans-Georg Lundahl

So becoming a Geocentric is to you "abandoning reality"?

robertwc82

sorry the facts dont lie

Hans-Georg Lundahl

Facts do not lie. Some interpretations do.

Has it ever occurred to you that heliocentrism is not a directly observed fact?

That it is a conclusion, an interpretation of observations.

Real, real many observations, granted. But in each case an interpretation. And not the most obvious one either.

robertwc82

yes it has occured to me. has it occurred to you that geocentrism is no more directly observed. has it occurred to you that the evidence is overwhelmingly stacked in the favour of heliocentrism? if you look at the facts with an objective open mind, heliocentrism is the most obvious. instead of trying to interperate the facts in a way that confirms your pre-drawn conclusion. you realize the fact that there is no firmament up there also contradicts the bible?

Hans-Georg Lundahl

Has it occurred to you that this is part V, that video part I can have dealt with supposed proofs for heliocentrism and that I can have answered under that video, and possibly following ones?

robertwc82

im sure its the same fallacious garbage that has been said by other aplogists. heard it all before. but you admit that you didnt look at the evidence and come to the realization that it pointed to an earth centered univerese. you drew the conclusion that the earth was in the center and then view the evidence through this lense and attempting to mold it to your conclusion. why such blind faith in the anonymous authors of ancient books riddled with copying errors and demonstrably untrue claims?

Hans-Georg Lundahl

The most direct interpretation of the evidence remains geocentrism.

"heard it all before"

How many Geocentric apologists have you been debating? Young Earth Creationist no doubt a few, but how many Geocentric ones?

robertwc82

2 others (not debated, heard their claims.)

Hans-Georg Lundahl

ok, Geocentrism seems to be spreading ... thanks for the good news (I feel less lonely)!

Their claims were ... what? If you care for a little debate, that is.

robertwc82

so explain the physical forces behind retrograde motion. heliocentrism only has to assume gravity. you have to assume gravity, and a whole series of other forces to account for the observations. heard of occam's razor? amongst competing hypothesis, the one with the least amount of assumptions should be selected. and you think yours is the most obvious? lol.

Hans-Georg Lundahl (tried to give the following answer but was hindered by sabotage on youtube or more probably the library where I am sitting:)

The physical forces behind retrograde motions of planets would be angels.

The complexity of "explaining them" is no complexity in physical forces assumed by people believing Geocentrism and angels, but only a complexity of explaining how one is going about to draw a diagram of them (epicycles and so on).

(Problem fixed and it seems the old system of Paris Library computers was outdated since it is replaced today.)

(Same day I find out that with new system there is an automatic maximum of minutes on internet, irrespective of how many usagers there are in a library. Even if library is empty and I have used up my minutes, this precludes me from continuing on my account. Will it work? It may very well provoke an afflux on Georges Pompidou that will backfire on the decision. What provoked it? Probably some sham science from psychologists speaking about "internet addiction". As if human communication were some kind of drug.)

robertwc82

so now you must demonstrate that angels A: exist, and B: effect planets. for what purpose do angels cause retrograde motion. angels?! you really think thats the most obvious explanation? what are you five? do you think thunder is God bowling too?

Hans-Georg Lundahl

A: existence has been historically proven many times over. Look at the Angels at the Resurrection or at St Raphael in the book of Tobit.

B: if there were no angels affecting the planets, or other artistic wills, how come that planetary motions, when abstracted from daily motion of the heaven around earth, form such an intricate and flowery pattern?

One verse of the Bible would seem to indicate that lightnings also are angelic actors.

Anything against that world view, 4 u? Atheist prejudice?

robertwc82

A. what you call "proof" i call the unsubstantiated claims of human beings, who as we know are fallable and deceitful. just because a human says something is true does not make it true.

B. the fact that it is similar to the pattern of a flower and you happen to find it pretty, is merely co-incidental and arbitrary. it does not logically follow that angels must have done it because it looks like a flower. if we assume mars is the center of the solar system we would get a very similar pattern.

Hans-Georg Lundahl

A) I think human beings are far more likely to be fallible when concluding against the miraculous than when telling their or their ancestors' story.

B) The flowery pattern is ascertaind in so far as observations from earth are taken as being from the right angle.

If they are true, mere gravitational play is totally ruled out. Some artistic will is necssarily behind this.

You did not answer whether you harboured any prejudice ruling this explanation out. Do you?

robertwc82

ahhh hahahaha you seem to be getting stupider by the day. you see being an atheist means not believing in gods of any kind, not just yours. therefore i do not follow any scriptures. if there is no god the universe could be arranged in any way imaginable, it would not be in conflict with a belief. its a seriously retarded question. a god could arrange things in any way it wanted. heliocentrism does not rule out the possibility of god. it merely contradicts the word of MAN you blind gullable fool!

Hans-Georg Lundahl

" you see being an atheist means not believing in gods of any kind, not just yours."

Ah, there is after all some prejudice against a will with artistic intentions being behind the universe as it is? You are an atheist? Ah, I am so sorry for you!

"if there is no god the universe could be arranged in any way imaginable"

If there IS a God, it can be arranged in any way, if not only in ways that seem automatic enough. Which would rule out the florid patterns. Atheism only rules out geocentrism.

robertwc82 [to video]

the fact that we have landed on the moon is an even bigger problem who think genesis is an accurate description of the world. according to genesis the moon is alot closer and alot smaller and passes through windows in a solid dome. and the stars are supposedley nothing but little christmas tree lights fixed to the solid dome. above the dome is water

Hans-Georg Lundahl

what exact number of kilometres does your version of Genesis assign to the moon?

Douay Rheims does not tell (nor does Vulgate or, as far as I know, LXX)

Having stars inside a solid dome (with some room for wiggling shown as "double stars", "parallax" etc. in our science manuals) does not bother me. I find it credible.

... on Chomsky's take on the Internet or Unstructured Research

What is Education For? (Chomsky)
Noam Chomsky The Purpose of Education
http://www.youtube.com/watch?v=DdNAUJWJN08

1) Chomsky states that education is for open investigation along the student's own lines, not for indoctrination.

2) When it comes to internet, he reverses it totally.

If one hasn't got a "proper framework" (and young students are not suppoed to have it unless cleared as having such by their professors), though one should be willing to ask if it is the right one (but that is safest to leave to professors) the internet can harm more than help (so let's replace educational freedom with doctrine).

I do however owe Chomsky. For his good history of English from Chaucer to Standard US. Or if that was by a disciple of his, it is still good and in a way his merit.

I also owe him for the amusing, though in my view inaccurate, view about meaning being determined by temporal position in word order in an idealised way.

Acc. to Chomsky, if I get him right, the "underlying" structure of any cria on "er hatte ihn lieb" is:

A) [daß, wenn, etc.] er ihn lieb hatte.

This can change in relatives to:

B) den er [ihn=den] lieb hatte

C) der [er=der] ihn lieb hatte

D) hatte er ihn lieb [hatte=hatte]

E) er hatte [er=er] ihn lieb [hatte=hatte].

The last being of course the usual position in main clauses.

If this explains the meaning, rather than forms like nom sg = indic sg > acc or lieb being in "predicative case" how does Chomsky analyse an example like this:

Und der gute Dieb

Erfur daß ihn lieb

Hatte der Herr, des Davids Sohn.

It has a surface and deep structure like:

F) daß [er=er] ihn lieb hatte ["er"=] der Herr.

No, I find it more credible that meaning is determined by forms like er and ihn for difference between subject and object, that word order in usual sequence can help, especially in "cases" where both nom and acc nouns are nom/acc ambiguous, that adjective is used as pred. by non-suffix

And that lieb is an AdjP qualifying BOTH V and NP of VP.

So, if I think Chomsky's grammar is less informing (except perhaps for purposes of pragmatic use, since inversions of typical order do contribute to how a sentence strikes one) than traditional one, if furthermore I think he was wrong in discovering the most typical innate grammar in the pidgins, which got their grammar as McWhorter said, from slaves held in Africa teaching slaves meant for Transatlantic sale English vocabulary with their own grammar underlying, he has intrigued me. I owe him.

But owing someone does not mean one cannot disagree when he is very wrong.

I do agree:

- higher education should encourage one to look further than one's models if possible;

- higher education should not be about passing exams.

Nor should any education be that.

But they should be about the acquired knowledge or know-how which also helps you pass exams.

An exam can show if you have read a book, but it is reading it which is educational for you. As CSL once remarked (Lilies that Fester?)

I do not agree that education needs to be or even can achieve being non-indoctrinational, totally.

Nor do I believe vocational training has not been unduly neglected.

If a boy feels he is a man at fourteen and wants a wife and children, he should have had the opportunity to have learnt how to shepherd or mend fishing nets or weave or knit or make macramé or play songs that people pay to hear well before fourteen.

But that does not mean higher education should be rebooted into vocational one.

But there is a real disagreement on who is unduly stifling the creativity of learning and who is not.

He has come full circle from the Enlightenment.

They would call Jesuit schools places of indoctrination and claim they wanted full freedom of research, but when someone does these days get more freedom of research than Chomsky likes, he calls their opportunity a cult generator.

He mentions that going through a library of biology will not make one a good biologist if one does not know what to look for.

But it is not just meaning of language which we have an innate capacity for. It is also - and that is how language is learnt - constructing meaning as facts come along.

Chomsky feels we should know what we are looking for and have an open mind about the framework.

I feel his open mind about the framwork is really lip service, unless unstructured research is permitted and encouraged.

The best way to judge whether something is real or not is to have lots of real knowledge about reality.

The best way to get it is to welcome any piece of knowledge you can get. And the best way to do so, is not to concentrate on what one is looking for but to welcome anything that may come along. Unless you have a particular reason to reject it.

That is how I was self taught, and I think it worked.

He may feel it did not work: that I became a cultist. If he is right, it was at least not through internet, that only gave me an opportunity of expression, and of correcting some of my first hunches insofar as I saw them in need of correction, but by reading. [Books, printed such, on paper] His "ban" on unstructured research in the end means a ban on libraries.

His example of biology seems to me to hint at his view of creationism, as something proper to cultists.

I may not be an ace on biology, but I do know the laws of Mendel, I do know what chromosomes are, I do know what telomeres and centromeres are, and I do know they pose a problem to evolutionism. One that P. Z. Myers has "solved" only insofar as he is fine with "new chromosome pairs" being telocentric ones.

One where I debated under his blog post about his solution, and where I was told to ask expertise, did ask medical such and was told I should of course have asked an evolutionary biologist.

He has - at least from the computers I access - hid comments on that post if posterior to 2009. It was in 2011 that I started posting and debating in that comment section.

I feel it is all right that a Jesuit school should transmit the Catholic answer to the 124 questions in St Peter Canisius' Catechism. But in return Jews are free to open schools for Jews, where the wrong answer to a lot of them is transmitted.

In the modern system, all believers and non-believers are supposed to be welcome, supposed to be taught an open mind, but are really educated within a system as closed as, if not more than the system of the Jesuit school or the Yeshiva.

The Jesuit school may have taught some to label Jews Kikes - or the propensity of its pupils to strike a young boy named Noam because he was Jewish may have come from elsewhere than from the teachers. The Yeshiva may have taught some to label non-Jews Goyim va Minim.

The Modern System is teaching to label for instance a Creationist and Geocentric as a Cultist. And with Noam Chomsky we get as high as we can in tracking where that comes from.

Right in this video he is doing it.

Unless of course he meant something quite different from Creationism.

But is for instance 9-11-trutherdom really so stupid that one can honestly label it a cult?

It brought on a war some people wanted for other reasons even before the Taliban had been oppressing any Christians, since they were "backward".

It brought on New World Order - like Air Port Tyranny ([expression] courtesy of Mgr Williamson) or non-terrorist Muslims running ENFORCED security all over France (big cities, anyway).

This was posted here by, at, in:

Hans-Georg Lundahl
BpI Georges Pompidou, Paris
Pentecost Sunday
19-V-2013

... on reality of existence of numbers (and on Pythagoreans and Bruno)

1) ... on reality of existence of numbers (and on Pythagoreans and Bruno), 2) Reality of Numbers, but Not of Numeric Infinity, 3) Jamma starts giving examples! Yeah!

Video answered:
numberphile : do numbers EXIST
http://www.youtube.com/watch?v=1EGDCh75SpQ

a) You missed a shade between Nominalism and Platonism, namely Aristotelianism. A Platonist would argue that any set of three objects has its threeness directly derived from Holy Trinity (if he is a Christian).

A true Nominalist would argue that any set of three objects is indeed a set of three objects if you call it that, but that the threeness of three sisters and the threeness of three dots on dice are not just physically separate, but the concept is only the same to us.

Whereas an Aristotelian would argue that any set of three things shares a basic threeness with any other set of three things.

A threeness which to a Christian Aristotelian is an image of Holy Trinity, but not necessarily a participation.

b) you do the mistake of calling "sqr root of two"* a number when it is a proportion and "sqr root of minus one" a number when it is an algebraic fiction.

Just because "sqr root of minus one" is a fiction does not mean "three" is a fiction.

*Sqr root of two is diagonal of a square compared to one quarter of circumference. And π is circumference of circle compared to its "diagonal" or diameter. These proportions are always the same, they are quite as reliable concepts as three, but they are geometrical and not arithmetical. They do not count separate quantities but measure continuous ones. Therefore the only exact value of them is precisely those names. Try to use it in arithmetic operations rather than geometric demonstrations, you need a value and that must be numeralised, that numeralisation is a fiction (because numeralising what is in itself not a number) and it results in an approximation. And in the sphere of physics and technology, where these claculations apply, approximation works.

related:

video answered:
numberphile : root 2
http://www.youtube.com/watch?v=5sKah3pJnHI

Ha, first of all, Euclid and Aristotle were no Pythagoreans.

Second of all, Pythagoreans were pretty much a freemasonry.

But, mathematically, even if ratios are number to number ratios, they are not numbers.

A triangle 3-4-5 does not have three separate items on one side and so on, but here numbers are used as comparisons. And obviously comparisons can be divided into the continuum. Some are non-numeric ratios, like pi or sqrt of two.

That is pi or sqrt of two rationally defined.

Now, your problem is whether you can rationally define complex numbers.

Can you rationally define zero or minus one as numbers, even?

Of course you can "redefine number" as some try to redefine marriage.

But you can't make two men beget children and you can't make zero or minus one rational answers to rationally asked question "how many".

Giordano Bruno was burned for saying that each universe (what he called universes is what you would call solar systems, supposing each star to have exoplanets) had a soul and that God was the soul of our solar system, or in his words, of our universe, but another universe had another soul and therefore another God.

Both pantheism and polytheism in a baptised Christian.

And of course he did NOT prove any of these. Any more than zero has been proven a number.

aqua1993:

Pi and sqrt(2) are non-numeric ratios? What definitions are you using for number, ratios, and non-numeric? I see that in another post you seem to say that being able to answer the question "how many" defines it as a number. Alright. Let's define a unit length. We can copy this length and thereby ask "how many unit lengths is this segment?" Next, construct a square with a side of 1 unit length. Connect any of the two diagonals. How many unit lengths is this diagonal? sqrt(2), no?

Hans-Georg Lundahl:

Number: narrow definition "many" (as opposed to one). Broad definition: "one or many".

Ratio: relation of two quantities (discreet as numbers or continuous as lengths, weights, etc.) such that relation remains the same if both quantites are augmented or diminished by same *ratio*.

As such a ratio may be numeric and also fall between the numeric ratios.

"Adding" centimeter to centimeter may accidentally say "how many centimeters", but really "how big in ratio to the centimeter". Not nec. a #.

aqua1993:

As for pi, construct a circle with a radius of 1/2 unit length. How many unit lengths is the circumference? pi. I've outlined how to construct pi and sqrt(2) in such a way that answers your question "how many". So, why aren't pi and sqrt(2) numbers? Of course, I've assumed that we would agree on many things. If you disagree with anything I did, feel free to post a rebuttal.

Hans-Georg Lundahl:

Pi is not a number. The question "how many unit lengths is the circumference" is a malformed question. Pi would be the only correct response, but it is only by making it the repsonse to this malformed question that you make it a "number" at all.

The proper question with measurements is "what is the ratio" (either between two concerned measurements or between one concerned and one standard unit length).

And the correct answer to that correct question is: "pi is the ratio, and it is irrational."

snakedude517:

Wait a sec... if the sqrt of 2 is a irracional number how can it be represented by a fraction longEdge/shortEdge?

Hans-Georg Lundahl:

Because long edge and short edge are not necessarily related in a numeric way. On A4 format they are, ideally, not.

LostHisMarbles

Hans i see some of your comments and you're being kind of ridiculous. The current definition of number is not singularly defined by you. Why are you arguing for your incredibly archaic definition of it. Meanings and definitions change over time as new information is gained and changes.

All ratios are numbers, Pi is a number. Irrational NUMBERs are numbers. It is so much a number in fact it's part of a set called 'Real Numbers'.

Hans-Georg Lundahl

I would call "real numbers" unreal numbers. They are however real ratios.

Excepting of course when they are in fact natural numbers.

"Meanings and definitions change over time as new information is gained and changes."

If that were so it would not be a gain of information. It would be a shift of wording in existing information. ONLY if definitions rest the same can informations duly augment.

I am not trying to "define the current" meaning, but to adhere to the Classic one (set by Aristotle).

aqua1993

I see what you're saying about ratios and measures, but I'm not buying that pi isn't a number. If i did buy into your ideas, then I would also say that 1 isn't a number. 2,3,4,5,6,7,8... and so on would also not be numbers. They are just ratios to the unit length. If I have 3 watermelons, then it's just a ratio of 3:1 with my unit watermelon.  Anyways, this doesn't really seem like a matter any of us will be able to settle decisively. It comes down to the arbitrary notion of number.

Hans-Georg Lundahl

When 2 is twice as long as the unit length, it is not a number but a length. It is in a numeric ratio to the unit length. Between numeric ratios to it (like 1:1, 2:1, 3:2) there are also non numeric ratios to it, like sqr rt of two or pi.

When 2 is twice as many as one single, then it is truly a number.

In "2 oranges" 2 is a number, in "2 cm" 2 is a numeric ratio.

Lauri Markkula:

So having children makes you married...?

Hans-Georg Lundahl:

Not the having them per se, but the purpose in advance of both begetting and raising them together in lifeling fidelity, expressed before one's relevant communities (above all Church, for Christians) by an act called wedding which includes a mutual promise.

Lauri Markkula:

What about the people who don't get children? What if either the man or the woman is sterile? What if the woman gets married after menopause? You can't get sterile men and barren women to beget children. Should we not ban marriage between them?

Hans-Georg Lundahl:

As to people who voluntarily sterilise themselves, the Catholic Church already considers that a mortal sin, and marriages contracted after such an illdeed are null and void, due to lack of intent.

As to women after menopause, the intent need not be lacking if for instance one were prepared to accept children begotten by miracle (Sarah, Elisabeth, St Anne the grandmother of Christ) or after reactivating ovaries by hormonal therapy, which sometimes has that effect.

video answered:
numberphile : problems with zero
http://www.youtube.com/watch?v=BRRolKTlF6Q

What about my radical solution: zero is NOT a number. It is perfectly good as a "numerical relative", like in addition/subtraction +/- zero means "same as previous, no difference", just as */: 1 in multiplication/division.

It is also perfectly good as a value, geometric or similar (most famously thermometers, perhaps) where "zero" as a value is very far from any real zero of whatever it is a value of.

But it is neither one, nor many, hence no number. Call it a number, you get these problems.

[added one day later after getting no answer:]

All here numberline fundies (and even Gaussians)?

No Roman Numerals fans?

No takers?

Appendix I, square root of two:

In arithmetic there is none such. Reason, square number and square root number are interrelated. Just as only even numbers are double numbers that have half numbers, so only square numbers can have root numbers.

In geometry there is one. As two squares can be any ratio to each other, they can be the ratio of 2:1. In that case the sides are in a ratio of square root of two to one. And as any paper lover knows, there is paper where the rectangular sides of same paper are that ratio.

Now, square root of two is often given as 1.414... and that obviously only applies to geometry, since arithmetic offers no inbetweens between 1 and 2.

It is also as obviously an approximation, because it is an irrational geometric ratio. And it is irrational because in arithmetic 2 is no square number.

But since it is a question of geometry, it is purely conventional, and apt to confuse it with arithmetic, to give that approximation in decimal fractions. If we use feet, the fractions are given in duodecimals.

One square has side one foot, and obviously the surface one square foot. What is the side of a square the surface two square feet?

The rough approximation offered by using whole inches would be 17 inches or one foot and five inches. It gives a square of 289 square inches. One square inch too many, since two square feet are 288 square inches.

A little finer, use lines as well, twelve lines to the inch just as you have twelve inches to the foot.

(1 ft, 4 in, 11 li)² = 203 li*203 li = 41,209 li² which is nearly two square inches too little.

If England had had the older French system, there would have been also 12 points to the line.

1 ft, 4 in, 11 li, 7 pt = 2443 pt is the nether approximation.

2444 pt is obviously the upper one.

If one square foot = 2,985,984 pt², then two ft² = 5,971,968 pt².

Square the two approximations, you will get 5,968,249 pt² for the nether and 5,973,136 pt² for the upper one.

And as square root of two is irrational, there is no exact number of subdivisions of the foot that can be exactly the answer. But that does not really matter practically, since the points are closer together than one milimeter. The approximation is more exact than the thickness of an ordinary pencil./HGL

Appendix II, "irrational numbers" are non-numeric ratios between numeric ones (table, two examples)

greater numeric ratio	non-numeric ratio	lesser numeric ratio
4:1	> π >	3:1
32:10	> π >	31:10
315:100	> π >	314:100
3142:1000	> π >	3141:1000
2:1	> sqrt (2) >	1:1
15:10	> sqrt (2) >	14:10
142:100	> sqrt (2) >	141:100
1415:1000	> sqrt (2) >	1414:1000

Appendix III, proof sine, cosine, tangent are not numeric per se

You recall the Amerindian chief Sohcahtoa?

OK, there are angles for which all of these are numeric ratios, like the narrowest angle of the Egyptian triangle:

SOH, Sine = Opposite/Hypothenuse = in this case 3:5
CAH, Cosine = Adjacent/Hypothenuse = in this case 4:5
TOA, Tangent = Opposite/Adjacent = in this case 3:4

And now there are some math wizzes who will know what I do not know, how great this angle is in degrees.

But as obviously there are triangles with clearly non-numeric ratios. Sine or cosine of 45° is inverse ratio to sqrt (2), since it is a side size (simplest form) 1 to another side which to it has the ratio known as sqrt (2). And 30° will have a sine 1/2 but a cosine or a tangent involving sqrt (3). And these, as previously said, have no reality in arithmetic, properly speaking, in the science of odd and even, of prime and compound, of triangular or square or pyramidic or cubic numbers. They belong to the other branch of pure mathematics, known as geometry.

Added app. II and III on Ascension Day, 9-V-2013./HGL

Continued on:

... on Mathematics and Semantics
http://assortedretorts.blogspot.fr/2013/06/on-mathematics-and-semantics.html