Sungenis Also Answered CMI's Video

CMI vs Geocentrism, Again · Spirograph Patterns · Sungenis Also Answered CMI's Video

Video was here, but see below:

Geocentrism Debate: Carter/Sarfati vrs. Sungenis
"Première diffusée il y a 5 heures" | Robert Sungenis Channel
https://www.youtube.com/watch?v=mpWeDf6xNSk

Format of the (former) video : Sungenis and collaborators cut up the previous one by Sarfati and Carter and add comments.

Format of my post : I have already previously commented on their video, now it is about Sungenis' comments. I stop the video at the time signatures and then comment where I think his defense of Geocentrism needs some completion - or appreciation. It may be updated or get completions, as I get further around the video. Right now I am on 21 minutes of more than 3 hours.

I

8:57 Kepler indexed 1664 ... note, the elliptical orbits were not the issue, solely Heliocentrism and perhaps also mechanic causes of moving celestial bodies were.

Riccioli advocating elliptical but otherwise Tychonic orbits and angelic movers was not put in that index as far as I know. His Almagestum novum was published in 1651.

On the first section, you missed that Buridan, Oresme and Cusanus were none of them Heliocentrics - or at least I don't know for Buridan. But it would somewhat surprise me.

Cusanus considered Earth is not absolutely immobile or center, since only God is such.

Oresme considered Heliocentrism theoretically possible, but pointless and therefore eschewable for reason of economy.

II

11:42 Parallax and aberration could obviously be explained by Neo-Tychonian model - but also as a misjudgement of proper movements of fix stars performed by angels, by angelic movers.

The latter is a good answer to the distant starlight problem.

What the Doppler effect has to do in "proofs for Heliocentrism" is beyond me.

III

18:07 It can be noted, one of Copernicus' arguments was "spirograph patterns are too complex to be regular and pretty and worthy of God's creation".

Geocentrism with Tychonian orbits involves Spirograph patterns:

The Strange Orbit of Earth's Second Moon (plus The Planets) - Numberphile
14th Sept. 2021 | Numberphile
https://www.youtube.com/watch?v=vU-g6mC1F0g

20:40 Ah, yes, exactly - "the precept that all celestial motions must be explained only by uniform circular motions or combinations of such" - thank you, I. Bernard Cohen!

Copernicus though spirograph patterns unworthy of God as Creator ...

From his "Revolution in science", 1985. p. 112.

Thank you Robert Sungenis Channel for the reference!

And for those to Kuhn and Feyerabend saying Copernicus did not add to exact predictions!

Vidéo non disponible
Cette vidéo a été supprimée par l'utilisateur qui l'a mise en ligne
https://www.youtube.com/watch?v=mpWeDf6xNSk

So, did youtube close the video for supposed copyright infringement, or did Robert Sungenis close it in order to not deal with my comments? I don't know.

It seems someone of these people, on CMI or on Sungenis' staff, is not OK with his material getting commented on by someone disagreeing./HGL

Spirograph Patterns

CMI vs Geocentrism, Again · Spirograph Patterns · Sungenis Also Answered CMI's Video

The Strange Orbit of Earth's Second Moon (plus The Planets) - Numberphile
14th Sept. 2021 | Numberphile
https://www.youtube.com/watch?v=vU-g6mC1F0g

2:00 Exactly the thing that Copernicus considered too ugly and irregular for God to create, hence geocentrism went out with him ...

3:38 Explanation : God and the angel moving Cruithne thing the pattern is (don't tell Copernicus!) ... pretty and therefore the angel performs it.

6:09 If gravitational physics were proven to be the sole factor affecting orbits of heavenly bodies, geocentrism would be impossible. It isn't and so it isn't.

... on a Number Identifying an Evil Man

666 - Numberphile
Numberphile | 12.IV.2012
https://www.youtube.com/watch?v=UkZqFtYtqaI

I

1:14 "written as three letters"

Back then, if so, the third would have been digamma, not in use in most dialects.

BUT we can't say if original used "numerals" (as in three Greek letters) or written out numeral words.

I'd say the latter is probable.

II

3:20 I checked the ASCII gematric value of PETEWATTS - it's 711 (now we know where you go shopping late in evenings - or we don't, if we believe gematria is mostly a one prophecy validity). Here is how I got it:

P		80		080
E		69		140		09
T		84		220		13
E		69		280		22
W		87		360		29
A		65		420		34
T		84		500		38
T		84		580		42
S		83		660	+	45	=	711

Obviously, adding a space makes it 743 (space is 32) and making any letters minuscule would also give another value (unaccented letters always have minuscule 32 more than majuscule).

III

5:09 When apocalypse was written, one may presume, Nero was already a past reference.

Known to have 666 in name.

About that time - check out the vocative MAPKOC NEPOYA and then abbreviate it M. NEPOYA. And such an abbreviation may have even appealed to him, since it reminded of MINEPOYA / Minerva / Latin for Pallas Athene.

On the other hand, it is impossible to get 666 from a simple application of Greek isopsephy on Domitian.

However, Nerva was arguably a much better man than his predecessor Domitian. Domitian tried to kill St John in boiling oil, when this miraculously failed sent him to Patmos. Nerva liberated him from there.

Now, get over to ASCII:

M		77		070		07
N		78		140		15
E		69		200		24
R		82		280		26
V		86		360		32
A		65		420	+	37	=	457

Add minuscules and / or space (one space, four minuscules = 160) in appropriate number, perhaps a . (46) too ...

457		617
160		+46
617		663

So, closest (or "most suspect value") in ASCII is "M. Nerva" = "663"

Now look at a very simple Latin vocative of Domitian:

D		68		060		08
O		79		130		17
M		77		200		24
I		73		270		27
T		84		350		31
I		73		420		34
A		65		480		39
N		78		550		47
E		69		610	+	56	=	666

IV

7:48 In AD 90, criticising Nero would already be fairly safe.

The problem is who will be the next 666?

I think an Exile on Patmos was not perfectly free to send mail anywhere he wanted, while Christ had given him letters to seven Churches, he could call the "mailman" (his surveillant Roman "prison" guard on Patmos) for one destination only.

So, he gives the book to that prison guard, who takes it, and ... I have something of the mind of a novelist (and I could be very wrong on how it was for this prophet of God, who could have known this too all along) ... fortunately Domitian is not obviously adding up to 666, and as he is somewhat dense about anything except getting what he wants, he would not get any very subtle gematria values ... and the prison guard tells him there is a new emperor who will get the mail.

"What's his name?"
"NEPOYAC, MAPKOC NEPOYAC"

Ah, OK, seems fine, wait, what if I abbreviate M for MAPKOC?

M		-		40,
N		-		50+40=90,
E		-		5+90=95,
P		-		100+95=195,
O		-		70+195=265,
Y		-		400+265=665,
A		-		1+665 and yes, we needn't go to Cigma, there is a vocative as well ....

Next time he hears from Caesar (as in Markos Nerouas) he is a free man.

It seems Nerva later abdicated.

I have written some Narnian fan fic in which he meets Pulverulentus Siccus in Telmar ...

En lengua romance en Antimodernism y de mis caminaciones : Nerva the Narnian in Telmar
https://enfrancaissurantimodernism.blogspot.com/2018/03/nerva-narnian-in-telmar.html

So, either St John was told to be Christ's postman to the seven Churches, when he left Patmos, or Nerva himself made himself postman for St John to the seven Churches. Or to all except Ephesus.

V

8:14 I recall prison, finding a paper clip (which we were supposed to apply to papers, the paper being a publicity for the clip, which was in plastic) ... on the paper clip, a triangle of dots, and the dots were on all sides of the triangle 36.

And yes, in a boring moment I had figured out multiplication tables for 11 - 20, including 18, or for prime numbers, including 37.

Formula for triangle number is side*(side+1)/2.

36*37/2
36/2=18
18*37 is 666

Guess who dropped that prison jobb quickly?

I was then asked to do sth else instead and studying Spanish was an available option, esp. as I was into languages before the incident...

VI

9:11 Nothing like?

Sure, A, B, C = 1, 2, 3 is DEFINITELY not anything like either Greek or Hebrew alphabets regularly used as numerals.

For one thing, you have a system in which C=100 and I=1 and in which MOST letters of MOST names have no number.

And for another, making C=3 is ad hoc, no use anywhere outside Apocalypse 18:13 context.

BUT we have computers now.

An at sign, @, is 64.
01000000
An Upper case A is 64+1, a k a 65.
01000001

Every visible sign on a computer screen (unlike months going from I to XII with very few Latin letters) is regularly (unlike ad hoc systems) represented by processes symbolised by 1 and 0, the binary number values of which can be taken out.

This makes ASCII very different.

Now, look at two men with 616 in ASCII (next comment).

I		73		070		03		H		72		070		02		456		(HITLER)
U		85		150		08		I		73		140		05		160		(change to Hitler)
L		76		220		14		T		84		220		09		616		(value of Hitler)
J		74		290		18		L		76		290		15
A		65		350		23		E		69		350		24
N		78		420		31		R		82		430	+	26	=	456
O		79		490		40
V		86		570	+	46	=	616

So I Uljanov (Iljitj Uljanov in his ancestry Swedish would be a relevant spelling) is 616 in BIG letters. Hitler is 616 in small letters (except initial).

As I'd say Lenin was more Satanic than Hitler, both being so somewhat, and as 616 fits only Nero (Hebrew for Nero Caesar) but not Domitian, and therefore 616 might seem to be a "runner up" to 666 ... I think this makes sense.

9:24 Except, in ASCII we don't get 1 to 26, we get 64+1 to 64+26 or 65 to 90.

VII

9:46 What is 2/3*1000 rounded off to whole numbers?

666 or 667?

I'd say 667 is the veritable 2/3 ...

V		86		080		06
E		69		140		15
R		82		220		17
I		73		290		20
T		84		370		24
A		65		430		29
B		66		490		35
L		76		560		41
E		69		620		50 - sorry, misrecalled, 670. I had recalled it as 667, my bad.

Here is a better one.

"the cat" and "the dog" could both be referred to as "the beast" (everyday meaning, not Apocalyptic). Now, check out the ASCII for the upper case, note that the 32s are seven, one for each lower case letter and one for the space.

T		84		080		04		|		441		443		(THECAT, THEDOG)
H		72		150		06		|		224		224		(the change)
E		69		210		15		|		665		667		(the cat, the dog)
C		67		270		22		D		68		270		23
A		65		330		27		O		79		340		32
T		84		410		31		G		71		410		33

Now, is there anything which can be termed any kind of beast which has an intermediate number?

Well, you could try going up from "the cat" to "the dat" - not much good.

Or you can go down from "the dog" to "the cog".

A cog in Medieval naval sense can be considered a "beast of burden" - comparable to donkeys or horses or oxen or camels carrying merchandise or drawing them behind them.

A cog in a much more modern sense, in a cogwheel, can be considered as a "beast of work" - comparable to a donkey tied to a pole walking round to make millstones grind ...

So, in a sense "the cog" can be considered as a kind of beast. Also, it is of metal, which in Antiquity was considered as modification of element earth.

(Cogs were of wood, of trees that grew in earth, inland, not in the sea).

AND treating men like cogs in a machinery is very emblematic of totalitarianism - precisely as required by the Apocalypse 18:13 context.

VIII

10:34 In fact, the reading 616 already existed in the day of St Irenaeus of Lyons.

And he said, "no it's 666".

He had tradition from a man (St Polycarp, or St Papias) who had known St. John, who must already have heard of it.

Since St Irenaeus explicitly excluded 616, he must have known "no, it's not Nero, he's already gone".

Did St Augustine Deny "Antipodes"? If So, in What Sense?

Antipodal Points - Numberphile
Numberphile | 22.VIII.2018
https://www.youtube.com/watch?v=G2Blr0LycOI

1:44 I take it the antipodal points of Milan and Carthage are right in the middle of the sea?

This has a bearing on a historical point.

St Augustine was in one moment actually denying there are "antipodes". He did not mean "antipodal points" he meant people walking with their "feet" exactly "opposed" to his own. Now, "feet opposed" is what "antipodes" literally means. Using it as short for "antipodal points" is secondary.

His reason had nothing to do with denying Earth is a globe, he just figured if they had crossed the Atlantic westward, they would have come back too, and humanity has only one origin. So, I am intent for the mathematical part on antipodal points ... since I recall a few years ago, I calculated in my own amateurish way that the antipodal points of the two mentioned cities (where St Augustine lived) are in the sea.

12:59 and Pampena is done.

Here is my proof.

Milan 45°28′N 09°11′E
AP 45°28′S ?W

Carthage 36.8528°N 10.3233°E
AP 36.8528°S ?W

180	180	170°60'	170.0000°
-09	-10	-00°11'	-00.3233°
171	170	170°49'	169.6767°

So, we go to 45°28′S 170°49'W and to 36.8528°S 169.6767°W.

But instead of looking it up on google maps, its easier to confirm by going back to the antipodal map earlier in the video.



6:25 It so happens, the overlapping transparent map looks really transparent both in Tunisia and Italy.

To get to their antipodal points, then, you take a shop from Australia past New Zealand, and ... when you get there, you'd better stay aboard ship if you want to be an "antipode" to people in Italy and Tunisia. That is, walk with your feet exactly against theirs.

Erdős papers published with ...

1) Erdős papers published with ... ; 2) Continued debate with Alarm Clock 65 (snappy version)

Imaginary Erdős Number - Numberphile
Numberphile
https://www.youtube.com/watch?v=izdZPx89ph4

I

Hans-Georg Lundahl

I am of another theory than Erdös (sorry, don't known the ASCII Code for double grave accented o, which in Hungarian is longer version of ö).

As long as I stick to coauthors (by quotation or inspiration) already buried under Christian grave stones, like C. S. Lewis, J. R. R. Tolkien, a little further back G. K. Chesterton, Hilaire Belloc, still further back Cardinal Newman, still further back Riccioli (yes, I did refer to him in an essay), St Robert Bellarmine (yes, he was misquoted and I did dig up the real quote) St Thomas Aquinas, Bishop Tempier, I am OK. If I ever should have more coauthors alive, including really genial ones like Sungenis and Tas Walker, I need to worry about my theological allegiance. We do live in an age of confusion ... as even mathematics shows (giving an Erdös number the value i counts as a good pun, but not as excellent mathematical understanding).

http://ppt.li/2i

II

Andrea Langley Sharp

I suppose this is amusing to mathematicians, but I'm totally lost on this one.

Hans-Georg Lundahl

Pun on "i" = called so because "imaginary number" and "i" = "conceptualised as 1 at right angles from the normal numberline". Which I still don't get how it fits definition of "i" = "defined as square root of minus 1". Except that both concepts are as such preposterous.

From me it gets a half amused "arf, arf".

Andrea Langley Sharp

The gymnastics of i seem purposeless to me (why assign a stupid non-value like square root -1 at all?). I assume that the form a + bi has some kind of computational usefulness, but it just seems like shorthand to me. As far as this video goes, I get that this is a pun on "imaginary", but ... I think I'm not nerdy enough to appreciate it.

Hans-Georg Lundahl

Well, I very totally agree with you.

Square roots are of numbers that are square numbers as numbers, not as adds or deductions. So even using -1 as an alternatvie square root for 1 ... though there it has at least a computational use.

Juan Manuel Muñoz

+Hans-Georg Lundahl

Take this example only within real numbers:

Let's say I have to solve x²-2=0, and I know nothing about irrational numbers. Now, I start scratching my brain about how it is possible that no numerical ratio will give me this number. Furthermore, it means that it has infinitely many decimal places, so it can never be known exactly.

This approach is wrong. I am finding uncomfortable results within the field of numerical quantities seen as proportions between countable things. But then I realise that this number is the solution to the question "how much does the diagonal of a side-1 square?" And I understand that I was too narrow-minded: numbers do not represent mere proportions: they can--and often do--represent lengths, which are not affected by anyone moaning that infinitely many decimal places are too many.

Exactly the same thing happens when discovering complex numbers:

Let's say I have to solve x²+2=0, and I know nothing about complex numbers.

Now, I start scratching my brain about how it is possible that no geometrical length will give me this number (which is i times the square root of two).

This approach is wrong. I am finding uncomfortable results within the field of numerical quantities seen as geometrical lengths in a numberline. But then I realise that this number is the solution to the question "which polar quantity, once the angle is doubled and the length is squared, will give me a 180º inclination and a length of two?" And I understand that I've been too narrow-minded again: numbers do not represent mere lengths: they can--and often do--represent polar lengths, so that the product of numbers is not only a product in the length, but there is also a directional factor which one has to take into account. This, again, is not affected by anyone moaning that negative quantities cannot be square-rooted.

Hans-Georg Lundahl

"Let's say I have to solve x^2-2=0, and I know nothing about irrational numbers."

It is very simple. First of all, you do not HAVE to solve an equation.

Second, the equation in question can be about relative sizes, but not about numbers, since including sqrt(2).

I think you might do well to consider my wording before you jump off at a tangent imagining I had considered sqrt(2) a rational number.

When we are concerned with NUMBERS only square numbers have square roots.

Andrea Langley Sharp

You both waaay lost me. Lemme simplify my i gripe.

If you want to indicate something two-dimensional, why is "x + yi" better than "(x, y)"? Seems unecessary.

In simple 2D graphics programming, the screen as a finite width (X axis), so i would be that length (for a 320x200 screen, i = 320). Indeed that's how drawing a simple pixel is coded: "x + yi" where (x, y) is the point and i is the screen width.

So for really basic 2D programming it makes sense that the a + bi notation makes sense, as it is literally how the point is located in screen memory.

But in an infinite 2D plane? Seems the assignment of i = sqrt(-1) seems arbitrary and misleading.

(I get the feeling I'm waay over my head here)

Hans-Georg Lundahl

When you deal with pixels, you can both get labels including i and numbers "below zero" because whoever designed the most general program that other programmers use was subscribing to that mathematical theory.

Now remember one thing: i was not developed to be a label on the y axis (and as said a superfluous one at that), it was developed I think by Gauss, to answer the question "what is the sqrt of minus one"?

And his reason for asking that question was he was observing "both minus one and plus one have plus one as their square".

I believe he was wrong on both counts.

Doesn't make the computer program wrong, just its labels are arranged according to a mathematical theory which is wrong.

Btw, having a zero in the middle rather than at one edge can be practical, means that one can count from middle outwards.

That does not mean "numberline" or "zero" or "numbers below zero" have any real existence as mathematical objects, any more than i.

Both of you, number basically means countable or countables but not just one.

Sqrt of two is a non-numeric ratio.

This means that the ratio is not between the NUMBER of sides but between their LENGTHS, plus that this ratio between their lengths does not parallel any one but fall between any two ratios of numbers, i e of countables.

A polarity is something different from a countable and from a length.

Once you state polarity, you are in artwork, like thermometers which has one value arbitrarily named zero - because when the scale was developed, one had not measured zero Kelvin degrees.

Temperature as such is comparable to lengths. No length is zero long, no length is minus anything long. But it is practical to have an arbitrary zero in computer screens and also on thermometers and that question is not just simply mathematical, it is applied maths.

AlarmClock65

+Hans-Georg Lundahl
Where'd you get this definition of number? If you take number to mean "an abstract label with which one counts," then you're not understanding the term correctly. Those "non-numeric ratios" of which you speak are CALLED "irrational numbers." If you claim that they are not numbers, then you have an incorrect understanding of the word "number." It's like saying "Oh, Australia's not a continent because I think it's too tiny." The rest of the world considers Australia large enough to be a continent. Similarly, the rest of the world considers irrational and complex numbers manipulable enough to be considered numbers. A number is an abstract mathematical object with which one quantifies, measures, and models. Suppose we wish to measured the displacement of a point in a plane from the origin. To do this, we need complex numbers. They are numbers because they are used to measure displacement, just as the natural numbers are numbers because they are used to measure counts.

Hans-Georg Lundahl

"Those "non-numeric ratios" of which you speak are CALLED 'irrational numbers.'"

These days, yes. I know. I consider it a real misnomer.

"If you claim that they are not numbers, then you have an incorrect understanding of the word "number."

Or those framing the modern terminology have so.

"It's like saying "Oh, Australia's not a continent because I think it's too tiny." The rest of the world considers Australia large enough to be a continent."

19th C. Australia was a Part-of-the World - the same which now is called Oceania - and Ulimaroa was the largest island in it.

Pluto was a planet and is no longer so. Remember?

As to the word continent, I consider it quite feasible to use it for only Eurasia with Africa - and consider the rest as a kind of "Earthsea" (island world).

However, of this continent (which has four corners - the SE could extand as far out as Ulimaroa as the NW extends to British Islands), there are Three Parts of the World - Asia, Africa and Europe. And of Earthsea, so to speak, one could consider Americas as distinct from Oceania.

When terminology changes, sometimes it is just a question of LIMIT.

But in the question of number, it is also a question of basic definition.

Numbers go 1, 2, 3, 4 ...

Geometry goes point, line, surface, body : each except point being indefinitely divisible into infinitesimals. And each except body being a division.

There are TWO objections I have against the new terminology:

• it blurs distinction between geometry and arithmetic
• it gives the very false impression that before one used the misnomer "irrational numbers" one tried to prove pi or sqrt of two were rational numbers, when "number" was in fact not at all the most basic classification.

For instance, for π or sqrt of two, the older terminology was that a square and a circle had diagonals (and a diameter counted as a diagonal) that were incommensurable with the circumferences.

If you have two sizes like 1 ft 3' and 9', the one is not a multiple of the other, but they do share a common measure the largest of which is 3 inches. This example has a ratio of 5:3. It is commensurable and therefore has a numeric ratio - usually called simply ratio. 5 in this case is not a number per se, but a proportion to the common unit of three inches. 3 also. But these two are at least expressible as numbers. They are the same ratio (except for the one being in sizes and the other in real numbers) as 5 apples to 3 apples.

This will never happen with π or sqrt of two.

The older terminology for this was either to say the diagonal was incommensurable or to call it an "irrational ratio". Ratio because like the 5:3 of 1 ft 3' and 9' it is a proportional relation. It could for instance be repeated as 2 ft 1' to 1 ft 3' (25:15 = 15:9 = in both cases basic ratio 5:3). But irrational because it cannot be adequately and exactly expressed like a ratio with a numeral on each side of a line or of a colon. Which is why I think non-numeral ratio might do as well.

So, if you want to know when "irrational numbers" as a phenomenon was discovered, you must not ask when that phrase came into vogue, but rather look for the older phrase "irrational ratio" or the older word "incommensurable".

Some think irrational ratios were only discovered when one renamed them "irrational numbers", that is like saying the Swedish geography book from 19th C. in which "Australia" = Oceania and "Ulimaroa" = Australia minus van Diemens land and Tasmania = "largest island of Australia" prove that only what you call islands had as yet been discovered while the continent Ulimaroa/Australia was either undiscovered or incompletely discovered and thought to be smaller than it was.

"Similarly, the rest of the world considers irrational and complex numbers manipulable enough to be considered numbers."

Irrational ratios did not start to be manipulable when they were renamed irrational numbers. They did not become one whit more manipulable by being reclassified as numbers.

"A number is an abstract mathematical object with which one quantifies, measures, and models."

A number is an abstract mathematical object which is counted.

A size is an abstract mathematical object which is measured (by being compared to a standard size).

A relation or especially a ratio (for additions and subtractions are also relations) is an abstract mathematical concept applicable to both sizes and numbers.

"Suppose we wish to measured the displacement of a point in a plane from the origin. To do this, we need complex numbers."

If you are too lazy to find out the hypothenuse of a triangle or if what you want is a coordinate system, you need coordinates in two axes.

What you do NOT need is pretending one axis is the square root of left-hand or nether polarity of other axis.

As Andrea Langley Sharp so sharply observed.

AlarmClock65

+Hans-Georg Lundahl There are two main ideas here. The first is the relation between terminology and actual properties. The second is whether it is pertinent to consider incommensurables to be numbers. I agree with you that a name obviously has no effect on the actual properties of an object. Regardless of whether incommensurables are numbers, they cannot be expressed as a ratio between any two integer lengths, almost all pairs of lengths in the natural world are incommensurable, etc. And, obviously, the Europeans discovered Australia the moment the first European explorer set foot there, even though he didn't yet call it Australia. Likewise, Columbus discovered America (for the Europeans), even though he never did recognize it as a continent. So I agree that "a rose by any other name would smell as sweet" applies here to some degree. So, if you want to say that there's a fundamental difference between natural numbers and everything else that is sometimes called a number, then I'll agree with you. Natural numbers are used to count; other, more general kinds of numbers are not. Just know that what you term "number," other people term "natural number."

However, I disagree with you when you say that it is a mistake to treat incommensurables and points on the plane as numbers. I agree that it is important to remember irrationals' origins as incommensurables, but why can't they be numbers as well as incommensurables? If we let them be numbers, then we can apply to them the ordinary arithmetic operations. Such application obviously has meaningful and useful results, but if they were not considered numbers, then they could not be added or multiplied with ordinary numbers. The same goes for complex numbers. If we let i be the square root of -1, then complex multiplication becomes an incredibly useful operation: as Juan Manuel Munoz said above, this allows us to create a point in the plane whose modulus is the product of those of two input points and whose angle to the positive x-axis is the sum of those of the two input points, algebraically. And think about things like the Riemann Hypothesis. This states that all non-trivial zeroes of the Riemann Zeta Function have real part 1/2. If complex numbers were not considered to be numbers at all, then the Riemann Hypothesis would not be statable (one can hardly apply a polynomial to a non-number). Yet, its truth would have enormous consequences for the study of primes, one consequence being a big O upper bound on the error between pi(n) (the function counting the number of primes less than or equal to a given natural number n) and Li(n) (the log-integral function). And, consider, as another example, Andrew Wiles' famous proof of Fermat's Last Theorem. In it, he had to use p-adic numbers, which are not even, in general, complex numbers, let alone natural numbers. Yet, using these numbers, he proved a statement solely about natural numbers: that there exists no quadruple of positive natural numbers (x, y, z, n) such that x^n + y^n = z^n for n>2. If p-adic numbers were not considered numbers, then such a proof, which undoubtedly relied on adding and multiplying them like normal numbers, would not have been possible. So, why do you think that math would be better off if only natural numbers were treated like numbers? Explain how such things as the Riemann Hypothesis, Euler's Formula, and Fermat's Last Theorem could be treated in this system.

Hans-Georg Lundahl

Glad you agree Roggeveen and James Cook had discovered [for our culture] the piece of land we now mostly call Australia [or was it Tasmania for Roggeveen?] before the day when a Swedish geography book listed the largest islands as:

• 1) Ulimaroa
• 2) Greenland ...
• (was 3 Madagascar or Sumatra or sth?)

"Regardless of whether incommensurables are numbers, they cannot be expressed as a ratio between any two integer lengths, almost all pairs of lengths in the natural world are incommensurable, etc."

I never disputed that.

It is ten years now that I have had people lecture me on that while I never even disputed it.

"Just know that what you term "number," other people term "natural number.""

You mean what I and most people in the world call "number" most or even all mathematicians call "natural number".

"I agree that it is important to remember irrationals' origins as incommensurables, but why can't they be numbers as well as incommensurables? If we let them be numbers, then we can apply to them the ordinary arithmetic operations."

I have nothing against practically once in a while treating them as numbers while they are not.

Logarithms is at its most basic, as on a slide rule, doing arithmetic with the means of geometry. Graph plotting and seeking equations for lines, circles, parabolic and hyperbolic figures etc. is at its most basic level doing geometry with the means of arithmetic.

I have nothing against either of them.

I am only saying there is a parallelism between the number 3 and the geometric ratio 3:1, the number 4 and the geometric ratio 4:1, but 3 and 4 are used in different ways.

This parallelism is of course behind the ideas of graph plotting and of logarithms. But parallelism is not identity.

"If we let them be numbers, then we can apply to them the ordinary arithmetic operations."

Even if we don't let them be numbers, we can still do so, because of the parallelism mentioned.

" If we let i be the square root of -1, then complex multiplication becomes an incredibly useful operation: as Juan Manuel Munoz said above, this allows us to create a point in the plane whose modulus is the product of those of two input points and whose angle to the positive x-axis is the sum of those of the two input points, algebraically."

I still do not get how a plane with two axes can have one axis as the square root of same length on the other axis' as long as it is the negative polarity of it.

Let us say a computer engineer wants a four dimension or four parameter coordinate system. How is calling a point "2 + 2i + 2j +2k" (with j = sqrt of minus i, with k = sqrt of minus j, obviously) superior to calling it "2x + 2y + 2z + 2w"?

Suppose the superioroty is this, that if one parameter is zero, you don't mark it. A two plane coordinate could have a point that is JUST 1 or JUST i, because the other coordinate is on the conventional zero value of the grid. Why is complex numbers better than calliing the one JUST x or the other JUST y, if shortness is the requirement (btw, I am not sure it is always a good one)?

"If complex numbers were not considered to be numbers at all, then the Riemann Hypothesis would not be statable (one can hardly apply a polynomial to a non-number)."

One can obviously apply a polynomial to sth fictionalised as a number - while still conisdering it fiction, not number.

Saying God created the world of Narnia allows CSL to make lots of theological statements that bypass the division of Old and New Covenant (or somewhat so) and therefore of Judaism and Christianity (and therefore of the real status of Judaism and the real presence of the Christian Church) in this world.

Must a theologian state as a positive belief that God really DID create Narnia in order to have access to those points?

No.

"And, consider, as another example, Andrew Wiles' famous proof of Fermat's Last Theorem. In it, he had to use p-adic numbers, which are not even, in general, complex numbers, let alone natural numbers. Yet, using these numbers, he proved a statement solely about natural numbers: that there exists no quadruple of positive natural numbers (x, y, z, n) such that x^n + y^n = z^n for n>2. If p-adic numbers were not considered numbers, then such a proof, which undoubtedly relied on adding and multiplying them like normal numbers, would not have been possible."

Since in logic a proof may use the reduction ad absurdum, I cannot see why a proof about real numbers could not involve fictional ones. [LIKE:]

"Even if such and such were a number, such and such real numbers could not have such and such relations."

[SHOULD BE INSERTED:]

"If p-adic numbers were not considered numbers, then such a proof, which undoubtedly relied on adding and multiplying them like normal numbers, would not have been possible."

No real contradiction.

My one concern is respect for the older terminology, so that the new one is not used as an excuse, as it is often, to pass off oldies as fogies who had not yet discovered such and such a thing PLUS admit it fits reality closer and therefore is a better clue to philosophical implications of mathematical concepts than the new terminology does. Apart from that I have nothing against the new mathematics.

"So, why do you think that math would be better off if only natural numbers were treated like numbers? Explain how such things as the Riemann Hypothesis, Euler's Formula, and Fermat's Last Theorem could be treated in this system."

I don't know any of these, but I have already taken on such a challenge about logarithms.

As an exponent if really such has to be a natural number, the usual statement of what a logarithm is makes no sense.

But first of all, any decimal fraction is still a fraction as written out. It is a ratio. Of course any written out ratio will only approximate the logarithm (except when it's just a real exponent of the base), but there you go.

I restated logarithms so that 2=10^x/y MEANS (as a short cut means a full statement) 2^y=10^x. And it worked as a means for me to get started in working out a few simple logarithms.

III (at the end of a longer thread I didn't read)

CowLunch

Anonymity is an important tool in the quest for truth.

IamGrimalkin

+CowLunch Well, not really. They weren't doing this to quest for truth, they were doing this for fun.

omp199

+CowLunch You are correct in some contexts: if you are looking for information that is illegal to possess, for example. But what if the truth you are looking for is something as simple as: "Who the heck wrote this?"

Hans-Georg Lundahl

+IamGrimalkin hope they enjoyed it.

Hope they enjoyed laughing at i so much they get trouble going back to taking it seriously. 

+omp199 Or sth as simple (in itself at least) as "who reviewed the paper before it got published" or the somewhat more complex one "who reviewed this unpublished paper I know about so it didn't get published"?

Belle La Victorie

+omp199

You want honesty? Then you best remove evil from this world.

People like you are the reason why totalitarian dictatorships happen.

Evil people will lie no matter what laws are placed and they will ABUSE those laws to fit their own agenda.

You want to force people to use their real names? What happens when someone evil stalks them, attacks them, tries to destroy them?

It happens all the time TODAY and some people NEED a fake identity in order to EXIST.

Ever heard of witness protection?

Yeah... I wonder how bad things will get when THOSE people are not allowed to use the identities to PROTECT themselves.

The problem with YOU is that you think that people don't have a right to protect themselves.

YOU are a controlling psychopath.

Change that username of yours into a real name NOW.

YOU clearly want OTHER people to follow rules that YOU yourself are not willing to follow.

omp199

+Belle La Victorie You are imagining that I am saying things that I have never said. It would probably take up a lot more space just to correct all your faulty assumptions than it would to add anything new and relevant to the discussion, and I'm sure we've already taken this discussion too far off the topic as it is, so I'll just bow out of this conversation now.

Austin Cook

+omp199
the purpose of the peer reviewing process is to make sure that people cant claim that things are true without proving it regardless of whether they are under a pseudonym or not.

Hans-Georg Lundahl

The purpose of making sure someone can't claim things without proving it is not as well served by prepublication review as by free review in freedom of reply.

So, not only does pre-publication review block one claim which is proven and would be accepted as such by a wider readereship than the pre-publication review committee, while another claim passes through their narrowminded uncritical acceptance of such a bad claim, while further blocking pertinent replies to it.

But also the use of pseudonyms covers up if such a thing has happened due to personal favour and disfavour between writer and reviewer.

+Belle La Victorie
Have you noticed that here where he is on youtube, he is not being published after a peer review only.

So, his pseudonym isn't thwarting a peer review honesty.

Reality of Numbers, but Not of Numeric Infinity

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 commented on

Infinite Fractions - Numberphile
Numberphile
https://www.youtube.com/watch?v=DpwUVExX27E

Hans-Georg Lundahl

"Infinite Fractions" - no such thing.

Potentially infinite serial fractions [what I meant is called "continued fractions], like ways of writing π as a sequence, yes. But are never actually executed.

And the relation of perimeter to diameter is not per se infinite, just not adequately numerisable for its accurate value.

For an approx value, that's another matter.

jamma246

So is there such thing as a fraction?

Honestly, these pseudo-philosophical arguments about what kinds of mathematical objects exist and which don't always end up being silly.

sibtain ali

There are infinite numbers so infinite fractions

Hans-Georg Lundahl

A finite fraction very certainly exists, like 1/3 or 2/5. It is very certainly also executed.

Certain ratios also exists which could be reinterpreted as infinite series of serial fractioning. but those serial fractionings are never executed any more than a geometer ever executes "take a line of infinite length".

So, no, what kinds of mathematical objects exist and what kinds do not exist is a very legitimate philosophical - not pseudophilosophical but really philosophical question which very much interests me.

Oh, by the way, the kind of ratios that cannot be expressed accurately and exactly as finite fractions but only as infinite serial fractions, like π, are never number-to-number ratios but more like domain of size-to-size ratios or similar mathematical continua outside arithmetic proper.

sibtain ali, no, there is no such thing as a number which is infinity and there is no such thing as a fraction which contains fraction within fraction up to infinity being reached.

The series of different numbers like 1 2 3 4 and of different fractions like 1/2, 2/2, 3/2, 4/2 ... 1/3, 2/3, 3/3, 4/3 and so on are potentially infinite in so far as mathematicians cannot know when the next number or possibly even the next fraction ceases to count or account for something in the universe in its mathematical aspect.

jamma246

"A finite fraction very certainly exists, like 1/3 or 2/5. It is very certainly also executed."

I'm sorry, I have no idea what you are talking about. What do you mean by "executed"? What is your criterion for a certain mathematical object "existing", what does that even mean?

Does the square-root of 2 make it onto your list of mathematical idealisations which "exists"? Does the set of natural numbers "exist"?

Honestly, what you are saying is total nonsense:

"The series of different numbers like 1 2 3 4 and of different fractions like 1/2, 2/2, 3/2, 4/2 ... 1/3, 2/3, 3/3, 4/3 and so on are potentially infinite in so far as mathematicians cannot know when the next number or possibly even the next fraction ceases to count or account for something in the universe in its mathematical aspect."

There is no claim that this quantity "accounts for something in the universe"; how would one even define what that means? That seems ridiculously subjective for me, and yet you speak about it with such authority.

Hans-Georg Lundahl

"What do you mean by "executed"? What is your criterion for a certain mathematical object "existing", what does that even mean?"

I mean that the mathematician overlooks every "number" of the fraction and its fractionality.

It is executed by the fact of writing it. [By writing it out in full.]

While a serial fraction is never executed, never written out in full, never given a fully accurate simplification if it is "infinite".

That is what I mean.

"Does the square-root of 2 make it onto your list of mathematical idealisations which "exists"?"

As a piece of geometry, yes.

As a piece of arithmetic, no.

It is comprehended as for instance "hypotenuse of any right angled triangle of which both kathetoi (not sure what that is in English) are same length, relative to that length taken as one".

It is not a numerical execution, but a comprehensible one. Of a piece of geometry.

"There is no claim that this quantity "accounts for something in the universe"; how would one even define what that means?"

I might say I am not Kantian. I do not believe the universe is infinite.

Number of atoms is limited.

Number of conglomerates of atoms is limited.

Number of events are limited.

Some numbers handled theoretically in Arabic numerals and perhaps with a "*10ⁿ" may be beyond any finite number of finite things or events to count.

But the meaning in which numbers are "potentially infinite" is that we have no mathematical way in which to decide what that greatest de facto real number would be.

Hans-Georg Lundahl

The only sense in which I am "subjective" is the fact that I refuse to be intersubjective with people attributing infinity to the creation and doing that in mathematcial ways.

I am no more subjective than any other serious believing Catholic.

jamma246

The philosophy of mathematics is an interesting subject, but many of these observations have already been answered and, to be honest, you are speaking a load of gibberish.

There are certainly interesting foundational questions; what things can and cannot be proved in mathematics, which constructions are or are not permitted... given the initial axioms!. For example, it is perfectly acceptable to say that one has different results or methods depending on whether or not one assumes the truth of the Axiom of Choice. Constructivist mathematics has a different flavour to non-constructivist mathematics. But it is pointless to ask whether or not the AoC is true or "exists". It is simply an axiom. Similarly, it is meaningless to declare some mathematical object or another as "existing" in a real sense. All mathematical constructions are idealised constructs, by definition.

We've moved past the time where people would shun, for example, the complex numbers for not being "real". Our understanding is now far more sophisticated than that. Number 2 is no more "real" than π or sqrt(-1) is, but one may still work with initial axioms which do or do not permit certain constructions. There is great generality with which one can extend these ideas, see for example Topos Theory.

[2 and π are both real. But in diverse disciplines, see a previous commentary. But sqrt(-1) and even "-1" if taken as a number rather than as a "relative number" or "numeric relation", if taken as "sth less than zero" is not. Nor is zero.]

Hans-Georg Lundahl

My axioms and the common sense ones are:

• number means either one single or one single several times over.
  
  Start arithmetic from there;
  
  
• size relations can be like relations between numbers (e g number 3, 4, 5 can have the same relation between them as the 3, 4, 5 sides of the Egyptian triangle);
  
  
• size relations can also be NOT like relations between any numbers (e g a triangle with two sides equalling each other and having a right angle could call that equality a 1:1, a 2:2, a 3:3 equality, whichever they liked, but either way the relation of the third side, of the hypotenuse, to each of the others would be sqrt(2) which is simply NOT a number).

Geometry needs more axioms than these to work, but these are two basic ones so as not to confuse it with nor over separate it from arithmetic.

Unlike arbitrarily chosen axioms, these are rooted in the nature of the kind of things that mathematics actually studies. Or used to study.

Hans-Georg Lundahl

After actually watching the video:

• a man can go on with the Stern Brocot sequence and the fractions it generates as long as he likes or can manage, but that is a VERY finite amount which is executed, like on the triangular form he executed down to x/4 and x/5 but no further;
  
  
• God can execute all of the sequence at once - but He has also chosen how much of it which corresponds to meaningful and correct information about any relations of quantities in the universe and which other ones do not.

I thought we were dealing with something else, a but more complicated.

π Continued Fraction
http://mathworld.wolfram.com/PiContinuedFraction.html

Continued Fraction
http://mathworld.wolfram.com/SimpleContinuedFraction.html

In these case each fraction itself by being infinite is never fully executed.

jamma246

Please stop.

Hans-Georg Lundahl

People who are as uninterested in philosophy as you might do well to leave maths alone as well.

But I am stopping as I have made my point.

jamma246

I can assure you that people in mathematics often love philosophy. But they don't enjoy meaningless pseudo-philosophical ramblings.

Hans-Georg Lundahl

Nothing in what I said was pseudo-philosophical and nothing in what I said was meaningless.

codediporpal

The universe disagrees. Just because you can't compute it doesn't mean the universe isn't doing it all the time.

jamma246

Hi[s] reasons depend on dogmatism and "God". I wouldn't bother trying to argue with it - meaningless waffle, the antithesis of mathematics.

Hans-Georg Lundahl

Oh, no.

An "infinite distance" is for example an oxymoron.

Any distance is between two points, any point at the end of a distance ends it there, any distance ended in two points is finite.

So, no such thing as an infinite distance.

So, I have full rational backing for my observation - it's you atheists who have none.

Summa Theologica I P, Q7, A3
Article 3. Whether an actually infinite magnitude can exist?

"Objection 1. It seems that there can be something actually infinite in magnitude. For in mathematics there is no error, since "there is no lie in things abstract," as the Philosopher says (Phys. ii). But mathematics uses the infinite in magnitude; thus, the geometrician in his demonstrations says, "Let this line be infinite." Therefore it is not impossible for a thing to be infinite in magnitude."

And skimming over rest of objections and skimming over his systematic answer we get the answer to this one:

"Reply to Objection 1. A geometrician does not need to assume a line actually infinite, but takes some actually finite line, from which he subtracts whatever he finds necessary; which line he calls infinite."

The mathematician in this video proceeded no differently. He only executed the sequence to a not just finite but even very low magnitude. We were only dealing with x/4 and x/5 here.

The point is not just that these are finite, but that however much greater he had executed it to, he would still have executed only a finite sequence and its last items would still be finite.

Here is the whole article, and note the next one:

First Part Q7. The infinity of God
Article 3. Whether an actually infinite magnitude can exist?
http://newadvent.com/summa/1007.htm#article3

Ibidem : Article 4. Whether an infinite multitude can exist?
http://newadvent.com/summa/1007.htm#article4

The next one concerns us even more. There is no such thing as an actually infinite multitude.

jamma246

Hahaha, from 'The Summa Theologica of St. Thomas Aquinas'.

Well, have fun continuing to base your philosophies on your religion. In the meantime, mathematicians and scientists will continue making fundamental and important contributions to the real world, using actual mathematics, which can perfectly well cope with infinities, and has done for centuries.

There's a reason why logic and science always say a lot more about the real world, and are a lot more useful than philosophical prejudice.

Hans-Georg Lundahl

"Hahaha, from 'The Summa Theologica of St. Thomas Aquinas'."

I quite agree, except on the "hahaha" part.

I am as said not BASING my philosophy on my religion.

I am ACCEPTING religion as a corrective to philosophy whenever faulty, but in this case, the case for the Thomistic position is very clear independently of Catholicism.

"In the meantime, mathematicians and scientists will continue making fundamental and important contributions to the real world,"

As a Thomist, I like observing and understanding it correctly before making a contribution to it.

"using actual mathematics"

So did St Thomas. Here.

"which can perfectly well cope with infinities, and has done for centuries"

"Cope with infinities" is something other than using infinity, other than as a concept verging on fiction.

St Thomas' example with the Geometrician whose "infinite line" is just a line from which he can deduce as much as he needs is pretty close to what mathematicians do to this very day.

"There's a reason why logic and science always say a lot more about the real world, and are a lot more useful than philosophical prejudice."

That's a nice philosophical prejudice on your side!

Now, philosophy and science are normally coterminous. There is a correct and logical way to do it, like St Thomas did, and there is a prejudiced way, like you do.

Mathematicians have and use some kind of concept of "infinity" - your prejudice is that their terminology is correct and complete. My observation is one would at least need to add "potential" to "infinity" before it makes any sense.

jamma246

Well, I'm sorry, but the ideas of Thomas Aquinas have been almost wholly demolished by this point. He had nothing useful to say about reality whatsoever. Welcome to the more enlightened 21st century.

He was clearly an intelligent person, but his religious convictions lead him to naive and unreasoned statements about reality. It is no coincidence that when we stopped pretending that mathematical concepts were physical ones, the subject leapt forward and we started making real progress. It doesn't matter whether negative numbers 'exist' or complex numbers 'exist' - they are useful and well-defined tools (and asking whether such things 'exist' is meaningless anyway). The same goes for infinity.

Can you tell me any actual contributions that philosophers such as Thomas Aquainas made to science or mathematics? Anything to back up the claim that they saw the world more clearly than a pure mathematician such as, say, Grothendieck? What useful mathematics did Thomas Aquinas ever come up with? The mathematicians with fewer prejudices (such as against infinity) who saw the subject for what it is, as abstraction, were the ones who proved actual rigorous results with real world consequences. Take any list of the greatest mathematicians of the last thousand years, and they wouldn't have had these silly prejudices against mathematical concepts just because they couldn't cook up something from the real world which seemed to resemeble the mathematical concept. There were a couple of construtivists, such as Brouwer, but most of these seemed to understand that doing constructivist mathematics is simply to study a different branch of mathematics, where certain axioms aren't assumed, rather than to claim that the other approach was 'wrong'.

Infinity pervades mathematics. Even in subjects such as combinatorics it is useful to use infinity. It is simply a tool, just as any concept of mathematics is, and is as well-defined as any other mathematical concept. Talk to actual mathematicians and they will have no idea what your "potential" infinities are, and these are the people who understand infinity most clearly. You are talking a load of nonrigorous nonsense, in a subject that is now easily understood for someone who wants to take the time to study it.

Your line, for example, infinite in length or not. How many points does it contain? Do right-angled triangles 'exist'? Does a right-angled triangle with two sides of length 1 exist? If so, then irrational lengths exist, since the square root of two does. But to express the square root of two, one needs something like a non-periodic infinite decimal, or an eventually periodic infinite continued fraction. Do you have any reason for thinking that space is only made up of finitely many points? Even if it is, do you not think that it is useful to approximate it by something of infinitely many points?

All of these silly points can be avoided by simply not holding to these petty convictions about what does and doesn't 'exist' in mathematics, and instead take the modern approach. Mathematics is about axioms and deductions that follow from them, which in themselves are subject to the reality of logic. Not placing arbitrary restrictions is the best way. Your ideas are 10 centuries out of date.

Hans-Georg Lundahl

"He was clearly an intelligent person, but his religious convictions lead him to naive and unreasoned statements about reality"

"Naive" perhaps to the over sophisticated. Unreasoned? Never.

"It is no coincidence that when we stopped pretending that mathematical concepts were physical ones, the subject leapt forward and we started making real progress."

In making more and more complex calculations, yes.

In understanding them properly - definitely no.

"It doesn't matter whether negative numbers 'exist' or complex numbers 'exist' - they are useful and well-defined tools (and asking whether such things 'exist' is meaningless anyway). The same goes for infinity."

It matters for our understanding.

I am not denying they are useful as fictions. So is reading Tolkien. Or C. S. Lewis. Some might even cite Isaac Asimov, though I wouldn't. But do not smudge out the difference between mathematical realities, which are one side of physical realities, and mathematicians' fictions.

"Can you tell me any actual contributions that philosophers such as Thomas Aquainas made to science or mathematics?"

His doctor while a student at Sorbonne, St Albert, was a great zoologist, and laid grounds for geology and palaeontology.

The latter's philosophical opponent Roger Bacon gave us eye-glasses and laid the grounds for optics.

In geology St Albert was not really superseded until Steno, in optics Roger was not really superseded till Newton.

"Anything to back up the claim that they saw the world more clearly than a pure mathematician such as, say, Grothendieck? What useful mathematics did Thomas Aquinas ever come up with?"

What use have we had of Grothendieck's mathematics, when it comes to that?

"The mathematicians with fewer prejudices (such as against infinity) who saw the subject for what it is, as abstraction,"

Abstraction and fiction are different concepts.

Three is an abstraction from such things as three apples, three Graces, three goddesses, three dimensions, three parts of time, three parts of mind (memory, understanding, will), Holy Trinity - some of which are fictional (not the last one).

Infinity is - in mathematics - either a short way of saying "potentially infinite", as St Thomas took it, or, when forgetting that, a fiction, the usefulness of which varies depending on context.

In pixar repeating a smoothing out "to infinity" means repeating it till it looks smooth. A fractal is never drawn out to infinity. Neither by computer nor by anyone else - the zooming in to thousand times smaller at the same time zooms out the original picture, every version of a fractal is finite and operated by a finite number of steps by the computer.

In understanding of the universe "infinity" played as bad tricks on Kant as "zero" and "minus" is playing on Krauss. Prenamed Lawrence. Famous for being part of film The Principle, for saying things like "a star died so that you can live", or for calling the universe a "quantum fluctuation in absolute nothing".

Zero is a useful fiction even with a fictiionally negative side on the other side of the positive side, but taking that sense of the word and mixing it with the other meaning as "nothing", like Krauss does, is catastrophic.

"were the ones who proved actual rigorous results with real world consequences."

A fiction can have real world consequences.

JRRT's fictional characters have lots of real world consequences in paper, ink, films by Peter Jackson, students of Quenya, live role players and - partly at least - in a new understanding of communal ethics and in some cases conversion to Catholicism. Not to mention giving me a hint of angelic movers theory also found in St THomas Aquinas.

"Take any list of the greatest mathematicians of the last thousand years, and they wouldn't have had these silly prejudices against mathematical concepts just because they couldn't cook up something from the real world which seemed to resemeble the mathematical concept."

That would be 1014 to 2014 ... the list would include at least Thomas Bradwardine, a scholastic who stumbled on the concept of logarithms, i e of geometrical ratios (logoi) that shadow numbers (arithmoi), when discussing physics. Obviously he wasn't the one who worked it out.

Zero was not accepted as anything but a fiction until 1500-1600 sth.

"Talk to actual mathematicians and they will have no idea what your "potential" infinities are, and these are the people who understand infinity most clearly"

They consistently use it as meaning a potential or a fiction. Even when not using the terminology.

And St Thomas understood infinity clearer.

"Your line, for example, infinite in length or not."

Only finite is possible. Any line between two points is ended in both ends. I e finite.

"How many points does it contain?"

A malformed question, or the answer is, so far, two.

If you draw a midpoint, it has three actual points. And so on.

There are infinitely many points at which one CAN divide the line, so the number of points is POTENTIALLY infinite. But there are not infinitely many points at which it is actually DIVIDED, so the number of points is not infinite.

Any of the "infinite number of points" between the end points would simply be a kind of endpoint to an "infinite number" of other lines, smaller than the one we are looking at. But these other lines are not as yet realised any of them, so these infinities are just ... potential. Again, some of these potentialities can be realised. You can draw a midpoint, for instance. That augments the number of actual points to three and the number of actual lines to three also - the whole, the one part on one side of mid point, the other part on other side of mid point.

"Do right-angled triangles 'exist'?"

Certainly. SOME of them even, exotically or emblematically enough for geometry, have size relations that MIMIC number relations.

Like the Egyptian triangle.

But 3:4:5 means one thing when applied to three apples, four apples, five apples and another thing when applied to the Egyptian triangle. In one case we talk about number, in another case about relative magnitude.

Magnitude and multitude are not the same.

"Does a right-angled triangle with two sides of length 1 exist?"

Indeed, and less exceptionally this involves a size relation which cannot be parallelled in number relations.

Triangle sides AB=3, BC=4, CD=5 has for each side an exact parallel in apples.

Triangle sides AB=1, BC=1, CD=sqrt(2) have a size relation which functions only as a size relation, but not when counting apples. That is true for any "irrational number" and that is exactly how they were treated in the Middle Ages. As belonging to geometry but not to arithmetic.

Same is true of π.

"If so, then irrational lengths exist, since the square root of two does."

Lengths always have ratios to each other, it is just that not all of these mimic number to number ratios.

"But to express the square root of two, one needs something like a non-periodic infinite decimal, or an eventually periodic infinite continued fraction."

To express the sqrt of two you can write sqrt(2).

Any decimal expression is an approximation forever inexact of this in successive numeric ratios.

In itself the lengths are not numbers and their ratio is no number.

"Do you have any reason for thinking that space is only made up of finitely many points?"

Space is NOT actually made up of points at all. Any actual point is a division of a line, any actual line of a surface, any actual surface of a body.

Remember the line with only two points? One end point - other end point.

"Even if it is, do you not think that it is useful to approximate it by something of infinitely many points?"

Approximations are fictions. Very useful fictions in some contexts, but fictions.

Sqrt(2) is an exact expression. 1.414 is an approximation. Useful enough for calculations (how much paper do I need for a square with twice the surface - multiply by 1.414), but less useful for understanding what sqrt(2), since giving a false impression it is kind of a number.

"All of these silly points can be avoided by simply not holding to these petty convictions about what does and doesn't 'exist' in mathematics, and instead take the modern approach."

The points are not silly.

The answers are instructive - if taking the Thomistic approach.

jamma246

Exactly, if taking the Thomistic approach. Which has shown itself to prove useless in talking about mathematics.

Hans-Georg Lundahl

As said, take the Thomistic approach and you get instructive answers. Take your approach and you found the questions or points silly yourself. In other words, your modern approach was not able to get an instructive answer out of them, it is your modern approach which has proven useless, not in applying mathematics, or rather even there, since applications don't strictly depend on taking it, but very much in talking about it, in doing the philosophy of mathematics.

... on a Mathematical Fable from Harvard with a Question to its Author Barry Mazur

A Mathematical Fable
Numberphile
https://www.youtube.com/watch?v=ItiFO5y36kw

Barry Mazur, I am not much Harvard minded previously since learning about how the University in question destroyed the intellect and possibly soul of one John Romanides. I am still less Harvard minded since learning that though the Black Mass was cancelled on campus, it was just moved to the next China Restaurant.

BUT, what you state about scaling up and down triangles ... I think I got it and one Rick DeLano missed it in this debate:

HGL's F.B. writings : Internet Trouble and Pontifical Malfaisance, plus a Trap in Discussion
http://hglsfbwritings.blogspot.com/2014/05/internet-trouble-and-pontifical.html

It has some intro about internet matters, but the main dish is a continuation of second debate from previous message.

IF - and on Geocentric tenets I hold that is the case - all we have is an angle per a time period (like 0.76 arc seconds back and forth each half year for α Centauri, obvious one, since greatest angle of positive parallax), we do not know how long any sides are. One can imagine them scaled up and down at pleasure.

Or would you put distance from Earth to Sun into the triangle including that angle on a Geocentric view?

Apart from these points, I think the king was stupid to not fire his surveyor who changed the story about how the pieces of land really looked from day to day.

And the counsellor was stupid or dishonest for not suggesting it.

[As far as I had patience to watch it, that is.]

... on Coastlines and Fractals being No Challenge to Thomistic Concept of Mathematics

1) ... on Honesty of Numberphile / Cambridge University, Mathematics, 2) ... on Coastlines and Fractals being No Challenge to Thomistic Concept of Mathematics

Video commented on:

Measuring Coastline - Numberphile
[They have a logo which is a π, which is not a number ...]
https://www.youtube.com/watch?v=7dcDuVyzb8Y

Speaker and Calculator:

Steve Mould

Coastline per se

Sinuosity of rivers earlier mentioned may suffer from a similar problem?

A ruler getting into millimetres would be getting hundreds and millions of times greater than the ordinary scale?

I would say rather that the lesser the scale of the ruler, true, the longer you get, but the less is proportionally added. Meaning that even the first measure is a fair approximation.

[I was wrong, see further down.]

Besides, getting millimetres can never be a true answer of a coastline, since the water gets up and down on a scale of decimetres or even a metre or two, excepting tidal regions with even greater variation.

The variation of waves needs to be evened out by an average for a fixed as opposed to fluctuating coastline to exist at all. In tidal regions this can of course mean two coastlines. Inner and outer. But even those are not fixed, since along the month tidal variations vary in intensity. There you get an even greater area of averaging out.

You might answer that the actual length of a coastline without averaging exists and fluctuates.

In that sense, man cannot measure it. Man has not the resources to pick out a moment and measure the smallest details of the coastline at that precise moment. It has a length, and a finite length though. And what it is is known - for each moment - to God.

And the second answer for a coastline length was actually including islands - which are off the coastline. Might be part of reason why it is more than double.

Actually I tested by using Koch sequence as each step meaning *4/3 and got from 3 to 39 ... I see your point.

Let us add that God knows the length at each moment as measured in each possible scale (English feet, French feet, English inches, French inches, English lines, French lines AND French points, not to mention any un-known to man of which there are infinitely more - which may give an idea how Divine Omniscience means "infinita scire"). But man who can only measure with one unit at a time does not.

On fractals, metioned as a parallel

The parallel you make with what looks like a side of a Koch snowflake (yes, I had to look Koch up) ... two points.

The total is NEVER at once three and four times the detail.

The detail is a third of total length previous to adding it and a quarter of total length simultaneously to adding it.

Any fresh addition is an addition which may be made ad infinitum, in the sense there is no limit predetermined on how much you can add, except the practical ones.

And if we look at the computer simulation of a Mandelbrot sequence ... well the smaller details do not physically exist in the pixels until you zoom in.

Saying that the length of the circumferences of a Mandelbrot sequence are infinite is treating it as it never ever exists in reality.

Hardly a solid basis for redefining certitudes about more practical realities, as some Pyrrhonists would abuse it!

... on Honesty of Numberphile / Cambridge University, Mathematics

1) ... on Honesty of Numberphile / Cambridge University, Mathematics, 2) ... on Coastlines and Fractals being No Challenge to Thomistic Concept of Mathematics

Video commented on

Numberphile : Pi me a River - Numberphile
http://www.youtube.com/watch?v=TUErNWBOkUM

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Hans-Georg Lundahl

Has no one found other data?

Reminds me of a problem I have.

Now, if Earth rotates around Sun and Mars rotates around Sun, while Sun has a relatively stable position, different orbits, different "years" (if you consider a Martian year as not an oxymoron) ... you should be able to predict how the parallax of a near star like Alpha Centauri differs on Mars as opposed to from Earth.

If alpha Centauri is however as near or as far as Sirius, in a more or less footballskin like sphere of fixed stars (with some thickness, but not at all as much as to overawe the distance between us and nearest stars), moved by an angel, as a pen is moved by a hand, and same being true of planets and Tycho being right and Kepler wrong about most basic geoemtry of universe, then observing its parallax from Mars would give another value. Or shape. Or .... you know.

Thing is, according to NASA we have already put astronomic equipment on Mars, one has already been checking "how do the constellations look from Mars", but as to my question, whether for parallax or even for aberration, I have heard no answer since 2011 when I posed this question.

HGL's FB Writings : Creationism and Geocentrism are sometimes used as metaphors for obsolete because disproven, incorrect, science
short link : http://petitlien.com/creageo

Ichijoe2112

Wake me on Tau Day....

Cannonbo

if you were to try and get an average of all the rivers in the world, you'd have to discard any rivers near modern human settlements. so many rivers have been straightened or diverted by man...

Danijel Drnic

Squaring the circle .. headbands equal to the square of the same rubber cubes.

"Top des commentaires"

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Ichijoe2112

Wake me on Tau Day....

Cannonbo

if you were to try and get an average of all the rivers in the world, you'd have to discard any rivers near modern human settlements. so many rivers have been straightened or diverted by man...

Danijel Drnic

Squaring the circle .. headbands equal to the square of the same rubber cubes.

Johann Blake

Rivers and Pi

This is a rather unusual puzzle concerning nature. What does the mathematical value of Pi (3.14) have to do with rivers?

Apparently, if you take the length of a river and divide it by the the direct distance from the start of the river to its end (as the crow flies) - a value known as "sinuosity" - the value will be close to 3.14. Presumably, if you took all the rivers of the world and calculated there sinuosities and averaged them all out, the value would be 3.14.

Nobody has actually done enough tests to see whether this is true, but I certainly wouldn't be surprised if it turned out to be. Virtually everything in nature either has Pi thrown into it or or is based on fractals. Just more evidence of "Creation by Design".

Other debate

lower down, visible even now, partly:

TheInterlang

Did the Bible really say Pi = 3.0, or is that verse supposed to be a simple approximation?

If people are protesting evolution and the theory of relativity, why aren't they protesting Pi=3.14?

J00rcek

It is a passage where the author describes how Solomon's temple was built and it says:" Now he made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference." While I believe that the author simply didn't care for exact measurements, I also believe there were some extra-zealous people who would take it as a fact (and enforce it). One more thing: Bible rarely mentions fractions of a cubit (i.e 1/3 of a cubit, 1/2, 1/4) so you can guess authors didn't care for the "scientific" approach. If the lenght of measurement rope was, let's say, 31.4 cubits, they would just round that down to a closest cubit. Mind also they didn't really care for standards (ie exactly how long a cubit is) so a cubit for one mason (or metal worker) could be different from another one.

Long story short, it is probably just an approximation so don't fret over it. There's more than enough really nonsensical (is that even a word?) and illogical stuff in the book we should be asking questions about (both from scientific and philosophical point of view)

Gamer Phile

because pi has been proved and most people believe that then they did not have the knowledge that pi = ~3.1415. But people still don't believe the fact of evolution for some reason or another.

Can you guess

which comment becomes visible when I log in again?

Hans-Georg Lundahl

The verse in question might be saying neither, since dealing with different parts of same circular object. You know rims and such.

Ten cubits across at the rim. Thirty cubits around a bit lower down - where object was more slender. A bit difficult to measure "across" further down than at rim.

... on Napier - with Admiration

1) ... on Classic Mathematics Logarithms - Revisited, 2) ... on Napier - with Admiration

Video Commented on:

Numberphile : Log Tables (extra bit)
https://www.youtube.com/watch?v=vzV50goW_WM

Hans-Georg Lundahl

Admiring Napier!

As said, I did a try at working it out directly from base ten (expressing it in duodecimal fractions of feet to honour geometricity of slide rule, which is completely different from trying base 12 !) but I did not get very far trying it that direct fashion, and I would not have guessed at any base slightly lower than 1.

However, I was comparing bases to get fractions between exponents, and one way to achieve accuracy was precisely to compare very similar ones, like exponents of ten with at one occasion eleven at one occasion nine to get base ten logarithms for those. If one is not very accurate, one can check out of their addition adds up to something close to 2:1, since that would be base ten logarithm for 100 while 9*11 is close by 99.

I never guessed a base lower than one, though.

Of course it means that unlike the usual logarithms, as the logarithm rises the antilogarithm sinks.

... against an algebraic formula taken for arithmetic

Video commented on:

Numberphile : ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
http://www.youtube.com/watch?v=w-I6XTVZXww

My comment:

• 1) answer to series:
  
  "1 - 1 + 1 - 1 ..."
  
  is NOT "1/2" BUT "1 OR 0"
• 2) in physics you do not measure infinities, correct - in a finite universe (as a Thomist considers the Created Universe to be) any series has an ectual, though of course arbitrary end.
• 3) If time after other physicians come up with "-1/12" for "1 + 2 + 3 ...." that implies something is misstated as compared to actual mathematical realities.
  
  Let me give a very easy parallel to what I mean.
  
  "(a - b) sqrd = a sqrd - 2ab + b sqrd", right?
  
  Not really. It is more like "= a sqrd - ab - (ab - b sqrd)". The usual simple answer "a sqrd - 2ab + b sqrd" is a simplification of it, it is in nature algebraic rather than geometric. It goes for the simplest expression rather than the one reflecting what happens in physical geometry when for instance you take a square of paper size "a sqrd" and first cut off an "ab" and then an "ab - b sqrd".
  
  This involves that "infinity" as in "infinite series" (or "infinite length" or ...) is a sham concept. It has its uses, but it is not really there in the mathematical reality which the mathematical expression is supposed to be about. Something else is, which can be expressed that way, no doubt, but not that itself.
  
  Very unlike the case in which "3 = 1 + 1 + 1" per definition gives a clue to what a statement involving the number 3 means.

... on Classic Mathematics Logarithms - Revisited

1) ... on Classic Mathematics Logarithms - Revisited, 2) ... on Napier - with Admiration

Video commented on:

numberphile : Log Tables - Numberphile
http://www.youtube.com/watch?v=VRzH4xB0GdM

Hans-Georg Lundahl

(essay type multicomment)

Before getting to Napier, I would like to state I have:

a) reformulated definition of logarithms (esp. fractional exponents)

b) used that definition to work out a table of base ten formulated in feet, inches and lines and points (12 points = 1 line, obviously, French subdivision)

c) translated that very scarce table to decimals and found it agrees with usual table fairly well

thereby proving I was right in my reformulation.

a decimal series is a fraction is a ratio

a ratio as exponent is a ratio between exponents

100 to exp 3/2 = 1000

=

100 to exp 3 = 1000 to exp 2

So, look here:

10 to 1 = 2 to 3 (roughly)

10 to 2 = 2 to 7 (roughly)

Is the log for 2 6/21 or 7/21? Between, rather.

If we multiply both sides by 2 we get 12-13-14/42 [a less binary choice]

4398046511104 (4 rounds down) = 2 to 42

1000000000000 = 10 to 12

9223372036854775808 (9 rounds up) = 2 to 63

10000000000000000000 = 10 to ...

Not 18, but 19. So 19/63 is an approximation to base ten log of 2. And so on.

0,3010299956639 ... base ten log for two according to calculator

0,3015873015873 ... 19/63

My goal was not to make useful logarithmic tables, just to check if my understanding of what logarithm means could help me make a sufficiently accurate one to check I was on the right track.

As you saw, it could.

Meaning I can also dispose of logarithms as an argument for irrational numbers. A log is not the number of times that ten is multiplied by itself, it is a ratio.

And in my book, so to speak, irrational ratios are quite ok, it is only irrational numbers that are out of the possible.

Pi and Sqrt of 2 are not there in the arithmetic of Boethius, but they are sure there in his Geometry.

And a logarithm is really a geometric size to size ratio, even if the most famous ones are so for size ratios there are whole numbers for.

So are of course sine, cosine, tangent (remember soh-cah-toa).

Look at this quote:

Objection 1. It seems that there can be something actually infinite in magnitude. For in mathematics there is no error, since "there is no lie in things abstract," as the Philosopher says (Phys. ii). But mathematics uses the infinite in magnitude; thus, the geometrician in his demonstrations says, "Let this line be infinite." Therefore it is not impossible for a thing to be infinite in magnitude. ...

Reply to Objection 1. A geometrician does not need to assume a line actually infinite, but takes some actually finite line, from which he subtracts whatever he finds necessary; which line he calls infinite.

Summa Theologica I, Q7, A3
http://www.newadvent.org/summa/1007.htm#article3

Precisely likewise, what is useful for the mathematician is not the irrational ratio itself of the logarithm, except in the geometry of a slide rule, but in tables the useful things are approximations, which are rational ratios.

Appendix
If I wanted to reinvent logarithms (not to correct Napier, just to know how he did, or replace if his work is lost or so), I might use base two:
1	0	51	a, f
2	1	52	e, 2
3	a	53	o
4	2	54	3a, 1
5	b	55	b, d
6	a, 1	56	c, 3
7	c	57	a, g
8	3	58	i, 1
9	2a	59	p
10	b, 1	60	a, b, 2
11	d	61	q
12	a, 2	62	j, 1
13	e	63	2a, c
14	c, 1	64	6
15	a, b	65	b, e
16	4	66	a, d, 1
17	f	67	r
18	2a, 1	68	f, 2
19	g	69	a, h
20	b, 2	70	b, c, 1
21	a, c	71	s
22	d, 1	72	2a, 3
23	h	73	t
24	a, 3	74	k, 1
25	2b	75	a, 2b
26	e, 1	76	g, 2
27	3a	77	c, d
28	c, 2	78	a, e, 1
29	i	79	u
30	a, b, 1	80	b, 4
31	j	81	4a
32	5	82	l, 1
33	a, d	83	v
34	f, 1	84	a, c, 2
35	b, c	85	b, f
36	2a, 2	86	m, 1
37	k	87	a, i
38	g, 1	88	d, 3
39	a, e	89	w
40	b, 3	90	2a, b, 1
41	l	91	c, e
42	a, c, 1	92	h, 2
43	m	93	a, j
44	d, 2	94	n, 1
45	2a, b	95	b, g
46	h, 1	96	a, 5
47	n	97	x
48	a, 4	98	2c, 1
49	2c	99	2a, d
50	2b, 1	100	2b, 2
35 = circa = 28
37 = circa = 211
a = 8/5 / 11/7?
a = 56/35 / 55/35?
a = 224/140 ... 220/140
3140 = 6,26...*1066
2224 = 2,69...*1067
2223 = 1,34...*1067
2222 = 6,74...*1066
= circa = 3140 = 6,26...*1066
a = 222/140 = 111/70
And so on for all other logarithmic components (all being incommensurable if totally exact, which they never get anyway), then add them up, which will involve making a common denominator for two such components (like .../35 was for 8/5 and 11/7).
Now, whichever base you calculate your logarithms in, you will get equal distances between those for 2, 4, 8, 16, 32, 64, 128 and so on, and also between 10, 100, 1000 - "and so on" if you go on. And the logarithm for two added to the logarithm for ten will give you the logarithm for twenty. True for base ten logarithms, in which twenty gets 1+logarithm mantiss for 2, true for base two logarithms, in which 20 gets 1+logarithm mantiss for 10.
This means that once you have enough logarithms - like for all the whole number antilogarithms between 1 and 1000 - you can set out to convert any of these into any unit you chose. If you start out with base 2 logarithms, in order to get an order where 10=logarithmic one, all you need to do is give the "one" of above table a value like 30.1 millimetres so that the value of ten becomes somthing close to a decimetre. If you chose to make two the unit and each unit an inch you will get a very similar though slightly off and incompatible scale.
And the fact that logarithms are the same relation whichever base you chose, illustrates that as they are irrational, they are also no numbers. Like lengths the "unit" is arbitrary rather than a real unit. Meaning, their place is not in arithmetic but in geometry. It is only their application (tables or slide rules) which is useful in arithmetic - or for calculating without overusing your knowledge of arithmetic. Which, as I have said elsewhere, is not the same as understanding arithmetic correctly in a philosophical way./HGL