need English translation of Cantor's Ueber die Ausdehnung eines Satzes aus der Theorie der Trigonometrischen Reihen

[redsto...@163.com]

I need English translation of Cantor's Ueber die Ausdehnung eines Satzes aus der Theorie der Trigonometrischen Reihen, I am unable to find it online.

[redsto...@163.com]

I want to know what Cantor said about the relationship between his definition of real(or irrational) numbers and geometry.

[Eram semper recta]

On Thursday, 15 April 2021 at 08:38:48 UTC-4, redsto...@163.com wrote:
> I want to know what Cantor said about the relationship between his definition of real(or irrational) numbers and geometry.

Forget about what the idiot Cantor said and pay attention to what _I_ say:

There is no such thing as a "real number".

All the operations of arithmetic are defined geometrically. The abstract unit is what we use in algebra. Since we cannot measure everything with the abstract unit, algebra is weaker than geometry. In geometry we can perform ALL the operations of arithmetic exactly.

How to understand the concept of number:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

My free eBook:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO

[FredJeffries]

On Wednesday, April 14, 2021 at 11:52:17 PM UTC-7, redsto...@163.com wrote:
> I need English translation of Cantor's Ueber die Ausdehnung eines Satzes aus der Theorie der Trigonometrischen Reihen, I am unable to find it online.

If Dave L Renfro doesn't know about it, it's pretty safe to bet that it doesn't exist.

https://math.stackexchange.com/questions/3487081/does-there-exist-a-latex-word-rewrite-of-georg-cantors-works/3487222#3487222

[FredJeffries]

On Thursday, April 15, 2021 at 5:38:48 AM UTC-7, redsto...@163.com wrote:
> I want to know what Cantor said about the relationship between his definition of real(or irrational) numbers and geometry.

Philip E B Jourdain, in his translation of 'Contributions to the Founding of the Theory of Transfinite Numbers' has a couple paragraphs regarding this article in his introduction, starting page 24. On page 29, 30 he give the axiom:

<quote>
To each numerical magnitude belongs also, reciprocally, a determined point of the straight line whose co-ordinate is equal to this numerical magnitude. This theorem is called an axiom, for in its nature it cannot be demonstrated generally. It also serves to give to the numerical magnitudes a certain objectivity, of which, however, they are completely independent.
</quote>

https://books.google.com/books?id=Jw9SAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false

[Eram semper recta]

Yep. Crank Cantor definitely contributed to the delusion that a number corresponds to a determined point on a straight line.

The funniest part is: "This theorem is called an axiom because it cannot be demonstrated generally." LMAO.

Learn what it means to reify a number line, morons!

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

>
> https://books.google.com/books?id=Jw9SAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false

[konyberg]

It never happens that axiom and theorem is used in the same sentence in that booklet. You are just inventing it!
Show me! Axiom is used two times, and theorems is used one time in this, but not the same sentences.
KON

[FredJeffries]

It's on the fifth line of page 30.

Cantor's original appears on the first line of page 6 of his original article: 'Ich nenne diesen Satz ein Axiom, weil es in seiner Natur liegt, nicht allgemeinbeweisbar zu sein.'

https://www.maths.tcd.ie/pub/HistMath/People/Cantor/Ausdehnung/Ausdehnung.pdf

[Alan Mackenzie]

FredJeffries <fredje...@gmail.com> wrote:
> On Thursday, April 15, 2021 at 4:29:55 PM UTC-7, konyberg wrote:
>> torsdag 15. april 2021 kl. 19:47:17 UTC+2 skrev Eram semper recta:
>> > On Thursday, 15 April 2021 at 12:27:09 UTC-4, FredJeffries wrote:
>> > > On Thursday, April 15, 2021 at 5:38:48 AM UTC-7, redsto...@163.com
>> > > wrote:

>> > > > I want to know what Cantor said about the relationship between
>> > > > his definition of real(or irrational) numbers and geometry.

>> > > Philip E B Jourdain, in his translation of 'Contributions to the
>> > > Founding of the Theory of Transfinite Numbers' has a couple
>> > > paragraphs regarding this article in his introduction, starting
>> > > page 24. On page 29, 30 he give the axiom:

>> > > <quote>
>> > > To each numerical magnitude belongs also, reciprocally, a
>> > > determined point of the straight line whose co-ordinate is equal
>> > > to this numerical magnitude. This theorem is called an axiom, for
>> > > in its nature it cannot be demonstrated generally. It also serves
>> > > to give to the numerical magnitudes a certain objectivity, of
>> > > which, however, they are completely independent. </quote>

[ .... ]

>> > > https://books.google.com/books?id=Jw9SAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false
>> It never happens that axiom and theorem is used in the same sentence
>> in that booklet. You are just inventing it! Show me! Axiom is used
>> two times, and theorems is used one time in this, but not the same
>> sentences.

> It's on the fifth line of page 30.

> Cantor's original appears on the first line of page 6 of his original
> article: 'Ich nenne diesen Satz ein Axiom, weil es in seiner Natur
> liegt, nicht allgemeinbeweisbar zu sein.'

This isn't a particularly persuasive argument. In German, "Satz" means
"sentence". It can also mean "theorem". Is there any evidence that
Cantor actually meant "theorem" as distinct from "sentence", here?

Is there even any evidence that a German mathematician would conceptually
distinguish a theorem from a sentence? I have found it difficult trying
to explain the difference between "safety" and "security" to German
speakers, as they use the same word "Sicherheit" for both.

> https://www.maths.tcd.ie/pub/HistMath/People/Cantor/Ausdehnung/Ausdehnung.pdf

--
Alan Mackenzie (Nuremberg, Germany).

[Gus Gassmann]

On Thursday, 15 April 2021 at 20:57:41 UTC-3, FredJeffries wrote:
> Cantor's original appears on the first line of page 6 of his original article: 'Ich nenne diesen Satz ein Axiom, weil es in seiner Natur liegt, nicht allgemeinbeweisbar zu sein.'
>
> https://www.maths.tcd.ie/pub/HistMath/People/Cantor/Ausdehnung/Ausdehnung.pdf

Very interesting source. Thanks for sharing. There are a couple of typos in this transcription. Do you know of a place that would handle corrections?

[konyberg]

He obviously means sentence (satz), because on page 7 paragraph 3, he use the word theorem.
KON

[FredJeffries]

Just to clarify, the 'translation' 'This theorem is called an axiom' is Jourdain's, not mine. It is from page 30 of
https://books.google.com/books?id=Jw9SAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false

I merely quoted it in an attempt to give a partial answer to the original question. I claim absolutely no linguistic or translation skills.

The pdf of the Cantor article is from Professor David Wilkins. I have no idea whether he is responsible for the transcription. He offers other formats:
https://www.maths.tcd.ie/pub/HistMath/People/Cantor/Ausdehnung/

A digitized version of the Mathematische Annalen article may be found here:
https://gdz.sub.uni-goettingen.de/id/PPN235181684_0005?tify={%22pages%22:[130],%22view%22:%22info%22}


A French translation from 1883 that appeared in Acta Mathematica is available here (open access):
https://doi.org/10.1007/BF02612168
https://projecteuclid.org/journalArticle/Download?urlid=10.1007%2FBF02612168

and the passage in question is translated 'J'appelle ce theoreme un axiome' (please forgive the transliteration) on page 342 of the journal, page 7 of the pdf. I do not find the name of a translator.


This same original question was posted on Stack Exchange and resulted in a small discussion (including a comment by Dave L Renfro, whom I referenced, and the link to the French translation)
https://math.stackexchange.com/questions/4102911/need-english-translation-of-cantors-ueber-die-ausdehnung-eines-satzes-aus-der-t

[Gus Gassmann]

I would agree with that assessment, even though Cantor uses the word "Satz" about ten times in the document, and every other time he clearly means "theorem". The only time he uses the word "Theorem" is in a formal statement on page 7 in David Wilkins' pdf file. If Cantor meant "Satz" in the meaning of "theorem" in line 1, on page 6, the reference implied by "diese[r] Satz" would at the very least be ambiguous. It really cannot refer to anything else but the previous sentence. Jourdain seems to have gotten it wrong.

[redsto...@163.com]

Thanks every one ! Does Cantor explain why his definition of real(or irrational) numbers at the start of his essay is independent of geometry but rather relate the two later by an axiom in the essay ? I expect something like what Richard Dedekind had said in his [Essays on the Theory of Numbers](https://www.gutenberg.org/files/21016/21016-pdf.pdf):
For, the way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes—which itself is nowhere carefully defined—and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself...Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone.

[redsto...@163.com]

And what motivation caused Cantor to put forward his definition of real(or irrational) numbers?

[Eram semper recta]

On Saturday, 17 April 2021 at 04:34:46 UTC-4, redsto...@163.com wrote:
> Thanks every one ! Does Cantor explain why his definition of real(or irrational) numbers at the start of his essay is independent of geometry but rather relate the two later by an axiom in the essay ? I expect something like what Richard Dedekind had said in his [Essays on the Theory of Numbers](https://www.gutenberg.org/files/21016/21016-pdf.pdf):
> For, the way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes—which itself is nowhere carefully defined—and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself...Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone.

It is impossible to derive the number concept without geometry because geometry gives you the basic steps, such as ratio and measure. A ratio need not be a distance per se, but distances are the easiest to work with after the foundational concepts such as point, line, etc are systematically derived.

You can't even begin to talk about arithmetic without geometry because the entire theory of fractions and the arithmetic operations are fully derived from similar triangles:

https://youtu.be/h_RtgDExaIY

https://youtu.be/TS9Asz6fZrs

"And what motivation caused Cantor to put forward his definition of real(or irrational) numbers?"

Cantor realised that an indexable set is one whose members can be systematically named, such as the natural numbers, ie, choose any radix and the radix representation of each element becomes the UNIQUE name. He then thought how it might be possible with an imaginary set such as the "real numbers". Cantor knew that set or "real numbers" could not be indexed, but not for the reasons he thought. Cantor accepted that every real number can be expressed as an "infinite decimal expansion". If this were true, then it is possible to systematically name the set of infinite decimal expansions because of bijective cardinality between infinite sets and that would make the set of reals indexable(countable) contrary to Cantor's claim that it cannot be indexed. So, Cantor devised an illogical argument called the Diagonal Argument which has fooled thousands of ignorant academic nincompoops in the mainstream.

In this video I show you how the bullshit "set of reals" based on "infinite decimal expansions" (which are themselves a myth), can be proved countable. Of course there is no such thing as an infinite decimal expansion and no such thing as a "real number" and this is why the set of reals is not countable - it does not exist!

https://youtu.be/hlqTuuhR3-4

Cantor was a delusional crank and the father of all mathematical cranks in the mainstream. His ideas were not only absurd, but toxic in every respect. The man ended up in a mental asylum because he was a loon.

Every minute you waste studying that fool's ideas is a minute that could have been spent studying real mathematics. Don't waste your time. Cantor had no clue what is a "real number" because there is no such thing as "irrational number" or "real number".

To understand the concept of number, you need to study my article:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Without me, you cannot understand what it means to be a number because I was the first in human history to define number:

A number is a name given to a measure that describes a magnitude or size.

[Quantum Bubbles]

On Saturday, April 17, 2021 at 1:20:02 PM UTC+1, Eram semper recta wrote:

"It is impossible to derive the number concept without geometry because geometry gives you the basic steps, such as ratio and measure. A ratio need not be a distance per se, but distances are the easiest to work with after the foundational concepts such as point, line, etc are systematically derived. "

How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4 for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.

Kind Regards

[FredJeffries]

On Saturday, April 17, 2021 at 2:25:18 AM UTC-7, redsto...@163.com wrote:
> And what motivation caused Cantor to put forward his definition of real(or irrational) numbers?

The answer to that question is right in the title: Trigonometrischen Reihen.

He was trying to understand convergence of trigonometric series.

See Dauben, Joseph W. “The Trigonometric Background to Georg Cantor's Theory of Sets.” Archive for History of Exact Sciences, vol. 7, no. 3, 1971, pp. 181–216.

or just search for 'Cantor trigonometric series'

[FredJeffries]

On Saturday, April 17, 2021 at 1:34:46 AM UTC-7, redsto...@163.com wrote:
> Thanks every one ! Does Cantor explain why his definition of real(or irrational) numbers at the start of his essay is independent of geometry but rather relate the two later by an axiom in the essay ?

Joudain discusses that issue in his introduction
https://books.google.com/books?id=Jw9SAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false

[Eram semper recta]

In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think) correlation of number with objects is very much like primate Georg Cantor's ideas wrt sets. Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number). Animals cannot conceive anything, so any talk of independence from our ideas of number is moot. The animal mind is based solely on instinct. It can be trained but this is also part of its instinctive architecture.

So to summarise, animal recognition of number is similar to yours - set theoretical and superficial. The comparison mechanism in animals is once again instinctive and so very limited.

This will all probably be too much for your pea-sized brain, but it gave me a chuckle.

Psychology and psychiatry are pseudo-sciences.

>
> Kind Regards

[WM]

Eram semper recta schrieb am Samstag, 17. April 2021 um 22:35:17 UTC+2:
> On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:

> > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4

at least 7

> for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.

> In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think)

That is nonsense!!! Animals and humans are only gradually distinct. Some species can communicate even with humans.

> Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number).

They have a concept that does not need geometry and therefore is better than your unfounded and rather silly claim that arithmetic starts from geometry. Computers can very well process numbers. They need not the least geometry. Early herdsmen did not need geometry but had to count their cattle.

> Animals cannot conceive anything, so any talk of independence from our ideas of number is moot. The animal mind is based solely on instinct. It can be trained but this is also part of its instinctive architecture.
>
> So to summarise, animal recognition of number is similar

to that of all sensible humans.

Regards, WM

[Quantum Bubbles]

My question was not specifically about animals, it merely mentioned them. Evidence indicates that humans have two innate systems; one discrete, one continuous. That animals have an innate system, indicates that it isn't some special fact about humans, even if we do a lot more with them.

Psychiatry doesn't enter into it as far as I know.

Psychology is a label that applies to a rather wide range of things, however the study of learning, memory, cognitive development and perception isn't pseudoscience by any sensible definition and certainly falls under the heading of psychology.

Kind Regards

[comment redone because of typo]

[Eram semper recta]

On Saturday, 17 April 2021 at 17:24:45 UTC-4, WM wrote:
> Eram semper recta schrieb am Samstag, 17. April 2021 um 22:35:17 UTC+2:
> > On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:
>
> > > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4
> at least 7

The actual cardinal number is irrelevant. Since their brains are "biological computers", it would be unremarkable if they could correlate with much higher values.

> > for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.
>
> > In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think)

> That is nonsense!!!

Nope. It is fact. Animals cannot think or reason.

> Animals and humans are only gradually distinct.

It may be that you are only gradually distinct from animals, but could that be due to your brain damage perhaps?

> Some species can communicate even with humans.

Bullshit. Communication between humans has no parallel to any conditioning of animals that are imagined capable of communication.

> > Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number).

> They have a concept that does not need geometry and therefore is better than your unfounded and rather silly claim that arithmetic starts from geometry.

Since animals have no awareness, they are unable to conceive anything. That is what "instinctive" means. Look it up before you continue to make a fool of yourself.

> Computers can very well process numbers.

Chuckle. Do you know who programs computers?

> They need not the least geometry.

Absolute nonsense. You would not have a clue how to program any computer to perform calculations on fractions unless the theory of fractions was already known. Newsflash for you Wolfie: the theory comes from similar triangles. LMAO. So, yes. The programmer would have most definitely passed his primary school education at the very least.

Now if you say a human can learn to work with fractions without knowledge of geometry, this is of course true, BUT the knowledge that is taught was realised from geometry. You can't get away from geometry - no matter what science you are talking about.

> Early herdsmen did not need geometry but had to count their cattle.

Right. They did it very much like you and Georg Cantor - with almost zero understanding of the concept of number.

> > Animals cannot conceive anything, so any talk of independence from our ideas of number is moot. The animal mind is based solely on instinct. It can be trained but this is also part of its instinctive architecture.
> >
> > So to summarise, animal recognition of number is similar

to that of all incorrigibly stupid humans.

>
> Regards, WM

[Quantum Bubbles]

On Sunday, April 18, 2021 at 12:08:40 AM UTC+1, Eram semper recta wrote:
> On Saturday, 17 April 2021 at 17:24:45 UTC-4, WM wrote:
> > Eram semper recta schrieb am Samstag, 17. April 2021 um 22:35:17 UTC+2:
> > > On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:
> >
> > > > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4
> > at least 7
> The actual cardinal number is irrelevant. Since their brains are "biological computers", it would be unremarkable if they could correlate

> > Computers can very well process numbers.
> Chuckle. Do you know who programs computers?

In the case of the biological computers, if the systems are innate, they don't need to have been programmed by anyone (evolution by natural selection).

Kind Regards

[Eram semper recta]

On Saturday, 17 April 2021 at 17:33:36 UTC-4, Quantum Bubbles wrote:
> On Saturday, April 17, 2021 at 9:35:17 PM UTC+1, Eram semper recta wrote:
> > On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:
> > > On Saturday, April 17, 2021 at 1:20:02 PM UTC+1, Eram semper recta wrote:
> > >
> > > "It is impossible to derive the number concept without geometry because geometry gives you the basic steps, such as ratio and measure. A ratio need not be a distance per se, but distances are the easiest to work with after the foundational concepts such as point, line, etc are systematically derived. "
> > > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4 for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.
> > In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think) correlation of number with objects is very much like primate Georg Cantor's ideas wrt sets. Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number). Animals cannot conceive anything, so any talk of independence from our ideas of number is moot. The animal mind is based solely on instinct. It can be trained but this is also part of its instinctive architecture.
> >
> > So to summarise, animal recognition of number is similar to yours - set theoretical and superficial. The comparison mechanism in animals is once again instinctive and so very limited.
> >
> > This will all probably be too much for your pea-sized brain, but it gave me a chuckle.
> >
> > Psychology and psychiatry are pseudo-sciences.
> >
> > >
> > > Kind Regards
> My question was not specifically about animals, it merely mentioned them.

Your question was indeed about animals since you mentioned them in an attempt to refute the facts I stated.

> Evidence indicates that humans have two innate systems; one discrete, one continuous.

That is debatable theory, not evidence and in my opinion it's garbage.

> That animals have an innate system, indicates that it isn't some special fact about humans, even if we do a lot more with them.

No. Animals only have innate instinct. I would gladly have discussed my theory of KATIS (knowledge acquisition through inferential suspension) that is both innate and dynamic in humans from birth, but it would be like trying to get a chimpanzee to understand advanced mathematics, because the intellectual gulf between you and me is unsurpassable, what with you having no clear distinction from animals.

>
> Psychiatry doesn't enter into it as far as I know.

Well, as far as animals are concerned, it does not, but I also talked about humans.

>
> Psychology is a label that applies to a rather wide range of things, however the study of learning, memory, cognitive development and perception isn't pseudoscience by any sensible definition and certainly falls under the heading of psychology.

It is pseudoscience in every respect. There is no way to measure learning, memory, cognitive development, etc. About the closest I can think of is an IQ test, but most of these are not reliable.

Any science involves measure and cannot be a science without measure.

[Eram semper recta]

Natural selection is a bullshit theory that is more holey than Swiss cheese.

>
> Kind Regards

[Quantum Bubbles]

An unexpected reply I must confess.

What alternative would your propose or endorse, to what is usually referred to informally as 'the theory of evolution by natural selection' ? Is it intelligent design style creationism, Rupert Sheldrake's sort of stuff or what?

Kind Regards

[Eram semper recta]

I wouldn't use any of those labels or categories.

I am inclined to think that the entire physical universe is a product of being/s with higher intelligence than ours and composed of indestructible matter (not physical and I can't answer past this idea). If indeed evolution were sensible, then it too would have been set in motion by these higher beings, but since evolution is the biggest bunch of crap ever to be proposed, I doubt these beings would have gone down that path. As I said, there are innumerable problems with the theory of evolution that cannot be explained or resolved.

>
> Kind Regards

[Eram semper recta]

One of the most convincing problems with evolution is the gender question. When did living things decide to become male and female? Chuckle. This is one of the hilarious aspects of the garbage theory of evolution.

But let's go back to the simplest logic:

i. It is inconceivable that matter simply came into being from nothing or that something was always there without a first cause. The physical universe has not always existed. Therefore, whether big bang or otherwise, something must have started it. We can't be idiots like that crippled moron Stephen Hawking who claimed "It was always there just as the south pole was always there and there is nothing south of the south pole".

ii. It takes intelligence to give rise to other intelligence.

iii. Order does not arise out of chaos.

iv. Statistically the chances are ZERO that a soup of chemicals would have developed into RNA and DNA. There was engineering on a galactic scale and that could only have been possible by higher beings.

These are but a few reasons, but by no means the completion.

[WM]

Eram semper recta schrieb am Sonntag, 18. April 2021 um 01:08:40 UTC+2:
> On Saturday, 17 April 2021 at 17:24:45 UTC-4, WM wrote:
> > Eram semper recta schrieb am Samstag, 17. April 2021 um 22:35:17 UTC+2:
> > > On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:
> >
> > > > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4
> > at least 7
> The actual cardinal number is irrelevant. Since their brains are "biological computers", it would be unremarkable if they could correlate with much higher values.
> > > for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.
> >
> > > In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think)
>
> > That is nonsense!!!
> Nope. It is fact. Animals cannot think or reason.

You are unable to understand it. Rather bad for a genius.

> > Animals and humans are only gradually distinct.
> It may be that you are only gradually distinct from animals,

of course, like you. We are animals with a bit more brain.

> > Some species can communicate even with humans.
> Bullshit. Communication between humans has no parallel to any conditioning of animals that are imagined capable of communication.

Now I understand why you believe that you have no parallel. You seem to hate parallels.

> > > Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number).
>
> > They have a concept that does not need geometry and therefore is better than your unfounded and rather silly claim that arithmetic starts from geometry.
> Since animals have no awareness, they are unable to conceive anything. That is what "instinctive" means. Look it up before you continue to make a fool of yourself.
> > Computers can very well process numbers.
> Chuckle. Do you know who programs computers?

People who need not know anything about geometry.

> > They need not the least geometry.
> Absolute nonsense. You would not have a clue how to program any computer to perform calculations on fractions unless the theory of fractions was already known.

Fractions don't need geometry.

Numbers are properties like coulours, strengths, surface structures and so on. The colour describes what wavelengths are mainly reflected, the number describes into how many parts a thing can be or has been divided. There arise also the fractions. A very mundane origin. No Gods, no Greeks, and no geometry at all are needed.

>
> Now if you say a human can learn to work with fractions without knowledge of geometry, this is of course true, BUT the knowledge that is taught was realised from geometry.

No. Your preference for Euclid blinds you. Numbers were used way earlier than geometry. Unless you think that dividing a sheep in parts is geometry.

> > Early herdsmen did not need geometry but had to count their cattle.
> Right. They did it very much like you and Georg Cantor - with almost zero understanding of the concept of number.

What you understand is your own invention and is rather uninteresting to mathematicians.

> > > So to summarise, animal recognition of number is similar
> to that of all incorrigibly stupid humans.

It is similar to that of humans (there are tribes knowing less than 3 numbers) which you call stupid because you are not aware and cannot comprehend their accomplishments.

I know from own experience that animals can think and act rationally.

Regards, WM

[WM]

Eram semper recta schrieb am Sonntag, 18. April 2021 um 01:46:20 UTC+2:


> i. It is inconceivable that matter simply came into being from nothing or that something was always there without a first cause.

But the creator(s) need no firts cause.

> The physical universe has not always existed.

But the theological univers has?

>Therefore, whether big bang or otherwise, something must have started it. We can't be idiots like that crippled moron Stephen Hawking who claimed "It was always there just as the south pole was always there and there is nothing south of the south pole".

But you seem to believe that the creators were always there?

>
> ii. It takes intelligence to give rise to other intelligence.

Your arguing about intelligence is no convincing to intelligent beings.

>
> iii. Order does not arise out of chaos.

In physics this happens regularly.

>
> iv. Statistically the chances are ZERO that a soup of chemicals would have developed into RNA and DNA.

The blind golver who puts an ass. In billions of years it will happen abundantly.

> There was engineering on a galactic scale and that could only have been possible by higher beings.

who were created by higher beings who were created by higher beings. Why did they wish to descend so deep?

Regards, WM

[Eram semper recta]

On Sunday, 18 April 2021 at 07:33:44 UTC-4, WM wrote:
> Eram semper recta schrieb am Sonntag, 18. April 2021 um 01:08:40 UTC+2:
> > On Saturday, 17 April 2021 at 17:24:45 UTC-4, WM wrote:
> > > Eram semper recta schrieb am Samstag, 17. April 2021 um 22:35:17 UTC+2:
> > > > On Saturday, 17 April 2021 at 08:26:33 UTC-4, Quantum Bubbles wrote:
> > >
> > > > > How would you respond to studies in empirical psychology which suggest that even some animals have a discrete/counting number concept up to about 4
> > > at least 7
> > The actual cardinal number is irrelevant. Since their brains are "biological computers", it would be unremarkable if they could correlate with much higher values.
> > > > for example, and that this is independent of our crude pre-theoretical continuous/measurement idea of number? In other words we seem to innately have two primitive systems.
> > >
> > > > In animals, the instinctive (animals do not have awareness like humans and so cannot reason or think)
> >
> > > That is nonsense!!!
> > Nope. It is fact. Animals cannot think or reason.
> You are unable to understand it. Rather bad for a genius.

And a moron like you understands it, yes? Chuckle. When you can't even understand simple things like the fact that Euclid's Elements do not require use of ruler and compass.

> > > Animals and humans are only gradually distinct.
> > It may be that you are only gradually distinct from animals,
> of course, like you. We are animals with a bit more brain.

Indeed. Unlike you, I am an animal with a lot more brains.

> > > Some species can communicate even with humans.
> > Bullshit. Communication between humans has no parallel to any conditioning of animals that are imagined capable of communication.
> Now I understand why you believe that you have no parallel. You seem to hate parallels.

Pffft. Childish illogical rant.

> > > > Animals associate the objects with a cardinal value (one can't call it a number, because animals have zero concept of number).
> >
> > > They have a concept that does not need geometry and therefore is better than your unfounded and rather silly claim that arithmetic starts from geometry.
> > Since animals have no awareness, they are unable to conceive anything. That is what "instinctive" means. Look it up before you continue to make a fool of yourself.
> > > Computers can very well process numbers.
> > Chuckle. Do you know who programs computers?
> People who need not know anything about geometry.

Knowing about fractions, requires knowing about geometry first.

> > > They need not the least geometry.

Keep telling yourself nonsense like this and you'll grow dumber.

> > Absolute nonsense. You would not have a clue how to program any computer to perform calculations on fractions unless the theory of fractions was already known.
> Fractions don't need geometry.

The arithmetic on fractions is 100% geometric in origin. Perhaps if you bothered to study the Elements instead of reading your many comic books, you might some day learn this fact.

>
> Numbers are properties like coulours, strengths, surface structures and so on. The colour describes what wavelengths are mainly reflected, the number describes into how many parts a thing can be or has been divided. There arise also the fractions. A very mundane origin. No Gods, no Greeks, and no geometry at all are needed.

Who is talking about "gods"? Chuckle. A "god" is a being that is worshipped. Since I do not worship any gods, please refrain from raising stupid topics.

Of course the Greeks are not needed to realise geometry, but eat your heart out Kraut! They were the first to realise the perfect concepts.

> >
> > Now if you say a human can learn to work with fractions without knowledge of geometry, this is of course true, BUT the knowledge that is taught was realised from geometry.
> No. Your preference for Euclid blinds you.

Assertions are of even less worth than old-wives tales.

> Numbers were used way earlier than geometry. Unless you think that dividing a sheep in parts is geometry.

You love argument by false equivalence.

> > > Early herdsmen did not need geometry but had to count their cattle.
> > Right. They did it very much like you and Georg Cantor - with almost zero understanding of the concept of number.
> What you understand is your own invention and is rather uninteresting to mathematicians.

Actually it is not my own invention. I understand that it would be uninteresting to morons who prefer to discuss Cantor's useless theories all their lives with no possible agreement. Chuckle.

> > > > So to summarise, animal recognition of number is similar
> > to that of all incorrigibly stupid humans.
> It is similar to that of humans (there are tribes knowing less than 3 numbers) which you call stupid because you are not aware and cannot comprehend their accomplishments.

He said, she said, bla, bla, bla. Here we are trying to talk about rationality and mathematics, not your beliefs and opinions which are groundless. Stop reading comic books and try studying real mathematics.

>
> I know from own experience that animals can think and act rationally.

Dreams are also an experience. Chuckle. As long as you continue to waste your time on Cantor's useless bullshit, it's inevitable that your brain will be affected more.

>
> Regards, WM

[Eram semper recta]

On Sunday, 18 April 2021 at 08:24:18 UTC-4, WM wrote:
> Eram semper recta schrieb am Sonntag, 18. April 2021 um 01:46:20 UTC+2:
>
>
> > i. It is inconceivable that matter simply came into being from nothing or that something was always there without a first cause.
> But the creator(s) need no firts cause.

Again, false equivalence. I am not saying that. What I am saying is we do not know how creators could always have been there. It is impossible to understand how an intelligent being could have existed into past perpetuity. But, the fact that I am typing this means it is proof even though the details cannot or have not been understood.

> > The physical universe has not always existed.
> But the theological univers has?

I don't waste time with theology as you do.

> >Therefore, whether big bang or otherwise, something must have started it. We can't be idiots like that crippled moron Stephen Hawking who claimed "It was always there just as the south pole was always there and there is nothing south of the south pole".
> But you seem to believe that the creators were always there?

Yes. They couldn't have suddenly been created out of the inanimate realm of perfect concepts. Chuckle.

> >
> > ii. It takes intelligence to give rise to other intelligence.
> Your arguing about intelligence is no convincing to intelligent beings.

You couldn't know! LMAO.

> >
> > iii. Order does not arise out of chaos.
> In physics this happens regularly.

Rubbish.

> >
> > iv. Statistically the chances are ZERO that a soup of chemicals would have developed into RNA and DNA.
> The blind golver who puts an ass. In billions of years it will happen abundantly.

Arguing like a silly child again because there is no analogy between a blind golfer and the complexity that is found in a living cell. But yes, there are imbeciles who are too stupid to think about these things.

> > There was engineering on a galactic scale and that could only have been possible by higher beings.
> who were created by higher beings who were created by higher beings.

I don't know. Thus far, none have deemed me important enough to reveal who they are. LMAO.

> Why did they wish to descend so deep?

Stupid question which does not follow.

>
> Regards, WM