cactus flower wrote:

Geometry needs to be able to deal with flexibility and softness. The attachment diagram is substructure, rather than superficial decoration, but EVM is close.





Then there is sound.

Of course. That is where I am hoping our research in Higher Geometry will lead. However, we literally have to begin at the beginning.

In this regard I am starting with the Axiom of Dimensionality, in geometry, and the very fundamentals of arithmetic in Gaelic Mathematics. I have great freedom in this regard as I never studied mathematics through Irish, so I have a real opportunity to study the language and how it is used both linguistically and conceptually to ensure that that best adaptations of the mathematical language are made, adaptations which respect our genius and traditions.
Not everyone will necessarily agree with my approach but hey! what is research if not a little controversial.

TheGeniusOfCork wrote:

cactus flower wrote:

Geometry needs to be able to deal with flexibility and softness. The attachment diagram is substructure, rather than superficial decoration, but EVM is close.





Then there is sound.

Of course. That is where I am hoping our research in Higher Geometry will lead. However, we literally have to begin at the beginning.

In this regard I am starting with the Axiom of Dimensionality, in geometry, and the very fundamentals of arithmetic in Gaelic Mathematics. I have great freedom in this regard as I never studied mathematics through Irish, so I have a real opportunity to study the language and how it is used both linguistically and conceptually to ensure that that best adaptations of the mathematical language are made, adaptations which respect our genius and traditions.
Not everyone will necessarily agree with my approach but hey! what is research if not a little controversial.

You are involved in an interesting project there tgoc. The pattern above looks vaguely Celtic itself - what is it? It's lovely.

Auditor #9 wrote:

TheGeniusOfCork wrote:

cactus flower wrote:

Geometry needs to be able to deal with flexibility and softness. The attachment diagram is substructure, rather than superficial decoration, but EVM is close.





Then there is sound.

Of course. That is where I am hoping our research in Higher Geometry will lead. However, we literally have to begin at the beginning.

In this regard I am starting with the Axiom of Dimensionality, in geometry, and the very fundamentals of arithmetic in Gaelic Mathematics. I have great freedom in this regard as I never studied mathematics through Irish, so I have a real opportunity to study the language and how it is used both linguistically and conceptually to ensure that that best adaptations of the mathematical language are made, adaptations which respect our genius and traditions.
Not everyone will necessarily agree with my approach but hey! what is research if not a little controversial.

You are involved in an interesting project there tgoc. The pattern above looks vaguely Celtic itself - what is it? It's lovely.

Well my son says that it's a mandala. It redminds me a little of Lissajou patterns, or maybe a representation of atomic shells. Maybe cf would post the source.

After a little further investigating I would suggest that it is a representation of an aura emanating from a chakra.

Ye are really me.

Yellow Bell

I like the bit about the Harmony of the Spheres

This is what it is, TGO'Cork.

Yellow Bell

The 12 Lu, Pythagoras, and the Song of the Phoenix.

"Ling Lun selected bamboo pipes for the Yellow Emperor of the Xia Dynasty which became the standard for music as they perfectly matched the Song of the Phoenix. All emperors who followed took great care to balance and harmonize the essence of their empire by adjusting their standard to elaborate and enhance the Yellow Bell's beauty. The Lu are the 12 pitches formed by the Pythagorean method which builds the notes using the ratio 3 to 2. From these 12 tones, Pentatonic Modes are selected by emperors and music theorists alike."


Huang Zhong (Yellow Bell), Da Cu (Red), Gu Xian (Cyan), Zhong Lu (Green), Lin Zhong (Orange), Nan Lu (Blue), Ying Zhong (Indigo), Qing Huang Zhong (Violet)
The ratios of the musical notes represent the Music of the Spheres, the harmonic proportions of the movements of the heavenly bodies which is reflected in the depictions of the chakras of the body, most notably the The Ajna Center or Third Eye.

"Whereas science is still gaining an understanding of Music and it's use in healing, the field of Cymatics shows promising insight. In acupuncture treatment, tuning forks are used to vibrate the needles, directly transmitting the resonance to the Qi. The qualities of the Wu Xing, the 5 Elements, as related to the pitches below, are used to harmonize the Qi and effect positive change."

Chinese and Western Pitch Ratios Compared » C. C. Evans

Western
Chinese

Pitch
Pythagoras
Zarlino
SAT
Note Name
Pitch Name (with
Huang Zhong as gong)

Unison (doh)
1:1
1:1
1:1
Huang Zhong
Gong (earth)

Pythagorean Limma or Minor Diatonic Semitone (doh#)
256:243
16:15
2187:2048
Da Lu


Major Whole Tone (re)
9:8
9:8
9:8
Da Cu
Shang (metal)

Minor Third (re#)
288:243
6:5
19683:16384
Jia Zhong


Major Third(mi)
81:64
5:4
81:64
Gu Xian
Jue
(wood)

Perfect Fourth (fa)
4:3
4:3
177147:131072
Zhong Lu
qingjue

Tritone (fa#)
1024:729
64:45
729:512
Rui Bin
bianzhi

Perfect Fifth (sol)
3:2
3:2
3:2
Lin Zhong
Zhi
(fire)

Minor Sixth (sol#)
768:486
8:5
6561:4096
Yi Ze


Major Sixth (la)
27:16
5:3
27:16
Nan Lu
Yu (water)

Minor Seventh (la#)
16:9
16:9
59049:32768
Wu Yi
run

Major Seventh (ti)
243:128
15:8
243:128
Ying Zhong
biangong

Octave (doh1)
2:1
2:1
531441:262144
Qing Huang Zhong
qinggong

Apologies for the flattened table - you can find it here LINK





Huang Zhong (Yellow Bell), Da Cu (Red), Gu Xian (Cyan), Zhong Lu (Green), Lin Zhong (Orange), Nan Lu (Blue), Ying Zhong (Indigo), Qing Huang Zhong (Violet)

You would be surprised what you will find. Sound Science

TheGeniusOfCork wrote:

You would be surprised what you will find. Sound Science

If i go in through that little window TGOC, will I ever get out again?

cactus flower wrote:

TheGeniusOfCork wrote:

You would be surprised what you will find. Sound Science

If i go in through that little window TGOC, will I ever get out again?

As I too discovered CF, I nearly got lost for a month. Time to wrap this thread up. By the way the twelve Lu are the twelve women in the story of Lúgh's birth. But enough about that.

What I reall could do with is a short course in Vector and Tensor analysis, using symbolic rather that index notation. It should be viewable off-line as my research machine is currently off-line. I have a memory stick so transport is not a problem. It should be available free of charge, and also I may wish to distribute it to other members of our research group so it should have a GNU public licence.

A good drawing package capable of producing quality mathematical diagrams in two and three dimensions. Mac OSX 10.3 compatable, and again with some form of GNU public licence, and capable of being incorporated into Latex.

While my research machine was connected I stumbled upon a program or site which seemed to make it much easier to create mathematical formulae for Latex. If such a system could be found it would prove quiet usefull.

Finally some of the posts I have written here and down below on P.ie, could prove publishable once polished up by an editor. If I happened to get a few bob for my opinions it would be gratefully received.

Finally, finally could you please ask the editor of P.ie to ban me for a month. I really need to focus on the geometry.

I will drop down here occasionaly to my Higher Reality thread with a report from the high ground.

Perhaps Ibis might be able to help you with the banning. Or you could do a computational job on Libertas's accounts - that would probably get you banned.

If you are going to be away, I wonder if you would just post any thoughts and assistance on the concept of 0 and how it is useful in mathematics before you go. I will do my best to keep going on that topic until your return.

Good luck with the work.

cactus flower wrote:

Perhaps Ibis might be able to help you with the banning. Or you could do a computational job on Libertas's accounts - that would probably get you banned.

If you are going to be away, I wonder if you would just post any thoughts and assistance on the concept of 0 and how it is useful in mathematics before you go. I will do my best to keep going on that topic until your return.

Good luck with the work.

People have done enough messing around with my systems over the years, that I would never resort to that sort of action. Any way a self-imposed exile requires a little more discipline and if I need to flick my little twig, where better than P.ie.

In relation to zero I now have a different interpretation, which is the story of The Zero Scrolls.

Whilst searching for an Irish word for zero, all of them on www.focal.ie, are direct adaptations of Latin terms. The sanskrit word is shunyam and since I grew up in Kerry, I would use a colloquial word, neadar. This can be used in the context of a conversation when you are asked a question, and you have nothing to say. So nothing:neadar. This extends the concept of zero, beyond it's normal mathematical usage, as a placeholder. Nothing is the source of everything, neadar, may contain an egg, which hatches to become an éan, which grows to become áon, which matures to become Aon.

The first part of the first aphorism, sutra:umtha, in the zero scrolls is ekadikena, one more than, aon níos mó ná. Going from Sanskrit, to English, to Irish. Taking a little poetic licence, the phoneme correlation between Sanskrit and Irish can be tightened, as in eka-dik-ena, aon-ním-ona, I still have to work with an expert in Sanskrit on this.

From the first sutra all the other numbers emerge after Aon has hatched.

It is the essence of Aonró.

Aonró

Aon.

Éan suas sa spéir.

Aon,
ding dong dideró,
a Dó.

Aon,
aon níos mó na é,
a Dó,
ding dong diderí,
a Trí.

Aon,
aon níos mó na é,
a Dó,
aon níos mó na é,
a Trí.

'S araille,
abhaile libh anois.

Uile go dtí a naoi,
an deireadh Deich.

There's a lot packed into that. As far as I know Gael Taca in Cork may have a recording of me reciting this. It is the first lesson in my method for expressing mathematics. Obviously I grew up in Tralee, and ding dong dideró was the virtual anthem of Siamsa Tíre.

In fact here we have the first two aphorisms of The Zero Scrolls. I believe that when shunyam was making it's way across the Arabian Desert, the camel got a bit cross and the knowledge of how to use it properly to avoid singularities fell out of the messengers pocket. So when he arrived in Europe his pockets were empty, and all he remembered were the nine digits, and the symbol of zero, as a place holder.

I further believe, and this may seem unusual, that the The Zero Scrolls were destined for that one group of people who could understand them, and that was the people living at the most westerly extremity of Europe.

I haven't managed to get the aphorisms down there yet, but I'm hoping to do so. They have already been on their way for nearly a hundred years. So a few more weeks or days won't matter. If anyone knows anyone down there who wants to communicate with me, or work with me on the internet, have them contact me.

By the way the next aphorism, which I adapt as díreach is transach, contains the starting point for all of linear algebra.

Slán.

Quote :

neadar, may contain an egg, which hatches to become an éan, which grows to become áon, which matures to become Aon.

This is a dialectical zero, TGOC, that contains its opposite ! Bravo!

Unfortunately I am even more deficient in the Irish department than in maths, so if anyone would kindly translate (if translateable), I would most appreciate it.

TheGeniusOfCork wrote:

cactus flower wrote:

Perhaps Ibis might be able to help you with the banning. Or you could do a computational job on Libertas's accounts - that would probably get you banned.

If you are going to be away, I wonder if you would just post any thoughts and assistance on the concept of 0 and how it is useful in mathematics before you go. I will do my best to keep going on that topic until your return.

Good luck with the work.

People have done enough messing around with my systems over the years, that I would never resort to that sort of action. Any way a self-imposed exile requires a little more discipline and if I need to flick my little twig, where better than P.ie.

In relation to zero I now have a different interpretation, which is the story of The Zero Scrolls.

Whilst searching for an Irish word for zero, all of them on www.focal.ie, are direct adaptations of Latin terms. The sanskrit word is shunyam and since I grew up in Kerry, I would use a colloquial word, neadar. This can be used in the context of a conversation when you are asked a question, and you have nothing to say. So nothing:neadar. This extends the concept of zero, beyond it's normal mathematical usage, as a placeholder. Nothing is the source of everything, neadar, may contain an egg, which hatches to become an éan, which grows to become áon, which matures to become Aon.

The first part of the first aphorism, sutra:umtha, in the zero scrolls is ekadikena, one more than, aon níos mó ná. Going from Sanskrit, to English, to Irish. Taking a little poetic licence, the phoneme correlation between Sanskrit and Irish can be tightened, as in eka-dik-ena, aon-ním-ona, I still have to work with an expert in Sanskrit on this.

From the first sutra all the other numbers emerge after Aon has hatched.

It is the essence of Aonró.

Aonró

Aon.

Éan suas sa spéir.

Aon,
ding dong dideró,
a Dó.

Aon,
aon níos mó na é,
a Dó,
ding dong diderí,
a Trí.

Aon,
aon níos mó na é,
a Dó,
aon níos mó na é,
a Trí.

'S araille,
abhaile libh anois.

Uile go dtí a naoi,
an deireadh Deich.

There's a lot packed into that. As far as I know Gael Taca in Cork may have a recording of me reciting this. It is the first lesson in my method for expressing mathematics. Obviously I grew up in Tralee, and ding dong dideró was the virtual anthem of Siamsa Tíre.

In fact here we have the first two aphorisms of The Zero Scrolls. I believe that when shunyam was making it's way across the Arabian Desert, the camel got a bit cross and the knowledge of how to use it properly to avoid singularities fell out of the messengers pocket. So when he arrived in Europe his pockets were empty, and all he remembered were the nine digits, and the symbol of zero, as a place holder.

I further believe, and this may seem unusual, that the The Zero Scrolls were destined for that one group of people who could understand them, and that was the people living at the most westerly extremity of Europe.

I haven't managed to get the aphorisms down there yet, but I'm hoping to do so. They have already been on their way for nearly a hundred years. So a few more weeks or days won't matter. If anyone knows anyone down there who wants to communicate with me, or work with me on the internet, have them contact me.

By the way the next aphorism, which I adapt as díreach is transach, contains the starting point for all of linear algebra.

Slán.

There is a native Irish word for zero, neamhní- which little means an unthing (neamh-ní), a no thing as it were, nothing zero zilch. It's scots gaelic counterpart is neoní and both are used within the same context. Náid is probably just a phonetic transliteration of the word naught from English, and nialas is no doubt from the latin Nihilus.

However, neadar is not what you think it is. Rather it is n'fheadar, literally meaning 'I don't know' and it is a defective verb rather than a statement of fact. More often than not, it can be used in the context of 'I wonder', as in 'n'fheadar an rachaidh mé ar an drabhlás anocht' 'i wonder if I'll go carousing tonight'. Therefore, when some responds to a question with the word 'n'fheadar', it means they simply do not know. It is found throughout most dialects, so I would not consider it colloquial, however, only in munster can it be conjugated to all persons, in both positive and negative. Strangely enough, it uses the past tense endings.

n'fheadar- i don't know
n'fheadraís- you don't know
n'fheadair- he/she doesn't know
n'fheadraíomair- we don't know
n'fheadraíobhair- you (pl) don't know
n'fheadraíodar- they don't know.

feadar- i know
feadraís- you know
feadair- he/she knows
feadraíomair- we know
feadraíobhair- ye pl know
feadraíodar- they know.

It is a defective verb because there is no past or future tense. However, it may transcend tenses :-)

**riadach has posted above

I'll have a shot at translating this much:

éan is bird or hen
áon is one
aon is any

Nice one tgoc - it reminds me of a Kinsella poem that I copied here before...


The Hen Woman, Thomas Kinsella

Quote :

However, neadar is not what you think it is. Rather it is n'fheadar, literally meaning 'I don't know' and it is a defective verb rather than a statement of fact. More often than not, it can be used in the context of 'I wonder', as in 'n'fheadar an rachaidh mé ar an drabhlás anocht' 'i wonder if I'll go carousing tonight'. Therefore, when some responds to a question with the word 'n'fheadar', it means they simply do not know. It is found throughout most dialects, so I would not consider it colloquial, however, only in munster can it be conjugated to all persons, in both positive and negative. Strangely enough, it uses the past tense endings.

No relation to the Spanish "nada" = nothing then ?

cactus flower wrote:

Quote :

However, neadar is not what you think it is. Rather it is n'fheadar, literally meaning 'I don't know' and it is a defective verb rather than a statement of fact. More often than not, it can be used in the context of 'I wonder', as in 'n'fheadar an rachaidh mé ar an drabhlás anocht' 'i wonder if I'll go carousing tonight'. Therefore, when some responds to a question with the word 'n'fheadar', it means they simply do not know. It is found throughout most dialects, so I would not consider it colloquial, however, only in munster can it be conjugated to all persons, in both positive and negative. Strangely enough, it uses the past tense endings.

No relation to the Spanish "nada" = nothing then ?

Nope, nada

So does anyone have a word for the nothing that is becoming something, or that has the potential to become something ?

Auditor #9 wrote:

**riadach has posted above

I'll have a shot at translating this much:

éan is bird or hen
áon is one
aon is any

Nice one tgoc - it reminds me of a Kinsella poem that I copied here before...


The Hen Woman, Thomas Kinsella

In fairness, aon means one and any. I've never seen aon with a síneadh fada over the a, with the possible exception of very old texts.

cactus flower wrote:

So does anyone have a word for the nothing that is becoming something, or that has the potential to become something ?

Well if you take the neamh away from neamhní, you have a thing. Of course if you are to adopt a system, as TGOC cleverly does, where one establishes an associated meaning based on phonological resemblences and not etymological ones, one can that state that neamhní could also mean heavenly thing, given neamh means heaven too.

Thanks TGOC, Auditor #9 and Riadach. I am thinking that now that a modern 0 needs to allow for the possibility of becoming, or having been something before, or existing in a different universe. A heavily pregnant 0 if you like.

Thomas Crilly's book "50 mathematical ideas you need to know" starts with 0 zero. He poins out that neither the Greeks or the Romans had 0.

The Mayans had various forms of 0. Claudius Ptolemy, astronomer used a symbol as a placeholder to show the difference between 15 and 105 but didn't use it as a number in its own right.

The Indian mathematician Brahamgupta treated zero as a number and set out the rule that the sum of a positive number plus zero is positive and the sum of zero and zero is zero. This idea took another 500 years to catch on in Europe.

More about zero later.

One question I have always wondered, are we discovering new mathematics or are we inventing new mathematics? It's maths like the laws of physics, or is it more like a methodology to discover the laws of physics?

**riadach has interesting post above

cactus flower wrote:

Thanks TGOC, Auditor #9 and Riadach. I am thinking that now that a modern 0 needs to allow for the possibility of becoming, or having been something before, or existing in a different universe. A heavily pregnant 0 if you like.

Thomas Crilly's book "50 mathematical ideas you need to know" starts with 0 zero. He poins out that neither the Greeks or the Romans had 0.

The Mayans had various forms of 0. Claudius Ptolemy, astronomer used a symbol as a placeholder to show the difference between 15 and 105 but didn't use it as a number in its own right.

The Indian mathematician Brahamgupta treated zero as a number and set out the rule that the sum of a positive number plus zero is positive and the sum of zero and zero is zero. This idea took another 500 years to catch on in Europe.

More about zero later.

1000, 1111, 1100, 1001

You're welcome, if it helped. I don't think the Irish word for "bird", éan, is directly related to the english word "hen" but it sounds similar enough. I didn't realise that aon had no fada either.

Zero is used in number place value and bases just to show that there are no units. It's like having an empty moneybag. In base 10 (or any base - 2, 5, 7, 8, 16) if it's the rightmost number then number 1 means "one unit"; the number 10 (in any base) means "no units and one of the base" in the case of base 10 it's like a roll of ten pennies. It's handier to have a ten penny coin instead though.

Zero - nature abhors a vacuum.

Auditor #9 wrote:

You're welcome, if it helped. I don't think the Irish word for "bird", éan, is directly related to the english word "hen" but it sounds similar enough. I didn't realise that aon had no fada either.

There is a good chance they are both indo-european cognates. In much the same way the word cú and hound are said to be related.

• However, neadar is not what you think it is.
  

It was really just a memory, of an incident which happened to me when I was doing my first Irish course, and Ella our teacher asked me a question, and I could think of nothing to say, so I siad, neadar, and she smiled and moved on, what I ment by a colloquialism related to how it crops up in English conversation from time to time.

• neamhní
  

That's nice. That which is not, that which is beyond, that which is within, that which is transcendent. I remember once doing a graphic which represented the expression of something from nothing. It consisted of three processes. The first was a circle, with a dot at the very centre, representing the potential for expression, or the expressor. The second was a circle. Representing the process of expression, in my view all process of computation are circular. The final was represented by a circle with a dot on top of it this represented the value emerging, the objective value of the computation, the expressed value.

• Kinsella Poem
  

Must read it again. I found it a little long, maybe I was too tired, anyway I don't tend to read other poets work.

• No relation to the Spanish "nada" = nothing then ?
  

That reminds me that, the first language that I began adapting my teaching methods into was Spanish. Tús, deireadh, lé chéile. Primo, ultimo, jhunto. First, last together. A technique for multiplying by 11.

• So does anyone have a word for the nothing that is becoming something, or that has the potential to become something ?
  

I suppose based on what I said before oudh, where the transcendal value is in the o, u represents the opening of the mouth, and dh represents something curling off the tongue.

• In fairness, aon means one and any. I've never seen aon with a síneadh
  fada over the a, with the possible exception of very old texts.
  

I sometimes use it instead of Aon, in my name, as it is a little less strong. To me you could have the sequence aon, áon, Aon, representing a three in one value for 1.

• More about zero later.
  

Zero is the equivalent of the unifield in computation, the empty set in mathematics, the transition state in Chemistry, it is the source, the course, the goal of all computation. If we place a 1 inside the zero we get the absolute number, if we rotate it about 90^o, we get Pi, the transcendental number.

• One question I have always wondered, are we discovering new mathematics
  or are we inventing new mathematics? It's maths like the laws of
  physics, or is it more like a methodology to discover the laws of
  physics?
  

Wow! What a huge question phrased so simply.

That is basically the the question as to whether mathematics exists without us. It is the antropomorphic question. Do we discover mathematics or do we invent it. If we invent it, then how can prime numbers exist, are they a consequence of our rules of arithmetic. The eact same questions can be asked of physics.

In my view the only way that this can be resolved is if the universe itself is intelligent. In fact modern research in Unified Field Theories suggest that at the level of superunification the field becomes self-interacting, in other words it becomes aware of itself. Also at this level when we transcend the planck scale dynamics the universe becomes more mind than matter. So the mathematics may pre-exist in some potential form but unless we posess the necessary skill we cannot discover all of it.

One thing to note is that although a mathematical fact may always be true, the way we use that truth depends on context. Like for instance we may know that 7x8 = 56, but the way we compute it depends on our computational skills. Each time we explore a new path from process description to resolution we are expanding not only our own awareness, but also potentially that of others as well. There have been a number of examples, the invention of calculus for example, where ideas spontaneously emerge in different individuals, or groups.

Ultimately, and this may not answer the point clearly, I would say that we both invent and discover mathematics/computation.
There may be mathematical rules governing the primality of a number, but for us to discover whether or not a number is prime, we must observe it in some way.

A big question for me is what kind of mathematics does the universe itself practice. I cannot for one moment conceive that it solves differential equations in order to determine the path of a sliothar through the air. It uses a much more refined method, and I beleive that by expanding our own awareness we may tap into and use the computational processes of the Cosmic Mathematician.

• **riadach has interesting post above
  

You bet.

• Zero is used in number place value and bases just to show that there
  are no units. It's like having an empty moneybag. In base 10 (or any
  base - 2, 5, 7, 8, 16) if it's the rightmost number then number 1 means
  "one unit"; the number 10 (in any base) means "no units and one of the
  base" in the case of base 10 it's like a roll of ten pennies. It's
  handier to have a ten penny coin instead though.
  
  Zero - nature abhors a vacuum.
  

In arithmetic zero is used as a place holder, however in other mathematical forms the concept of zero exists and is very rich. My particular interests lie in exploring some of it's computational properties and it's relationships to language.

At the very end of my unifield chart for Gaelic physics I wrote,


in bunchló simply because it felt right. That is with the phonemes pulled apart. To me it represents the absolute deep royal brimming intelligence which guides the laws of nature. A word I coined for natural computation is dútháireamhíocht to me it is of similar significance as dúthgaois, dúchas.

• There is a good chance they are both indo-european cognates. In much the same way the word cú and hound are said to be related.
  

The first time I became aware of the relationship between Irish and the languages of India, was about twenty five years ago when I was watching a TV program about a group of explorers going down a river in the Himalayas. The asked a local what was the word in his language for boat, and the word I heard was bád. A number of years ago I was talking with a man whose brother had been in Kashmir during WWII, and according to his story, he said that listening to the locals speaking their own language was like listening to people from Connemara, but not quiet being able to understand them.

Just the other day in Tralee I had a similar experience with two men from Kosovo, who were speaking their own dialect of Albanian. In our subsequent discission one of them confirmed for me that at least some of our anscestors had migrated from the region of the Danube delta to here.

• Transpose and Apply
  

This is the name of the next aphorism in English. In sanskrit it is Parávartya Yogayet, and it relates amongs other things to transformations in sign, or multiply to divide, when a number or symbol goes from one side of an equation to another. I wonder what would our language experts make of it.

TheGeniusOfCork wrote:

• One question I have always wondered, are we discovering new mathematics
  or are we inventing new mathematics? It's maths like the laws of
  physics, or is it more like a methodology to discover the laws of
  physics?
  

Wow! What a huge question phrased so simply.

That is basically the the question as to whether mathematics exists without us. It is the antropomorphic question. Do we discover mathematics or do we invent it. If we invent it, then how can prime numbers exist, are they a consequence of our rules of arithmetic. The eact same questions can be asked of physics.

In my view the only way that this can be resolved is if the universe itself is intelligent. In fact modern research in Unified Field Theories suggest that at the level of superunification the field becomes self-interacting, in other words it becomes aware of itself. Also at this level when we transcend the planck scale dynamics the universe becomes more mind than matter. So the mathematics may pre-exist in some potential form but unless we posess the necessary skill we cannot discover all of it.

One thing to note is that although a mathematical fact may always be true, the way we use that truth depends on context. Like for instance we may know that 7x8 = 56, but the way we compute it depends on our computational skills. Each time we explore a new path from process description to resolution we are expanding not only our own awareness, but also potentially that of others as well. There have been a number of examples, the invention of calculus for example, where ideas spontaneously emerge in different individuals, or groups.

Ultimately, and this may not answer the point clearly, I would say that we both invent and discover mathematics/computation.
There may be mathematical rules governing the primality of a number, but for us to discover whether or not a number is prime, we must observe it in some way.

A big question for me is what kind of mathematics does the universe itself practice. I cannot for one moment conceive that it solves differential equations in order to determine the path of a sliothar through the air. It uses a much more refined method, and I beleive that by expanding our own awareness we may tap into and use the computational processes of the Cosmic Mathematician.

Interesting stuff. I've read down to the Prime Numbers bit - why is us inventing Mathematics incompatible with the existence of Prime Numbers? Maybe we invented some of Mathematics - a Prime Number is something which is divisible equally by itself and one only. They are relatively rare. But does nature have any need for the notion of a Prime Number? Or division for that matter (in our sense of it - grouping things by number)

There are some studies that claim to show that elephants can count. I'm not sure that they do this through any concept of what we think of as numbers. It might be interesting to take a look.

I had always assumed that serious counting started, like writing, when agriculture started and surpluses were produced and recorded. Up until then, there wasn't enough of anything for it to be worth counting.

Auditor #9 wrote:

Interesting stuff. I've read down to the Prime Numbers bit - why is us
inventing Mathematics incompatible with the existence of Prime Numbers?
Maybe we invented some of Mathematics - a Prime Number is something
which is divisible equally by itself and one only. They are relatively
rare. But does nature have any need for the notion of a Prime Number?
Or division for that matter (in our sense of it - grouping things by
number)

Possibly the best source for a discussion on primes is The Man Who Loved Only Numbers - The Story of Paul Erdos and The Search for Mathematical Truth.

p.s. How do I get an umlat.

It's a while since I read it, but on opening it today the first thing that jumped out was Goldbach's Conjecture that every even number is the sum of two primes. S.K. Kapoor has resolved this conjecture in terms of vedic geometry, although his resolution still requires some work to make it conformable with the more logical western approach to mathematics. According to his work, the conjecture is true. So if we did not have prime numbers, we could not have even numbers. That only lets us have odd numbers, and if we did not have even numbers we could not have addition since the sum of two odd numbers is obviously even. The lack of prime numbers would therefore spell the end of arithmetic, and thereby the end of all mathematics and computation.

Therefore using that most beloved phrase of western scientific inquiry, Occams Razor, the only conclusion that one can draw is that primality pre-exists our discovery/invention that 1+1=2, that primality is really primal.

How exactly nature uses primality, is possibly much more significant a question than hunting large primes, and categorising different types of primes. To be honest at this stage I don't know, but I feel that it may be structured in geometry. It will definitely form a topic for discussion in one of our research booths, in our Higher Geometry forum.

Did I meet you up there.

cf There was a recent study I recall which suggested that monkeys in Japan had better numerical skills that some students!

Either the monkeys are very intelligent and properly trained, or the general education globally is in deep crisis.