How deep is math?

What is the basis for reason? And mathematics?

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Philosophy Explorer
Posts: 5634
Joined: Sun Aug 31, 2014 7:39 am

How deep is math?

Or how involving is math? By deep I mean that in its broadest sense so feel free to interpret it your particular way.

I'm an explorer of math and run into situations that make me wonder. For example, with factorials, I've checked the internet and found no patterns with them listed there.
Here's a case I've discovered:

1! = 1
3! = 2•3
5! = 4•5•6
7! = 7•8•9•10

There is no method that would have led to this pattern. You can see this is a four-line pattern that doesn't go any further. Some would say you can prove anything in math which isn't true and patterns are special - you just can't come up with any pattern.

I chose this particular example as it's easy to understand and follow for many people. Yet it's part of the math mysteries which isn't easy to explain.

So how deep is math for you?

PhilX surreptitious57
Posts: 3449
Joined: Fri Oct 25, 2013 6:09 am

Re: How deep is math?

Mathematics for me is the only truly perfect discipline because unlike any other I think it was discovered instead of invented
The symbols might be of human origin but the fundamental truth it conveys is too profound for it to have been created by us
The language of physics is mathematics which means the entire history of the Universe can be written in mathematical form

Eodnhoj7
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Joined: Mon Mar 13, 2017 3:18 am

Re: How deep is math?

Infinite, otherwise it would not have the stability to maintain itself as the observation of constants.

Eodnhoj7
Posts: 4517
Joined: Mon Mar 13, 2017 3:18 am

Re: How deep is math?

The more I think about it the more I am coming to the conclusion that math and logic is the study of infinity.

Philosophy Explorer
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Joined: Sun Aug 31, 2014 7:39 am

Re: How deep is math?

Here is another case I've just discovered with factorials:

3! + 2 = 2⁳
4! + 3 = 3⁳
5! + 5 = 5⁳
6! + 9 = 9⁳

Something to think about.

PhilX Eodnhoj7
Posts: 4517
Joined: Mon Mar 13, 2017 3:18 am

Re: How deep is math?

What we understand of definition is strictly an application of 1 as both a constant and fluxing spatial boundary that provides the foundation for how we both observe and define reality through a third median space as neutrality.

1 is a dimensional boundary in itself that manifests all measurements as observation of unity and multiplicity (through individuation). 1 is the boundary from which all measurements begin and end. In these respects, it manifests the foundations of all axioms as a universal dimension in itself.

EchoesOfTheHorizon
Posts: 356
Joined: Mon Oct 23, 2017 6:08 am

Re: How deep is math?

Philosophy Explorer wrote:
Tue Nov 28, 2017 3:26 pm
Here is another case I've just discovered with factorials:

3! + 2 = 2⁳
4! + 3 = 3⁳
5! + 5 = 5⁳
6! + 9 = 9⁳

Something to think about.

PhilX I'm probably embarrassing myself, but looking at the wiki page for factorials, I'm not seeing this.

https://en.m.wikipedia.org/wiki/Factorial

Can someone explain how he is saying this? I'm not disputing it as I can't even grasp what is being said.

That wiki may be wrong, but gotta go doublecheck Archimedes Sandreckoner, has been many years, but it looks like the basic structure for myriad-myriad calculations. It is pyramidal. But think that was more addition that multiplication. You can play out the structure for the size of irregular numbered units in classical armies along a similar mathematics, you progressed in rank relative to the number of men under you, and this grew (if you commanded infantry as the core of your army) from a basic file, to a rank and file formation, then higher up until you ended up as a senator. It never quite mathematically balanced out as tactical efficiency never matches mathematical purity, but it got close enough for a amateur historian about two years ago to theorize that the Roman military system and early structure of the voting blocks of the republic was built around a system of Pythagorean mathematics not too dissimilar to this rule. He posted on several websites, I can track it down if anyone is interested.

It got to the point that I can easily project the makeup of any classical army in my head unto a hypothetical battlefield, comes handy when you have absurdities in the historical record claiming a couple hundred thousand soldiers fought in a siege, such as the German siege of Roman Milan, I knew something was bizarre about that set up measuring everyone on the field, went and found a calculator online that gives average space a person standing needs per area, crunched the numbers, and it didn't match the area of the city known archaeologically for that era.

There is validity in stuff like this, but you gotta remember mathematics aren't always arranged around numbers, it can be patterns too. The whole Monad to Dyad to Triad structure can closely parrellel this, and nobody in the classical world would of made a fuss about it precisely because everyone would of been able to literally see it worked out in imagery before them.

Difference is, this climbs to a much higher interger than they ever would of tried.

And I agree with Eod, I think. Sorta, 1 isn't a number by itself, so the early stages of this table are false. Zero likewise isn't a number. One is a number when it is applied in a series to other numbers, which this IS a series, but zero has no obvious place here as one acts like zero would (smallest possible sum). Think this was more for insisting a larger pattern exists.

Example, why couldn't we extend this back farther using negative numbers, or decimal points, to achieve new patterns? The larger series from n3=n!6 should hold no issue if you do that decimal, but I don't know if negative numbers would work, going prior to "0".

Philosophy Explorer
Posts: 5634
Joined: Sun Aug 31, 2014 7:39 am

Re: How deep is math?

EchoesOfTheHorizon wrote:
Mon Dec 04, 2017 5:06 am
Philosophy Explorer wrote:
Tue Nov 28, 2017 3:26 pm
Here is another case I've just discovered with factorials:

3! + 2 = 2⁳
4! + 3 = 3⁳
5! + 5 = 5⁳
6! + 9 = 9⁳

Something to think about.

PhilX I'm probably embarrassing myself, but looking at the wiki page for factorials, I'm not seeing this.

https://en.m.wikipedia.org/wiki/Factorial

Can someone explain how he is saying this? I'm not disputing it as I can't even grasp what is being said.

That wiki may be wrong, but gotta go doublecheck Archimedes Sandreckoner, has been many years, but it looks like the basic structure for myriad-myriad calculations. It is pyramidal. But think that was more addition that multiplication. You can play out the structure for the size of irregular numbered units in classical armies along a similar mathematics, you progressed in rank relative to the number of men under you, and this grew (if you commanded infantry as the core of your army) from a basic file, to a rank and file formation, then higher up until you ended up as a senator. It never quite mathematically balanced out as tactical efficiency never matches mathematical purity, but it got close enough for a amateur historian about two years ago to theorize that the Roman military system and early structure of the voting blocks of the republic was built around a system of Pythagorean mathematics not too dissimilar to this rule. He posted on several websites, I can track it down if anyone is interested.

It got to the point that I can easily project the makeup of any classical army in my head unto a hypothetical battlefield, comes handy when you have absurdities in the historical record claiming a couple hundred thousand soldiers fought in a siege, such as the German siege of Roman Milan, I knew something was bizarre about that set up measuring everyone on the field, went and found a calculator online that gives average space a person standing needs per area, crunched the numbers, and it didn't match the area of the city known archaeologically for that era.

There is validity in stuff like this, but you gotta remember mathematics aren't always arranged around numbers, it can be patterns too. The whole Monad to Dyad to Triad structure can closely parrellel this, and nobody in the classical world would of made a fuss about it precisely because everyone would of been able to literally see it worked out in imagery before them.

Difference is, this climbs to a much higher interger than they ever would of tried.

And I agree with Eod, I think. Sorta, 1 isn't a number by itself, so the early stages of this table are false. Zero likewise isn't a number. One is a number when it is applied in a series to other numbers, which this IS a series, but zero has no obvious place here as one acts like zero would (smallest possible sum). Think this was more for insisting a larger pattern exists.

Example, why couldn't we extend this back farther using negative numbers, or decimal points, to achieve new patterns? The larger series from n3=n!6 should hold no issue if you do that decimal, but I don't know if negative numbers would work, going prior to "0".
If you're talking about the second example I gave, you won't see it on the internet which I already checked. It seems that the Wiki contributors aren't interested in factorial patterns.

PhilX EchoesOfTheHorizon
Posts: 356
Joined: Mon Oct 23, 2017 6:08 am

Re: How deep is math?

Oh, given it seems nonsensical to me, I would fully expect that to be the case, I'd be worried if it was found elsewhere.

Can you please explain it to me, that little bit, cause I don't know how you know this, as it seems deeply incorrect. My speciality isn't mathematics, but ethics, so need my hand held through simple maths sometimes that a grade schooler would laugh at. I am seriously lost in the pattern, it comes off too confusing to me. 90% certain it is just me.

Philosophy Explorer
Posts: 5634
Joined: Sun Aug 31, 2014 7:39 am

Re: How deep is math?

EchoesOfTheHorizon wrote:
Mon Dec 04, 2017 7:20 am
Oh, given it seems nonsensical to me, I would fully expect that to be the case, I'd be worried if it was found elsewhere.

Can you please explain it to me, that little bit, cause I don't know how you know this, as it seems deeply incorrect. My speciality isn't mathematics, but ethics, so need my hand held through simple maths sometimes that a grade schooler would laugh at. I am seriously lost in the pattern, it comes off too confusing to me. 90% certain it is just me.
Do you know what a factorial is?

PhilX Eodnhoj7
Posts: 4517
Joined: Mon Mar 13, 2017 3:18 am

Re: How deep is math?

Philosophy Explorer wrote:
Mon Dec 04, 2017 6:36 am
EchoesOfTheHorizon wrote:
Mon Dec 04, 2017 5:06 am
Philosophy Explorer wrote:
Tue Nov 28, 2017 3:26 pm
Here is another case I've just discovered with factorials:

3! + 2 = 2⁳
4! + 3 = 3⁳
5! + 5 = 5⁳
6! + 9 = 9⁳

Something to think about.

PhilX I'm probably embarrassing myself, but looking at the wiki page for factorials, I'm not seeing this.

https://en.m.wikipedia.org/wiki/Factorial

Can someone explain how he is saying this? I'm not disputing it as I can't even grasp what is being said.

That wiki may be wrong, but gotta go doublecheck Archimedes Sandreckoner, has been many years, but it looks like the basic structure for myriad-myriad calculations. It is pyramidal. But think that was more addition that multiplication. You can play out the structure for the size of irregular numbered units in classical armies along a similar mathematics, you progressed in rank relative to the number of men under you, and this grew (if you commanded infantry as the core of your army) from a basic file, to a rank and file formation, then higher up until you ended up as a senator. It never quite mathematically balanced out as tactical efficiency never matches mathematical purity, but it got close enough for a amateur historian about two years ago to theorize that the Roman military system and early structure of the voting blocks of the republic was built around a system of Pythagorean mathematics not too dissimilar to this rule. He posted on several websites, I can track it down if anyone is interested.

It got to the point that I can easily project the makeup of any classical army in my head unto a hypothetical battlefield, comes handy when you have absurdities in the historical record claiming a couple hundred thousand soldiers fought in a siege, such as the German siege of Roman Milan, I knew something was bizarre about that set up measuring everyone on the field, went and found a calculator online that gives average space a person standing needs per area, crunched the numbers, and it didn't match the area of the city known archaeologically for that era.

There is validity in stuff like this, but you gotta remember mathematics aren't always arranged around numbers, it can be patterns too. The whole Monad to Dyad to Triad structure can closely parrellel this, and nobody in the classical world would of made a fuss about it precisely because everyone would of been able to literally see it worked out in imagery before them.

Difference is, this climbs to a much higher interger than they ever would of tried.

And I agree with Eod, I think. Sorta, 1 isn't a number by itself, so the early stages of this table are false. Zero likewise isn't a number. One is a number when it is applied in a series to other numbers, which this IS a series, but zero has no obvious place here as one acts like zero would (smallest possible sum). Think this was more for insisting a larger pattern exists.

Example, why couldn't we extend this back farther using negative numbers, or decimal points, to achieve new patterns? The larger series from n3=n!6 should hold no issue if you do that decimal, but I don't know if negative numbers would work, going prior to "0".
If you're talking about the second example I gave, you won't see it on the internet which I already checked. It seems that the Wiki contributors aren't interested in factorial patterns.

PhilX Not yet at least.

Averroes
Posts: 269
Joined: Thu Jul 20, 2017 8:48 pm

Re: How deep is math?

Philosophy Explorer wrote:
Mon Nov 27, 2017 4:40 pm
Or how involving is math? By deep I mean that in its broadest sense so feel free to interpret it your particular way.

So how deep is math for you?
This is a very interesting topic PhilX. And thank you for the freedom of interpretation of the subject. Such kind of intellectual position can only serve to enrich the exchange and the flourishing of ideas.

I will answer your question, if God wills, by taking an example. Let us talk about the Golden mean or the Golden ratio.

Note: If one happens to be here reading this and is overwhelmed by mathematics, then there is no need to worry! In the concluding section at the end of this post, an easier way to understand the gist of this post is provided.

From Wikipedia: "In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities."

The figure below illustrates the Golden ratio with a geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The Golden ratio is found throughout the world around us: in flowers petals, in the various measurements of the human body, in the structure of shells, in the structure of spiral galaxies, tree branches, hurricanes, and DNA molecules among so many other examples.

The Golden ratio is also to be found in verses in the Holy Quran, and in the Holy Quran as a whole as well!

A. Golden ratio in the verse of the Quran mentioning Mecca.

For instance, the Golden ratio in a particular part of Quran for example in Chapter 3 verse 96, where God, The Almighty says (interpretation of meaning)

Indeed, the First House set up for mankind is at Bakkah (i.e. Makkah)- blessed and a guidance for the worlds. [Holy Quran, interpretation of meaning 3:96]

Now, the Holy Quran was revealed in Arabic and only the Arabic text is called the Holy Quran, even though no doubt the translations provide valuable materials for understanding the message of the Holy Book. As for myself I learned much about the Holy Quran through the translations by the Islamic scholars, well before I could read from the Arabic text itself.

Now in the Arabic text, the translated verse just quoted contains 47 Arabic letters in total. The number of letters before the word Mecca and including that word is 29. The remaining letters are thus 18. Now, 29/18= 1.6111(0.7% difference from golden mean) and 47/29=1.620 (0.3% difference from Golden mean). Less than 1% difference is a negligible amount, so this verse express the Golden ratio with reference to the word "Mecca".

B. Golden ratio in the whole of Quran.

The Golden mean with respect to the whole of Quran is more beautiful (in mathematical terms I mean), if I may say so, because it involves three levels of mathematical coding!

As one might already by now know, the Holy Quran is organised into chapters which are numbered as well as named, and each chapter is further organised into verses, which are also numbered. For example, the first chapter is called Al-Fatiha (meaning The Opening) and it consists of seven verses; the second chapter is called "The cow" and it consists of 286 verses etc... So let us define an ordered triplet such that (C,V,S) where C is the chapter number, V is the total number of verses in that chapter and S is the sum of C and V, i.e. C+V. Under this scheme then, the first chapter is (1,7,8), and the second is (2,286,288). And also, let us underline and bold the even S-sums which occurs for each triplet so that we can distinguish them from the odd S-sums. Let us do this for the whole Quran:

(1,7,8), (2,286,288), (3, 200,203), (4,176,180), (5,120,125), (6,165,171), (7,206,213), (8,75,83), (9,129,138), (10,109,119), (11,123,134), (12,111,123), (13,43,56), (14,52,66), (15,99,114), (16,128,144), (17,111,128), (18, 110,128), (19,98,117), (20,135,155), (21,112,133), (22,78,100), (23,118,141), (24,64,88), (25,77,102), (26,227,253),(27,93,120), (28,88,116), (29,69,98), (30,60,90),(31,34,65), (32,30,62), (33,73,106), (34, 54,88), (35,45,80), (36,83,119), (37,182,219), (38,88,126), (39,75,114), (40, 85,125), (41,54,95), (42,53,95), (43,89,132), (44,59,103), (45,37,82), (46,35,81), (47,38,85), (48,29,77), (49,18,67), (50,45,95), (51,60,111), (52, 49,101), (53,62,115), (54,55,109), (55,78,133), (56,96,152), (57,29,86), (58,22,80), (59,24,83), (60,13,73), (61,14,75), (62,11,73), (63,11,74), (64,18,82), (65,12,77), (66,12,78), (67,30,97), (68,52,120), (69,52,121), (70,44,114), (71,28,99), (72,28,100), (73,20,93), (74,56,130), (75,40,115), (76,31,107), (77,50,127), (78,40,118), (79,46,125), (80,42,122), (81,29,110), (82,19,101), (83,36,119), (84,25,109), (85,22,107), (86,17,103), (87,19,106),(88,26,114), (89,30,119), (90,20,110), (91,15,106), (92,21,113), (93,11,104), (94,8,102), (95,8,103), (96,19,115), (97,5,102), (98,8,106), (99,8,107),(100,11,111), (101,11,112), (102,8,110), (103,3,106), (104,9,113), (105,5,110), (106,4,110), (107,7,114), (108,3,111), (109,6,115), (110,3,113), (111,5,116), (112,4,116), (113,5,118),(114,6,120).

Now let us calculate the following sums,
(1) the sum of all the chapter numbers,
(2) the sum of all the verses
(3) the sum of all the even-S-sums
(4) the sum of all the odd-S-sums.

(1) Sum of all chapter numbers:
(i=1, i=114)∑ C_i = n(n+1)/2= 6555. [Note:this is a triangular number! We had seen this formula some weeks ago on one of your threads; now we make use of it! ]

(2) Sum of all the verses:
(i=1,i=114)∑ V_i= 7+286+200+176+120+...+4+5+6=6236

(3) Sum of the even-S-sums :
Sum of all the bolded-underlined numbers= 6236

(4) Sum of the odd-S-sums = 6555

Two levels of mathematical coding!
It turns out that:
(1) the sum of the chapter numbers = the sum of all the odd S-sums of chapter and verse numbers.
and
(2) the sum of all the verses = the sum of all even S-sums of chapter and verse numbers.

This is the first two levels of mathematical coding. Note that were any of the numbers in the original matrix differently arranged, then the whole scheme would have fallen apart, and these results would not have been obtained!

Third level of mathematical coding

Now, if we analyse the values for S=C+V, we observe that some of them are repeated numbers and others are non-repeating. For example for each of chapters 111 and 112, S=116 whereas for chapter 1, S=8 and no other chapter has this value for S. So let us take the unique values for S and sum these values. And then let us take the repeated values for S and again sum these values. So we have:

Sum of non-repeating S= 8+288+203+180+171+213+138+134+123+56+66+144+117+155+141+253+98+90+65+62+219+126+132+81+85+67+152+86+75+74+78+97+121+99+93+130+127+122+104+112= 4885

Sum of the repeating S= 125+83+119+114+128+128+133+100+88+102+120+116+106+88+80+119+114+125+95+95+103+82+77+95+111+101+115+109+133+80+83+73+73+82+77+120+114+100+115+107+118+125+110+101+119+109+107+103+106+114+119+110+113+102+103+115+102+106+107+111+110+106+113+110+110+114+111+115+113+116+116+118+120=7906

Now, these numbers stand in the golden ratio:

7906/4885= 1.618

and

(7906+4885)/7906=1.618

C. Golden ratio in the physical location of Mecca on the globe.

Here, we are going to analyse the position of Mecca on the globe with respect to the system which is actually used to determine position on the earth, namely latitude and longitude. First, I will analyse the longitudinal component and then I will tackle the latitudinal element, if God wills.

(i) Analysis of position in the longitudinal direction, i.e. North-South direction.

The position of Mecca with respect to the North pole and the South Pole stand in the Golden ratio. One can verify this with the Google Earth Pro software freely available on the internet.

Now, the North and South Pole have coordinates (90° N, x E) and (90°S , y E) respectively. The variables x and y can be any number, it does not matter, as at the poles all longitudes converge, so it is only the latitudes that are sufficient to determine the poles on the globe. As an aside, the Poles were initially defined to be about 20,000 km apart, as part of an initiative by the French Academy of Sciences to adopt an international system (SI) of measurement. And the reference was originally (more or less) the distance between the poles. So, this distance was originally meant to be in the definition of the metric system, and that is why it is such a "neat" number! For more information on this check: http://mathforum.org/library/drmath/view/57566.html

The geodetic coordinates of Mecca are around 21°25'35.9"N, 39°49'32.27"E.

The distance from the North Pole to Mecca is about 7631.68 km (estimated with Google Earth Pro)
The distance from the south Pole to Mecca is about 12348.32 km (estimated with Google Earth Pro)

Now, these distances too stand in the Golden ratio!

12348.32/7631.68= 1.618
and
(7631.68+12348.32)/12348.68=1.618.

The North and South poles are not only geographic locations, but also have significance in physics in being the points through which the axis of rotation of the Earth passes; which rotation amounts to phenomena such as the alternation of the night and the day. In this way, it can be construed as a natural phenomena. Hence, in the longitudinal direction, we were able to establish a golden ratio, quite accurately, with respect to the position of Mecca. Now, it needs to be said that Mecca was built by Prophet Abraham and his son Prophet Ishmael (peace be upon them), and was already well established for at least a thousand years BCE, as a place of worship of only God, the Almighty, much before Prophet Muhammad (pbuh) was sent with the message of the Holy Qur'an. In the following video is a short beautiful 3D illustrated story of Mecca: https://www.youtube.com/watch?v=6htVBB0Vrro

(ii) Analysis of position in the latitudinal direction, i.e. east-west direction

Here, I was not able to use Google Earth Pro to determine the distances along lines of same latitude, because each time that I tried to measure these distances, the software was giving me the great circle distance instead of the latitudinal distances. I have not found the functionality in the software to allow me to compute what I wanted. So, I had to go old school here and do the calculations by hand with pen and paper.

Now before I proceed to the calculations, there is an extremely important thing that must be brought to attention. Unlike the North and South Poles which are natural occurring phenomena, the reference for longitudinal determination is a conventional scheme adopted though what is called the freewill of human beings. There is the popular belief that our conventions are not a part of the natural phenomena. For example, the reference agreed upon today, which is the Greenwich Prime Meridian, was adopted by an international convention in 1884. There is a tendency to think that it could have been otherwise. This is quite understandable. In philosophical jargon, one often refers to this as a contingent fact. For instance, the international reference might have been that of Paris, passing through the Paris Observatory instead of the current one which is based on the Royal Observatory in London! These two references are off by about 2°20′14.03″. Had the Paris reference won international support, then my calculations would have been somewhat affected! My take is that a Being who can know all this in advance can only be One of much Superior Wisdom, which is incomprehensible for mankind. Anyway this would be material for further individual and collective thinking!!

So, I did some calculations based on the conventional (i.e. freewill of humans) reference used nowadays, and the result is between 95% to 98% in agreement with the golden mean in the latitudinal direction! Given my coarse model and approximations (radius of the Earth, and latitudes and longitudes of Mecca), this is a beautiful result which for all intent and purposes shows that in the latitudinal direction as well, Holy Mecca stand in a Golden relationship!

As there are physicists and mathematicians here, I will give my calculations, if God wills, so that they can verify it, if they wish to do so.

Now, since the Earth only deviates from a perfect sphere by only about 0.3% (i.e. a very small amount); so for all practical purposes, it is mathematically modeled as a sphere. And here I have followed this standard practice. So I calculated, the distance along the latitudinal direction using (α/360)*2*π*R*cosθ, where R is the radius of the earth at the equator; θ is the latitude in degrees; α is the difference in longitudinal angle. I took the radius of the earth at the equator from NASA fact sheets: 6378.137 km. One can use a mean radius of 6371 km as well and there is not any noticeable difference in the end result anyway.

Schematic representation:

AM(180°W)-------------PM(0°)------K(39°49'32''E)-------------AM(180°E)

PM- (Greenwich) Prime Meridian
AM- AntiMeridian
K-Mecca
• Latitudinal distance between westward Antimeridian and Mecca: (180°+39°49'32'')/360*2*π*6378.137 *cos(21°25'35.9")
=22779.59101km
• Latitudinal distance between eastward Antimeridian and Mecca: (180°-39°49'32'')/360*2*π*6378.137 *cos(21°25'35.9")
=14525.68381km
• The circumference of the circle at latitude 21°25'35.9" is the sum of the two values just calculated:
=2*π*6378.137 *cos(21°25'35.9")=22779.59101+14525.68381= 37305.27482 km.

Now, 22779.5910/14525.6838= 1.56822 (less than 5% discrepancy from Golden ratio)
and
37305.27482/22779.5910= 1.6376 (less than 2% discrepancy from Golden mean!)

On a flat map such as those which are in the UTM coordinate system (most common), the ratio of these distances involved will be indistinguishable from the Golden ratio for Holy Mecca!

Conclusion.

So for all practical intent and purposes, it can be said scientifically and mathematically that Holy Mecca is the only place on the surface of the earth which has a Golden Position! If all these mathematics were difficult for anyone to follow, there is no need to worry; I then invite you to watch the following short YouTube video (9mins), which presents the same subject but instead of the mathematics, it uses beautiful computer graphics to illustrate the mathematical statements: https://www.youtube.com/watch?v=8Vtnlj79RIk
_________________

So you asked:how deep is maths for me?

Well, I would say that for me it is as deep as my limited intellectual faculties allows me to perceive/conceive of its depth. And I readily admit that that this is just the tip of the iceberg and we must continue working by exploring new horizons and other ways of thinking.
_________________

Eodnhoj7
Posts: 4517
Joined: Mon Mar 13, 2017 3:18 am

Re: How deep is math?

Averroes wrote:
Tue Dec 05, 2017 9:17 am
Philosophy Explorer wrote:
Mon Nov 27, 2017 4:40 pm
Or how involving is math? By deep I mean that in its broadest sense so feel free to interpret it your particular way.

So how deep is math for you?
This is a very interesting topic PhilX. And thank you for the freedom of interpretation of the subject. Such kind of intellectual position can only serve to enrich the exchange and the flourishing of ideas.

I will answer your question, if God wills, by taking an example. Let us talk about the Golden mean or the Golden ratio.

Note: If one happens to be here reading this and is overwhelmed by mathematics, then there is no need to worry! In the concluding section at the end of this post, an easier way to understand the gist of this post is provided.

From Wikipedia: "In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities."

The figure below illustrates the Golden ratio with a geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The Golden ratio is found throughout the world around us: in flowers petals, in the various measurements of the human body, in the structure of shells, in the structure of spiral galaxies, tree branches, hurricanes, and DNA molecules among so many other examples.

The Golden ratio is also to be found in verses in the Holy Quran, and in the Holy Quran as a whole as well!

A. Golden ratio in the verse of the Quran mentioning Mecca.

For instance, the Golden ratio in a particular part of Quran for example in Chapter 3 verse 96, where God, The Almighty says (interpretation of meaning)

Indeed, the First House set up for mankind is at Bakkah (i.e. Makkah)- blessed and a guidance for the worlds. [Holy Quran, interpretation of meaning 3:96]

Now, the Holy Quran was revealed in Arabic and only the Arabic text is called the Holy Quran, even though no doubt the translations provide valuable materials for understanding the message of the Holy Book. As for myself I learned much about the Holy Quran through the translations by the Islamic scholars, well before I could read from the Arabic text itself.

Now in the Arabic text, the translated verse just quoted contains 47 Arabic letters in total. The number of letters before the word Mecca and including that word is 29. The remaining letters are thus 18. Now, 29/18= 1.6111(0.7% difference from golden mean) and 47/29=1.620 (0.3% difference from Golden mean). Less than 1% difference is a negligible amount, so this verse express the Golden ratio with reference to the word "Mecca".

B. Golden ratio in the whole of Quran.

The Golden mean with respect to the whole of Quran is more beautiful (in mathematical terms I mean), if I may say so, because it involves three levels of mathematical coding!

As one might already by now know, the Holy Quran is organised into chapters which are numbered as well as named, and each chapter is further organised into verses, which are also numbered. For example, the first chapter is called Al-Fatiha (meaning The Opening) and it consists of seven verses; the second chapter is called "The cow" and it consists of 286 verses etc... So let us define an ordered triplet such that (C,V,S) where C is the chapter number, V is the total number of verses in that chapter and S is the sum of C and V, i.e. C+V. Under this scheme then, the first chapter is (1,7,8), and the second is (2,286,288). And also, let us underline and bold the even S-sums which occurs for each triplet so that we can distinguish them from the odd S-sums. Let us do this for the whole Quran:

(1,7,8), (2,286,288), (3, 200,203), (4,176,180), (5,120,125), (6,165,171), (7,206,213), (8,75,83), (9,129,138), (10,109,119), (11,123,134), (12,111,123), (13,43,56), (14,52,66), (15,99,114), (16,128,144), (17,111,128), (18, 110,128), (19,98,117), (20,135,155), (21,112,133), (22,78,100), (23,118,141), (24,64,88), (25,77,102), (26,227,253),(27,93,120), (28,88,116), (29,69,98), (30,60,90),(31,34,65), (32,30,62), (33,73,106), (34, 54,88), (35,45,80), (36,83,119), (37,182,219), (38,88,126), (39,75,114), (40, 85,125), (41,54,95), (42,53,95), (43,89,132), (44,59,103), (45,37,82), (46,35,81), (47,38,85), (48,29,77), (49,18,67), (50,45,95), (51,60,111), (52, 49,101), (53,62,115), (54,55,109), (55,78,133), (56,96,152), (57,29,86), (58,22,80), (59,24,83), (60,13,73), (61,14,75), (62,11,73), (63,11,74), (64,18,82), (65,12,77), (66,12,78), (67,30,97), (68,52,120), (69,52,121), (70,44,114), (71,28,99), (72,28,100), (73,20,93), (74,56,130), (75,40,115), (76,31,107), (77,50,127), (78,40,118), (79,46,125), (80,42,122), (81,29,110), (82,19,101), (83,36,119), (84,25,109), (85,22,107), (86,17,103), (87,19,106),(88,26,114), (89,30,119), (90,20,110), (91,15,106), (92,21,113), (93,11,104), (94,8,102), (95,8,103), (96,19,115), (97,5,102), (98,8,106), (99,8,107),(100,11,111), (101,11,112), (102,8,110), (103,3,106), (104,9,113), (105,5,110), (106,4,110), (107,7,114), (108,3,111), (109,6,115), (110,3,113), (111,5,116), (112,4,116), (113,5,118),(114,6,120).

Now let us calculate the following sums,
(1) the sum of all the chapter numbers,
(2) the sum of all the verses
(3) the sum of all the even-S-sums
(4) the sum of all the odd-S-sums.

(1) Sum of all chapter numbers:
(i=1, i=114)∑ C_i = n(n+1)/2= 6555. [Note:this is a triangular number! We had seen this formula some weeks ago on one of your threads; now we make use of it! ]

(2) Sum of all the verses:
(i=1,i=114)∑ V_i= 7+286+200+176+120+...+4+5+6=6236

(3) Sum of the even-S-sums :
Sum of all the bolded-underlined numbers= 6236

(4) Sum of the odd-S-sums = 6555

Two levels of mathematical coding!
It turns out that:
(1) the sum of the chapter numbers = the sum of all the odd S-sums of chapter and verse numbers.
and
(2) the sum of all the verses = the sum of all even S-sums of chapter and verse numbers.

This is the first two levels of mathematical coding. Note that were any of the numbers in the original matrix differently arranged, then the whole scheme would have fallen apart, and these results would not have been obtained!

Third level of mathematical coding

Now, if we analyse the values for S=C+V, we observe that some of them are repeated numbers and others are non-repeating. For example for each of chapters 111 and 112, S=116 whereas for chapter 1, S=8 and no other chapter has this value for S. So let us take the unique values for S and sum these values. And then let us take the repeated values for S and again sum these values. So we have:

Sum of non-repeating S= 8+288+203+180+171+213+138+134+123+56+66+144+117+155+141+253+98+90+65+62+219+126+132+81+85+67+152+86+75+74+78+97+121+99+93+130+127+122+104+112= 4885

Sum of the repeating S= 125+83+119+114+128+128+133+100+88+102+120+116+106+88+80+119+114+125+95+95+103+82+77+95+111+101+115+109+133+80+83+73+73+82+77+120+114+100+115+107+118+125+110+101+119+109+107+103+106+114+119+110+113+102+103+115+102+106+107+111+110+106+113+110+110+114+111+115+113+116+116+118+120=7906

Now, these numbers stand in the golden ratio:

7906/4885= 1.618

and

(7906+4885)/7906=1.618

C. Golden ratio in the physical location of Mecca on the globe.

Here, we are going to analyse the position of Mecca on the globe with respect to the system which is actually used to determine position on the earth, namely latitude and longitude. First, I will analyse the longitudinal component and then I will tackle the latitudinal element, if God wills.

(i) Analysis of position in the longitudinal direction, i.e. North-South direction.

The position of Mecca with respect to the North pole and the South Pole stand in the Golden ratio. One can verify this with the Google Earth Pro software freely available on the internet.

Now, the North and South Pole have coordinates (90° N, x E) and (90°S , y E) respectively. The variables x and y can be any number, it does not matter, as at the poles all longitudes converge, so it is only the latitudes that are sufficient to determine the poles on the globe. As an aside, the Poles were initially defined to be about 20,000 km apart, as part of an initiative by the French Academy of Sciences to adopt an international system (SI) of measurement. And the reference was originally (more or less) the distance between the poles. So, this distance was originally meant to be in the definition of the metric system, and that is why it is such a "neat" number! For more information on this check: http://mathforum.org/library/drmath/view/57566.html

The geodetic coordinates of Mecca are around 21°25'35.9"N, 39°49'32.27"E.

The distance from the North Pole to Mecca is about 7631.68 km (estimated with Google Earth Pro)
The distance from the south Pole to Mecca is about 12348.32 km (estimated with Google Earth Pro)

Now, these distances too stand in the Golden ratio!

12348.32/7631.68= 1.618
and
(7631.68+12348.32)/12348.68=1.618.

The North and South poles are not only geographic locations, but also have significance in physics in being the points through which the axis of rotation of the Earth passes; which rotation amounts to phenomena such as the alternation of the night and the day. In this way, it can be construed as a natural phenomena. Hence, in the longitudinal direction, we were able to establish a golden ratio, quite accurately, with respect to the position of Mecca. Now, it needs to be said that Mecca was built by Prophet Abraham and his son Prophet Ishmael (peace be upon them), and was already well established for at least a thousand years BCE, as a place of worship of only God, the Almighty, much before Prophet Muhammad (pbuh) was sent with the message of the Holy Qur'an. In the following video is a short beautiful 3D illustrated story of Mecca: https://www.youtube.com/watch?v=6htVBB0Vrro

(ii) Analysis of position in the latitudinal direction, i.e. east-west direction

Here, I was not able to use Google Earth Pro to determine the distances along lines of same latitude, because each time that I tried to measure these distances, the software was giving me the great circle distance instead of the latitudinal distances. I have not found the functionality in the software to allow me to compute what I wanted. So, I had to go old school here and do the calculations by hand with pen and paper.

Now before I proceed to the calculations, there is an extremely important thing that must be brought to attention. Unlike the North and South Poles which are natural occurring phenomena, the reference for longitudinal determination is a conventional scheme adopted though what is called the freewill of human beings. There is the popular belief that our conventions are not a part of the natural phenomena. For example, the reference agreed upon today, which is the Greenwich Prime Meridian, was adopted by an international convention in 1884. There is a tendency to think that it could have been otherwise. This is quite understandable. In philosophical jargon, one often refers to this as a contingent fact. For instance, the international reference might have been that of Paris, passing through the Paris Observatory instead of the current one which is based on the Royal Observatory in London! These two references are off by about 2°20′14.03″. Had the Paris reference won international support, then my calculations would have been somewhat affected! My take is that a Being who can know all this in advance can only be One of much Superior Wisdom, which is incomprehensible for mankind. Anyway this would be material for further individual and collective thinking!!

So, I did some calculations based on the conventional (i.e. freewill of humans) reference used nowadays, and the result is between 95% to 98% in agreement with the golden mean in the latitudinal direction! Given my coarse model and approximations (radius of the Earth, and latitudes and longitudes of Mecca), this is a beautiful result which for all intent and purposes shows that in the latitudinal direction as well, Holy Mecca stand in a Golden relationship!

As there are physicists and mathematicians here, I will give my calculations, if God wills, so that they can verify it, if they wish to do so.

Now, since the Earth only deviates from a perfect sphere by only about 0.3% (i.e. a very small amount); so for all practical purposes, it is mathematically modeled as a sphere. And here I have followed this standard practice. So I calculated, the distance along the latitudinal direction using (α/360)*2*π*R*cosθ, where R is the radius of the earth at the equator; θ is the latitude in degrees; α is the difference in longitudinal angle. I took the radius of the earth at the equator from NASA fact sheets: 6378.137 km. One can use a mean radius of 6371 km as well and there is not any noticeable difference in the end result anyway.

Schematic representation:

AM(180°W)-------------PM(0°)------K(39°49'32''E)-------------AM(180°E)

PM- (Greenwich) Prime Meridian
AM- AntiMeridian
K-Mecca
• Latitudinal distance between westward Antimeridian and Mecca: (180°+39°49'32'')/360*2*π*6378.137 *cos(21°25'35.9")
=22779.59101km
• Latitudinal distance between eastward Antimeridian and Mecca: (180°-39°49'32'')/360*2*π*6378.137 *cos(21°25'35.9")
=14525.68381km
• The circumference of the circle at latitude 21°25'35.9" is the sum of the two values just calculated:
=2*π*6378.137 *cos(21°25'35.9")=22779.59101+14525.68381= 37305.27482 km.

Now, 22779.5910/14525.6838= 1.56822 (less than 5% discrepancy from Golden ratio)
and
37305.27482/22779.5910= 1.6376 (less than 2% discrepancy from Golden mean!)

On a flat map such as those which are in the UTM coordinate system (most common), the ratio of these distances involved will be indistinguishable from the Golden ratio for Holy Mecca!

Conclusion.

So for all practical intent and purposes, it can be said scientifically and mathematically that Holy Mecca is the only place on the surface of the earth which has a Golden Position! If all these mathematics were difficult for anyone to follow, there is no need to worry; I then invite you to watch the following short YouTube video (9mins), which presents the same subject but instead of the mathematics, it uses beautiful computer graphics to illustrate the mathematical statements: https://www.youtube.com/watch?v=8Vtnlj79RIk
_________________

So you asked:how deep is maths for me?

Well, I would say that for me it is as deep as my limited intellectual faculties allows me to perceive/conceive of its depth. And I readily admit that that this is just the tip of the iceberg and we must continue working by exploring new horizons and other ways of thinking.
_________________

Interesting post, if I remember correctly the muslims had significant influence in the development of algebra and logic. Some modern philosophers, and I can't remember their names...or even if they were modern, were able to link algebra and logic together if I remember correctly.

Averroes
Posts: 269
Joined: Thu Jul 20, 2017 8:48 pm

Re: How deep is math?

Eodnhoj7 wrote:
Wed Dec 06, 2017 4:02 am
Interesting post
Thank you my friend. But this is because it is the Holy Qur'an. Holy Qur'an is interesting. So all praises and thanks be to God, The Almighty.

There are some other interesting patterns as well, but from here, there is the prerequisite of understanding the subtleties of the Arabic language. And with respect to the subject of this thread, it would be called statistical frequency analysis. This involves counting the occurrence a particular word or phrase in the Holy Qur'an.

1. Land and Sea.

For example if we count the singular form of the words "the land"(البر) and "the sea" (البحر) in the Holy Qur'an, then we will get a count of 12 occurrences for "the land" and 32 occurrences for "the sea". Adding these value, we get a total of 44. The percentage of "the land" to this total is 100*12/44, which is about 27.3%, and the percentage of "the sea" to this total is about 72.7%. If you check the latest statistics, you will see that the percentage of water on the earth is about 72%, and the rest is land!

From livescience.com: " Some 72 percent of Earth is covered in water"

Now in this count I have not included the plural form of "sea" like for example "the two seas" (البحرين) and also "a sea" (بحر), but I have included exactly "the sea" (البحر). Anyway, one thing that I can mention here is that for some of the verses which contain "the two seas" (البحرين), it is in fact a reference to a scientific statement which has just recently been discovered by modern science. I just mention here that the Holy Qur'an was revealed more than 1400 years ago.

And He is the One Who has released the two seas, one palatable and sweet and the other salty and bitter, and He has placed a barrier between them, a partition that is forbidden (to be passed). [Holy Quran, interpretation of meaning 25:53]

The substance of the above verse is repeated in some other Quranic verses where the phrase "the two seas" is mentioned. Now, from the experts in this field I have the following information:

"Modern science has discovered that in the places where two different seas meet, there is a barrier between them. This barrier divides the two seas so that each sea has its own temperature, salinity, and density (Principles of Oceanography, Davis R., 1972, p.92)"
Please check the site for further details on this here.

2. Frequency analysis with names of Prophets.

We can also do frequency analysis with the names of Prophets. For example, we can do a frequency analysis with the name of Prophet Jesus and compare it with the name of Prophet Adam (peace be upon them).

God, The Almighty says in the Holy Qur'an (interpretation of meaning):

Indeed, the likeness of Isa(Jesus) with Allah is like that of Adam. He created him from dust; then He said to him, "Be", and he was. [Holy Qur'an, interpretation of meaning 3:59]

We know that Prophet Jesus (pbuh) was born without a father, but he (pbuh) had only a mother. And Prophet Adam(pbuh) had neither a father nor a mother, but he was created from dust by God, The Almighty.

Now, the name of both Jesus and Adam (pbut) occurs 25 times each in the whole of Qur'an! Furthermore, in the verse in which God, the Almighty compares Prophet Jesus with Prophet Adam, it is the seventh occurrence of each of these names from the start of the Qur'an. The nineteenth occurrence of both these names occurs simultaneously in the nineteenth chapter of the Qur'an! And the nineteenth chapter of the Qur'an bears the name of the mother of Jesus (pbuh), i.e. Mary (may Allah be pleased with her). In the Qur'an, Mary (may Allah be pleased with her) is described as the best of all women.

And when the Angels said, "O Maryam! Indeed, Allah has chosen you and purified you and preferred you over the women of the worlds." "O Maryam! Be obedient to your Lord and prostrate and bow down with those who bow down." [Qur'an, interpretation of meaning 3:42-43]

We can do this frequency analysis with other words of Qur'an as well, and the results are all very interesting as well.

Another mathematical example that can be mentioned here is: a networking of verses for a whole chapter of the Holy Qur'an forming a ring structure! Recently, a linguist professor, Dr Raymond Farrin, has written an academic paper on this amazing structure. The following YouTube video presents in visual format the gist of that paper: https://www.youtube.com/watch?v=KLKheiGXHZg

Averroes
Posts: 269
Joined: Thu Jul 20, 2017 8:48 pm

Re: How deep is math?

Eodnhoj7 wrote:
Wed Dec 06, 2017 4:02 am
if I remember correctly the muslims had significant influence in the development of algebra and logic.

Yes, you remember correctly! Algebra is in fact an Arabic word! It is derived from the Arabic word الجبر, which is transliterated as al-jabr and which means "completion" or "restoration".‎
How this word came to describe the branch of mathematics as we know nowadays is accounted for by the book written by the discoverer of algebra. It was a Muslim mathematician and polymath by the name of Muhammad Ibn Musa al-Khwarizmi who discovered the method of algebra and who wrote a book about it in the early 9th century CE (around 820 CE). The title of the book is translated as The Compendious Book on Calculation by Completion and Balancing . And, as an aside, the word "algorithm" in the English and French language is derived from the latinised name of al-Khwarizmi, who was known as Algoritmi in Latin.
You can have a look at the following YouTube video about the history, development and importance of algebra nowadays. This fits like a hand in a glove with respect to the subject of this thread; it is a short documentary by a British Professor of theoretical physics, Jim Al-Khalili: https://www.youtube.com/watch?v=sAxWF_W6Q9w

For the logic part, some facts need to be pointed out first. Formal logic was discovered by Aristotle out of the blue. Most subjects are contributed by many intellectuals over a span of many years if not many decades or centuries, so that it is difficult to pin point a source. But in the case of logic, we can pin point to Aristotle. For formal logic it is like that: there was a before Aristotle, and then there was an after Aristotle! And even now after the introduction of modern logic, Aristotle's logic is still taken as a paradigm for logical reasoning in many non-specialized introductory books or popular media.

Now this is where and how it is correct for you to say that the Muslims had a significant influence in the development of logic. The logic and philosophy of the ancient Greeks, epitomized by Aristotle, fell mostly onto deaf ears for the most part of late Antiquity. It was under the medieval Islamic rule of the Middle-East and the Mediterranean Basin that Ancient Greek logic and philosophy were taken seriously again and revived by the Muslims. And with these early Muslims, these subjects (i.e. logic and philosophy) among others would be again studied, furthered and propagated until it reached the West at about the 13-14th century CE (the scholastics), and later during the Renaissance. Some philosophers, among many others, who contributed to the development of logic in these times were Al-Farabi, Avicenna (Ibn Sina), Al-Ghazzali, and Ibn Rushd (known as Averroes in the West, the real one!). Ibn Rushd was also a Muslim theologian, jurist, and judge; and a physician (i.e. a medical doctor) as well. To give you an idea of how these great intellectuals (and the Muslims in general) viewed the scientific and logical works of the Ancients, let me quote passages from Ibn Rushd's writtings, who, by the way, is called the father of philosophy of the modern West!
Ibn Rushd wrote:If someone other than us [the Muslims]* has already investigated that [syllogistic logic]*, it is evidently obligatory for us to rely on what the one who has preceded us says about what we are pursuing, regardless of whether that other person shares our religion or not. For when a valid sacrifice is performed by means of a tool, no consideration is given, with respect to the validity of the sacrifice, as to whether the tool belongs to someone who shares in our religion or not, so long as it fulfills the conditions for the validity. And by "not sharing [in our religion]," I mean those Ancients who reflected upon these things before the religion of Islam.

It is not for someone to say, "Now, this kind of reflection about intellectual syllogistic reasoning is a heretical innovation, since it did not exist in the earliest days [of Islam]." For reflection upon juridical syllogistic reasoning and its kinds is also something inferred after the earliest days, yet it is not opined to be a heretical innovation. So it is obligatory to believe the same about reflection upon intellectual syllogistic reasoning-and for this there is a reason, but this is not the place to mention it. Moreover, most of the adherents to this religion support intellectual syllogistic reasoning, except for a small group of strict literalists, and they are refuted by the texts [of the Qur'an].
(Decisive Treatise by Ibn Rushd, pg 4, translation Charles E. Butterworth)
The asterisks (*) at the inserted text is my insertion, the others are that of the translator.

And to quote another Muslim on this, I take Al-Kindi who was a philosopher, mathematician and engineer who was also known as the philosopher of the Arabs. Al-Kindi is also credited for having discovered frequency analysis, from Wikipedia: "The first known recorded explanation of frequency analysis (indeed, of any kind of cryptanalysis) was given in the 9th century by Al-Kindi, an Arab polymath, in A Manuscript on Deciphering Cryptographic Messages."
Al-Kindi wrote:We should not be ashamed to acknowledge truth from whatever source it comes to us, even if it is brought to us by former generations and foreign peoples. For him who seeks the truth there is nothing of higher value than truth itself.

If you want still more detailed information on this period of history, there is an excellent article on PhilosophyNow, which addresses this topic masterfully. I highly recommend this article: https://philosophynow.org/issues/23/It_ ... hat_Did_It
___________________
Eodnhoj7 wrote:
Wed Dec 06, 2017 4:02 am
Some modern philosophers, and I can't remember their names...or even if they were modern, were able to link algebra and logic together if I remember correctly.
Yes, correct again!

Yes, it can be said that they were modern and philosophers, but they were primarily and mostly known as mathematicians. They were mostly English mathematicians such as George Boole who first linked algebra and logic in his book the laws of thought in 1854. In this work, Boole algebraized the logic of Aristotle. There are also other mathematicians who contributed to this field initially, like Augustus De Morgan needs to be mentioned as well, but they were influenced by Boole. Check this article on Wikipedia for more information on this: https://en.wikipedia.org/wiki/The_Laws_of_Thought

And still later, if not building upon the work of Boole, but at least being influenced by the environment which had been set up by Boole's pioneering works, Gottlob Frege came with modern logic. Bertrand Russel, Ludwig Wittgenstein, David Hilbert, Gerhard Gentzen and others would then later join in the wagon to further works in this then new field of mathematics. And now we talk of mathematical logic!

That's it from me for now my friend. I hope you find these interesting too. Anyhow, it was nice exchanging with you, and I wish you a good weekend.

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