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.
_________________