Googolplex

Maatthew

New member
This thread is dedicated to one of, in my opinion, the most mind boggling concepts in math and science. A googol as you may already be familiar with is 10^100 or simply a 1 with a hundred 0's behind it, not too complicated right?​
Well this is where it get's crazy, a googolplex, written as 10^{10^{100}} in scientific notation, is a 1 followed by a googol zeros. This may be hard to wrap you mind about so I will give you an example on a smaller scale. Think on a million, which is 1 with six 0's behind it, or 1,000,000. Now try writing a million 0's behind it. Maybe that helped.​
A googlolplex is such a large number that according to Carl Sagan's estimation's, to write it out in number form would be impossible because it would require more space than the known universe provides.
The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around about 1.51×10^92 years, which is about 1.1×10^82 times the age of the universe, to write a googolplex.

A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, which is approximately 4.222×10^−105 m3 = 4.222×10^−99 cm3. Thus 2.5 cm^3 contain about a googol Planck spaces. There are only about 3×10^80 cubic metres in the observed universe, making the number of Planck spaces in the universe to be about 7.1×10184 quantum spaces in the observed universe, so a googolplex is far larger than even the number of the smallest spaces in the observed universe.

This may be hard for anyone to wrap their mind around it, but I find it fascinating about how large the concept of a Googolplex is. You can also use this thread is just for discussion about fascinating concepts of math and science.
 
That is an interesting concept Matthew! Mathematics has always been one of the subjects that has fascinated me for years. I came across a system of Mathematics known as ' Vedic Mathematics' developped by the great Indian Scholar, Bharathi Krishna Tirthaji Maharaja, during the early parts of the 20th century. The system proposes 16 basic 'sutras' or aphorisms which he claimed to have found after years of studying the 'vedas' one of the holy texts of the Hindu religion.

Basically they are calculation strategies which aims to simply some calculations and enables us to do them much faster than conventional methods and can be used in day to day activities as well. I shall explain two out of the 16 aphorisms and its associated corollaries so all those here you does not know of this can use it to their benefit as well. Its not all that difficult to understand and just requires basic maths knowledge. Hope you guys enjoy and appreciate it.:)

Concept 1 (translated)- All nine and the last from ten.

When substracting from a large power of ten with many columns of zero's ( 1000, 2000, 10,000 etc), it is not neccesary to write the notation for 'borrowing' from the column on the left. One can simply substract the last (rightmost) digit from 10 and each other digit from 9.
For ex 1: 10,000-4,679, the left most of the three digits of 4,679 are 4,6 and 7. These leftmost digits are substracted from 9 to yeild 5,3 and 2 respectively. The rightmost number, 9 is substracted from 10 to yeild 1. Thus the answer to the problem is 5,321.

A few more examples:

100-63, 9-6=3, 10-3=7, so the answer is 37!

1000-732, 9-7=2, 9-3=6, 10-2=8, so the answer is 268!!

5000-3246, alright this one is a bit tricky but with little thought can be solved used the same principle. The first leftmost number, 3 should be substracted from 4 ( that is one less than the number in the 5 in 5,000) and the rest is the same.
So the calculation is
4-3=1, 9-2=7, 9-4=5, 10-6=4 , so the answer is 1,754!!

Now we don't even need a calculator to do calculations such as this. ;)

Concept 2: Multiplying by 11
This is actually a corollary ( a branch of the main concept). It is best explained with an example

11 x 35 = 385

1. The 5 in the ones place of the answer is taken from the number 35.

2.The eight in the answer is the sum of 35 (3+5)

3. The 3 in the hundreds place of the answer is taken from the 3 in 35.

Pretty snazzy huh? :p

However if the sum in the second step exceeds 10, the sum's left digit is added to the number multiplied by 11. For example

11 x 59 = ?

Step 1: 9 takes the ones spot (rightmost digit) as per the concept

Step 2: 9+5=14 and since the sum is greater than 10, the right digit is taken as the middle number of the solution which is 4.

Step 3: Now the 5 from the number is added with 1 from the number 14 in the previous step to get 6. So the answer is
649!

More examples

11 x 96=?

Step 1: 6 takes ones spot

Step 2: 9+6=15, so 5 takes middle spot

Step 3: 9 from 96 is added to 1 from 15 obtained from the previous step to get 10, which takes the left most spot. So the answer is

1056!!

I hope these two helped atleast a few here.
Link for other 14 sutras and examples

http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha's_Vedic_mathematics
 
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Oooh math, I just hate it so much lol!
I love Biology though
Scientists now have discovered the area of the brain linked to dyscalculia, demonstrating that there is a specific part of the brain essential for counting properly. In a report published in the March 13 issue of the Proceedings of the National Academy of Sciences (PNAS), researchers explain that the area of the brain known as the intraparietal sulcus (IPS), located toward the top and back of the brain and across both lobes, is crucial for the proper processing of numerical information.
 
Hey man... I'm just trying to keep my head above water in trigonometry class. I can't handle these concepts.
 
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