olors64's Wide Wide World

Is it a wiki? Is it a blog? No, it's olors64's Wide Wide World full of all sorts of stuff that may interest you:

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News

• [5/2/23]

  My favorite sequence is the powers of 2.
  As a kid, after I learned 1+1=2 and 2+2=4, I thought of this as the start of a pattern.

  1. 1+1=2
  2. 2+2=4
  3. 4+4=8
  4. 8+8=16
  5. 16+16=32
  6. 32+32=64

  64 was the last number on this sequence under a hundred. 64 is my all time favorite number; hence why I use the alias "olors64." The number 60 is a similar size, and that number is awesome for it's own reasons.
  Also, 64 = 2^6 = 4^3 = 8^2.
  But this isn't a post about 64, it's about 2^n.

  As I got older and started playing some video games, I learned that older consoles were 8-bit, 16-bit, 32-bit, or 64-bit. This is due to how they store memory in binary. A bit is a single binary digit, either 0 or 1. 8 bits have a total of 256 configurations, from 00000000 (zero) to 11111111 (255 in decimal). 8 bits = 1 byte. Therefore, 16 bits = 2 bytes, 32 bits = 4 bytes, 64 bits = 8 bytes and so on. Both sides of this conversion are 2^n, with different offsets. These quantities get very large, which is good, since it means computers can handle very large numbers in it's nanoscopic transistors.

  How large can they get?

  Let's take the earlier pattern of addition and turn it into a multiplication pattern.

  1. 2=2
  2. 2*2=4
  3. 2*2*2=8
  4. 2*2*2*2=16
  5. 2*2*2*2*2=32
  6. 2*2*2*2*2*2=64
  7. 2*2*2*2*2*2*2=128
  8. 2*2*2*2*2*2*2*2=256

  As you can see, in order to get such big numbers, we have to keep multiplying 2 by itself repeatedly. So instead, we'll use exponential notation 2^n.

  1. 2^1=2
  2. 2^2=4
  3. 2^3=8
  4. 2^4=16
  5. 2^5=32
  6. 2^6=64
  7. 2^7=128
  8. 2^8=256

  Now for 16, 32, 64, 128, and even 256 bits.

  • 2^16 = 65,536
  • 2^32 = 4,294,967,296
  • 2^64 = 18,446,744,073,709,551,616
  • 2^128 = 340,282,366,920,938,463,463,374,607,431,768,211,456
  • 2^256 = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936
  
  
• [3/16/23]

  π is not my favorite number. It's not even my favorite irrational number, nor even my favorite transcendental number.

  Why π isn't My Favorite Number

  Now don't get me wrong, I still consider π as one of the best transcendental numbers, but that's not because of the value ~3.14159265. In fact, I remember π's digits up to the second 5 because of Night at the Museum 2. It's because of another constant which is tau. Tau, represented with τ, is equal to 2π. Both constants can be used in similar contexts, but because of this, it's arguable as to which constant is better than the other. I don't have that high of an opinion of τ either.

  My Favorite Number is e

  I love e more than I love π (or τ). e makes calculus easier, because e^x = e^x — though perhaps it made it too easy as to make calculus a requirement for my compsci major. It's first several digits are easier to remember than π's, since e starts with 2.718281828, but it's important to know that the next 1828 sequence won't show up in the decimal expansion until much later. If e worked as a number base, it would be the most efficient, since base e has the smallest radix.
  The infinite tetration x^x^x^x^x... only converges if x ∈ [e^−e, e^1/e]

• [2/14/23]

  Here's a video about loneliness, Happy Valentine's Day:

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