Conundrum - Banking - Lecture Slides, Slides of Banking and Finance

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Conundrum

• So, there is a dichotomy.
• Leaving out information can lead to loss of quality
• But we must leave out something else we can’t produce a model.

Compact Disc Analogy

• Consider the compact disc.
• Uses digital sampling to approximate a sound wave.
• By sampling at a rate of 44.1Khz at a resolution of 16 bits we get
• A recording with a dynamic range of approx 96dB and a maximum frequency of 22050Hz.

Good Enough?

• But CD deemed to be ‘good enough’
• What about compression?
• 1 second of CD audio requires:
• 44100 x 16bits x 2(stereo channels) = 172.27Kbytes
• = 10.09Mbytes per minute

Mini Disc & MPEG-

• How do mini-discs get the ‘same’ sound into such a small space?
• How does MPEG-3 compress audio to about 10% of its size without us noticing the difference?
• We make assumptions and abstractions

Systems Modelling?

• So how do we model a system accurately without losing information?

We Don’t Know

• Anyone fancy doing a PhD?

The Jackson Approach

• In my opinion, Jackson’s approach is a major step towards an accurate model.
• Consider the following:

“If you want to understand some aspect of the Universe, it helps if you simplify it as much as possible, and include only those properties and characteristics that are essential to understanding. If you want to determine how an object drops, you don’t concern yourself with whether it is new or old, is red or green, has an odour or not. You eliminate those things and thus do not needlessly complicate matters.”

“Can’t you form a simulation of the simulation?” asked Hummin. “You would go down another degree.”

“In that case, you would have to eliminate some characteristic of the phenomenon which you want to include and your system becomes useless. The LPS - that is ‘the least possible simulation’ - gains in complexity faster than the object being simulated does and, eventually, the simulation catches up with the phenomenon.”

“Thus, it was established thousands of years ago that the Universe as a whole, in its full complexity, cannot be represented by any simulation smaller than itself.”

“In other words, you can’t get any picture of the Universe as a whole except by studying all the Universe.”