Summary
Highlights
The lecture begins by explaining the necessity of information representation for writing algorithms and data. It outlines the core questions to be addressed: what representation is, different types of representation, and its utility in the context of algorithms. The speaker highlights that previous lessons introduced block-based representations in apps, making the audience somewhat familiar with the topic.
The speaker introduces key concepts: all representations of interest are symbolic and rely on alphabets, making them enumerable. This means everything can be represented through numbers or sequences of numbers. A crucial point in computer science is that everything can be represented in binary (two-state elements) due to its ease of construction. The lecture aims to explain why numbers are 'disappeared' and challenge the notion that 2+2=4.
Representation is re-presenting information. The concept draws from semiotics, distinguishing between the 'signified' (the meaning or concept being represented) and the 'signifier' (the graphic element or symbol used to represent it). The 'semiotic triangle' further elaborates by separating the signified into 'sense' (what we have in our mind) and 'referent' (what is in the external world).
The lecture compares iconic (pictorial) and symbolic representations. Iconic representations are more expressive and closer to reality but lack compositional rules, making them difficult to create and interpret universally. Symbolic representations, while seemingly less expressive, are regulated by clear compositional rules, making them more standardized and efficient. The talk uses examples like musical notes versus a detailed jazz scene to illustrate this difference.
Symbolic representations are arbitrary; there's no inherent connection between a symbol (like the word 'dog') and what it represents. This arbitrariness is a significant advantage, allowing humans to agree on and modify representations. This is demonstrated by the varying onomatopoeic sounds for animal noises across different languages, with the word 'mama' being a rare exception of universality.
Natural language, despite its richness, poses problems for machine instructions due to its expressivity and ambiguity. 'Expressive richness' means a single concept can be conveyed in countless ways (e.g., different ways to phrase an enrollment request). 'Ambiguity' means a single signifier can have multiple meanings (e.g., 'uomo' or 'imposta'), or the meaning can depend on word correlation (e.g., 'borsetta di pelle di nonna'). For machine instructions, ambiguity is unacceptable, while expressive richness, if harnessed, can be advantageous.
The discussion shifts to analogical and digital representations, which are similar to iconic and symbolic but distinct. Analogical representation captures continuous information, while digital representation breaks it into discrete elements, much like symbolic representation. The use of pixels in digital images is given as an example of converting continuous visual information into discrete symbols, even when representing text.
For effective symbolic representation, especially for machines, the number of symbols in the alphabet must be small and manageable. The complexities of Chinese/Japanese ideograms, which require special methods for ordering and searching due to their vast number, illustrate why a limited alphabet is crucial for computational systems.
The conversation moves to numbers and their representation. It highlights that numbers are represented through an alphabet (digits), and understanding their value requires a rule to convert the signifier to the signified. The current decimal system (base 10) uses ten digits and assigns value based on position (units, tens, hundreds, etc.), where each position corresponds to a power of 10. This system is a historical accident, not an inherent truth.
The speaker challenges the assumption that base 10 is natural, pointing out that it likely stems from having ten fingers. This prompts the question: why not use a different number of digits? The fundamental principle of positional numbering systems (where position values are powers of the base) holds true regardless of the chosen base. This sets the stage for introducing binary (base 2), which uses only two digits (0 and 1) but follows the same mathematical principles for converting symbolic representation (like 101 in binary) to its numerical value (5).