Exponential growth curve

As explained in Fast Python: High performance techniques for large datasets

An exponential growth curve represents a quantity that increases by a constant multiplicative factor over equal increments of its input.

An exponential growth curve represents a quantity increasing by a constant multiplicative factor over equal input intervals. It makes rapidly widening differences easier to see than verbal descriptions alone. section 1.1

In data processing, exponential growth frames a widening contest between generated data and the hardware available to transfer, store, and analyze it. The gap increases as data rates double faster than computing capacity. section 1.1

Data rates versus computing capacity

Edholm’s Law models telecommunications data rates doubling every 18 months, while Moore’s law models transistor counts doubling every two years. Internet traffic broadly follows the data-growth pattern, illustrating why processing and storage requirements escalate. section 1.1

Figure 1.1 The ratio between Moore’s law and Edholm’s law suggests that hardware will always lag behind the amount of data being generated. Moreover, the gap will increase over time.

Compare the curves for data generation and hardware capability to see why the hardware deficit widens over time. section 1.1

How Fast Python: High performance techniques for large datasets covers it

How deep it goes

Illustrates doubling laws and comparative plots but stops short of mathematical derivation.

Examples

Uses telecommunications data rates, transistor density, internet traffic, and comparative growth figures.

What you can do after

Evaluate why processing and storage resources can fall behind rapidly growing data volumes.

How it connects

Links exponential growth to Moore’s law, Edholm’s Law, internet traffic, and data processing.

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Also explained in

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Related concepts

• linear growth patterncontrasts with · A linear growth pattern is change at a constant additive rate, producing approximately equal increases over equal intervals.
• k-d treeaddressed by · A k-d tree is a binary space-partitioning tree that organizes points in multidimensional space by recursively comparing coordinate dimensions.
• mean squared errormeasured by · Mean squared error is the arithmetic mean of the squared differences between corresponding predicted and target numerical values.
• training datasetproduced by · A collection of examples or observations supplied to a learning procedure to fit or adapt a model or learn its patterns or parameters.
• input-output pairalternative to · An input-output pair is an input instance paired with its corresponding output, whether observed, specified, or intended as a target.

This explainer was generated by Manning's knowledge graph from the text of Fast Python: High performance techniques for large datasets. The section links point to the parts of the book it draws on.