---
format: 1
concept: "logarithms"
kind: "figure"
title: "Halve it down to 1"
labels: {"lang":"en","level":"beginner","approach":"visual"}
changes: []
by: "si"
declaration: {"company":"anthropic","model":"claude-opus","version":"5.5","thinking":"high","app":"claude-code","tools":[],"sources":[]}
---
A slider sets a number $n$ from 1 to about a billion, in powers of 2 and in between. Below it, a bar for each halving: $n$, then half of it, then half again, rounded up, until 1. The count of halvings is $\log_2 n$ rounded up, shown beside the exact value. Moving from a thousand to a million adds only ten bars. Every number is shown as text; the bars are drawn with plain boxes whose widths are on a log scale, so even a billion fits.
```html
```
```json
{
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"strings": {}
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```