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San Francisco, USA

 

Google map scale

It always frustrate me to find maps don't come with scale. It is particular important if you try to judge whether a route is within walking distance. Google map is an incredible tool. But it needs to show the scale too!

So I have decided to make my measurements and come up with some reasonable estimate. I will use the zoom control as the scale. Up to 9 zoom levels were measured with level 1 being the most detail. The distance between the center of + mark and the - mark, is shown below. Beware that the projected images near the poles (e.g. Helsinki,Finland) seems significantly distorted.

LevelDistance
1230m
2450m
3870m
41.7km
53.3km
66.4km
712km
824km
947km

2005.06.24 [] - comments

 

Python's half open index notation

Beginner programmers often wonder about Python's sequence indexing and slicing notation. Array index starts from 0. Slicing uses half open notations, where L[a:b] is a subsequence with index x where a <= x < b.

Why is the endpoint excluded? Isn't it more intuitive if array index starts from 1 and the endpoint is included, so that a 3 elements array is referenced as L[1:3] with items L[1], L[2], L[3]?

It turns out this notation is an elegant and deliberate design and it has some excellent properties.

We write programs to operate on arrays, to find their length, traverse the subsequences, split them or join them. The half open notation always show a simple pattern. But the inclusive notation often requires adding 1 or substracting 1 to the indexes in many operations. Thus it is more vulnerable to off-by-one-error. This article One True Way of array indexing discuss this at length. I have reproduce its example (with corrections) below:

Operation Half open Inclusive
length of a slice L[a:b] b-a (b-a+1)
first n characters of L L[:n] L[1:n]
last n characters of L L[-n:] L[len(L)-n+1:]
The identity slice L == L[0:len(L)] == L[:] L[1:len(L)]
The empty slice L[a:a] is empty for any a. perhaps L[a:a-1]?
A slice of length n, from point a L[a:a+n] L[a:a+n-1]
Split L[a:b] at index c L[a:b] == L[a:c]+L[c:b] L[a:c-1]+L[c:b]

Another important property is an empty sequence can be expressed by L[a:a], while there is no natural way to express an empty sequence with the inclusive notation. But do we really need to care about a special case? Absolutely! In fact failure to account for empty input is one of the most common error. Just like zero is a fundamental concept in mathematics, always think how you program can handle null input. An inferior approach is to represent empty sequence by None or null pointer. This creates a special case so that a variable need to be tested before dereferencing. Failure to do so contributes to unexpected exceptions. It is an elegant design that L[a:b] can also represent sequences with 0 length.

C++'s STL also choose this notation to represent a range. According to the literature this is crucial because "algorithms that operate on n things frequently require n+1 positions. Linear search, for example (find) must be able to return some value to indicate that the search was unsuccessful." I have seen so many people flunked link list or data structure exercises because they have trouble dealing with the end of a list. Often a good solution is shift the focus beyond the n concrete objects to the n+1 positions around them. I hope this help to make sense of the half open notation.

2005.06.16 [, ] - comments

 

Mac goes Intel

This is my observation on Jobs' speech in the WWDC 05 Keynote.


Thanks Daniel for your coverage on the keynote. Reading this is as if I were there.

Jobs has made a very diplomatic presentation. Going Intel is so touchy that they have to introduce this with great care and sensitivity. The humor and cheerleading that is routine in this kind of event are markedly subdue. In place of it are lot more solemn and contemplative atmosphere. Making light joke on the bunny man on fire commercial and have the two CEOs embrace in front of the audience is a ritual for the past foes to make up. I think the ability to change without getting too entrenched or too religious is especially important for Apple to survive and to thrive.

Perhaps this can be a lesson for political adversaries too?

2005.06.15 [] - comments

 

past articles »

 

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Nasa confirms ocean moon mission (20 Aug 2019)

 

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Trump considers new tax cut to boost US economy (20 Aug 2019)

 

Robert De Niro's ex-aide sued for misusing funds and 'TV bingeing' (20 Aug 2019)

 

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SF Gate

 

Ship traffic, August 21 (20 Aug 2019)

 

The rise of the virtual restaurant (19 Aug 2019)

 

To power AI, Bay Area startup creates a giant computer chip (19 Aug 2019)

 

Shareholder value is no longer everything, top CEOs say (19 Aug 2019)

 

74% of economists in survey see US recession by end of 2021 (19 Aug 2019)

 

Ship traffic, August 20 (19 Aug 2019)

more »


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