h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Interpolation by Intuition - A1300672
Author: Old Hairy - U241325

This entry is best read in Alabaster or GOO, because the table titles disappear in Brunel. It also needs horizontal scrolling to read in Brunel (once only), but is not so wide that that is necessary in the other skins.

It deliberately does not give much of an explanation of linear interpolation. I may be mistaken, but the thought was that someone unable to grasp it from my meagre description would probably struggle with the rest of the entry.

I hope you find my maths sufficiently un-mathematical for the guide.

OH

Hi Old Hairy,

I made a first quick pass and to me the entry seemed to progress very logically and was easy to read.

More later

Awu.

Just had a thought about the title. It's not really about Interpolation by Intuition. After the first paragraph it's really very methodical and scientific.

Awu.

Hello Awu.

Thanks for the interest. The reason for the title is that the entry explains how to do something very general (interpolation of any degree using any collocation points) without much maths. The intuitive bit is using zero/one weight functions to do the work.

However, if you can come up with a nice punchy title, I'm all ears.

I think you have caused me to recognise a deficiency in the article. I don't think I ever say that the collocation points to not need to be equally spaced (as they are in all the examples). Does that need fixing, do you think?

OH

Hi Old H

I thought I'd see what new thing you had cooked up.

NB someone has contributed a thought as a new conversation, rather than via the PR thread.

Probably come at this at the wrong time of day, and without the necessary curiosity. I found it a bit heavy going, and when I saw the *big* table I skimmed to the end. Generally mathematics doesn't frighten me but I think this handling of the topic is not for the casual browser. It seems well written , but a bit 'dry textbook' for me to get enthused.

Pimms

Hi Pimms.

I'm surprised you found it "dry textbook", because I dipped it in water. I do not know of any text book that establishes the Langrange Interpolation Formula without a lot of maths, which is what, in effect, I did.

The "big" table is there because the other tables are small. No big table is needed to establish the points I make early on. But when I claim that accuracy has been obtained, I put in lots of intermediate values to demonstrate that there are no hidden holes.

The complaint that radioactive decay is a poorly understood example (made by A.N. Other = Traveller in Time) is valid, but I need an example which behaves like 2^-x and that was the best physical interpretation I could think, of which I thought everyone would understand (is half-life not a well known concept?). The point about this type of exponential decay is that no polynomial can perfecty represent it.

I also avoided changing the example data at every turn. I did not use a different example in each case, which might lead the sceptical reader to cry foul. But if you would like to help with this entry, and take some credit for that, please advise me how that is arranged. (I am still relatively new to h2g2, and have an uncomfortable feeling that I don't do things quite properly.)

You are as ever the logical lettuce.

OH

OH

I hope there's no misunderstanding - I think you've done a good job with explaining this . My reservation is that the subject is such that it may only appeal and be appreciated by a specialist few.

I'm not sure that I will be able to assist as much with this entry as with the other one. The general procedure for crediting other people in entries you write (and there can only be one author* editing an entry even if you add other researchers) is to add their U number to the list in the box below the entry when editing it.

*You can get around this by creating a dummy researcher and sharing the login details with other researchers who you want to have editing rights, but generally this is not worth the bother.

As far as when to add other researchers it is normal to offer the co-credit in the thread if you think a researcher's contributions have significantly added to your entry (so not typos or style points, more research and valuable alternative explanations that help explain or expand on your points). I say 'offer' as quite a few experienced commentators in PR will turn down the offer (but appreciate being appreciated ).

One thing to bear in mind is that while in PR you will be listed as editor, and co-researchers as writers, once an entry is in the EG the sub-ed is the editor and all researchers are listed a writers in U number order (so people who've been around on h2g2 longer come first).

Pimms (but not much longer, may soon revert to my first smiley: )

Hello Pimms.

Thanks for the tips.

The subject is technical. However, there are some neat tricks which I aim to describe, but presently cannot, because there is nothing which describes interpolation. The other topics include

A) how to draw curves of absolutely any shape you like
B) how to find an accurate maximum or minimum from a spread-sheet table

I had the notion that technical subjects could be dealt with if suitably simplified. That was the aim. Have I failed?

(There is a similar problem with Boolean things. There are threads asking about Karnaugh maps, but nothing about truth tables which are needed to explain them.)

OH

I leave this entry to Awu, who clearly is more at home with the technicalities. I fear this will never be described as easy-reading

Pimms

Hello Pimms.

Nothing from AWU since his first reply, so I won't hold my breath.

Never meant it to be easy reading. Once you go beyond straight lines between two dots, interpolation is a bit technical. But when (and now if) I write something simple, which relies on interpolation, I can refer to this entry and leave it at that for the technicalities.

I do not like technical things to have loose ends. Thus, when I did truth tables, and all the rest I am/was doing about matters Boolean, I stick rigidly to true/false. This avoids certain conundrums, which I can allude to because I wrote "Electronic Logic Conventions" first.

I'm here! I'll try to go over it in depth tonight.
Awu.

Good stuff . I applaud your method OH .

Hopefully you won't find the need to write entries explaining maths from the most basic axioms to get to the point of what you wanted to write first - it took Russell and Whitehead a number of large books, and unless I'm mistaken *they* weren't too simple to understand

Pimms

Hello Pimms.

Thanks for the compliments.

Now, a bit off topic, but you might know the answer.

If you go The Universe->The World of h2g2->The h2g2 University->The College of Everthing->Numbers and Logic, and persevere with the "withdrawn by author" result from the first link, you can find a good (heavy) entry on "Cantor's Diagonal Method". The entry is what I would call comprehensively hidden.

By the same route, you can also find the much lighter entry "Rational Numbers". However, this entry is quite easy to find by the route Everything->Science (and) Technology->Mathematics, a route I have been down often.

You cannot find "Cantor's Diagonal Method" by the easy route. Who presides over (and more importantly) fixes such things. It's part of the apparent dumbing down which I have mentioned elsewhere. I think you would agree that this sort of thing gives an impression, but that first impression could be, I admit, incorrect. But it is the impression, none the less.

I would think in the case of this example, the thing to do would be to add the good link to the short route, and remove the bad link from the long route. Several other things might also be made visible by either route. Is the long route a vestige of something historic?

Thanks for your attention.

By the way, I'm never sure whether its correct to say "Thankyou" or "Thank you", so have been using "Thanks" instead, which is not quite my style (In the real world, its much easier to look up). A good mnemonic for getting this right would be nice. I'm sure I could test it on you, and soon.

OH

Note: the route via 'University' may take you into entries that never became edited if the relevant university project was unfinished - the first Cantor entry you mention is not in the EG.

Personally I rarely search hierachically, usually attempting the 'search h2g2' via my best guess at a likely key word - don't expect it to work well with two words, as it seems to rank by number of occurrences of either word within the entry, so entries mentioning both words could well be ranked out of sight below entries that mention one word frequently.

'Cantor' will find entries, but not necessarily relevant ones to number theory.

To suggest alterations <./>Feedback-Editorial</.> could well be the place to leave a message

Pimms
ref: thank you, I believe two words is appropriate cf. Bless you, F*** you (I merely offer these as a mnemonic aid ) or other directives are always condsidered as two words and not concatenated.

Hello Pimms.

Thank you.

I need a f**k three or four times a day at least, but I just don't understand while asterisks are necessary to say knife and f**k.

I have been mislead (yet again) by the system. The routes into the edited guide can lead you to unedited entries. That I really would not have thought of. I've just been logged out at random, yet again, and am beginning to wonder if anything around here "does what it says on the can".

Thank you again.

OH

this has got a bit off topic - how do you think the PR is going on the entry?

Pimms

Hello Pimms.

I think its stopped.

OH

oops. try putting 'sex' in the title, it works on magazines

'night

Pimms

Interpolation in Middlesex?

Oh, an entry which has 'sex' in it?

Here are some typos:
The error increase rapidly -> increases
Remembering that L0 and L0 are -> second L0 should be L2
gives WORSE approximation that simple linear interpolation -> than
problems we have note -> noted

The huge table has 'plain skin' users scroll horizontally too. I had to decrease font size to 80% and move closer to the display screen. But, since the tag isn't approved GuideML, I'm afraid there's no way around it.

The description is nice and to the point . However, the entry falls off rather abruptly towards the end. As a conclusion, I'd like to propose something along the lines of

'... this entry explains its point from the bottom up. There's also a top-down point of view: if the graphical representation of your measurement data doesn't look like pearls lined up on a string, but you still assume a mathematical function working behind the scenes, then quadratic approximation is your first choice. If this isn't sufficient, try the cubic one. Note that linear approximation entails a polynomial of degree 1, quadratic approximation is degree 2, cubic approximation is degree 3. If neither of these turns out to represent the data accurately enough, you're going to end up with a polynomial of degree N. That is, what you're developing is a series expansion of an unknown function. At this point, it might be useful to draw the measurement points on logarithmic paper (or to apply equivalent manipulations to the x/y axis in your software package) to figure out what your unknown factors are. Or, assume an exponential times a trigonometric function and try to fit these to your data.' --- or somesuch


Bossel