# Boards

## Speak maths to me in a language I can understand.

What does this mean: 'results are log-normalised to 1 for the highest value'?

I presume log means logarithm. But I don't understand what a logarithm is.

I've tried looking it up, but it seems I would need to spend hours teaching myself basic maths. And I'm a lazy, stupid man.

Any help gratefully accepted.

Wow! What a GREAT thread!

## holy maths batman

## This is going pretty much

as well as I expected.

## i didnt even read it

does that help?

## Probably.

## its about probabilties?

## Bally moths J-Dawg

.

## I can tell you as that log

does indeed mean logarithm.

That's about it, though. I'm putting my further maths A-level to such good use these days.

You need to find jp100, he the maths man.

## 2 + 2 = 4

.

## x^2 differientiates to 2x

## differentiates*

## context?

## Logarithms

are the hardest thing ever.

## I h8 Maths

with a passion!

## Logarithms are used to shorten scale differences.

As I remember the number that results for a log to a base of 'n' is the power you'd have to raise 'n' to in order to bring back your original number.

Most logarithms are either in base 10 or base e (where the term 'ln' is used). So if something's in base 10 then just do 10^value = original value.

If you open up the Windows calculator (it's in Programs -> Accessories and change the view to 'scientific' you can test this out:

Type a number

Press 'log'

Store the number

Type 10

Press x^y

Retrieved your stored number from the 'log' operation

You'll get the original number back.

In this case your results have then been normalised so that the largest possible value is '1' (or 10 if you un-logarithm it).

I guess the only reason to do this is to make life simpler but it doesn't really affect how the values would look in a graph.

Off hand I'm guessing you may have been given the scaling factor used for the normalisation? The point about Logarithms is that they'll give you a linear relationship where the original one curved upwards (if I remember correctly).

Therefore you can linearly scale all your log results to achieve the above normalisation, whereas prior to logging this wouldn't have been possible.

## ln is the inverse of e^x

I remember something!

## Right, I think I get this.

This is the context:

the sizes of websites are being compared (in terms of number of webpages recovered by various search engines). For each search engine, results are log normalised, then each website is given a combined sum then ranked.

I guess this normalisation ensures that websites aren't disadvantaged by being under/overrepresented on a particular search engine for some reason (and therefore ranked properly).

Does that sound right?

## It might just be easier

to understand the numbers at the end.

like, if you don't log it you might get one website with 250000000016565 readers and one with 156897456333 and they're hard to compare easily.

but if you set the high value at one, then everything else becomes a fraction of one, and they're easy to understand.

i.e. you can easily tell how many readers they get in proportion to each other.

## Gotcha.

Cheers Mike! Cheers Theo!

## Yeah, Mike maketh the sense

The only reason to use the logarithm is to get rid of the differences.

i.e.

log 5,000,000 = 6.699

log 500 = 2.699

Then you'd divide both by 6.699 to get them normalised by 1.

But you can see that fitting 6.699 and 2.699 on the same graph is a fuck load easier than 500 and 5,000,000. As long as you realise you're looking at a log graph so you understand the bigger values are actually a LOT bigger then it's all okay.

## yup

though i think you may not use base ten, but instead choose the right base number to make log 5000000 = 1

and then stick with that value for the others.

it mightn't make a difference though

## ah right

That probably makes a lot more sense. I haven't done logs in YEARS.

## nor me

so i can't remember how to decide what base number you use, or how to calculate it.

might just be base 5000000 actually.

so yeah. maths. <3

## .

Remember the change of base formula and the equivalence should be clear. In theo's example, using base 10 and dividing, you're dividing all log(x) values by log(5,000,000). In your example you're taking log with base 5,000,000 for all x.

log(x)/log(5000,000) = log{base 5,000,000 }(x).

Which you choose probably comes down to the tools at your disposal (and how obtuse you wish to look).

HTH.

## Yep,

it's not me doing the graph, I'm just trying to work out the methodology behind someone elses calculations. But it makes sense now. Thanks again.

## i think

it basically means that your highest value is made to be one, then everything else is calculated off that using logarithms.

log being something to do with powers and things. but i can't quite remember how it works.

BUT, the important bit is that a log graph always looks the same or something. so if you log normalise you get that graph.

and it means that increases aren't incremental or something.

decibels are a log graph i think.

## decibels are logs

they're not on a graph. Each decibel is an order of magnitude louder than the last.

## there are graphs involved

i seem to remember the point with decibels is that they're a tiny unit. so log just makes them seem bigger.

and actually makes them all negatives or something.

i should know. balls.

:(

## Well you can put anything on a graph

and yeah, log graphs are those weird ones where the lines get closer together as you approach each '10'.

I just mean dbs are actually log values with or without a graph. I think that's where the 'deci' part of the name comes in but I'm not sure.

## The Decibel came into existence

because the original unit, the bel(B), was considered to large for everyday use.

So 1 dB = 0.1B

## They are indeed

## 'log'

heh.