Safe Speed Forums

Most interesting natural phenomena are counter intuitive and on;y understandable by careful mathematical reasoning. The relationship between speed cameras and KSI figures springs to mind.

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When I see an adult on a bicycle, I do not despair for the future of the human race. H.G. Wells
When I see a youth in a motor car I do d.c.brown

Does the sub-unity notation 0.01 count? These start with 0 and there could be a lot of them....

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Views expressed are personal opinions and are not necessarily shared by the Safe Speed campaign

No, I am talking about the first none 0 digit.

The probability distribution needs to be invariant under a change of units, as we have no idea what the units are.

I think you will find the answer amazing, and it really can be important in more everyday applications, as I will explain later. I have won many bets using it, in the past.

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http://kalvis.com/

If you still believe this, take a look at tables of physical constants (but those that are truly natural, rather than defined to be nice). These should have the same distribution, but look at how many start with 1 --- many more than 1/9.

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http://kalvis.com/

Yes. I am well aware of Newcomb's observation of that fact. But surely we have a total random distribution here, not a logarithmic one, so I am very dubious about applying Benford's law.

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When I see an adult on a bicycle, I do not despair for the future of the human race. H.G. Wells
When I see a youth in a motor car I do d.c.brown

In the current case, if there is an answer, the distribution must not change under a change of units, as I said we have no idea about the units used. Given that, there is only one answer to the question. And, yes it does give a logarithmic law for the probability distribution of the first digit.

So, if there is an answer, it is log(2)/log(10) = 0.30102999566398... .

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http://kalvis.com/

Of course it does. I My apologies. The answer is indeed log(2)

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When I see an adult on a bicycle, I do not despair for the future of the human race. H.G. Wells
When I see a youth in a motor car I do d.c.brown

I always think this sort of reasoning gives a good example of the mathematical approach to such problems.

And, also, how sometimes answers to simple questions can be unexpected.

I am glad we agree.

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http://kalvis.com/

So, for those of you who have not seen this before, if someone is guessing about some numerical quantity, which strangely often happens to people around me, turn it into a bet about the first digit, and bet on it being 1. I have really made money out of it.

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http://kalvis.com/

Dammit, I thought of that just 5 minutes ago (I've just got up).

It made perfect sense that things more often begin with 1 than 9. Then I thought about how things are displayed on a log graph (something I've been teasing spindrift with recently); 1 to 1.99999999 takes the biggest chunk of the axis, of course. (I wasn't sure if that was correct, but I was going to give it a go).

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Views expressed are personal opinions and are not necessarily shared by the Safe Speed campaign

It is a nice problem, and the answer is far from what most people expect. In this problem, we can prove the log scale is natural, in a sense.

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http://kalvis.com/

I like you trakgalvis, about 2.717 times more than I did yesterday

When I was a school kid I used a slide rule and my Physics teacher had the first electronic calculator from Sinclair. (Circa 72?).

I never owned one or ever got the chance to play with one but I remember it was weird to use, something about Polish notation

Back then I could find the square root of a number using long hand. Not now I can't...

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The views expressed in this post are personal opinions and do not necessarily represent the views of Safe Speed.
You will be branded a threat to society by going over a speed limit where it is safe to do so, and suffer the consequences of your actions in a way criminals do not, more so than someone who is a real threat to our society.

I remember those days!

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http://kalvis.com/

Are you sure it's not 3.1417 times, just to make it a nice, round number?



We were banned from using slide rules in exams, as we could write crib notes in the channel underneath the slider



Reverse-polish notation, or RP. Some of the early HP calculators used it

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Only when ideology, prejudice and dogma are set aside does the truth emerge - Kepler

That was it! Can you give an example Pete? It was something like if you wanted to do a simple calculation of 2x2 you had to enter something like x2x2 to get 4? I'm probably way off there, I think it was more strange than that even, but I remember it was something equally silly; not at all intuitive like today.

I saw one a few years ago in the museum at Gloucester, for the first time since i left school, brought back memories I can tell you...

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The views expressed in this post are personal opinions and do not necessarily represent the views of Safe Speed.
You will be branded a threat to society by going over a speed limit where it is safe to do so, and suffer the consequences of your actions in a way criminals do not, more so than someone who is a real threat to our society.

I designed and built a computer that worked in RPN. Used the FORTH language. Had the advantage of not needing an address field in the instruction word since all the operands were on the stack.

Interesting how many old engineers oppose speed cameras. BRAKE would say it was because we were old and unable to adjust to new ideas. i would say it is because we are engineers trained in evaluating new ideas.

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When I see an adult on a bicycle, I do not despair for the future of the human race. H.G. Wells
When I see a youth in a motor car I do d.c.brown

That number almost makes me hungry - almost

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Views expressed are personal opinions and are not necessarily shared by the Safe Speed campaign

Anyone for a slice of Pie? Just trying to prove I'm keeping up

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The views expressed in this post are personal opinions and do not necessarily represent the views of Safe Speed.
You will be branded a threat to society by going over a speed limit where it is safe to do so, and suffer the consequences of your actions in a way criminals do not, more so than someone who is a real threat to our society.

I would say that it's because we have well-developed BS detectors.

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Only when ideology, prejudice and dogma are set aside does the truth emerge - Kepler

Well, you should have noticed that it is not pi to the displayed number of figures!

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http://kalvis.com/