Wikipedia:Reference desk/Archives/Mathematics/2007 October 21

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October 21

early mathematics

Dear all,

I have a question.

How advanced were the multiplication and division skills of people in the 16th century? I found the following paragraph very strange. Did they really not know how to multiply? Did they not have mathematical tables? --Kushal^t 20:39, 21 October 2007 (UTC)

I quote:

Its immediate applications were obvious: [...]given a number through his projected 'Universal Characteristic ' […] (Ross, 2000). Instead of fruitless arguing, people would say, 'Let us calculate ' – and they could do so by setting the dials and cranking the handle of his machine (one of a number of Leibnizian schemes satirised in Swift's Voyage to Balnibarbi) (Ross, 2000).

Ross, G. M. (2000, July). Leibniz. Retrieved October 20, 2007, from University of Leeds Electronic Text Centre: http://www.etext.leeds.ac.uk/leibniz/leibniz.htm

Thank you very much.

Regards,

Kushal --Kushal^t 20:39, 21 October 2007 (UTC)

The quote you give is referring to Leibnitz's characteristica universalis, by which he hoped to reduce all logical reasoning to calculation (which could then be carried out mechanically). As for arithmetical skills in the 17th century (note this is when Leibniz lived, not the 16th), I expect that then, as now, most educated people were fairly innumerate , but certainly it was known how to multiply, mathematical tables of many kinds were in use, and (without calculators) some people had to perform huge numbers of calculations in the course of their work. Algebraist 21:48, 21 October 2007 (UTC)

Reading the quoted paragraph, it speaks about the mechanical calculation device, not about the characteristica universalis. It says its usefullness is due to the fact that "at the time even educated people rarely understood multiplication", which is probably what prompted this question. -- Meni Rosenfeld (talk) 22:25, 21 October 2007 (UTC)

Yes, Meni. You are correct. BTW, does the paragraph talk about the ability to multiply with a table or the understanding of the concept of multiplication of two numbers?

I wonder if it could this be a minority view or a widely accepted one. In case of the latter, could my fellow Wikipedians provide me a resource right off the bat (hopefully one that I can cite). --Kushal^t 00:57, 22 October 2007 (UTC)

One educated person living at the time, who did not know his multiplication tables, and complained in his diary about the difficulty of multiplication, was Samuel Pepys. See [1]. Whether this was the exception, or the rule, I do not know. --NorwegianBlue ^talk 17:30, 24 October 2007 (UTC)

Bookmaking

I'm interest in calculating the probabilities of events. I though I look towards the experts in the field. According to this article Mathematics of bookmaking it says

This is achieved primarily by adjusting what are determined to be the true odds of the various outcomes of an event in a downward fashion (i.e. the bookmaker will pay out using his actual odds, an amount which is less than the true odds would have paid; thus hopefully ensuring a profit).

But it does not say how the hell do the expert bookmakers determine the true odds of events. Isn't that the absolutely crucial bit of bookmaking? For example, if bookmaker A uses method A to determine the true probability of an event to be 0.2 while bookmaker B uses method B to determine the true probability of an event to be 0.5 while bookmaker C uses method C to determine the true probability of an event to be 0.8 then who is right and who is wrong? I am so confused. 202.168.50.40 22:55, 21 October 2007 (UTC)

If I'm reading that right, it would seem that the bookmaker is (like most successful business people) bottomline minded. That is to say that he will pay out more for a bid which will more likely yield a profit for him, and vice versa. A math-wiki 10:46, 22 October 2007 (UTC)

See also Odds#Gambling odds versus probabilities. "True odds" are often not "true" in a mathematical sense but the term reflects what the bookmaker really thinks the probability is, and that is different from the odds he offers to gamblers. Note that often there is coordination between the odds offered by different bookmakers, so the underlying "true odds" may not reflect what the individual bookmaker believes. If there was no coordination then situations could arise where gamblers had a guaranteed profit by simultaneously playing on one outcome at a bookmaker giving better odds on that, and the opposite outcome at another bookmaker. PrimeHunter 14:06, 22 October 2007 (UTC)

Such opportunities do exist. I think arbitrage betting covers this idea. Basically with so many bookies around there will be instances where betting on both home, away and the draw will guarantee a return when you cover the cost of all 3 bets. I understand my friend, who is a professional gambler, often looks out for these. He also looks out for wildly-unusual odds - apparently sometimes the sites accidently input the odds incorrect into the web-update and if you get a bet in before they fix if you will be given it at the odds specified (i.e. the whole sold as seen style setup). It's actually a very interesting area of business I find. ny156uk 18:53, 22 October 2007 (UTC)