jonno
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nil satis nisi optimum
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Post by jonno on Jan 16, 2024 18:13:56 GMT
Call me pedantic, but 0.9^50 = 0.5%. You need to iterate 59 times to reach as low as 0.2%, since 0.9^59 = 0.2% Your pedantic 
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Post by bernythedolt on Jan 16, 2024 18:19:45 GMT
Call me pedantic, but 0.9^50 = 0.5%. You need to iterate 59 times to reach as low as 0.2%, since 0.9^59 = 0.2% Your pedantic My pedantic? 
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michaelc
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Post by michaelc on Jan 16, 2024 19:13:24 GMT
Call me pedantic, but 0.9^50 = 0.5%. You need to iterate 59 times to reach as low as 0.2%, since 0.9^59 = 0.2% Call me pendantic but you don't need to iterate any more than you need iterate AxB as B+B+B....B A times. Unless you're a computer of course.
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benaj
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Post by benaj on Jan 16, 2024 19:20:22 GMT
Not sure computer really thinks A x B or A + A (B-1) Times. I thought on the processor level is just numerous logical operations.
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michaelc
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Post by michaelc on Jan 16, 2024 20:52:08 GMT
Not sure computer really thinks A x B or A + A (B-1) Times. I thought on the processor level is just numerous logical operations. B times not B-1. I agree there are more efficient algorithms that a typical ALU would implement taking advantage of its binary architecture. I think I'm going way off topic here.
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angrysaveruk
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Post by angrysaveruk on Jan 16, 2024 20:53:16 GMT
Call me pedantic, but 0.9^50 = 0.5%. You need to iterate 59 times to reach as low as 0.2%, since 0.9^59 = 0.2% Whatever Dude.
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Post by bernythedolt on Jan 16, 2024 22:22:31 GMT
Call me pedantic, but 0.9^50 = 0.5%. You need to iterate 59 times to reach as low as 0.2%, since 0.9^59 = 0.2% Call me pendantic but you don't need to iterate any more than you need iterate AxB as B+B+B....B A times. Unless you're a computer of course. I've always considered exponentiation as fundamentally an iterative construct, but if you have a better turn of phrase than the one I used, I'll happily reconsider.  Obviously nobody sits at their calculator and repeats the operation 59 times, because they have an x y key and a life to lead, but fundamentally it's still an iterative process at heart, even if the calculator uses a neat and quickly converging power series expansion to evaluate it. "Unless you're a computer of course".Funnily enough, I think it's quite the reverse: whereas a human might be tempted to iterate to a degree, the computer WON'T be doing any iterating. I believe 0.9 50 would be evaluated on a calculator or computer along these lines. All calculators have a built in function to evaluate the power series for e x to a few terms and ditto for the natural log function ln(x). These will be based on the Taylor series expansion of those functions (or similar/even faster derivatives). Since 0.9^50 can be expressed as e^( 50 ln(0.9) ), the calculator will only need those two functions to firstly evaluate ln(0.9), multiply that by 50, and feed that result as the argument for its expansion of e x. Answered in a flash and no iteration. You won't be surprised to hear that, when I first started work all those decades ago in the early 1970s, I spent all my first week's wages on buying an electronic hand-held calculator . The look on my dear old dad's face when he saw just what it was capable of in an instant was priceless!
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michaelc
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Post by michaelc on Jan 16, 2024 22:31:17 GMT
Call me pendantic but you don't need to iterate any more than you need iterate AxB as B+B+B....B A times. Unless you're a computer of course. I've always considered exponentiation as fundamentally an iterative construct, but if you have a better turn of phrase than the one I used, I'll happily reconsider. Obviously nobody sits at their calculator and repeats the operation 59 times, because they have an x y key and a life to lead, but fundamentally it's still an iterative process at heart, even if the calculator uses a neat and quickly converging power series expansion to evaluate it. "Unless you're a computer of course".Funnily enough, I think it's quite the reverse: whereas a human might be tempted to iterate to a degree, the computer WON'T be doing any iterating. I believe 0.9 50 would be evaluated on a calculator or computer along these lines. All calculators have a built in function to evaluate the power series for e x to a few terms and ditto for the natural log function ln(x). These will be based on the Taylor series expansion of those functions (or similar/even faster derivatives). Since 0.9^50 can be expressed as e^( 50 ln(0.9) ), the calculator will only need those two functions to firstly evaluate ln(0.9), multiply that by 50, and feed that result as the argument for its expansion of e x. Answered in a flash and no iteration. You won't be surprised to hear that, when I first started work all those decades ago in the early 1970s, I spent all my first week's wages on buying an electronic hand-held calculator . The look on my dear old dad's face when he saw just what it was capable of in an instant was priceless! Great answer Berny !
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pikestaff
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Post by pikestaff on Jan 17, 2024 8:05:45 GMT
I've always considered exponentiation as fundamentally an iterative construct, but if you have a better turn of phrase than the one I used, I'll happily reconsider. Obviously nobody sits at their calculator and repeats the operation 59 times, because they have an x y key and a life to lead, but fundamentally it's still an iterative process at heart, even if the calculator uses a neat and quickly converging power series expansion to evaluate it. "Unless you're a computer of course".Funnily enough, I think it's quite the reverse: whereas a human might be tempted to iterate to a degree, the computer WON'T be doing any iterating. I believe 0.9 50 would be evaluated on a calculator or computer along these lines. All calculators have a built in function to evaluate the power series for e x to a few terms and ditto for the natural log function ln(x). These will be based on the Taylor series expansion of those functions (or similar/even faster derivatives). Since 0.9^50 can be expressed as e^( 50 ln(0.9) ), the calculator will only need those two functions to firstly evaluate ln(0.9), multiply that by 50, and feed that result as the argument for its expansion of e x. Answered in a flash and no iteration. You won't be surprised to hear that, when I first started work all those decades ago in the early 1970s, I spent all my first week's wages on buying an electronic hand-held calculator . The look on my dear old dad's face when he saw just what it was capable of in an instant was priceless! Great answer Berny ! Interesting though this diversion has been, the reality is that the Houthis will be resupplied by Iran, so in real life the series won't go to zero. And provoking Iran in this way is having wider consequences. I don't think Iran would have done something like this a few months ago: www.theguardian.com/world/2024/jan/16/iran-launches-airstrikes-on-sunni-militant-bases-in-pakistan
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Post by bracknellboy on Jan 17, 2024 8:38:58 GMT
They were happily supplying the Houthis to launch many drone strikes on Saudi Arabia in the past. And have also of course previously launched attacks on US base in Iraq (albeit one can very reasonably argue that they WERE provoked in that case). I think the evidence that the above is direct result of action against the Houthis is likely illusive: it could just as well be that they are taking advantage of the general instability in the region; the focus on Gaza; even maybe taking advantage of a view that the US will counsel caution due to fear of escalating the general situation. I'm not sure we should be talking about having 'provoked' Iran: action was taken against their proxies specifically designed to stop them attacking shipping in international waters. Both a US naval vessel and a UK naval vessel had themselves been directly attacked prior to this. I'm not sure I'm fully supportive of the action taken in the way it has been. Nonetheless, a counter argument that we should not take action when directly attacked in international waters, or that we should allow the international community to be 'bullied' into treating the area as a no go zone - all contrary to international law - is not a compelling one.
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registerme
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Post by registerme on Jan 17, 2024 9:14:36 GMT
If we take military action off the table, has anybody got any actual suggestions as to what to do about the Houthis shooting at / hijacking international shipping?
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angrysaveruk
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Post by angrysaveruk on Jan 17, 2024 9:45:00 GMT
Call me pendantic but you don't need to iterate any more than you need iterate AxB as B+B+B....B A times. Unless you're a computer of course. Since 0.9^50 can be expressed as e^( 50 ln(0.9) ), the calculator will only need those two functions to firstly evaluate ln(0.9), multiply that by 50, and feed that result as the argument for its expansion of e x. Answered in a flash and no iteration. You won't be surprised to hear that, when I first started work all those decades ago in the early 1970s, I spent all my first week's wages on buying an electronic hand-held calculator . The look on my dear old dad's face when he saw just what it was capable of in an instant was priceless! Due to the binary nature of the way floating point numbers are stored on computers (ie base 2) X^Y is nearly always calculated as 2^(log2(X) * Y) - even on your 1970's calculator. e^x may have nice properties mathematically it is not so useful when dealing with electronic based calculations.
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benaj
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Post by benaj on Jan 17, 2024 9:47:31 GMT
might be team up with enemies of the rebel to wipe them out, or starving their supplies.
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angrysaveruk
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Post by angrysaveruk on Jan 17, 2024 9:48:00 GMT
If we take military action off the table, has anybody got any actual suggestions as to what to do about the Houthis shooting at / hijacking international shipping? Try to get a ceasefire in the Israel/Palestinian conflict.
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adrianc
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Post by adrianc on Jan 17, 2024 10:00:44 GMT
If we take military action off the table, has anybody got any actual suggestions as to what to do about the Houthis shooting at / hijacking international shipping? Try to get a ceasefire in the Israel/Palestinian conflict. Do feel free to expand on that one...?
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