Ibra Posted August 10, 2020 Report Share Posted August 10, 2020 (edited) On 8/9/2020 at 1:44 AM, Blue on Top said: We're still negatively buoyant with the chute. Appropriately for this thread, it is drag that keeps the sudden stop at the end from being more than we can handle Under limited resources (fuel & money), you can’t have high performance & efficiency without some loss in stability & safety margins or increase in complexity Draggy & simple is good but boring All summarised in the most “beautiful equation” cited previously where one has to be exponentially (e) imaginative (i) to go round (Pi) load of complexities just to offset some real negativity (-1) and end up with no-free lunch (0) For those living in perfect continuous harmony with good analytical minds, the maximum infinite amount of positivity is achieved by living on the edges (maximum principal for analytical/harmonic functions), if the amount of positivity is believed to be limited and bound they will gladly accept any compromise away from the edges as it give the same amount of happiness & positivity (Liouville thorem) Edited August 10, 2020 by Ibra Quote Link to comment Share on other sites More sharing options...
carusoam Posted August 12, 2020 Report Share Posted August 12, 2020 Ibra, you had me a holomorphic.... MS theorem of the day.... https://en.wikipedia.org/wiki/Liouville's_theorem_(complex_analysis) I probably need Erik’s help in explaining the math.... Best regards, -a- 2 Quote Link to comment Share on other sites More sharing options...
Hank Posted August 12, 2020 Report Share Posted August 12, 2020 On 8/10/2020 at 8:12 AM, Ibra said: For those living in perfect continuous harmony with good analytical minds, the maximum infinite amount of positivity is achieved by living on the edges (maximum principal for analytical/harmonic functions), if the amount of positivity is believed to be limited and bound they will gladly accept any compromise away from the edges as it give the same amount of happiness & positivity (Liouville thorem) Some of us do not think that positivity or wealth are limited and must be divided amongst everyone. Create some of each wherever you go. 1 Quote Link to comment Share on other sites More sharing options...
Ibra Posted August 12, 2020 Report Share Posted August 12, 2020 26 minutes ago, Hank said: Some of us do not think that positivity or wealth are limited and must be divided amongst everyone. Create some of each wherever you go. Oups, that quickly slipped away from aeronautical engineering trade-offs to social sciences & economic policy I will stick to my subjects (maths & design) but I agree 99.314% that if you don't create there is nothing to split Quote Link to comment Share on other sites More sharing options...
cliffy Posted August 12, 2020 Report Share Posted August 12, 2020 Someone once said- "Simplify, simplify, simplify! In a complex world a battery has but two posts- one positive and one negative Life can be broken down to being a battery, the same two choices at the "fork in the road" (not the Slauson Cutoff:-) (Where's Johnny?) When we reach a "fork in the road" one can chose the positive approach to life or the negative approach to life. A simple choice. A binary choice. Keeping with the aeronautical theme - "Keep up thine airspeed lest the earth come up and smite thee". Again, a simple positive vs negative, two ways to go, fork in the road, choice to stay alive. Keep up your airspeed or you die - your choice. Simple. Just a binary choice. To add a little levity to a complex world we can break it down to this - 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted August 12, 2020 Report Share Posted August 12, 2020 6 hours ago, carusoam said: Ibra, you had me a holomorphic.... MS theorem of the day.... https://en.wikipedia.org/wiki/Liouville's_theorem_(complex_analysis) I probably need Erik’s help in explaining the math.... Best regards, -a- Louisville's theorem is usually stated in terms of analytic functions of one complex variable. There are many equivalent statements as to what analyticity is equivalent to but usually its stated in terms of there is a convergent infinite power series representation of the function and the series is convergent at least in an open disc containing the center point. Holomorphic functions are about a complex function at a point that is differentiable in an open disc about the point. There are several theorems that connect these two things at least more so for single complex variables. The word holomorphic does not usually appear in undergrad analysis of complex variables but instead we just use the word analytic and holomorphic is usually discussed when we are thinking about functions of several complex variables. Other interesting things result there too. My favorite weird theorem in complex variables is about pretty much the opposite of analytic which is a function with an essential singularity - lets call it a singularity of infinite type, then you get Picard's great theorem. Which is really a bizarre result - and great. 1 1 Quote Link to comment Share on other sites More sharing options...
Trailboss Posted August 12, 2020 Report Share Posted August 12, 2020 On 8/10/2020 at 7:12 AM, Ibra said: Under limited resources (fuel & money), you can’t have high performance & efficiency without some loss in stability & safety margins or increase in complexity Draggy & simple is good but boring All summarised in the most “beautiful equation” cited previously where one has to be exponentially (e) imaginative (i) to go round (Pi) load of complexities just to offset some real negativity (-1) and end up with no-free lunch (0) For those living in perfect continuous harmony with good analytical minds, the maximum infinite amount of positivity is achieved by living on the edges (maximum principal for analytical/harmonic functions), if the amount of positivity is believed to be limited and bound they will gladly accept any compromise away from the edges as it give the same amount of happiness & positivity (Liouville thorem) 50 minutes ago, aviatoreb said: Louisville's theorem is usually stated in terms of analytic functions of one complex variable. There are many equivalent statements as to what analyticity is equivalent to but usually its stated in terms of there is a convergent infinite power series representation of the function and the series is convergent at least in an open disc containing the center point. Holomorphic functions are about a complex function at a point that is differentiable in an open disc about the point. There are several theorems that connect these two things at least more so for single complex variables. The word holomorphic does not usually appear in undergrad analysis of complex variables but instead we just use the word analytic and holomorphic is usually discussed when we are thinking about functions of several complex variables. Other interesting things result there too. My favorite weird theorem in complex variables is about pretty much the opposite of analytic which is a function with an essential singularity - lets call it a singularity of infinite type, then you get Picard's great theorem. Which is really a bizarre result - and great. This is why I come here...I could spend time over at Cirrus learning about which BMW to buy next, or which Rolex matches the corinthian leather interior...but I come here for the math. I tell the guys at my FBO, after getting out of the airplane a Mooney pilot looks back and marvels at the fine vehicle he's granted opportunity to operate. A Cirrus pilot looks back and wonders why it doesn't have power door locks.... 3 3 Quote Link to comment Share on other sites More sharing options...
MooneyMitch Posted August 12, 2020 Report Share Posted August 12, 2020 1 hour ago, cliffy said: “Someone once said- "Simplify, simplify, simplify!” “When we reach a "fork in the road" one can chose the positive approach to life or the negative approach to life.” Did someone say simplify? “When you come to a fork in the road, take it” Yogi Berra . 1 1 Quote Link to comment Share on other sites More sharing options...
AH-1 Cobra Pilot Posted August 12, 2020 Report Share Posted August 12, 2020 2 Quote Link to comment Share on other sites More sharing options...
Blue on Top Posted August 12, 2020 Report Share Posted August 12, 2020 I'm all about simplifying, but getting back on topic. Sometimes the fork in the road isn't a simple, binary operation. Here's an aviation example. Pushing forward on the yoke makes the airplane go down and accelerate. Pulling back on the yoke makes the airplane go up and decelerate ... until it goes down and accelerates. Just sayin'. 1 Quote Link to comment Share on other sites More sharing options...
aviatoreb Posted August 12, 2020 Report Share Posted August 12, 2020 “When you come to a fork in the road, Take it”! Yogi Berra 1988. Quote Link to comment Share on other sites More sharing options...
Ibra Posted August 12, 2020 Report Share Posted August 12, 2020 3 hours ago, cliffy said: Again, a simple positive vs negative, two ways to go, fork in the road, choice to stay alive. Keep up your airspeed or you die - your choice. Simple. But what if someone wanted the complicated truth? tell him "You can't handle the truth!" 1 Quote Link to comment Share on other sites More sharing options...
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