studiot

For those of us to whom this equation is less well known, what do the symbols represent and what are the conditions imposed under which it is valid please?

Think about it if p = 1 then p + 3p2 = 4. So you are saying there is a probability of 4 of a connection if every switch is closed. This is clearly wrong and what the first column of the spreadsheet was all about. I was wrong in my initial statement about the parallel situation; it works like this. If pi = probability for switch i closed qi the chance of switch i open and If P = probability for network connection Q the chance for network disconnection then pi + qi = 1 and also P + Q = 1 For a series situation 1)Any switch open will loose connectivity 2)All switches have to be closed for connection. So the chance of network connection depends individually on every switch P = p1 x p2 x p3 x ..........pi For a parallel situation the obverse situation occurs. 1)Any switch closed makes continuity. 2)All switches have to be open to loose connectivity This time we calculate the chance of loosing network connectivity since it involves all switches Q = q1 x q2 x q3 x ..........qi But we want the chance of the network connected, not the chance of it disconnected so P = 1 - Q = 1- {q1 x q2 x q3 x ..........qi} We can't use case 1) for parallel probability becase the probability for (say) switch 1 being closed is p but this includes situations where switch 2 etc is also closed and cases where it is not. so we would be counting it twice if we simply totted up the probabilities in the parallel branches without subtracting the cases where the connection is made anyway. This is where the negatives come in.

Yes you are correct there is more to it than I first thought. If q is the probability of failure of an element (no circuit connection) then the probability of success (a valid connection) is For a series connection of n elements. [math]{P_{success}} = \prod\nolimits_1^n {\left( {1 - q} \right)} [/math] and for a parallel connection of n elements [math]{P_{success}} = 1 - \prod\nolimits_1^n {\left( q \right)} [/math] My original thoughts led to [math]{P_{success}} = p + 3{p^2}[/math] Which is clearly wrong as substituting p =1 shows. Meyer had [math]{P_{success}} = p + 3{p^2} - {p^3} - {p^4} + 3{p^5} - {p^6}[/math] I did not get this when substituting q = 1-p in the above but got [math]{P_{success}} = 3p - 4{p^2} + {p^3} + 4{p^4} - 4{p^5} + {p^6}[/math] I expect Meyer is right and I made one of my silly arithmetic bobos however both my expression and Meyer's leads to a credible distribution running from 0 to 1 as expected as in the following spreadsheet.

ISO-Metric is not perfect either. Do you buy one kilogramme of bread or one loaf of bread? And while we are on this why is the kilo (prefix) gramme the base unit? And when we get to volume Is 1 cubic metre or 1 litre better?

Or maybe earlier than you think. https://en.wikipedia.org/wiki/Metre The first international agreement listed by 1889.

So what is the current century? and what was quoted (lightheartedly) from post#4? Edit That was probably due to the americans messing up good old imperial engineering units. "A pint of pure water weighs a pound and a quarter." Goes the old Rhyme. So a gallon of pure water very cleverly weighs ten pounds. How much does a US gallon weigh?

Has no one noticed today's date?

Why would the americans wish to regress in time?

Photobucket is a platform for adverts that do not support this site and a pesky nuisance to boot. Please place your images here in the thread.

I think it's called artistic licence, John. All mathematicians have it.

Yes you can use the t-test. The t distribution is defined for a sample size of n = 2 or greater. But remember to check your definition of the 'degrees of freedom' to enter the table I use degrees of freedom = (n-1) and sample size n , but some define it as n and in that case the sample size is (n+1).

What have you done towards this question so far? Since you have posted in mathematics, I assume it is the electrical connection that is causing difficulty so to translate from electrical switching circuits to mathematics Parallel connections are equivalent to the mathematical OR or the Union of sets in a venn diagram Series connections are equivalent to the mathematical AND or Intersection of sets in a venn diagram So all the switches can be replaced by their probabilities plus the appropriate connective AND / OR in a probability tree diagram. These can then be replaced by the mathematical operations + for OR and x for AND operating on the probabilities. For example Contacts 1 & 3 are connected in parallel The parallel connection containing {1 & 3} is in series with contact 2. So that branch has equation {p OR p} AND {p} {p + p} x {p} = 2p2

Cpg, your post is a welcome extension of mine, but one small point needs some clarification. Along with your picture, this could be taken to imply that the end of the cochlea is open. It is not open but covered or closed by a membrane.

One of my best fluid mechanics textbooks at university was Essentials of Engineering Hydraulics by J M Dake of the University of Lagos. So there is proper science conducted there somewhere.

Yes, as Sensei said this is incorrect. Due to radioactivity the uranium 'decays' into something else as described. This something else (Thorium also has weight) so only a small amount of weight is lost during one half life. Weight is not a good measure here, since the weight depends on location (Earth, Moon, Mars space). The mass of something is the same wherever it is. Finally radioactive decay is only one one many processes that half a 'half life' so is nothing special. For example the voltage of a discharging capacitor follows the same law and has a half life during which the voltage falls to half its initial value. No one asks why does the the rest of the voltage remain. It's simply that many processes take time to work through. Nothing holds the undecayed atoms stable, they will all decay in the end.

Perhaps it has something to do with the way our education system singles out wave/particle duality as something special and unusual that makes students stumble so much over the idea. But the situation is not unusual or special at all. There are many many situations in physics where no one model that we have is good enough for all situations but we just breeze through these without difficulty. Is there such a thing as a light inextensible string or do all stringa possess some weight and some stretch? Is water compressible or incompressible? Is air compressible or incompressible? Are the field lines between the paltes of a capacitor straight or curved? All the above and many more may be modelled either way - and we do so quite naturally depending upon the situation of application. So it should be with waves v particles. ~We should chose either waves or particles or some combination we call wavelets that best suits the situation.

Note the juxtaposition of these two posts in todays list. Finished a new song - Tranquility - composed by Daedalus How to make a nuclear bomb - closed by swansont

Yes this is all true, but misses important things out.

Not significantly. The energy in sound is small compared to the heat capacity of materials like the solids and liquids forming the ear. The standard atmospheric pressure on the eardrum is far, far greater than the pressure variations that are the sound waves. If the eardrum had to support anything approaching that magnitude of pressure difference it would burst. That is what the Eustachian tube is there for. To equalise the standing pressure on either side of the eardrum. Yes exactly, and then it is not exact, and is called a finite fourier transform, except the sample period is zero for an analytical Fourier Transform. You mean the interval of integration , which runs from minus infinity to plus infinity, not the sampling period. In fact the ear is a measurement device that measures an amplitude time plot or graph. But it has multiple sensors, each responsive to different frequencies. It does not perform a Fourier transform even a finite one since the sensitivity of these receptors is not constant. The finite transform it does generate is still subject to the vagaries if aliasing and windowing as with any finite time domain to frequency domain transform. It is also sensitive to 'crossover distortion' for sounds that whose frequency spectrum have significant components with the range of more than one sensor. The receptors themselves comprise fine hairs growing along the basal membrane, which is just ove 30 mm long) within the cochlea. The higher frequencies are detected at the end near the exciting membrane, called the oval window, and the lower frequencies at the remote end.

Fourier transforms are not enough. They provide an instantaneous spectrum of frequencies, ie a spectrum at every instant that (in general) varies from instant to instant. Real sounds have a time envelope (attack, duration, decay) which also characterises them. Varying these is used in electronic synthesisers to turn one basic oscillation into copies of many different sources.

Here is an image from the textbook I was referring to, written by a Fellow of the Royal Aeronautical Society. There is also a simple explanation of lift using Bernoulli, but not relying on fluid 'coming back together' on the following pages.

Nat King? If you have studied at flight school you should have been taught that the lift force is often not vertical and the vector diagrams for the different flying conditions (level flight, banking, diving, ascending etc). The sail on a boat generates drive by the same mechanism turned sideways.

I don't think any evidence to support this has been offered so far.

I am not convinced any charge regulation is required, but until MW research deigns to respond we shall all remain in the dark about the subject.

It's a while since I said +1 swansont, but that comment on Bernoulli was short and bang on the button. With regard to deflection, this takes place before the airfoil, since air cannot pass through the airfoil itself.