studiot

Why do you not answer my questions? How can we have a dicussion if I am supposed to believe everything you say but you are allowed to ignore all that I say?

Because if it used a different particle it would not be an electron microscope. This is not a facetious answer, perhaps you do not know that there are many types of microscope? For example the Field Ion micdorscope uses larger particles than electrons. The optical microscope uses particles that, as far as I know, do not constitute a health hazard. So what are you actually trying to say?

Looking over this thread I see that several times I have offered friendly pointers and even made a few short unequivocal statements. All of which you have wafted away with an imperious wave of the hand and some rudeness. Considering your fixation with 'certainty', especially in mechanics, I am suprised that having been told that There are mechanical systems where the mathematics cannot be solved and There are mechanical systems where there are no mathematical formulae You have not enquired what I think these are. Are you afraid you might learn something? Did you follow up my pointer to the theory (famous in the history of Sscience) that matched your statements and ideas exactly? What do you actually mean by certainty? Give three warfarin tablets daily is certainty (if three are indeed handed out). But that could kill the patient with nearly 10 times too much warfarin if blue ones are taken instead of brown ones.

Since you eschew statistics and also estimation (which is not the same) what is you opinion of approximation theory? Worse, you are looking at mechanics through rose tinted spectacles. There are many problems for which the equations cannot be solved. Worse still there are problems in mechanics that have no explicit equations to solve. I am not saying that statistics is the answer to these, for it is not, but over to you for your opinion.

If you ever come to London you will have the opportunity to visit Kew Gardens. What many never see there, hidden away, is the Marianne North Collection. Marianne North was a rich victorian lady who used her inheritance to travel to exotic places. She was an artist, but she never sold anything, she painted purely for pleasure. Wherever she went she sketched and painted the local flora and fauna, many of which were unknown in Europe. These works were so good that they were adopted as the standard representation in botanical and biological texts and her style was copied almost universally. In her will she left the entire collection to the Nation and bequeathed enough money to build a fine housing for it. This museum was constructed in Kew Gardens. It also houses an unrivalled collection of (some polished) wood panels from every tree she could obtain material. Again these are an excellent basis for a collection of scientific samples, although again originall collected for their artistic merit. http://www.google.co.uk/search?hl=en-GB&source=hp&q=marianne+north+gallery&gbv=2&oq=marianne+north&gs_l=heirloom-hp.1.1.0l10.1156.3578.0.5719.14.13.0.0.0.0.250.1984.0j4j6.10.0....0...1ac.1.34.heirloom-hp..4.10.1984.lyvcuc08XQk

I was reminded of picks theorem. Google is very artsy about this http://www.google.co.uk/search?hl=en-GB&source=hp&q=pick%27s+theorem&gbv=2&oq=picks+th&gs_l=heirloom-hp.1.0.0i10j0l2j0i10j0l2j0i10j0l2j0i10.1500.4000.0.6531.8.8.0.0.0.0.203.1078.0j6j1.7.0....0...1ac.1.34.heirloom-hp..1.7.1078.b1U92oOu8rY

That's an interesting question because either will produce a wavelength and a bit. This is a bit like asking how many decades are there in 0 - 10. I really only posted this to show that I am not picking on swans.

So by definition there is more than one answer since there must be at least two answers to superpose.

Me too +1

Is the cat dead or..................... or if you prefer something mathematical how many solutions has the equation x2 + x - 6 = 0

I am sorry you do not wish to learn about things you know naught about. I have wasted enough time on this thread.

OK so smileys over we can return to rational discussion of the topic. Robowhatsit, there are many uses (and abuses) of statistics. You seem to have embraced the so called 'clockwork universe' in your thinking. If you have not heard of this you should look it up, it was a milestone in scientific development several hundred years ago. In its day it was a fine concept, but it has been surpassed in the theoretical world. But back to the practical world. I have indicated where the proper use of statistics improves the quality of production in industry and commercial activity. But it also has been brought into the design process so that now it is fully integrated. You may, or may not, have heard the phrase 'Limit State Design'. It is the philosophy that underlies modern design codes and actual practices. It works like this. We can discuss this rationally in an adult fashion if you like or not at all. Take a bridge (design). A bridge has the longest design life of any man made artifact. So what are the loads you are going to design for? and how are you going to impose them on your design model? You cannot predict what will attempt to drive over that bridge 100 years after your death. What will the bridge be made of? How can you ensure that every last scrap of material will possess at least the strengths you specify? And what of durability and climate and possible ground movements? What happens when the bridge is 100 years old and the materials of construction have deteriorated with age? I will grant you something that no designer has ever possessed or is ever likeley to possess. A perfectly accurate model at the time of design. How are your calculations coming along?

Would you like it delivered to the south pole?

Six bags? Do you have any idea how much 2 and a half kilotonnes is?

Go , how?

Since you mention concrete, this is a good subject about which to discuss statistics. Let us say you are in charge of a concrete production plant outputting 2500 tonnes of concrete per day. How do you make sure the concrete is up to specification? I should tell you further that the concrete is particularly high specification, because it is to provide the runways for jumbo jets to land on and failure of substandard concrete could lead to landing accidents with subsequent loss of life and runway functionality. This is a real world problem I have faced, and met with success, in the past, with proper use of statistics to help me.

In research, yes. But with the greatest respect, in the quality control situation we have been discussing there is no room for art or pattern recognition. A batch of product either falls inside or outside of the quality control limits, as calculated in a particular way. This twist in the tail is more important than might at first appear.

Perhaps you have a poor maths (statistics) teacher. A good strategy would then be ask lots of questions about the whys and wherefores, rather than branching out on your own with what appears to be an attack on statistics itself. I would agree that there is a great deal of poor or even false statistics about. There are even books, radio and television programmes about that very observation. But neither poor teaching nor poor practice invalidated good teaching and practice.

Perhaps you are new to discussion forums. So this is meant to be helpful. Each time I have extracted the part of your post I wished to discuss and put it in a light blue quotes box. Exactly as I have done above these words. Then I have made my point about this extract. Consider the following: A manufacturer of medicinal pills requires to have just exactly the correct amount of the correct drug in each pill. So what to do? There is only one certain way to ensure that every pill has the correct amount of the correct drug and that is to test each and every pill. Unfortunately testing destroys the pill. So having tested his pills to perfection the manufacturer finds his patients dying for lack of pills, since they were all destroyed in the testing. Alternatively the maufacturer can test some of the pills and hope the rest are correct. But what does he do if they are not? And how certain can he be if the test pills are OK, that the rest are OK. That is precisely the situation I meant in my first post for the proper use of proper statistics.

Yes, of course you can use your formula. But not all future questions will be the same so I hope this thread has helped you understand more. In answering questions I find it a good idea to list all the information provided as we did here and then list the equations that might be relevant and see how they match. Go well in your future studies

You made definitive statement, I addressed it by asking a question.

I like to try to keep things simple and address one point at a time. I asked a very simple question in my post 4. What is a very simple answer, please.

With no acceleration, that is constant velocity. Distance = velocity x time s=ut; initial velocity ( = u) = final velocity (=v) If there is constant acceleration ( I will use f for its symbol) then we have sevaral formulae, you should have met before reaching the formula you quote. v = u + ft s = ut + 0.5ft2 v2 = u2+2fs The first two contain time, which we do not know but the third is the equation I was asking for. Now the acceleration (f) = g, u = 0 and s = 3.6 So substituting we have your formula v2 = 0 + 2g (3.6)

Voila you have u=0, s=3.6, What is the acceleration during the whole of the downward journey from A to the water? And then we return to the formula I asked for in post6

And if I could prove the opposite, without mathematics?