studiot

Nice taeto, well done. +1

Sorry one small booboo. The Kreutz stainless was 0.4% carbon (now corrected on the last post)

Hardness is basically a function of carbon content. Hard steels, like tool steels are basically those with a carbon content of around 4% or greater. Most stainless steels are austenitic with a much lower carbon content. This leads to a more ductile steel. It is possible to increase the hardness of stainless - so called surgical steel is stainless and hard enough. I don't know what level are hardness you are seeking. Here are some actual results from a paper I wrote years ago, following a materials failure investigation. The (just under) 0.4% carbon stainless steel achieved around 575 Vickers. Pretty hard by most counts an about in the middle of the tool steel range which goes up to about 750 Vickers. However if you note the fracture toughness of this steel (it was martensitic) it was hopelessly low - equivalent to a pure aluminium can. Thus the steel was well hard enough but cracks could (and did) propagate due to the flow fracture toughness. The steel was too brittle.

If this is the only thing you are asking, please tell me what you think a shadow is made of? That should avoid contentious isses.

To appreciate energy in Science you need to understand the terms object, process and property. Energy is a property of object or process. The objects may substantial or insubstantial (ie theoretical or virtual). If the OP ever comes back we can develop this further.

Forming or foaming?

[math]\sqrt {\left( {A - B} \right){{\left( {\frac{k}{{r\cos \varphi }}} \right)}^2}} d\varphi = \sqrt {\left( {A - B} \right)} \left( {\frac{k}{{r\cos \varphi }}} \right)d\varphi [/math] [math] = C\frac{D}{{\cos \varphi }}d\varphi = E\sec \varphi [/math] Which is a standard integral.

Well before the mods shut this thread down as going nowhere fast, I would like to offer my thanks for providing a thread that lasted at least 6 pages and where some learned things new to them. I hope that you did as well, though I am fearful you did not. +1 for that and future encouragement.

Such as stated by Wikipedia here We both know that. I was just observing that users of finite differences expect the finite difference to be other than zero. This is a mathematical operation, not a physics or engineering one though it is (was) much used in both.

No apology needed, it was not meant as a complaint. Yes Jehovah's etc are basically a one trick pony show.

I thought it was you started a thread entitled does the universe have a centre or similar. I apologise if it was not you. Please take the rest on board.

I was debating with myself whether to start a new thread in answer or leave it here. I see the moderators have moved this thread to General Philosophy, where IMHO it sits much better. This also give me more latitude in my reply. So I will leave it up to the moderators if they want to spin it off at this point. So here are my thoughts on Thermodynamcs, Quantum Mechanics, Determinism, Indeterminism and Free Will. Consider the equation 3X = 15. This provides an example of determinism. X is completely determined by the equation. Mathematically there are no degrees of freedom. Now consider the equation 2X2 + 7X = 15 This is indeterminate without further information since there are two possibilities for X, although we can determine either or both with further information. The indeterminism in Quantum Mechanics does not arise in this way. QM indeterminism arises on account of the non zero commutator which means that operation A followed by operation B produces a different result from operation B first followed by operation A. This type of indeterminancy cannot be resolved by additional information. In other words we cannot even in principle resolve QM indeterminancy. Spectroscopists observe this directly in the 'smearing' of spectral lines interpreted as the time for an electron to actually emit the EM radiation (delta t) correlated with the frequency smearing (and thus the delta energy term in Heisenberg). The delta E and DeltaT are the operators referred to above. This yields a small continuous range of possible answers. Infinite because the range is continuous. Where this is sufficient or not to introduce free will on a mathematical basis, I can't say. I offer Thermodynamics first because it is a much simpler example of a subject that includes determinism and indeterminism but does not include free will. However it sets a pattern for what follows. Thermodynamic theory divides the universal set, applicable to the system under consideration, into the system and the surroundings or rest of the universe. The system is endowed with state variables, which are in principle completely deterministic. So the state variable called temperature must have one defined value throughout the system, and the energy of the system is a defined total of the whole system. In the surroundings there may be a defined amount of energy available or it may be so large that in is effectively infinite and therefore indeterminate. The temperature of the environment may be defined or it may be meaningless as it varies from point to point. This meaningless condition is another form of indeterminancy. So far I have descibed indeterminancy that has a value, just that we can't determine it. Finally for Thermodynamics it offers the idea of the exchange variables as the means by which the system can interact with its environment to change the values of its state variables. It can for instance change its system temperature by loosing / gaining heat from the environment. The process is deterministic. OK so we can draw Venn boxes to show this approach, let us try it to include free will. I have again drawn a universal box divided into system and rest of the universe. Because the situation is dynamic, not static, something happens. There can be no free will if nothing happens. For something to happen it requires an agent as well as the thing that undergoes the happening. I have added a further box extending into both partitions and labelled it agents. The agents must be either part of the system or part of the rest of the universe. Since this box extends into both partitions I have labelled the part of the agents box in within the system as A and the other part as B. Now we should consider what agents are permissible in A and B. Consider an agent that produces a defined effect. The effect is defined to act on the whole system (or the system is defined to be all that which is affected). So if the agent is included in Box A it acts on itself as well as the rest of the system box and is therefore determinate and not subject to free will. If the Agent is included in Box B it need not act on itself so may be invoked/applied or not by a free will process. This "almost a Russell paradox" is enough for now but it is also instructive to examine other cases.

Not sure how any of this is a response to my post? I have not disputed that some turn to religion in straightened times, but I did mention comparative figures since I have personal experience of some who turned away for the same/similar reasons.

Note from the Frame Police, room 101. All points and frames have the equivalent priveledges. It is politically incorrect to think otherwise. I think you are still trying to impose a static model on a dynamic situation, like with your centre of the universe question. Static models are simplifications that are inherently less complicated and carry less information. That is why they are useful when we can use them. Dynamic models are more general.

How many more turned to it because of a traumatic event in their life? I hear there is a big turnover. . . Not being a religous person, I know of no comparative figures do you? If you can source any such figures, what conclusions do you draw from them?

A virtual observer 'looking/working backwards through the chain of events' perhaps. Such an observer would not need to be at the point of the BB, so long as she could calculate correctly. No because we do not (can not) know the motion of that point relative to subsequent events. That is what light cones are all about. Note that light cones only encompass points directly causally connected. Each such point will have its own light cone, which may encompass points both within and outside the original cone so establishing a chain of events is tricky to say the least. Perhaps Marcus may be able to offer more about that.

Mathematical modelling is a huge and vastly incredibly important topic. It is also incredibly varied. Dynamic similarity is about using or not using the same equations to compare the activity of two systems. You mentioned the falling leaf. Would you use the same equations for a leaf and a handful of buckshot? How about the leaf or buckshot falling through treacle? The point here is that the are no equations in Physics that produce the values of all the necessary coefficients for each situation. Some are available and dynamic similarity is what that is all about. But some have to be measured. These coefficients determine what actually happens. Have you used a simulator as a form of modelling? I did a lot of this in my applied Maths degree - it was great fun. But another area of modelling is finite element analysis. Here we establish a grid or network of points in space or on a graph (like my avatar) And calculate values of the mathematical property of interest at the grid points. Now we don't usually use the actual mathematical formula from Physics for this, but a much simplified one or the calculation may be to onerous, even for todays supercomputers. We than have to decide how well our calculations will match the 'real' values by 'calibration'. We have to decide for instance whether just the values match or the values and first derivatives match or the values, first and second derivatives and so on. At every bounday (eg the beginning and the end) we have to invent fictitious points , values and derivatives because there are no real ones outside the boundary. We can also sometimes call on the fundamental theorems of calculus, Gauss's , Stoke's and Green's theroems to link boundary values to interior values and reduce the calculation burden. This is then called boundary element analysis. >>>>>>>>>>>>>>EDIT>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Here is a very simple example of mathematical modelling and (non dynamic) similarity. I have a lawn of size Lmetres by Wmetres. I pay a contractor £p per linear metre to trim the edges and £q per square metre to cut the middle. My neighbour has a lawn twice as wide and twice as long. What factor should be applied to my costs to calculate the cost for my neighbour's cost if he employed the same contractor?

The 'because' is just wrong. What we need is sufficient determinism to have free will. Even if quantum randomness plays some role in the brain, it at most would disturb, breaking the determined chain from sensory input, processing in the brain, and the motoric output. It would explain 'jerks' in our behaviour, not e.g. acting on grounds. But I am proposing something further to enable rational analysis of the situation. That is the separation of the system that undergoes whatever process is under consideration and the agent that applies/causes/enforces that process. The system can never have or contain "free will", by definition or the specified process may not occur at all. The agent may be subject to practical and/or physical constraints but must be able to enforce some aspect of the process. This need not be an either-or situation, (to enforce this or a different process) it could simply be a rate (shall I eat my box of chocolates at one a day and make them last a fortnight, or two a day and finish the box in a week?). I agree that all of us (including empleat) have been rather lax is reading and writing about the actual question asked and the issue of free will seems to have taken over from QM. So empleat please clarify which you are more interested in?

There is currently a discussion going on where a mathematical modelling process is emerging. Perhaps you could use it as a real example for your question? https://www.scienceforums.net/topic/115474-table-tennis-lawn-tennis-badminton-smashes/?tab=comments#comment-1062510 In you box partitioned into system1 and system 2, how would you introduce dynamic similarity? There is a whole detailed (mathematical) theory of this. How also would you introduce statistics and probability, for example in a Latin squares experiment?

That is not incompatible with with I said, except that you can only smash along a direct line. Other trajectories would bring other factors into play. That is where the skill of the player comes in. The underlined is inaccurate for most table tennis play. As I said it occurs in a straight line in smashes. In other situations spin plays a major part. Spin also complicates tennis but less so because as you mention the inertial forces (weight) are a greater proportion of action. Nevertheless top tennis players can impart significant topspin, sufficient to lift the ball over the net in a powerful drive. I can't do this in tennis but can in table tennis, where the result is even more significant. Neither of these strokes are considered smashes. No I don't agree. A ballistic trajectory is a downward curve under the action of gravity. Spin plays a far larger part in trajectory modification (The Magnus effect).

Well my observation is that both prash and pavel are right and wrong, all mixed up. But +1 to prash for observation and politely sticking to his guns. The three games have some features in common and some differences and pavel correctly highlights some of these. Each game is a combination of skill, the peculiarities of its rules and brute force. These work very differently in each case. The smash is a common feature and employs brute force to nullify any aerodynamic effects to ground the projectile in the target area, making return difficult. The projectile travels in pretty near a direct line from racket to target ground there is no sideways or up and down movement in the air from that line due to the aerodynamics of the shot. A consequence of this is that there must be a line of sight or direct line from projectile to target area at the moment it is struck. Many shots in all three games occur below the top of net level where this is thus impossible. In simple terms the projectile must be high enough. In badminton, as Pavel points out, once the projectile is grounded the rally is over and return forbidden so that is the end of it. Alternatively the oppononent must hit the shuttle before it strikes the target area. In contrast, in table tennis the opponent must not hit the ball before it strikes the target area. However the top of the net is low compared to the players so there are many opportinuities to effect a smash after the ball has bounced. Further the opponent may strike the ball a long way back from or to the side of the table. Much table tennis play is done from this position. So yes prash is right that top players can and do countersmash in table tennis. In tennis, by contrast, the opponent may strike the ball before it bounces (in badminton he must) so can take the opportunity to find a direct line to the target area. This usually occurs to a high ball and the smash stroke can get right on top of it, driving it hard down so that it bounces very fast back (or sideways) from its strike of the target area out of reach of the opponent. The direct line to smash back may well not occur until the ball is well into the crowd. So tennis smashes are difficult to return, let alone to smash back.

Boron (salts) is such a minor element in the makeup of the Earth's crust that there is not much literature about it. However there is some in sea water leading desalination in modern times to address the problem of excessive levels, exceeding safe levels (the stuff is poisonous) https://www.sciencedirect.com/science/article/pii/S0011916410003486 If the OP were reboiling sea salt, which many use in the kitchen, he would have the boron content of that sea salt sample. Of course, simply throwing it into a pot and constantly reboiling would not increase its concentration as the only mass loss is the water vapour. There have been some American studies of atmospheric boron, transferred from the ocean to the atmosphere. https://www.google.com/search?q=atmospheric+boron&ie=utf-8&oe=utf-8&client=firefox-b

Well I'm still waiting for you to post a viable question or discussion point instead of rambling round the roses. 3 lines of proper text will do fine thanks.

Except this was posted in quantum theory and the answer asked for in terms of quantum mechanics. I did consider suggesting the thread be moved to philosophy are you going to do this? I actually prefer my hard science approach. I find the difficulty with the above is that is mixes up the determiner and the determinant. Hard science separates these to useful effect and result in the analysis. I see a significant parallel with Thermodynamics where failure to perform exactly this separation so often leads to failure to get valid results in that subject.

Slipping the golden ratio into spatial volume calculations is a neat trick. Do you also cast spells on a Sunday?