studiot

So you used my agreement with you on the one hand to support your conclusion that this bias is somehow bad - a conclusion on the other hand I disagree with. That's what I call twisted logic. Both swansont and I have asked you a question Why does it matter ? Please answer it. I have also noted that your first link does not work I note that the second link does not take me to the referred material either. Please brush up your support links.

I agree with you. Scientists are biased towards the easy way. So what? Why shouldn't they be ? That is why I said it is not suprising. Here is a true concidence. I initially responded quickly because I had just quickly added something in another thread and was ready to finish when you posted, not because my response was hasty or dismissive. Is the time lapse to this post more to your liking ? I have not had the time to try your link and all I get is Bad Gateway Error. So I am stuck with the graph you extracted (probably the most important part of the article). I am a bit worried by the quality of the investigation for instance according to the graph X does not occur at all in 65% of physics formulae. Y does not occur in 100% of them. Cotangents do not occur. So take a typical maths formula that of resection. Two basic methods of solution are available, those involving sin and cos and those involving tangent and cotangent. Tables of the first 3 functions have long been readily available, but there are few cotangent tables on offer. Tienstra (the tan/cot method) is actually easier to work, but the sin/cos method has become ingrained because of the availability of tables in the past. With modern computers that should not matter but tradition dies hard. But what exactly is a 'randomly' generated scientific formula ? Surely there will be an automatic bias towards common and commonly available functions ? The plot surely bears this out with so few functions listed. Also how did the study treat composite function. For instance the trigonometric pythagoras theorem has sin2, cos2 and tan2

Did you catch the irony of my reply to your actual question ? In plain language it means that scientists, like acounts and others, prefer to calculate the easy way. So the curve is not suprising..

Is it a coincidence that on the same day someone else is posting here about the P v NP problem in computing ?

Interesting thank you +1.

Delta T = Final temperature - Initial temperature = 300 - 450 = -150 which is negative as I said. But you seem to have used it the other way round (450 - 300) when you substitute numbers into the formula.

Since this needs just a short reply and @Halc needs a much longer one I will deal with this first. However How would you manipulate that ruler since it is moving relative to you? Perhaps you could do it by drone if the relative movement was slow enough. But the spaceship in this example is moving at nearly 0.8c. Also you have to take into account the time for control signals to pass back and fore. What I mean here is that you or someone else has to straddle the spaceship (ie be comoving with it) and run the tape measure over it. That does not have to be done at the flyby. All you need is that someone does it and records the measurement as the proper length. As the ship flys by at some point you will actually be perpendicular to its direction of motion. That is the moment to make the measurement and with a photograph you can get both ends at once. That way you will be observing in the spaceship direction of motion and so be witnessing the shortening. Length or distance measurement is differenet from time measurement as a a clock will retain a permanent record of the time dilation after the eventful journey. This has been experimentally verified with aircraft and satellites on Earth. But the spaceship does not retain any evidence of its length contraction and measures 100m again when it returns to Earth and docks.

Good point +1 Somewhere in the beginning of this saga superconductivity was invoked. Yet Cooper Pairs were not mentioned. I wonder why not ?

Surely delta T is negative ?

Why in the world do I bother since you do not respond to what I write but to some made up fantasy you substitute for my words. I wrote How does that become a head on collision course ? I accept that this But I did say So yes you can measure the length of an object in a frame moving relative to yours, but the measurement will not be the proper length. As far as I can tell it is impossible to directly measure the proper length of something moving relative to yourself. If you think that is possible please describe how it might be done. So do you know what stadia are ? That sort of resolution is silly. I referred to passing at close distance. I have spent the last 53 years since leaving university measuring distance with stadia in telescopes. Distance or length measuring marks on the reticule of optical equipment started to come in around 200 years ago. I will elaborate for a more polite and understanding response.

Actually not a bad thought at all. I don't know enough cosmology to know where one might go looking for dark matter it may just be too far away. There was a Ray Bradbury Book entiltled The Golden Apples of the Sun Which had a similar idea but to gather solar material to start a fusion reactor. This was known to be really not practicable even then.

Thanks for that clearer picture. +1 A really disappointing non scientific response. Density and specific gravity are interconvertible and in the correct circumstances numerically equal. Of course temperature also plays a part but we are then talking of several decimal places and you have yet to mention the effect of sample temperature on your measurements. Since you could not find all my alloys, my mid 1970s copy of Lange gives the following information, including wt % I no longer have access to up to date handbooks to compare with. Finally this is the fourth and last time I ask my most important question, which has been steadfastly ignored.

The operative word being compute, not measure. You have just told me that the proper length of a ship is 100m. Since this is only defined in the that ships's own inertial frame, where we are agreed it appears at rest, and will be different in any other frame and measured as such by an observer in that frame. For instance Say I have a super duper camera that is equipped with length measuring stadia. From my observatory on a planet, where I am stationary, I monitor the ship's approach and at the instant its centre passes my telescope, I take a photographic mesasurement of the length of the ship. I observe 60 m So in my frame the length of the ship is 60 m. So yes if I am also measuring the ships velocity, in my frame, I will be able to compute that it has a length of 100m in its own frame. So yes I can compute the proper length, but I cannot measure it in my frame. I mentioned a while back that confusion over the difference between length and distance is the reason why the term 'proper' is depracated by some authorities and why Wikipedia says Incidentally in this world of hurry up and short cuts far too many make the mistake of saying The velocity c is invariant. It is most decidedly not.

Don't worry, this is really good as these little things (like the brackets) are reallyhelping to gauge how to present my material. Note I said that fig 2 is an example of a function that is given by a mathematical expression or formula, unlike fig 1 which is a function given by a table of corresponding values. This was the important part. I slipped in the brackets in the text to find out what would happen if you saw them, The same with the square root symbol you obviously recognised. The whole V shaped plot is the function, not just any particular value. Remember you can pick any value on the X axis or the independant variable and find out what the value of the function is by reading it off on the Y axis. As with fig 1 the axes form a necessary part of the function. If you are interested the posh mathematical names are:- the X axis is the domain and the Y axis is the co-domain In this case the square root of x squared is of course x for positive x and -x for negative values of x. These two graphs are also meant to lead back to 5the things you can do with numbers expanded which is for next time. Fig 2 especially was only a very small part of the overall post. How did you get on with fields etc?

Fig 2 is just a function between numbers. The X axis is the independant variable and the Y axis records the value of the function which is The square root of x squared. I was going to do more but it is a purely numeric example of a function. So no days no temperatures all non physical. Since I used value as a general term that includes many things that have a value, but not necessarily a numeric one, I use magnitude as a purely numeric value. That allows the value of a vector to include both the value and the direction and for us to do different appropriate actions with each.

OK so scalars. I am going to use a different kind of fraction called decimal fractions as I am trying to avoid more complicated numbers such Every night I jog 1 mile for exercise. Or I jog 1.6 kilometres. The point is that the magnitude of the distance I run is the same whether I measure it in miles or kilometres. That is why I used value not magnitude for my first use of numbers. Two different numbers for the same magnitude. In fact we can convert mile to kilometres by multiplying by a scale factor or scalar. Kilometres = 1.6 x miles. In this case the scalar is a scalar constant, which means it is always 1.6. In this use of a scalar we call it a coefficient of the distance. Coefficients can be much more complicated than a simple numeric multiplier, but they always multiply the quantity of interest. Speaking of quantities, remember I quoted some temperatures outside my house ? Well I have drawn a graph of these for a few days. Fig 1 The graph has two axes conventionally called the X and Y axes. The Y axis give a daily figure for the temperature and the X axis tells us which day we are talking about. This was why I asked if you understood graphs. So please tell me if this is understood. In order to describe the physical quantity 'temperature' I require only to quote a single value on any one day. A physical quantity that require only one piece of information or magnitude to specify it is also called a scalar. So temperature is a scalar. But this time it has a different value on different days or it varies from day to day. So we call it a scalar variable Further we call temperature the dependant variable since its value depends upon the day. We call the day the independant variable since we can pick choose any day to suit us. This graph represents a function which connects a dependant variable to an independant variable. In Physics the independant variable is very often time and is also called the running variable. The function is The whole graph, including the dependant and independant variable axes and the plot of every value. The relationship between the dependant and independant variables is given by a table of values in the first case, but more commonly it is given by a formula or rule as in Fig 2. Fig 3 takes us back to temperature again. Here I am showing a plan view of a bucket of water into which I have stuck a hot poker. The concentric circles show contours of decreasing water temperature away from the central poker, just as we discussed contours before. A field is an region of space, like the bucket of water, where we can assign a quantity value to each and every point in it. In this case it is a temperature field and since temperature is a scalar it is a scalar field. Going back to distance, my nightly run goes around local paths at random. So it only has the magnitude of 1 mile. London is 150 miles east of me. This distance value has a second part - east, which specifies a direction. Quantities that have two parts are called Vectors. Most physical vectors have a magnitude and a direction. So distance can be a simple scalar as in my jogging, or it can be a vector as in the distance to London. You will come across other quantities that lead a double life like this such as velocity. In some circumstances we can place a vector at every point in some region of space, like with the temperatures in the bucket. Suprisingly such a placement is called a vector field. I have shown one such vector field in fig 4 concerning the flow of water in a river. The magnitudes of the flow (ie water speed) are given by the lengths of the arrows and the arrows themselves show the direction of flow. This sort of flow when everything is smoothly in step is called laminar flow and shows speed variation from top to bottom. Fig 5 shows what happens over a rough bed. The water turns turbulent and though the overall flow is still left to right, the water now moves up and down and sometimes even backwards as shown by the arrows. Also the even gradation of water speed is lost. Any questions ?

Quick response. I didn't do negative numbers - or many other types. I did just enough to open the door to my next bit which is half prepared and hopefully will help with many of the technalities Mordred is putting up. I'm glad you picked up on my 'difference between equality and identity' This and my other number operations, including inequalities, will be fleshed out a bit next. But remember that my goal is not to make you a good calculator -- Others will already have crunched the numbers for you. Yup that's good enough. We will come to scalars next. Welcome back. 😀

A further thought. I don't know if this model has an internal cooling fan or fans. These are computer type fans whcih ar not designed to be lubricated. They can sometime develop a rattle due to unbalance aused by dirt. The effect will slowly exacerbate itself as sloppy bearings wear. Sometimes cleaning is enough otherwise the solution to this to replace the worn fan I'm afraid. Rust/ corrosion on the case meantsw that exposed metal has become chemically active and must be passivated before other treatment. If the panel can be removed this cna be done with fine emery paper. If not a fibre glass pen can be used, obtainable from photographic and electronics retailers. Alternatively a small lick of chemical passivator can be painted on. Use phosphoric acid (jenolite) from auto repair places or concrete cleaner from builders merchants. or hydrochloric acid (drain cleaner). Do not use battery acid (sulphuric acid). Wear rubber gloves. After passivation the paint can be touched up with either clear varnish or the correct colour.

I've never looked inside a play station but I am assuming you want to lubricate the dvd mechanism ? Singer oil is a good light machine oil but tends to attract dirt and dust so is not really suitable as most parts will be self lubricating if clean. Firstly nylon or other plastic gears, worms etc should not be lubricated. Secondly parts should be cleaned before any lubrication, air dusters are good for this. Plastic slideways, door flaps etc can be lubricated with silicone spry lubricant and there may be one or two points where a tiny spot of silicone grease would help

It says exactly what I wrote in the clearest manner that I have come across. Which is true in one frame and one frame only. and Which is true in all frames and therefore invariant So the Wiki article makes a clear distinction between proper length and proper distance They are not interchangeable.

Did you not read the very clear Wiki article I referred to ? Proper length only exists in one frame; it has no meaning in other frames. So it can't be invariant. Proper distance, however is an invariant that exists in all frames.

You are misreading my point. Yes, but if you are told what its constituents are then you have more information than just the overall density. If the only information you have on a sample is its density it is impossible to determine the alloy. This was why I asked earlier about the spectroscopy part of the original OP picture. To date I have received no answer to this question or the very natural one of What else do you need ?

SG alone not going to be enough information. For instance looking at random in Lange Invar, Cyclops 17 and Ferro Nickel valve steel all have sgs of exactly 8.0. Yet they have very different compositions. Many others cluster in the region 7.8 - 8.2

This is why I said it's tricky and also why many authorities these days have veered away from the the categorisation 'proper'. Proper distance is an invariant in all inertial coordinates. You have defined proper length which exists in only one particular inertial system. https://en.wikipedia.org/wiki/Proper_length

But you said the ship is stationary in its own frame. So in which frame are the two planets 2Ly apart? The ships frame or the planets frame ? I'm questioning this because it is not as easy as you initially made out to explain this and parts of your explanation seem to me at variance with each other.