studiot

I think you need to peer a little more deeply into the mathematics.

6.4C above incoming ? SJ was looking for 14C That copes incoming air 7.6C or above. Currently the air outside has risen from 0C first thing this morning to 7C now. Perhaps that explains why what most estate agents in the UK would call a good sized double bedroom that tend to have 2.5kw wet radiators these days. Yes you could get preheated air from somwhere else and then you might get away with a smaller heater, but of course you would need another heater to preheat it.

What's spooky about it anyway ? It's spookyness certainly fails my ground pepper test.

You have a good memory +1

Humans love to classify thing into 'pigeonholes', but Nature rarely plays ball with our efforts. It is easy to think that abstract things can be fact or fiction. However one test of 'reality' is the question can it influence our real world ? The problem comes when I note that Harry Potter (fiction) has definitely influenced the world more than I have. It is said that the writings of Swift (a factual character) about Gulliver ( a fictional character) was all about the perceptions in our minds. And who is the more famous, Swift or Gulliver ?

Chapter 15 of the second book I recommended by Prof Mills is all about this. Ch15 treats the data, the observer, the observation, the 'watcher', the role of consciousness, superposition, what is included in the wave function and more. The maths is not as difficult as Joigus' although he still makes makes use of some specialist quantum notation - the bra and ket notation, identified by the < and > symbols.

I am skeptical about this. 600w is a very low powered heater and it depends upon the construction of the room and what you mean by warm. [aside] One thing I noticed about heat pumps is the impression that a source- to air pump (ie one which drive a non electric fan heater) generates an impression of warmth much more quickly than source -to-water pumps. This also applies to electric fan heaters and fan assisted radiators. They only heat the air and the effect dissipates very rapidly when the heat is turned off.

@iNow is correct, of course animals can see and moreover distinguish colours. Since there is a huge range of animals it would not be suprising to find there is a range of capability in this respect. You know that a dog will chase a thrown bone or stick but can distinguish between bones and sticks. Here is some scientific testing to show that they can distinguish some colours as well. Ok so you cup is red. Now that you have recorded this fact online that fact (and the cup) will still be there if the ground suddenly opened up and swallowed you.

Did you understand this ?

That is not a definition, that is one example that would satisfy (i expect) most definitions. But obviously there would be many examples that would satisfy one definition whilst not satisfying another.

Personally I think slit experiments are about the worst experiments for the study of quantum v non quantum effects. There are just so many factors to consider. There is the number of slits, the size of the slits, the spacing of the slits, the distance from the source to the barrier and from the barrier to the detector, there is the positioning of the detector, there is the thickness of the barrier, there is the 'sharpness' of the edges of the slits. What happens when there is no detector ? You can find the answer to this out with water waves, but not with light waves.

I am not a fan of Ryle. His cricket match example, for instance, suggests to me that neither Ryle nor the author of his Wikipedia article has ever played cricket in their lives. As regards you runner, yes I would contend that the runner did 'do' two things, which are different. It may not have been necessary to break to world record in order to win. Equally 8 seconds may not have been a winning time as another may have run faster. As regards the exam, the candidate can obviously decide (free will) to fail the exam. Conversely the candidate can decide not to fail the exam (but to try hard) Connected to this, and just like the runner, is another event. Pass or fail. I do agree that limiting causes to neurological impulses microseconds before an action is a very sever restriction of what constitutes free will. What about my comments on coercion and external constraints ?

Nice to have an engineer casting his MK 1 eyeball over the figures. +1

So, OP, what is your definition because I couldn't find one in your opening post. So somewhere along the line I did agree that it would be a good idea to understand it.

The ancient greeks allegedly threw someone of a boat into the sea for releasing the discovery of irrational numbers like Pi, they were so frightened of them. Today no one is suprised by them or the fact that you can easily get to them by drawing the diagonal of a square, even though you can't actually write the number down. The Copenhagen 'interpretation' was meant to avoid a similar crisis, but actually did not do so. I have shown a simple mechanical example which should dispel the magic and woo associated with decoherence. Obviously it is not exactly the same but then projectile mechanics and quantum mechanics are not the same and neither is the same as the diagonal of a square so the actual realisation is different in each case.

We now have a situation where the term 'free will' is important, if not crucial, in sevaral threads at once. It is difficult switching back and fore. I have not actually tried to propose a definition of free will, just analysed some of the consequences and implications. I have yet to see a convincingly comprehensive definition as a result of the tensions within the coupling and In one of these threads I posted a detailed analysis of this tension coupling. I do not actually have a definition but I note that others are trying to enforce theirs. So long as I know what each person is using I am comfortable to answer in those terms, but I reserve the right to point out consequent difficulties and omissions arising from the use of any particular definition. Coercion has been introduced. Coercion implies the existence of and introduces a second will which may or may not be free itself. Inherent also is the ability to predict. Coercion is usually associated with threats. All of this runs counter to at least one proposed definition of free will. If you want to introduce the subject of category errors then surely you should have the good grace to state what exact quote is involved. What category it is alleged to belong to and what category you think it should belong to instead. That would allow discussion to proceed.

No that part is not correct. Each of dy and dx are called differentials. dy/dx is one way of representing the derived function also called the derivative. It is a function, not a number. Being pernickety is not so important in basic calculus but becomes important in multi dimensional calculus.

In the late 1970s a programme of measuring total ice volumes by isotopic dilution analysis was started. In part this was calibrated against the sea level of a sea area that has seen no ice for thousands of years. Here are 1979 results. Im sure there are more recent ones, but I don't have them.

You are right in thinking time is a factor, though not quite in the way you perhaps imagined. Up to about the 1960s it was thought that the water was simply moved between stored ice in the cold periods, which lowered sea level and returned to sea water in the warm periods, which raised sea levels. This thus offered a simple calculation using the volume of the trapped and released water to estimate sea level change, the water simply moving from the land to the hydrosphere and back. However it has become apparent that the distribution of both the water and the land is much more complicated than this. Firstly isotasy plays a part. Unloading of the continental crust from the melting of the last Scandinavian icesheet has led to a rise in the land, relative to the sea, of 300m. A much more modest rise of 14m has been recorded with the corresponding loss of the much smaller Scottish ice sheet. Secondly the increased water places an increased load on the thinner ocean crust depressing it and reduci ng the sea level rise. Thirdly in warmer periods more of the water enters atmousphere and is retained there. Fourthly we have discovered much more recently that significant amounts of water is subducted into techtonic processes, taking many thousands of years to reappear via igneous outbursts. So the question should be when as well as how much.

That's good, so we can move on. On thing to note is that the mathematics of probability and statistics was not properly understood in their time. Startling though this my seem, both suffered from the shadow of Fisher, Pearson and Gosset through the end of the 19th and into the early 20th centuries. These men were not wrong but just dominated and thereby limited the subject until the mid and latter 20th century. The first physics text I know of to acknowledge that there are at least four significanly different meanings to the term 'probability' is in the Manchester Physics series Statistics - A guide to the use of Statistical Methods in the Physical Sciences by Barlow, published in 1989. I also note that there remain questions we do not know the answers to in Quantum theory, it is not perfect and has been continually updated from its inception. One of its founding principles, in Physics is that everything you might want to know, or indeed can know about the material world, can be derived from the wave function. But there have been bumps in this road. The first was the change from the original formula for the energy of an oscillator from nhν to (n+ ½)hν to introduce the so called zero point energy. The original theory was called the 'old quantum theory' and the replacement called the 'new quantum theory'. The second was the realisation that the original set of 3 quantum numbers (from the solutions to the quantum wave equation) was deficient and a fourth number not appearing in that equation was added. This fourth one was the spin quantum number. Who can tell what the next one will be ? Back to Wilczek He starts the section I post with his word 'Complementarity'. Now Yin and Yang or the idea of 'Two sides of the same coin' are thousands of years old. This is one idea the ancients got dead right. But they ancients did not have our mathematical sophistication to take it any further. We now know that what mathematicfians call duality and reserve complementarity for something different (I will explain in a moment) appears all over mathematics and the physical sciences. Even school mathematics. Some schools like to find practical demonstrations of maths and one such is an art or craft called curve stitching. How do you make a circle ? Well one way is to fix the centre and use a string and pencil to draw the circumference. Another way is to work you way round the circumference drawing tangents. This is done by stretching strings across suitable points outside the circle, all the way round. This dualism reappears in very advanced applied maths, in relativity, cosmology, engineering and other places using the duality provided by the relationship between an object and its boundary. But a line of strung tangents is not the same as a centre peg and radius, though they both show aspects of the same thing and each shows other things besides that are not shown by the other half of the dual. So it is with wave - particle dualism. Light shows neither all the characteristics of waves nor all the characteristics of particles, and you have to set your show up in advance to see either one or the other. You will never see both at the same time. It was these real observations in the material world about one or the other, but not both at the same time, that led Einstein to propose the word 'quanta' for the quantum characteristics and the rest is, as they say, history. OK complementarity Wilczek is a very talented physicist. Mathematicians use this term to denote mathematical objects that take complements. When we solve the Wave (differential) equation we are looking for solutions (there are an infinity of them) in what is known as the space if square integrable functions. That mouthful tells us the to form the square we are looking for functions and their 'complement'. Usually squaring something means to multiply by itself but Squaring such functions involves not multiplying by itself but multiplying by its complement. One result falling out of such a procedure is that order of multiplication becomes important because A*its complement is not equal to its complement*A. The Heisenberg Uncertainty principle can be derived from this. Telling you about the Physics, Wilczek describes how there are some pairs of quantities that when you measure them both the result depends upon the order of measurement in a similar fashion. In fact there is a similar theorem in the classical wave equation for a vibrating stretched string so it does not only occur in Quantum Theory. I think that is enough for the next installment, see if you can pick out these and any other important points from my Wilczek post.

Yes well said. +1

Depends what you mean by ' here'. I think the stance of many others (including myself) is that we are making choices all the time. All those choices are subject to different measures of free will, constraint and forcing. So my example student was continually making choices. Which one or ones did you mean ? Of course they did. Otherwise the implication of what yo uare saying is that free will requires a special sort of thinking cap that we don't possess. The use of the term 'free will' throught history has assumed that is not the case. Are you proposing this ? Again you are ignoring probability. The statistics I presented relies on the averaging of an indefinitely large number of such students.

Have you now found out how to use the quote funtion ? Thank you for answering my question. This is good that you have heard of them. We can proceed from there, though I am trying to avoid more advanced mathematics. ~~So for an ordinary, or for our purposes an algebraic equation, has a solution or solutions which are numbers. for example the solution to x+3 = 7 is x = 4; quadratic equations (involving the squre of something) have two solutions, also numbers. A function is the complete set of values (numbers) of a more complicated expression or equation. The solution or solutions (note the plural) to a differential equation is not a number but a function or functions. So here is a classical situation that leads to a quadratic equation. In the current Russia - Ukraine conflict both sides have 'dug in' below the level of high ground. So when firing at each other the projectiles need to clear the high gound, trees, walls etc and land below their firing point. The details of the mathematics don't matter, the details of the physical reality do. I have sketched the path on one such a projectile and set the origin of coordinates at its firing point . The path is a plot of a function. The function has a quadratic equation, so has two solutions. No one bats an eyelid when I say tha there is only one solution that intersects reality - the target position. Yet the other solution remains mathematically, and is always there even thougn its position is both behind the firing position and underground. So onward to quantum theory. The equations of QM are differential equations whose solutions are functions. Eminently much more complicated than my target practice example. But just the same, all the solutions are always there mathematically. And just the same the intersection with the real material world selects one particular solution and makes it real. But for some reason too many cry Magic, Collapse and other dramtic words. How are we doing are you following my drift ? If so I hav emore to say on some other choice terminology, particularly ones Wilczek introduced. Since you asked here is the book the quotes are from. You may also like this one by Professor Robert Mills, of Yang Mills Theory.

+1 In particular I find the idea of 'collapsing' of a wave function over dramatic. This was the reason for my question to Luc about differential equations and there is more detail later in this post, or my next one. Also I agree that the interaction is a far more sober term to use than observer. Thanks +1 I am rather concerned about the statement Because it implies that there is only one measurement, unless they are using measurement to mean interaction (observation) as above. My concern is that quantum interactions are not of the 'only one' type. That is the point of the Uncertainly Principle and the Commutator.

This is not an answer. It shows no reasoned development of your insulting and bald claim whatsoever.