studiot

Physics ? Maybe you are looking at the wrong Science ? I am not a social scientist but I understand that (early) Christianity is scientifically classed as "Primitive Socialism". How dows that play out with your definition of Socialism? +1 by the way for actually offering a definition of a term you are intending using. This necessary courtesy is all too often omitted.

So far I have refrained from commenting on this thread because it already involves some rather juvenile mud slinging, as all too many global warming threads seem to attract. So +1 for bringing some SCIENCE to the table. I agree totally that the statistics so far presented are wholly inadequate for the job, especially when the theory of time series analysis goes back to the early 20th century and even a bit beyond. I don'r think LOWESS analysis is the way to go though, it is very short term. I would suggest a properly thought out moving average analysis , based on my initial guess of using a 10 year average, would definiteley show the relatives sizes of Mistermack's smaller rise to the later possibly accelerarting rise in the posted graphs. I would observe that including error bars on these plots has more to do with the fancy graphics abilities available nowadays at the push of a button, than the statistical purpose of the graphs. In my opinion such stuff actually obscures the trend lines. If ssomeone has a table of values I would be happy to turn them into a proper time series analysis.

I rather thought that I was doing a pretty good job of ignoring. 🙂

And what did you make of "Riemannian Calculus" ?

I wish. Unless, by using the plural of definition you mean that science has multiple meanings for many important words and concepts.

Yes I agree but as I have discovered, there is much more to this than that observation. https://opendatascience.com/ai-sentience-friend-or-foe/

You seem to be wanna-ing ? the aspects of philosophy that are not really amenable to scientific analysis. Remember this is a scientific site and we are supposed to be discussing the scientific aspects in subjects that are not directly scientific. You might be better off asking for these in an arts forum for instance, take Love. In Suits there are many scenes where the 'love' Donna has for Harvey is explored. In one she says " I don't love him like that , I love him like a brother" So remember many words do multiple duties so it is a good idea to specify which one you mean at the outset of any serious work.

Many thanks for this thread and introducing me to a whole new area of concepts. I had never heard of the mirror test before, but looking into the subject I see that much thought has already gone into the subject area and I have much to look into. +1

Hello, Steve and welcome. I read your article and I must say I was pleasantly suprised as it addressed several thoughts I had when I initially saw your thread. I particularly liked the idea of defining what you mean by a rocket. So +1 for a good start. Now for some comment. Unfortunately it is difficult to say much more without any context as to what the article is meant for. [ Like TheVat I question terminology a bit it is hardly in the format of a (scientific) paper which is why I refer to it as an article. ] You have posted this in Homework Help so I assume you have read the rules for this section of ScienceForums. But you haven't indicated what his article is meant for and at what academic level ? Tell us a bit more so interesed members can offer better help.

12 Area units is correct Here is my derivation, avoiding equations one way or another. I use the property of rectilinear similar figures that the areas are in proportion to the squares of corresponding sides. So firstly complete the rectangle ANIM by adding 3 extra squares, making 6 in all. DH is a right bisector of two sides so passes through the centre of the rectangle at K AI is also a diagonal of the rectangle and more importantly bisects CE. Thus CK is equal to KE. Call this s. CK is one side of the triangle CKJ which we are given has having 1 square area unit. Triangle CKJ contains the same angles as triangle AMI since AN is parallel to MI. Hence triangle CKJ is similar to triangle AMI., with side CK corresponding to side MI Since the length of each side of a square is 2s and side MI occupies 3 squares its length is 6s. So the area of triangle AMI is (6)2 times the area of triangle CKJ or 36 area units. Triangle AMI is exactly half the rectangle ANIM. So the total area of the rectangle is 72 area units. The rectangle is comprised of 6 squares so each square has an area od 12 area units as required.

So AI is the diagonal of a rectangle 3 squares wide by 2 squares high and K must be the centre point of this rectangle. So by no equations I assume that I can use formulae you mean no equations need solving ? So I can say the area of this rectangle is 3 squares x 2 squares which makes 6 squares.

Let KI intersect EF in M. The triangle ABJ is similar to JCK is sim to KEM is sim to FMI. That is the triangles along the diagonal all have the same angles and areas in proportion. I take it ABCD, CEFG and EHIF are squares.

Since there is some interest in this subject I will post the outline mathematics. I am sorry I can no longer do the LaTex since SF will not let me post from WinXP. So if anyone can help with that I can expand. Basically we start with Laplace's equation in 3 dimensions, in polar format, and apply a potential , V. This can be colour value /intensity, or other quantity to produce the 'ripple' across the object. Successive radial (r) values of V are calculated for various values of two sectional angles theta and phi., where it intersect the object from geometrical model This is my first equation. The general subject is called spherical harmonics, which is concerned with solutions to this equation. A homogeneous algebraic equation separating r and the angles in the form of my second expression, rnf(theta, phi) gives values of V satisfying the first equation, in polar coordinates. These are known as solid spherical harmonics of the nth degree. The function f(theta phi) is known as a surface spherical harmonic of the nth degree. The equation can be simplified by symmetry when V is independent of phi. This lead to my second equation whcih upon the transformation indicated becomes Legendre's equation The solutions are known as Surface Zonal Harmonics, as indicated by John Cuthber. These may result in 'patterning'. This is not only used in CGI but also in computer tomography (CT scanning) via a finite element mesh. The equations are normally solved numerically by substituting suitable simple function such as' hat' functions on the mesh, with the computer doing lots of calculations.

You have shown it to this Mathematician. And I thought there were too many misunderstndings in it to be worth detailed consideration. So +1 to Genady for the patience to do this. +1 also to PhiforAll who got in before me when I was about to complain. A word of advice. You can expect ridicule as answers when you make such wildly and obviously incorrect statements. Such as claiming the non existence of zero. Consider this sequence of integers ...-4, -3, -2, -1, 1, 2, 3, 4... ...Even, odd, even, odd, odd, even, odd, even... Do you notice anything missing ? It implies that there are more odd numbers than even numbers. By the way do you understand the ... symbol? It is called an ellipsis. You have also been arguing wrongly about the meaning of the equals sign. It stands for two different properties - Identity, and simple equality. Sometimes the identity symbol with three bars not two is used instead for this.

Embarrased or not, your teacher was not so far wrong. Car Tyres are indeed an entirely different case. Not only that but there are further complications I will try to elaborate. The friction theory they teach at elementary level only refers to the contact of dry solids. Some textbooks and teachers make this point, some do not. A car tyre is in general neither solid nor dry ! The study of forces involved between bodies in contact is called tribology. Furthermore a car is a dynamical system, with constantly changing velocities, directions and accelerations. More of this later. Here is a well produced table by Professor Sir Charles Inglis of Cambridge University. Note very carefully what he says about reactions and contact area. You were taught only the left hand column. Once again car tyres are neither solid nor dry. They are actually a mixture of all three types (type 3 = partially lubricated) - about as complicated as you can get. Why do I say all this ? Well the forces of interest for car tyres and the road surface are collectivelly known as the grip. Here is a simple summary from https://www.racecar-engineering.com/tech-explained/tyre-grip/ Note that they describe tyres as having viscoscity. Solids don't have viscoscity, liquids do. Viscoelastic refers to a mixture of characteristics. But even this does not tell the complete story. You are asking why early racing cars and modern road cars have thinner tyres. Well road cars have a dry coefficient of friction of 0.8 dry and zero to 0.6 wet. Modern racing cars enjoy a coefficient of 1.4 to 1.7, on their fatter tyres. Cars are not like your diagram of a solid block with full or nearly full contact area and a simple C of G load point. The loads are distributed to the four extreme points. They are dynamical systems (when running) which means that the loads are also constantly changing with the overall motion of the car as it goes not only forwards but twists and turns as well. So the parts suffer accelerations not only due to the car's overall motion, but also due to load transfer. With modern cars this transfer is modified by being transferred through springs. For example a racing car's coeffiecient of friction can drop to 1.2 when also suffering sideways loads from cornering. As noted in the linked article the tyres themselves have an internal dynamical structure which also modifies the friction laws. There is even more to the subject as the tyres distort and recover and use energy, heating up in the process, leading to the so called rolling resistance or coefficient of rolling friction. Also the wider tyres give a safety margin against slipping and locking which is needed for the higher speeds and stresses involved in F1.

Here is your first error. It is incorrect to write an equation with infinity on one side. That is it is incorrect both mathematically and physically. In fact your whole thesis ls built on a very shaky understanding of ' infinity'. Things are a great deal more complicated in both maths and physics and indeed other sciences. Please tell me what the tangenrt of Pi/2 is ? There are many equations in Science employing the tangent function. A simple example would be to do with friction. Physical Chemists use a totally different form of infinity called infinite dilution. In fluid mechanics a property called specific energy tends to infinity in a fluid structure called a hydraulic jump. I have already told you about what is probably the simplest one - density, which is handled by a French discovery L'Hopital's rule. Another French infinity is the formation of a square wave from and infinite series of sinusiodal waves. Note I am not saying that Man can reach 'infinity, just that it can be valid in Physics or other sciences and must be handled accordingly. There are as many ways of handling infinities as there are examples.

Are you being deliberately obtuse ? What was unclear about my first and most important question? There were no spelling mistakes and it was written in textbook correct English. Since I placed 3 question marks in my first post I referred to 3 questions in my second post. So why do you reply in the singular ? Note I spotted and enquired about a contradiction in your original post. It was also unclear to me whether you main interest concerned the mathematics and or physics of infinity, as the title suggests, as against a particular effect in Physics.

I asked you 3 questions. All of which you ignored. One of those questions actually contains the answer to your reply question. Do you call this a discussion ? I can assure you the rules here do not.

Surely your title is contradicted by your first line. If infinity is not defined in Physics how could it be permissible to use it ? Of course it is well defined. And why to you need such an exotic example as the Casimir Effect ? What is wrong with schoolboy Physics. Density = mass/volume So what is the density at a point, which has zero volume ?

But did the makers pay anyone for the use of the older material ? That is the key question that was in the original article I linked to and even extracted the key paragraph. And that is what makes it different from the Luddites. The luddites were complaining because someone had found a machine that could make cloth more cheaply then they could. But actual cloth still had to be made. What the Managers are proposing is that once they have a single print of someone, they can had the punters a photocopy in future. Would you as a customer be satisfied with a recording of some opera star played to you, having bought a ticket to see the real mcCoy ?

Thank you for your reply. I would just like to point out that there are many other members interested in the subject as evidenced by their occasional posts and the best part of two thousand views. The diagonalisation argument is a direct result of the fact that there are more real numbers than there are natural numbers, even though both are transfinite. The ramifications of this fact are enormous and widespread so it is a good idea to review them and note the relevant ones. One area where phyti has already made a misstatement is that it means that for many sets, a set with more members that the original may be constructed. This was not fully grasped at the time of diagonalisation. But the killer conclusion is that it is not possible to form a list of all the real numbers, or even all the real numbers in a finite interval. This conclusion is the essence of diagonalisation. But because of this also leads to ideas of density and completenessnd more structure, there are other ways to prove the result. That this all hangs together is gives further support to the belief that we are on the right track, even though we know we haven't finished yet. There are still more queastions to be asked and resolved.

Something like this may have happened in the past when the Earth's atmosphere and was known as the great rust event, when much of the widely distributed oxides ov iron were formed. https://www.amnh.org/exhibitions/permanent/planet-earth/how-has-the-earth-evolved/banded-iron-formation +1 for trying to think out of the box. However I am firmly of the opinion that rather than employing more big business at great cost to clean up after the activities of other big business, it would be better if big business did not create so much carbon dioxide in the first place. Both the creation and clean up only benefit the greed of such business; the vast mojority continue to suffer the cost and pay for the enrichment of the few.

@wtf I was suprised to see that you are apparantly not even parsing the contributions of others here. It seems to me that everyone is concentrating on too narrow a view. It would be better to take a long term overview sincenot only was Set Theory not built in a day, but it has changed dramatically over more than 2 centuries. Cantor did not wite it down all at once. I am posting to short extracts from the Stanford Encyclopedia which are highly relevant to this discussion. Noting the years 1850 to 1930 as critical, though we could easily extend this timeline by 50 years or more if we wish to included the Bolzano theorem (1817) Cantor relied so heavily on for his first proofs or we wish to discuss computability which came well after Cantor's death and which is still a busy area of active reserch and debate. @phyti Simply declaring Cantor was wrong is not enough. He modified his theories quite substantially as he went along, and that process contues today. Here is his significant breakthrough, when he was first experimenting with sets and did not know about many infinities. In realising that the set of real numbers must be somehow bigger than the set of natural numbers he kick-started the whole thing off. Here is the link to the full Plato article https://plato.stanford.edu/entries/settheory-early/

Thanks. I hope this thread and your other one has been of use. Good luck with your studies, and don't be afraid to ask.

Interesting idea, but exchemist has done and exhaustive job of demonstrating it's impracticability. +1 However the idea of only carting 2g of hydrogen and not the extra 16g of oxygen with you, but finding it already there is one of these theoretically attractive but practically less useful, so should not be ridiculed. Some similar was shown in that great film "The Martian", as was the danger og burning hydrogen to get water.