studiot

The whole question of how many D is one of mathematical convenience, rather than physical reality. Peano et al showed that it is perfectly possible to catalogue every point in the plane with what are now known as Peano curves and every point in 3D 'solid' space by what are known as space filling curves. These curves are one dimensional objects. The problem is they do not have usable metrics or neighbourhoods so this makes maths on them very tricky.

With zero value? Please think about what I am saying - I am unable to draw any diagrams at the moment to help. Your cross shows two pairs of equal and opposite vectors at every point, both of which cancel each other out or sum to zero. Consider only the E (or H ) component. When the E wave is positive there is nothing in the negative half plane, but you are showing a vector there that expands and contracts as does the real one in the positive half plane. Similarly when the E wave changes sign only the negative half plane is active. Edit I appreciate that your circle can be considered as a wavefront. But in that case it should not pulse in and out as that implies a longitudinal wave and light is a transverse wave. Instead a series of outwards spreading pulses that expanded and disappeared would be more appropriate. Please don't get me wrong. I think it is (would be) a great animation, if you can get the details correct.

Just get TRVs (thermostatic radiator valves) on each rad and turn them right down in the rooms you hardly want to heat. Allowing too large a temperature differential will cause significant heat to flow from the warmer room to the colder - it will find a way. In really cold weather you will also get condensation in the colder room which can lead to mould growth and corrosion of metal items.

But the cross of vectors adds up to a constant big fat zero. Where does the pointing vector point from that cross?

Nice animation pic at the end, but it has a fatal flaw. The expanding cross and circle should surely be a rotating quadrant in which the H and E fields are positive?

@falolero I understand what you are trying to say, without the proper maths. However your examples are, like your title, set in a Euclidian universe. Newtonian Physics is Euclidian. 'Size' variation with position is non Euclidian.

But I did address your question in my post#19

I don't follow the OP's full train or question as it is too long, but his post#6 on size is suggestive of non linear geometry, where exactly those issues arise. The last posts by Strange and Strangelove are about projective geometry which is different again.

Consider your post#7 quoted. We already do computer reaction simulation like this in pharmacology, albeit at great expense. If you have big drug company money behind you, you can access 'pharmaco libraries' containing details of hundreds of thousands of compounds and functional groups and computer simulate many combinations and the expected resulting products. This is done to select suitable promising ones for real world tests for a particular application.

@wtf So why wasn't your post at elevator length? But I really like it anyway +1

Then this similar question from FrankP might interest you http://scienceforums.net/topic/101678-organic-chemistry-where-to-begin/ Franks has also posted some other threads that may interest you. Edit There are two ways of looking at reactions. You can list the types of reaction and consider all the compounds that undergo each type of reaction. This is the modern chemistry way for both organic and inorganic chemistry. Or you can list all the compounds and then sublist all the reaction each compound takes part in. Older texts and courses worked this way. There is a really interesting and modern background textbook by a leading professor from Oxford university, P Atkins entitled 'Molecules'. I would recommend it as pre course reading to anyone.

Unfortunately the quote functions doesn't work in this acer netbook so please pretend I have quoted your OP. There is nothing in the question or your own page to tell us the level or context at which you are asking these questions so I am going to guess you are moving from high school to college. Yes there is significant interplay between the structure of molecules and the reactions they participate in and the way in way they take part in these reactions. Activity of general interest to chemists takes part between the electrons of a molecule, and usually only some of the outer ones at that. This is true of both organic and inorganic chemistry. To answer one of your questions above. To explore a particular proposed reaction you need to study three things. First how to balance a chemical reaction. Second chemical energetics (thermodynamics) . This will tell you if the reaction is possible by itself. But a reaction that is theoretically possible may take (nearly) forever to happen, either because of energy barriers or because it is very slow. Thirdly chemical kinetics. This can tell you how fast a reaction proceeds and how far depending upon the concentrations of the reactants and products. One other aspect worth mentioning. The size of molecules plays an important part in separating the nature of reactions. When a small molecule has stuff added or removed by reaction it usually makes major changes to the nature and structure of what is created or left. The whole molecule can be said to participate in the reaction. For large to very large molecules the situation can be somewhat different, when only a small part of the molecule is actually involved in the reaction and the rest just tags along for the ride. This is of great interest particularly in the life sciences such as biochemistry and pharmacology where these large molecules regularly arise. Here molecular shape plays a much more important role as one part of the molecule can get in the way of the active part and interfere with a reaction. Much of our knowledge of life science chemistry is based on this. Finally there are entire textbooks about these aspects of chemistry. Spice: Molecular Binding and Structure Stranks: Chemistry a Structural View Wells: Structural Inorganic Chemistry So over to you to tell us more about your needs?

Firstly you were told not to reopen this subject by a moderator, But some good points have been made and the mods appear prepared to let this go on a least for a bit. So I will make some observations. Mordred mentions the difficulty reconciling the idea of multiple behaviours (eg particle and wave) But in classical macro-mechanics this is no surprise. The trouble is: IMHO too little classical stuff is taught today and too much black magic aspiration from the coalface of science. Take particles. Particles are an idealisation. There is no such thing as the perfect particle from classical mechanics. Consider the Earth, a tennis ball and a brace of jacks. Are they particles? Indeed what are particles? Well for the purposes of kinematics a particle is small enough that its dimensions are small compared to the system dimensions. So for the purpose of solar orbital mechanics, the Earth is a particle. But for the purpose of bouncing a tennis ball or playing jacks, Is the Earth still a particle? And what off the ball and the jacks? Does shape matter? Certainly Earth gravity varies, depending on where you play ball or jacks. But can the ball or jacks be considered particles? Well what happens when you toss the ball onto a concrete path? It bounces along and describes surprise surprise a wave? It is only our imperfect world that prevent this wave continuing forever. And the jacks. Do they act the same when tossed? No the motion is quite different, perhaps you can continue the discussion?

Sorry, I really meant what are the circumstances leading to sufficient water to cause flooding? Remember I noted this to be a regional rather than a local problem and I still think this. These are some typical UK local solutions.

Where does the flood water come from?

Hello Steve, You need to beef up Fig 5 by labelling the axis and then providing some explanation. You state that the blue trace is [math]\left| {\frac{\pi }{4}} \right|[/math] but the modulus of pi divided by four is a constant. So how does this work? Otherwise you have some very pretty pictures that have come a long way from your original thesis. As regards you terminology, I suggest you draw a distinction between what are known as pseudo-vectors or axial vectors to avoid confusing readers.

I'm glad you are taking the time to think about things. that's the best way forward. +1 Please don't think the technical ideas and terms were offered without the opportunity to ask further questions about them. I have noted a considerable development (improvement) in the quality of your posts since you started here. Keep up the good work.

The geologically recent (holocene) history of the whole area has been one of shifting channels. Looking at the level/gradient figures you gave, along with some have from elsewhere I note how low and how flat everything is. In these circumstances European experience, both in Holland and where I live in Somerset has been that the level of forestation makes little difference to the disposition of water, especially in flood conditions. Unlike the Mississippi, the Rhine delta has been stable for a long time. Manual control is essential in the form of drainage channels and flood protection works in the form of levees and berms. Somerset has suffered over the last couple of decades from failure to dredge the channels, leading to the substantial floods in 2015. Approximately 30% of Somerset is at or near sea level, as is a greater % of Holland. In both areas the both the main and minor river channels are artificial and sometimes above local ground level. Water has been pumped into them since Roman times. A big difference from the Gulf is the outlet conditions. Both the North Sea and the Irish Sea have exceptionally large tidal ranges, so the drainage channels are gated and drained at low tide in normal circumstances. The incoming water must have somewhere to go. In exceptionally high tide conditions, with a strong westerly wind also piling water, the draining rivers cannot drain to the sea so incoming water backs upstream and inland and floods occur. Because of the large swath of low lying land the floodwater spreads out unless constrained by defences. I fear that in the case of Baton Rouge, local drainage measures will be subsumed in the regional situation so you are left with protection defences as we are.

Thanks for the answers Ken. I will have to think about what you said. Have you read Brian Fagan "The attacking Ocean" on the subject?

I'm having a little trouble reconciling the left hand picture with the satellite view. The intention on the left hand sketch is clear enough. But where are these meanders on the sat view? What is the wiggly river on the left half of the sat view ?west? of Baton Rouge? Which way are the rivers flowing? Why is it necessary to remove natural berms and levees? Surely that makes a greater flood risk than removing trees? Is the intention to create a new waterway?

Interestingly both are dangerously flammable in the wrong circumstances. Kay and Layby give Acetone Ethyl Acetate Lower flammable Limit 3% 2% Upper Flammable Limit 13% 12% Flash Point -19C -4C Auto ignition temp 538C 410C

Organic Chemistry where to begin? And where to begin an answer? You will find all the same stuff in organic chemistry that you found in non organic but the emphasis will be different. In addition organic chemistry sports the richest collection of reactions and combinations of any element. Stoichiometry is very very very important. ( we have talked about this before I seem to remember). Acids and bases yes. Remember Acid + Base = Salt plus Water? Well in organic chemistry you will meet another one. (organic) Acid plus Alcohol = Ester + water. Did I say alcohol? That introduces the idea of functional groups. Did you mention valency? Carbon is tetravalent (has a valency of 4). It readily joins to other carbon atoms with a single double or triple bond. It can join with other elements, notably hydrogen, oxygen, nitrogen and sulphur and the halogens (chlorine bromine iodine etc) to form a 'sub molecules' called functional groups that appear gain and again. Carbon generally participates in covalent bonding. In order to form ionic compounds (it does) it combines with other elements into one of these functional groups to form the cation or anion. A simple example is the hydroxyl group OH. This is connected to a carbon atom by a single bond C-OH and forms the basis of the alcohol functional group. Functional groups are often indicated by the letter R Another important function group is CH3, the methyl group That is one carbon atom connected to 3 hydrogen atoms, as shown in Fig1. If you were keeping count you would note that this leaves one carbon bond unaccounted for. If this fourth bond is connected the hydroxyl group as above we have the simplest alcohol - methanol as in Fig2 If instead of a hydroxyl group we connect just a single hydrogen we get a compound containing only carbon and hydrogen. These are called hydrocarbons (note the o does not stand for oxygen or water here) and this example as in Fig3 is the simplest and called methane. Alternatively we can connect our methyl functional group to another methyl functional group as shown inf Fig4. We then obtain the second hydrocarbon, called ethane, in the very important hydrocarbon gas series that we get from natural gas and oil. This leads directly on to another speciality of organic chemistry. - Homologous Series. When you a compound, you get many, may be thousands, more by simply changing the functional group each time. These are called homologous series and the hydrocarbon gas one above goes, methane, ethane, propane, butane, pentane etc which are called the alkanes. These all have a common formula CnH(2n+2) where n is 1,2,3,4...... So I finish where I started. Stoichiometry is very very very important. Hope this is a good start for you. Edit Now to get a beer, see if you can use the above information to put functional groups together to get drinkable alcohol. called ethanol. This should tell you something about naming between different series as well. Compare the alkanes and the alcohols.

Since you are using the word probability so freely here is a little question for you. What is the meaning of the statement the probability of an event is 1 (one). Does it mean a) Absolute certainty? b) Something else?

OK so you have posted this in Mathematics so I assume you want to explore what is meant by the term dimension in mathematics? There are quite a few different ways of looking at 'dimension' in mathematics. For some purposes these ways can produce the same number, for others they can offer different numbers when approaching the same situation, but from a differnt point of view. It really depends upon what you want dimension to do for you or allow you to do. The first question to answer is. Do you want to restrict the number of dimensions associated with a given situation to integers or will you allow fractions or real numbers? If you want to consider scale and scale invariance then you will need to follow Beniot Mandelbrot into fractals. The famous essay "How Long is the Coastline of Britain" is accessible in a number of places, not least his book "The Fractal Geometry of Nature" You should have no trouble understanding all but a few bits. I am not sure how you want to explore dimension theory, your opening post hints at three ideas in maths Fractal Geometry Peano Curves Parametrisation Most of the mathematical effort has gone into the last on the list because it is the only one that allows us to do calculus and leads to the forms of topology and geometry most associated with (modern) physics. Mordred and I started discussion about this here http://www.scienceforums.net/topic/101339-what-exactly-is-the-fourth-dimension/ : see post#17 et seq. Geordief has also been inquiring, as have others, so it is a popular current topic. Finally here is a definition that allows us to work on the last view. 1) The dimension of the empty set is -1 (yes minus1) 2) The dimension of a space is the least integer n for which every point has arbitrarily small neighbourhoods whose boundaries have dimensions less than n

Sigh In the face of such rude defiance, should I try one last time? Yes you are correct in saying Newton's law states that the gravitational force between two objects is proportional to the mass of each object. But that is just it. It is separately and independently proportional to each mass. So the force is proportional to m1 and separately proportional to m2 [math]F \propto {m_1}[/math] [math]F = {k_1}{m_1}[/math] and separately [math]F \propto {m_2}[/math] [math]F = {k_2}{m_2}[/math] Arithmetically the correct arithmetical procedure to combine these two statements is to multiply not add. This is because they are both contributing to F and so it is the same F in both equations. [math]F = {k_1}{m_1}\left( {{k_2}{m_2}} \right)[/math] [math]F = {k_1}{k_2}{m_1}{m_2}[/math] [math]F = {k_1}{k_2}{m_1}{m_2}[/math] we can combine the two constants in to one single constant because they are constants or scaling factors [math]F = k{m_1}{m_2}[/math] But we cannot do this with the masses. It is a very important fact in physics (and maths) that if a thing is proportional to something and also (or separately) proportional to something else then it is proportional to the product (not sum) of those two somethings. It is important because a great deal of theory is absed on this fact and the solution of many important equations also depends on it.