studiot

Suppose there were two observers travelling in the dark so they could not observe anything external to themselves at all. Observer A is travelling along a wall (he can't see) that emits parallel jets of air always pushing him sideways to his left. Observer B is subject to an electrostatic attraction towards her left so that she travels in a circle. How would each observer determine what sort of motion they were executing, given that they can't see anything of the outside universe.?

Why not? The clue was in my post5, set nearly half an hour before yours. What do you get if you add 1 to infinity? All you need is a suitable number system that includes infinity.

I have a crepe pan with aluminium base that blackens/burns on the underside/base because it has very low sides. The blackened aluminium base gets regular cleaning with hydroxide based spray oven cleaner. Yes it dulls the surface and probabaly removes a microlayer. But equally that microlayer is probably smaller than the one removed by mechanical wire brushing/grinding processes.

Where was it specified that the solution has to be a real number?

Get a better maths book [math]\mathop {\lim }\limits_{x \to \infty } \left( {\frac{x}{{x + 1}}} \right) = 1[/math]

1) Boil up a generous tablespoon of Persil for 1/2 hour to 1 hour. 2) Stubborn stains can be removed with sodium hydroxide, cheaply obtainable as drain cleaner. Best done outside. Flush with lots of water after. 3) Finally polish with metal polish so yes then you will need the elbow grease.

There that should be better, but I hate splling as well

(A) Yes I came back because I realised that after I left, but you beat me to it. Thanks. (B) and I would like to say I hate LaTex.

Well the angular momentum number, L is related to the orbital momentum number l by the relation edit formula corrected [math]L = \hbar \sqrt {l\left( {l + 1} \right)} [/math] Since l takes the vlues 0, 1,2, 3..... (n-1) where n is the principal quantum no the smallest value that L can have is with l = 0 and is non zero.

Are you having sport with me suh?

Actually you will find the Max function defined in many maths textbooks, particularly those that deal with numerical methods (as we are) or metrics. This is a fun thread though and it shows just how ingenious people can be.

Look up the Kronig-Penny model.

I am always happy to appreciate jokes made at my expense, so long as it is clear they are jokes. I like a good joke. Any good Engineer will tell you that the first question to resolve is Hardware or Software? Mindless changing of boards will not resolve the latter. But enough of this off topic. Mathematical models and physical reality are not identical. I have offered some thoughts on their differences. Please continue to comment technically on them.

Strange, please compare your directly personal approach here to that of ajb and note the difference in the level, quality and progress of the conversation.

Yes there are things in Mathematics that are not in Physics and vice versa. That was partly why I recently started a thread on that very subject, though not many answered. We are not supposed to advertise our own threads so no link I'm afraid, but it was in Mathematics. Engineering is the application of Science and a valid and respectable part of this website. I recently had cause to note there the difference in handling of the word 'Field' in Mathematics and Physics. Elsewhere we had a question posed Why do energy bands form in semiconductors? There are many presentations of this subject online and elsewhere, but they generally seem to state that they do form bands, without explanation. Interestingly the explanation is mathematical, but the also demonstrates a difference between the handling of complex numbers in Mathematics and Physics.

Well put, I keep telling Mike that, and it was a point I made several times in the now closed thread. +1 My emphasis added.

In much of electronics it is bad practice and sometimes dangerous to connect two outputs together, as each device tries to assert its own output. Tristate was invented to cope with this so that two outputs could be connected in opposition without damage by putting one into a don't care (indeterminate is actually a bit of a misnomer) state. Other parts of the circuitry will then determine when the tristate chip output is active or valid, or not. If you like it's the Engineer's answer to how to apply an irresistable force to an immovable object. Edit I see I xposted with John Cuthber. Thank you JC, I note you are using an admittedly incorrect model to cope with the inadequacies of the mathematical modle here. The device is not physically disconnected. If it weere there would be no need for tristate devices. So your model is inadequate in that it cannot distinguish between disconnected and tristate. Edit2 It is ironic that as we chat here I am fixing a Hewlett Packard PC that looks like its ethernet connection has suffered physical damage from the recent electrical storm on Exmoor. Tristate rules OK.

You are wriggling The above is in direct opposition to your other statment in the same post.

So offer me a mathematical model of the output of a 74C126.

Yes indeed, I am not talking about circuit failure or incorrect circuit action. There is a family of logic chips that can be deliberately put into an indeterminate state. This is known as Tri state logic. http://en.wikipedia.org/wiki/Three-state_logic

I suggest physical reality is more complicated than that. That is why I asked about the output of a 74C126 integrated logic chip in my post 264 and received a rude raspberry for it (not from yourself) I chose that chip because there is no calculation or observation that can be performed which can unambigouusly answer the question What is the output state of the chip? The chip is part of a family of chips designed to reflect a sort of Godel's Theorem in electronics where the output can be definitely 1 or definitely 0 or indeterminate.

You don't. Science models nature, not math. Yes you are strictly correct my wording was bad. Maths has axioms and deduced statements. Physical reality has observations. However that does not cover up the fact that a mathematical model must contain mathematical axioms and at least one unprovable mathematical deduction. All these are taken on faith as I said if you are to believe that they also apply to the physical reality. There may be statements in the model that are not reflected in reality. Equally statements in the model may lead us to statements in reality that we have not previously discovered. My position is still the same as set out in my posts 251 and 283 and also by ajb in his post 267.

So how do you model the axioms or the unprovable deduction(s)?

Of course it does or I wouldn't have said it. Though, equally of course, I am happy to explain further. Every system of mathematics has two characteristics, both of which have to be taken on faith. Taken on faith means accepted without question. These characteristics are (1) the axioms and (2) the unprovable deduction(s) required by Godel. (2) is the 'incompleteness' if you like.

Appears? You made the assertion so it is up to you to support it with a logical train of thought, not wishy washy flannel.