studiot

In the past when I wanted to test or check something something during composing a reply a reply I could leave that thread make my check and then return to the original thread. So long as I simply clicked in the reply box before I did anything else, my previous typing reappeared and I could carry on. Why does this useful feature no longer work ?

[math]\int_a^b {df=f(b) - f(a)} [/math]

It would be helpful if you indicated what you mean by 'solve an integral'. I suspect you are looking for what is known as 'the primitive' in what is known as the fundamental theorem of calculus.

what an excellent reference. Also useful on the existence thread and good to quote to others about scientific method. +1 One thing I couldn't find in it was the companion, balancing quote

This thread is to open a discussion about this quote, its meaning and implications.

In my secondary school, there were two girls who could easily beat me at running (did I mention they both ran mid distance for England) and also one lad who could swim to the other end of the pool faster than I could get across it. (did I mention that he also swam for Emgland) Did that bother me ? Not in the least, though I did my best to beat them. Would it have made any difference if their genders were any different? I doubt it. Were there other pupils intermediate between myself and them? Yes of course. but I also represented the school in those sports.

So I'm as entitled to my view of 'fair' as Zapatos is entitled to his.

I don't see that the OP introduced fairness at all. So any suggestion concerning the current level of fairness is moot.

I am not interested in your age, but since you clearly think you know more than the experts here, I can only suggest you get a good book on NMR (Nuclear Magnetic Resonance) and the vibrational modes due to quantum angular momentum. Bu I have to tell you that you will find that rotational quantum mechanics has nothing to do with string theory, which has already been long discredited, as you have already been advised.

How is that what Richard asked ? ie how is the the probability P(y=g), which is the given question ? Edit Yes I see what you are saying now. +1

I think the question is ill posed. P(anything) is positive or zero. But the conditions given could include y(x) < 0 for all or some x.

Good idea. Most of Chemistry is to do with electrons in one way or another. It was once said that if you rubbed yourself with pig fat and chicken excrement it would cure syphillis. That was untrue then as it is now. Studying atomic vibrations is good, very good. How much do you know about vibrations ? Do you know, for instance, the difference between a wave and a vibration ? Talking of vibrations, I asked a few useful questions in a previous post. Are you going to answer them ? They were designed to be helpful.

Is it 'fair' that taller sportsmen and women generally make better fast bowlers and tennis players ? Is it fair that my eyesight has never been good enough for me to excell at my favourite sport ? Life is full of unfairness and inequity. Yet we have to somehow reach conclusions or results. They are rarely 'fair' as a result.

Here is some more meat, following on from my previous answer to your question. Modern teaching of set theory is generally oblivious to the deeper issues that occupied the minds of those around at the time of Russell such as the effect on the properties of the sets v the properties of the elements. Here is and interesting extract from a postgraduate textbook of the time which does not mention intersectioction, union and so forth whcih are the current foundations but spends several chapters exploring the above issue.

'Fairly'. Therin lies the whole intractable, squaring the circle problem. YOU (whoever makes the decision) has to be unfair to someone. YOU has to make a decision on something that cannot be completely resolved. Note I support neither side here and am sorry to read today's news about Lineham, whose antics I definitely don't support.

To put my figures in perspective say you had a picture of a string on an A4 sheet of paper. Then to put a picture of an atom on a piece of paper at the same scale you would need a piece of paper to be 0.3 x 1025 metres. 1 light year is approximately 1016 metres so your paper would need to be 3 x 108 light years or 300,000,000 light years This is the distance to 'nearby' clusters of galaxies, not stars or even individual galaxies. https://en.wikipedia.org/wiki/Coma_Cluster

Hello, Grayson. Are you sure you mean string theory not something else ? Your goal seems more about some form of quantum theory. Are you aware of the size difference between atoms (of the order of 10-10) metres and strings (of the order of 10-35) metres ? This makes atoms 10,000,000,000,000,000,000,000,000 times larger than strings so you would not really see strings on pictures of atoms. By the way, I see you are just starting calculus, trigonometry and chemistry and you have posted this in applied chemistry so do you understand this mathematical notation ? Just ask, we can help with.

I believe the language is equal to the objective, and the presumptions of its properties is misplaced. It is based on both subjective and the objective values- Both the State and direction of existence. Thank you for replying. You have certainly gone well beyond the boundaries of my native English as I certainly didn't understand what you mean, except that you think English is up to the job of expressing whatever it is you want to express. So please explain further.

Yes I agree I learned my driving in London and I used to say that it was a greater pleasure to drive there than any other city ssince the drivers had long learned the value of cooperation in the pohilosophy of "Let one go" There were so many interconnecting side streets in London that drivers would spread out and know that one car at a junction would automatically be allowed into the stream, because the other drivers would not have very far to go before they would also need to make the selfsame manouver. Sadly many connections have been blocked and I note a corresponding deterioration in driving manners and competence. I don't know what the regulations are in America but in the UK that strategy would be technically be illegal and a cause of driving test failure. In the UK a green light does not mean 'go'. It means @You may proceed for caution if your way is clear.' Drivers have become so bad at this that for some years we have had yellow boxes hatched onto the road. It is illegal to enter such a box 'unless your exit is clear' Stopping in such a box is alo illegal and many have been prosecuted for this. The problem is that too many drivers at junctions enter such zones in the middle of the junction when there is clearly already a jam at their exit. The result is that no one else can use the junctio and gridlock ensues. I don't know if you have such regulations in America ?

This is the point where I invite @iNow to step in with their famous cartoon.

I assume so are referring to this rather inelegant piece of English. Sorry about the spelling. First let me point out that existance in mathematics means is consistent with the axioms and other conditions assumed. Most of Mathematics is composed of abstract nouns. Whereas in Physics we are generally looking for existance to mean the physical instantiation or possibility of one, although there are abstract nouns in Physics as well. I understand the OP to lean towards the Physics meaning by it use of the word 'our' in the title. Some immediate examples in Maths, as you ask, would be the development of 'orders of logic' and their use in resolving the paradoxes (@Russell etc) that arise in first order point set theory. I am preparing to be away for a few days so will probably not be able to respond again until next weekend.

I agree. +1 More rigour please, Steve.

I am trying to keep my discussion at least covering a much wider field than just Mathematics. I am impressed by your choice of title an in particular the usee of the phrase 'nature of existence'. In my opinion this is so much better than asking what is existence, as so many do. I am also impressed with 'the nature' of your discussion in this thread. So +1 for all that Existence is a noun. The English language admits of two kinds of noun viz abstract and concrete. This is very useful in exploring existence and its nature. It is useful because it is possible because concepts are, in general, abstract nouns but we are, in general, interested in the effects of something in the physical world. So it is easy to see how a concret noun like 'football' can affect another concrete noun like 'window' (by breaking it). But the game becomes really interesting when you realise that abstract nouns can affect concrete ones and the action in the physical world can give rise to (many) abstract nouns like toughness, vulnerability and so on.

Yes seems like, and many dismiss the question without adequate consideration but would you want your emergency ambulance to be You could of course ask if the journey shoul be undertaken at all if there is 'not enough fuel'. But how do you know what is enough fuel ? Electric cars can vary by a reduction in available mileage of 50% worst case in cold weather. How would your algorithm cope with that. Equally, how much would be allocated to headlights, cabin heating/cooling and so on ? And what happens if the motorway is closed for an incident and vehicles are subject to a 50 to 100 mile diversion ? Living near the Severn Bridge it is suprising how many otherwise sensible people set off across the water with insufficient fuel to reach the other side. The Bridge Authority does not allow ordinary or private breakdown services to operate on the stretch between the junction at each end, charging a very hefty fee for their own service, partly to dicourage people chancing it.

I really think this discussion is pushing against the boundaries of language here. It should be remembered that in both ordinary and scientific English many words have not only multiple meanings but also multiple shades of those meanings. Furthermore folks sometimes try to combine words that although the combination follows the rules of grammar it results in nonsense, simply because some words cannot be combined with some others. Existence is such a word. For example if you have a hole, what does half a hole look like ? Is a hole of measure 5 the same of different from a hole of twice its measure (whatever measure means) or is it one hole or two holes or what ? Many of these 'philosophical' arguments that rand round and round in circles, like this thread is doing, or ran into an impasse, have found their counterparts in more modern mathematics where some solutions have been founf but these are not altogether satisfactory.