studiot

Yes you have mentionted 'satellite navigation' several times now, though you have completely failed to mention what you mean by this. Please demonstrate how this relates to the topic in hand, which is the (im)possibility of artificial consciousness. Since intelligence is different from consciousness we should not be discussing that subject either, according to the rules and regulations of this forum.

My head hurts with all that thinking. I need a cool beer.

I see little point in going into the detailed history of structural engineering since you have avoided responding to my main point about the decline in engineering capability after the fall of Rome, the Church of St Sophia not withstanding. The Romans were not scientists, they were technologists/engineers par excellence. Nor was the decline confined to Europe, western or otherwise. The nomadic 'babarian' hordes conquered into China, Mongolia, India and Indochina. In the Americas, warring indegenous civilazations conquered each other and some destroyed themselves. I would say that prominent landmark technological developments were Fire, stone tools and weapons, bronze tools and weapons, ferrous tools and weapons, agriculture, electricity. Gunpowder doesn't even make the second grade. The besigers of Rochester Castle did not have gunpowder but managed to contrive an equally powerful, and a damn sight more reliable, alternative, also known to the Romans. That is the volatility and explosion potential of pig fat at very high temperatures.

Agreed. We have a real expert on this subject as a member. I will lask @swansont put you right on your grasp of Physics.

One issue that has not been raised about voting is how the 'winner' is decided. In some systems I could end up 'voting' for the candidate I wished to vote against. Life is never that simple.

+1

Good question. +1

I consider my case that technological advances stagnated on balance during the stated period. That is enough to demonstrate that the OP case for continued advancement disproven. The need for subsequent reinforcement (the famous X structure) in the centre of Wells Cathedral, The failure of the South Wall of St Peter's Church Bampton due to not appreciating roof loads. In fact if you look into the records of many churches, built in those times, you will find either an actual collapse or sufficient movement to have required strengthening. Sadly some have yet to learn these lessons to this day.

That's what I was saying. +1

Yes there were 'dogooders' in every time and era. I think more land was distributed to ex soldiers than anyone else though, following the Punic Wars, especially the second one.

Apart from being physically impossible, that's too harsh. You learned things in the past, lots of things. When in the present or the future you come across something relevent to what you learned in the past you need to recall it. I am / about to face a particular situation What did I, my father/uncle/brother/colleague do in that situation I witnessed it for the first time ? The key is of course it has to be relevent going forward, not some morbid fascination with the past.

I agree so +1 to iNow. I would make a comment on this idea as follows Perhaps this is an inherited survival trait ? But as in so many things in Nature it is also a question of balance. (Do you remember that record ?) And the balance between all our traits can so easily get out of kilter. There are many 'Talking Therapies' from CBT to 'The Turnaround Principle'. You may not have heard of this latter one but it involves in re-examining the belief by considering the opposite "If I am worried about X - What if The oppiste of X is true ? "

Thank you for sharing this. +1 This tie up between the extreme northern peoples reminds me of this epic novel, wwhich I found to be a really good read. https://en.wikipedia.org/wiki/Last_of_the_Breed

Just a thought (well 2 actually) sologuitar has posted a series of similarly worded titles and these are in the homework thread. I wonder if this has triggered some additional anti bot /anti spam software here. I have seen some other maths sites swamped by what are clearly repeat posts.

Well it would be helpful if you has indicated that your expansion comments were not in opposition to what I meant but additional to it. I was responding to your assertion ( which I agreed with) that for practical operational reasons individuals were (and still are) called or elected to represent a whole bunch of people, usually geographically defined. I am simply pointing out that historically many (most?) of these individuals actually only represented their own personal interests and noboby else's.

I understand the situations you are referring to but they are not what I mean. It's very difficult to explain if you just keep simply telling me I'm wrong, when you are not even understanding what I am saying. Baronial landowners didn't vote for or against "Husbands voted against their own wives, daughters and mothers." Such matters didn't even come into their consideration.

So far as i can see all these check out. But you should not use use to check work you are going to submit for marks. Here is a simple check you can run for yourself. Say you are asked to simplify expression A / expression B and end up with expression C / expression D You want to know if they are equal ie you have not made a mistake. [math]\frac{A}{B}? = \frac{C}{D}[/math] CROSS MULTIPLY The results should be identical if you are correct. a simple example should show what I mean To test if [math]\frac{{{x^2}}}{{{x^3}}} = \frac{1}{x}[/math] CROSS MULTIPLY [math]{x^2}*x = {x^3}*1[/math]

No, read it again more carefully. The land (and later industrial) Barons represented noone but themselves individually.

I wish that were true, but the mental state of far too many is that even in good or the best of times they still dwell on past bad times and even imagine that these are still there or are afraid that they will return. Phsychiatry has yet to come up with satisfactory measures in this case, though positiveism helps some.

I'm sorry to tell you that you have completely missed my point. Self interest is exactly that. A simple example the Member (of Parliament) for say Oxford was a local Landowner. He represented his large landholdings, ie himself, although officially he 'represented' all those who live on and around his land.

Not really. but there is some confusion in this thread. I see that you are looking for values of x that make the fraction undefined ie division by zero. If x is a real number that is correct. But it is confusing at least and incorrect at worst to say x = 0 works. For the reason you have already given putting x = 0 leads to the fraction being undefined. So x is not equal to 0. We are all agreed on this. You are also correct to note that there is no real number p such that (p2 +1) = 0 So the correct form of reasoning goes that x cannot be equal to p, whatever p might be, since it is not a real number. Thus the only restriction on numbers that you cannot choose for x or must exclude to be x = 0

https://www.bbc.co.uk/news/business-66656369 Robots are trained to help revive coral reefs

My understanding of all past 'democracies', all the way back to the Magna Carta and beyond to SPQR, was that the voters only represented their own self interest, they did not represent anybody else (ie those who were not allowed to vote).

Yes it cannot be changed, but is it really 'gone'. I thought that was the whole point of this thread. Surely Dan was feeling the influence of past events and wished to find ways to mitigate this? @DanGonzal Welcome this is a topic that affects everybody to some degree or other. +1

Nothing at all. I'm sorry, it was me not you. Preparing latex formulae is difficult for me these days as I have to do it on my old computer,save it, and then transfer it to a newer computer when I can get on one. Whilst I was doing this for probably your first of the 'bunch' you must have added more so I only quickly posted in this one which was the wrong thread. Thus I didn't understand why the formula under discussion had 'changed'. I deleted my post but had to put something in its place. Sorry if this caused more confusion. But hey, never mind, I see we have new mathematically minded member so welcome @e jane aran FYI please note the site 5-posts-in- the- first- 24-hours limit. This is a security measure that greatly reduce the rubbish the overworked moderators have to deal with. After that time expires you will be unlimited. Thank you for the help you offered. +1