studiot

Years ago there was much counselling about instruments with electronic numeric readouts, from blood pressure machines to navigation equipment to calculators etc. Basically any device or algorithm designed to return an answer will always do that, however ridiculous. It of course physically unable to do anything else. So humans were advised to use experience an be on their guard against false output - either too precise or just ridiculous.

So did I but I wanted to check for the reasons below, which I'm sure you appreciate. If you don't understand them or want to say anything about them why did you post them? A Do you know what a hydrogen bon is and why it is not part of valency calculations ? B & C Yes if you are using the conventions that carbons are not explicitly labelled. However that does not explain why site B is trivalent and site C is quadrivalent. D on nitrogen is allegedly divalent and the other allegedly trivalent and connected to another allegedly trivalent carbon. As noted by exchemist, a load of gobbledegook.

Really ? You don't seem to have addressed my last comment Perhaps you will address this one. You have completely failed to distinguish between Work and Power, thus making your statements dimensionally inconsistent.

I expect to be away most of this weekend so don't rush. Iused the term 'connected path', which is common in maths and I think desxribes your meaning. Using this also gives the opportunity to distinguish singly connected; doubly connected: triply connected etc.

I asked you to explain the valency, not tell me that it is 'OK'. Specifically at these points indicated in the diagram you posted. A What is type of bond does the broken line represent ? B What is located at the triple junction ? C Again what is located at the triple junction ? D How are these nitrogens trivalent ? Please use the quote function in future when responding to queries.

I owe you an apology. As an applied mathematician I don't usually worry about matters at the base of mathematics and as I have already pointed out, this is really the only area of maths where one can hold an 'opinion'. However maths is not a belief system - I leave that to religious folks. I have just remembered that there is a branch of maths called 'constructive mathematics'. Your prefacing it with 'Real' threw me so I welcome the change to Necessary (though by its own tenets youhave to proove the use of the word) Depending upon where you are in the world you may not have come across this reference and source. https://plato.stanford.edu/entries/mathematics-constructive/ My take on constructive mathematics is that it is sometimes at odds with physical reality and I prefer a base closer to the system noted in the extract about groups that I posted, with definitions and undefinitions. So as a system it is missing out on some matters. For instance it is possible to define a number system that does not agree with addition or some of the other basics of peano arithmetic, yet is used everyday all over the world. Interestingly this tems from religious superstition. There is also an other entirely different approach in logic to deal with the problem of when and how it is appropriate to apply 'the law of the excluded middle'. Once such approach is by defining 'orders' of logic so that logic using this law is called first order logic and logic excluding it is called second order and so on. I have already alluded to this with tristate and don't care logic which appears in the physical world. I also wish that this third way or option appeared on ballot papers so that I could vote for 'none of these'. This issue is also a failing of multple choice questionaires, exams and the like and particularly of computer based forms.

I think the biggest difference between Science and Religion is that religion has no mechanism for advancement. Science and religion started seriously diverging about 500 years ago. If I look only at the last hundred years It is interesting to to compare how many times Science has sought out evidence and revised things to general benefit, with Religion that has remained mired in thoughts form over a thousand years previously. I do acknowledge that there have been some atempts to update by breakaway religious sects but they are in the definite minority.

Did not not agree with my shortform history of mathematics over the last 5000 to 7000 years ? Like all sciences, maths is a developing subject, with an accelerating pace of development as history proceeds. This development implies that there is no 'core' that will always carry forward or be relevent. In my own time and experience I started writing on slates with chalk, then progressed to paper and pencil, then to using logarithms and tables for calculations, then to slide rules and nomograms, then to calculators, then to primitive computers (which have grown more capable with time) . So in that short time much 'core' learning has become redundant. So despite being offered a mathematical reference to your own holy book, that you ignored, you continue to promote religeous mystical woo.

I'm glad to see you are now proposing more than one time(like) dimension in your update. The main purpose of my last post was to demonstrate that to support your hypothesis there has to be more than one time dimension. Because our universe can only ever be a part of this 'multiverse'. I see you are defining linear as a connected path. In some ways this is unfortunate as linear has a different specific meaning in both Maths and Physics. As a result of the two above observations, you need to resolve the second point in my previous post, that of non uniqueness. You have yet to do that. You should also find a way to distinguish between the stage or coordinate system of dimensional axes for you manifold and the activity itself. It is interesting to note your introductions of shadows. I often use the lack of these and one reason for the choice of 3 spatial dimensions and time rather than some other numbers. There are other reasons such as 3D is closed under spatial rotations, but neither 2D nor 4D are.

Additionally to swanson't comment, Planck's force is a unit of measure not a type of force.

Can you explain how your first diagram follows the normal rules of valency ?

I wanted to have an opinion of your understanding of a sequence of core concepts for your topic of most basic operation and activity in (philosophical) mathematics and based on the answer see how I determine what maths is for human beings in society as aspect. I read the part about science and maths proof, and it is helpful about confirming what proof is, and thought that math proofs don't require much regarding difficulty of structure, and it's how it is using words that keep the proof held. I haven't got a good answer for the purpose of math at the time. I unfortunately do not think we could give a core place for math in all society since there's a lot to still discover and better comprehend about society and what we expect mentally. There's a lot to consider in world implications that need math and your answer is great for current knowledge and the capabilities humans use and experiment until this time. I'm confirming that math can be done using minimal things and that it can function in general. I'm using the example of Von Neumann as well as minimal instructions since this would be closer to that basic necessary thing. I understand in principle with basic combined computer / program all math more or less is slow and sure. I'm trying to confirm the basic necessities for the philosophy of mathematics with example, and to have confirmation with it. Maybe there's another example more simplistic that can illustrate the core. I asked you two specific questions in reply to your earlier comments, evidenced by the question marks at their end in the above quote. Thank you for any apology but how is any of your surrounding text an answer to either question ?

No, not in the least bit. In fact, unlike a dumb Von Neuman machine that can only obey Turing and Churches' theorems and being human I feel quite affronted that you have not mentioned a single word that I recently posted. Back along you also mentioned semantics - the Science of Meaning. Do you understand that such a machine cannot even distinguish between a line of data and a line of instructions) ? So how can it be expected to understand the meaning of such lines of cocde ? You keep wittering on about 1 and 0. Have you ever heard of Tristate logic or Don't care states in K-maps ? Do either of these represent a 1 or a 0 or something else entirely ?

Well I asked because I don't think you have the right of it.

Can you demonstrate the correctness of these statements in elctrical circuit theory ? Cells are generators, they do not pass current or voltage, they generate it. If you need a bypass then why do you need that bypass to be a diode ?

Well we know that 'practical mathematics' developed in early civilisations in Asia, the Middle East and independently the Americas. By practical maths I mean measurement for agriculture and building and taxation and even some more sophisticated measurements like river gauging in some places. Also developed were mathematical systems for timekeeping. We know this from written records where maths appears about the same time as other forms of writing. What is interesting is that, even in those early days, there were a few 'theoretical mathematicians' who explored further into the maths they had. Again we know this from their writing about the the solution of quadratic equations. The ancient Greeko-Romano ciivilisations were the first to try to work more systematically through theoretical material, particularly in geometry. Not much more was achieved in the theoretical (pure) maths until the middle of the 17 hundreds when there was a burgeoning of theoretical maths which carried on into 18 hundreds and even the beginning of the 19 hundreds. At this point many it became apparent that many theoretical concepts playe a much more important and fundamental role than was realised, for instance in group theory which started off as a purely theoretical concept, like greek geometry, but led to important relevations in basic physics. Both pure and applied maths have continued to develop apace since that time, each offereng the other insights . As a result the 19hundreds have seen a much more coherent overall structure for the subject. About proofs and axioms etc. It is debatable whether there is such a thing as scientific proof since the concept is at odds with the basic scientific tenet that it only takes one observed exception to disprove a rule, making observation King. Proof in the general everday sense is for lawyers. Mathematical proof is different in that no observation is required . Maths proof is really a demonstration that the proposal does not contradict any of the premises or axioms. It does not examine whether the axioms are 'correct'. Here are a few pages about this in relation to group theory.

A trawl round the net shows various support frames, nearly all have underpurlins, including your pictures. I did find some glorified deck chairs and some interesting sloping plasic tubs weighted with bags of earth or stone. These latter raise an interesting point as you seem to be thinking of buying only panels and assembling your own support. Have you considered climate conditions ? The panels are like sails or fence panels and are subject to significant variable wind forces. The variability means that the ground reactions are contantly being worked back and fore, which is how fences blow over as the posts works loose in the ground. This will also continually flex the panels themselves. A final thought. Panels are rated for 20 - 25 years life, but I wonder what suppliers / manufacturers would say about the guarantee if they are not mounted on the recommended supports. In the UK many suppliers resort to the " Not installed in accordance with recommendations/instructions." to wriggle out of early failure.

I have no idea what this means. Nor does this make any sense to me. You do realise that there are physical quantities in the material world that cannot be represented by a single number ?

Sure, post what it is you want to discuss. I would also be grateful if you would take note of my comment (now made several times) that there is a lot of Mathematics that is not about numbers. Maths is not a party trick to get you an answer. Unifying is actually quite a reasonable statement, probably more than you know, but the price of this is that there are explicit conditions to be met.

Interesting - substitution, also called replacement. Of course that is the function of the klein 4-group I was illustrating. But I'm not sure I would call group theory the most basic.

I see you have been back a few times now. Have you given up on this ?

There is not enough information about your proposal to properly comment. Surely the panel frame provides the support and specifies mounting methods ? I think what you might need for an array would be what roofers call an underpurlin. Certainly you would need to support the frame edges at these points, John's idea, though interesting, is not really suitable as these supports are designed to be as near as possible the same horizontal level, quite unlike yours.

I don't understand this connection to 'high frequency' All changes in electromagnetism and gravity move at the same speed - the speed of light. This is regardlees of any frequency components of that frequency.

Clearly you are both mistaken since not all maths relates to numerical operations. I have been trying to hint at this fact with the pictures I have been posting. Today most humans can count. And most, if they tell you anything, will say that maths is founded on set theory. But go back to the stone age or even further and you will find a more basic operation that of creating a tally. Archaeologists have found bone, stick and stone tally sticks. Set theory relies on an operation that is essentially the same as tallying, only is is called putting into one to one correspondence. What is counting anyway ? Interestingly the Austalian Aboriginals have (had) a number system that went - one, two, many. You don't need to actually count if you tally or put whatever you are counting into one to one corresponcence with a list of numbers. But before you can do that you need a yet more basic operation. You need to to be able to distinguish A from B, Here is a little imaginary tale from the land before time. A leader or chieftan (who could actually count modest numbers) wanted to get an idea of the size of the wild goat herd they were stalking. So he gave a lad a stick and a sharp flint and sent him to tally the heard (the boy could not count) telling hime to cut a mark on the stick for every different goat he saw, and to be sure not to tally the same goat twice (so the boy needed to be able to distinguish goat A from goat B). On another occasion he sent the boy to tally a band of enemies that he was worried about. Here are tales from more modern times "Come in number 5, your time is up" said the guy at the fairground. So what is number 5 ? Horse number 5 came in first place in the derby. Horse number 1 came in third. What happens if you add first to third ? or what is the arithmetic of ordinal numbers ? What happens if you add number 5 to number 1 or what is the arithmetic of numbers as labels ? So you have cardinal numbers (that you can add together) Ordinal number that you can't add together Numbers used as labels that you also can't add together and finally you have counting numbers - the natural or counting numbers do not include zero as if you count zero objects, you haven't counted anything. But be careful about saying you can add them together because sometimes it doesn't work. All of the above can be used to establish a basic set theory, which in turn can establish counting numbers from nothing at all (I said this before but you didn't spot it) Once that is done it can be extended to theories of infinities which allow us to work with the concepts. I think that is enough to be going on with but I would very much like to learn of KJW's response to my question.

Of course, this is a discussion site. And you normally offer thoughts of value, so I for one welcome them.