imatfaal

ignore - just testing attachment mech

Interval training is changing the acceleration often, even if you don't stop completely. The average of the acceleration will have less impact on the arc length then the number of changes and the size of the change.

The average of the acceleration will be zero - I have no velocity at the beginning or the end. Interval training is change in velocity and it is exactly the number and size of the change of velocity that would be neatly captured

 

I called it normalised because it only works if you don't vary the time or the distance between runs, which has the same effect as a normalisation.

It is not normalised - one just needs to understand the units. I could tell you that my last ride was at an average power of 24.7 gigaMade-ups and you would know nothing; but if I said it was at 345 Watts then you would know something - moreover if I said that I averaged 345 Watts for 100 yards - meh, over 1 mile it would be unimpressive, but over 60 miles it would be good, over 160 miles bloody amazing.

This is all related to some kind of variability. Not necessarily the acceleration itself, but the number of times it changes. In your particular example, it would mainly give a measure of the number of times you stopped and started again. It also only works because it is normalised in the way that the distance is always the same. Things that are correlated with the variability, could also be correlated with the arc length.

edit: of course: you could just do some kind of regression analysis instead.

It is necessarily related to the acceleration in a velocity time graph - a constant velocity is a straight horizontal line (min length of curve) constant acceleration through period is a straight line, varying acceleration is a curve; the more time spent accelerating and the more violent that acceleration the higher the arc length. I am sure I could dig out a ride with almost no stops or restarts yet with massive variation in velocity - interval training would be the obvious example (many small periods of rapid acceleration followed by short recovery)

And I would not say normalised - it is a relative comparison which could be made absolute.

You talk about correlation with the variability - how are you measuring/quantifying the variability? That is the nub - is there a nicer and more obvious measure than the arc length?

And I am not talking about statistical correlation - but rather the more concrete connexions; acceleration needs force ->torque -> power

Yes, I'm sure that's right. I don't think it affects the topic particularly though.

We don't know that EM is the most fundamental level of matter or energy. An EM clock might be a derivative of some even more fundamental processes that we are nowhere near discovering. But it all works at our present level of knowledge.

At high energy scales we know that the forces unify - we have known about the electroweak for a long time now. If you need to know more about that topic ask elsewhere. The invariance of speed of light is a phenomenon at our everyday energy levels and it is an Electromagnetic effect - the invariance of the EM wave pops out of the Maxwell equations and is axiomatic to the most successful theories of physics

I thought time moved slower the closer you got to a source of gravity...

Yeah. The weaker the gravitational potential (ie the further from the source) the faster the clock ticks compared to one at higher potential

Thinking about velocity time plots - and to simplify a set with equal area under the line (distance travelled) and equal change in t (time taken) - does the arc length provide useful information about the amount of acceleration? By useful I mean that the data are summarized in the arc length in a way that is relatively unambiguous (obviously it is blind to concavity/convexity), translatable to the physical quantity, and useful in interpreting the information provided.

For example - I have a set of velocity time plots of identical time and distance covered (every day to the office and back home, within 2 percent same time and exact same distance) - those with an abnormally high arc-length will be exactly those with high energy expenditure(I track this too) and I bet with higher than average Heart beats per min

Changing the scale, or the units, will change the arc length, so no. It would also require adding different units.

But your argument would apply to the area under the curve as well - and there is most definitely a very useful physical interpretation to that. I cannot see a useful meaning to the arc-length yet - but yours is not a valid counterargument

Like if I have a parabola of velocity versus time or position versus time, is there any physical meaning to the arc length of that function?

The dimension of the area under a velocity time graph is length - although I think I have phrased that awfully it makes sense. What is the dimension of the arc-length of a velocity time graph?

Just came across this article.

https://daily.jstor.org/the-qwerty-truth/

 

It says there were two key events in the development of the current layout:

 

1. Remington put all the keys needed for a salesman to spell out the product name (Type Writer) on the top row.

 

2. When people started learning to touch type, they went to courses run by ... Remington

All but one letter of the top row were in place before sale of desgin to Remington. Sounds like a bit of an ex post facto rationalization to me - sure a bright spark in Sales noticed that all they needed to do was swap the R into top row to be able to type typewriter with just the top row; but as a rationale for layout - no, that was to stop commonly used letters being next to each other

..

My question is talking to other English speaker how do you determine what evil is or what type of evil you mean when talking. Well surly you don't apply evil theft stealing stuff as evil as say killing or torture.

...

When you want to describe something as evil you use the word evil - and when you do not you do not. You might also use modifiers to express your opinion of another's moral compass -"so-called evil", "allegedly-evil", "if you live under a misogynist bronze age religion that still thinks patriarchy is brilliant you call it might called it evil" etc.

But at the end of the day "evil" is a moral judgment and thus subjective

That of course is true Sensei - I had forgotten that it was I who had introduced the idea of the the leading zero. So do we presume there is still a "school level" answer to the initial OP?

There are infinitely many numbers of the form 10^m, but only finitely many possible remainders/equivalence classes modulo k, so by Pigeonhole Principle, at least two (in fact, infinitely many) distinct numbers of the form 10^m must have the same remainder/be in the same equivalence class. Then their difference is divisible by k.

 

This is a palindrome because it's of the form 99.....9900...00, which can be turned into 00...0099...9900..00 with exactly as many leading as trailing 0s.

 

For example: 14. The remainders modulo 14 of the first few powers of 10 are: 1, 10, 2, 6, 4, 12, 8, 10, 2, 6, 4, ...

 

So 10^1 and 10^7 have the same remainders, so 10^7 - 10^1 is divisible by 7. 10^7 - 10^1 = 9999990 = 09999990, which is a palindrome with that leading 0.

Brilliant - thanks

Galtonian banned as another suckpoppet of MikeMikeV

please post question here - lots of members will not go to third party site to download

. Point of order, please.

When you guys are referring to "opiates" what exactly do you mean? I assumed you meant heroin and other morphine derivatives which in USA are illegal - it seems from the conversation that "opiates" is used as a generic term to mean prescription pain-killers

It's true for any positive integer. More specifically, every integer is a factor of some number of the form 10^m - 10^n, which is automatically a palindrome if you allow leading 0s. Proof isn't hard through the Pigeonhole Principle.

can you elaborate please? no need to get too technical - but that is kinda "and then a miracle occurs" without a bit more explanation.

Wow! Great news. I loved my Masters - great fun compared to other levels; serious but not draining. As all my studies are in Law and in the UK I will refrain from guessing at the answers to your questions