Mot

I just began reading Principia Mathematica by Isaac Newton.

...

Unfortunately the book has been translated from Latin...

I am pretty sure that it was originally written in Latin.

 

Cheers,

Mot

If Jesus doesn't come soon, I think some of us should go see him - at least send the people who are waiting for him. Visitation goes both ways or so they said in family court. If you decide to go visit, pack well because it could be hell getting there.

 

Cheers,

Mot

Everything uses math, so that's why I chose that field, plus I could usually work the 'lab' problems out with a pencil and a piece of paper. No matter what you do the job offers will come if you are competent.

 

Cheers,

Mot

Rereading "What is Mathematics" by Robbins and Courant.

 

Cheers

Mot

wat exactly is the creationists idea

That the world was created by some mythical entity a short while ago. I always try to one up them when they spew their tripe near me. I say the world didn't start 6k years ago, rather it started 15 seconds ago. They say something to the effect that that is impossible because they were talking to me then. I calmly reply that they are mistaken because God put those memories in their head and we have all just been created. Any argument they put against it, I calmly reply that God made the conditions that way and the evidence is indisputable. They usually give up after a while, but they rarely notice that my argument is the same and just as sound as what they give for the 6k year answer.

Mathematical operators can be compared loosely to punctuation in written English. They help make the expression more understandable.

 

There is little difference between subtraction and addition. One can usually substitute one for the other without penalty, but don't make the same assumption with multiplication and division because that substitution can open a whole can of worms. I am not going to go off on a tangent until I understand better what you are asking.

PPS Get a membership in the AMA (american mathematical association) or at least the magazines. You may be able to find them at the library. The essays and proofs will tend to be in the weeds for a laymen, but they may give you some ideas of what is on the cutting edge.

I don’t have my math texts with me or I could give you a better answer, but here are my thoughts off the top of my head.

 

I will assume your understanding of the courses you listed is passable. If you want to learn more basic math try “What is Mathematics”. It is an old book, but it is still in print and will get you into some discrete math. You may want to consider looking into real analysis. As I have always said, all you need are the three R’s. Rudin, Royden and ‘rythmatic. Baby Rudin is tough but can be gotten through without a mentor and big Rudin and Royden will get you past what most people ever see in math except for Phds. I would advise you to find a mentor if possible. It doesn’t have to be someone who knows the math you wish to look at, but it should be someone who has a willingness to explore ideas and can handle subtle reasoning. You might be able to find a math club in your area by looking at ads, schools and internet. Be prepared to spend 2 months on background before you can get through one chapter of some of these books.

 

One other book that I love is “Introductory Functional Analysis With Applications” by Erwin Kreyszig.

 

All this should keep you busy for a few years or longer.

 

If you breeze through these, there is a whole bunch more. Game theory, combinatorics, tensors, etc...

 

My best advice is for you to follow your interests. If you are working out one proof and discover Bezel functions and they sound interesting, then go explore them. Have fun whatever you do.

 

Cheers,

Mot

 

PS Keep a good calculus book and a good ODE/PDE book around because sometimes you have to review basic concepts to understand what is in the harder books. Maybe E.T. Bell for some interesting not always true math history.

[math]{e^{2Ii\pi}}=1[/math] and [math]{e^{\frac{(4I+1)i\pi}{2}} = \sqrt{-1}[/math] etc... where [math]I[/math] is an integer. To find the roots of a [math]\R[/math] number, simply put it in this form (polar coordinates). Then divide until you get all the roots.

 

Example: [math]\sqrt[4]{16} = 2e^{\frac{8i\pi}{4}}, 2e^{\frac{6i\pi}{4}}, 2e^{\frac{4i\pi}{4}}, 2e^{\frac{2i\pi}{4}} = 2e^{2i\pi}}, 2e^{\frac{3i\pi}{2}}, 2e^{i\pi}, 2e^{\frac{i\pi}{2}} = 2,-2i,-2,2i[/math]

 

You will generally get more than half your roots in the complex plain. I chose [math]\sqrt[4]{ }[/math] because I could do it in my head.

I think you are underlining an old idea of mach's (or his followers). If you doubled the amount of mass in the universe your (you at the same mass)inertia would double' date=' if you halfed it your inertia would decrease by half.

 

Obviously no experimental results on that one![/quote']But how does my mass know the other mass is out there? Is it a constant in the universe or does it depend on how close I am to other mass? If it is proportional to distance then there must be a critical mass (or event horizon). I don't know how to design an experiment to test this unless somebody has a handy anti-gravity chamber they could lend. I am a math guy, so the only lab I have ever used consisted of a pad of paper and a pencil (and some computer simulation these days).

 

Thanks for pointing me to Mach. That will probably keep me busy for a bit while I figure this out some more.

Mot

 

PS This is par for the course for not being on the cutting edge of science, but at least I was expecting this to be old hat to somebody this time. I came up with a bunch of new math in the area of infinite series to work out some 2D shallow water equations in a discrete environment back in the 90's only to discover after a bit of research that it was all done and published in the early 1900's. Talk about a bummer. I was excited for an hour or two. I still found a leaf or two of knowledge but not a whole branch like I first thought.

Ok let me try again. Take away all matter from the universe. Put in one small jumbo jet sized space station. Let's apply some force at right angles to the axis of rotation. I agree that during the application of force to get the space station spinning that there will be artificial gravity associated with the force applied. After the jets are cut off, what reference can say that the space station is spinning? I don't buy that you will just feel artificial gravity from the spin. There has to be something acting on the body to make the observer in the body feel the 'gravity'. I am assuming it is an aspect of gravity. Even in free fall, a space ship is still being acted on by gravity. I only have four forces to work with and it seems the most likely, so take away any gravity well then it shouldn't matter how fast the space ship spins, there will be no spin felt once the jets quit. I think I am outside the realm of counting infinity and in the realm of Aleph One or Two to make a math comparison. If you assert that there is an artificial gravity if there is a spin, then explain where your reference point is. Did you set a small camera in space before you started this thought experiment to watch the acceleration of the space craft? Anyone know where a good source of information for this type of inquiry is? I like Brian Greene, but it is not in his books, and I am limited to internet at the moment.

 

On the time question. The reason I asked it is because I think time is meaningless in an area with no gravity and also in an area with infinite gravity. In between time flows slower in high gravity such as a black hole has and faster as the gravity decreases, but if the observer is in the black hole or in a place with little or no gravity acting on them, then they would not notice a change in time. You could say that time and weight are in some sense inverse to each other. I think this question is easier to tackle than the spinning space craft though they are linked. I just don't have an understanding of how they are linked.

2. No. The spinning will have virtually no effect on a mass that is not spinning with the space station.

The question I am trying to ask is different. Let's assume all the mass in the space craft is spinning too. Now take away all mass outside the space station. If you are outside any gravity or reference how can you even say that the space craft is spinning and how can there be any artificial gravity acting on the mass inside the station? Now let us put an identical spacecraft next to ours and on the same axis. Have it not spinning? Which one has artificial gravity? How can you tell?

I don't understand why you say yes to 2a. Do you know a reference or two that would explain in more detail for both question 1 and question 2?

 

thanks

Mot

I think these questions are linked, but I don’t really know how to find the answers.

 

1) Does time exist outside of a gravity well? I was listening to Science Friday and remembered these questions. I believe that time only exists if there is a mass acting on the observer even if that mass is the observer.

 

2 If you are in a space station that is spinning to give artificial gravity, then will spinning the space station always cause artificial gravity? My guess is that in order to have the acceleration, the space craft has to be in a gravity well. The corollary question is, does a change in the gravity well affect the perceived gravity inside the space station?

 

Thanks

Mot