Do you find some mathematical activities useless?

[Maximilian Hohmann]

(04-01-2018 07:29 PM)pier4r Wrote:  Wait a moment.

I think you got me wrong :-) What I was trying to say is that if my bank account saldo (or paycheck balance) is as long as the last currently known decimal of pi then I certainly don't need to worry about completing my collection of HP calculators. I would just buy every calculator museum on this globe...

[pier4r]

Ah.

But wouldn't you have still less than 3.5 euro though? With a lot of decimals, but less than 3.5 .

Also I wonder the bank fees to store the changes to your account.

[John Keith]

(04-01-2018 02:30 PM)rprosperi Wrote:  I never purchase top-of-the-line graphics cards or CPUs, they are always priced stupidly high for 1%-ers that want that kind of edge for gaming (or more recently, mining), however as the top of the line moves up, all the mid-range move up as well, and typically at the same price points, so this year's mid-range is as much as 75-100% faster than last years, but at the same price. So I get the benefit of those silly top-end components, without buying one. Bottom line is I'm glad all those folks are buying top-end components for mining.

That can be said for computer hardware in general. The "state of the art" almost always has a lousy price-performance ratio and is "obsolete" a week after you buy it.

Back on topic, I use only simple math in my day job but I enjoy programming and solving math problems in my spare time. It helps to prevent my aging brain from fossilizing.

John

[Dan]

(04-01-2018 06:00 AM)Paul Dale Wrote:  How many years was it before conic sections were useful? Over 2,000 years.
Pauli

Another example is number theory and its applications in cyber security.

[Csaba Tizedes]

Yes, pier4r, as I get older, I think these stuffs are totally useless and boring things. I can remember to my studies and I think if I can learn mathematics again I want to learn more useful algorithms, like swarm behaviour or how the predators are hunting or how to cover up a robbery, etc... This is full of math and more interesting to make an argumentation like "If 1/(aa) = 0.0(bb)(bb)(... and 1/(bb) = 0.0(aa)(aa)(..., then show that (aa) and (bb) is divisor of 990."

Csaba

[zeno333]

(04-01-2018 02:30 PM)rprosperi Wrote:  

(04-01-2018 01:48 PM)Maximilian Hohmann Wrote:  Maybe so, but have you tried to buy a state of the art graphics card in these days? They are either unobtainable or carry silly price tags because the whole production goes into those abominable Bitcoin mining farms. I guess we have to wait for the impending Bictoin collapse until we can benefit from fast processors and graphics chips. Not long hopefully.

I never purchase top-of-the-line graphics cards or CPUs, they are always priced stupidly high for 1%-ers that want that kind of edge for gaming (or more recently, mining), however as the top of the line moves up, all the mid-range move up as well, and typically at the same price points, so this year's mid-range is as much as 75-100% faster than last years, but at the same price. So I get the benefit of those silly top-end components, without buying one. Bottom line is I'm glad all those folks are buying top-end components for mining.

I agree...I am not a gamer, so my AMD Ryzen 5 1400 CPU with R340 rather slow graphics card works fine...

[Joe Horn]

(04-01-2018 12:29 PM)Maximilian Hohmann Wrote:  I know that mathematics is useful, to a degree at least. But I see no beauty in it.

Thank goodness that "beauty" means different things to different people. To me, "e^(i*pi)=-1" is a striking example of beauty in mathematics. My mind is just as aesthetically thrilled by thinking about that equation as my eyes are aesthetically thrilled by gazing upon the beauty of nature's best surprises, such as double rainbows, the Northern Lights, or the Grand Canyon. Something about the combination of surprise and symmetry makes my heart skip a beat... which is what all Great Beauty, of any kind, does to me. Ditto for great architecture, great poetry, great music, great meteor showers, great human physiques, and those glorious snippets of mathematics which I, at least, find immensely beautiful.

Yes, maybe Euclid alone has looked on Beauty bare, but she needn't be naked to be beautiful. Even the mere sound of her massive sandal set on stone, heard but once and then but far away, is beautiful. (Thanks, Edna!)

[Maximilian Hohmann]

(04-05-2018 04:51 AM)Joe Horn Wrote:  To me, "e^(i*pi)=-1" is a striking example of beauty in mathematics.

This is an excellent example of how human ingenuity invented complex numbers to link two seemingly unrelated natural constants. Almost as amazingly incredible as E=mc^2 (which is rather physics than mathematics of course). But as you write, "beauty" is something different for everybody.

[zeno333]

(04-05-2018 05:55 PM)Maximilian Hohmann Wrote:  

(04-05-2018 04:51 AM)Joe Horn Wrote:  To me, "e^(i*pi)=-1" is a striking example of beauty in mathematics.

This is an excellent example of how human ingenuity invented complex numbers to link two seemingly unrelated natural constants. Almost as amazingly incredible as E=mc^2 (which is rather physics than mathematics of course). But as you write, "beauty" is something different for everybody.

People did not invent Complex numbers, they were "discovered"...

[SlideRule]

(04-05-2018 06:15 PM)zeno333 Wrote:  People did not invent Complex numbers, they were "discovered"...

Mathematicians seem to embrace more than one theory w/ respect to the origin of numbers;
a: platonic theory
b: intuitionist theory
c: formalist theory
d: logistic theory
e: fictionalist theory
among the most referenced theories: pick one & expostulate accordingly.

BEST!
SlideRule

[zeno333]

(04-05-2018 07:55 PM)SlideRule Wrote:  

(04-05-2018 06:15 PM)zeno333 Wrote:  People did not invent Complex numbers, they were "discovered"...

Mathematicians seem to embrace more than one theory w/ respect to the origin of numbers;
a: platonic theory
b: intuitionist theory
c: formalist theory
d: logistic theory
e: fictionalist theory
among the most referenced theories: pick one & expostulate accordingly.

BEST!
SlideRule

No labels needed...God controls everything...anything that is logical is that way because it agrees with the Essence of God...math and any component of that math is the current sum total of our exposure to the laws of Logic according to god, in which at any given time our knowledge of that can only be partial.

[Paul Dale]

(04-06-2018 03:19 AM)zeno333 Wrote:  God controls everything...

Which leads directly to the ultimate and perfect sorting algorithm.


Pauli

[pier4r]

Pauli I wish use that!

[SlideRule]

(04-06-2018 03:19 AM)zeno333 Wrote:  No labels needed … … our knowledge of that can only be partial.

I find this publication, [attachment=5819]by Owen Gingerich most apropos.
an excerpt from a review:

We live in a universe with a very long history, a vast cosmos where things are being worked out over unimaginably long ages. Stars and galaxies have formed, and elements come forth from great stellar cauldrons. The necessary elements are present, the environment is fit for life, and slowly life forms have populated the earth. Are the creative forces purposeful, and in fact divine?

Owen Gingerich believes in a universe of intention and purpose. We can at least conjecture that we are part of that purpose and have just enough freedom that conscience and responsibility may be part of the mix. They may even be the reason that pain and suffering are present in the world. The universe might actually be comprehensible.

Taking Johannes Kepler as his guide, Gingerich argues that an individual can be both a creative scientist and a believer in divine design: that indeed the very motivation for scientific research can derive from a desire to trace God's handiwork. The scientist with theistic metaphysics will approach laboratory problems much the same as does his atheistic colleague across the hall. Both are likely to view the astonishing adaptations in nature with a sense of surprise, wonder, and mystery.

In God's Universe Gingerich carves out "a theistic space" from which it is possible to contemplate a universe where God plays an interactive role, unnoticed yet not excluded by science.

I found the publication an enlightening read with keen utility for moderated engagement.

BEST!
SlideRule

[Joe Horn]

(04-05-2018 06:15 PM)zeno333 Wrote:  

(04-05-2018 05:55 PM)Maximilian Hohmann Wrote:  This is an excellent example of how human ingenuity invented complex numbers ...

People did not invent Complex numbers, they were "discovered"...

"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk." ("God made the integers, all else is the work of man.") -- Leopold Kronecker

[Jim Horn]

I used to claim that the universe runs on differential equations. One of my college professors disagreed and pointed out that it runs on convolutions. He had a point!

With the way matrix math can describe multibody motion as state spaces, convolution describes all sorts of responses using (nonexistent) unit pulse inputs and other such features of Mathematics, I can see why there's belief in "The Book". Algebra, geometry, calculus and more were drudgery in school - but discovering how they represent and resolve real things (and can drastically simplify more elementary approaches) was always a terrific revelation and delight.

I *do* recommend http://www.3blue1brown.com/ for some well done introductions and demonstrations of some truly elegant aspects of math that aren't very well known.

[Gerald H]

(04-05-2018 06:15 PM)zeno333 Wrote:  

(04-05-2018 05:55 PM)Maximilian Hohmann Wrote:  This is an excellent example of how human ingenuity invented complex numbers to link two seemingly unrelated natural constants. Almost as amazingly incredible as E=mc^2 (which is rather physics than mathematics of course). But as you write, "beauty" is something different for everybody.

People did not invent Complex numbers, they were "discovered"...

What country were they discovered in? Were they lying on the surface or buried in the earth? Were they situated in a larger body of maths artefacts?

[Gerald H]

(04-07-2018 03:07 AM)Joe Horn Wrote:  

(04-05-2018 06:15 PM)zeno333 Wrote:  People did not invent Complex numbers, they were "discovered"...

"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk." ("God made the integers, all else is the work of man.") -- Leopold Kronecker

Kronecker - Very good at maths, but I wouldn't buy a used car from him.

Maths, & all numbers, are human artefacts, constructed to help people manipulate their environment to improve living conditions.

God has no use nor interest in maths and numbers - He knows & can manipulate as He wills.

[pier4r]

(04-07-2018 04:57 AM)Gerald H Wrote:  What country were they discovered in? Were they lying on the surface or buried in the earth? Were they situated in a larger body of maths artefacts?

An answer could be:
There is the universe. There are the law of universe that allow everything that happens, also thinking. One cannot do or think something that is not allowed to happen (looking at you Parmenides. I understood you years later!). So "math" (or whatever one thinks) can be thought because the universe allows the possibility to think about it. Therefore every new thought or action or what not is a discovery of a possibility that was there (maybe all the time) but no one did it until then.
The same could be applied to "oh X invented the engine". No, "X discovered the concepts and the procedures to build an engine that were there waiting for someone since - well we don't know"

You can see it as "I discovered a new lake" if you abstract and think about concepts and activities about the map of possibilities that one can do.
I remember that the same concept was exposed way better by Montesquieu around 1700 in the persian letters.

Of course, as slide rule mentioned, this is one possible perspective.

Anyway the topic was about what you think about some mathematical activities.

[Dan]

(04-06-2018 12:18 PM)SlideRule Wrote:  Gingerich argues that an individual can be both a creative scientist and a believer in divine design

Many past and present scientists believe in God. I read somewhere that Isaac Newton wrote more on theology than on science.