Do you find some mathematical activities useless?

[Gerald H]

(04-07-2018 07:42 AM)pier4r Wrote:  

(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.

I presume you adhere to the group that claims Michelangelo discovered David in a stone, the figure was there all the time?

Yes, the thread is about maths activities; These are purely human endeavours of invention to help make our lives better, or do you suppose that hammers were discovered or the internal combustion engine?

You belittle human creativity, allocating creativity to a different realm of existence.

As a maths example, did Kronecker discover the Kronecker Symbol

https://en.wikipedia.org/wiki/Kronecker_symbol

[Maximilian Hohmann]

(04-07-2018 08:14 AM)Dan Wrote:  I read somewhere that Isaac Newton wrote more on theology than on science.

This is because the universities back then were centered around the theology departments. Every other subject, be it medicine or natural science, was regarded as a specialisation of theology and one had to study theology (or attend a priest seminar) first.

And mind you, one of the greatest astronomers of all times (who was required to study theology for some time in the town where I live), Johannes Kepler, earned his money as an astrologist, something he never believed in and even ridiculed ("Die Astronomie ist die weise Mutter, die Astrologie ist die törichte Tochter, die sich an jeden, der sie bezahlt, verkauft, damit sie mit ihrem Hurenlohn ihre weise Mutter unterstützen kann."). He was young and needed the money...

[pier4r]

(04-07-2018 09:18 AM)Gerald H Wrote:  I presume you adhere to the group that claims Michelangelo discovered David in a stone, the figure was there all the time?

Well why not? (Interesting that you created a similar example like Aristotle. The "sculpture in power" of a piece of stone)
Again, mine is one of the possible perspectives. I am not claiming that this should be THE perspective. It is my current perspective of choice as it appears quite solid to me.

One could argue like Berkeley and say "look, neither you nor my body exist. it is all a dream of mine". That is another perspective again.

Someone else can say "nah, I believe everything is chaotic" and so on.

Slide Rule posted a list of the most common ones.

Quote:You belittle human creativity, allocating creativity to a different realm of existence.

Not at all. It is you seeing my approach as belittling.

To make an analogy for me some are like playing a very strong game of chess. Can you enumerate all the possible chess games under X moves? Sure (well, with enough time and resources, plenty of them. Optimized sysRPL programs help since the search space is huge)
Nonetheless to find/discover the proper moves in reasonable time you need plenty of what we call creativity.

Some moves may require enormous amount of creativity that only few people with very particular conditions can achieve each hundreds of years.

But this doesn't change the fact that those moves are there waiting to be discovered, it is not that one creates them out of thin air. They are legal moves allowed by the game.

Same with reality. Some entity (god, the universe, whoever you want it is not the main matter here) may - I don't want to claim the truth. This is a possible idea of the many ideas that can exists on the subject - set the rules. And we live according to them.

The David was one of the possible sculptures that could have resulted by the work of Michelangelo. He was great enough to take a path that lead to the David as we know it.

Could I have worked on the same block of stone? Sure. Could I have taken the same decisions of Michelangelo that lead to the David? Not even if I try 1 billion times. Maybe not even if I try forever, as I can end up exploring only a certain type of combinations missing out the important ones.

There is a short story of Borges. The immortal. He gives an interesting idea that living forever is boring, as living forver one could achieve everything. I reflected about it and I am mostly agreeing with him. But it is also true that only having one type of infinite resource (time) doesn't help that much. For example if one can keep in mind only a certain amount of concepts one may be unable to find revolutionary concepts on his own, since he will be limited by his abilities even if he can try over and over.

(04-07-2018 10:42 AM)Maximilian Hohmann Wrote:  (" damit sie mit ihrem Hurenlohn ihre weise Mutter unterstützen kann.").

Interesting perspective.

[Dan]

(04-07-2018 10:42 AM)Maximilian Hohmann Wrote:  

(04-07-2018 08:14 AM)Dan Wrote:  I read somewhere that Isaac Newton wrote more on theology than on science.

This is because the universities back then were centered around the theology departments. Every other subject, be it medicine or natural science, was regarded as a specialisation of theology and one had to study theology (or attend a priest seminar) first.

Actually that's not quite right. The overarching dogma in European universities at the time wasn't Christianity, it was Aristotelianism. Newton wasn't in agreement with all of the doctrines of the Church of England and asked King Charles II to exempt him from the requirement to be ordained as a minister in order to continue to teach at Trinity, which (unusual for the time) was granted. He wrote prolifically on religion and theology, including works on Trinitarianism, Biblical chronology and interpretations of the prophecies of Daniel and St. John. It is important to note that none of these works were published during his lifetime, probably because he was afraid of being charged with the crime of heresy. There is no doubt Newton had a deep belief in God. He wrote "I have a fundamental belief in the Bible as the Word of God, written by men who were inspired. I study the Bible daily".

[pier4r]

a good example of apparently not useful quest.

Plotting part of the solutions of 85 million cubic equations with integer coefficiens going from 200 to -200 (the equations were 25 billions, only 85 millions fell in range).
https://www.reddit.com/r/math/comments/8...lex_plane/

Now I wonder what they guy learned. because I am pretty sure one can get quite some patterns doing this.

[Valentin Albillo]

(04-23-2018 03:04 PM)pier4r Wrote:  a good example of apparently not useful quest. [...] Now I wonder what the guy learned. because I am pretty sure one can get quite some patterns doing this.

Probably not much. He used quite arbitrary choices for both the range of the coefficients and the window of acceptance so the alleged patterns in the resulting images would surely reflect this and would probably be quite different with other choices.

Also, this technique of getting fractal-like images from roots of polynomials is nothing new, just Google Images for "Littlewood polynomial roots fractal" for some classical images and links to relevant articles (Borwein et al. popularized this in some of their excellent books on Experimental Mathematics).

Last but not least, what's an "useful" quest ? Is the quest for beautiful, artistic images "useful" ? Is it "useless" ? What about mathematically-generated art ?

I recently wrote my own 2D fractal generator program, a simple personal affair developed in 30-plus-year-old hardware, OS, and programming language, just for the sheer fun of it all, and despite me being into fractals since reading the first seminal article that made the cover of Scientific American that many decades ago, I've been utterly astonished by what the simplest of formulas, a simple palette, and a simple coloring algorithm can produce, i.e. absolutely unexpected images, indefinitely zoomable and explorable, that no one but me has ever seen since the Universe began, among a multi-infinity of them existing (or not) in some Platonic realm.

Everytime I use my program I casually discover scores of them, totally different from the previous ones, which leaves me gasping in amazement.

Is this a "useless" quest ? Not for me.

Regards.
V.
.

[Egan Ford]

(03-31-2018 10:29 AM)pier4r Wrote:  At the last Mathjam in Berlin there was the topic about searching digits of PI or similar quests apparently pointless. For example computing PI, square root of 2, e, biggest prime, etc. Of course the quest can be also theoretical, not only of numerical nature.

I do not think any of these or other mathematical activities are useless. Esp. if it's fun and/or something (anything) is learned or discovered (self). I can think of many other useless activities. Math will never be one of them. :-)

Computing Pi to a large number of digits requires some learning about disciplines that are not necessary purely mathematical, e.g. hardware design, computer architecture, storage, availability, power consumption, networking, algorithm optimization, etc...

I while ago, when I had more personal time, I learned 10ish popular assembly languages from the 8008 to the 68000 and computed Pi to 1000 digits on each of them. Each required it's own math code to be optimized for the features (and lack there of) of each processor. I did this because I wanted to better understand the evolution of early microprocessors. But I did it mostly because it was fun. I also learned how to write emulators, timing with 8086 interrupts, how the 8008 evolved to the 8080/8085 and 8086, etc... good times.

Quote:the newly idea of cryptocurrencies* (see primecoin), and so on.

I've been working with blockchain and cryptocurrencies for the last 3 years. My team built an Ethereum-based edge computing platform (https://bluehorizon.network) using our own instance of Ethereum. And, we created our own currency (bacon and bacon-bits). An incredible amount of learning and thought was a byproduct of this exercise.

Re: Proof-of-Work (POW) and power consumption. It is a known issue, worse however, is the lack of transaction throughput. Other consensus algorithms are being worked on, e.g. Proof-of-Stake. If cryptocurrencies are going to have a chance of being mainstream, these issues have to be resolved. There is an incredible number of people focused on these issues.

[Egan Ford]

(04-24-2018 05:27 PM)Valentin Albillo Wrote:  Is this a "useless" quest ? Not for me.

I could say this for every single one of your challenges. Time very well spent. Thank you for "some mathematical activities" that some may deem "useless".

[pier4r]

Egan thanks for the contribution and the link. Though in your first paragraph it seems that for you math is useless. I guess a not is missing

[Egan Ford]

(04-25-2018 09:13 PM)pier4r Wrote:  Egan thanks for the contribution and the link. Though in your first paragraph it seems that for you math is useless. I guess a not is missing

Did not state that. Unsure how that was conveyed. Math is not useless and activities like computing Pi IMHO are not useless.

Wait, found the missing *not*. Thanks!

[Valentin Albillo]

(04-25-2018 08:58 PM)Egan Ford Wrote:  I could say this for every single one of your challenges. Time very well spent. Thank you for "some mathematical activities" that some may deem "useless".

You're welcome, thanks to you for your kind comments and interest in my challenges. I still fondly remember your outstanding contributions to my Short & Sweet Math Challenge #20 "Oh, So Easy", most especially the part dealing with Göbel-like sequences, which you extensively worked out despite being extremely busy with professional and personal matters.

Best regards.
V.
.

[pier4r]

One of the endless examples.

Poisson distribution https://en.m.wikipedia.org/wiki/Poisson_distribution .
Known to be published at least in 1711 then again in 1837, applied in 1898 .

Now it is ubiquitous in simulations.

[pier4r]

Today is god...err, Gauss day on Google.

A quote I agree with.

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment"