What book are you reading?

[SABRE]

Just started reading SPQR by Mary Beard (pic below) these days. So far enjoying reading it and those of you who are fans of Roman Empire and want to delve into the early history of ancient Rome, then this book might be a good start for beginners.

It starts from the very ancient history of Rome, where Mary Beard tells about the various myths and legends associated with the origins of Rome. The story of Romulus and Remus as well as the famous and legendary Trojan prince Aeneas who is considered the original founder of Rome. The famous seven Tarquin kings of Rome (there were supposed to be other kings in between because the timeline of the monarchy is so stretched as per ancient historical sources that each of the seven king should have live for 100 years) and Rome's transition from monarchy to republic after Tarquinius Superbus's (the last Tarquin king) tyranny. But Mary Beard doesn't explain the details of every myth/legend and events mentioned as she just glosses over them, so I would urge readers to go about and read or watch videos on those events just to get the general idea.

However, Mary Beard cautions its readers that much of that ancient history should not be taken for granted, because its very long and stretched with limited evidences from archeology and historical texts etc. Most of the ancient history of Rome (if written) was "lost to flames" after the sack of Rome by Gauls in 390 BC and therefore later 1st Century BC historians and writers of Rome themselves had no primary source available and therefore much of such myths/legends or events were exaggerated at best. Also as per consensus Roman history got actually recorded after the sack from 390 BC onwards and it transitioned from myths to facts.

View attachment 97309

What are the chances? Reading the same book.

 

[SiliconBit (silicon0000)]

Disclaimer: I haven't read any of them.

 

[SiliconBit (silicon0000)]

Disclaimer: I haven't read any of them.

 

[Joe Shearer]

Disclaimer: I haven't read any of them.

Now that's an ambitious no-reading list.
Kudos.

 

[markhor]

The linearity of Newton's F=ma is "good enough" in vast bulk of day to day cases of our localised use. Similar to how I explained to joe recently that we can treat the world as flat in our local reference, whether it actually turns out to be curved in reality.

Ah yes, engineers (physicist?).. reminds me of this:

 

[markhor]

Interested to hear what parts of what Sinek mentioned stood out to you the most or you found most applicable to your team. I skimmed through it (for now), but really I'm interested more in your takeaways/applications.

Revisiting and reinforcing basics is important, even if folks dont know or dont have the time for the original form sources.

You find some building blocks on some matter, then you realise just how much folks get distracted by circumstances, contexts and even coincidences. But human emotions lend to that outer layer first....it was first contact and impression and dictates lot of perceptions that make deeper dispassionate delve harder or less interesting + less important to many folks in the end.

The linearity of Newton's F=ma is "good enough" in vast bulk of day to day cases of our localised use. Similar to how I explained to joe recently that we can treat the world as flat in our local reference, whether it actually turns out to be curved in reality.

We've similarly over many 100s and 1000s of years made use of discretization as this was much more readily harnessed and tangible to us compared to the continuous.

Putting aside the RGB (well ROYGBIV, though my mom taught it first to me as VIBGYOR) I think I mentioned earlier visually (and putting aside Newton's very consequential development here too.... bridging Descartes+Fermat with Maxwell and Einstein downstream)....with our (arguably 2nd most important sense) ears we segregate a continuous spectrum of sound for the intrinsic reasons we do into an octave and its bands C D E F G A B + C and a few intermediaries based on this (sharps and flats).

I explained these (briefly to friends in various places) one set of building blocks to make an endless number of arpeggios when you have just one instrument (or one range) at hand...but even with this "constraint" ....there are some distinct aesthetics connected with patterned-separation that pop up (chords, progressions keys et al)....connected to some deeper truths (that then take much more time to explore).

Then it is all a matter of what imprints by some chronology and circumstance particular to us in the end....from that "outside" as it first intersected with us from our initial tabula rasa.

It is instructive even with just the constrained form....the guitar I play, the chords and arpeggios that most struck out to me....their earlier sound during the lute era for example and the andalusian cadence of the western ear that was formative for so much.

I told a buddy one time, one of our favourite bands (regarding a song that reminisces about a place growing up) using E C A as its basic progression hits the mark so well by its simplicity even taking the vocals away. But it was the vocal style (copied a few years after) by another band that brought up a court case (a lesser known one compared to some others in music)....the infringement stuff discussed earlier brought this to my mind just now heh. But the 2nd song also elects a similar progression (more conventional - E G A) and aesthetically sounds similar (i.e the basic reason of why E and A sound good) if you have the ear for it. Then the lyrics do their bit to further contrast, separate away and disguise what is more connected in fundamental essence....though even here something of an inverse relation is built up.

You add more sets of instruments (especially that searing sound of bowing a string rather than just plucking it...and the somewhat mellower hybrid a piano does with its string hammering)...and all kind of aspirated instruments too (for whatever ensemble - orchestra you can expand this with)..... you can start to add more complexity and contrast as Bach did taking counterpoint to the new levels and richness he did....so much so that the andalusian cadence got submerged to a substrata (though it has re-appeared+re-invigorated maybe mostly due to American music "back to basics" in its new world context).

i.e its really up to a person's interest to explore the earliest contours or to really grasp finer detail in the long form development of underlying theory and history....in most modern praxis its good enough if they know and can use and have their conceptualisation of building block importance past that.

i.e This linearity + discretization is essentially inbuilt in our perception, non-linear and continuous forms of the same spectrum and essence simply end up being lot harder and more noisy in comparison, at least without time invested into it.

Hence building blocks being important as larger phenomenon.

This connects with some of my earlier replies as to the math side of things..... all the way from why certain archetypes appear in number theory (as to why the building blocks of the smallest integers end up dictating what and where certain things break down in higher dimensional spaces that say algebra and geometry visualise and explore more) and all the way to its connective aggregation in say the pareto principle (80% of outcomes coming from just 20% of the causes).

Reading the last few (longer) posts on yours, it seems you have a keen interest in emergent behavior among very simple agents. It reflects your interest in game theory and/or swarm intelligence. I am poignantly reminded of the lectures I took from the great Georg Kampis (https://kampis.web.elte.hu/) on the simulation of complex systems through simple agents. There were many interesting discussions throughout, some that stood out were, how building a highway through a natural habitat (like a forest or a desert) whereby the animals of the same species or prey/predator are separated can cause extreme changes in the diversity of the population. Another one was floods and their causes and a recurring pattern that is observed in their devastation style.

 

[SiliconBit (silicon0000)]

Now that's an ambitious no-reading list.
Kudos.

The number of books I started is far greater, but after reading a few pages, most of them were left unfinished. Only when I was in the mood to read till end, or if I found a few particularly interesting ones, were they actually finished.

I know that this habit of mine is not good ...

 

[Joe Shearer]

The number of books I started is far greater, but after reading a few pages, most of them were left unfinished. Only when I was in the mood to read till end, or if I found a few particularly interesting ones, were they actually finished.

I know that this habit of mine is not good ...

JOIN THE CLUB.

 

[Nilgiri]

Reading the last few (longer) posts on yours, it seems you have a keen interest in emergent behavior among very simple agents. It reflects your interest in game theory and/or swarm intelligence. I am poignantly reminded of the lectures I took from the great Georg Kampis (https://kampis.web.elte.hu/) on the simulation of complex systems through simple agents. There were many interesting discussions throughout, some that stood out were, how building a highway through a natural habitat (like a forest or a desert) whereby the animals of the same species or prey/predator are separated can cause extreme changes in the diversity of the population. Another one was floods and their causes and a recurring pattern that is observed in their devastation style.

Yes building blocks and simple agents interest me greatly. These are connected to the eigenvalue problem intrinsically....be they linear or non-linear....i.e they either represent something of the eigenvector directly or characteristic in close conjunction/derivative of it.

The sensitivities (which you mention with animals in this case w.r.t their habitat and some new forces introduced) of the larger space and its vector field of interest to them...and of course the bounds of relevance past which things break down gradually or abruptly (as your first post regd the Indian mathematician lady's discovery some pages ago).

Eigen itself means "own" or "characteristic" in German.

One sees it manifest in lot of structured puzzles for example that are more tangible for people to behold and grapple with patterns and make some early understanding on the matter at hand even if they are unable to solve it.

Take the rubiks cube and solving it by "brute force" layer by layer.

The first layer is pretty nominal (I can teach this to most people in under 10 minutes with them able to replicate it)....these are where the first simple agents process (basic rules of getting something moved and fixed relative to something else, cross and corners as I call it) illustrate themselves.

The second layer is the first real algorithm (since you have to not upset the first layer, so you need a longer cohesive extension of the earlier simple agents)... I call it the T algorithm, and this one takes more time for folks to learn/implement compared to 1st....it is not so nominal (to place basically up to 4 edge squares).

Then the third final layer involves advanced algorithms (the easiness "breaks down" substantially and exponentially as it would further do so if you move to a 4v4 rubik and its 4th layer). Replicating the cross this time is harder than with 1st layer...and the corners as well).

Then finding even better algorithms and intuition "on the fly" where you need not do it layer by layer for more optimal solving is its own longer heading to get into....I have only had so much time to get into these....since to me I have a solution that works in reasonable time already.

I'm a chess player (elo around 2100) as well, and you see same pattern in it being common accepted knowledge for "normie" skill levels to simply know 1. e4, d4, c4, Nf3 as the best by test 1st moves for white and then the responses by black for them to make some opening repertoire (ruy lopez, QGA/QGD, french, italian, pirc, slav, indian et al.. and all their further variants....you name it).

But the actual complexity of the game increases exponentially further away from starting move (and its set of best simple agents from feedback of millions of games) given possibility tree expansion even though the core simple agents are consistent always (i.e the ways pieces move and other rules)....so it all boils down to the logic and intuition being as close to the eigenvalue problem so to speak to keep this inflation/drift (to suboptimal cascade and error proliferation etc) as mitigated as possible.

But this is the pattern of increasing complexity that transcends and connects to why the mapping broke down at some dimensional level as illustrated in that mathematical discovery you mentioned.

I jotted down back then (depending on how the convo would turn out here) in my notebook one representative investigation (there are many that could be done) with basic building block phenomenon in the early counting numbers compared to later ones.

In that if you express all numbers as: dots and jumps connecting dots (i.e the initial simple agents or topological units as I will call them for this purpose....not fully accurate, but it will do) and can each successive induction be defined completely using all before it.

1 would be just one dot: o (topological precursor, lacks a jump)

2 would be 2 dots with a jump in between: o - o (basic topological unit)

3 would similarly be: o - o - o (or topologically 2 + 2)

4 would be o - o - o - o (or topologically 3 + 2)

Up to 4, you can always define by using everything that has come before it entirely..

But with 5: o - o - o - o - o , this can no longer be done
it can topologically said to be 3+3 or 4+2, but there is no way to use 2, 3 and 4 completely in one definition with rules we have set in this investigation.

There is a more complicated "through the looking glass" side investigation where you go in opposite direction and have negative jumps where it can be shown you can define 5 from what 6 is (and define 6 from what 7 is and so on) using the same basis of units....which I won't go into as its going to get difficult to illustrate properly....but basically there exists a breakdown between 4 and 5 as to directional preservation in this induction "populating" process.

This is why I brought up Galois before, the root of the issue he discovered when it comes to polynomial factorisation is very much related to the building blocks and voids that can no longer match at some point with "twists, turns" applied in a growing dancing chairs game so to speak (as to elegantly proving why the quintic has no algebraic solutions unlike the quartics, cubics and quadratics and nominal 1st orders).

i.e What does not neatly align like before by the very proliferation of numbers and permutations/transformations and 1:1 and onto mappings based upon them (and what this means for when they represent whole dimensions and their mappings rather than just countable units) from early simple start (1, 2, 3 and sometimes a few more) to much larger inductive finer resolutions so to speak on march to infinity.

This is the simplest way I can explain that (why things break down and get exponentially complicated, it has to do with the numbers themselves doing so relatively quickly after they "get started")....and connect it (for now) to how this discussion all started. Hope it wasn't too confusing heh.

When you have non-living units, you can model and map these fairly robustly the more (combined intellectual lifetimes you have at hand to grapple with it) you throw at it.

When its living units (i.e say human lives), you have same process at hand, but more X-factors as humans are not so predictable like say air molecules to integrate stochastically with brownian motion et al (given consistent forces and spherical volumes of interaction etc) to develop thermodynamics and/or navier stokes....and why these are reliant on very large population numbers + cohesive characteristics from that.... and dont apply so well to small or tiny populations where randomisation starts to break in as a factor again (sort of the inverse to the earlier small number vs large number phenomenon).

But some things do normalise more with larger collective populations that can be studied w.r.t authorities that are much more finite (i.e say 200 countries with 8 billion people in total.....8 billion is a far larger number than 200)....making the calls for them. That is how game theory fits into my reference w.r.t say physics which I am much more comfy with....given my own time integrals invested etc. But what you dont know as much about (but you sense similarity or utilitarian use in some way) is often more interesting to delve into with later spare time.

 

[markhor]

Yes building blocks and simple agents interest me greatly. These are connected to the eigenvalue problem intrinsically....be they linear or non-linear....i.e they either represent something of the eigenvector directly or characteristic in close conjunction/derivative of it

Eigenvalues and vectors are familiar to many people as they are everywhere, so it's nice to introduce them here, more people might appreciate this discussion. As you have mentioned, eigenvalues are essential in structures and their dynamics. An unusual place where I encountered them was computational geometry, where we had to put constraints on the shape of agents (say assembly robots) and the environment they were in (say factory assembly line). Making sure that if the constraint of one agent is valid it must request invalidation or alter its behaviour optimally.

Another one, since this is a hot topic these days, eigen stuff is also employed in some neural network models (ewww - the disdain I have for the modern AI paradigm and its peasantry and patheticness, the so-called deep learning, is unfathomable; but that's a discussion for another time), in particular graph neural networks which must possess invariability to the topology and permutation of the input graph. Graphs themselves, are a very good case for this discussion. The possible configurations of graphlets (inside a bigger graph) of n nodes, is an increasing function of n of course, however, its relevance to the application and finding graphlets say when n is 10 or greater becomes computationally infeasible (that is assuming the parent graph is big enough so that the embeddings of these graphlets don't represent a large portion of it, or worst case, all of it).

they either represent something of the eigenvector directly or characteristic in close conjunction/derivative of it

can you please point me to a source on it?

I'm a chess player (elo around 2100) as well,

My goodness, wow. Do you also, like others, memorize old games? And do you actually calculate probabilities on the fly or do you recognize a move and retrieve its counter from a hardcoded table in memory?

given possibility tree expansion even though the core simple agents are consistent always (i.e the ways pieces move and other rules)....so it all boils down to the logic and intuition being as close to the eigenvalue problem so to speak to keep this inflation/drift (to suboptimal cascade and error proliferation etc) as mitigated as possible

This tree expansion and the Monte Carlo Tree Search combined with off-line reinforcement learning done at deepmind was just fabulous (it is one of the very few AI companies that I respect), although it was for Go.

This is the simplest way I can explain that (why things break down and get exponentially complicated, it has to do with the numbers themselves doing so relatively quickly after they "get started")....and connect it (for now) to how this discussion all started. Hope it wasn't too confusing heh.

NGL, I got lost in the topology parts, ha. You've sold me on number theory I would say, now I'll go on a hunt completely ignoring the humongous backlog. When you get some time, would you be kind enough to give some introductory source on the topic, preferably text (not necessarily a book), targeted for someone so brilliant at writing proofs he memorized his way through a real analysis course (\s).

There are a few members here (I can count on one hand, or maybe if I had polydactyly) who write so well. And they know it. I read some posts and can't help feeling like a monkey picking out fleas. Have you guys considered taking on writing as a profession or even a side hustle? Thank you for the effort you put into this thread making it uncomfortable thought-provoking.

 

[Nilgiri]

can you please point me to a source on it?

It is more my own take on what they are fundamentally...from about 20+ years working with them at different tiers.

Take a pure rotation of the entire 2D plane by some theta. The only invariant is the point which the plane is rotated around. In a way its an eigenpoint...or a collapsed/degenerate eigenvector (it can be expressed in the complex plane, not the real one), but everything else is referenced to it.

When you take the pure rotation of the entire 3D space, the invariant does express itself as a vector this time (the axis around which the 3D space rotates itself) adding to the eigenpoints infinitely arrayed along it.

When you add more transforms simultaneously (stretches, skews, translations what have you), these mirror say the cleaving of your forest for its animal inhabitants (where a pure rotation would be something more intrinsically characteristic)...and the eigenvectors also change (or start to show up to begin with depending on what parameters/coefficients you are defining and studying), though they would have trace correlations (before vs after) with each other as the forest is the forest in the end compared to a highway built (affecting it) through it.

I forget if I am using the right terminology precisely (I am more visually oriented + solutions guy), but it will have to do heh.

My goodness, wow. Do you also, like others, memorize old games? And do you actually calculate probabilities on the fly or do you recognize a move and retrieve its counter from a hardcoded table in memory?

Probability calculation on the fly is extremely difficult for humans (in chess) and waste of time as it requires proper delve in all the possibility branches.....intuitively we cut off the branches that do not make sense in some way so we rarely have a denominator to work with in our head.

Human training and intuition in chess (w.r.t improving skill level) relies on some memorisation for sure, especially where time optimal like in the openings which have been traversed by far more games magnitudes more than say middle games (and their divergences).

Then with divergence coming more into play (middle game and end game, but sometimes also in the opening with atypical "off the beaten path" choices elected for).... you basically fall back on higher order pattern recognition (w.r.t tactics which are kind of like eigenvectors), crucial square recognition (positional/intersectional fulcrums which are like eigenpoints) and general strategy (long term end game state visualisation to cultivate/retain advantage there....something like simplification/liquidation to 2D from a current 3D space).

These do develop the more games you look at from older players (Capablanca notably in my case regd elegant positional strategy and precursor crucial patterns involved with this)...but basically you have to develop the higher order approach as you cant memorise everything specifically....no one can.

GMs (elo >2500) and super GMs (elo> 2700) have just commited to this in an extraordinary capacity to add to whatever natural prodigious talent they had for it to begin with (i.e folks like Morphy being emblematic of that in the romantic era just before modern era of Chess, even though Morphy "as is" maybe has an elo of 2400 in todays metrics downstream).

Computer training in chess (and humans using computer results in positions) is very different in comparison as it brute force checks every "decent enough at first glance" branch to its miniutiae and often finds surprising optimal moves (that look strange to human eyes) compared to a human who rejects various sub branches early from our own learning patterns that have been constrained by finite time impacting on us (during our formative + refined learning of chess) lot harder than it does with a computer and its brute processing capacity.

This tree expansion and the Monte Carlo Tree Search combined with off-line reinforcement learning done at deepmind was just fabulous (it is one of the very few AI companies that I respect), although it was for Go.

Yes I watched all of that with great interest. We have used AI for propietary development in FEM/CFD interactions in aero-engineering which is my domain increasingly as it can make very good decision making during deep data searches.

NGL, I got lost in the topology parts, ha. You've sold me on number theory I would say, now I'll go on a hunt completely ignoring the humongous backlog. When you get some time, would you be kind enough to give some introductory source on the topic, preferably text (not necessarily a book), targeted for someone so brilliant at writing proofs he memorized his way through a real analysis course (\s).

w.r.t number theory and topology.... there is little better than Gauss and his student Riemann. Any book or deep delve regarding them would be good and then you get down the rabbit hole according to your taste.

I have written some notes on both over the years that I can try look up later and see if there are sources to help you....they have kind of come to me in ad-hoc way I have congealed together in my own fashion for my own use, which I can also produce some example of if it so merits or gives me a chuckle later.

They both continue to astound me....so much so alongside Euler, Ramanujan and a hypothetical Galois (if he could have lived even just another 10 years, given his sheer teenage brilliance)...it is really these two I would have no argument over if they are picked by someone as 1st spot for the best ever mathematician.

There are a few members here (I can count on one hand, or maybe if I had polydactyly) who write so well. And they know it. I read some posts and can't help feeling like a monkey picking out fleas. Have you guys considered taking on writing as a profession or even a side hustle? Thank you for the effort you put into this thread making it uncomfortable thought-provoking.

I use this thread as another sounding board to hone my writing craft for sure. It helps when it matters lot more writing long reports to superiors to convince them of where things are vs ought to be headed in some project under my purview etc. So it is already intrinsically part of my profession.

You are most welcome, it is one of few threads I plan to stick around as its politics-free. Politics accumulates the worst of the human psyche very easily, and burdens us with zero sum thinking on matters that are not zero sum at all. Things that tend to sit in a more collective positive sum manner are more appealing for me to engage, especially as time goes on.

 

[Nilgiri]

I got lost in the topology parts

I forgot to add, the insight I gained from my study of all this that I was trying to illustrate with this particular investigation basically correlates to the underlying reality of numbers at their start vs later....and effects of phenomena (that are reliant on 1 to 1 and onto mapping etc) when expanded in some macroscopic way (like whole dimensions of 1, 2 3 4 space etc)

Basically from 1 to 2 is a full doubling. From 2 to 3 is an increase of 50%. From 3 to 4 is an increase of 25% and so on. There are component phenomena in various larger studies that are tied to doubling or are tied to 50% increase and so on that are reliant on early story continuing as is....but it doesnt continue in reality which is the point in the end I suppose....reality is different to early induction trends....i.e world is flat locally versus curvature globally.

i.e When you take some late stage very very large number the increase is negligible, almost zero.

Then everything in between (and often quite early like with the quintic factorization and Galois)

i.e the building block phenomena early on (heck 2 is the only even prime and also the first prime, and 1 is a "precursor" prime?) and deterioration of this as x-->infinity and vast vast voids open up relatively speaking (though the study of primes through this space is its own great interesting subject)....compared to how everything was super cosy at 1, 2, 3 , 4 (phenomena pair and match up easier in bounded permutations, which I tried to express a bit with all kind of variants of musical chairs that you can play).

These have fundamental consequences in number theory and algebraic theory and analytical geometry and everything else in maths in end. Gauss called number theory the "queen of mathematics" for a reason.

 

[panzerfaust 3]

Disclaimer: I haven't read any of them.

Heyy ! You're messing with intellectual property rights

 

[_NOBODY_]

Heyy ! You're messing with intellectual property rights
View attachment 97842

 

[panzerfaust 3]

De

View attachment 97851