Minkowski coordinates measure the interval between events as √(t²-x²-y²-z²) . — noAxioms

c=1?

1. Tenure-Chasing Supplants Substantive Contributions — Art48

Substantive contributions? Who decides that? Possibly like a clique of mathematicians who gather together to praise the subject to which they have devoted much time and effort. I've been there and done that and then looked with unbiased clarity and found little of consequence in a larger scheme of ideas.

In the math profession one achieves favorable results through a convergent sequence of mistakes — jgill

Converging in what sense? From what I understand is converging on the correct answer by process of elimination (series of errors). I feel this is not just applicable to maths but across the board. Probability underlies most of not all interactions/processes right? — Benj96

Getting closer and closer to the solution of a problem through a sequence of mistakes. It's a play on math terms, but probably applies to most problem solving.

Perfection is a distant and cruel god. Even refereed published math papers frequently have mistakes, simple typos mostly, but sometimes flaws in reasoning which are much more serious. A highly respected Oxbridge mathematician far up in years, like me, claimed to have solved a long lasting and major problem in analytic number theory, but those who read his paper shook their heads in sad recognition of creativity being a spectacle of youth. :chin:

As for feeling badly when you make a mistake - get back in the saddle and do better.

I've been reading some of his earlier posts and when he moves away from purely philosophical banter they read like a novel, fascinating at times. I wonder, did this guy get a PhD in math eventually? He sounds very distracted from the intensities those programs normally exhibit. In his later incarnations on TPF did he ever get into math discussions?

'The sage' as a philosophical archetype, one who'sees things as they truly are' not in the narrow sense required by the precise sciences, but as a general grasp or insight into the imperfection of our sensory knowledge — Wayfarer

It would be good see more personal experiences recounted in these discussions to give meat to things said centuries, even millennia, ago. As a mathematician I had the handicap of only fully grasping abstract ideas when bringing them down to specific, more elementary examples.

In the present thread I am reminded of a drive I took several years ago into nearby mountains. As I drove over a hill and looked down on a small bridge I saw a bear leaning against a guardrail. This was no surprise as I had seen bears in this site before, but as as I approached the bridge the bear shifted into an old stump leaning propped the rail.

When I analyze this experience I think of the fact that seeing a bear there before had triggered a slight rise in emotions, which would make embedding in memory a tad stronger than usual. Then driving down the hill the subconscious would seek and find and present what had been enforced in memory stronger than normal. An "insight into the imperfection".

I would be surprised, however, if my suggestion were to take root. Philosophy is not a game to be played on a personal level. Profound statements are the ticket. Good luck with that. :cool:

THIS is the only thing of substance on this thread IMO. Penrose deserves praise for his contributions to physics and math, but as a philosopher I'm not so sure. For example, his notion that complex numbers are fundamental in QM seems a stretch - though they certainly facilitate the wave equations.

Personal correspondence. I was convinced of his credentials. But I could have been mistaken. He was from the Netherlands.

What surprises me is the person I have in mind has a graduate degree in physics and has reappeared on several occasions in various lively personas. Not a math person like me. Oh well. Good work, Inspector.

Well, Inspector Wayfarer worked it out. I had no idea — Baden

Kudos to the man down under. :cool:

green flag was banned for being returning banned member Hoo. — Baden

That's a surprise. I would have guessed someone more recent.

We are human, mistakes are both inevitable and necessary - to learn from — Benj96

In the math profession one achieves favorable results through a convergent sequence of mistakes. :cool:

My question would then be, why is the government and military so untrustworthy that civilians feel that gun ownership is a requirement to feel safe/protected? — Benj96

Sadly, frequently the police can only come in and pick up the pieces. And I doubt that large numbers of Americans fear their own military. Quite a few of us served.

that the enemy, finally seen, turns out to be us — green flag

Pogo's words reverberate through time. I once pulled a skiff through murky waters up to my chest in the Okefenokee much like Humphrey Bogart in "African Queen". That same week someone had lost control while water skiing not far away and had died, having fallen into a nest of water moccasins.

Stay away from this guy. Throw yourself into adventure. — jgill

Zapffe was a climber ! — green flag

Practicing what he preached?

This is a tragic break in nature, as Zapffe clearly laid out — schopenhauer1

Stay away from this guy. Throw yourself into adventure.

That story could have turned out very differently! It makes me wonder about what happened leading up to the story that brought together a fourteen year old, a mafioso, and a frequently fired stolen gun — Fooloso4

I would spend part of the summer with my grandparents on the Gulf coast, very loosely supervised. I went crabbing and sold my take to Angelos Restaurant, where some mafia guys would eat. I noticed one of them would drive his Cadillac convertible into the parking lot behind the restaurant and leave it open. I hid in some bushes one evening with my bicycle and when he went in I opened his unlocked glove compartment and took the gun, getting on my bike and peddling furiously.

I also broke into a couple of antebellum mansions lying boarded up on the coast, their spacious lawns complete with ancient oaks, Spanish moss hanging from branches. Inside, the decor was post Civil War with deep somewhat tattered red velvet drapes and a sword or two hanging from the walls. I stole two old guns from those break-ins. One, a pistol, disappeared yeas ago and probably is still out there, functional from the 1890s.

Angelos and many of those impressive homes were destroyed by hurricane Camille in 1969.

These stories show how tapestries of gun ownership evolve.

I quit being a crime lord in the Fall of 1951.

What is it like to be a cockroach ? — green flag

If AI gains eminence we will all find out. :worry:

I know and confess that I'm caught in this game of playing the hero, and that's how I play the hero. — green flag

:chin: :cool:

The majority of people favor gun control. — Fooloso4

It's the details where things go awry. Over 300,000,000 guns out there, how would one start to deal with the sheer numbers? And they last so long, they are so well made.

When I was fourteen I stole a handgun from a mafia member. This was 1951, and the gun was a Colt semi-automatic in .380 caliber, dating from about 1915 or so. Its lands and grooves were pretty much gone from considerable firing, but it was definitely still usable. I gave it to my father a few years later and it disappeared sometime before 1968. It's still out there somewhere, untraceable and lethal.

Personally, I would like to see assault weapons banned, and that might be enforceable to some extent due to records being kept. But the political will is lacking.

Well, if jgill cant help . . . — universeness

The late Dr McCarty seems to have been a man of many talents, including studies of logic. Beyond me, I fear. The length of this piece is challenging on its own. I didn't get far. @TonesinDeepFreeze might find it interesting. The idea of relating math to solipsism is bizarre (to me, at least).

He is arguing against the ultimate reality of objects in spacetime — Art48

Ultimate or not, being bitten by a snake or run over by a train is a strong argument for what appears real.

I know, "I refute it thus" has fallen into disfavor. But something connects with the kicker's foot, and it might as well be the Illusory rock.

This reminded me of a discussion that apokrisis participated in — T Clark

Yes. He seemed very trustworthy on technical subjects like this. I miss his participation.

Emergence is not well understood in all its varieties.

In Wikipedia Mark A. Bedau observes:

Although strong emergence is logically possible, it is uncomfortably like magic. How does an irreducible but supervenient downward causal power arise, since by definition it cannot be due to the aggregation of the micro-level potentialities?

At its simplest level it is characterized as an automobile, which involves a pattern or arrangement of parts. Under downward causation in Wikipedia:

Downward causation does not occur by direct causal effects from higher to lower levels of system organisation. Instead, downward causation occurs indirectly because the mechanisms at higher levels of organisation fail to accomplish the tasks dictated by the lower levels of organisation. As a result, inputs from the environment signal to the mechanisms at lower levels of organisation that something is wrong and therefore, to act.

Downward causation might be a key to understanding consciousness, but mathematically it is not well understood. The explorations I have done in infinite compositions of functions might eventually play a minor role, especially inner compositions which relate mathematically to the convergence of continued fractions. Don't worry, I won't get started. :nerd:

Please sign ChatGPT on as an honorary member of the forum. :cool:

The way this question is phrased amounts to meaningless internet blather. — Wayfarer

:up:

What I'm arguing is that there is no existence without mind and that the nature of the universe outside any mind is unintelligible and unknowable. That's why I keep referring to the book Mind and the Cosmic Order, which is not a philosophy book, but a book about neural modelling — Wayfarer

At age 91, Dr Pinter is still intellectually active it seems. But he made his mark in mathematics, not metaphysics or neurology. His speculations about why we see multiple objects simultaneously and not isolated single objects is perhaps of interest to some. But to stretch this to imply "there is no existence without mind" seems a tad sketchy. :roll:

Suppose, instead, that there is a measurement at the slits — Andrew M

Does this measurement physically affect a photon on its way to the far screen?

Time, therefore, elides the multi-forms of creation into a universal oneness of blissful wholeness. — ucarr

Where do you buy your weed? A blessed product.

Science fantasy at best. :roll:

The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, actual measurements always find the physical system in a definite state. Any future evolution of the wave function is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution — ”Wiki: Measurement problem

This will probably turn out to be really dumb, a lesson not to mess in physics when one is not a practitioner, but nevertheless: Here is a stripped down version of the Schrödinger equation, showing its simple solution. Note that the solution is originally dependent upon a constant, ${{C}_{0}}$. This is the measurement at time t=0. Whatever value this constant assumes will then determine the time evolution of the (wave) function.

There are an infinite number of solutions depending upon that constant (measurement) - a superposition. Then the measurement takes place and a "collapse" occurs giving a particular solution. Did the measurement "do something" to the system, or does one simply experiment to find the appropriate value of the constant? Where is the magic?

Being dumb in QM, I am missing some subtlety, I admit. :chin:

$\frac{d\psi }{dt}=ik\psi \text{ }\Rightarrow \text{ }\frac{d\psi }{\psi }=ikdt\text{ }\Rightarrow \text{ }\ln \psi =ikt+C\text{ }\Rightarrow \text{ }\psi (t)={{e}^{C}}{{e}^{ikt}}={{C}_{0}}{{e}^{ikt}}$

${{C}_{0}}=\psi (0)$

I apologize for the muddled message. It was not intended as a formal mathematical definition, but more like a poetic metaphor of mirrored universes — Gnomon

Thanks for the reply. Neat image. :cool:

Is scientific Cosmology trespassing in the domain of Theology, when it tries to explain the implicit existence of a mathematical point-of-convergence (zero point singularity) between Space-Time and Infinity-Eternity? — Gnomon

Not sure what this means in a math context. The north pole of the Riemann sphere is, in a sense, "the" point at infinity in the complex plane. So in the chordal metric one gets closer and closer to "infinity".

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? — jgill

Any rational sentient beings would presumably make some of the same discoveries. That’s the meaning of ‘true in all possible worlds.’ — Wayfarer

You answered the second question, not the first. If the potential of existence of rational beings is extinguished, would the potential of mathematics vanish as well?

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? The potential of rational beings is a necessary condition for potentials of mathematics. But is it a sufficient condition?

Can't have one without the other though. — Wayfarer

What if the purely "mechanical" act of measurement produces a numerical result that goes automatically into a computer file and is never "observed" as it sits there and rots? :smile:

I think it's useful since we are observers. At any rate, since our understanding of quantum mechanics is incomplete, there's going to be differences of opinion on the best way to talk about it. — Andrew M

Thanks for your thoughtful reply.

If you do lose your quantum car keys, you can just call your local quantum mechanic. — Andrew M

Who could be anywhere :lol: — Wayfarer

Having imbibed a bit too much at the local pub he enters a state of superposition, thoroughly confused, an unknowing victim of a partial differential equation.

Measurement results a physical fact (in interpretations with physical collapse), and observation results in knowledge of that fact. — noAxioms

:up: :cool:

Except maybe the measurement dials! — Andrew M

The entire quantum subject would be better served if "observer" were eliminated everywhere and replaced by "measurement". Then the casual physics dilettante could think, Yes, if I aim my flashlight at my keys on the table I don't disturb the keys, but if the keys were quantum size I might disturb them in the act of "observing" them. Just a comment.

The US followed an insidious path to a now intractable problem. — Banno

So it's likely that the huge numbers of guns in circulation in the US and the extraordinary number of gunshot deaths, becomes, as I said, a vicious circle — Wayfarer

Yes, the gun problem is intractable.

On the other hand, for those of us in the middle class life is pretty good, despite stubborn inflation. When we go to a restaurant it is crowded with patrons, and when I go to a local fitness gym it is full of young people enjoying life. Driving and shopping are relatively safe when you look into the statistics. The parks are full of lively activities and I suppose theaters are not doing badly, although we don't go to movies - so much is available at home. And immigrants keep pouring in, looking for a better existence. I only wish we would immediately give them employment opportunities.

I don't know wtf I'm talking about, jgill, but somebody with real QM chops is bound to come along who can talk mathematical physics to a mathematician. :sweat: — 180 Proof

Real-life Q-physicists have been chased away, I fear. Kenosha Kid tried to get some sympathy for the Transactional approach, but had unsatisfactory experiences and left the room to play his guitar. I know very, very little about Q-theory beyond the elementary stuff. Feynman's path integral I can follow if I take the simplified version involving time splitting. In my old age I dabble in very elementary mathematics (in the professional sense), finding the road I am on challenging enough. :cool:

In more recent years, a sort of cowboy fascist gun, don't tread on me, anti-government, etc. culture has developed in various parts of the country--mostly rural areas. A lot of these yokels are anti-urban. — BC

A reflection . . .

When I was in high school in the early 1950s I belonged to the NRA. I recall the American Rifleman being about target shooting and both small game and large game hunting. I dropped out when I entered college in 1954. A decade later the Vietnam conflict began and I had completed my military service and was a captain in the USAF Reserves. I remember seeing a copy of the magazine with a cover showing military men with weapons. Firearms became weapons. Hunters switched from the beautiful bolt action rifles of the past to ugly military-style semi-autos.

Recently, in urban areas in my state, there have been car-jackings by armed teenagers. Occasionally they shoot car owners who offer no resistance. In one incident a car owner shot back and, although several teenage girls escaped from the car the driver was injured and later died. He was twelve.

How does one try to protect one's self or family? Unfortunately law enforcement merely picks up the pieces. Yes, I've read of the probabilities of family tragedies due to having a firearm handy in one's dwelling. But there are three hundred million guns out there, and they are mostly well-made to last several generations.

I'm not sure my little exposition should be a reference point. That's how I perceive change over time. I can also go backwards in time, showing there need not be a conflict between infinite regression and first causes.

Particle physicists refer to worldlines (or many-worlds branchings) and statistical mechanics refer to entropy gradients — 180 Proof

Where a lot of that begins is the Schrödinger equation, which is fundamentally a partial differential equation with the independent variable t = time. When solutions are computed, all of a sudden mystical superpositions and wave collapses occur with experimentations. Why is time so vital here?

I'm with Victor Toth on this one. Gravity is a force. The force is counteracted by the upward force of the plane before the parachutist leaps away. Then it's force due to gravity counterbalanced by force due to air resistance as he falls, each force changing a bit with distance, which is determined by time's passage. The effect of him falling is determined by several "causes", including jumping out of the plane and the force of gravity. I don't think "cause and effect" is relegated to the junkpile of philosophy (or physics, for that matter) because at some infinitesimal scale it's hard to discern which is which. I agree with in that regard.

(I model mathematical causal chains - in time - as compositions of functions. A result (effect) at a time t is, say, z. The next temporal step, and the scale of time can vary, is to compute s, where s=f(z), then after that, r, where r= g(s), and so on. There's a whole theory herein. But I think it more realistic to assume several functions act on z, not just one. Like differing forces. So each step - and these are associated with intervals of time - has as outcome the influence of a number of "forces", rather than a single function.)

Sorry, got carried away with a current research topic of mine. Maybe it's relevant here.