Not totally sure what he does, something with creating new algorithms. I think he had wanted to teach originally. — Count Timothy von Icarus

Universities are increasingly using adjunct faculty, which is a travesty since the pay is extremely low and no benefits. Of course, if you are brilliant and get your doctorate from Princeton or the like there are ample opportunities. These days new faculty tend to be recruited from other math departments.

Once that's settled, is philosophy sexy? :smile:

Yes, it is a simple matter that (D) is the correct answer. — TonesInDeepFreeze

Of course. :roll:

Hello Z. I retired as professor of mathematics at a branch of a state university over twenty years ago, so its possible the undergraduate curriculum has changed a little since then. Since you belong to TPF I assume you have an inquisitive mind and are good at the math you have used. That will make your academic journey much more pleasant. What university are you attending? That could make a difference in my advice. Are you of typical age for a freshman in college, or older?

Do you have an end goal in mind? It should be easy to find a teaching job at the high school level with a BS, but an academic career at the college level much more problematic. And I don't know what opportunities there are in private businesses and government, although I suspect they exist.

I received a math BS in 1958 from a large state university, went into the USAF and studied meteorology, becoming a weather officer, then went back to school for an MA in math, taught for three years at a small college, and finally a PhD in 1971. I would have been better off academically had I gone straight through, but I was not that dedicated at the time.

You will have to take a number of courses in various areas of math, some of which you will enjoy, but others not so much. To go all the way through a doctoral program requires many more math courses, increasingly difficult. Again you would like some but not others. I only felt like a real mathematician when I reached the point where I could actually explore ideas that intrigued me and do original research. So that career path is long and hard.

So, tell us a bit more about yourself (if you are willing to do so). :cool:

Francisco Varela's homepage: F. Varela's Homepage

A bit confusing for me. The math is pretty vague with the first appearance making no sense. A little later on his discussion of dynamical systems is a tad more palatable. Overall, what he writes (in great length) could be brilliant or a satire on science. I assume the former since Stanford is behind the publication.

Peter Lynds writings make more sense to me, although he is an amateur physicist. Initially, he agreed with Bergson that time had no "instants", but rather interludes, an approach to the nature of time that drew considerable criticisms from the physics community.

To illustrate non-linear time, this graph shows the correspondence between ground observer time (horizontal axis) and proper time (vertical axis) for a spaceship going at v(t)=ct^(.1) over a time interval [0,1]. Although the clock on board ticks at a linear rate, to the ground observer a short interval in his time frame on the horizontal axis, going up to the red curve and over to the vertical axis shows a smaller interval of elapsed time on board the ship. The blue curve shows that, for a stationary spaceship, the elapsed times are the same, measured in linear form. (ignore gravity)

My response to this is that seven billion people on Earth has not hit the minimum headcount that would make my advice work by way of creating a critical mass of willingly paying customers for philosophical insight. — god must be atheist

I think this is the best contribution to this thread. Thank you, gmba.

Kind of like herd immunity in reverse.

[My math paper:

1. log24=2

Therefore...

2. The Riemann Hypothesis is true.] — Agent Smith

You funny. :cool:

Are there other non-numerical things? — Raymond

I used to teach point-set topology. A delightful topic.

I try be brief :smile:

How are math theorems found? — Raymond

I be brief. Usually by playing with existing mathematics. At first a conjecture, then comes a proof.

Can time be a variable? How do you vary time? — Raymond

Pondering

I’ve taken infinite to mean it’s always existed. — AJJ

Eternal, perhaps?

This is done to the tiniest details to avoid inroads of criticism. You explain everything, like in a math proof, leaving nothing to guesswork. — god must be atheist

Well, here's a difference between a PhD math thesis and a publishable math paper: In the thesis the grad student is encouraged to spell most arguments out in at least some detail, but a math research paper frequently glosses over any details that have relatively brief proofs and experienced mathematicians can be expected to fill in the blanks.

Which makes me wonder if this is true with philosophy papers as well?

[joke] Even your two takes on the subject are just long, convoluted ways of saying tl;dr. [/joke] — T Clark

I try be briefer in future. :snicker:

Can't believe this thread is still going on. :roll:

Do philosophy people have a reputation? — TiredThinker

From my perspective (an old mathematician) philosophy people looove to talk and write, sometimes going on for paragraph after paragraph elaborating upon a concept that I would have described in a couple of sentences. But I see that as my fault, being too concise, failing to expand and not enjoying writing as much as others do. The writing on this forum can be very impressive in both quality and content, but I fade away after reading a few lengthy paragraphs. :yawn:

Whatever mankind does to itself will ultimately be dwarfed by what nature does. Beyond looming climate change, which might be benign by comparison, the Yellowstone cauldron and similar eruptions, plus an asteroid or two can be truly catastrophic.

It's just that moving clocks seem to move slower. If you accelerate them they actually move slower. — Raymond

The clock hypothesis is the assumption that the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity

Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference

(Wiki)

However, I am certain that time dilation (whatever it is) did not involve Absolute Time. — god must be atheist

Not sure there is any such thing. As we watch a spaceship fly by at half the speed of light times the linear 0< t<1, both the spaceship crew and you and I experience time as linear, however the passage of time on the spaceship as recorded here on Earth is curvilinear.

Time dilation during the early stages of the Big Bang makes the notion of an infinite past debatable. It would seem that an "infinite past" would be bounded nevertheless.

On the concept of the number of many worlds in quantum theory, David Wallace (2011) has this to say:

To be sure, by choosing a certain discretisation of (phase-)space and time, a discrete branching structure will emerge, but a finer or coarser choice would also give branching.
And there is no “finest” choice of branching structure: as we fine-grain our
decoherent history space, we will eventually reach a point where interference
between branches ceases to be negligible, but there is no precise point where
this occurs. As such, the question “how many branches are there?” does not,
ultimately, make sense.

Not an argument, just an observation somehow related to the OP.

*if* the information content of the universe is finite, *then* the number of possible universes is countable — hypericin

You are assuming another possible universe is simply an extension of the one we are in, adding features here and there. How could you possibly know what a different universe might be? It might be indescribable from our limited perspective. You seem to be simply shuffling around the features of our universe and applying them to other universes. Its physics, if it had one, might be incomprehensible. Its math could be different, in which case the word "possible" in the OP makes little sense.

It's clear I'm not seeing these many worlds from your perspective. And I'm not restricting myself to solutions of wave collapse in our universe.

I would ask, "Why is the causation 1/2^n power? — Philosophim

OK. At the present time we have a result of causation from an event having taken place 1/2 a year ago. At that time a previous event caused that result, the previous event having taken place 1/4 of a year prior to that event. Keep going back in time in this manner and you never reach an origin for this causation sequence, although the causation sequence started no further back in time than one year ago.

Silly nonsense.

If an infinite regress of prior causes leads to a contradiction, then there has to be a first cause. — Agent Smith

Suppose the infinite regress is a causation sequence that, going back toward an origin, is of the form 1/2^n. You never reach the origin, but the chain exists. Just babble :roll:

Most of these articles will not be worth the paper they are printed on, no matter how brilliant they are. They will remain still born — Tobias

Fortunately, it's the exploratory effort that gives them meaning. Publication and citing gives them reward.

If it is finite, we can encode it as a (very, very, *very* large) integer. Think of binary data as a universal medium of information. All binary data, no matter how large, is just a base 2 integer — hypericin

This type of comment comes up every so often. Alexandre used it some time back. Exactly how do you do this encoding? Is it arbitrary?

So then the set of all possible universes is representable as an infinite array of integers. — hypericin

Hence, you assert the "number" of possible universes is countable. That's a big "if".

The only way I can see the op succeeding is if the information content of the universe is finite, there are only a finite number of possible universes, and by some law universes cannot repeat in the multiverse — hypericin

Alexandre made that assumption also.

If there are other universes the principles of probability we have assembled may not be the same. We can say absolutely nothing about the nature of other universes. But they can make for good science fiction. :smile:

Something doesn't add up — Agent Smith

All of us who use Wikipedia should contribute some $ now and then. It will continue to exist but may have to start accepting ads.

That is exactly what we do in academia nowadays... we are not trained to be revolutionaries. Part of me resents it, but another part of me sees wisdom in this slow but meticulous grinding of our lens... — Tobias

Yep. I like the "little pepper-corn" analogy. I've mentioned before that the number of new research papers in math alone arriving at Cornell's ArXiv.org surpasses 250 per day.

What's fascinating about reality requiring an observer is that there must've been at least ONE from the very beginning of reality — Agent Smith

Right. Otherwise it could not exist now.

Some time back the president of the American Mathematical Society could do this juggling trick.

What is it about these big-shot intellects that they are attracted to this sort of thing? :chin:

Either the state of the universe can be represented by a real or it cannot. — hypericin

It would make more sense if you questioned whether the number of objects in the universe was finite or infinite, then countable or uncountable. What does it mean to say the "state of the universe"?

Sorry, makes no sense to me. If you're talking about dynamical systems and their states you must explain all the details.

In brane theory, a 3d brane, on which matter is constrained, is emerged in a 4d space. When the branes . . . — Raymond

It's intriguing to think these things "exist", an effort to comprehend the physical universe - or simply a devise to create working models.

Either the universe can be so represented, or it cannot, because the universe is too complex. But if the latter, then my argument is only strengthened. — hypericin

nullum sensum facit

Why are these pictures misleading? — Raymond

Implied by

You are completely right. It is wrong to think that ‘geometrization’ is something essential. It is only a kind of crutch (Eselsbrücke) for the finding of numerical laws. Whether one links ‘geometrical’ intuitions with a theory is a … private matter

Einstein, from a translation of a letter to Reichenbach in 1926.

Drop a brick on your foot. No force, huh? :lol:

But in GR space is curved inherently. — Raymond

Once one moves into 4-D, the "curvature" of space becomes an algebraic concept, not a geometric concept. And implications back to 3-D probably remain algebraic. Einstein called gravity a force. All those images of Earth sinking into a net and balloons expanding are misleading. IMHO. :cool:

You are missing that space for an accelerated guy is curved. That's the weird thing about space. — Raymond

In four dimensions, yes.

You are now the third person, who I have discussed cosmology with, who has stated, with serious conviction that they know the structure and origin of the Universe.
Each as convinced as the other that they are right and the current popular hypotheses are wrong. — universeness

:cool: :up:

I have a proof that time is real. I'll show it to you — Banno

That's unreal!!! :gasp:

Space expands, objects such as solar systems or galaxies do not expand as they are gravitationally bound. A common analogy is pen marks on the surface of a balloon being blown up — universeness

Thanks. It's nit-picking, but space itself has no substance and does not "stretch" as the balloon analogy suggests. The metric changes and objects not influenced by gravity move apart. This is one way of looking at the expansion of the universe. Spacetime is more complex. There's lots of material on curvature in mathematics, but I'm not sure about applications to pure space. Beyond my paygrade.

Isn't so called (velocity/gravitational) time dilation, a case of warping the 4th dimension (time); however, unlike space in which case a straight line becomes a curve, with time, a curve becomes a straight line. — Agent Smith

Curvature occurs in spacetime, rather than in 3-D space is my (pathetic) understanding.

so, expansion of space, is the notional 'clock' ticking. The current expansion rate is accelerating — universeness

Is it space itself that expands, or matter within space?

(A year of physics at GaTech in 1956 didn't prepare me for the modern world of physics)

Mathematicians can play with time, real or unreal:

Playing with Complex and Distorted Time

If there was any physical substance to time it would be a topic in fluid analysis. Perhaps it flows in the aether? :chin: