Improving the shining hour

I'm still spending a fair bit of time resting, so I decided to pick up some history I didn't have a good handle on, and have been listening to The History of Byzantium Podcast.

The Monophysite dispute was needlessly sad. I wish someone like Socrates had had a little talk with some of the people early on, before grievances grew: "What do you mean by 'Nature?' Can you even use the word 'nature' in the same way with both the Uncreated and the created?"

Two times

Just noodling for fun. This is speculative, not authoritative.

And, on inspection, I clearly have run Blogger's TeX interface way past its limits. I don't know if splitting this up will help--I doubt it. Ah well. Where you see boxes around things, just read the TeX inside, or skim over it. I may have to try to embed gifs, or maybe make a pdf. It's hard to see if I made a typo. And I don't know how to put large parentheses around the matrix--Blogger doesn't handle some of the TeX options.

What does a world look like if it has two dimensions for time instead of just one?

Your intuition undoubtedly says--"That's silly, it would have to look very different from ours, so why bother?"

• Because it is an amusing way to spend time on the bus
• Because some string theorists have come up with modest arguments that we do have two time dimensions. Bars, Vongehr, and Gogberashvili have been looking at systems with 2 time dimensions. I hold no brief for string theory, but hey, it's an excuse.
• In one of his speculative moods, Eddington wrote about interfaces between (3,1), (2,2), and (1,3) spaces, where the numbers in parenthesis are the number of space and time dimensions respectively. The notion fascinated me ever since.
• Because there are serious problems with invisible mass in cosmology, and visibility of matter on other timelines is probably going to be a problem—just as an intuitive guess.

I just want to take a preliminary look right now--not trying to figure out what quantum mechanics would look like, for instance. And by macroscopic time dimensions I mean large enough to use a wall clock or a calendar to measure.

---

There are a few questions about visibility, the speed of light, and causality that don't have obvious answers. I'll try to keep it logical. Assume that the speed of light always appears constant. I'll also assume that objects on different timelines can interact--at some point they had to, so why not now also? Also, if A measures B's relative timeline angle, it should be the same as B measuring A's.

Wait, what do I mean by a "timeline?"

Assume that the two time directions can be viewed as a Euclidean plane, with time-1 in one direction and time-2 at right angles. As an undisturbed object ages, it will assume time-1 and time-2 ($t_1$ and $t_2) values which lie along a line in the plane.

Here are two examples. In the left the upper line has the object moving more along $t_1$ than $t_2$, and the lower line tilts more along $t_2$. Where zero is is arbitrary, by the way.

The right-hand image shows a complication that we need to keep in mind. Timeline A is kind of banal. Timeline B, relative to A, also seems ordinary. It has positive components of its timeline direction both parallel to A and perpendicular to A. So from A's perspective B will not go backwards in time.

However, when B meets C, it will appear to be going backwards in at least one time component.

Should we allow that in our initial study? We can work non-causality in if we rely on small interaction rates, or demand that it only work on small distances, but that seems ad hoc. Let's pretend it isn't going to happen and plo

The obvious first approach is to modify the Einsteinian formalism. In some coordinate system, denote points by $(t_1, t_2; x, y, z)$, where I separate space and time components with a semicolon. Use the same convention for momentum: $(E_1, E_2; P_x, P_y, P_z)$. For two points $a$ and $b$, assume an analogous invariant to Einstein's: $(t_{1a} - t_{1b})^2 + (t_{2a} - t_{2b})^2 - (x_a - x_b)^2 - (y_a - y_b)^2 - (z_a - z_b)^2$. Assume that a transformation to a different frame of reference will be linear.

To keep things simple, just ignore $y$ and $z$ for now, and use $\delta {t_1}^2 + \delta {t_2}^2 - \delta x^2$ as the separation.

A linear (and symmetric) transform can be parameterized as

${x}^'$				1	$\alpha$	$\beta$		$x$
${t_1}^'$	=	$A$		$\alpha$	$\lambda$	$\epsilon$		$t_1$
${t_2}^'$				$\beta$	$\epsilon$	$\tau$		$t_2$

Invariance requires that ${{t_1}^'}^2 + {{t_2}^'}^2 - {x^'}^2 = {t_1}^2 + {t_2}^2 - x^2$, from which we can derive equations which specify $A$, $\tau$, $\epsilon$, and $\lambda$ in terms of $\alpha$ and $\beta$, where the latter act like the $\beta$ in the usual 1-time dimensional theory, just for the two different time axes. Think of them as $\beta_1$ and $\beta_2$. By looking at the limit $\alpha=0$ we can determine the right sign for the square root.

For ease in reading the result, define:

$\gamma \equiv {1 \over{ \sqrt{1 - \beta_1^2 - \beta_2^2}}}$

$A=\gamma$

$\epsilon = {{\beta_1 \beta_2} \over {\beta_1^2+ \beta_2^2}} (1 - {1 \over \gamma})$

$\lambda = 1 - {{\beta_2^2} \over {\beta_1^2+ \beta_2^2}} (1- {1 \over \gamma})$

$\tau = 1 - {{\beta_1^2} \over {\beta_1^2+ \beta_2^2}} (1- {1 \over \gamma})$

And of course $\beta_1$ and $\beta_2$ are the speeds as a fraction of c along the $t_1$ and $t_2$ axes respectively. Their squared sum will never exceed 1, and so $\gamma$ is always real. Yep, this assumes that nothing exceeds the speed of light in any frame. And if you define a rotation in the $t_1:t_2$ plane--a rotation to a different timeline--you can turn a simple boost with one time direction to one with a mix, and it matches the parameterization here ($R^{-1} B_{1,0} R = B_{\beta_1,\beta_2}$), where $\beta_1$ and $\beta_2$ are the original $\beta^'$ times the sine or cosine.

Recalling that energy is non-negative (skipping QM subtleties), an object with momentum $(E_1, 0, p_x, p_y, p_z)$ will not break into objects with non-negative $E_2$, since there's no existing energy in that "bin" to give them. It could break into $(E_1^', 0, p_x^', p_y^', p_z^') + (E_1-E_1^{'}, 0, p_x-p_x^{'}, p_y-p_y^{'}, p_z-p_z^{'})$, but not something with a positive $E_2$ component.

In practice that means that if you don't have any local $t_2$ activity, you won't get any. The situation is stable.

Is there any way to detect the other time dimension?

Typically you and everything about you is going along the same timeline--what is there to make it change? Your best bet would be something distant, or something from a great distance that comes to pay a visit.

Suppose that you always measure the speed of light as the same, no matter what timeline it is on or came from.

Suppose you have two objects, with the same timeline direction, but one starting from a different $t_2$ time, $T_2$. It is at some nearby position $x$.

Suppose the first object has interacted with something in its past so that it has a certain amount of $E_2$ energy available to emit a photon that can reach, and bounce off, that second object. Without that, you'll never emit anything with $t_2$ component non-zero, so you'll not hit the second object. OTOH, assume that the first object has enough $E_1$ that the total $E_2$ is negligable. That way the bulk of what you measure is along the $t_1$ line.

In this thought experiment, what you would measure is the time between the emission and absorption of the photon along the $t_1$ axis, since by assumption you're not measuring anything in $t_2$. That time will be twice the travel time $\tau$, as projected onto $t_1$ axis, or $2 \sqrt{x^2 - {T_2}^2}$. (Observe that if $T_2 = x$, the photon will only reach it going along $t_2$, without any $t_1$ component. It will go there and back again in $0$ $t_1$ time; not detectable. If larger, the separation is time-like, but in a time direction invisible to you; again it will seem dark.)

Since the speed of light is always measured as the same, you will predict $\tau^2 - {x^'}^2 = 0$; that the $x^'$ will appear to be closer to you.

OK, so far so curious.

If you receive a photon from a different timeline, and only measure the energy component parallel to your own, you will underestimate the photon's energy.

But if you measure a foreshortened distance, and can also measure how many wavelengths away the object is, you will predict the photon's wavelength to be less, and therefore its energy higher. If you know a priori what kind of photon you emitted, and measure the energy of the returning one, the energies won't match.

This little contradiction might offer a way to indirectly detect other timelines--one of the assumptions won't hold.

Headless computers

The little ones fit nicely in out-of-the-way spaces, and do what they're supposed to (mostly), up until you need to replace the router--and the little thing needs configuration. Then you need to scrape up a working monitor and keyboard and balance them on top of the piano.

The Raspberry Pi was all the rage for a while, but its price kept rising and a little 4x4x1 box does pretty much the same thing; and I didn't need much horsepower.

Exit row seating

True, there's no seat in front to shove a bag under, but airplane exit row seating has leg room, which pretty much doesn't exist outside of business class--at least for those of us of a certain height.

I gather you may have to pay extra these days for the privilege of not getting cramps.

At any rate, I remember the question before takeoff--Are you physically able to operate the door in an emergency? I always figured I could.

But I wonder if there's a way to check. Suppose one had a partial mockup of a cabin--just a row and the bulkhead--with the exit door in place. And a big timer display above where the flight attendant straps in.

The candidate enters the little room, straps in, and is told to brace for impact. The flight attendant straps in, the room drops about 6" for a jolt of verisimilitude, and the timer starts. The attendant tells you what to do (scenario has them busy with somebody hurt), and you get to see how hard it is and how long it really takes to get the door unlocked, open, and stowed.

It might be a little humiliating, but I'd think it'd be fun to try. I'd bet some people would pay for the experience--especially if the airlines knocked a bit off the extra fee if you could show you'd passed.

Of course different planes have different doors, but just learning one is better than nothing.

February is a long long month

Bony fingers sifting through the habits of a life
Splitting needs from hungers as a clean dissecting knife
  Invoking an accounting of my ways.

Golden-blooming hours mid dead days that wasted sun
Myriad intentions; thousand starts; but pittance done
  Presuming on a bank account of days.

Museless hours have hid his gold – please vend another year!
Snoozing time is over; oil is low; the groom is near.
  With wick that sputters, wait for what he says.

Humor

I wonder how far that's true.

AVI has written a good deal on humor not aging well, and that may be related--the jester is putting together something temporary. That could get hard on you (as the title Treadmill to Oblivion suggests).

I generally do pretty well adding light humor to a conversation, and provide my share of Dad jokes, but if you corner me and say "Tell a joke" the headlights glare in this poor deer's eyes.

And I've found that after the conversation, no matter how many bon mots flew, I rarely remember any of them. They were things of the moment: yes, apples of gold in pictures of silver, but maybe more like unkeepable manna than actual gold.

I hesitate to draw conclusions from this: some people have written enduring humor. But a lot of times humor doesn't keep well, or translate well. In good conversation it doesn't have to, because for the moment it's alive. I wonder how much of our humor is taking these evanescent butterflies and tying windup motors to them to make them show up when I want them to.

Watch an elephant disappear

So there "is no Epstein list". Ah.

I don't remember who pointed me at the link--perhaps AVI--but the author brought up an aspect I hadn't considered, which seems convincing. Presuming that Epstein was cooperating/coordinating with other intelligence agencies(*), the lists could have included people those other agencies were working with and didn't want to give up on yet. We do rely on sharing information with other country's agencies, and if e.g. France says "Ne divulguez pas ces informations si vous vous attendez à ce que nous coopérions avec vous" or something like that, I think we'd consider cooperation with France as a national security issue. A little bit of bare-face lying is merely a small political price. And it doesn't matter what political party is involved. Everybody will hide the lists.

And, of course, the other country's real objections might be trivial, but if they dig in their heels to protect somebody, what are you going to do?

I wish I remembered the author's name: credit where due.

(*) I don't think blackmail was key; helpful people who keep your image clean seems more likely. If he'd been blackmailing people word would have gotten around and he'd have been out of business. Just provide fresh-looking pliable girls at the island and the opportunity for conversations with famous people and let the real agents work.

Time dimensions

My sisters took exception to my statement that the story about the claim that physics simplified if time was really three dimensions playing roles at different scales was all over the news. I guess we read different news.

Anyhow, I felt well enough to tackle the paper today, and well, ...

He sort-of motivates this framework, and gives a pretty generic description of it in Section 2. I was hankering to see where the different scales kicked in. I'm still waiting.

In Section 3.1 he pulls a rabbit out of a hat. Likewise in 3.2. And... He never shows how he derives anything.

But: "The theoretical predictions and numerical calculations presented in this paper are fully described within the text"

Maybe the rest of the text is somewhere else? He cites some of his own work Charge as a Topological Property in Three-Dimensional Time which goes into a bit more detail, but I still don't follow how the different time scales emerge, nor how you can have the specified symmetry if they do have different scales. Nor how he gets 1/3 of a charge for quarks but whole numbers for leptons.

Maybe he explains how they have different "symmetry orders" in another paper he cites. I will not hold my breath.

Two time dimensions apparently are plausible possibilities in string theory, except that they don't work very well there. I did a little of my own noodling on possibilities, which I'll try to post--no string theory required.

Fireworks and family

When I was young and in California, Mom wasn't fond of fireworks or cap guns, and I didn't have the budget to buy them anyhow. Dad didn't seem to mind them, but he went along. I found out later he was a decent shot--he'd been in the Pacific in the war and the Naval Reserve afterwards, so he'd had training.

Things changed. When the civil war got closer and closer to Monrovia, and the booms were light artillery and the cracks in the distance weren't firecrackers, it got on both of their nerves after a while. You never knew when Taylor's men would make a breakthrough, or if government troops would go freelancing.

The US evacuated its citizens (with just a suitcase each), and they came back to the States for a while. (And couldn't leave to go to work in Ivory Coast until they paid the evacuation costs, but the gov't couldn't figure out what the costs actually were for months.)

But neither of them enjoyed fireworks displays after that.

I do, but this year I think I'll rest; maybe watch the neighbor's instead. Not a lot of energy back yet.

Manipulating bird song

We've probably all heard the novelty Christmas songs with dogs barking or cats meowing the notes; and if we're old enough probably remember Marvin Suggs and his Muppaphone.

A bark can approximate a note in the scale, and if it isn't quite there you can tune it to fit, and with enough samples you could program your synthesizer to bark out whatever tune you cared to. All you need to worry about is the note, duration, and volume, and a good synthesizer will know how to deal with key velocity. You have an alphabet; you can plug in whatever sounds you want.

But what about birdsong? What would you need to take into account if you wanted to compose music using recorded bird chirps, cheeps, chips, warbles, etc?

Bird chirps run faster than human-sung notes. In the time it takes me to sing "la" the bird runs through a trill and a chirp to top it off, even shifting back and forth between notes. Maybe it crescendos, rises and falls. The warbling won't be the same frequency from one species to another.

Matching one "note" to the next isn't like picking letters from an alphabet, but matching textures, speeds, even which sets of notes were used in what isn't a chord. It's more like picking characters from a Chinese typewriter.

You could get around that by slowing the bird calls way down, trimming out a clean part, and "autotuning." It would probably sound interesting, and maybe even good, but I doubt it would sound much like the birdsong it came from.

Maybe the Chinese typewriter is the way to go. To get started, suppose we limit ourselves to 2 octaves of the primary note: 24 primary notes. No warble or warble at a set frequency (we can fiddle with the sound to fit one of our set values): say 8. The secondary note: probably a choice of 8, but some will sound nice together with different ones. Rise and fall shape: 5. Hmm. So far that's 7680 different sounds in the sound bank, with 4 descriptors. I hate to think how many calls you'd have to listen through to settle on that number.

Of course you can take different parts of a single call to represent different ... I can't call it a note, because it's more than just the note ... complexes. Still, even without more descriptors, that's a lot of time somebody (you) has to invest to sort out the complexes, before you start playing.

OK, start simple. Sort out a single type of sound you want to work with (warble type, flat "rise and fall", secondary note difference from the primary). That'll be maybe several weeks of work to get 24 notes (getting a feel for the territory takes a while), and then you program your synthesizer and try it out.

I'd bet that it wouldn't sound quite clean right out of the gate--that attack will be hard to make smooth; and probably some things I didn't think of will jump out at the musician who tries to play it for the first time.

Maybe start even simpler: take some bird chirps, split them into sections, and find the primary frequency for each--if there is one. If there isn't, trying to shoehorn them into notes may not be the way to go. You might have fun trying to assemble your own bird calls, though.

Would it be good enough to be an instrument in its own right, or merely a novelty?

No clue.

I suppose it is, at that

"Buy used: $49.95"

Not brand new, anyway.

I've gotten spoiled

The default printer paper and copier paper is good heavyweight stuff, and the fonts have been massaged for maximum readability on screen or print. Copies are crisp, and even single-spaced type is easy to read.

I got a binder of my parents' letters, mostly from '64-'66 (one from '54). Some are handwritten; some were typed on various typewriters. Most were on thin paper, others on airmail letter forms. Bleeding was a bit of an issue. Some were carbon copies. Remember those? Blurry lettering. And the typewriter spacing put lines just a hair too close together--the blogger composition screen is much easier to read. I guess maximizing the number of words per page was key. From the looks of one of the typewriter fonts, that's the only excuse I have for it.

I'd forgotten. That's what I grew up with, and didn't think anything of it then.

Somebody gets it

About fear of heights: the void reaches out for you, and your muscles rehearse every possible way you could fall.

Communications in wartime

From an interrogation of Commander Nishino about the battle of Surigao Strait. His ship (the Shigure) was in the Second Squadron, and was the only survivor of that encounter with American forces. Apparently the overall commanders weren't talking to each other very clearly, and even after Kurita had been chased off and their overall time-table screwed up, everybody was instructed to go on as planned. Second Squadron got there four hours early and went in, and got mauled. Second Squadron's flagship blew up and Nishino couldn't figure out who was supposed to be in charge. Eventually he figured everybody was done for and headed out--the Shigure was just a destroyer.

On the way out he spotted Admiral Shima's force advancing in. From the interrogation:

A. About 0350 I sighted Admiral SHIMA's force advancing northward, while we were repairing the rudder.

Q. Did you communicate with Admiral SHIMA's force to tell him what damage had occurred?

A. I signaled to Admiral SHIMA by blinker because the telephone was broken.

Q. What did you tell Admiral SHIMA?

A. I signalled to the approaching force requesting them to identify themselves, as I was not sure but that they might be American surface units. The answer received was "I am the NACHI". I answered "I am the SHIGURE, I have rudder difficulties." There was no communication after this message.

Q. Why did you not inform Admiral SHIMA of the course of the battle?

A. At 1200 hours of the 25th I sent the following dispatch to Admirals TOYODA and KURITA, "The Third or 'C' Force has been annihilated, location of enemy unknown, please send me your instructions. I have trouble with my rudder, my wireless, my radar, and my gyro, and I received one hit." The reason I did not communicate directly with Admiral SHIMA and inform him of the situation was that I had no connection with him and was not under his command.

Q. Under such circumstances as you mention, was that the usual procedure? Was it not Japanese practice to exchange useful information between separate forces?

A. I assumed that SHIMA knew conditions of the battle and that he would get his instructions from his Commanding Officer, Admiral KURITA or from TOYODA.

Q. How did you assume he had learned of the battle in the entrance to the Gulf?

A. In my opinion Admiral SHIMA would know the situation by sighting the burning ships FUSO and MOGAMI, and by seeing me on a retiring course.

Q. That being the case, it was not considered necessary to give any other further information?

A. Yes, that is correct.

Q. Why was it necessary to wait until 1200 to send the message to KURITA and TOYODA?

A. Because my wireless was not functioning, and secondly I was busy with the air attack.

Q. At what time approximately did you complete repairs to your wireless?

A. I used my auxiliary wireless set, the "TM" set. This set had been in commission all the time. I probably could have used it earlier to send the message. When I sent the message I relayed it through Admiral SHIMA because of the short range of the TM set. Its range is about 150 miles.

Drone weapon market

Trent Telenko's latest thread about drones and snipers suggested a million drones minimum would be required for training our own forces. The numbers don't seem crazy. We train snipers with optics and rifles now while the next battlefields will be using drones for both spotting and shooting.

The first thing that came to my mind was "How many will fall off the back of a truck?" A few years ago AP did some research on how many weapons the US military, and came up with 1900 over 10 years (2010's). 190/year doesn't sound too terrible. FWIW, the AP article is pretty crappy: it only gave numbers for a single burglary (6 M4's and 10 pistols). I'd bet that quite a few of those counted were explosives, e.g. grenades, which are a bit hard to track after use.

I suspect that the presence of a gigantic market for civilian arms depresses the market for stolen military ones in this country. Of course, if our military were as corrupt as Mexico's, economies of scale might enter. But aside from homemade automatic weapons like the Glocks modified with the switch, I hear more about truly automatic weapons (instead of "newspaper automatics") from instances in Europe. Maybe that's some kind of sampling bias in favor of the dramatic, or maybe stricter rules for civilian weapons make military ones a larger share of the market. (And there've been some serious civil wars on that landmass with plenty of room for tools to go missing and no big oceans to cross to get them to market.)

At any rate, I suspect the Mexican cartels will get a lot of their military-use drones from their military, and our local gangsters buy from them or from China, and not bother with US military stuff.