Category Archives: Nostalgia


noun: “playfully quaint or fanciful behavior or humor.” (OED)

To me, it speaks of playfulness, perhaps some randomness, a willingness to play along and see where things go. Perhaps somewhere between the Pkunk and Dirk Gently.

If you played the old M:tG ‘Shandalar’ computer game[1], you may remember this card.

But I’m speaking of whimsy today because I had recently noticed that I had been feeling much less of it my life, due to some stressful circumstances that (I think) have now dissipated. You may have been following my writing for a while, and this is a large part of why I have not written in months, with the few sporadic mostly-picture posts being the most that I could put together.

I’ve been working with my life coach for some time now, on a number of things. One of the largest ones was finding space to create. I had spent a lot of time focusing on making physical and temporal space for creation, but had forgotten about creating the mental space, to be able to deal with distractions.

I almost said ‘push away’ distractions, but similar to the discussion of Saidin and Saidar, pushing away distractions is okay as a crutch, but being able to relax into the flow is much more powerful.

Either way, I’m excited to be feeling creative again, and have some ideas[2] about how to keep this going, even through the next set of distractions that will inevitably crop up.

It’s going to be an interesting year, thanks for being here with me.

-Nayrb 😀

[1]Still one of my favourite games of all time, and I think, even with all its faults, the best M:tG computer game.

[2]Interestingly, a bunch of these are around meditation, which I feel I only discovered very recently.

1997: The year they made Contact

20 years ago, I watched Contact in the theater with my family[1]. Tonight, I watched it again, with S.

To me, it held up well as a movie. All the characters were believable, and the science and the effects were well within the normal parameters of suspension of disbelief.

What struck me[2] was how hopeful a movie it was, that our better natures would win out, that our endless curiosity would take us places we’ve never imagined.

[Note that spoilers follow]

It’s always interesting the things you remember 20 years later. “Why not make two, at twice the price?” The destruction scene. The prime numbers sounding so ominously alien from the aether. The speaking through her father. The 18 hours of static[3].

Interestingly, I had remembered that 18 hours of static as being the vindication at the end of the movie, that she was not crazy, that something had indeed happened, but I had forgotten how much it was covered up.

The one (gaping) plot hole I had missed the first time around was the absence of study and testing before a human was sent through the machine. If you look at the history of the Apollo program, you see that it was preceded by Mercury and Gemini, with dozens of sequential missions, each testing new parts, to make sure that each part of the system and plan were well-enough understood to ensure successful missions. The idea that they would build a half-trillion-dollar system in Contact and not fully study it (especially if it’s generating strange EM radiation) before sending a human through it ‘strains credulity’. Even the EM it’s radiating would be a fantastic discovery for humans.

But I can understand how they would cut out things to make a move that was watchable, and which was able to spend its time focusing on the humans in the story.

The alternative view of events that the NSA directory was trying to convince people of at the end of the movie was reminiscent (for me) of the big con[4] at the end of ‘Watchmen’, albeit at the opposite end of the hope-fear axis.

Apparently, like Bladerunner, the ending was supposed to keep your doubt alive as to whether the events she experienced had actually happened. To me, it didn’t, as 18 hours of static (and whatever metallurgical data they could get from the sphere) would be enough to prove the story.

I laughed, I cried, I am full of hope. A new year dawns. Time to use that hope to build something meaningful, starting with some words.

[1]We immediately followed it with Men In Black. I’ll leave it to you to enjoy this juxtaposition.

[2]If you’d read or watched any Carl Sagan, this would probably not be surprising. “The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars.”

[3]I had remembered it as 18 minutes.

[4]In ‘Contact’, it was posited that a billionaire had faked first contact to inspire humans to push themselves outwards. In ‘Watchmen’ (the graphic novel[5]), Adrian Veidt fakes an alien invasion to scare humans into working together against a common foe.

[5]’Watchmen’ the movie simplified the plot to have Doctor Manhattan be the scapegoat. this lead to a much tighter movie, but slightly less appropriate for my analogy, however much he played with space and time.

When Your Partner Succeeds, How do You React?

Recently, a friend of mine posted this article, which talks about a study where the experimenters measured how participants felt about themselves after hearing that their partner either did very well or very poorly on a test.

Interestingly, the male participants[1] felt better about themselves when they were told[2] that their partners did poorly, and worse about themselves when they were told that their partners did well[3].

Perhaps more interestingly, this only happened when measuring ‘Implicit self-esteem[4]’, but was absent (or much less pronounced) when measuring ‘Explicit self-esteem[5]’.

So, what does this mean? Many or most of us are feeling something subconsciously. Unfortunately, this can be difficult to detect, as the expression can vary widely from person to person and event to event. In the article, the author described one example thus:

“Not long ago a friend’s first book was published, so when I arrived at her home for a visit I eagerly voiced my enthusiasm and congratulations for her accomplishment. Moments into the interaction, her husband strode across the living room to a bookcase and returned with a copy of a book he authored 15 years ago.”

I remember acting like this once[6], and ascribing it to “trying to take away someone else’s success”, or “trying to take their success for your own[7]”. I compensated for it by explicitly giving praise and support whenever someone told me something they were proud of[8].

More recently, I talk with pride about the accomplishments of my partner[9].

Similar things could also manifest as ‘waiting to talk’ rather than ‘listening’, a calling out I remember vividly from early on in my efforts to learn how to communicate.

So, if this is a subconscious feeling, what exactly is it that you’re feeling? Some kind of threat, but what kind of threat? Some kind of threat to yourself? Some kind of threat to how you see yourself or your place in the world? Why does your subconscious think it’s bad for someone else to succeed[10]?

Why does your subconscious see this as a zero-sum game? What are you afraid of? What is the training that you took in as you were growing up that motivated you to think/act this way?

Knowing that, how can you deal with it? You could start by imagining how your partner being successful would help the both of you. As Belgarion said[11], when you notice yourself reacting to something more strongly than you might expect, you can pause, delve into that emotion, try to understand it, and think about it.

Outwardly, you can try listening and praise. Figure out what the person is proud of, why they’re proud of it, and try to find something along that axis to compliment them on. Usually, when your partner is telling you something, it’s like a bird bringing a present back to the nest for their partner. It’s important to acknowledge them and their gift[12]. There will be more than enough time for you to talk about the things you’re proud of, to talk about how you feel. Let them have this moment.

So, how do you react when your partner succeeds? Do you have coping mechanisms for dealing with subconscious issues like this? Share them in the comments below!

[1]”The mean age of participants was 18.9 years (SD 1.52). The average relationship length was 10 months and did not moderate any study results.” All hetero- couples, presumably of college-going demographics.

[2]Interestingly: “Extensive debriefing revealed that all but two participants
believed the feedback. Data from those two participants were
dropped from analysis.”

[3]The effect was opposite, but not statistically significant for female participants.

[4]”The self-esteem IAT assesses associations among two concept categories (self and other) and two evaluative attributes (good and bad) by requiring that participants categorize stimulus items representing the four categories as quickly as possible using two keys of a computer keyboard.”

[5]”Global explicit self-esteem was measured using the Rosenberg (1965) Self-Esteem Scale (RSE). The RSE consists of 10 statements related to overall feelings of self-worth. The items were answered on a 4-point scale ranging from (1) Strongly Disagree to (4) Strongly Agree (Cronbach’s alpha = .77).”

[6]’once’ as ‘in the past’, not ‘one time’. 🙂 It would undoubtedly have taken me multiple occurrences to have noticed the pattern, and likely multiple calling-outs.

[7]’Trying to take their success for your own’ is a separate issue, with its own long and terrible history.

[8]This was actually quite difficult for me at first, as I had to learn it by rote, as my parents found this difficult to do for me as I was growing up.

[9]This may or may not be related. I like telling stories about how cool she is, and cool things she’s done or is doing make for good stories.

[10]There’s a long literature on this topic, probably the most explicit is Wired’s article on how male computer game players who are losing the game are more likely to harass women.

[11]I can’t find the exact quote, but basically, he discovered something about himself that he didn’t like, and he had to take it out, look at it, and think about it for a while. (I think it was him. It was in something by David and Leigh Eddings.)

[12]This is from ‘Blink‘s discussion of successful couples.

When You Wish Upon a Star…

So, a good friend of mine recently posted the following meme:

Depressing thought...But is it true?
Depressing thought…But is it true?

“According to astronomy, when you wish upon a star….
You’re actually a few million years late.
That star is dead.
Just like your dreams.”

It’s a really depressing thought, perhaps even more depressing than the Nietzsche/Kubrick mashup: “God is dead, and you are alone in an uncaring universe.”[1]

At least with an uncaring universe, something with persist after you are gone. If all the stars are dead before you can even see them, would there even be anything left after we are gone?

But extraordinarily depressing statements require extraordinary evidence. So let’s take this sentence apart and define some things.

First: “According to astronomy” means that we get to (and have to) use astronomy in our proof or disproof. It also likely refers to modern astronomy, as it did not specify a time/technology period. (It may be interesting to see if any answers would be different under astronomy from a different time period, but that will be a secondary investigation.)

Second: “when you wish upon a star….” has a few different readings. The phrase seems to come (at least most recently) from the song written for Disney’s Pinnochio. In that movie, Gepetto says the following:

Look! A wishing star!

Starlight, star bright, first star I see tonight…

I wish I may, I wish I might have the wish I make tonight.

This is an ‘English language nursery rhyme’ first published in the late 19thC (Wikipedia).

Interestingly, it seems to refer to ‘shooting or falling stars’, or meteors. These would certainly be ‘dead’ (as they are vaporizing in the atmosphere during the ‘wish’, but not for ‘millions of years'[2], as the distance from the viewer to the meteor can be measured in tens or hundreds of kilometers, an insignificant time light distance[3].

But going back to “When you wish upon a star, the meme-maker seems to be clearly referring to the 1940 Disney song and film. Looking at the occurrences of this song in the film:

At 0:34, you can see the image of Gepetto wishing upon the star:

The star is clearly stationary, as can also be seen in the reprise at the end of the film, where Jiminy Cricket is looking upon the same star, still unmoving:

So, this restricts us to the realm of non-moving (or slowly-moving) celestial objects[4]. From the film, the star also seems significantly brighter than the surrounding stars, but the exact extent to which this is true could be dramatic license.

The rhyme mentions ‘first star I see tonight’, which also suggests that the celestial object seen is unusually bright.

So, non-moving (or slowly moving) celestial objects which are bright. This leaves us with comets, planets, and bright stars[4][5].

Comets are objects orbiting through the solar system, and unless they fall into the sun, impact another body, or otherwise breakup, they tend to go on ‘living’ after we see them. (Halley’s comet has been known since at least 240BC.)

Planets could easily look like stars, often like unusually bright stars. Venus was called the ‘evening star‘[6] since antiquity, and it would be bright enough (up to apparent magnitude -4.9) to be significantly brighter than anything else in the sky. Venus could be considered ‘dead’ because it may have once supported life before a runaway greenhouse effect millions of years ago, but this seems an unlikely metaphorical interpretation. Mercury (up to apparent magnitude -2.45) would also be significantly brighter than anything but Venus (and the moon and sun), but has never been ‘alive’, being too close to the Sun[7]. Mars (up to apparent magnitude -2.91) could have been alive at some point, in the same vein as Venus. One or more of the moons of Jupiter (up to apparent magnitude -1.61) or Saturn[8] (up to apparent magnitude 1.47) could have been home to life, under this same metaphorical definition. (The other planets and other bodies in the solar system are too dim to ever be a ‘bright star’.)

So, a planet could be a metaphorical source for this quote, but this seems unlikely, as the quote seems to be referring to the fact that the celestial object is no longer emitting the light itself.

This leaves us with bright stars. Looking at the brightest star in the night sky, Sirius (up to apparent magnitude -1.46), it[9] is only about 8.6 light years away, so we would know in less than a decade if something were to happen there.

The next 91[10] brightest stars are listed here:

You will note that even the furthest among these, Deneb is still only 2600 light years away, much closer than the ‘few million years’ mentioned above.

Based on all this evidence, it would seem that the original meme:

“According to astronomy, when you wish upon a star….
You’re actually a few million years late.
That star is dead.
Just like your dreams.”

is false, which is good, because it would be super-depressing otherwise.

If you enjoyed this sojurn through astronomy, you may like the rest of my blog. Comment below with things you want me to talk about or investigate!

[1]If you have a better source for this, please let me know.

[2]If you want to be pedantic (and I know you do), you could say that meteors are the dead husks of possible (or tidally destroyed) planets, and their burning up in the atmosphere is hundreds of millions of years after they ‘died’.

[3]Much less than a second, even if you assume they impact the Earth’s atmosphere thousands of kilometers away.

[4]A close supernova might also qualify, as it could easily be brighter than anything else in the night sky, would last just long enough to be a ‘wishing star’, and would have been ‘dead’ for some time before it was seen by a human observer. This might indeed be source of this rhyme, where a ‘guest star‘ could inspire wishing and omens. However, looking at this list of supernovae, any supernova which would have been visible as a ‘bright star’ with the naked eye would be at most tens or hundreds of thousands of light years away, not qualifying for the ‘few million years’ mentioned above. I also personally see supernovae more as a seeding of the galaxy with heavier elements, and thus wishing upon one of these would be wishing that the spreading of heavier elements would inspire life to form elsewhere in the universe.

[5]I see no way that any reasonable person could confuse the Sun or Moon with a ‘wishing star’.

[6]Interestingly, the Babylonians had figured out that the ‘evening star’ and the ‘morning star’ were one and the same. It took the Greeks a significant amount of time to discover this themselves, calling them ‘Phosphorus’ and ‘Hesperus’. How many times have there been such dark ages, where knowledge needs to be rediscovered? Was there a Greek ‘renaissance’, or were the Babylonian star charts lost until modern archaeology? Did mere dregs survive to inspire subsequent scientific revolutions?

[7]…unless there was life along the terminator, at some point in the past…

[8]Or [spoiler alert]:

One of the planets themselves!

[9]They, really, as Sirius is a double star, but that is outside the scope of this post.

[10]93, including the Sun, Sirius and the next 91 of magnitude 2.5 or greater.

“I Want To Be Her!”

Today, we went to see the new Ghostbusters movie.

Before I go any further, there may be spoilers below, and you should go see this movie. S loved it. For me, it was worth it just for the bad-ass ghost fighting, for Kate McKinnon stealing every scene, for the closing credits. Just go see it. (Also, Market Square on Front is a great theatre.)

The review that best captures the feeling for me, I saw on facebook shortly before we saw the movie, and I quote part of it here:

I’m almost 30 and last night was the first time I saw a movie where a woman fucking did a thing and was funny without crying into a pint of ice cream and was badass without being a pinup and all I could think was… I really didn’t know that was an option. I really didn’t know you could save the world without looking like you’re trying to pose for Sports Illustrated Swimsuit Edition at the same time. I have never, in 30 years, seen a major movie that didn’t reinforce the message that how I look is more important than what I do.

The Atlantic talks about how the new movie is a product of its time, just like the old movie:

In that sense, though, Ghostbusters is engaging in one of the most valuable aspects of the culture’s current reboot mania: It is serving, in its very re-ness, of evidence of all that has changed, for better or for worse, since 1984. In the years since the original Ghostbusters premiered, 9/11 happened. The web happened. CGI improved. Feminism got normalized, and then commercialized.

Here, believing in ghosts makes one not iconoclastic, as it did for the men of the original, but potentially that most loaded of gendered epithets—“crazy.”

The film is, in many ways, a study on what would have happened if the original Ghostbusters had been female. They are treated totally differently, routinely called ‘crazy’, even at the end of the movie, the powers that be want to keep them swept under the carpet.

Chris Hemsworth was fantastic as Kevin. I think he should do more comedy.

Kate McKinnon’s fight sequence near the end of the movie was to die for. If they don’t make her a superhero movie, there is no justice in this world. She also stole just about every scene that she was in.

A new movie for the kids of today, a new product of its time. Go see it (and stay all the way to the end!)

How do You Measure Inflation?

Inflation is supposed to be one, measurable number. There’s a number that’s quoted in all the newspapers, and is used all over the place, to help determine how well the economy is doing, to index pensions, to negotiate union contracts, etc, etc…

This is generally known as the ‘CPI’, or ‘Consumer Price Index’. I’ve reproduced the numbers for Canada from Statcan[1] below:

Consumer Price Index, historical summary
(1996 to 2015)   	All-items 	Change from previous year
  	2002=100 	%
1996 	88.9 	1.5
1997 	90.4 	1.7
1998 	91.3 	1.0
1999 	92.9 	1.8
2000 	95.4 	2.7
2001 	97.8 	2.5
2002 	100.0 	2.2
2003 	102.8 	2.8
2004 	104.7 	1.8
2005 	107.0 	2.2
2006 	109.1 	2.0
2007 	111.5 	2.2
2008 	114.1 	2.3
2009 	114.4 	0.3
2010 	116.5 	1.8
2011 	119.9 	2.9
2012 	121.7 	1.5
2013 	122.8 	0.9
2014 	125.2 	2.0
2015 	126.6 	1.1

These numbers should dovetail well with what you read in the news. They even nicely break the CPI down by type of item:

Consumer Price Index, by province (monthly)
(Canada)   May 2015 April 2016 	May 2016 April 2016 to May 2016 May 2015 to May 2016
  	2002=100 	% change
All-items 		126.9 	128.3 	128.8 	0.4 	1.5
Food 			140.8 	143.8 	143.3 	-0.3 	1.8
Shelter 		133.2 	134.9 	135.1 	0.1 	1.4
Household op & furn. 	119.7 	121.6 	122.1 	0.4 	2.0
Clothing and footwear 	95.0 	96.0 	96.0 	0.0 	1.1
Transportation 		128.0 	127.8 	129.4 	1.3 	1.1
Health and pers. care 	120.7 	122.2 	122.3 	0.1 	1.3
Rec, ed, & reading 	109.9 	110.3 	111.7 	1.3 	1.6
Alc. & tobacco products 151.9 	156.5 	156.8 	0.2 	3.2
Special aggregates
All items excl. food 	124.2 	125.3 	126.1 	0.6 	1.5
All items excl. energy 	124.8 	126.9 	127.2 	0.2 	1.9
Energy 			152.4 	143.4 	146.9 	2.4 	-3.6
Source: Statistics Canada, CANSIM, table 326-0020 and Catalogue nos. 62-001-X and 62-010-X.
Last modified: 2016-06-17.

But many peoples’ experience of inflation can be very different.

I’ll use an example near and dear to my heart:

Today, I had the

Vegetable Chow Mein from my favourite food truck: Wokking On Wheels!
Vegetable Chow Mein from my favourite food truck: Wokking On Wheels!

I first visited the Wokking on Wheels food truck sometime during the fall of 1996, when I was working on Calculus with J (Thanks, J!). At that time, they had five daily specials which, if I recall correctly, they were selling for $3.75. These included the special Thursday special, ‘Singapore Fried noodles’, which you could persuade them to add red sweet sauce to. Delicious!

Anyway, the Vegetable Chow Mein was the least expensive thing on their menu today, at $7.

So, 20 years later, how has inflation fared? By the CPI deflator above, you would expect a $3.75 item in 1996 to cost $3.75*128.8/88.9 = $5.43, about $1.50 less than the actual.

Even if you use the ‘food’ number above, you get: $3.75*143.3/88.9 = $6.04, or about $1 less than the actual.

There are a number of reasons for this (which are beyond the scope), but it’s enough for now to note that there are reasons that people have a different feeling of inflation than what is ‘official’.

[1]The numbers for Ontario seem to be about the same to me.

“It felt like flying.”

Walking, walking, walking. It felt like that was all he ever did. He didn’t mind, though, it was actually kind of fun. Most of the time, there would be new things to see, or at least new people. In a city of five million, you would rarely see the same person twice, unless you were specifically going somewhere to meet someone.

But today was different. He was biking instead. He had avoided it for years, after an accident in his youth, where his back carrier had become detached, lodged in the spokes of his back wheel, throwing him over his handlebars.

He had wondered if riding a bike was really ‘like riding a bike’, that you never actually forgot. He wondered how all of the muscle memory (if that was what it really was) worked, to help him keep his balance. He wondered if he’d ever be as balanced as those who biked without hands.

And so he went out and bought a bike. It was nicely coloured, and had front and rear shocks. Not too expensive. It spoke to him somehow. Strongly enough that he didn’t notice that pun until many years later.

Slowly at first, he tried the bike. It rode well, and it turned out that riding a bike was in fact ‘like riding a bike’.

He rode that bike for years, his trusty steed, even getting it repaired for more than it cost to purchase, after an unfortunate overnight stay in a bad neighbourhood. But it was too important, and he was too attached to it to let it go. They continued, and had many adventures together, braved travails and stress, pain and joy.

Some time later, he and the bike moved on to a new place. They continued their adventures, but they were increasingly discovering that riding was causing him pain in the knees. It was time to move on, but he wanted to make sure the bike would continue adventuring, especially because of all they had been through together.

So he put out the call. He put a price on it, not because the money was important, but because he wanted whomever the new person was to take it seriously.

He met the new person, he was a good person. He went away with the bike, sending back a picture as a momento. But the bike had given him an even better parting gift.

Looking back many years later, the bike’s new person had become a good friend. One last time, the bike brought him together.

But perhaps some of that spirit had transferred to his new trusty steed. Biking down the street near what would be their home, his new bike brought him towards a person who would end up being very special indeed.

Numerical Jokes

So, a person walks in to a bar. As they enter, someone up on stage says ‘one hundred and fourty seven’, and the whole bar erupts with laughter.

The person walks over to the bartender and asks ‘What are they doing? Why did everyone laugh just then?’

The bartender says ‘Well, a few years ago, they realized that they were just telling the same jokes over and over again, so they wrote them all down and assigned numbers to them. Saves a lot of time.’

‘Oh! Let me try!’

The person runs up on stage, and yells ‘Fifty-two!’. Dead silence. ‘Fifty two?’ Dead silence. They disconsolately walk off the stage and back to the bar. The bartender says ‘It’s alright.’

‘What did I do wrong?’

‘Just watch.’

A person from the crowd, a regular it would seem, walks up onto the stage. ‘Fifty two.’

The crowd erupts with laughter again.

‘What? Why did that work?’

‘Well, it’s all in how you tell a joke.’

Then a different person comes out of the crowd, and walks slowly up to the stage. They pause for a while, and then say ‘One thousand, two hundred and seventeen.’

There is a pause. Another pause. Then one person starts laughing, then another, soon the whole bar is laughing.

‘What did they just do? Why did the crowd react like that?’

‘That was one they hadn’t heard before.’

Notes: I think I heard this one from my dad for the first time when I was very young. I’ve always enjoyed it. It felt difficult to ambiguate the gender of the participants, but it felt necessary. I think there are two endings above, everything after ‘it’s all in how you tell a joke’ is an alternate ending, but I enjoy the whole thing together, if only because you get to surprise people twice.

Slide Rule Accuracy and F=ma

Earlier this week, we were talking about drawing a Large diagram as one of the lasting and important things I learned in Prof. Collins’ Structure & Materials course.

Here are some of the others:

‘Slide Rule Accuracy’

This is the idea that in the real world[1], you’re never going to use more than three digits of accuracy (or four if your number starts with a ‘1’)[2]. Beyond that, things will get lost in the noise, or other inaccuracies, whether it’s budget contingencies, manufacturing defects, or whatever. (It would be interesting to see whether this has changed for manufactured parts with increased automation.)

The ‘3 laws of engineering'[3]:

1) F=ma

Simple, yet profound. When you’re dealing with non-relativistic systems (pretty much all of them), you push on something, it will move or react proportionally. This is not limited to physical systems.

2) You can’t push on a rope.

Also simple, has a number of applications for mechanical systems, but is probably the most ‘Engineer-y’ useful statement for dealing with other people.

3) In order to solve an engineering problem, you must first know the solution.

This one doesn’t really make sense on first blush, but I’ve experienced it. I mentioned earlier that the brain is often a structure that problems flow through, and in a sense this is a statement of that. You’re going to try to fit a new problem you’re looking at into the structure(s) of all the problems that you’ve seen before, and you have a huge advantage if you’ve seen similar problems before, or seen other problems you can apply by analogy.

We also had a ‘notebook’ that we put all of our class notes in, including cut and pasting from technical sheets, and this ‘notebook’ was our open book for the exam. It was a great exercise in focusing note-taking and coalescing your thoughts onto a medium-small piece of paper.

“When someone is paying you $100 for an hour of work, it’s worth paying a few extra cents for a good sheet of paper to give it to them on.”

The course had special ‘engineering notepaper’ that they wanted us to hand problem sets in on. There wasn’t any penalty for not doing so, but the lesson was that a little bit of professional presentation went a long way.

[1]This is when you’re dealing with things of reasonable size. I’m guessing when you’re looking at gravity waves or Higgs bosons, you might be using somewhat more accuracy. But at the same time, you’re probably not really looking at more than the last few digits…

[2]This is one of those subtle things which is actually quite important and powerful. On a slide rule, the portion which starts with a ‘1’ is fully 30% of the length (log10(2) ~=0.301), so unless you use the fourth digit here, you’re losing a substantial portion of your accuracy. There is a better explanation of this here:

[3]For a slightly different set of three Engineering laws, look here: