S2E03 - Turing Machine (Computation) - Gaming with Science

Episode Transcript
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Stephen (00:00):
Music.

Brian (00:06):
Hello and welcome to the gaming with science podcast
where we talk about the sciencebehind some of your favorite
games.

Jason (00:11):
Today, we'll be talking about Turing Machine by Scorpion
Masque. All right. Welcome back.Everyone to gaming with science.
This is Jason. This is Brian.And today we have very special
guest Stephen Granade. Stephenwe know from science track at
Dragon Con, which I think peoplehave heard us talk about before.
He is the lead guru and ringmaster of the science track, and

(00:33):
manages to keep all the thingsrunning and fight for our space
and make sure we have theresources we need. So we are
very grateful to him.

Brian (00:41):
The Grand Poobah.

Stephen (00:42):
You make me sound so organized.

Jason (00:45):
All you need is the illusion of organization, and
you're fine.

Stephen (00:49):
That's right,

Jason (00:49):
anyway. But if you can kind of introduce yourself to
the guest, what's yourbackground? What's your what's
your story?

Stephen (00:54):
So my background is that I spent my undergraduate
years at a small liberal artscollege as a member of the major
of the Month Club. But as mychemistry professor said, I
never dropped any of the majors.So after cramming four years
into five, I had a Bachelor ofScience, dual major, physics,
chemistry, and then a bachelorof arts, theater arts, with a

(01:17):
math minor. And I looked aroundat the options there and
decided, you know, where thereal business is. That's
physics. Why I went to graduateschool in physics. I studied
atomic cooling and trapping,where we would use lasers to
cool down atoms to ultra coldtemperatures to the point where
they started to act in concert.And you would get a basically a

(01:39):
quantum super fluid, if you'veever heard of like liquid
helium, where you cool it downenough that it doesn't have
friction or things like that. Wewere doing that, but with dilute
gasses of atoms. So also, again,just a great career decision.
Lots of people wanting to coolatoms down a lot, but
fortunately, it also involvedlasers and optics. So I moved

(02:00):
into working for companies doingsensors and image processing,
which of course, turned intomachine learning. So I just have
this mishmash of differentexperiences and background

Brian (02:11):
that is remarkable. I have tried to explain, tried to
explain laser cooling to myoldest son, to no avail.

Stephen (02:20):
Oh, yeah, I bet.

Brian (02:21):
But can you explain? How do you cool something with a
laser beam?

Unknown (02:26):
The most straightforward way is a method
called evaporative cooling thatworks like it sounds. It's sort
of like what tends to happen ifyou've got a hot cup of coffee
where the liquid in there isreally, really hot, and so the
water molecules bounce around.And then occasionally, they
bounce around in such a way thatone of them gets more energy and

(02:47):
the other gets less energy, likethe overall total is conserved,
but one of them gets enoughenergy that it can turn into
vapor and escape, leaving behindcooler atoms. So we would start
with just as many atoms as wecould pile into a trap that was
formed out of theelectromagnetic potential that
you could create with atomiclaser beams. And then you would

(03:09):
it. So if you could imagine theatoms are all like rolling
around in this laser beam, liketrap that is sort of like
marbles in a bowl, and then youkeep lowering the edges of the
bowl, and what that ends updoing is it lets the hottest
atoms, the ones with the mostenergy after a collision,
escape, and the rest of them getcolder. And so then you lower
the bowl a little more, moreatoms escape with more energy.

(03:30):
The ones that are left getcolder. And you just sort of
keep doing that and reducing itin temperature until you're as
close to absolute zero as youcan get.

Brian (03:37):
You're almost like filtering out the slow atoms.

Stephen (03:41):
Yeah, you're you're making it easier for the hottest
atoms after they collide toescape, carrying off more than
their fair share of energy, sothat the remaining atoms drop in
energy and are colder and aremoving less fast.

Brian (03:54):
Wow, I study onions.

Jason (04:00):
Hey, there is some fascinating stuff going on with
those onions and all thechemistry there. You told me
about this. Anyway, we usuallystart with some sort of fun
science fact. And Steven, as youare our guest, we give you
priority. Do you have somethingfun you want to share?

Unknown (04:12):
Yes, I love collecting science facts. I think that's
part of what has ended uphappening with me being involved
in the Dragon Con science track,because I get exposed to all of
these other scientificdisciplines that I am kind of a
dumb, dumb about. My favoritecurrent fact is that your
fingernails grow at about thesame rate that plate tectonics
move.

Brian (04:34):
Yeah, I've heard that before. That's great. It gives
such a fantastic visualrepresentation of what's
happening, right?

Stephen (04:40):
Well, it's such it feels like so very different
scales, because you've got the,you know, inch, like fingernails
on your fingers, and then you'vegot these giant plates, and
they're both moving and growingat roughly the same kinds of
speeds. And that's just wild tome to think about.

Jason (04:55):
and yet, when I think of it like that, I think, wow,
those plates are moving reallyfast. Because, like, I've seen
this. In his book of worldrecords, of those people that
never cut their fingernails. Andthat's like, feet of fingernails
over a lifespan. So that's,that's more than I would have
expected.

Brian (05:09):
Jason has fast growing fingernails confirmed?

Jason (05:12):
I no, I have the nervous habit of picking em. I've never
let them get that long. Like, ifthey start getting over, like,
two millimeters, like, Oh no,they're bothering me. I must get
rid of them.

Brian (05:23):
Should I do my fact too? I mean, absolutely. So I have to
turn everything I have a hammerof bacteria and genetics, so I
have to turn everything into anail. So what I found is it's a
it's a pretty old story, butit's actually, it's not such an
old idea at this point. A lot ofthis work was pioneered by a
synthetic biologist and DNAguru, George Church, of using

(05:43):
DNA to store digitalinformation. So I thought that
was appropriate for this. So DNAis incredibly dense in terms of
the amount of information thatyou can store in a really small
space, and it's also verystable, like you can under the
proper conditions have DNAretain that information for
1000s of years, which we don'treally have good storage media

(06:03):
that could actually hold up tothose long term archival states.

Jason (06:07):
Yes, although, as we learned in the last episode, a
chunk of Amber is not anappropriate archival state for
DNA.

Brian (06:13):
No, it is not. No, it is not. In fact, they're even
putting some archivalinformation into living cells,
so then you get the repair andreplication mechanisms. So
they're sort of like droppinglittle Rosetta libraries of
human information into livingorganisms, kind of very like
very sci fi. So it's great forarchival. You can keep it for a
long time. The problem is it'sabsolutely ridiculously

(06:34):
expensive to write to DNA,because you are synthesizing new
DNA molecules. You're storingdigital information, you know,
binary in the A, G, C's and T's,it's actually not too bad to get
it back out again, because youcan just sequence the
information and turn it backinto digital information. So
that's not cheap, but it's a loteasier than synthesizing the
DNA.

Stephen (06:54):
How do they put that together? What does the
synthesis step look like?

Brian (06:58):
Oh, you can actually run through a process through just
raw from raw chemical bases,synthesize a specific DNA
sequence, like from scratch,stick it in a test tube. They
were here. They're alwaysworking on, like, new ways to do
this.

Jason (07:11):
Yeah, I think currently the limits probably about 100 to
150 base pairs is all you canget in one but then there are
tricks to stitch them togetherso you can, like, yeast is
apparently very good. If theends are are match up to a
relatively small out, like 20,30 base pairs, the yeast will
take a look like, Oh, thosebelong together, and they will

(07:31):
just glue them together at thatspot. And I think that's how
they made there's a lot of stuffabout making a fully synthetic
genome about 10 years ago, whichthey did through this process of
like starting from these tiny,little building blocks and then
slowly building it up throughmany, many, many, many cycles of
this recombination. It's calledto glue them together, and
presumably many, many, many,many hours of technician and

(07:54):
graduate student time actuallymaking this work and figuring
out how to work, and figuringout all the ways it could go
wrong, because they had to dothings like the other problem
with DNA is it's fragile. It'sliterally at one atom thick, and
so any shear forces can just ripit apart. And so the pipettes we
normally use sheer DNA down toabout 10,000 base pairs, which
is way too small for anythingactually living. So they had to

(08:16):
do all sorts of crazyworkarounds to be very gentle
with the DNA as they werehandling it, so it wouldn't just
get ripped to shreds by themtrying to move it around.

Stephen (08:25):
Well, that's wild.

Brian (08:27):
That artificial synthetic genome also has watermarks in
it. They wrote their names and apoem and a couple things. They
left an HTML link in the DNA ofthis organism. So it's really
weird.

Stephen (08:39):
That is amazing. Biology is weird and squishes.

Jason (08:46):
That's why I love biology, is it's it's
phenomenally complex, and youget all sorts of very
interesting emergent propertiesout of it. I mean, when you get
down to it, most of us are whathydrogen, carbon, oxygen and
nitrogen, and they're justrearranging certain things, and
you get phenomenally complexthings like podcasters and
plants and stuff. So

Brian (09:07):
yes, biology is squishy and stinky and fun.

Stephen (09:11):
Well, thinking back to my orgo days, I'm like, All
right, so what's the synthesissteps that gets you from pile of
chemicals to podcaster

Brian (09:19):
a couple billion years, yeah,

Jason (09:21):
so we had a previous episode in evolution, so we'll
just link that in the shownotes. Nice. Yeah, give it about
4 billion years and a wholebunch of trial and error, mostly
error and right, what works willbe around still, all right, but
we're not talking about biology.Today. We are talking about
computation. So let's dive intothis game. So today we are
talking about Turing Machine byScorpion Masque, which was

(09:44):
designed by Fabien Gridel andYoann Levet. I hope I'm
pronouncing those right. This isa very interesting game. Brian
and I played this. This isoutside our normal area. It is a
deduction game. So the mostfamous deduction game that
you're probably familiar with isClue, the. Idea being that the
point of the game is to uncoversome particular piece of
information and clue. It's like,okay, who did the murder, where

(10:07):
and with what? And the designersof Turing Machine really liked
the duction games, but they sawthere was one major flaw, is
that usually you are askingquestions of the other players,
so the players all have parts ofthe information, and you're
trying to assemble the whole butusually some information is more
valuable than other information,and so some players might get an

(10:27):
advantage just by the cards thatare dealt, or whatever include
this would be, I'd say probablythe rooms have the most value
because they're the hardest toget to, and there's the most of
them. So if you happen to get ahandful of rooms, you have an
advantage over everyone else. SoI'll put in the show notes a
link to the designer diary. It'sactually really fascinating all
the iterations they went throughover this, but they eventually
hit on the idea of, well, wewon't have them ask other

(10:49):
players. We'll have them ask thegame itself. And that's how we
have Turing machine. So the waythis is set up is there's a
central piece which is actuallyunnecessary. It's just a cool
little visual piece.

Brian (10:58):
We need a word for that, for things that are totally
unnecessary for the function ofthe game, but just make the game
look a little cooler. Oh, yeah.Like fun, clicky element to it
or something. I still haven'tcome up with it yet. What did we
come up with? Jason?

Jason (11:10):
I think boondoggle was the closest we got.

Brian (11:13):
Yeah,

Jason (11:15):
goober, if we want to take from spider verse,

Stephen (11:18):
yeah,

Jason (11:19):
widget, that's probably too useful. It's too I mean, a
spandrel is actually kind ofuseful. It does something. So
it's not just that.

Brian (11:26):
Well, listeners get in the discord. What term is this?
We need to we are missing aterm, and that's not allowed.

Stephen (11:33):
You know, I would have originally said those kinds of
things were absolutely optional.I spent, you know, a chunk of
time playing cheap ass gameswhere you got basically the
rules and some cardboard, like,if there was going to be a
board, you'd get sort of thincard stock with it on there. And
then they're like, you havedice, you have tokens, you have,
you know, chits to count upthings. Just pull those from

(11:54):
monopoly or whatever other sadgame that you should put to one
side to play cheap ass games.And I like that. I was in grad
school. I had no money, but Ihave gotten to really like the
ones where it's like, we spent alittle extra money, and now the
meeples have a little bit ofheft. You're like, Oh, that's
really nice. Actually, somethingnice and tactile about those
things.

Brian (12:14):
Yeah, I'm a sucker for some glossy card stock. I know
that Jason is as well.

Jason (12:19):
Yeah, no, I like the tactile sensation. And so what
this central thing? It's just ahexagon with some little like
eight bit computer faces on it.It's just to organize things,
because the real meat of it hasthere are six faces and around
that you put anywhere from fourto six cards, which are your
condition cards. The goal ofthis game is to deduce a number
that is hidden. And the thingis, the rulebook comes with

(12:41):
about 20 of these. There's awebsite where they have, like, 7
million of them that they'veprogrammatically generated. So
like, you're never going to runout of puzzles to solve, but you
have to get it because it isthis very specific setup. So you
set it up, you put out your fourto six condition cards that have
the conditions you're testing.I'll talk more about that in a
minute. And then now each one ofthose is tied to a verification
card, which tells youinformation. And the way this

(13:03):
game works is you have a set ofnumber cards, and so you put
together a three digit number.The digits only go one to five.
So there's five times five timesfive equals 125, possible
numbers it can be and you takethe three and there are tabs,
whether it's the first digit,the second or the third. You put
them together, and they havethese punches in each of them,
and it looks like an oldfashioned computer punch card,
and they designed it so thatwhen you put your three digit

(13:24):
code together, there is alwaysexactly one hole open out of all
of them, and every 125 differentones has a different hole open.
And you hold this up to theverification card, and you get a
check or an X. And thatbasically tells you that with
its condition card, whether yournumber passed the condition or
not, and you use thatinformation to try to deduce
what the actual real number is,because the real number passes

(13:47):
all of the conditions out on thetable. The one further wrinkle
of this is that the conditioncards do not have a single
condition on them. They actuallyhave multiple conditions,
anywhere from two up to nine,and only one of those is
actually being tested. So yourjob is first to figure out which
of the many conditions on theboard are actually in use, and
then to determine from thosewhich single number satisfies

(14:09):
all of the conditions. And theauthors are very clear in the
rule book that in every puzzle,every single condition is
needed. You can never just skipone and come to the answer,
except by luck, like you needall of them in order to get it,
which leads to some weird thingswhere there are some conditions
that can never be used in thegame, because, like, one of the
cards says the number of threes.There can be one three or there

(14:31):
can be two threes, or there canbe three threes. If there are
three threes, that one cardtells you the solution,
therefore that condition willnever be used. At least weird
stuff like that. And the bestway of thinking about this, this
can be played one player ormultiplayer. It's one to four
players. This is one where Ithink maybe the one player
version might actually be themost popular, because it's it's

(14:52):
competitive puzzle solving.Think of it as if you were doing
competitive Sudoku with a bunchof your friends. It's very much
a solitaire. There's no way tointerfere with each other
whatsoever. Your little cluesand stuff are hidden. You can
play it cooperatively if youwant. That's definitely an
option. Or you can play it solo.And I did that a few times, and
I could definitely see we saythis a lot, actually, several of
these games would be good apps.This would be a great app to

(15:14):
just pull open and do with, likeWordle or connections or turning
machine in the morning, just tokind of stretch your brain cells
a little bit. I can see a lot ofpeople liking it for that
reason.

Brian (15:24):
But wouldn't you lose something without the little
cards getting to pick them upand make the grid and hold them
up to the thing and the sort ofweird mathematical magic of, how
does this work?

Jason (15:34):
Well yes, you would lose the tactile sensation of it.
Yes. On the other hand, youwouldn't have to have Turing
machine set up for you to playevery single morning, which is
difficult with cats and children

Stephen (15:44):
So just the dedicated Turing Machine table off on one
corner.

Jason (15:49):
Yes, and there's an interesting history. So right
now, the final version of thegame is pure numbers. It's just
you have the three digit numberyou're trying to solve. They
actually tried skinning it a fewdifferent ways during
development. So first, and for along time, you were trying to
find out, like the number ofdifferent animals on the farm,
and each of the farm hands onlyknew one thing, like, there are
more pigs than chickens, or ifyou add up all the animals, and

(16:10):
they are greater than six, whichseemed like some pretty
uninformed farm hands, but itwas the metaphor of the game.
Then to try to tie it to TuringAlan Turing, which we'll talk
about more in a bit, they themedit as being trying to discover
components of the German army,like, how many tanks did they
have? How many infantry did theyhave, et cetera. And at the end,
they decided that, you know,we're just gonna stick to pure
numbers. We're just gonna makeit a pure number deduction game,

(16:32):
which I think is, I mean, Icould see the skin being nice,
but I really think what theywere going for, they really just
like the pure logical deduction.And I think keeping it pure like
that really reinforces the feeland the vibe of the game they're
going after.

Stephen (16:46):
Yeah, I feel like, if this, where games where you have
that skin, where it really yousee sort of the abstract working
of the mechanisms underneath thedifferent engines, or things
like that, then I want the skinto still be thematically
resonant with the game. Youknow, if I think about something
like wingspan, which at itsheart is just, you're producing
more resources that you put outin the form of, you know, eggs

(17:10):
and things like that, and you'relaying out the places for the
birds and all of that. So you'regetting your birds. The theme
informs what those things are ina way that feels like actual
birds and their habitats. Theskinned versions you're talking
about sounds more like, well,this is the thing that you're
going to end up mostly ignoringand treating as abstract anyway.

Jason (17:28):
I agree. I think that's why it works better as just pure
numbers. Because ultimately,even though it bills itself as
like the punch card computergame, it's really a game about
logical deduction, and it's notactually a computer. The rule
book actually says it's a protocomputer, but I guess whoever
was in charge of the box wantedto say it was a punch card
computer game,

Stephen (17:47):
right

Jason (17:47):
And it does feel a little magic to put all the punch cards
together. There's always thatone hole that's open and you get
to look through and get youranswer. And Brian, I've known
this for several weeks, and I'vehold off playing like I figured
out the magic or how thathappens, the mathemagic, the
mathematic, they describe itvery clearly in their design
diary, and it turns out to bereally, really simple.

Brian (18:08):
OK! I'm excited to hear about it. But you, you made a
point when we started thisendeavor. We can't just do
biology games. We have to mix itup. You know, in the whole idea
of STEM science, technology,engineering and math. This is
our first this is a Math game.That is what this is, right? I
don't think there's a lot ofthose out there. I don't think
so well, where they justcompletely go for it. It's like,

(18:30):
it's fully abstracted, justnumbers. We don't need any
theming,

Stephen (18:34):
right

Brian (18:34):
Okay, now explain to me how this works, like, because I
want to know.

Jason (18:37):
So when I first saw it, I was like, Oh, I thought this

Stephen (18:38):
It's decimalencoded. It's a decimal place encoded
would be like, Spot it, orDobble which I saw a video on a
year ago. I'll link it in thenotes. In spot it, you have this
collection of cards, and everypair of cards shares exactly one
symbol. And there's this wholemathematical thing to ensure
that happens. I thought it'd besomething like this. So every
trio of cards would shareexactly one hole. And then it
explains like, oh, you take all125 numbers, you put them in a

(18:58):
grid, and then you randomizethem, and then you just take
whichever card. So this is thefirst digit, and it's a one. So
all the ones that have a one inthe first digit have a hole in
them, and all the ones that havea two in the second digit, when
you go into that one, you put ahole in them there.
basically, oh, that's supercool.

Jason (19:16):
The first versions, they actually had them in long strips
because they were all adjacentto each other. They later
realized it was actually muchmore fun when they randomized
them. And so that's what wehave, the final one. So there
are basically 125 spots on thecard where there could be a
hole, anything that has thatmatches the digit of that card
has this hole punched out. Andso by definition, when you put

(19:37):
all three of them together,there's only one hole left open.
So

Stephen (19:39):
you have, like, all of the 500 numbers punched on the
500 card and all of the, like,30 numbers that have number
three number on the three cardin the middle. Yeah, that's
really cool.

Jason (19:50):
And it's not completely random. They did put in some

Brian (19:51):
Yeah,
rules, because, I mean, youcould do this, like, a bajillion

Jason (19:52):
they're laid out in a 12 by 12 grid, with some of the
different ways. So I think whatthey did is they just generated
a bajillion different ones, andthen they screened. Them because
they wanted to make sure, okay,nothing has more than two in a
row. You don't form any weirdangles that might catch and
tear. And the end resultactually looks a lot like old
fashioned computer punch card,because you all have these, like
one and two slot holes all nextto each other, and they're all

(20:14):
spaced out and in differentdirections and stuff. And it
looks really cool. And I thinkyou're about to ask Brian about
the numbers. So there's 125possible codes.
corners left off for somesymbols you use to match it up.
But there's a, I think there's133 available slots, which means
there must be eight squares thatare just never used,

Brian (20:35):
and that must be things like the 333, right?

Jason (20:38):
No, 333, is a valid number. You'll have a hole going
through it there. It could be avalid code, just not with that
one card. It could be a validcode for a different set of

Brian (20:46):
Oh, man, yeah, I'm over my head. But that's okay. That's
cards.
okay.

Stephen (20:50):
I wonder if, if they added some blank ones so that
they could ease the constraintsof making sure that you wouldn't
have cases where there wereweird corners you could catch
on, or they were too close, orthings like that.

Jason (21:03):
Maybe. I suspect it's just that a 12 by 12 grid is the
smallest square grid you can fit125 different numbers on. And so
they just worked with that inthe early versions of the game,
it was actually a four digitcode you were going after, and
they dropped it down to threebecause it let them have smaller
number of holes and biggerholes. So it worked out better,
like bigger symbols, biggerholes, fewer of them. So that

(21:24):
worked out well. They also usedto have a lot more esoteric
conditions. So now it's like,oh, the sum of these is equal to
four or greater than four,whatever. Or this is odd. This
is even. It used to be thingslike all of these things
multiplied together, are this orthis is a prime number, or other
much more mathematical thingsthat the the publisher said, No,
these are too esoteric.

Stephen (21:45):
There's one non prime digit

Jason (21:48):
Exactly.

Brian (21:50):
So they wanted to make sure that the conditions were
things that didn't have too manyassumptions about mathematical
knowledge other than odds andevens bigger or lesser. Yeah,
it's like that.

Jason (21:59):
The thing I want to know still, though, is that there are
48 condition cards. Each has atleast two conditions on it, and
many have more than that. Butthere's only 95 verification
cards, which means some of themhave to be pulling double duty.
And I don't know how that works.That's the part they actually
intentionally did not explain inthe designer diary, so they left
that one a mystery. Anyway.That's the game. If you like

(22:22):
Sudoku, you will probably likeTuring machine. That seems to be
the pattern from what I'vegotten online. If you want to
check it out, definitely watchsome videos. It is not intuitive
to most people the first timearound, but once you get it,
it's like, once I figured, I waslike, Oh, I get it, then I could
do pretty well about 90% of thetime. And then I'd forget
something and make some stupidmistake and completely mess it

Brian (22:40):
I mean, when we played, we played once on normal
up.
difficulty. We both did great.We got it on the same round of
guesses. I think you used onefewer piece of information, no
issues. We clicked out thedifficulty one notch. We could
not solve this code. We bothsccrewed up multiple different
times, right?

Jason (22:58):
Well, I know where I messed up.

Brian (23:00):
Okay.

Jason (23:01):
We had one of the ones where there were like, six
different conditions, and Iaccidentally, I misinterpreted
my result and thought I hadeliminated five of them, when
I'd actually only eliminatedfour of them, and so I was going
off of wrong information. Allright, so that's enough about
the game. Let's move on to thescience, and Stephen, I'm hoping
you can help fill in theinformation here, because
although I work inbioinformatics, like, I'm not a

(23:22):
computer scientist. I'm notheavy into that. I want to start
with the namesake. So this isnamed after Alan Turing. It's a
Turing machine. So who was AlanTuring, and what was his machine?

Stephen (23:30):
So Alan Turing was a British mathematician and ended
up founding a lot of likefundamental thought about how
digital computers would work. Hewas doing a lot of this work in
the 30s, and then, of course, inthe 40s, got swept up in the
race to crack the German'sEnigma machine that they were

(23:52):
using to encode secret messages,where a lot more sort of
approaches to and tactics aboutdoing digital computation
occurred at a point where therewere no general purpose digital
computers. Everyone was havingto do analog circuitry and wind
things together. But what Turingdid was reason mathematically

(24:14):
about how these computers thatdidn't quite exist yet might
work. And He came up with amathematical model that, I
believe he called it like the Amachine, and then it later his
advisor renamed it to be theTuring machine, but it was,
rather than an actual machine,sort of a mathematical model, a
thought experiment about howdigital computers could work and

(24:35):
how you could describe a systemthat, then you could do
mathematical reasoning aboutbecause Turing was really
interested to dive into thequestion of like, Are there
problems that a digital computercan't solve? He was playing in
some of the same kinds of areas.If you've ever heard of Gödel
and Gödel's conjecture thatthere are axioms in any

(24:56):
mathematical system that cannotbe proven, you can ever have a
perfectly self provingmathematical system. There's
always going to be some axiomsthat you just sort of have to
assume as first principles.

Jason (25:06):
And bit of vocabulary for listeners, axiom is basically
the foundation, bedrock of math.They're the things you start
it's like, okay, we know X, Yand Z from that we can derive
other stuff. Your axioms arethose that first bedrock stuff
you lay down. It's

Brian (25:20):
It's also the ship in Wall-E.

Stephen (25:21):
It's also the ship in Wall-E. So Alan Turing was
trying to look for some of thosesame kinds of principles in
these digital computationmachines that you know don't
exist yet. So he came up with asystem. The idea is that you've
got this infinite roll of tapethat can be slid forwards and

(25:41):
backwards underneath this littledevice that is looking at each
little cell on the tape. So thetape is divided into regions,
and you've got this devicecalled a head that can look at
one of the regions, and it canread the symbol that is written
there. It can write a new symbolon there, and it has this set of
rules called states that saywhat it does when it encounters

(26:05):
a given symbol. So you couldimagine, for example, a four
symbol tape. You can have A, B,C, or D on one of these cells,
and so when it looks at say anA, it says, Okay, move the tape
one cell to the right. If itsees a B, move the tape one cell
to the left. If you see a C,write a D, if you see a D, don't

(26:26):
do anything. So now you've got asimple set of rules for moving
the tape around and manipulatingthese symbols on the tape. The
next level up is you say, Okay,those are the first set of rules
for A, B and C, but if you see aD, now you're going to swap in a
second set of rules. You'regoing to go to another state in
the state machine. So it shiftsa new set of rules about what it

(26:49):
does with A, B, C or D, andmaybe there's a third set of
rules and a fourth set of rules.So it can swap in and out these
rules depending on what symbolsthat it sees. So it could have
a, you know, a case where itsays, All right, an A says I
move left, and then a B says Imove right. But if I see two B's
in a row, now I'm going tochange my rule, so now that B

(27:09):
means I shift it to the left. Soit's simple sounding but
abstract. But it turns out thatgiven those operations, you can
simulate any computer algorithmlike top to bottom, they can get
really complex. You can build upa whole set of symbols and a
whole set of these rules, thesestates that the machine swaps in
and out. But you can use that tohave any digital algorithm. You

(27:34):
can describe it using thatmachine and the proper set of
symbols and rules.

Jason (27:38):
Do our computers work like that? This is one thing
I've never been able to figureout. Like, is the Turing Machine
an abstract concept, or is thisessentially the foundation on
which all actual hardware isbuilt?

Stephen (27:48):
It is an abstract concept because it turns out,
number one, if it's going to bean actual Turing machine, the
tape has to be infinite, if youknow,

Jason (27:58):
okay, only minor, minor issue there.

Stephen (28:00):
It's a small, small wrinkle in building one of these
things, yeah, because it turnsout, if the tape is not
infinite, let's say it's justmerely super, super, super big,
like you've got a Googol's worthof cells, there are some
algorithms you're not going tobe able to describe. So it's
more that it was simple enoughthat you could do mathematical

(28:20):
reasoning about it and createmathematical proofs to answer
some of the questions that AlanTuring had about how digital
computers would work.

Jason (28:28):
This almost seems like in biology, we have our model
systems which are like ourlittle like the lab mice and the
E coli bacteria, which have beenlike they're very simple,
they're very reduced, but we cando a lot with them to try to
understand how things work outin the real world is that kind
of this for computation? It's avery simplified model system
that you can find out some rulesand then apply that out into
real computers.

Stephen (28:48):
Yes, you you have stripped the idea of a digital
computer down to like the fewestthings that you can get away
with and still be able todescribe all of these different
algorithms.

Jason (28:59):
Okay, And in looking up research for this episode, I ran
across a phrase called Turingcomplete, which apparently
describes something aboutcomputers. But I couldn't figure
out exactly what, what is Turingcomplete?

Stephen (29:10):
So if a device is Turing complete, it means that
it can do all of the digitaloperations necessary to express
these computer algorithms. So ifyou have a device that is not
Turing complete, you are limitedabout the kind of algorithms
that you can use, that you candescribe with it, that you can,
you know, create on this device.If it is Turing complete, then

(29:33):
it matches the samecharacteristics as this
hypothetical Turing machine, andshould be able to express any
digital algorithm that you cancome up with,

Brian (29:42):
Even though it doesn't have an infinite stretch of tape

Stephen (29:45):
Even though it doesn't have an infinite tape. Yes,
yeah, thankfully, they managedto figure out how to do it
without infinite tape.

Brian (29:51):
Think anytime you need infinity, maybe it's only it
because very esoteric andabstract.

Stephen (29:57):
Oh listen, I come from physics. We ran into infinities.
So we're like, you know how youget rid of those infinities? You
divide them by other infinities,and we will call it
renormalization.

Jason (30:07):
So it sounds like most of our digital computers nowadays
are Turing complete, at least,like for me as a user, it seems
like they're capable of runningbasically anything we want on
them. Is that right? Like, is mycell phone Turing complete?

Stephen (30:18):
Yes, it has all of the operations necessary to create
these digital algorithms, youend up being limited by the
amount of memory that you haveavailable, whether that's memory
where you can shove all of thenumbers that it's operating on
in working memory, or to storeit onto a disk or other medium,
but it's able to do all of theoperations that make it

(30:38):
equivalent to that Turing device

Jason (30:41):
got it so I said it Turing complete in Theory and
Practice, like storage becomesan issue, but in theory, right?
What's what's not Turingcomplete then?

Brian (30:49):
yeah, like, what's an example from modern life of
something that doesn't qualify?

Stephen (30:54):
I really should have looked up this, because at this
point, I'm not sure we've got alot that isn't Turing complete,
the fact that you can, you know,run Doom, literally on your
toaster. Computer chips havebecome so cheap and so readily
manufacturable that it is, Ithink, harder to get a device

(31:14):
that is not Turing complete, atleast on the computer side. A
lot of this came out of thepoint where, as I mentioned,
they were building computersusing analog circuits, and there
were a limit to the numbers andkinds of operations that you
could create by windingresistors and getting capacitors

(31:35):
and soldering them all together.So I think that was a much
bigger barrier when you'retalking about the 40s with the
early steps of digitalcomputing, with the UK's bombes
that were working to crack theEnigma code, than it is at this
point where computer chips aresuper cheap and super easy to
get and you just don't do muchin the way of analog computing

(31:57):
anymore.

Jason (31:58):
So I just did a quick search on this and pulled up the
Wikipedia page, and apparently,I think you're right, because
there's, there's a list ofthings that are accidentally
Turing complete, which includesstuff like Microsoft Excel,
Minecraft and Magic, TheGathering. Yes,

Brian (32:12):
wait, I'm Sorry. What does that mean?

Jason (32:16):
Run computer programs in magic. And I have seen the
YouTube video that explains howto do so I'll link it in the
show notes.

Brian (32:22):
Yes, please put that in the show notes.

Stephen (32:24):
You can do it in Excel with its formulas. You can
create basically computersystems in Minecraft using the
redstone bridges and the, youknow, linking them all together
and the switches that they'vegot available. You can create
the different kind of logicgates that are required to build
up to more complex mathematics.

Brian (32:43):
but Magic, the Gathering too. So yes, you can design
loops in magic.

Jason (32:47):
Yes, you can is the world's most boring game of
Magic, but you can do it.

Brian (32:54):
So when you were talking about the Turing machine, the
analogies that you made, you hada read head and a writehead, you
know, a long line of tape,symbols. I mean, all this sounds
like magnetic tape. Is that?That's not a coincidence? Is it?

Stephen (33:07):
No, and it gets to the thing you were talking about
earlier, about like, how do youstore information? Turing's
machine, his mathematical model,used a symbol table, and you
could have four symbols or fivesymbols, or things like that.
But it turned out that it was alot easier to build up these
systems. If you just have twosymbols, you have true and
false, you have one and zero,and then you start building

(33:29):
those up from there. And itturned out that you could store
this in the direction of amagnetic moment. You know, if
you think about the little oldbar magnets, where you've got a
North End and a south end, youcan say, all right, if the North
End is pointing up, that is oneor true. If it is pointing down,
then that is zero or false. Andyou can encode that on a

(33:51):
magnetic tape by having theferromagnetic particles where
you hit them with a magneticfield to flip the direction that
they're in. And then itpersists, at least for a while.
Eventually, the magnetism sortof wears off, depending on, you
know, if you leave a tape inyour hot car when you're, you
know, 10, and then come back amonth later and discover that

(34:13):
it's all kind of gone.

Jason (34:16):
Yeah, but so tapes weren't actually the first one,
though, and this plays rightinto the game, because the game
has the whole punch card thing,and punch cards were among the
first actual ways of storinginformation. They're not
digital, like magnetic tape, butwhat I was reading like the Code
Cracking for World War Two, theywere generating like, 2 million
punch cards a week to try to runall their computational stuff.

(34:38):
Have you ever run a punch cardcomputer?

Stephen (34:39):
I have not but I have used punch cards and the ways
that they were never meant to bedone, because I was in a laser
lab at a university where theprofessor had gotten what was
probably multiple graduatestudents, entire PhD researches
on punch cards, and then takenthem away because they have
little holes in them if you'retrying to align a laser. Beam.

(35:00):
It's really nice to have a placewhere you can have a little hole
and pull it away, and a littlehole and pull it away. So that's
what we used our punch cardsfor.

Jason (35:07):
oh my, those poor graduate students, they're
probably, I know, hopefully theyweren't dead, but if they were,
they probably were rolling overin their graves.

Stephen (35:15):
Yeah, I used to be pretty blase about the fact that
we were using ex grad studentsgraduate life work basically as
a cheap way to not have to use ahole punch on cards. I was like,
you know, whatever. But then Isort of realized what that felt
like, because we were doing atomcooling and trapping, and there
was a lot of race to try to bethe first group to create a Bose

(35:38):
Einstein condensate that hadbeen predicted by Bose and
Einstein back in like the 30s,and it was this giant effort.
People couldn't get it to workand couldn't get it to work, and
eventually did in like 95 and itwas impressive enough that they
were getting Nobel Prizes for itin 98 which is just a
ridiculously fast turnaround forthat. And then, like, by the

(35:58):
year 2000 it was a very commonundergraduate lab, like
everybody was making BoseEinstein condensates in the lab
just, you know, over two days,it's like, okay,

Brian (36:10):
Nobel Prize to undergraduate laboratory
exercise in a couple of years.Amazing,

Jason (36:15):
yeah. But no, when I was looking up this punch card
things, I mean, I did notappreciate, I understood that
punch cards were used to programcomputers back in the day. I
didn't appreciate they were datastorage. They were the floppy
disks of their day, becausethere wasn't actual permanent
computer storage. And so you'dhave all these punch cards, and
they had to be read in in order,because you flip two of them,
you completely mess up theprogram, you mess up the data.

(36:37):
And so they'd have these bigstacks. They'd have like,
Sharpie lines on them to helpyou figure it out. And multiple
places, I found something to theeffect of woe betide the
graduate student who droppedtheir stack of punch cards, and
they just scattered everywhere,and you had to try to figure out
how to get them back in order.

Brian (36:52):
Were they not numbered?

Stephen (36:53):
Well, originally, they were just like long pieces of
cardboard with a row of numbers,and then, you know, multiples of
those rows, and they would bepunched by hand, and then later,
they would type in the thingthat you wanted, and it would
encode it into the space of thepunch cards, because it's, it's
spatial information storage inthe same way that the game is

(37:15):
storing information about thenumbers. You know, each of those
cards, for example, has theposition of every number that
starts with a three. Every threedigit number that starts with a
three is encoded by holespositionally punched on those
cards. And I think because youwould end up with just like
stacks and stacks and stacks ofthem, because it was not a very
information dense way of storingthat information. You had

(37:38):
bunches of them, and it took awhile to get to numbering them.
You would occasionally have onesthat were a certain statement or
operation that would be prettycommon, like adding two numbers
or, you know, moving informationaround. And so you could have
punch cards that were commonlycreated that you just like, oh,

(38:00):
I need one of these. Perhaps,instead of like, I'm going to
hand create every single oneeach time. So yeah, I think
there were some quality of lifethings that people had to come
up with, like, numbering them,

Jason (38:10):
probably via lots of pain, because that's generally
what happens. Like someonemesses up, like, oh, I should
have done that. Let's do thatfrom now on, yes.

Brian (38:19):
Oh I'm sure I'll never drop it. It'll be fine. I'll be
careful.

Jason (38:22):
So the history of these things is fascinating. I didn't
realize I think about them withthe 50s. So apparently, the
first wide scale use was in the1890 census. Because they're
like, it's going to take us 15years to tally the census we
have to do every 10 years. Likethis is not going to work. And
there's someone who came up witha punch card system that you
could just count. It was alwaysdoing, was tabulated, it was

(38:43):
counting stuff, but it made itso they got it in like, three or
four years, so super fastrelative to what they thought.
And that guy formed a companythat, like, three or four name
changes later became IBM,International Business Machines,
which is still around. That's apretty good record for a
company, I think. And if you goback further, like, the first
one that everyone brings up isthe first punch card, like proto

(39:03):
computer thing was used forweaving.

Stephen (39:05):
Yes, the Jacquard loom,

Jason (39:07):
yeah, it would determine where which parts would get
lifted up and which parts wouldstay down. So you could make
patterns and can make themreproducible. Some version of
this is what powers the playerpianos you see in the old
westerns, where they've got allthe holes in the circular paper
that's determining which keysget pushed. Okay, in the grand
scheme of technology, 200 yearsis not a long time, but it's way
older than I thought it was.

Stephen (39:27):
Yeah, folks started to realize that you could encode
information in holes in papermuch earlier than you might
imagine, especially if you'reused to thinking of, yeah,
computers are the things thatkind of came out of World War
Two and then really got a, youknow, a jump start during the
space race, and they're like, ohyeah. Jacquard loom,s were
creating patterns for weavingthat you would just bolt onto

(39:48):
the side of your loom and haveit do operations based on the
holes in the cards.

Brian (39:53):
So stupid question. Is a player piano Turing complete?

Stephen (39:58):
I do not believe so. Because it is not doing any
operations, it has no ability toswap rules in and out. It's just
when this hold comes by, I pressthis key,

Jason (40:08):
I think a player piano is basically read only,

Stephen (40:10):
yeah.

Brian (40:11):
Okay, so it's that, it's that is a key difference. You
can program something that canjust read. So a music box is
programmable, but it has noability to change what is on the
recording, right? You can'twrite, you can only read, and
that's the key difference?

Stephen (40:26):
Yeah.

Brian (40:26):
Okay, cool, yay.

Stephen (40:27):
Now I'm, I'm curious if there are any Turing complete
devices that would be read only,and I don't know, I guess if
it's an infinite tape, but maybeyou can get away with it, right?

Jason (40:42):
Hey, y'all quick aside here. So after we recorded this
episode, I looked this up, andit turns out that while you can
have a read only Turing machine,it is not Turing complete. Some
operations just can't be donewhen you can't write to the
table. So just want to put thatin here, so we had the answer.
And now back to the show. Weprobably actually need to start
wrapping this up. There's been agreat conversation. There's a

(41:03):
few things I want to touch onbefore we do one is the great
mystery of computers to me, howdo you do math with just ones
and zeros? You talked about howit's much easier to do all these
operations if you just use onand off with the magnetic
fields. But when you get down tohow those actually mesh inside
the CPU and are doing math andare doing the calculations that
show what's on my computerscreen, all that I do not

(41:25):
understand how that works, likewhat is going on there in the
guts of the CPU.

Stephen (41:30):
If you go all the way down to the base level, you're
looking at Boolean algebra thatwas created by a mathematician
named Boole back in, I think,the 1890s where he was looking
at what kind of algebraicoperations you could do if you
had just ones and zeros. There'smore to it, but for our

(41:52):
purposes, let's just stick withones and zeros. So every number
is a one or a zero, and you canstack those together. So in
decimal, where we would go012345, instead, you go 01, 10,
11, 100, 101, 110, 111, 1000 soit's more properly base two

(42:12):
numbering, where we're used tobase 10 numbering, and then you
introduce, three operations, youintroduce, AND you introduce, OR
you introduce NOT. So if I havetwo one digit numbers that can
be either 0 or 1, if I AND themtogether, the result is a one if
both of the numbers that youstarted with is one. So if I
have a 1 and I have a 1 and IAND them together, I get a 1. If

(42:35):
I have a one and a zero, if azero and a one half a zero and a
zero, I get a zero. So both thefirst number and the second
number have to be one to giveyou a one. The OR operation is
like that, but it's a littlemore permissive. If one of the
numbers or the other number isone, then it results in a one.
If both of the numbers are zero,it results in a zero, and then
the NOT operation changes thenumber. If you have a zero, the

(42:59):
not of the zero is one. If youhave a 1, the NOT of the 1 is 0.
So you can start to take thoseoperations, and you can take
longer numbers, so you can andtwo bit numbers together. So
like an 11 and a 10 addedtogether, gives you 10, because
the first digit is one on bothof them, but on the second
digit, only one of them is if Ior a 10 and 11, I get 11. If I

(43:23):
take 10 and I not it, I get a 1.So you can build up longer
algorithms using only thosethree operations and OR and NOT.
There are algorithms that letyou start to create, for
example, addition. It lets youcreate multiplication. If you
want a really deep dive intothis, I'd say, go look up a

(43:46):
YouTube video describing how thehalf adder h, a, l, f, half
adder algorithm works for addingnumbers together using just bits
and ANDs, ORs, and NOTs.

Jason (43:58):
It sounds like we're back in the Turing Machine territory,
where you've got a very simplesetup, and then through this
like layers and layers ofcomplexity, you manage to build
up to something that we wouldrecognize,

Stephen (44:08):
Yep, yeah. So that, like, computers don't natively
know how to do division, butwe've got clever algorithms that
let the computers do operationsthat result in a division that
are stacks of these logic gates,they're called ANDs, ORs, and
NOTs, and rules about how youapply them.

Jason (44:26):
Okay, well, thank you, Brian, do you have any last
questions or comments you wantto put out?

Brian (44:30):
I have my one joke about binary. Well, you've probably
heard before there are 10 typesof people in the world, people
who understand binary and peoplewho don't

Stephen (44:37):
Now, the really fun thing as somebody who came out
of laser cooling and trapping,one of the things that people
end up doing once you can startto manipulate these atoms in
their quantum states, as theystart to build quantum
computers, where you havequbits, Q, U, B, I, T, S, where

(44:57):
they are particles that are in aquantum superposition. So maybe
they're both one, maybe they'reboth zero, we're not going to
know until we actually make themeasurement. And all kinds of
wacky algorithms are possibleonce you start to have enough
qubits together that you can doin effect, kind of parallel,
probabilistic computation.

Jason (45:18):
I hear about those every now and then, although my
understanding is that they'refacing the infinite tape
problem. In that last I checkedlike they can get like 15 or 20
qubits, maybe 50.

Stephen (45:28):
There are systems where you can have more of them, but
they're not in sort of theclassical superposition. There's
this thing called an Isingstate, about where you can get
atoms in a crystal alignedproperly in a ways that let you
do some aspects of quantumcomputing, but not the ones that
people are really bothinterested and afraid in, like

(45:49):
breaking cryptographic numbersreally, really fast, so that all
of your banking accounts can besucked dry.

Jason (45:55):
Yes, that's mostly what I hear. Is that if we manage to
get quantum computing to work,all our current encryption goes
to pot.

Stephen (46:02):
Yes, that is the headliner application for it.

Jason (46:06):
All right, so Brian, you have your nitpick corner. Do you
have any nitpicks about thisgame you want to bring out?

Brian (46:11):
I mean, it's not a computer. So that's, that's kind
of a thing, like, you know, itsays it's the punch card
computer, but it's not really acomputer. I don't know what it
is, but it's not that.

Jason (46:21):
It's a proto computer the rulebook clarifies.

Brian (46:23):
What does that mean?

Jason (46:24):
I don't know.

Stephen (46:27):
Yeah, I guess it's using like computer, like
storage or encoding ofinformation, but there is no
computation going on. It's sortof like the old school version
of computers, which were peoplewho did computations. You're the
one doing the computation byputting them together.

Brian (46:43):
That's true. We're, we are the punch card computers.

Stephen (46:47):
You are your own Turing machine. Congratulations.

Jason (46:51):
I have two nitpicks, and these are little ones, but one
is, it's a four player game, butthey only include three sets of
the number cards. I assumethat's a cost saving thing,
because they seem like they'reeither very nice cardboard or
maybe very thin plastic. That'sprobably just a cost thing,
because I assume custom punchingout all of these different
numbers is kind of expensive.The other one is actually,
recently, you talked about thehardest thing about a game is

(47:13):
writing the rule book, becauseby the time you get to that, you
know it so well. You're not youdon't know how to explain it to
a newbie. I think that happenedhere, because nowhere in the
rule book do they actually say,by the way, you're the code
you're looking for is the onethat satisfies all the
conditions on the table. It sortof alludes to that in one or two
places. It kind of assumes youget that, but never actually
says that outright.

Brian (47:33):
I actually got that from watching a YouTube tutorial.
It's like, by the way, if youwant to play this game, you need
all of the condition cards.

Jason (47:40):
So that's my nit pick. Is, like, that's a fairly
important part of the game thatI think they left out of the
rule book. It probably needs tobe corrected.

Stephen (47:47):
Gosh, yeah, that's a great point. So my dad was a
historian, and his specialitywas Civil War, and so he would
play the Avalon Hill gameGettysburg with his classes. And
so I grew up with this AvalonHill Gettysburg game, which had
all these pages of densely typedrules, and they were all

(48:08):
subsections. So you'd like, oh,according to 3.2 point 7.1,
point four, when it is muddy, myterrain is modifier is such and

Jason (48:16):
Oh no this is steller Horizons
such.

Brian (48:18):
The game ran by an engineer.

Jason (48:20):
All right, so let's get on to letter grades. Brian throw
this to you. What do you thinkabout gameplay?

Brian (48:25):
I dont know this is a weird one, because this isn't
the kind of game that we wouldtypically play. But if you just,
like, want to play a light gameor something this, like, I kind
of agree with you. This might bethe one game that's worth having
in solo mode, where you just setit up every once in a while. I
guess I'll just give it a B. Ithink it's, I think it's kind of
its own little unique niche.There's nothing really competing

(48:46):
with it.

Jason (48:47):
our sphere, no, I I'm gonna give it higher, I'm going
to give it an A-, and I'm gonnagive it that because for what
the game sets out to do, I thinkit does very well. The only
reason I'm getting a littlelower is because I think there's
a barrier to entry that can putoff a lot of people. In fact,

(49:08):
when I was doing research, I ranacross a Reddit thread by
someone who's a professionalgame explainer who is basically
asking for help, because no oneever understood Turing machine
the first time he explained itto them, and so he's asking for
help trying to figure out how toexplain it better to people, and
usually by the second or thirdtime, they figured it out. But
he just had trouble with that.And I wish they'd made that
barrier to entry lower, but onceyou get past it, I think it can

(49:28):
be fun. And if this is your jam,then I think it's a great game.
It's not my jam, but I candefinitely see what the appeal
would be.

Brian (49:34):
Does it have Quick Start rules like, Hey, play this
puzzle. These ones. Let usexplain how this works. Does it
do that, I don't think it does.And that, honestly, just like
here, let us walk you through asimple puzzle. Yeah,

Jason (49:46):
it gives an example round, but it does not walk
through an entire gamededuction. It gives examples of
the components, but it neverputs it all together until,
like, Oh, here's your this isyour first game of Turing
machine, so you understand howit works.

Brian (49:58):
This is the perpetual. Challenge. When you have experts
trying to talk to amateurs,right? It's, it's very, very
difficult to keep thatbeginner's mindset.

Jason (50:07):
But like I said, overall, I think for what the game sets
out to do, I think it actuallydoes it very well, especially we
talked about the lack ofskinning it. It's like, it's a
very pure This is a logicaldeduction game, and there's very
few bells and whistles aroundit. It is trying to be a logical
deduction game, and I think itdoes that great. Steven, do you
have thoughts? I mean, youdidn't have a chance to play it
because we're unfortunately toofar apart from each other.

Stephen (50:27):
Right, I did get to watch some of the aforementioned
YouTube videos. I really admiregames like this that can pull
off an experience without a lotof the sort of what I think of
as traditional skinning andother elements of it to add to
the experience. You know, if youthink about like bluffing games,

(50:50):
like Sheriff of Nottingham orsomething like that, like part
of the fun is pretending to bethe people smuggling the food in
and out around the Nottinghamwood. Here, it's just numbers
and operations, like youmentioned Sudoku, like you
mentioned Wordle, I think whenthat kind of game is done, well,
I really admire it, because Ithink that feels to me like a

(51:12):
much harder lift to come up withsomething that is that abstract
and still interesting, thatdoesn't feel like I am playing
Excel, the spreadsheet as mygame tonight,

Brian (51:23):
or magic the computer game.

Stephen (51:24):
Yes, magic the computer game.

Brian (51:27):
It still is a pretty game, but there's no fluff. It
just it is what it is.

Jason (51:32):
I mean, the punch cards, they did a little bit of fluff
there, but not very much. Imean, the randomization is
really the only fluff componentthere, and that's mathematically
equivalent to having them notrandomized. So you might as well
do it.

Stephen (51:43):
Yeah,

Brian (51:44):
and a hexagon of unnecessary little digital faces

Jason (51:47):
There we go. That is the one unnecessary aesthetic thing
they put in there, the hexagon.Actually, many of the people who
play a single player apparentlydon't use that. They just lay
them out straight in a row. Soonto science.

Brian (51:58):
How do you grade this? It's math.

Jason (52:02):
I'm going to give the mathematical answer and say that
the science grade is undefined.

Stephen (52:06):
Nice.

Jason (52:07):
This game is not trying to represent any scientific
concept, which I don't think wefully realized when we picked it
up and put it on the showschedule. It's a game of logic
and deduction. There's not ascientific process. It's trying
to represent. And so I don'tthink it's fair to give it a
science grade, because it'sthat's not what it's doing.

Brian (52:24):
Yeah, it's like, again, it's in STEM science,
technology, engineering, math,it's math. So we can give it a
math grade, and it did math.

Stephen (52:32):
Yeah, it feels like it is touching on some of the
tools, the building blocks thatyou use as part of scientific
inquiry. The idea of, like, ifI've got a system, how do I
query it? What questions shouldI be asking? How do I get
information out of this systemthat I'm dealing with? And it is

(52:53):
very much, in that case, a toymodel, but it's an interesting
exercise, I think, to go throughto force yourself to do that in
this constrained environment.

Brian (53:02):
That'san interesting way to think about it.

Jason (53:04):
Yeah, I hadn't thought about that because I often say
that science is the world'sbiggest game of guess and check.
That's that's what we do when wemake a hypothesis and we test is
we are making a guess and we'rechecking to see if we're
correct, which makes it soundbad, except that the alternative
is guess and not check, which iswhat a lot of other things do.
So yeah, I hadn't thought aboutyou're right, because, you know,
there's some conditions youdon't know which you make a

(53:25):
hypothesis of your number. Youcheck it to see if it actually
fits or not, but you only getpartial data. You have to figure
out that's actually really cool.I hadn't thought about that.

Brian (53:35):
There are some examples of logical deduction in biology.
Again, we were talking about itwith the grid, right? We figured
out by pure principles, that tobe able to code for 20 amino
acids, that you'd need to haveat least three digits to do it,
because you can't do it withtwo. So the smallest number
would have to be three, whichmeans we've got more options.
And like that was just sittingdown and thinking about what

(53:56):
made logical sense.

Jason (53:57):
Well there's another tie back to Turing. So he came up
with what's called a Turingpattern, which is basically you
have these very simple rulesabout things that are like
making some molecules, usuallyat least two different types,
one of which has a differentlifespan than the other, and
they diffuse out. And from verysimple rules, you can get super
complex patterns. Everythingfrom like cheetah spots to
fingerprints to the folds of thehuman brain, are thought to

(54:20):
arise from these Turing patternprocesses. I'm actually studying
one in corn right now, where Ithink that a Turing pattern is
involved in how this certainfeature comes out.

Stephen (54:29):
Oh, that's neat.

Brian (54:30):
Science is really fun, actually. Like, I was joking
about onions, but like, they areinteresting too. Corn is
interested. Everything isconnected,

Jason (54:38):
all right. Well, that's where we should probably wrap it

Brian (54:38):
Have you done The Core? Did you subject people to The
up, Stephen. Thank you so much.It's been wonderful having you
on. Thank you for teaching usabout laser cooling and
computational operations and allsorts of stuff like that. And it
didn't come up here, but I'mgoing to link in the show notes
what I think is probably yourgreatest and most lasting
contribution to the field, whichis the science vs. movies panel

(54:58):
at DragonCon, which for those ofyou who haven't seen this,
there's no real science in thispanel, except by accident. It's
where Stephen makes poorscientists suffer through some
of the worst science shown inHollywood, and then explain why
it's right, actually. And it'shilarious. I'll throw some links
in the show notes. They aretotally worth watching.

Jason (55:15):
I have subjected people to The Core.

Brian (55:15):
so Stephen, if people want to find you, where should
they look you up?

Stephen (55:18):
So you can search for my name, I have won the Google
Core? You must have.
search for Stephen with a pHgranade, G, R, A, N, A, D, E, my
website is stephen.granades.combecause one of the French

(55:39):
branches of the family that areout in California got
granade.com Before I could but Igot my revenge. He ended up
having to link to me early on,where he was like, Yeah, you're
probably looking for thisStephen granade.

Jason (55:53):
All right, well, then we'll call it there. Thank you
everyone. Thanks for listening.Have a great month and happy
gaming.

Brian (55:59):
Have fun playing dice with the universe, see ya this
has been the gaming with SciencePodcast copyright 2025

Jason (56:04):
listeners are free to reuse this recording for any non
commercial purpose, as long ascredit is given to game with
science. This podcast isproduced with support from the
University of Georgia. Allopinions are those of the hosts,
and do not imply endorsement bythe sponsors. If you wish to
purchase any of the games wetalked about, we encourage you
to do so through your friendlylocal game store. Thank you and
have fun playing dice with theuniverse. You.

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S2E03 - Turing Machine (Computation)

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.css-14f5ked{margin:0;word-break:break-word;display:-webkit-box;-webkit-box-orient:vertical;box-orient:vertical;-webkit-line-clamp:2;overflow:hidden;}S2E03 - Turing Machine (Computation)