Twelve and a half orders of magnitude, in a single move.
Sixteen rungs from a planet down to one junction between two cells in one
human brain, and every one of them is a real photograph or a real
measurement. The number in the corner is the true width of what you are
looking at, not a caption.
Down from the sky
Earth, 12,742 km. NASA's Blue Marble by day and VIIRS city lights by
night, mixed by which way each patch of ground is facing, so the terminator
falls where the geometry actually puts it. The lights are measured, not
drawn: that is the light cities throw away upward.
Eastern North America, 3,000 km. New England, 400 km. Satellite
passes on single days, so the cloud is real weather rather than a cleaned
plate. The dates were chosen by measuring cloud cover across ten
candidates, because the first one picked came back as a featureless white
rectangle.
Boston, 24 km, and one block of it at 420 m. USGS aerial survey. At
the bottom of this stretch you can make out individual trees and individual
cars. The step from there down to a person is 244 times, which is the
largest jump above the tissue, and it is left as it is rather than padded
with frames that would add nothing but numbers.
A person
One metre seventy two. Not a stock 3D character. This is
BodyParts3D, an anatomical atlas built by the Database Center for Life
Science, and the reason it is here rather than a nicer-looking figure is
that it ships the skin, the skeleton and the brain as separate meshes in
one coordinate frame. With a bought model I would have had to place
the brain inside the head by eye, and eye-placing the one thing this page
is about would have been the only invented object in the whole sequence.
As the scale descends past this rung the skin comes away, then the
skeleton, and the camera closes on the head. What is left is where the
scanner found the brain.
The atlas figure is anatomical, which is to say undressed, so there is a
winking emoji over it until a clothed model arrives. Its position is not
eyeballed either: it is placed on the atlas's own genital-system mesh, dead
centre and at 50.0 per cent of body height, and it leaves when the skin
does, because after that there is a skeleton on screen and nothing left to
cover.
The check that the frames really are the same. Two
meshes arriving in the same archive is not the same claim as two meshes
being in the same space, and a silent origin or unit mismatch would put the
brain somewhere in the chest with nothing on screen looking obviously
broken. So: the figure measures 1,719 mm, the brain sits at 94.5 per cent
of that height, every corner of the brain falls inside the body, and a
point a quarter of a body-height above the head does not, which is what
makes the previous test mean anything. The one that settles it is the
skull: the top of the skeleton clears the top of the brain by 5.8 mm. That
is the thickness of bone, and it only comes out right if all three meshes
are genuinely in one frame.
The brain
15.1 cm. The Allen human reference atlas as packaged by the HuBMAP
Human Reference Atlas: 283 named structures, the outer surface drawn as
glass so the thalamus, hippocampus, brainstem and cerebellum inside it are
visible.
Two rungs came off this page, and the reason is the
zoom. It used to run brain, then cortical surface, then white matter,
then a whole slice. But a brain is 15.1 cm and its cortical surface is
17.0 and its white matter 17.8, so those are larger than the brain
they come out of. The zoom had to stop dead in the middle, sit at one scale
for three rungs while the content changed, and start again. The page
explained that at length, and the explanation was true, and the sequence
was still wrong: a ladder whose middle does not descend is not a zoom. The
white matter and the cortical surface have their own pages, where they are
the subject rather than a pause. The build script now refuses to write a
ladder in which any step fails to zoom in.
A section of its cortex
8.7 cm, 4.3 cm, 2.2 cm. Straight from the brain into real tissue.
BigBrain: a 65 year old woman's brain, embedded in paraffin, cut into
7,404 slices at 20 micrometres, every slice stained for cell bodies and
photographed. This is one of those slices, three times, twice as close
each time. The cortex in cross section, the white matter branching
underneath it like a tree, and then the ribbon itself: about three
millimetres from the outer surface down to the white matter, and that
three millimetres is where almost all of the thinking happens.
One cubic millimetre, 3.9 mm. H01: a piece of a living woman's
temporal cortex, with all 49,379 of its cell bodies in the place the
microscope found them. Photographing this much tissue took 1.4 petabytes.
One neuron, 1.16 mm. A layer 5 pyramidal cell from that block,
followed by hand through the whole volume, carrying 3,117 incoming
synapses.
300 µm, 80 µm, 20 µm. The same cell, three times closer, each crop
taken around the position of one particular synapse so the descent lands
somewhere rather than merely getting smaller.
One synapse, 3 µm. That synapse. An axon ending and the dendrite it
is talking to, pulled straight out of the electron microscopy. The gap
between them is about 20 nanometres.
This used to be one step of seven hundred times, onto
the wrong cell. The ladder went from a 2.13 mm neuron straight to a
3.04 µm synapse, where nothing else near it steps by more than six. Worse,
the neuron was segment 5015035926 and the synapse was on 3470629528, so the
zoom flew into one cell and landed on a junction belonging to a different
one. Nothing on screen said so, which is exactly why it needed saying. The
neuron rung is now the cell the synapse is actually on, and the three crops
between them come from that one mesh, around that one synapse: 3.9, 3.7,
4.0 and 6.6 times. The closest point of the cell surface to that synapse is
0.13 µm, which is the check that it really is on this cell.
At 21 micrometres you can see that cells are there, and
not much else. A human cortical cell body is between half a pixel and
one and a half at that sampling, so the stipple in the deepest BigBrain
rung is cells, but no individual one of them can be picked out. This page
tried to count them and threw the count away: it returned forty per square
millimetre where histology says about two thousand, and it returned more in
white matter than in cortex, because isolated glia against a pale
background give crisper contrast than cell bodies packed shoulder to
shoulder. What the resolution does support is the layering, which is what
BigBrain was built for. Measured from the image alone: pale at the surface
where the molecular layer holds almost no cell bodies, 1.7 times darker
0.85 mm down through the densely packed layers, then falling away again
into white matter.
Why this is sixteen scenes and not one
Earth is 1.3×107 metres across. A synaptic cleft is
2×10-8. That is fifteen orders of magnitude, and a 32-bit
float carries about seven significant digits, so a single scene holding both
ends would lose the synapse to rounding error long before it reached the
screen.
So each rung is drawn normalised to its own size, and its true extent in
metres travels alongside it. Each one grows steadily as the ladder descends
past it, so the thing you are looking at swells and you fall through it into
the next: before its own rung it is small and approaching, after it, it is
oversize and on its way out of frame. The growth rate is a fixed factor per
rung rather than the true ratio, because those ratios run from 1.7 to 701
and driving the picture with them would make one step a lurch and the next
barely move. So the growth now follows the real ratio between neighbours,
clamped between two and nine: below two the move does not register as a
zoom at all, above nine it is a lurch. Only the two steps in the sky are
large enough to hit that ceiling. The zoom you see is continuous; the arithmetic
behind it never spans more than one rung at a time. The readout is computed
from the real measurements, so it cannot drift away from the picture.
The jump from a cell to a synapse is the biggest one
below the sky. Everything else at this end steps down by a factor of a
few. That one steps down by seven hundred, and there is no honest way to
smooth it: a neuron really is that much larger than the junctions covering
it. The cell you just left has 3,347 of them arriving on it, and this is
one.
Nothing here is glossy. These cells were submerged in
fluid, and submerged tissue has almost no refractive step at its surface, so
it should read as soft and translucent rather than as painted plastic with a
highlight. The rendering uses a real three-point light rig with high
roughness and no metalness, and keeps emission low, because pushing emission
up to make things visible is what flattens a picture and kills every shadow.
The photographs are the exception and are drawn unlit: a photograph already
contains its own light, and running it through the tissue rig would tint a
measurement with a key and a fill and make it look like a rendering.
The colours are ordered, not decorative. The cell
bodies in the cubic millimetre are tinted by their depth below the surface,
on a ramp of explicit stops that climbs in lightness from deep blue through
violet to gold. Walking a blue-to-gold ramp round a hue wheel instead would
pass through green, and green would appear in the picture carrying a meaning
neither end of the scale contains.
Two things here are not free to reuse. BigBrain is
CC BY-NC-SA, which is noncommercial and share-alike, and the body is
CC BY-SA, which is share-alike. Everything else on this site is clear for
any use, so if those rungs ever have to come out, that is why.