sphere radius
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THE GROUND / STRATUM / VERIFICATION VENUE · THROUGH THE DOOR
You were born at one point in spacetime, and from that event a sphere has been expanding ever since at exactly the speed of light. It is expanding right now; it will never stop. Its radius today is your age in light-years — and that is both more and less than it sounds. Enter your birth year below: watch the sphere stay a near-invisible speck against the galaxy, name the stars it has actually reached, and meet the one wall it can never cross.
“The eternal silence of these infinite spaces frightens me.”— Blaise Pascal, Pensées (1670), fragment 206
A light-year is a distance, not a time: it is how far light travels in one year. So the radius of the sphere swelling outward from the moment you first drew breath has a value you already know without measuring anything — it is your age. A photon that left your birthplace the instant you were born is now exactly as many light-years away as you are years old. Everything inside that sphere occupies space a signal from the event of your existence could have reached. Everything outside it could not. The limit is not technological — not signal strength, not a better antenna. The universe has a speed limit, and the news of you is travelling at it, and it has not yet arrived everywhere.
Pick your year and watch.
Each tile is a real star with a measured distance; it lights when your sphere has grown past it. The dot on the galaxy is drawn to true scale — at this size the whole sphere is smaller than a pixel, which is the honest picture. The inset magnifies it so the stars have somewhere to be.
However old you are, the radius is tens of light-years, and the Milky Way is about 100,000 light-years across. Most people alive are a sphere between twenty and ninety light-years wide — a mote against the disk, far too small to draw to scale without cheating. And yet it is not nothing: within fifty light-years there are roughly 1,300 star systems (about 1,800 stars), of which only some 130 are bright enough to see by eye, and your sphere has almost certainly swept past most of the nearest hundred. Somewhere out there, a few of those tiles you just lit are real suns with real planets, now formally inside the causal reach of the event of you.
Most of the universe does not know you exist. Not yet.
And here is the part that turns the frame: the sphere does not stop when you do. Long after you die it keeps expanding at the speed of light. A candle you lit at ten is, right now, more than a decade out, its photons still in flight, still crossing fresh space, still carrying the infinitesimal causal imprint of that small event. Your influence does not end when your life does. It ends — if it ends at all — when the sphere reaches a wall. We will get to the wall. First, the shape of the thing.
The sphere is one half of a deeper figure. In spacetime, every event sits at the tip of two cones. The future light cone opens upward — all of spacetime your birth can ever influence, the three-dimensional sphere above being just its slice at the present moment. The past light cone opens downward — everything that could have causally reached you, a thirteen-point-eight-billion-year funnel of prior events narrowing to the single point where you happened.
The slope of the cone is fixed: light moves one light-year of space per year of time, so the cone's edge always rises at 45° on a diagram drawn in those units. The glowing ring is now — the sphere from Instrument I, seen edge-on as the present slice of the upward cone. Every atom that became you arrived along the lower cone; everything you will ever touch leaves along the upper one.
This is not a metaphor. It is the causal structure of spacetime as relativity describes it: every event that ever contributed to your existence is, by definition, inside your past light cone, and every event you can ever affect is inside the future one. You are where an enormous number of older cones happened to overlap and give rise to a new one. The universe is a fabric of these nested, expanding cones; the overlaps are what we call causation; and you are a knot in it — a place where many past cones converged, and from which a fresh one now expands at three hundred thousand kilometres a second. The sphere is not only what you can affect. It is also what you are made of.
If the sphere grows forever, does it eventually reach everything? It does not — and the reason is the strangest true thing on this page. The universe is not only expanding; the expansion is accelerating, driven by what we label dark energy. Beyond a certain distance, space is being stretched apart faster than light can cross it. A signal you send toward a galaxy past that distance will never arrive: the gap it has to close is widening faster than the signal travels. That distance is the cosmic event horizon — and it is not the edge of what we can see (that larger boundary is the particle horizon, set by the finite age of the universe). It is the edge of what we, or anyone here, can ever reach.
The slider walks the event horizon across its plausible present-to-asymptotic range (today ~16, future limit ~17.6 Gly comoving). The fraction we can still reach is the cube of the ratio of the radii — and it is a few per cent however you set it.
Run the numbers and the figure is bleak and exact. The observable universe reaches out to a comoving radius of about 46.5 billion light-years; the event horizon sits at roughly 16 billion. The reachable fraction is the cube of their ratio — about four per cent of the observable universe by volume. The other ninety-six per cent is already, today, beyond any signal we could ever send. Counted by galaxies rather than by volume the picture is no kinder: of the galaxies we can currently see, only about five per cent can ever be reached or signalled (Toby Ord's 2021 census of the “affectable universe”); the rest sit beyond a redshift of about 1.8 — the threshold Abraham Loeb fixed in 2002 — receding too fast for any message to close the gap.
The universe is mostly elsewhere, permanently.
So the sphere of you is bounded after all — not by your lifespan, which it outlives, but by the geometry of an accelerating cosmos. It will keep expanding for billions of years, sweeping up stars and galaxies the whole way, and then it will asymptote against a horizon it can approach but never pass. What is inside is, in the most literal physical sense, within the reach of the fact of you. What is outside never will be. Both things are true at once, and the second one is the older.
running…
r·H₀/c ≈ 10⁻⁸ — far below any digit shown. The star count. It is an estimate, not a census: the local stellar number density is anchored to the peer-reviewed Gaia-era 10-parsec sample (Reylé et al. 2021 — ≈ 375 stars in 339 systems within 10 pc ≈ 32.6 ly, the catalogue the RECONS consortium feeds) and extrapolated by volume, so the page reports order-of-magnitude figures and says so. The derived density (~0.0026 stars/ly³, a lower bound — faint dwarfs are still being found) sits at the low end of the often-quoted ~0.10–0.14 stars/pc³ range (the higher figure is binary/IMF-corrected for the true density). Density also varies with galactic direction (denser toward the plane and centre). The correction the gate made. The deposition that proposed this page quoted “0.14 stars per cubic light-year” — but 0.14 is the standard solar-neighbourhood density per cubic parsec; converted, that is ~0.004 stars/ly³, about 35× smaller (a parsec is 3.26 ly, so a cubic parsec is ~34.7 cubic light-years). Its companion figure, “360 systems within 83 ly,” matched the RECONS count of nearby stars but at the wrong radius — that count belongs to 10 parsecs (32.6 ly), not 83. Both are corrected here and recomputed from the census. The galaxy. 100,000 ly is the classic Milky Way stellar-disk diameter; modern estimates of the faint outer disk run larger (~150,000–200,000 ly), which only makes your sphere a smaller fraction, never larger. The horizons. Comoving distances in flat ΛCDM (Davis & Lineweaver 2004, concordance H₀≈70; cross-checked against Ord 2021): particle horizon ≈ 46.5 Gly, present event horizon ≈ 16 Gly (Ord's “affectable” reach 16.5 Gly), asymptotic ~16–18 Gly depending on the comoving-vs-proper convention. A clean cross-check: affectable (16.5) + observable (46.4) = 62.9 Gly, the limit of everything we will ever see. The reachable-by-volume figure is (R_event / R_particle)³ ≈ 4%; the reachable-by-galaxy-count figure (~5%, Ord 2021) is a different calculation and the two are kept separate, not conflated. The often-repeated “3% reachable” is avoided here on purpose — it mistakenly uses the Hubble sphere (≈14.4 Gly, where recession reaches c) rather than the event horizon, and understates the reach. Everything recomputes in research/sphere-of-you/verify.mjs and live in the check above.
Kindred ground — The Farthest Point (a fact about your place in space re-derived from defining constants) · The Wall That Was Never There (the other piece that came through the door; there a claim of visibility fails, here a claim of reach) · Incommensurable (a quantity — there a ratio, here a cosmos — that refuses to be wholly contained).