She's got snakes in her hair
##She's got snakes in her hair WellWell, the snakes for hair one is easy, with proper genetic engineering, some thoughtful blood vessel design and immune response planning, and unethical use chimeric technology (just go to Transnistria). In other words, the being would be part-woman, part-snake, part-snake, part-snake, part... you get the gist. Massive blood vessels would feed the snakes, and neural connections from all the snake eyes to the big brain would pass relevant information even while her main head is turned some other direction. Unfortunately (for our Medusa), the creature is only producible in a lab, as natural reproduction would lose the snake chimerism but not the genetic adaptations for it and therefore probably result in some horribly non-viable specimen. On the upside, the promise of (future, always future!) offspring might serve as a great way to keep the creature working under design parameters.
And her looks can kill...
##And her looks can kill... NowNow the stone-gaze would be tough, since we have no physical way of transmuting elements (outside of particle accelerators). However, it is much easier to interpret this a bit less literally, and simply have the folk get the deer-in-the-headlights effect, except perhaps for a longer (uh, even permanent) duration, while remaining noticeably flesh-based. Obviously this may or may not realistically work at arbitrary distances (should seeing her through binoculars from an airplane have this effect or no?) This means we have two paths to victory here:
1. Basilisk effect.
###1. Basilisk effect. SomethingSomething about her messes up human cortical signals and sends the brain into a long-term paralytic seizure. This could be optical or electromagnetic.
- Optical/Visual assumes that there is a visual pattern that can hack the human brain into paralysis, just like seeing flashing lights can trigger an epileptic attack in some. This would work as described in the mythos (even, say a non-reversed image of her placed on a shield would work), but is difficult in effect - consider that people may not be perceiving the pattern in full, at the correct angle, or through sun-glasses or welding-type masks.
- Electromagnetic direct-brain stimulation - Medusa generates a precisely tuned electro-magnetic field, using transcranial magnetic stimulation, much like the Induced Hemianopsia answer, except with paralyzing rather than non-discriminant effect. This would most likely only work at short range, given the precision of the desired effect.
2. Poison effect.
Medusa's tearducts are modified to spit a paralytic neurotoxin at short range, or perhaps she just exudes a trail of it wherever she goes, and it remains active in the air for several minutes to an hour. Anyone breathing it in, or even making skin contact with this neuro-active poison, loses all voluntary muscle control, perhaps including involuntary muscle control such as hear-beat. Her victims freeze into a death grimace. On the downside, a full hazmat suit would render one immune, as long as the hazmat suit stays intact.