Massively bigger. You can think of a parabolic reflector as a huge set of simple antennae in an array so that they are appropriately phased. You only see dish reflectors when the wavelength is a small fraction of the reflector size. If you want more directionality on a Yagi, add more elements. A dish for 10MHz would only become useful at say a few hundred metres in diameter. On the plus size, you wouldn’t need a solid dish, just a wire mesh of a pitch small wrt the wavelength. But not viable for the problem at hand.
Ok, let’s say that it’s you and another person. Could you make two radios to communicate with one another. Doesn’t have to be voice, (though that would be ideal) but something like Morse could do it.
A clockwork radio maybe?
Transmitting requires a power source. There is no generator needed for a crystal radio set to receive existing signals. Assuming you can develop a generator for power you could use large spark gap devices as Marconi did to make a radiotelegraph. There you are headed into witch territory.
With enough time you could create a fully functioning thermionic tube in the 12th century. Lifetime and performance would be pretty shabby but working. Chemical batteries similarly so. With enough basic knowledge a lot would be possible.
Seems to be a recapitulation of The Flying Sorcerers.
In any event, you’d need to get directionality somehow. You don’t just want to know whether the source exists; you want to find it. In principle, you could find the source by moving around and seeing when the signal gets louder or quieter, but that has a lot of downsides: If the distance you’re moving is small compared to the distance to the source, the change will be very small, and you’ll have to compare the loudness to your memory from the last time you set up, which was some time ago (and it’s possible that there are changes in either the source or the environment in that time that will also change the intensity). Plus, “warmer/cooler” requires a lot of moving around to get enough information. By contrast, it’s probably much quicker to rotate your detector than to relocate it, and you immediately learn which way you need to go to get closer.
How does this idea sound for sensing directionality:
You make your antenna a very wide, flat, thin piece of metal. Wouldn’t it pick up less signal when it was edge-on to the source, than when it was presented wide to the source? I’m just thinking in terms of how many radiofrequency photons it would be likely to intercept. (Or would their long wavelength make the antenna’s orientation moot?)
Could an elephant cage work?
The long wavelength would make this moot. What you want (I think) is a big loop antenna.
@F.U.Shakespeare , I think that would need more complicated electronics to make it work. Nothing difficult for a modern tech base, but more than what you’d get from whiskers, razors, and crystals.
How large is a time vortex relative to the local space? Will it always be found at ground level, not suspended in the air or buried somewhere?
Are there multiple vortices? Do they stay in one place? Are they always in that place or do they come and go? If not permanent then how long do they last?
Oh, now you’re just making the problem difficult. 
Assume one magical get-you-back-home macguffin, which will stay around for a while and then disappear FOREVAR.
Magnets?
In the 12th Century?
unless you are in China—try again.
Yup, probably have to try a few times. But you’ll find one eventually.
I don’t know how common it was, but lodestone was known in Europe in the 12th century. Vikings were making compasses out of it by the 10th century or so. All throughout Europe, lodestone’s attraction to iron had been noticed, though nobody really understood much about magnetism back then.
There’s a point to be made that the Chinese were making compasses out of it a thousand years before that, but lodestone was around. Even the ancient Greeks knew what it was well into the BC centuries. The ancient Greeks thought that lodestone’s attraction to iron was caused by lodestone actually containing a soul. Europeans in the 12th century wouldn’t have had much of an understanding of magnetism, but lodestone wasn’t a complete unknown to them.
It probably wasn’t sitting around on the shelf of ye olde general store, but if you ask around for that strange rock that is attracted to iron, someone is going to know what you are talking about and will point you to a hunk of it.
Well a long thin piece of metal is a wire. You don’t need any width. What you are basically describing is a dipole antenna. And yes, they are directional. In a perfect world they have a null end on. In an imperfect world they still receive a lot worse end on.
A Yagi is basically an extension of a dipole with additional elements that increase directionality. They have the advantage that they have unidirectional gain, so there isn’t a question of which of two opposite directions the source lies in. They could be trivially made with sticks and wire. The entire contraption could be suspended from a pole to allow it to be swung around. The longest element would only be about 5 metres, aka 16 feet. A multi element yagi of useful directionality could be made easily enough to be portable and set up as needed.
Making a magnet is another thing that given enough time (I’m going say the enterprise to make the whole receiver could be a year or so’s project.) You need some steel. Steel was known in the 12th century. You also need a coil of wire, and lastly a way of sending a large current through the wire. I’ll go out on a limb here, but construction of a suitable static electricity machine may provide a suitable enough peak current to get you a passable magnet. You will need to play with the steel, heat treating it to a significant hardness. Then it will retain magnetism. Wind a coil around it, and finally run as large a current through the wire as you can. Modern magnets are made by using a capacitive discharge into a field coil. The trouble with a static electricity machine is that the circuit may resonate, which would be a very effective way of making a demagnetiser. So a nice pile of home built chemical batteries may be the next best thing. Copper and zinc and sulphuric acid - aka a Daniel Cell, is again within 12th century capabilities. Then the possibilities become much wider.
I’m currently on my phone. So I will just say I love this thread and y’all
My understanding from that science documentary, Gilligan’s Island, is that you first need to find a coconut…
You can make a (weak) magnet by heating steel and hammering/vibrating it aligned with the Earth’s own magnetic field, no wires or generator needed. I don’t know if that will suffice for radio purposes.
I’ve always wondered if multiple magnets could be used to increase the strength of a single magnet. Suppose you made a bunch of beaten magnets like that. If you made two bundles of these magnets and oriented a piece of steel or iron between them, would that create a new magnet that is weaker or stronger? Do you ever get anywhere or do you just end up making weak magnets?
But it’s in Medieval England, a temperate zone. How are coconuts getting there? Are you suggesting coconuts migrate?