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To begin with, while we can get a crude idea of what it is like to navigate by echoes (walk around a room blindfolded and shout - you can often distinguish when you are near a wall or far from one), it is hard to imagine what a honed sense of echolocation would be like. Considering the basic way that the process works - send out signals that bounce off objects and send back new information about where and what they bounced off of - a sense of echolocation almost seems more analogous to our own sense of vision than our sense of hearing.
Imagine standing in a completely dark room and looking around. You see nothing. Now give yourself the ability to produce beams of light, say by a small flashlight. Now, by flicking the flashlight on briefly, you send out a signal which in turn bounces off of objects and sends back a signal that your sense organs are able to absorb. Depending on the shape, size and location of the objects, the signal has certain characteristics (wavelength and such) which allow your brain to automatically interpret so that you gain that information. The end result: you see the environment. You have a sort of mental image or mental map of your immediate space based on bounced signals.
Echolocation similarly seems to give a mental image or mental map of the surrounding space to the user. Of course, it lacks certain information such as color that a sense of vision gives. So is our sense of sound in the end a closer analogy? Not necessarily. More often than not it seems that sound alerts us to changes in our environment rather than orienting us to its basic layout and structure. Even a blind person tends to learn the arrangement of a room through tactile contact and moving around rather than listening to the details of the room.
Yet even though our sense of vision might in some sense be analogous, can we really know what it is like to sense the way echolocators do? Dolphins use sounds in a range familiar to us, so that we can perhaps imagine our own wall-shouting honed to act like our vision does. However, bats use ultrasonic sounds above the range of human hearing. When they sense their environment, how similar is it to the analogies used so far? Is hearing an ultrasonic sound similar to hearing a normal sound?
If this seems like a silly question, consider how limited our sense of vision is. We can only see visible light. We can use technology to transform infrared signals into visible-light images, but we are not actually perceiving the infrared, just a representation of it. What would it be like to perceive ultraviolet light? Or further out on the spectrum, x-rays and gamma-rays? In the other direction, what would it be like to perceive radio signals? We listen to our radios every day, but they in fact simply take the radio-wave light and transform it into audio signals in the range of human hearing. Again we do not perceive radio waves - we do not see or hear them - but only a representation of them constructed by technology to project in the range we do perceive.
If a sense organ developed to directly perceive ultraviolet light or gamma rays or radio waves, would it be vision just because it is receiving light signals and turning it into information about the environment? Or would it be an entirely different sense? We probably will never know, short of biotechnology giving us this sort of organ and finding a way to integrate it into our physiology. Installing a sensor for such signals which in turn sends nerve impulses to the brain which represented the sensed information is certainly plausible - but without evolution tailoring the brain over countless generations, could we find a way to integrate these translated signals into something the mind perceives?
It is not so simple as stimulating our optic nerve with these new impulses that originated in the newly-installed sense organs, for that might just end up stimulating new visual experiences that seem random and are not actually integrated in any meaningful way (like pressing on your closed eye causing spots and lines to appear in your field of vision). Or it might just lead to a strange criss-crossing of the sense interpretation pathways similar to the phenomenon of synaesthesia, where sounds have colors or words have taste. A person in such a situation might pick up on correlation between certain objects (like sunshine, known to be full of ultraviolet radiation) and certain synaesthetic experiences. However, this would not necessarily be a new sense, a truly new form of perception.
Thus, getting back to echolocation, we can only generalize our own sense experiences and abilities so far before we enter a territory where we truly cannot say what it is like to be a bat, for example. The limitations are even more apparently when considering another sense found in the animal kingdom: electroreception. A group of creatures known as elasmobranchii - including sharks, rays and skates - actually have a sense that does not seem very directly similar to any of our own.
All living things give off an electrical field with every heartbeat or muscle movement. Through electroreception, sharks and their relatives can actually sense changes in the local electrical field and use it for hunting and communication. Many sharks can detect these fields at a distance of up to three feet through special receptors on their head. These receptor cells convert the signal into a physiologically significant message which is transferred to the primary afferent nerves (the sensory nerves that carry impulses to the central nervous system), and in turn that message is transmitted to the brain which analyses the signal and allows the animal to respond accordingly.
This sense is strong enough that a predatory elasmobranch will use it to attack an electrical field source even in the complete absence of chemical cues. A shark does not need to see, smell, hear, touch or taste prey in order to locate and attack it.
Again one can ask what it is like to perceive in this way, but it seems to me we can only scratch our heads and wonder. No more can we understand what it is like to be a shark electrically scanning the water in front of its face than we can understand what it is like to be a bat just because we ourselves have hearing and vision, senses that seem related in basic process (bouncing, receiving and interpreting signals) and function (creating a mental image or mental map of the environment - those terms being used loosely for whatever form the representation actually takes).
Indeed, we can speculate about aliens which perceive in even more strange and abstract ways than a bat or an elasmobranch. Perhaps they experience something like color when the gravitational field around them shifts; or perhaps they experience something akin to music as streams of countless neutrinos pass through their bodies every minute of every day. Perhaps they even experience things we cannot ever experience, even in theory, things we could not comprehend.
We cannot imagine what it would be like to be such a creature, to be in its place and perceiving as it perceives (seeing through its eyes one might say, if it were not for the lack of eyes), but surely it would be distinct enough from us that if they also developed intelligence and consciousness to the extent we have, they would still probably not end up living or thinking or interacting like we do.
If such creatures had something that could be called language, it would surely not be easy to translate into our own languages. Consider how much information is lost translating between spoken human languages; or between spoken human language and signed language like ASL (American Sign Language, which apes have been taught to use or comprehend perhaps as proficiently as young human children). Getting a chimpanzee or gorilla to communicate with us in human language (even at a young child's level) is an impressive feat, but apes come from a similar evolutionary ancestor and have an innate advantage toward learning our sort of language in that way. If dolphins were capable of language - of semantics and symbol use and all the rest that goes with it and sets language apart from simple signal calls - surely it would be much harder, if not impossible, to teach them to communicate using and understand our languages. (Attempts have been made, but on a much narrower scale than with apes).
A creature even more distinct from us in evolutionary history, sense apparatus and basic physiological form would surely have an even harder time communicating with or understanding us linguistically. The point here being that not only do we have trouble imagining what it would be like to perceive the way these other creatures perceive, but even a tool like language would not provide a simple solution to that problem. Neither species could easily explain themselves and what they feel - even if language had the power to fully capture subjective experience (it doesn't). So it seems there is to some extent an inseparable divide between us and creatures which interact with the world through different sense mechanisms.
The conclusions of this are intriguing. For one thing, it means that if computers ever develop artificial intelligence and awareness, their 'senses' - the ways in which they receive and process information from the environment - may turn out to be very different from our own. Even if they evolve out of current robotic designs that utilize something like vision-navigation, they might not process the incoming signals the same way we do, and so an intelligent computer's experience (its sensory perceptions) might not be similar to our own.
Thus, if today's rudimentary computer technology someday reaches a level where it is undeniably intelligent and conscious, aware and sentient, we might not be able to communicate with it in any deeper manner than we can with dolphins. This of course does not bode well for the Turing Test as it is most commonly imagined - a chat interface between human and computer. Current attempts at 'intelligent' chat interface work on very simplistic principles which do not suggest real understanding or utilization of human language in the way we or even trained apes use it. There is no reason to think that if or when computers reach a high level of intelligence and consciousness, they will still be using a higher-evolved version of a chat interface; rather one might suspect that they would develop their own methods of communication and language tailored to the way they exist and perceive.
This potential divide of communication and understanding between different entities also suggests some positive things though. As mentioned above, we now know that apes are capable of some level of language comprehension and use. They do not simply respond to verbal signals with trained behavior in the way a pet rat seems to. Rather, they appear to invent new signs or sign-combinations and find new uses for old signs. Some are alleged to make jokes that involve plays on words and sign-homonyms, to create insults and to build meaningful linguistic strings that they have never been exposed to (i.e. picking up semantic rules). Considering our shared evolutionary history with these creatures - and thus the similarity in our sense systems and how we perceive the world - we can now recognize the potential for deeper inter-species communication than may have been imagined fifty years ago. Through communication and the knowledge of our shared experience, perhaps we can come closer to learning what it is like to be a chimpanzee or a gorilla. And that is an amazing thing.