No one succeeded to prove that a function must be recursive in order to be effectively calculable. This is (as Post noted) a "working hypothesis" supported by overwhelming evidence. We don't know of any effectively calculable function which is not recursive, by designing new TMs from existing ones we can obtain new effectively calculable functions from existing ones and TM computability stars in every attempt to understand effective calculability (or these attempts are reducible or equivalent to TM computable functions).

The Turing Machine itself, though abstract, has many "real world" features. It is a blueprint for a computing device with one "ideal" exception: its unbounded memory (the tape is infinite). Despite its hardware appearance (a read/write head which scans a two-dimensional tape inscribed with ones and zeroes, etc.) – it is really a software application, in today's terminology. It carries out instructions, reads and writes, counts and so on. It is an automaton designed to implement an effective or mechanical method of solving functions (determining truth value of propositions). If transition from input to output is deterministic we have a classical automaton – if it is determined by a table of probabilities – we have a probabilistic automaton.

With time and hype, limitations of TMs were forgotten. No one can say that Mind is a TM because no one can prove that it is engaged in solving only recursive functions. We can say that TMs can do whatever digital computers are doing – but not that digital computers are TMs by definition. Maybe they are – maybe they are not. We do not know enough about them and about their future.

Moreover, demand that recursive functions be computable by an UNAIDED human seems to restrict possible equivalents. Inasmuch as computers emulate human computation (Turing did believe so when he helped construct ACE, at time fastest computer in world) – they are TMs. Functions whose values are calculated by AIDED humans with contribution of a computer are still recursive. It is when humans are aided by other kinds of instruments that we have a problem. If we use measuring devices to determine values of a function it does not seem to conform to definition of a recursive function. So, we can generalize and say that functions whose values are calculated by an AIDED human could be recursive, depending on apparatus used and on lack of ingenuity or insight (the latter being, anyhow, a weak, non-rigorous requirement which cannot be formalized).

Polyphonic with its richer tonal quality sounds better than monophonic but when compared to MP3 quality it sounds pretty weak. Midi format may be adequate for basic ringers and great for greeting cards but if it’s real sound that you want for your cell phone, keep reading.

C) Truetone And Mp3’s The future of sound for ringtones seems to be hifi quality. The real tone or true tone ringtones that can be downloaded onto your cell phone are equivalent to an MP3 player quality and sounds a little like an iPod.

True tone technology will allow user to hear recorded voices such as Austin Powers announcing “You’re phone is ringing, baby, yeah”. This recording is so convincing that people will be looking for Mike Myers. Songs like Outkast’s “Hey Ya” and Starsky and Hutch theme song are downloadable as well. With a built in microphone you can record your own or someone else’s voice. True tone ringtones will even mimic a real old fashioned telephone ring. How’s that for retro?

A Brief Glimpse At Ancient History

In almost ancient past, cell phones came with one ringer and no features at all. Wall paper was something that decorated your home and SMS was unheard of. Cell phones were big and cumbersome and used only by elite or as marketing gurus put it, “Early Adopters.” Very few people owned cell phones because of size and expense.

Digital technology changed all. All of a sudden a lot of people were buying and using cell phones. This was confusing because every time a phone rang, everyone in room started to rummage through their bags and pockets to answer it. A unique sound was answer and that is how ring tones of every description came into being.

Ringtones – Where Do We Go From Here?

Some technical websites declare that cell phone of tomorrow will replace MP3 player of today. This will be possible once a dual use battery is invented that can hold a sufficiently long enough charge. The power would last more than a few hours and be easily recharged. The “techies” declare that memory capabilities must be enhanced so that user can download and store hundreds of thousands of songs. This isn’t that far off, in fact an MP3 player being replaced by a cell phone is considered possible within 5 years according to most technical websites.

Other Products Available On Ringtone Websites

Sound mixers and Recordable Devices A 2002 Motorola cell phone came with an audio mixer that could harness hundreds of musical instruments in a midi format. This cell phone has greatly evolved and allows you to program special effects. Effects include echo and reverb to name just a couple. You can program your own ringtone, download it onto your phone and then enhance it with above hifi effects.

Wall paper and Logos Many cell phones are used to connect to Internet and also do double duty as palm pilots. This has necessitated a larger screen and with that you need special wall paper. You can choose from a multitude of assortments. Your favorite logos are also downloadable. Logos of every sports team are available.

Java Games Whether you’re waiting for dentist or bus, passing time is far quicker by playing a computer game. Java games are available from same websites that offer huge assortments of wallpaper and ringtones. Google word Java Game or Gamer and there’s lots of websites sites to choose.

SMS (Short Message Service) ICQ (I Seek You) was pioneer of SMS technology and still remains on cutting edge of SMS technology. ICQ is pretty advanced and still progressing. It offers availability of staying in real time communication and allows a large address book. As part of ICQ community, there are message boards, chat rooms and user lists available. ICQ also offer unique ringtones as well. SMS Google is catching up quickly and now provides user with option of text messaging a query directly to its web site using a cell phone.

What Can You Say About Ringtones

So there you have it, what can you say about ringtones? It seems in today’s wireless world and with cutting edge technology, quite a.bit. Gone are days where a single bell chime or as Lily Tomlin put it so well: “one ringy dingy, two ringy dingy” had to sound to get your attention. Today choices are endless so shop around for what suits you best in your own unique ringtone. Stay in touch!