When activist investor Carl Icahn recently disclosed his large stake in Apple (AAPL 0.52%) on Twitter, the company's ailing stock surged. Investors believed that Icahn could finally force CEO Tim Cook to make some dramatic changes to boost shareholder value. When Icahn recently revealed that he also owned a 16% stake in speech recognition pioneer Nuance Communications (NUAN), the creator of Siri, frenzied speculation that he would force Apple to finally buy Nuance flooded the Internet.

There could be huge implications for the health care industry if this happens, as it is already a major consumer of Apple's iPads and Nuance's voice-recognition software in electronic health records, or EHRs.

Would Apple buying Nuance actually make sense for either company, though? Let's take a look at the facts and figures fueling these rumors.

Stagnant growth at both companies
Both Apple and Nuance posted unremarkable top and bottom line growth last quarter. Apple's revenue inched up 0.9%, but its earnings dropped 21.8% from the prior year quarter. Nuance's GAAP-adjusted revenue rose 8.8%, but it posted a GAAP-adjusted net loss of $0.11 per diluted share compared to a profit of $0.25 a year earlier.

Revenue at Nuance's health care business surged 29.1% to $238.1 million, but its mobile and consumer segment reported a 16.2% decline to $111.0 million. This suggests that pressure from other voice recognition products on the consumer end, most notably Google (GOOGL -1.97%) Now, is starting to take its toll. Nuance also suffered from an ongoing shift from sales of upfront licenses to cloud-based options.

Apple's Nuance-free Siri could be Apple Maps revisited
To add further pressure to Nuance, Apple is creating a Nuance-free version of Siri that could potentially end the companies' longtime partnership. That looming threat is one of the main factors that have caused Nuance shares to slide 20% over the past twelve months.

The development of its own speech-recognition engine is part of Apple's broader plan to free itself from Google's ecosystem. In June, Apple announced that Siri's default search engine in iOS 7 would be Microsoft's Bing instead of Google Search. The company also announced that it was deepening its ties with Yahoo! to create more apps for the iOS ecosystem.

This desire to free itself from Google also led to Apple's worst failure in recent memory, however: Apple Maps. The combination of several different GPS mapping technologies in the software melted digital roads and left travelers stranded.

Google then struck back by releasing the Google Chrome web browser, which has proven to be a popular alternative to Apple's Safari. It then released Google Now for iOS, pushing the voice wars straight back into Apple's backyard.

United we stand, divided we fall
The desire to resolve that central conflict and help Apple and Nuance start growing again in Google's shadow is the reason why investors believe that Icahn should push Apple to simply buy Nuance instead of trying to outsmart it.

With a market cap of $6 billion and $2.35 billion in debt, Nuance wouldn't be a huge purchase for Apple, which has $42.68 billion in cash and equivalents. Assuming an acquisition premium of 50%, the whole purchase could cost less than $15 billion.

Apple's health care ambitions
With the Nuance purchase, Apple would control one of the two most widely used speech recognition technologies used by the health care industry -- the other being Medquist's M*Modal.

Nuance's Dragon speech recognition software is widely used by leading EHR providers, such as Epic, General Electric, Allscripts, Greenway, and Cerner (CERN). These companies all implement a combination of Nuance's CLU (clinical language understanding) and NLP (natural language processing) technologies to help physicians document patient data more quickly.

Prior to the installation of Nuance and M*Modal's speech recognition software in EHR programs, 93% of physicians surveyed by Nuance stated that their EHR software had slowed down their daily routines. Around 79% believed that the solution was to merge a spoken physician narrative with the point-and-click templates widely used by EHR programs. The result has been an explosion of CLU solutions, such as Nuance's 360 mobile health care products.

Cerner notably has one of the strongest relationships with Nuance in the field. Last October, Cerner integrated Nuance's cloud-based medical speech recognition software across all of its EHR platforms, and tied its radiology information product with Nuance's radiology reporting suite. It strengthened that partnership further with an agreement in March 2013 to integrate Nuance's CDI (clinical documentation products) into its EHR programs.

The Foolish bottom line
In the world of health care, Apple already has an overwhelming lead over any other tablet maker. Thanks to its identical hardware and software configuration in every generation, iPads are much easier to develop apps for in comparison to Google's fragmented universe of Android devices.

According to Manhattan Research's annual survey of digital usage statistics in the health care industry, 72% of physicians are currently using tablets. Over half of them favor using the iPad, thanks largely to its wider selection of medical apps such as medical reference app Epocrates and full-featured mobile EHR apps like Cerner's PowerChart Touch.

In closing, I believe that Apple is looking the wrong way. Rather than struggling to free itself from Google and Nuance to go at it alone, the company should simply buy Nuance for an instant lead in the booming health care tech industry. This would be a better use of funds than any stock buybacks or increased dividends that other investors are demanding.